The profit amount for the vendor who bought a pair of jeans wholesale for $90.00 and sold it for $120.00 including taxes is $30.00
Profit amount refers to the monetary gain or excess of revenue over expenses that a business or individual earns after deducting all costs and taxes. It represents the positive financial outcome of a business operation or an investment.
Profit = Selling price - Cost price
First, we need to calculate the selling price including taxes.
The GST and PST rates are 5% and 7%, respectively.
Therefore, the total tax rate is:
Total tax rate = GST + PST
= 5% + 7%
= 12%
The amount of taxes paid is equal to 12% of the selling price, which can be calculated as:
Selling-price × 12% = Taxes paid
Selling price = Taxes paid ÷ 12%
Now, we can find the selling price as:
Selling price = Cost-price + Taxes paid
Selling price = $90.00 + ($90.00 × 12%)
Selling price = $90.00 + $10.80
Selling price = $100.80
Finally, the profit amount can be found as:
Profit = Selling price - Cost price
Profit = $120.00 - $90.00
Profit = $30.00
Therefore, the profit amount for the vendor is $30.00.
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Does the cost of the chemical increase or decrease over time,and by what percentage per years does it do so?
The actual percentage change in the cost of a chemical per year can vary widely depending on market conditions and other factors specific to that chemical. Market fluctuations, supply chain disruptions, technological advancements, and regulatory changes can all impact the cost of chemicals in different ways.
The cost of a chemical can either increase or decrease over time, depending on various factors such as market demand, supply, production costs, inflation, and market competition. The percentage change in the cost of a chemical per year is determined by the rate of increase or decrease in its price over that period.
If the cost of the chemical increases over time, the percentage increase per year can be calculated using the formula:
Percentage Increase = ((New Price - Initial Price) / Initial Price) * 100
For example, if the cost of a chemical increases from $100 to $120 over a year, the percentage increase would be ((120 - 100) / 100) * 100 = 20%.
On the other hand, if the cost of the chemical decreases over time, the percentage decrease per year can be calculated using the formula:
Percentage Decrease = ((Initial Price - New Price) / Initial Price) * 100
For instance, if the cost of a chemical decreases from $120 to $100 over a year, the percentage decrease would be ((120 - 100) / 120) * 100 = 16.67%.
It's important to note that the actual percentage change in the cost of a chemical per year can vary widely depending on market conditions and other factors specific to that chemical. Market fluctuations, supply chain disruptions, technological advancements, and regulatory changes can all impact the cost of chemicals in different ways.
Therefore, to accurately determine the percentage change in the cost of a specific chemical over time, it is essential to consider the specific market dynamics and factors influencing its price.
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Diana observes a snail moving away from herself. The snail moves 2 inches in 4 seconds. The snail is 9 inches away from Diana after 3 seconds. Write an equaton for the snail's distance from Diana, y, as a function of time, x.
After 10 seconds, the snail is 14 inches away from Diana. Let's assume that Diana is at the origin (0,0) and the snail moves at a constant speed. Let's consider the snail is at point (x, y) and Diana is at the origin (0,0). The snail is moving away from Diana at a constant speed. It moves 2 inches in 4 seconds.
Then the distance traveled by the snail in 1 second is
= 2/4inches
= 0.5 inches.
So, the distance the snail travels from (0,0) in x seconds is 0.5x. After 3 seconds, the snail moves
= 0.5(3)
= 1.5 inches away from Diana, and its distance from her is 9 inches.
So, we have y = 9 + 0.5x. This is the equation for the snail's distance from Diana, y, as a function of time, x.
We can see that the equation y = 9 + 0.5x provides the snail's distance from Diana. Here, y is the distance between Diana and the snail and x is the current time. We can observe that the snail moves at a constant pace of 0.5 inches per second since the coefficient of x is equal to 0.5. The constant term in the equation is 9, which stands for the separation between Diana and the snail at the initial value of x, or 0, the starting point.
Therefore, we can infer that the distance between the snail and Diana, y, as a function of time, x, is represented by the equation y = 9 + 0.5x. The distance between Diana and the snail can be calculated at any time using this equation. The distance between Diana and the snail after 10 seconds, for instance, can be calculated using this equation.
For this,
we substitute x = 10 in the equation and get
y = 9 + 0.5(10)
= 14.
Therefore, after 10 seconds, the snail is 14 inches away from Diana.
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Nora finished the race 3. 8 seconds before Maria. Select the variable expression that shows Nora’s finishing time when m represent Maria’s time in seconds
The variable expression that represents Nora's finishing time, given Maria's time (m) in seconds, can be expressed as (m - 3.8). This expression shows Nora's finishing time by subtracting 3.8 seconds from Maria's time.
To determine Nora's finishing time, we start with the given information that Nora finished the race 3.8 seconds before Maria. This means that Nora's finishing time must be less than Maria's time. By subtracting 3.8 seconds from Maria's time (represented by the variable m), we obtain Nora's finishing time. The expression (m - 3.8) provides the relative time difference between Nora and Maria, where Nora finishes 3.8 seconds earlier than Maria. Therefore, by substituting the value of Maria's time into this expression, we can calculate Nora's finishing time.
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Chocolate sprinkles cost as much per pound as sugar. Find 1/10 the baker’s total cost for 100 pounds of chocolate sprinkles.
1/10 of the baker's total cost for 100 pounds of chocolate sprinkles is 10x dollars.
To find 1/10 of the baker's total cost for 100 pounds of chocolate sprinkles, we need to determine the cost per pound of chocolate sprinkles.
Let's assume the cost per pound of chocolate sprinkles is 'x' dollars.
Since it is mentioned that chocolate sprinkles cost as much per pound as sugar, we can assume that the cost per pound of sugar is also 'x' dollars.
Now, let's calculate the total cost for 100 pounds of chocolate sprinkles:
Total cost = Cost per pound * Number of pounds
Total cost = x * 100
Total cost = 100x dollars
To find 1/10 of the total cost, we multiply the total cost by 1/10:
1/10 of total cost = (1/10) * (100x)
1/10 of total cost = 10x
Therefore, 1/10 of the baker's total cost for 100 pounds of chocolate sprinkles is 10x dollars.
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Monty Ricker obtained a used car loan of $6000 at 8% for 36 months. The monthly payment is $187. 80. The balance of the loan after 12 payments is $4159. 90. The balance after the 34th payment is $380. 60
To find the amount of the payment that goes towards interest at the 12th payment, you should multiply the balance at the 12th payment by the interest rate which is 8%.
The balance of the loan after 12 payments is $4159.90.
Thus the amount of the payment that goes towards interest at the 12th payment is:
4159.90 × 0.08 = $332.79
The principal amount paid at the 12th payment is the difference between the monthly payment of $187.80 and the amount of interest paid of $332.79.
The principal amount paid at the 12th payment
= $187.80 − $332.79
= −$144.99
The negative answer means that the amount paid is the interest.
To find the balance of the loan after the 35th payment, we will subtract the monthly payment from the balance after the 34th payment.
Therefore, the balance of the loan after the 35th payment is:
380.60 − 187.80 = $192.80
To find the amount of the payment that goes towards interest at the 35th payment, you should multiply the balance at the 35th payment by the interest rate which is 8%.
The balance after the 34th payment is $380.60, so the interest payment at the 35th payment is:
380.60 × 0.08 = $30.44
The principal amount paid at the 35th payment is the difference between the monthly payment of $187.80 and the amount of interest paid of $30.44.
The principal amount paid at the 35th payment
= $187.80 − $30.44
= $157.36
Therefore, the balance of the loan after the 35th payment is:
192.80 − 157.36 = $35.44.
The balance of the loan after the 35th payment is $35.44.
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a kite starts in the ground and slowly ascends into the sky. it flies at the same altitude for about 10 mins and then quickly drops to the ground. sketch a groah of the behavior of the kite over time
The graph of the kite's behavior over time starts with a rising slope as it ascends from the ground. It then levels off, depicting a flat section indicating a constant altitude. Finally, the graph shows a steep decline as the kite descends and returns to the ground.
The behavior of the kite over time can be depicted as follows:
The kite initially starts from the ground and gradually ascends into the sky, maintaining a steady altitude for approximately 10 minutes. However, after this period, it experiences a sudden descent and returns back to the ground.
The kite's journey can be visualized as a graph with time on the x-axis and altitude on the y-axis. At the beginning, the graph starts at ground level, representing the kite's position on the ground. As time progresses, the graph steadily rises, indicating the kite's ascent into the sky. The upward slope of the graph represents the gradual increase in altitude.
For the next 10 minutes, the graph remains relatively flat, indicating that the kite maintains a constant altitude. This horizontal section of the graph denotes the period when the kite flies at the same height in the sky without any significant changes.
However, after these 10 minutes, the graph experiences a sudden drop, representing the kite's rapid descent back to the ground. The downward slope of the graph indicates the kite's decrease in altitude.
In summary, the graph of the kite's behavior over time starts with a rising slope as it ascends from the ground. It then levels off, depicting a flat section indicating a constant altitude. Finally, the graph shows a steep decline as the kite descends and returns to the ground.
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Find the perimeter and the area of ABC, as exact numbers. Then, find the measures of all the angles to the nearest degree
To calculate the perimeter, add the lengths of sides AB, BC, and AC. The area can be found using Heron's formula. To find the angles, use the law of cosines.
1. **Perimeter and area of triangle ABC**
To find the perimeter and area of triangle ABC, we need to use the given information about its sides and angles.
Let's assume that side AB has a length of "a", side BC has a length of "b", and side AC has a length of "c". The given angles are angle A, angle B, and angle C.
The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the perimeter P of triangle ABC is given by: P = a + b + c.
To find the area of triangle ABC, we can use Heron's formula, which states that the area A of a triangle with side lengths "a", "b", and "c" is given by: A = √(s(s - a)(s - b)(s - c)), where s is the semi-perimeter of the triangle, given by: s = (a + b + c) / 2.
Once we have calculated the area, we can use the law of cosines to find the measures of the angles. The law of cosines states that for a triangle with side lengths "a", "b", and "c", and opposite angles A, B, and C, the following relationships hold:
cos(A) = (b^2 + c^2 - a^2) / (2bc)
cos(B) = (a^2 + c^2 - b^2) / (2ac)
cos(C) = (a^2 + b^2 - c^2) / (2ab)
Using these formulas, we can calculate the measures of the angles A, B, and C.
To find the exact values of the perimeter, area, and angles, we would need the specific lengths of the sides and the measures of the angles. Please provide those values, and I can assist you with the calculations.
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Rob spends 1/2 of his earnings this weeks on bills and then buys a video game for $25. 75. How many much of his earnings from this week does rob have left?
Rob has (1/2) * x - $25.75 of his earnings left from this week. This is obtained by subtracting the amount spent on bills and the cost of the video game from his total earnings.
To find out how much of his earnings Rob has left, we need to calculate the portion he spent and subtract it from his total earnings.
Given that Rob spends 1/2 of his earnings on bills, he has 1 - 1/2 = 1/2 of his earnings remaining.
If Rob buys a video game for $25.75, we can subtract this amount from his remaining earnings.
Let's say Rob's total earnings for the week were x dollars.
Amount spent on bills: (1/2) * x
Amount spent on the video game: $25.75
Remaining earnings: x - [(1/2) * x + $25.75]
Simplifying the expression, we have:
Remaining earnings: x - (1/2) * x - $25.75
Remaining earnings: (1/2) * x - $25.75
So, Rob has (1/2) * x - $25.75 of his earnings left from this week.
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A lab currently has 70 mg of radioactive material that decays at 3. 5% per year. Federal regulation for the substance says that the material must be safely stored until it reaches its half-life, at which time the material can be disposed.
How many years will the lab have to safely
store the material before disposal?
The radioactive material currently has 70 mg that decays at 3.5% per year. The material must be safely stored until it reaches its half-life, at which time it can be disposed.
To find out how long it will take the material to decay to half its original amount, you can use the half-life formula, which is:t1/2 = (ln 2) / kw here t1/2 is the half-life, ln is the natural logarithm, and k is the decay constant. To find k, you can use the following formula: k = 0.693 / t where t is the half-life in years. Using the given percentage of decay per year, you can find the decay constant as follows: k = 0.693 / t = ln(100/96.5) / t = 0.03515 / t Therefore, the half-life is:t1/2 = (ln 2) / k = (ln 2) / (0.03515 / t) = 19.8 years So, it will take approximately 19.8 years for the material to decay to half its original amount.
The lab will have to safely store the material for twice the half-life, which is 2 × 19.8 = 39.6 years. Therefore, the lab will have to safely store the material for more than 39.6 years before it can be disposed of according to federal regulations.
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1.
Find the area of the quarter circle with a radius of 18 cm.
Use 3. 14 for it and round the answer to the nearest hundredth.
18cm
The area of the quarter-circle is
cm²
The area of a quarter circle with a radius of 18 cm is approximately 254.34 cm² (rounded to the nearest hundredth), using the value of 3.14 for π.
To find the area of a quarter circle, we can use the formula A = (π * r²) / 4, where A represents the area and r is the radius. Plugging in the given radius of 18 cm, we can calculate the area as follows:
A = (3.14 * 18²) / 4
≈ (3.14 * 324) / 4
≈ 1017.36 / 4
≈ 254.34 cm²
Rounding the answer to the nearest hundredth, we find that the area of the quarter circle with a radius of 18 cm is approximately 254.34 cm².
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A cake shop bakes a variety of brownies. The top-selling brownies are ones with toppings of chocolate chip, walnuts, or both. A customer enters the store. The probability that the customer will pick both toppings is 0. 4. What is the probability that they will pick neither the chocolate chip nor the walnut toppings? A. 0. 5 B. 0. 3 C. 0. 45 D. 0. 8 E. 0. 2.
The probability that they will pick neither the chocolate chip nor the walnut topping is, 0.7
Since, the total of all probabilities is 1.00, or 100%.
Now, In the Venn diagram, we have the probabilities 0.2, 0.4 and 0.1;
these sum to,
0.2+0.4+0.1
= 0.6+0.1
= 0.7.
Therefore, the probability that they will pick neither the chocolate chip nor the walnut topping is,
⇒ 1.00-0.7 = 0.3
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A dance school has 54 students who learn salsa, and 23 of those students also learn ballet. There are 15 students who do not learn salsa but learn ballet, and 10 students do not learn either salsa or ballet. Which table best shows the conditional relative frequency of rows for the data? Learn salsa Do not learn salsa Total Learn ballet 0. 29 0. 19 1 Do not learn ballet 0. 39 0. 13 1 Total 0. 68 0. 32 1 Learn salsa Do not learn salsa Total Learn ballet 0. 61 0. 39 1 Do not learn ballet 0. 76 0. 24 1 Total 0. 68 0. 32 1 Learn salsa Do not learn salsa Total Learn ballet 0. 43 0. 60 1 Do not learn ballet 0. 57 0. 4 1 Total 0. 68 0. 32 1 Learn salsa Do not learn salsa Total Learn ballet 0. 23 0. 15 1 Do not learn ballet 0. 31 0. 10 1 Total 0. 54 0. 25 1.
The table that best shows the conditional relative frequency of rows for the data is as follows: Learn Salsa Do Not Learn Salsa Total Learn Ballet0.43 0.12 0.55Do Not Learn Ballet0.28 0.17 0.45Total0.71 0.29 1The conditional relative frequency of rows is determined by dividing the number of people in each cell by the total number of people in that row.
The number of people learning salsa and ballet is 23. The number of students learning only ballet is 15. The number of students who do not learn either salsa or ballet is 10.Therefore, there are 54 - 23 = 31 students who only learn salsa. There are 54 - 15 = 39 students who learn either salsa or ballet, or both. There are 54 - 10 = 44 students who learn either salsa or ballet but not both.
Hence, the conditional relative frequency of rows is obtained as shown in the table above. The total number of students is 77, which is the sum of the number of students who learn salsa and ballet, the number of students who learn only salsa, the number of students who learn only ballet, and the number of students who learn neither salsa nor ballet. Since 54 + 23 = 77, the table is accurate. Learn Salsa Do Not Learn Salsa Total Learn Ballet0.43 0.12 0.55Do Not Learn Ballet0.28 0.17 0.45Total0.71 0.29.
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point D is located at (-2,-1). point E is located at (3,-4). Determine the slope intercept equation of line DE
The slope intercept equation of line DE is y = -1/5x - 3/5.
Step 1: Finding the slope of line DE
The slope of line DE is given by the formula: m = (y₂ - y₁) / (x₂ - x₁)where(x₁, y₁) = (-2, -1) and(x₂, y₂) = (3, -4)
Substitute the values in the formula:m = (-4 - (-1)) / (3 - (-2)) = -5/5 = -1
Step 2: Finding the y-intercept of line DE
We know the slope of line DE is -1. Let (x, y) be any point on line DE. Since the line passes through point E(3, -4), we have:y = mx + by = -1(x - 3) - 4y = -x + 3 - 4y = -x - 1
The y-intercept of line DE is -1.
Step 3: Writing the slope-intercept equation of line DE
The slope-intercept equation of line DE is given by the formula:y = mx + by = -1x + (-1)
On simplification, we get:y = -x - 1The slope-intercept equation of line DE is y = -1/5x - 3/5.
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In the drains at Mohenjo-Daro, solid waste was collected in square brick pits located along the of the drains.
In the ancient city of Mohenjo-Daro, solid waste was collected in square brick pits located along the banks of the drains.
Mohenjo-Daro was an important urban settlement of the Indus Valley Civilization, which flourished around 2600 to 1900 BCE. The city featured a sophisticated system of drainage, with well-planned brick-lined channels or drains that were constructed to manage wastewater and rainwater runoff. Along these drains, square brick pits were strategically placed to collect solid waste.
These brick pits served as designated areas for waste disposal within the city. The square shape of the pits likely facilitated easy maintenance and cleaning. The waste would accumulate in these pits, and periodic cleaning and removal of the solid waste would help maintain the cleanliness and functionality of the drainage system.
The careful planning and implementation of waste management practices in Mohenjo-Daro reflect the advanced urban planning and sanitation systems of the Indus Valley Civilization. The square brick pits along the drains played a crucial role in effectively managing solid waste within the city.
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Question: In the ancient city of Mohenjo-Daro, a unique waste management system was observed. Solid waste was systematically collected in square brick pits positioned along the ______________ of the drains. Fill in the blank with the appropriate word.
Answer choices:
a) Banks
b) Sidelines
c) Middle
d) Corners
What is in number should be in the box? 8 or 9? 63.749<63.[]2
In the question, it is asked whether the value 63.749 is less than 63.[]. On the other hand, if we take 9 in the box, we get:63.749 < 63.9This inequality is true because 63.749 is indeed less than 63.9.
Now, we will compare the value 63.749 with 63.[] and the answer will depend on the digit which is in the box. Let's try both the digits one by one. If we take 8 in the box, we get:63.749 < 63.8This is a false inequality because 63.749 is not less than 63.8.
Therefore, the answer to the given question is that the digit which should be in the box is 9 because 63.749 is less than 63.9 by the given inequality.What is an Inequality?An inequality is a mathematical statement that compares two values and shows their relationship to each other. It is represented by the symbols: > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to).
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A charity is selling tickets which may win prizes. The tickets all have 3 digits, from 001 to 999. A prizewinning ticket
has the first two numbers adding to give the third, e.g. 246. How many winning tickets are there?
A 45
B 54
C 63
D 90
There are 45 winning tickets (e.g., 123, 234, 345, etc.) among the range of tickets from 001 to 999 i.e., the correct answer is option A: 45 winning tickets.
The charity is selling tickets with 3 digits ranging from 001 to 999, and a winning ticket is one where the first two digits add up to the third digit.
We need to determine how many winning tickets there are among the available range of tickets.
To find the number of winning tickets, we need to count the number of combinations where the first two digits add up to the third digit.
Let's consider the possible combinations for each digit:
For the first digit, we have 9 options (1 to 9) since it cannot be zero.
For the second digit, we also have 9 options (0 to 9).
For the third digit, the value is determined by the sum of the first two digits, so we have a limited number of options based on the values of the first two digits.
To count the winning tickets, we need to consider all possible combinations and determine the valid ones.
We can start with the first digit, go through all the possible combinations of the second digit, and check if the sum of the first two digits matches the third digit.
By analyzing all the combinations, we find that there are 45 winning tickets (e.g., 123, 234, 345, etc.) among the range of tickets from 001 to 999.
Therefore, the correct answer is option A: 45 winning tickets.
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y is inversely proportional to the square root of x
when x=64 y=4
find the value of x when y=8
Given that y is inversely proportional to the square root of x. When x = 64, y = 4.Therefore, y∝1/√x We need to find the value of x when y = 8.Substitute the given values in the above equation and get:y∝1/√xx1/4= k where k is a constant.
the equation becomes y = k/√x Given that x = 64 and y = 4 ⇒ 4 = k/√64 = k/8⇒ k = 4 × 8 = 32Therefore, the equation becomes y = 32/√x Now, we need to find the value of x when y = 8. Substituting the given value of y in the above equation, we get:8 = 32/√x⇒ √x = 32/8 = 4⇒ x = (4)² = 16Hence, the value of x when y = 8 is 16.
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Which statement is needed to prove triangle ABC is congruent to triangle EDC using ASA?
To prove that triangle ABC is congruent to triangle EDC using ASA, the statement that is needed is "Angle BAC is congruent to angle EDC. Triangle ABC is congruent to triangle EDC using the ASA (angle-side-angle) theorem if the following conditions are met: Two pairs of corresponding angles are congruent in both triangles.
A pair of corresponding sides is congruent in both triangles. Therefore, to prove that triangle ABC is congruent to triangle EDC using ASA, the statement that is needed is "Angle BAC is congruent to angle EDC." To prove that triangle ABC is congruent to triangle EDC using the ASA (Angle-Side-Angle) theorem, we need to show that angle BAC in triangle ABC is congruent to angle EDC in triangle EDC, and also that the sides AB and AC in triangle ABC are congruent to sides ED and DC in triangle EDC. In other words, the two triangles are congruent if we can establish that one angle and the two sides adjacent to it in one triangle are equal to one angle and the two adjacent sides of the other triangle. In this case, we can use the ASA theorem, which states that if two angles and a side not between them in one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. Therefore, angle BAC is congruent to angle EDC is the statement we need to prove triangle ABC is congruent to triangle EDC using ASA.
So, the statement needed to prove triangle ABC is congruent to triangle EDC using ASA is that "Angle BAC is congruent to angle EDC."
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What is the sum of a geometric series of 12 terms that begins with 10 and has a common ratio of 2?
A) 240
B) 252
С) 20,480
D) 40,950
The sum of the geometric series with 12 terms, starting from 10 and with a common ratio of 2, is 40,950.
To find the sum of a geometric series, we can use the formula:
S = a * (1 - r^n) / (1 - r)
Where:
S is the sum of the series,
a is the first term of the series,
r is the common ratio,
n is the number of terms in the series.
In this case, the first term (a) is 10, the common ratio (r) is 2, and the number of terms (n) is 12.
Plugging in the values into the formula, we have:
S = 10 * (1 - 2^12) / (1 - 2)
Simplifying further:
S = 10 * (1 - 4096) / (1 - 2)
S = 10 * (-4095) / (-1)
S = 10 * 4095
S = 40,950
Therefore, the sum of the geometric series with 12 terms, starting from 10 and with a common ratio of 2, is 40,950.
The correct answer is D) 40,950.
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10. An airline estimates that the probability a randomly selected call to its reservation phone line results in a reservation being made is 0. 31. Suppose that 4 calls are randomly selected.
1. What is the probability that all 4 of the calls result in a reservation?
2. What is the probability that at least one of the calls does not result in a reservation?
1. The probability that all four of the calls result in a reservation is calculated by multiplying the individual probabilities together since the events are assumed to be independent. Therefore, the probability is 0.31^4 = 0.0303 (approximately).
The probability that at least one of the calls does not result in a reservation can be found by calculating the complement of the probability that all four calls result in a reservation. Since these events are mutually exclusive, we can subtract the probability of all reservations from 1. So, the probability is 1 - 0.0303 = 0.9697 (approximately).
To calculate the probability of all four calls resulting in a reservation, we multiply the individual probabilities together because the events are assumed to be independent. With a probability of 0.31 for each call, the calculation becomes 0.31^4, which equals approximately 0.0303.
For the probability of at least one call not resulting in a reservation, we find the complement of the probability that all four calls do result in a reservation. Since these events are mutually exclusive (either a reservation is made or not made for each call), we subtract the probability of all reservations (0.0303) from 1, resulting in approximately 0.9697.
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asap please and thank you
The correct statement is given as follows:
The can of pringles has a z-score close to zero, which means it's more likely to happen.
How to interpret z-scores?The z-score formula is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which:
X is the measure.[tex]\mu[/tex] is the population mean.[tex]\sigma[/tex] is the population standard deviation.The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).
The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.
The z-score for pretzels is given as follows:
Z = (25 - 23)/1.2
Z = 1.67.
The z-score for pringles is given as follows:
Z = (40 - 34)/4
Z = 1.5. -> closer to zero -> more likely to happen.
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Women's shoe sizes in the US approximately follow a Normal distribution with a mean of 8 and a standard deviation of 1.5. What is the probability that the average shoe size of five randomly chosen women is 9 more
To determine the probability that the average shoe size of five randomly chosen women is 9 or more, we need to calculate the z-score for this value and then find the corresponding probability using the Normal distribution.
In summary, we want to find the probability that the average shoe size of five randomly chosen women is 9 or more.
Now, let's explain the answer in more detail. The distribution of women's shoe sizes in the US follows a Normal distribution with a mean of 8 and a standard deviation of 1.5. To calculate the probability, we first need to find the z-score corresponding to a shoe size of 9 or more.
The z-score formula is given by z = (x - μ) / σ, where x is the value of interest, μ is the mean, and σ is the standard deviation. In this case, the value of interest is 9, the mean is 8, and the standard deviation is 1.5. Plugging these values into the formula, we get z = (9 - 8) / 1.5 = 0.67.
Next, we use a standard Normal distribution table or a statistical calculator to find the probability corresponding to the z-score of 0.67. The probability of obtaining a z-score of 0.67 or higher represents the probability that the average shoe size of five randomly chosen women is 9 or more.
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Grant is a member of a book club. He pays a $10 yearly membership fee and can purchase books through the club for $2. 75 each. His total annual cost is a function of the number of books, b, that he purchases in a year: C(b) = 2. 75b 10 Which statements are true about the variables in the yearly cost function? Check all that apply. The number of books purchased is the independent variable. The input is the yearly cost. The total yearly cost depends on the number of books purchased. The number of books purchased is determined by the yearly cost. The output is the yearly cost.
The correct options are:a) The number of books purchased is the independent variable.c) The total yearly cost depends on the number of books purchased.e) The output is the yearly cost.
Given,Grant is a member of a book club.
He pays a $10 yearly membership fee and can purchase books through the club for $2.75 each.
His total annual cost is a function of the number of books, b,
he purchases in a year[tex]C(b) = 2.75b+10[/tex]
We are to find which statements are true about the variables in the yearly cost function.
Calculations: Here, C(b) represents the total yearly cost and 'b' is the number of books purchased.
The yearly cost function is given by;[tex]:$$C(b) = 2.75b+10$[/tex]
Hence, the following are true about the variables in the yearly cost function:
The number of books purchased is the independent variable.The total yearly cost depends on the number of books purchased.
The output is the yearly cost.
Answer: Therefore, the correct options are:a) The number of books purchased is the independent variable.c) The total yearly cost depends on the number of books purchased.e) The output is the yearly cost.
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A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t2 40t 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0. 2 s and 2. 7 s. Which solution can be eliminated and why? The solution –0. 2 s can be eliminated because time cannot be a negative value. The solution –0. 2 s can be eliminated because the pass was not thrown backward. The solution 2. 7 s can be eliminated because the pass was thrown backward. The solution 2. 7 s can be eliminated because a ball cannot be in the air for that long due to gravity.
The solution -0.2 s can be eliminated because time cannot be negative. The solution 2.7 s can be eliminated because it implies that the pass was thrown backward, which is not possible.
The given equation h(t) = -[tex]16t^{2}[/tex] + 40t + 7 represents the height of the football at time t. To find the solutions when h(t) = 0, we set the equation equal to zero and solve for t:
[tex]-16t^{2}[/tex] + 40t + 7 = 0
Using the quadratic formula or factoring, we find that the solutions are approximately -0.2 s and 2.7 s (rounded to the nearest tenth).
Now, we need to determine which solution can be eliminated.
The solution -0.2 s can be eliminated because time cannot be negative. In the context of the problem, it doesn't make sense to have a negative time value.
The solution 2.7 s can be eliminated because it implies that the pass was thrown backward. Since the pass was incomplete, it is assumed that the quarterback was throwing the ball forward, not backward.
Therefore, the solution -0.2 s is the one that can be eliminated because time cannot be negative.
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A function is a relation in which every input has exactly one output
Which choice represents a function
A function is a relation where each input value (x) corresponds to exactly one output value (y). In other words, for every x-value, there should be only one y-value associated with it.
Let's consider some examples to determine which choice represents a function: The set of ordered pairs {(1, 2), (2, 4), (3, 6)}: This is a function since each input (x) has a unique output (y). For example, when x = 1, y = 2, and there are no other inputs with the same output. The set of ordered pairs {(1, 3), (2, 5), (1, 4)}: This is not a function because the input x = 1 has two different output values, y = 3 and y = 4. A function requires each input to have only one corresponding output. The equation y = x^2: This is a function because for every x-value, there is a unique y-value. No two x-values have the same y-value.
Based on these examples, the choice that represents a function is the first example: the set of ordered pairs {(1, 2), (2, 4), (3, 6)}.
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What is the solution to this system of equations?
One-fourth x + 1 and one-half y = StartFraction 5 Over 8 EndFraction. Three-fourths x minus 1 and one-half y = 3 and StartFraction 3 Over 8 EndFraction
The solution to the system of equations is (x, y) = (2, 1).
Given equations are,1. 1/4x + 1/2y = 5/82. 3/4x - 1/2y = 27/8 - 3/8
Now we will solve these two equations by elimination method:
Multiplying equation 1 by 3 and equation 2 by 2,3/4x + 3/2y = 15/8 -------------- (3)
3/2x - y = 6/8 -------------- (4)
Simplifying equation 3,3/4x + 3/2y = 15/8 -------------- (5)
Multiplying equation 4 by 3,4.5x - 3y = 3 -------------- (6)
Now, we will add equation 5 and equation 6,
3/4x + 3/2y = 15/8 -------------- (5)
4.5x - 3y = 3 -------------- (6)
______________15/4x + 0y = 39/8
Therefore, x = 2.Now, substituting x=2 in equation 4,3/2(2) - y = 6/8-3y = -3/8
Therefore, y = 1.
Hence, the solution to the system of equations is (x, y) = (2, 1).
We are given 2 equations as follows:1/4x + 1/2y = 5/8 ...(i)3/4x - 1/2y = 27/8 - 3/8 ...(ii)
Multiplying equation (i) by 3 and equation (ii) by 2,3/4x + 3/2y = 15/8...(iii)3/2x - y = 6/8 ...(iv)We can write equation (iii) as follows: y = (3/2x - 6/8)/-1 = 3/2x - 6/8Now we substitute this value of y in equation (i)1/4x + 1/2(3/2x - 6/8) = 5/8Simplifying,3/4x - 3/8 = 5/8 => 3/4x = 5/8 + 3/8 => 3/4x = 1 => x = 4/3
Now we substitute this value of x in equation (iv):y = 3/2(4/3) - 6/8 = 2/1 = 2
Therefore, the solution to the system of equations is (x, y) = (4/3, 2).
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Saul edistien shops at tudburys at its scratch-'n-save sale . Saul has a card that offers him a 15% discount on anything in the store. he buys some $45 cologne and a $10 tie. If sales tax is 10%, how much does he pay in all?
:Saul pays $49.725 in all. Saul will thus be charged 10% sales tax on $46.75:$46.75 purchase price x 10% tax = $4.675 tax. Saul's total purchase price is thus:$46.75.
Saul's cologne costs $45, and his tie costs $10. His total purchase is thus $55.00 before tax.Saul is entitled to a 15% discount on his purchase. His discount is calculated as follows:$55.00 purchase price x 15% discount = $8.25 discount. Saul's purchase price after discount is $46.75.
The sales tax is added to the purchase price after the discount has been applied. Saul will thus be charged 10% sales tax on $46.75:$46.75 purchase price x 10% tax = $4.675 taxSaul's total purchase price is thus:$46.75 purchase price after discount + $4.675 tax = $49.725
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Use "faithful" data in R studio. Extract waiting variable and compute only the average of less thanor equal to 50 minutes of waiting time to next eruption
The above command will compute the average waiting time of all the eruptions whose waiting time is less than or equal to 50 minutes.
To extract the "waiting" variable and compute only the average of less than or equal to 50 minutes of waiting time to next eruption using "faithful" data in R studio, follow these steps:
Step 1: Load the faithful dataset into R studio using the following command:```data(faithful)```
Step 2: Extract the "waiting" variable from the "faithful" dataset using the following command:```waiting <- faithful$waiting```
Step 3: Compute only the average of less than or equal to 50 minutes of waiting time to next eruption using the following command:```
mean(waiting[waiting <= 50])```
Note: The above command will compute the average waiting time of all the eruptions whose waiting time is less than or equal to 50 minutes.
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Gena and her friends each estimated the quotient of –137. 56 divided by –6. 12 using compatible numbers. Which shows the best estimate using compatible numbers?.
The best estimate using compatible numbers is approximately 23.33.
To find the best estimate using compatible numbers for the quotient of -137.56 divided by -6.12, we need to identify compatible numbers that are close to the given values.
Compatible numbers are numbers that are easy to work with mentally and provide a close approximation of the actual values.
Let's consider compatible numbers for -137.56 and -6.12:
For -137.56, we can use -140, which is close to -137.56.
For -6.12, we can use -6, which is close to -6.12.
Now, let's calculate the estimate:
-137.56 ÷ -6.12 ≈ -140 ÷ -6
Dividing -140 by -6, we get:
-137.56 ÷ -6.12 ≈ 23.33
Therefore, the best estimate using compatible numbers is approximately 23.33. By selecting compatible numbers close to the given values and performing the division using those numbers, we can obtain a reasonable estimate of the quotient.
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Maury picks up some old furniture that weighs 1123 pounds. The combined weight of the furniture and the truck is 8122 pounds. Maury drops off the furniture and picks up new items that weigh 876 pounds.
What is the combined weight of the new items and the truck?
____ pounds(s)
7,875 lbs.
Old furniture weighs = 1,123 lbs.
Combined weight of furniture and truck = 8,122 lbs.
New items = 876 lbs.
First, subtract the weight of the old furniture from the combined weight:
8,122 lbs - 1,123 lbs. = 6,999 lbs.
Then, add the weight of the new items:
6,999 lbs + 876 lbs. = 7,875 lbs.
