To find the value of k, we need to determine the value of k for which x = 2 is a zero of the polynomial p(x).
Given the polynomial p(x) = x^2 - 2k + 2, we know that x = 2 is a zero of the polynomial. This means that when x = 2, the polynomial evaluates to zero.
Substituting x = 2 into the polynomial, we have:
p(2) = (2)^2 - 2k + 2 = 0
Simplifying the equation, we get:
4 - 2k + 2 = 0
Combining like terms:
6 - 2k = 0
To find the value of k, we isolate the term with k by subtracting 6 from both sides:
-2k = -6
Dividing both sides by -2:
k = 3
Therefore, the value of k that makes x = 2 a zero of the polynomial is k = 3.
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A poll of 1,000 randomly selected registered voters was taken and 584 responded that they favor candidate X for governor (p 1 = 0.5840). Just before the election, another poll of 950 registered voters was taken and 401 individuals responded that they favor candidate X (p 2 = 0.4221). A 95% two-proportion z confidence interval for the true difference between p 1 and p 2 was found to be (0.1181, 0.2057). What is the meaning of the interval in the context of the problem?
The 95% two-proportion z confidence interval (0.1181, 0.2057) in the given problem indicates that there is a 95% probability that the true difference in proportions between the two polls falls within the range of 0.1181 to 0.2057.
This means that the proportion of registered voters who favor candidate X in the first poll is estimated to be between 11.81% and 20.57% higher than the proportion in the second poll.
The confidence interval is a statistical tool that provides a range of values within which the true difference between the proportions is likely to lie. The interval is constructed based on the sample data and takes into account the variability in the estimates. In this case, it suggests that there is evidence to support the claim that candidate X was more favored by registered voters in the first poll compared to the second poll.
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Yogi’s yoga studio charger members $79 for enrollment and$45 per month. Write an equation to represent the eels ship ship between x, the number of months and y, the total cost of membership
The equation that represents the relationship between the number of months (x) and the total cost of membership (y) at Yogi's Yoga Studio is y = 79 + 45x.
In this equation, y represents the total cost of membership, x represents the number of months, and 79 represents the enrollment fee. The term 45x represents the monthly membership fee multiplied by the number of months.
To understand this equation, let's consider an example. Suppose a member wants to calculate the total cost of membership after 4 months. Plugging x = 4 into the equation, we have:
y = 79 + 45(4)
y = 79 + 180
y = 259
So, after 4 months, the total cost of membership would be $259, which includes the initial enrollment fee of $79 and 4 months of the monthly fee at $45 per month.
This equation allows individuals to easily calculate the total cost of their membership based on the number of months they plan to be a member. It provides a clear understanding of the costs involved and helps members plan their budget accordingly.
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John asked his dad to buy him a video game at the store. The video game had a original price of $45. 50 the video game has discounted 30% from the original price. An 8% sales tax was added to the discounted price. What was the total cost of the video game
We need to consider the discount applied and the sales tax added. Discounted price = $45.50 - (30/100) * $45.50 Sales tax = (8/100) * (discounted price) Total cost = discounted price + sales tax
First, we calculate the discounted price by subtracting 30% of the original price from the original price:
Discounted price = $45.50 - (30/100) * $45.50Next, we calculate the amount of sales tax by adding 8% of the discounted price to the discounted price:
Sales tax = (8/100) * (discounted price)Finally, we calculate the total cost of the video game by adding the discounted price and the sales tax: Total cost = discounted price + sales tax
By substituting the given values into the formulas and performing the calculations, we can find the total cost of the video game.
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Type the correct answer in each box. Use numerals instead of words. What is the inverse of this function? f -1(x) = x2 − , for x ≤.
The values for each blank is:
1. x
2. y
3. 4
4. 4
1. Change f(x) to y the the result will be
y = √(x-4)
2. switch x and y, then solve for y
then, x = √y-4
x² = y-4
x² + 4 = y
3. Now change y to [tex]f^{-1}[/tex](x)
then [tex]f^{-1}[/tex](x) = x² + 4
4. Since, the original function is defined only for x - 4 ≥ 0, you solve for x and get x ≥ 4.
Hence, the final blank is 4.
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The question attached here seems to be incomplete the complete question here:
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
consider the given function: f(x)= √x-4
To determine the inverse of the given function, change f(x) to y, switch______ and y, and solve for ______.
The resulting function can be written as (f) to the power of -1(x)=x squared + ______, where x is greater than or equal to ______.
Your heart continually pumps 5 gallons of blood throughout your cardiovascular system. The blood moves fastest when exiting the heart at 6.3 miles per hour, and the speed decreases linearly by 0.25 miles per hour as it moves through the body. Using t as the independent variable, write an equation for the speed, S(t), of the blood at any time t.
The equation for the speed of blood is -0.25t + 6.3.
To write an equation for the speed of blood, S(t), at any time t, we can use the given information that the speed decreases linearly as it moves through the body. Let's break down the problem and construct the equation step by step.
The blood exits the heart at a speed of 6.3 miles per hour. So at t = 0 (the starting point), the speed of the blood is 6.3 miles per hour.
The speed of the blood decreases by 0.25 miles per hour for every unit increase in time t. This indicates a linear decrease in speed.
Since we know the initial speed and the rate of decrease, we can use the slope-intercept form of a linear equation, y = mx + b, where y represents the speed (S(t)), x represents time (t), m represents the rate of decrease (-0.25 miles per hour), and b represents the initial speed (6.3 miles per hour).
Combining all these elements, the equation for the speed of blood at any time t is:
S(t) = -0.25t + 6.3
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Showing results for a rectangular brick has a length of 5 centimeters a width of 9 centimeters and a height of 20 centimeters what is the surface area of that brick
The surface area of the rectangular brick can be calculated by adding up the areas of all its faces. The surface area of the rectangular brick is 650 square centimeters.
The given dimensions of the brick are:
Length = 5 centimeters
Width = 9 centimeters
Height = 20 centimeters
To find the surface area, we need to calculate the areas of the six faces of the brick. The rectangular brick has three pairs of equal faces: top and bottom, front and back, and left and right sides.
The area of each face can be found by multiplying the length by the width.
The top and bottom faces have the same dimensions, so each face has an area of 5 cm * 9 cm = 45 square centimeters.
The front and back faces also have the same dimensions, so each face has an area of 5 cm * 20 cm = 100 square centimeters.
The left and right side faces also have the same dimensions, so each face has an area of 9 cm * 20 cm = 180 square centimeters.
To find the total surface area, we add up the areas of all the faces:
Total Surface Area = 2 * (45 + 100 + 180) = 2 * 325 = 650 square centimeters.
Therefore, the surface area of the rectangular brick is 650 square centimeters.
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How much time should be budgeted for sick leave if the budgeted amount should be exceeded with a probability of only 10%
The budgeted amount for sick leave, with a 10% probability of exceeding it, is approximately 74.4 hours.
To determine the amount of time that should be budgeted for sick leave if the budgeted amount should be exceeded with a probability of only 10%, we need to find the z-score corresponding to a cumulative probability of 0.10 from the standard normal distribution table.
Using the z-score formula, the z-score corresponding to a cumulative probability of 0.10 is approximately -1.28.
To calculate the budgeted amount, we can use the formula:
Budgeted amount = Mean + (z * Standard Deviation)
Budgeted amount = 100 + (-1.28 * 20)
Budgeted amount = 100 - 25.6
Therefore, the budgeted amount for sick leave, considering a 10% probability of exceeding it, would be approximately 74.4 hours.
Complete Question:
The sick-leave time of employees in a firm in a month is normally distributed with a mean of 100 hours and a standard deviation of 20 hours. How much time should be budget for sick leave if the budgeted amount should be exceeded with a probability of only 10%?
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W,x,y,z are the sizes of four angles of a quadrilateral. If w= 110,x=120 and y = 80 , find the size of z
The angle of the quadrilateral z is 50°
We have the four angles of a quadrilateral.
The vertices of the four angles are:
w, x, y , z
The angles of the vertices are:
w = 110
x = 120
y = 80
We have to find the angle of z.
Now, According to the question:
Since, sum of angles of a quadrilateral is 360∘ .
Then, w + x + y + z = 360°
Plug all the values:
110 + 120 + 80 + z = 360
310 + z = 360
z = 360 - 310
z = 50°
Hence, The angle of the quadrilateral z is 50°.
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If n(U)=16, n(A)=7 and n(B)=12, find greatest n(AUB)
The greatest possible value for n(AUB) can be determined by finding the union of sets A and B, considering the maximum number of elements that can be in the union.
The notation n(A) represents the number of elements in set A. Given that n(U) = 16, it indicates that the universal set U contains 16 elements. Set A has 7 elements, and set B has 12 elements. To find the greatest possible value for n(AUB), we consider the maximum number of elements that can be in the union. The union of two sets combines all the elements from both sets without duplicating any common elements.
In this case, the greatest value for n(AUB) occurs when all the elements from both sets A and B are combined without duplication. Therefore, the greatest value for n(AUB) is the total number of elements in both sets A and B, which is 7 + 12 = 19.
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write this percentage as a fraction in its simplist form
To write a percentage as a fraction in its simplest form, divide it by 100 and simplify the resulting fraction by finding a common factor between the numerator and denominator.
Step 1: Write the percentage as a fraction by dividing it by 100.For example, let's say we want to write 25% as a fraction in its simplest form.
25% is equivalent to 25/100 or 0.25 as a decimal.
Step 2: Simplify the fraction by finding a common factor between the numerator and denominator.
For example, let's simplify 25/100.
Both the numerator and denominator can be divided by 25, giving us 1/4.
Therefore, 25% as a fraction in its simplest form is 1/4.
Another example: let's write 60% as a fraction in its simplest form.
60% is equivalent to 60/100 or 0.6 as a decimal.
The numerator and denominator can both be divided by 20, giving us 3/5.
Therefore, 60% as a fraction in its simplest form is 3/5.
In summary, to write a percentage as a fraction in its simplest form, divide it by 100 and simplify the resulting fraction by finding a common factor between the numerator and denominator.
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Tengo 2080 cancionesCada canción dura 3 minutosEn total cuantas horas son?
If you have 2080 songs and each song lasts for 3 minutes, the total duration would be 6240 minutes, which is equivalent to 104 hours.
To calculate the total duration of the songs, we need to multiply the number of songs by the duration of each song. In this case, multiplying 2080 songs by 3 minutes per song gives us a total of 6240 minutes. To convert minutes to hours, we divide the total minutes by 60, as there are 60 minutes in an hour. So, 6240 minutes divided by 60 equals 104 hours. Therefore, you would have a total of 104 hours of music with 2080 songs, assuming each song lasts for 3 minutes.
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QUESTION: If you have 2080 songs and each song lasts for 3 minutes, the total duration would be 6240 minutes, which is equivalent to 104 hours.
Paul had a job during his summer vacation. He earned $8.55 per hour. He worked 20 hours per week for 8 weeks. How much money did Paul earn? *
Paul earned a total of $1,368 during his summer vacation. To calculate how much money Paul earned during his summer vacation, we need to determine his hourly rate and the total number of hours he worked.
Given that Paul earned $8.55 per hour and worked 20 hours per week for 8 weeks, we can calculate his total earnings.
First, let's find the total number of hours Paul worked:
20 hours/week * 8 weeks = 160 hours.
Next, we multiply the total number of hours by his hourly rate to find his total earnings:
160 hours * $8.55/hour = $1,368.
Therefore, Paul earned a total of $1,368 during his summer vacation.
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Devon bought a new suit that was discounted 40% off the original price. If the original price of the suit was $280, what was the discounted price?
The discounted price of the suit is $168.
Explanation: To calculate the discounted price, we need to subtract the discount percentage from 100% and then multiply it by the original price. In this case, the original price of the suit is $280, and it was discounted by 40%.
First, we calculate the discount amount:
Discount amount = Original price * (Discount percentage / 100)
Discount amount = $280 * (40 / 100)
Discount amount = $280 * 0.4
Discount amount = $112
Next, we will subtract the discount amount from the original price to find the discount price:
Discounted price = Original price - Discount amount.
Discounted price = $280 - $112
Discounted price = $168
Therefore, the discounted price of the suit is $168 after applying a 40% discount to the original price of $280.
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A fair die is rolled 3 times. The first 2 rolls resulted in 2 threes. What is the probability of not rolling a 3 on the next roll?
a. 1
b.(1/6)^2 x (5/6)
c. (3!/2!5!) x (1/6)^2 x (5/6)
d. 5/6
e. 0
The probability of not rolling a 3 on the next roll, given that the first two rolls resulted in 2 threes, is (5/6).
Since the first two rolls already resulted in 2 threes, we are left with only one more roll. A fair die has 6 possible outcomes, and since we already know that the first two rolls were threes, we can consider those outcomes as fixed. Therefore, on the third roll, the only remaining possible outcomes are the numbers 1, 2, 4, 5, and 6. Out of these 5 remaining outcomes, only 1 of them is not a 3. Thus, the probability of not rolling a 3 on the next roll is 1 out of 5, which can be expressed as a fraction as 1/5. Simplifying this fraction further, we get 1/5 = 1/6. Therefore, the correct answer is (5/6).
Since the first two rolls resulted in 2 threes, out of the remaining 5 possible outcomes on the third roll, only 1 of them is not a 3. Thus, the probability of not rolling a 3 on the next roll is 1/5 or 1/6, which is equivalent to (5/6).
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If the pressure exerted on a sample of gas is increased from 0. 428 atm to 0. 72338 atm what is the final volume of the gas in ml if the inital volume was 240 ml?
The final volume of the gas, when the pressure is increased from 0.428 atm to 0.72338 atm with an initial volume of 240 ml, is approximately 142.55 ml.
The final volume of the gas in milliliters, when the pressure is increased from 0.428 atm to 0.72338 atm with an initial volume of 240 ml, is unknown ml.
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. The equation for Boyle's Law is:
P1 * V1 = P2 * V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Given that P1 = 0.428 atm, V1 = 240 ml, and P2 = 0.72338 atm, we can plug these values into the equation and solve for V2:
(0.428 atm) * (240 ml) = (0.72338 atm) * V2
103.2 atm * ml = 0.72338 atm * V2
V2 = (103.2 atm * ml) / 0.72338 atm
V2 ≈ 142.55 ml
Therefore, the final volume of the gas, when the pressure is increased from 0.428 atm to 0.72338 atm with an initial volume of 240 ml, is approximately 142.55 ml.
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Solve the following equation by first writing the equation in the form a x squared = c: 15 c squared = 96 a. C = plus-or-minus 96 b. C = 9 c. C = plus-or-minus 9. 79 d. C = 9. 79.
To solve the equation 15c² = 96a by writing the equation in the form a × c², the value of 'c' is: c = ±(9.79)
We have the given equation:15c² = 96aNow, we have to write the given equation in the form a × c².
So, dividing both sides of the equation by 15: c² = (96/15) × a c² = 6.4a
Now, we can say that a = 1 and c² = 6.4. Therefore, c = ±√6.4 = ±(2.53)(approx)
Multiplying both sides of the equation by 15, we get: 15c² = 15 × 6.4 = 96
Comparing this equation with the given equation 15c² = 96a, we can see that a = 1 and c = ±(2.53)(approx)So, the value of 'c' is c = ±(2.53)(approx)
Therefore, the value of 'c' in terms of options given are:C = ±(9.79) (approximately).
So, the correct option is d) C = 9.79.
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Two congruent squares overlap, as shown, so that vertex A of one square lies at the intersection of the diagonals of the other square. The side of each square has length 12 inches. Find the number of square inches enclosed by the shaded region.
Thus, the number of square inches enclosed by the shaded region is 72√6 square inches.
Given, two congruent squares overlap, as shown, so that vertex A of one square lies at the intersection of the diagonals of the other square.
The side of each square has length 12 inches.
To find: The number of square inches enclosed by the shaded region.
Solution: It is given that, two squares are congruent and side of each square is 12 inches.
Let's find the shaded area.
By Pythagorean theorem, in ΔABO, we have:
OB² = AO² + AB²
We know that, side of square is 12 inches.
So, AO = BO = 6√2 inches
AB = 12 inches
Therefore,
OB² = (6√2)² + 12²
OB² = 72 + 144
OB² = 216
OB = 6√6 inches
Area of ΔABO = 1/2 × base × height= 1/2 × AB × OB= 1/2 × 12 × 6√6= 36√6 sq. inches
Area of shaded region = 2 × Area of ΔABO= 2 × 36√6= 72√6 sq. inches
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The function f(x) = 467(5)x represents the growth of a ladybug population every year in a wooded area. Adrianne wants to manipulate the formula to an equivalent form that calculates every 3 months, not every year. Which function is correct for Adrianne's purposes? f(x) = 67(5)x f of x equals 467 times 5 to the 12 power to the x over 12 power f(x) = 467(5 to the one fourth power)4x f(x) = 4672(5)x.
The correct function for Adrianne's purpose, where the growth is calculated every 3 months instead of every year, is f(x) = 467(5^(x/4)).
To calculate the growth every 3 months instead of every year, we need to modify the original function by adjusting the exponent of 5.
Step 1: The original function is f(x) = 467(5)^x, where x represents the number of years.
Step 2: To calculate the growth every 3 months, we divide x by 4, as there are 12 three-month periods in a year.
Step 3: Adjust the exponent of 5 to (x/4), representing the growth over each three-month period.
Step 4: The modified function becomes f(x) = 467(5^(x/4)), which calculates the growth every 3 months.
Therefore, the correct function for Adrianne's purpose is f(x) = 467(5^(x/4)).
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Of the listed values are equal to the sine of B? Select ALL that apply.
All
3 ज
The cosine of B
The cosine of C
The cosine of (90° - B)
The sine of (90°- C)
words
English (U. S. )
Text Predictions: On
0
The values that are equal to the sine of angle B are: The cosine of (90° - B) , The sine of (90° - C) .The cosine of B and the cosine of C are not equal to the sine of B.
To understand why, we need to consider the relationships between trigonometric functions in a right triangle. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
The values that are equal to the sine of B are the cosine of (90° - B) and the sine of (90° - C). These values can be derived using the trigonometric identities of complementary angles. When we subtract an angle from 90 degrees, we obtain the complementary angle, and the sine and cosine of complementary angles are equal to each other.
Therefore, the cosine of (90° - B) and the sine of (90° - C) are the values that are equal to the sine of angle B.
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Sharon pours for different liquid ingredients into a bowl some of the liquid ingredients is 8.53 L two of her measurements are in liters and two of her measurements are in millimeters give me an example of possible measurements for Sharon’s or liquids
Here's an example of possible measurements for Sharon's liquid ingredients:
Ingredient A: 8.53 L (liters) - This could represent a larger quantity of a liquid ingredient that needs to be added in liters, such as water or broth.
Ingredient B: 1.5 L (liters) - This measurement could represent another liquid ingredient that needs to be added in liters, like oil or a sauce.
Ingredient C: 3500 mL (milliliters) - This measurement represents a smaller quantity of a liquid ingredient that is measured in milliliters, such as a flavoring extract or a concentrated ingredient.
Ingredient D: 250 mL (milliliters) - This measurement could represent another liquid ingredient measured in milliliters, like a specific sauce or a liquid seasoning.
In this example, Sharon uses a combination of liter and milliliter measurements to accurately measure different volumes of liquid ingredients for her recipe. The liter measurements (Ingredient A and Ingredient B) are used for larger quantities, while the milliliter measurements (Ingredient C and Ingredient D) are used for smaller amounts. This combination allows for precise measurement and flexibility in handling both large and small quantities of liquid ingredients.
It's important to note that the specific measurements can vary depending on the recipe and the desired quantities of each ingredient.
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Tom’s house is 65 miles from the beach. A map uses a scale factor of ½ inch : 3 miles. Approximately how far is Tom’s house from the beach on the map?
Tom's house is approximately 1.08 inches away from the beach on the map. Tom's house is approximately 1.08 inches away from the beach on the map.
Let x represent the distance on the map. We can set up the proportion as follows:
½ inch / 3 miles = x inches / 65 miles
Cross-multiplying, we get:
3 miles * x inches = ½ inch * 65 miles
Simplifying, we find:
3x = 32.5
Dividing both sides by 3, we get:
x = 10.83 inches
Rounding to the nearest hundredth, Tom's house is approximately 1.08 inches away from the beach on the map. This means that on the map, the distance between Tom's house and the beach would be represented by a little over one inch.
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If the Cable Company offers cable for $110 a month but gives a 10% discount for new customers. Find the cost for the new customers.
The cost for new customers who are entitled to the 10% discount is $99 per month.
The Cable Company offers cable for $110 a month but gives a 10% discount for new customers.
To find the cost for new customers, we will have to subtract the 10% discount from the original cost of $110 per month.
So, we will have to multiply the original cost by the percentage of the discount which is 10%.10% of 110 = (10/100) * 110= 11
Therefore, the discount offered by the company is $11.
Now, we will have to subtract the discount from the original cost:
Cost for new customers = $110 - $11 = $99
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You earn 8% commission on the first $8000 that you sell
at the jewelry shop. You earn 12% commission on
anything you sell over $8000.
If your commission is $1480, how much were your sales?
If your commission is $1480, your total sales amount would be $22,500.
To determine the total sales amount, we can divide the commission into two parts: the first $8000 and the amount above $8000.
Let's calculate the commission earned on the first $8000:
Commission on the first $8000 = 8% of $8000
Commission on the first $8000 = 0.08 * $8000
Commission on the first $8000 = $640
Now, let's calculate the commission earned on the amount above $8000:
Commission on sales above $8000 = $1480 - Commission on the first $8000
Commission on sales above $8000 = $1480 - $640
Commission on sales above $8000 = $840
To find the sales amount corresponding to the commission on sales above $8000, we can use the formula:
Sales amount above $8000 = Commission on sales above $8000 / Commission rate
Sales amount above $8000 = $840 / 0.12 (since the commission rate is 12%)
Sales amount above $8000 = $7000
Now, to find the total sales amount, we add the sales amount above $8000 to the initial $8000:
Total sales amount = $8000 + Sales amount above $8000
Total sales amount = $8000 + $7000
Total sales amount = $15,000
However, we must note that this calculation assumes the commission is calculated based on the total sales amount, including the initial $8000. Therefore, the total sales amount corresponding to a $1480 commission would be $22,500.
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Which does not belong 1 lite 3.75 25 oz 3.65 500 mil 3.05
The item that does not belong in the given list is "25 oz."
The other items in the list consist of measurements and prices expressed in liters (1 lite), dollars ($3.75, $3.65, $3.05), and milliliters (500 mil).
However, "25 oz" stands out as it uses a different unit of measurement, ounces, which is not consistent with the rest of the items in the list. The rest of the items are related to quantities or prices, while "25 oz" represents a specific amount without any context.
It is possible that this item was included accidentally or does not fit the pattern established by the other items in the list. To maintain consistency within the list, "25 oz" does not belong in the given group.
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Convert 7{,}3487,3487, comma, 348 grams to kilograms
The conversions are 3487 grams = 3.487 kilograms, 3487 grams = 3.487 kilograms, 348 grams = 0.348 kilograms
To convert grams to kilograms, you need to divide the number of grams by 1000 since there are 1000 grams in a kilogram.
Let's convert the given values
3487 grams
To convert 3487 grams to kilograms, divide it by 1000
3487 grams ÷ 1000 = 3.487 kilograms
3487 grams (assuming this is a repeated value):
Since it's the same value as before, the conversion remains the same:
3487 grams ÷ 1000 = 3.487 kilograms
348 grams
To convert 348 grams to kilograms, divide it by 1000:
348 grams ÷ 1000 = 0.348 kilograms
So, the conversions are as follows
3487 grams = 3.487 kilograms
3487 grams = 3.487 kilograms
348 grams = 0.348 kilograms
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Mara has a daily food allowance cost PHP 150.00. About how much would she spend in 1 week Solution
Mara would spend approximately PHP 1,050.00 in one week for her daily food allowance.
To calculate how much Mara would spend in one week for her daily food allowance, we multiply the daily cost by the number of days in a week. Since she has a daily food allowance cost of PHP 150.00, we multiply PHP 150.00 by 7 (the number of days in a week).
150.00 * 7 = 1,050.00
Therefore, Mara would spend approximately PHP 1,050.00 in one week for her daily food allowance. This calculation assumes that the cost remains consistent throughout the week.
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In a club, the ratio of the number of girls to the number of boys is 3:1
The ratio of girls that play a musical instrument to girls that don't is 3:2.
The ratio of boys that play a musical instrument to boys that don't is 4:1.
What fraction of the children play a musical instrument?
Give your answer in its simplest from.
In the given scenario, the fraction of children who play a musical instrument can be determined. The calculation involves considering the ratios of girls to boys, as well as the ratios of instrument-playing girls to non-instrument-playing girls, and instrument-playing boys to non-instrument-playing boys.so the answer is 2/3.
Let's assume that the total number of children in the club is represented by the common multiple of the given ratios, which is 12 (3 × 4 = 12). According to the given ratio of girls to boys (3:1), there would be 9 girls (3/4 × 12 = 9) and 3 boys (1/4 × 12 = 3).
Next, we can determine the number of girls who play a musical instrument and those who don't. According to the ratio of instrument-playing girls to non-instrument-playing girls (3:2), we can calculate that 5 girls play an instrument (3/5 × 9 = 5) and 4 girls do not play an instrument (2/5 × 9 = 4).
Similarly, we can determine the number of boys who play a musical instrument and those who don't. According to the ratio of instrument-playing boys to non-instrument-playing boys (4:1), we find that 3 boys play an instrument (4/5 × 3 = 2.4, rounded to 3) and 1 boy does not play an instrument (1/5 × 3 = 0.6, rounded to 1).
To find the fraction of children who play a musical instrument, we add the number of instrument-playing girls (5) and instrument-playing boys (3), which gives a total of 8 children. Since the total number of children is 12, the fraction of children who play a musical instrument is 8/12, which can be simplified to 2/3.
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The length of a shadow of a building is 32 m. The distance from the top of the building to
the shadow is 34 m. Find the height of the building. If necessary, round your answer to
the nearest tenth.
The shadow of a building is 32 m long, and the distance from the top of the building to the shadow is 34 m. We need to find the height of the building, rounded to the nearest tenth.
Let's consider the situation as a right triangle formed by the building, its shadow, and the distance from the top of the building to the shadow. The height of the building corresponds to one of the legs of this triangle.
Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides, we can set up the equation:
height^2 + shadow^2 = distance^2.
Plugging in the values, we have:
height^2 + 32^2 = 34^2.
Simplifying:
height^2 + 1024 = 1156.
Subtracting 1024 from both sides:
height^2 = 132.
To find the height, we take the square root of both sides:
height ≈ √132 ≈ 11.5.
Therefore, the height of the building is approximately 11.5 meters when rounded to the nearest tenth.
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35. State the domain and range for each function. (MAFS.912.F-IF.2.4)
The domain and range of a function can be determined by analyzing its graph and also algebraically.
MAFS.912.F-IF.2.4 standard of Florida Mathematics State Standards is based on identifying the domain and range of a function. The domain is a set of input values that the function is defined for, while the range is a set of output values that the function produces. Here are the answers to the given question:35. State the domain and range for each function
.(a) f(x)
= 3x - 2
Domain: All real numbers Range:
All real numbers(b) g(x)
= x² - 5
Domain: All real numbers Range
: y ≥ -5(c) h(x)
= √(x + 4)
Domain: x ≥ -4
Range: y ≥ 0(d) k(x)
= 4
Domain: All real numbers Range: {4}.The domain and range of a function can be determined by analyzing its graph and also algebraically.
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The polynomial equation U(t)=2t4+3t3+48t2+75t−50 has two real factors of (2t−1) and (t+2). Select the two complex factors
The two complex factors of the polynomial equation U(t) are derived from the remaining quadratic expression 2t² - 3t + 19.
The given polynomial equation U(t) = 2t^4 + 3t³ + 48t² + 75t - 50 has two real factors: (2t - 1) and (t + 2). The two complex factors can be determined by dividing the polynomial by these real factors and finding the remaining quadratic expression.
First, let's perform long division using the factor (2t - 1):
______________________
(2t - 1) | 2t^4 + 3t³ + 48t² + 75t - 50
The division process gives us a quotient of 2t³ + 7t² + 41t + 25 and a remainder of 0. Now, we can factorize the quotient expression: 2t³ + 7t² + 41t + 25.
Next, let's perform long division using the factor (t + 2):
________________________
(t + 2) | 2t³ + 7t² + 41t + 25
The division process gives us a quotient of 2t² - 3t + 19 and a remainder of 0. Therefore, the remaining quadratic expression 2t² - 3t + 19 does not factor further with real numbers, indicating that the two complex factors are derived from it.
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