Larry, Mary and Jerry's statements on the probability of drawing ping pong balls:.the probability of drawing a ping pong ball with an odd number, keeping it, and then drawing a yellow ping pong ball is 5/29.
Thus, there are 60 ping pong balls in total.Larry says the probability of drawing a blue ping pong ball, keeping it, and then drawing a ping pong ball with a 5 or a 6 is the greatest.Probability of drawing a blue ball: P(B) = 10/60 = 1/6Probability of drawing a 5 or 6, given that a blue ball has already been drawn: P(5 or 6 | B) = 2/9Probability of the desired outcome: P(B and (5 or 6)) = P(B) × P(5 or 6 | B) = (1/6) × (2/9) = 1/27
Mary says the probability of drawing a ping pong ball with an odd number, keeping it, and then drawing a yellow ping pong ball is greatest.Probability of drawing an odd number: P(O) = 30/60 = 1/2Probability of drawing a yellow ball, given that an odd-numbered ball has already been drawn: P(Y | O) = 10/29Probability of the desired outcome: P(O and Y) = P(O) × P(Y | O) = (1/2) × (10/29) = 5/29
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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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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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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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If a= (-2,-4) and B (-8,4) what is length of ab
Answer:
Length of ab = 10 units
Step-by-step explanation:
X1 = -2, X2 = -8
Y1 = -4, Y2 = 4
[tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} } \\\sqrt{(-8 -(-2))^{2} + (4-(-4))^{2} } \\\sqrt{(-8+2)^{2} + (4+4)^{2} } \\\sqrt{6^{2} +8^{2}} \\\sqrt{36+64} \\\sqrt{100} \\10[/tex]
The polygons are similar. Find the value of each variable. Round answers to the nearest hundredth.
To find the values of the variables in similar polygons, we need more specific information about the problem.
Similar polygons have corresponding angles that are equal and corresponding sides that are proportional. However, without knowing any specific measurements or relationships between the sides and angles, it is not possible to determine the exact values of the variables. Therefore, we cannot provide a numerical answer without additional information.
In order to solve for the variables in similar polygons, we typically need either the ratio of corresponding side lengths or the measure of at least one angle. With this information, we can set up proportions and solve for the unknown variables. However, since the problem did not provide any measurements or ratios, we cannot proceed with finding specific values for the variables. It is important to have precise information about the relationships between the sides and angles of the polygons in order to calculate the values accurately.
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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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Solve.
9. An engineer is designing a storage compartment in a spacecraft. The
compartment must be 2 meters longer than it is wide and its depth must
be 1 meter less than its width. The volume of the compartment must be
8 cubic meters.
a. Write an equation to model the volume of the compartment.
we get:(x + 2) × x × (x - 1) = 8x³ + x² - 2x - 8 = 0Thus, the equation to model the volume of the compartment is 8x³ + x² - 2x - 8 = 0.
Given that
the compartment must be 2 meters longer than it is wide and its depth must be 1 meter less than its width. Let's assume the width of the compartment to be x meters.
Then, the length of the compartment would be (x + 2) meters as it is 2 meters longer than its width. And the depth of the compartment would be (x - 1) meters as its depth must be 1 meter less than its width.
Now, the volume of the compartment would be given by; V = l × w × d V = (x + 2) × x × (x - 1)As given, the volume of the compartment must be 8 cubic meters.
Hence, we get:(x + 2) × x × (x - 1) = 8x³ + x² - 2x - 8 = 0Thus, the equation to model the volume of the compartment is 8x³ + x² - 2x - 8 = 0.
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Write algorithms that perform the operations u x 10m ; u divide 10m ; u rem 10m where u represents a large integer, m is a nonnegative integer, divide returns the quotient in integer division, and rem returns the remainder. Analyze your algorithms, and show that these operations can be done in linear time
The algorithms are solved and the time complexity of algorithm is O(m), which is linear.
Given data ,
a)
Algorithm for u x 10m:
Initialize a variable "result" to 0.
Repeat the following steps m times:
a. Add u to the result.
Return the result.
Analysis: The algorithm performs m iterations, and in each iteration, it performs a constant-time addition operation. Therefore, the time complexity of this algorithm is O(m), which is linear.
b)
Algorithm for u divide 10m:
Initialize a variable "result" to u.
Repeat the following steps m times:
a. Divide the result by 10 (integer division).
Return the result.
Analysis: The algorithm performs m iterations, and in each iteration, it performs a constant-time division operation. Therefore, the time complexity of this algorithm is O(m), which is linear.
c)
Algorithm for u rem 10m:
Initialize a variable "result" to u.
Repeat the following steps m times:
a. Set the result to the remainder when dividing the result by 10.
Return the result.
Hence , the algorithms are solved
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Abott simplified an expression. His work is shown below.
9.5 divided by 0.25 + 4 (0.25 + 0.5) + 6
Step 1 9.5 divided by 0.25 + 4 (0.75) + 6
Step 2 38 + 10 (0.75)
Step 3 38 + 7.5
Step 4 45.5
In which step did Abott make his first mistake?
step 1
step 2
step 3
step 4
Abbott made his first mistake in Step 2 of the simplification process. In Step 1, Abbott correctly divided 9.5 by 0.25 and simplified the expression within the parentheses, resulting in 38 + 4(0.75) + 6.
However, in Step 2, he made an error by multiplying 4 with 0.75 and obtaining 10. The correct multiplication would have resulted in 4(0.75) = 3.
This mistake in Step 2 led to an incorrect value in the subsequent steps. In Step 3, Abbott correctly added 38 and 7.5, but the value of 38 was incorrect due to the mistake in Step 2. As a result, the final result in Step 4, which is 45.5, is incorrect.
To correct the error, Abbott should have multiplied 4 with 0.75, which would yield 3. Then, the correct calculation in Step 3 would have been 38 + 3 = 41, leading to the correct final result. Therefore, the first mistake occurred in Step 2 when Abott incorrectly multiplied 4 with 0.75, resulting in an incorrect value for the expression.
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Un terreno de forma cuadrangular mide 36 m de lado ¿cuántos m2 tiene de área ? ( A = ℓ 2 )
The length of each side is given as 36 meters. Plugging this value into the formula. The square-shaped land, with each side measuring 36 meters, has an area of 1,296 square meters.
To find the area of a square, we use the formula A = ℓ^2, where A represents the area and ℓ represents the length of one side.
In this case, the length of each side is given as 36 meters. Plugging this value into the formula, we have:
A = 36^2.
Simplifying the equation, we get:
A = 1,296.
Therefore, the area of the square-shaped land is 1,296 square meters. The result is obtained by squaring the length of one side (36 meters) to find the total area within the square.
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Antonio made 1 1/3 pounds of trail mix. If he puts 1/3 of a pound into each bag, how many bags can Antonio fill? Write your answer as a fraction or as a whole or mixed number. bags
Answer: 4
Step-by-step explanation:
1 1/3 = 4/3
(4/3)/(1/3)
Basically, 4/1
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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
An optical inspection system is used to distinguish among different part types. The probability of correct classification of any part is 0. 98. Suppose that three parts are inspected and that the classifications are independent. Let the random variable x denote the number of parts that are correctly classified. Determine the probability mass function and cumulative mass function of x.
The probability mass function (PMF) for x is {0.0004, 0.0588, 0.3432, 0.941192}, and the cumulative mass function (CMF) for x is {0.0004, 0.0592, 0.4024, 1.0}.
The probability mass function (PMF) and cumulative mass function (CMF) for the random variable x, which denotes the number of parts correctly classified in an optical inspection system, can be determined.
Since the classifications of the parts are independent, we can use the binomial probability distribution to model this scenario. The PMF gives the probability of obtaining a specific value of x, and the CMF gives the probability of obtaining a value less than or equal to x.
The PMF of x is given by the binomial probability formula:
P(x) = (n C x) * p^x * (1 - p)^(n - x)
where n is the number of trials (number of parts inspected), x is the number of successes (number of parts correctly classified), and p is the probability of success (probability of correct classification of any part).
In this case, n = 3 (three parts inspected) and p = 0.98 (probability of correct classification).
Let's calculate the PMF for x:
P(x = 0) = (3 C 0) * (0.98^0) * (1 - 0.98)^(3 - 0) = 0.0004
P(x = 1) = (3 C 1) * (0.98^1) * (1 - 0.98)^(3 - 1) = 0.0588
P(x = 2) = (3 C 2) * (0.98^2) * (1 - 0.98)^(3 - 2) = 0.3432
P(x = 3) = (3 C 3) * (0.98^3) * (1 - 0.98)^(3 - 3) = 0.941192
The PMF for x is:
P(x = 0) = 0.0004
P(x = 1) = 0.0588
P(x = 2) = 0.3432
P(x = 3) = 0.941192
To calculate the CMF, we sum up the probabilities up to x:
F(x) = P(X ≤ x) = P(x = 0) + P(x = 1) + ... + P(x = x)
Using the calculated probabilities, the CMF for x is:
F(x = 0) = 0.0004
F(x = 1) = 0.0592
F(x = 2) = 0.4024
F(x = 3) = 1.0
Therefore, the probability mass function (PMF) for x is {0.0004, 0.0588, 0.3432, 0.941192}, and the cumulative mass function (CMF) for x is {0.0004, 0.0592, 0.4024, 1.0}.
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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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A rally car race course covers 515. 97 miles. The winning car completed the course in 6. 5 hours. What was the average speed of the winning car
The average speed gives us an indication of how fast the winning car was able to cover the race course on average. The average speed of the winning car in the rally car race was approximately 79.38 miles per hour.
To calculate the average speed of the winning car, we divide the total distance covered (515.97 miles) by the time taken to complete the course (6.5 hours).
Average speed = Total distance / Time taken
Average speed = 515.97 miles / 6.5 hours
Calculating the division, we find that the average speed is approximately 79.38 miles per hour.
The average speed gives us an indication of how fast the winning car was able to cover the race course on average. It is a measure of the car's performance and efficiency over the given time period.
In this case, the winning car had an average speed of 79.38 miles per hour, indicating a relatively fast and efficient performance throughout the race.
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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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Garfield decides to paint his 15 ft x 21 ft recreation room. His house has 9 ft ceilings. If a gallon of paint covers 400 sq ft, how many gallons of paint will be needed if he wants to put two coats of paint on the walls?
Garfield will need approximately 6.3 gallons of paint to put two coats on the walls of his 15 ft x 21 ft recreation room with 9 ft ceilings.
To determine the number of gallons of paint needed, we need to calculate the total area of the walls that will be painted and account for the two coats.
Step 1: Calculate the area of the walls:
The area of the walls can be calculated by finding the perimeter and multiplying it by the height.
Perimeter = 2 * (length + width)
Perimeter = 2 * (15 ft + 21 ft)
Perimeter = 2 * 36 ft
Perimeter = 72 ft
Area of the walls = Perimeter * height
Area of the walls = 72 ft * 9 ft
Area of the walls = 648 sq ft
Step 2: Account for two coats:
Since Garfield wants to put two coats of paint on the walls, we need to double the area calculated in the previous step.
Total area = 648 sq ft * 2
Total area = 1296 sq ft
Step 3: Calculate the number of gallons of paint:
Since a gallon of paint covers 400 sq ft, we divide the total area by the coverage of one gallon.
Number of gallons of paint = Total area / Coverage of one gallon
Number of gallons of paint = 1296 sq ft / 400 sq ft
Number of gallons of paint ≈ 6.3 gallons
Therefore, Garfield will need approximately 6.3 gallons of paint to put two coats on the walls of his recreation room.
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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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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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Noah needs to peel a lot of potatoes before a dinner party. He has already peeled some potatoes. If he keeps peeling at the same rate, will he finish all the potatoes in time?
If the remaining time is greater than or equal to N/P minutes, he will finish in time. Otherwise, he won't be able to finish before the dinner party.
To determine if Noah will finish peeling all the potatoes in time for the dinner party, we need to consider the amount of time he has left and his peeling rate.
Let's assume Noah has N potatoes left to peel and he can peel P potatoes per minute. If he keeps peeling at the same rate, the time required to peel all the remaining potatoes is given by N/P minutes.
If Noah has enough time before the dinner party, meaning the remaining time is greater than or equal to N/P minutes, he will be able to finish peeling all the potatoes.
However, if the remaining time is less than N/P minutes, it means there isn't enough time for Noah to finish peeling all the potatoes before the dinner party.
Therefore, to determine if Noah will finish peeling all the potatoes in time, compare the remaining time with N/P minutes. If the remaining time is greater than or equal to N/P minutes, he will finish in time. Otherwise, he won't be able to finish before the dinner party.
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Ray is purchasing a laptop that is on sale for 25% off. He knows the function that represents the sale price of his laptop is c(p) = 0. 75p, where p is the original price of the laptop. He also knows he has to pay 8% sales tax on the laptop. The price of the laptop with tax is f(c) = 1. 08c, where c is the sale price of the laptop. Determine the composite function that can be used to calculate the final price of Ray's laptop. C[f(c)] = 0. 81c c[f(c)] = 1. 83c f[c(p)] = 0. 81p f[c(p)] = 1. 83p.
The composite function that can be used to calculate the final price of Ray's laptop is f(c(p)) = 0.81p.
To determine the composite function that can be used to calculate the final price of Ray's laptop, we need to find the composition of the functions c(p) and f(c).
The function c(p) represents the sale price of the laptop, which is 25% off the original price. It can be expressed as c(p) = 0.75p.
The function f(c) represents the price of the laptop with 8% sales tax. It can be expressed as f(c) = 1.08c.
To find the composite function, we need to substitute c(p) into f(c). So, we have:
f(c(p)) = 1.08 * c(p)
Substituting c(p) = 0.75p:
f(c(p)) = 1.08 * 0.75p
Simplifying:
f(c(p)) = 0.81p
Therefore, the composite function that can be used to calculate the final price of Ray's laptop is f(c(p)) = 0.81p.
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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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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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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 beverage company sells juice in all the major restaurants. It costs the beverage company $0.75 to make each bottle of juice. The company uses a 35% markup. What is the selling price of the juice?
The selling price of juice that costs a beverage company $0.75 to make with a 35% markup is $1.01.
What is markup?
Markup is the difference between the cost of a product or service and its selling price.
The cost of a product is the amount spent on making or buying the product.
The selling price is the amount for which the product is sold.
Therefore, when a company wants to make a profit, it applies a markup to the cost of the product to determine the selling price.
The markup represents the amount of money a company adds to the cost of a product to make a profit.
Here's how to solve the problem:
A beverage company sells juice in all the major restaurants. It costs the beverage company $0.75 to make each bottle of juice. The company uses a 35% markup. What is the selling price of the juice?
Markup = 35% of the cost
Price = cost + markup
Step 1: Find the markup
Markup = 35% of 0.75
Markup = 0.35 x 0.75
Markup = 0.26
Step 2: Find the selling price
Price = cost + markup
Price = 0.75 + 0.26
Price = 1.01
The selling price of juice that costs a beverage company $0.75 to make with a 35% markup is 1.01.
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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.
Write an expression to represent the number of people called at 8:00 using a base and an exponent.
the expression to represent the number of people called at 8:00 using a base and an exponent is B = A x r^n.
In mathematics, the expression to represent the number of people called at 8:00 using a base and an exponent is:
B = A x r^n Where, B = the number of people called at 8:00A = the initial number of people calledr = the common ratio between each consecutive term n = the exponent or number of terms in the sequence.
If you have the first term A, the common ratio r, and the number of terms n, then the formula for the nth term, An is given by the formula:
A[n] = A x r^(n-1) If we know the first term, the common ratio, and the number of terms
, we can calculate the sum of the first n terms of a geometric sequence using the formula:
Sn = (A x (1 - r^n)) / (1 - r)
Thus, the expression to represent the number of people called at 8:00 using a base and an exponent is B = A x r^n.
This formula is based on the principles of geometric sequence, where B represents the total number of people called at 8:00, A is the initial number of people called, r is the common ratio between each consecutive term, and n is the exponent or number of terms in the sequence.
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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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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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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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