James baked some cupcakes. If he gave 3 cupcakes to each cousin, he would have 25 cupcakes left. If he gave 15 cupcakes to each cousin, he would need to bake 71 more cupcakes. (a) How many cousins did he have? (b) How many cupcakes did he bake?​

The collection of the like terms of the equation 5x^2 - 4x + 9x^2 + 2x  can be expressed as 14x^2 - 2x .

The concept here is collecting the like terms, Algebraic expressions can be made simpler by combining like terms. Combining similar phrases is another name for it. In order to accomplish this, we locate similar terms in an algebraic equation and combine them by either adding or subtracting.

To collect like terms, add up the quantities of the same thing. The sales of various sizes of the same article of clothing, such as a jumper, will be added up by a buyer.

5x^2 - 4x + 9x^2 + 2x

=5x^2 + 9x^2 - 4x + 2x

=14x^2 - 2x

Therefore, option C is correct.

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The total hours you study on Friday and Saturday is ; 3 hours

It is easy to calculate the Mean of a data table and we do this by Adding up all the numbers, then divide by how many numbers there are.

From the table, we are given number of hours spent for 5 days as;

Sunday = 0.75 hours

Monday = 1.5 hours

Tuesday = 0 hours

Wednesday = 2.5 hours

Thursday = 1 hour

Thus, if average for the week of 7 days is 1.25 and total for Friday and Saturday is x, then we have;

(0.75 + 1.5 + 0 + 2.5 + 1 + x)/7 = 1.25

x + 5.75 = 8.75

x = 8.75 - 5.75

x = 3 hours

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a. 0.7787; b. 0.0228; c. 0.7453; d. 0.9793. The probabilities are found by looking up the Z-value in Table 1 and finding the corresponding probability.

a. To find the probability that Z is greater than 0.74, we look up 0.74 in Table 1 and find the corresponding probability. The probability that Z is greater than 0.74 is 0.7787, which is the area to the right of the Z-value in the table.

b. To find the probability that Z is less than or equal to −1.92, we look up −1.92 in Table 1 and find the corresponding probability. The probability that Z is less than or equal to −1.92 is 0.0228, which is the area to the left of the Z-value in the table.

c. To find the probability that Z is between 0 and 1.62, we look up 0 and 1.62 in Table 1 and find the corresponding probabilities. The probability that Z is between 0 and 1.62 is 0.7453, which is the area between the two Z-values in the table.

d. To find the probability that Z is between −0.90 and 2.94, we look up −0.90 and 2.94 in Table 1 and find the corresponding probabilities. The probability that Z is between −0.90 and 2.

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Answer:

The measure of an exterior angle of a regular polygon with n sides is given by the formula:

360°/n

For a regular polygon with 36 sides, the measure of each exterior angle is:

360°/36 = 10°

Therefore, the measure of an exterior angle of a regular polygon with 36 sides is 10°.

Step-by-step explanation:

The graph of the function f(x)=(x-3)(x-1)(x+1) is given by the image presented at the end of the answer.

The function for this problem is defined as follows:

f(x)=(x-3)(x-1)(x+1).

The product is written as a product of it's linear factors, hence the x-intercepts are given as follows:

The y-intercept of the function is given as follows:

f(0) = -3(-1)(1) = 3.

The end behavior is given as follows:

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Answer:

7

Step-by-step explanation:

To find the mean of a set of numbers, we add up all the numbers and divide the sum by the total number of numbers.

For the given sample, we have:

10 + 6 + 8 + 6 + 5 = 35

There are 5 numbers in the sample, so we divide the sum by 5:

35 / 5 = 7

Therefore, the mean of the sample is 7.

The IQ score of the adult is 110.05.

A normal distribution in statistics is defined as the type of continuous probability distribution where the data are arranged in a symmetrical bell shaped graph.

Given that,

Area to the right of a normally distributed graph is 0.2525.

From the standard table, z score for the area given is 0.67.

z = 0.67

We have the formula,

z = (x - μ) / σ

Given Mean, μ = 100 and standard deviation, σ = 15

0.67 = (x - 100) / 15

x - 100 = 10.05

x = 110.05

Hence the indicated IQ score is 110.05.

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Answer:

b

Step-by-step explanation:

time debends in how long it going to take the longer the race the longer the time

The male in the 92nd percentile in height would be 73.75 inches tall.

To find the z-score corresponding to the 92nd percentile, we need to find the value on the standard normal curve such that 92% of the area is to the left of that value.

Using the standard normal table, we can find the z-score closest to 0.92 which is 1.75.

Now that we have the z-score, we can use the following formula to find the height:

height = z-score * standard deviation + average height

So, using the given values of average height (70.5") and standard deviation (2.5"):

height = 1.75 * 2.5 + 70.5

height = 73.75"

Therefore, a male in the 92nd percentile in height would be 73.75 inches tall.

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Anthony and Giovani will both go to the library on the same day every 12th day.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

To find out when both Anthony and Giovani will go to the library on the same day, we need to find the smallest number that is divisible by both 4 and 6.

We can start by listing the multiples of 4 and 6 until we find a common multiple:

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, ...

We see that 12 is the smallest common multiple of 4 and 6.

Therefore, Anthony and Giovani will both go to the library on the same day every 12th day.

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If we run tests that can reveal non random patterns in the time ordered data , then the four patterns that might be seen are : Points outside limits , Trend , Cycles and Bias .

The four patterns that might be seen in run tests which can reveal non-random patterns in time-ordered data are:

(i) Points outside limits: This pattern indicates that the data points fall outside of the control limits and suggests that the process is not in statistical control.

(ii) Trend: This pattern indicates that the data points are moving consistently in a particular direction, either increasing or decreasing over time.

(iii) Cycles: This pattern indicates that the data points are oscillating around a central value over time, with a repeated pattern of highs and lows.

(iv) Bias: This pattern indicates that the data points are consistently above or below the centerline over time, indicating a systematic error or shift in the process.

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The difference between the starting volumes is 200 milliliters, the first bucket has the larger volume.

We know that the volumes can be modeled by linear equations, and remember that a general linear equation is:

y = a*x + b

Where a is the slope and b is the initial value.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

For the first bucket we have the points (1, 2900), (10, 2000), then the slope is:

a = (2000 - 2900)/(10 - 1) = -900/9 = -100

So we can write:

y = -100*x + b

To find the value of b, we can replace the value of one of the points in the equation. I will use the first point (1, 2900)

2900 = -100*1 + b

2900 + 100 = b

3000 = b

Now for the other bucket, we have the points (1, 2725) and (10, 2050), so the slope is:

a = (2725 - 2050)/(10 - 1) = -75

So this line is:

y = -75*x + b

Again, replacing the values of one of the points we will get:

2725 = -75*1 + b

2725 + 75 = b

2800 = b

Then the difference in the starting volumes is:

3000  - 2800 = 200

The first bucket has 200 milliliters more.

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Answer:

7.95%

An annuity due is an annuity whose payment is due immediately at the beginning of each period. A common example of an annuity due payment is rent, as landlords often require payment upon the start of a new month as opposed to collecting it after the renter has enjoyed the benefits of the apartment for an entire month.

Answer:

$313.57

Step-by-step explanation:

Compound interests and and compound numbers need:

This means the original amount is multiplied in the first example by 106%, and the product of that is multiplied by 106%, until its done 10 times for 10 years.

Bank À is best

Answer:

man female women man women male female measurement measurement master mysteries milkman milkmaid monk non Mr Mrs nephew nice papa

Answer:

Day 1: 6 inches

Day 2: 21 inches

Day 3: 9 inches

Step-by-step explanation:

First, we need to convert the total rainfall from feet to inches. Since 1 foot is equal to 12 inches, 3 feet is equal to 36 inches.

On the first day, 1/6 of the total rainfall falls, so:

(1/6) * 36 = 6 inches

On the second day, 7/12 of the total rainfall falls, so:

(7/12) * 36 = 21 inches

To find the rainfall on the third day, we can subtract the rainfall on the first and second days from the total rainfall:

36 - 6 - 21 = 9 inches

Therefore, the amount of rainfall on each day, in inches, is:

Day 1: 6 inches

Day 2: 21 inches

Day 3: 9 inches

Answer:

240

Step-by-step explanation:

60/ 4=15

15×5=75

b) 4+5=9

540/9=60

4×60=240

The graph of the linear equation is on the image at the end.

Here we have the following linear equation:

y = (7/3)*x + 5

To graph that line we need to find two points on the line, to get them, we need to evaluate the line in two different values of x.

if x = 0

y = (7/3)*0 + 5 = 5

if x = 3

y = (7/3)*3 + 5 = 12

Then we have the points (0, 5) and (3, 12)

Now just graph these points and connect them with a line.

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The scenerio that represents an example of mutualism would be an ant colony living on an acacia tree and not allowing vines to grow on the bark. That is option D.

Mutualism is defined as the feeding relationship where by the both organisms which are involved work together to benefit from each other.

A typical example of mutualism is the relationship that exists between the ant and the acacia tree.Here, the ant colony living on an acacia tree and not allowing vines to grow on the bark shows that both organisms benefits from each other.

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The probability of getting the same outcome on all five dice is (1/6) x (1/6) x (1/6) x (1/6) x (1/6) = 1/6^5, or approximately 0.00077.

The probability that every one of the five dice show a similar result is equivalent to the probability of obtain a particular result on one pass on, increased by the probability of come by similar result on every one of the leftover four dice.

The probability of obtain a particular result on one pass on is 1/6, since there are six potential results (1, 2, 3, 4, 5, or 6) and they are similarly probable.

In this manner, the probability of obtain similar result on each of the five dice is (1/6) x (1/6) x (1/6) x (1/6) x (1/6) = 1/6^5, or roughly 0.00077.

This is the probability of moving a Yahtzee in a solitary throw of five dice, it are similarly prone to expect all results.

The probability of moving a Yahtzee, which is the point at which each of the 5 dice show a similar number, is determined by duplicating the probability of come by a particular result on one bite the dust (1/6) without help from anyone else multiple times. This gives a probability of 1 in 6^5, or roughly 0.00077.

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The number of different arrangements is 36,000

This is equivalent to the total number of combinations, it is given by the product between the numbers of options.

The numbers of options are:

12 for the noses

20 for the eyes

5 for the lips

30 accessories.

Then the number of different arrangements is:

N = 12*20*5*30 = 36,000

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The statement about the data the points appear to be on a straight line

From the question, we have the following parameters that can be used in our computation:

Equation of a trend line: y = 0.0001x + 12

The above equation is a linear equation

This implies that the data points represented by  the equation would appear to be on a straight line

Note that: The points may or may not be on a perfect straight line depending on the correlation value

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The vertical asymptote of the function [tex]f(x) = \frac{x^2 + 6x + 9}{x^2 - 9}[/tex] is at x = 3.

Asymptote is a line or curve that serves as the boundary of another line or curve in mathematics.

Given, A function [tex]f(x) = \frac{x^2 + 6x + 9}{x^2 - 9}[/tex].

Factoring the numerator and the denominator we have,

[tex]f(x) = \frac{(x+3)(x+3)}{(x+3)(x-3)}[/tex]

Now, The holes of the function are at [tex]f(x) = \frac{(x+3)}{(x-3)}[/tex], x + 3 = 0, x = - 3.

And the asymptote of the function is at x - 3 = 0, x = 3.

Therefore, The asymptote will be a dotted vertical line at x = 3.

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The rock will be 9 meters from ground level at a time of:

x = 5.76 seconds.

The quadratic function that models a projectile's height is given as follows:

y = -4.9t² + v(0)t + h(0)

In which:

The parameters for this problem are given as follows:

v(0) = 22, h(0) = 45.

Hence the height function is given as follows:

y = -4.9t² + 22t + 45.

The rock is 9 meters from ground level when:

9 = -4.9t² + 22t + 45.

-4.9t² + 22t + 36 = 0

4.9t² - 22t - 36 = 0.

Hence the discriminant is given as follows:

D = 22² - 4(4.9)(-36)

D = 1189.6.

The positive root, representing the time for the height of 9 meters, is given as follows:

x = (22 + sqrt(1189.6))/9.8

x = 5.76 seconds.

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Answer:

According to the 2010 ADA standard, the number of wheelchair spaces required in a classroom depends on the total number of seats in the classroom. Specifically, 1 wheelchair space is required for the first 25 seats, and an additional wheelchair space is required for each 25 seats thereafter.

For the 5 classrooms on the 1st floor, there are a total of 5 x 20 = 100 seats. Therefore, we need 1 wheelchair space for the first 25 seats, and 1 additional wheelchair space for the next 25 seats. So in total, we need 2 wheelchair spaces for the 1st floor classrooms.

For the 8 classrooms on the 2nd floor, there are a total of 8 x 35 = 280 seats. Therefore, we need 1 wheelchair space for the first 25 seats in each classroom, and an additional wheelchair space for the next 25 seats. This means that each classroom needs 2 wheelchair spaces. So in total, we need 8 x 2 = 16 wheelchair spaces for the 2nd floor classrooms.

Therefore, the total number of wheelchair spaces needed in all 13 classrooms is 2 + 16 = 18.

However, it's important to note that the question asks for the "fewest total number" of wheelchair spaces needed. Since we can't have a fraction of a wheelchair space, we need to round up to the nearest whole number. Therefore, the answer is 18 rounded up to the nearest whole number, which is 19.

So the correct answer is not one of the options given. The closest option is K. 21, but that is too high.

The quantity 2a 2c corresponds to the rate of change of the surface area with respect to a. So, Correct option is C.

When considering a rectangular prism with dimensions a, b, and c, there are three different measures that we can associate with the dimensions: the length, width, and height. These measures are important in determining both the volume and the surface area of the prism.

In this problem, we are given a quantity 2a 2c and asked to determine which measure of the rectangular prism it corresponds to. We can do this by considering the formulas for the volume and surface area of the prism, and taking the partial derivatives with respect to each of the three dimensions.

The volume of a rectangular prism is given by:

V = abc

Taking the partial derivative of this expression with respect to a, we get:

[tex]\frac {\partial v} {\partial a}[/tex] = bc

This is not equal to 2a 2c, so we can eliminate the possibility of the quantity corresponding to the rate of change of the volume with respect to a.

Taking the partial derivative of the volume with respect to b and c gives:

[tex]\frac {\partial v} {\partial b}[/tex] = ac

[tex]\frac {\partial v} {\partial c}[/tex] = ab

Again, neither of these expressions is equal to 2a 2c, so we can eliminate the possibilities of the quantity corresponding to the rate of change of the volume with respect to b or c.

Next, we can consider the surface area of the prism, which is given by:

A = 2ab + 2ac + 2bc

Taking the partial derivative of this expression with respect to a, we get:

[tex]\frac {\partial v} {\partial a}[/tex] = 2b + 2c

Substituting 2a 2c for 2b + 2c, we get:

[tex]\frac {\partial A} {\partial a}[/tex] = 2a 2c

This is the same expression as the given quantity, so we can conclude that the quantity 2a 2c corresponds to the rate of change of the surface area with respect to a.

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Answer:

[tex]C. \ \sqrt{58}.[/tex]

Step-by-step explanation:

1) coordinates of the given points are: A[-3;2] and B[4;-1];

2) the required distance can be calculated using  the next formula:

[tex]d=\sqrt{(X_A-X_B)^2+(Y_A-Y_B)^2} ;[/tex]

3) according to the folmula above the required distance is:

[tex]d=\sqrt{(-3-4)^2+(2--1)^2} =\sqrt{49+9} =\sqrt{58} .[/tex]

Answer:

Veronica's attempt at ordering the hikes from least to greatest by the number of animals seen per kilometer is not correct.

To order the hikes by the number of animals seen per kilometer, we need to calculate the number of animals seen per kilometer for each hike. We can do this by dividing the number of animals seen by the length of the hike in kilometers.

Using this method, we can calculate the number of animals seen per kilometer for each hike as follows:

Rivers Edge: 8/3 = 2.67 animals/km

Wooded Marsh: 24/8 = 3 animals/km

Canyon Creek: 35/15 = 2.33 animals/km

Based on these calculations, the correct order of the hikes from least to greatest by the number of animals seen per kilometer is Rivers Edge, Canyon Creek, Wooded Marsh.

Veronica's mistake appears to be that she simply ordered the number of animals seen in each hike from least to greatest, rather than calculating the number of animals seen per kilometer.

(A) The mean value of x is 1.12.

(B) The probability that x exceeds its mean value is 0.22.

The first answer is:

(a) To calculate the mean value of x, we multiply each possible value of x by its corresponding probability and add up the products. Mathematically, we can write:

x = (0 * 0.55) + (1 * 0.16) + (2 * 0.07) + (3 * 0.06) + (4 * 0.16)

x = 0 + 0.16 + 0.14 + 0.18 + 0.64

x = 1.12

Therefore, the mean value of x is 1.12.

(b). P (x >? x) = P (x > 1.12)

To find this probability, we need to add up the probabilities of all values of x that are greater than 1.12. From the table, we can see that the probabilities for x = 3 and x = 4 are both greater than 1.12. Therefore, we can write:

P (x > 1.12) = P (x = 3) + P (x = 4)

P (x > 1.12) = 0.06 + 0.16

P (x > 1.12) = 0.22

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Answer:

please type your questions well

Answer:

B

Step-by-step explanation:

Answer:

B: Distribute it to all variables by multiplying their exponents

Step-by-step explanation: