Caitlin ate 20 pieces of candy on Monday and 17 pieces on Tuesday. by what percent did she decrease her candy intake

Answer:

x = 7.98ft or x = 8ft

Step-by-step explanation:

Hope that helps :)

Answer:

y=4x+2

Step-by-step explanation:

Answer:

Step-by-step explanation:

X-intercept means y-coordinate of 0:

4x +7×0 = 28

 4x = 28

   x = 7         ← x-coordinate

Y-intercept means x-coordinate of 0:

4×0 +7y = 28

 7y = 28

   y = 4         ← y-coordinate

The expression that shows a difference of squares is option B, i.e., 16y² − x². We can represent it as (4y - x)(4y + x).Therefore, the correct option is B.

Difference of Squares is a squared quantity that can be represented as the difference of the squares of two variables or numbers. In simple terms, when two squares are subtracted, a difference of squares is produced. The squares of the two quantities, x and y, are subtracted from each other in the Difference of Squares.Here, the expression that shows a difference of squares is option B, i.e., 16y² − x². We can represent it as (4y - x)(4y + x).Therefore, the correct option is B. In this expression, we have the square of two quantities subtracted, which results in the Difference of Squares.Checking the other options, we can say that option A (10y² − 4x²) cannot be considered a difference of squares because there is no squared quantity subtracted from it. Similarly, option C (8x² − 40x + 25) and option D (64x² − 48x + 9) do not show the Difference of Squares as they do not have two squared quantities subtracted from each other.

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Step-by-step explanation:

[tex]91.8 \div 12 = 7.65 \\ 19.35 \div 3 = 6.45[/tex]

3 months

Assume all of the statistics used have a normal sampling distribution. Use 3 decimal places. Below are the steps of calculation:(a) For a 98% confidence interval for a population mean based on n = 11 observations with known: We know that margin of error formula = Zα/2 σ/√n, Where Zα/2 is the quantile of the normal distribution at α/2, σ is the population standard deviation and n is the sample size. In this case, α = 0.02, n = 11 and Zα/2 = 2.326. The sample size is small, and therefore we assume a normal distribution. Using the formula above, we obtain: margin of error = Zα/2 σ/√n = 2.326 σ/√11(b) For a 98% confidence interval for a population mean based on n = 11 observations with unknown. We know that margin of error formula = tα/2 s/√n. Where tα/2 is the quantile of the t-distribution at α/2, s is the sample standard deviation and n is the sample size. In this case, α = 0.02, n = 11 and tα/2 = 2.718. The sample size is small, and therefore we assume a normal distribution.

Using the formula above, we obtain: margin of error = tα/2 s/√n = 2.718 s/√11(c) For a 90% confidence interval for a population proportion, p, based on n = 11 observations. We know that margin of error formula = Zα/2 √((p(1-p))/n)Where Zα/2 is the quantile of the normal distribution at α/2, n is the sample size, and p is the sample proportion. In this case, α = 0.1, n = 11 and Zα/2 = 1.645.Using the formula above, we obtain: margin of error = Zα/2 √((p(1-p))/n) = 1.645 √((p(1-p))/11)(d) For a 92% confidence interval based on n = 14 observations for the slope parameter. We know that margin of error formula = tα/2 * SE. Where tα/2 is the quantile of the t-distribution at α/2, and SE is the standard error of the estimate. In this case, α = 0.08, n = 14 and tα/2 = 1.771.

Using the formula above, we obtain: margin of error = tα/2 * SE = 1.771 * SE. Therefore, the correct quantile for the margin of error of each confidence interval is as follows:(a) 2.670(b) 2.570(c) 0.512(d) 1.564.

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Answer:

Diameter= 10.2  -  Radius=5.1

Step-by-step explanation:

5.1 x 2= 10.2

10.2/2=5.1

Answer:

- 22719559.

Step-by-step explanation:

Answer:

m∠R = 123°

m∠S = 91°

Step-by-step explanation:

The measure of an inscribed angle is 1/2 the measure of the intercepted arc

m of arc QRS = 2 m∠P = 2(57) = 114

Now m of arc SPQ = 360 - 114 = 246

So, m∠R = 1/2(246) = 123

m of arc RSP = 2 m∠Q = 2(89) = 178

m of arc PQR = 360 - 178 = 182

m∠S = 1/2(182) = 91

Correct Question is:

A car company charges x dollars to rent a car plus extra options as shown in table.

Car seat = 50 $

Insurance = 75 $

Car Wash = 15 $

Three people each rented a car with insurance and one more person rented a car with a car wash. What is the expression for the total cost?

Step-by-step explanation:

3 people rented with insurance = (x + 75) * 3) = 3x +225

one person rented with car wash = (15+x)

Total car rental will be adding both equations = 3x +225 + 15 + x = 4x + 240

Answer:

75.935

Step-by-step explanation:

If V = Pe^rt and we are given P (the principle investment) =4630 ,

a rate of 5.7 % which as a decimal = 0.057 (% divided by 100 = decimal)

we can substitute this information in and get V=4630 e^(.057t).

then it says what will it be in 9 years? so we put 9 in for "t" and get

v = 4630 e^(0.057 * 9) simplify using a calculator and we will get our answer.

The assumption which is not true for multiple linear regression is that there will be a multi-collinearity effect. What is multiple linear regression? Multiple linear regression is a regression method where the response variable is dependent on more than one independent variable. Multiple linear regression is an extension of linear regression, where one response variable is dependent on one independent variable. It helps to determine the nature of the relationship between dependent variables and independent variables in the form of linear equations. It is used to find out the relationship between variables and make predictions based on that relationship. Assumptions of multiple linear regression1. Linearity, It is assumed that the relationship between the independent variables and dependent variables is linear. This implies that as the value of the independent variable changes, the change in the dependent variable is constant.2. Independence, There should be independence among the observations. This implies that there should not be any relationship between the residuals of the observations.3. Homoscedasticity implies that the variance of residuals should remain constant across all levels of the independent variable.4. Multicollinearity, It is the condition where the independent variables are highly correlated with each other. If there is perfect collinearity, it will not be possible to obtain the estimates of regression coefficients.5. Normality, The residuals should follow a normal distribution with mean zero and constant variance. The residuals should be normally distributed and centered on zero. The assumptions that are true for multiple linear regression are: The independent variables are not correlated. The residuals are normally distributed. The relationship between dependent and independent variables is linear. The assumption which is not true for multiple linear regression is that there will be a multi-collinearity effect. Hence, the correct option is D) There will be a multi-collinearity effect.

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Answer:

A

Step-by-step explanation:

Hello There!

This is the formula for volume of a cylinder

[tex]V=\pi r^2h[/tex]

where r = radius and h = height

we are given the height and diameter height - 10 ft diameter - 22 ft

we are not give the radius directly but we can easily convert the diameter to the radius by dividing by 2

22/2=11 so the radius is 11

now having found the radius and height we plug in the values into the formula (note: it says leave answer in terms of pi so we will not apply pi to the final answer.)

[tex]V=\pi 11^210\\11^2=121\\121*10=1210\\V=1210\pi[/tex]

so we can conclude that the answer is A

Answer:

1. 1/4

2. 43/10 or 4 3/10 either are correct.

3. 67/12 or 5 7/12 either are correct.

Step-by-step explanation:

I hope this helped.

Answer:

x = 6

y = 4

Step-by-step explanation:

5x - 7y = 2

x - 7y = -22 (Multiply by -1)

-x + 7y = 22

5x - 7y = 2

4x = 24

x = 6

x - 7y = -22

6 - 7y = -22

-7y = -28

y = 4

A:  The alternative hypothesis is that the population mean is not equal to the specified value

B: p-value for a two-tailed test with a t-value of 0.9945 is 0.3739.

C: 95% confidence that the true population mean falls within the range of 6.0172 to 11.6970

A. The null hypothesis is that the population mean is equal to a specified value (μ = specified value), and the alternative hypothesis is that the population mean is not equal to the specified value (μ ≠ specified value).

B. To perform the hypothesis test,

we first need to calculate the sample mean and standard deviation.

Since we have,

Sample size (n) = 7

Sample mean (X) = (13+9+10+5+10+7+9) / 7 = 8.8571

Sample standard deviation (s) = 2.1561

Using the formula for the one-sample t-test, we get,

⇒ t = (X- μ) / (s / √(n))

Assuming the specified value is 8, then we have,

⇒ t = (8.8571 - 8) / (2.1561 / √(7))

⇒ t = 0.9945

Using a t-distribution table with 6 degrees of freedom (df = n - 1),

we find that the p-value for a two-tailed test with a t-value of 0.9945 is 0.3739.

C. Based on this test, we cannot reject the null hypothesis that the true population mean is equal to 8 at a 5% level of significance since the p-value (0.3739) is greater than the significance level (0.05).

Therefore, we do not have enough evidence to conclude that the population mean is different from 8. In other words, we can state with 95% confidence that the true population mean falls within the range of 6.0172 to 11.6970.

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Answer:

24cm

Step-by-step explanation:

Assuming sides AC and BC are equivalent:

AC = 3cm + 9cm = 12cm

BC = AC = 12cm

AB = 3cm + 3cm = 6cm

AB + BC + AC = 12cm + 12cm + 6cm = 24cm

Answer:

30

Step-by-step explanation:

30

Answer:

5.5

Step-by-step explanation:

30-60-90 triangle rule is:

x - x[tex]\sqrt{3}[/tex] - 2x

11 = 2x

x = 5.5

Answer: 50

Step-by-step explanation:

because its rounded to its nearest 20ths'

The correct answer is option A which is y = 25x + 100.

Given the following:

To join a local square dancing group, Jan has to pay a $100 sign-up fee plus $25 per month

We need to write an equation for the cost (y) based on the number of months.

To solve the above problem, the answer is;a. y = 25x + 100

Explanation; Let's break down the problem

The $100 sign-up fee is a fixed cost that is added only once to the monthly fee which is $25. Thus the equation for the cost (y) based on the number of months can be expressed as; y = 25x + 100 where:y is the cost for the number of monthsx is the number of months

Therefore the correct answer is option A which is;y = 25x + 100.

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To join a local square dancing group,

Jan has to pay a $100 sign-up fee plus $25 per month.

The equation for the cost (y) based on the number of months is

y = 25x + 100,

where x is the number of months.

Option A is the correct equation for the cost based on the number of months.

Writing the equation:

y = 25x + 100

Where:

y = Cost based on the number of months

x = Number of months

Therefore, when Jan has been part of the local square dancing group for 1 month, the total cost will be:

$25 * 1 + $100 = $125

And if Jan has been a part of the group for 4 months, then the total cost would be:

$25 * 4 + $100 = $200

Therefore, option A is the correct answer.

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Multiply 6 by 1/2 to get 3

Ow you have :

3( h + 1) = 18

Distribute the 3:

3h + 3 = 18

Subtract 3 from both sides:

3h = 15

Divide both sides by 3:

H = 5

Main answer: fn(x) = xe converges uniformly to 0 on [0, ∞).

Supporting explanation: In order to prove that fn(x) = xe converges uniformly to 0 on [0, ∞), we need to use the definition of uniform convergence. Let ε > 0 be given. We need to find an N such that |fn(x) - 0| < ε for all n > N and x ∈ [0, ∞).So, we have|fn(x) - 0| = |xe| = xe < εfor all n > N and x ∈ [0, ∞).We can choose N = 1/ε, then we have|fn(x) - 0| = |xe| < εfor all n > N and x ∈ [0, ∞).This means that fn(x) = xe converges uniformly to 0 on [0, ∞). Hence, the proof is complete.

A series of fn(x) functions with n = 1, 2, 3, etc. For a set E of x values, is said to be uniformly convergent to f if, for each > 0, a positive integer N exists such that |fn(x) - f(x)| for n N and x E. An alternative definition for the uniform convergence of a series of functions is given below.

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Answer:

80%

Step-by-step explanation:

Percent increase is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

Increase = $27 - $15 = $12 , then

percent increase = [tex]\frac{12}{15}[/tex] × 100% = 0.8 × 100% = 80%

Step-by-step explanation:

Percentage Increase = Amount of Increase/ Orginal Amount x 100%

27-15= 12

$12= Amount of Increase

Percentage Increase= 12/15 x 100

                                  = 80% increase in stock price

Hope this Helps

Answer: `h² + 18h + 108`

We have to evaluate the difference quotient of the formula `f(x) when `f(6+ h)?

f(6)` and the expression will be simplified by dividing it by 'h.'

Difference quotient:

The difference quotient is a formula used to find the average rate of change of a function over a specific interval. The difference quotient is defined as:```f(x + h) - f(x) / h```

To find the difference quotient for f(x) = x³, we need to substitute the values as shown below:

f(x + h) = (6 + h)³f(x) = 6³f(x + h) - f(x) = (6 + h)³ - 6³

Now we can substitute these values in the formula of the difference quotient :

'f (6+ h). f(6)`h = (6 + h)³ - 6³ - h/ h

By simplifying the difference quotient we get;`

(6 + h)³ - 6³ - h/ h = (6³ + 3 * 6²h + 3 * 6h² + h³ - 6³) / h`

After simplifying the expression above, the terms 6³ and -6³ cancel out.

We can then combine the like terms (3 * 6²h and 3 * 6h²) and further simplify the expression as follows:`= (3 * 6²h + 3 * 6h² + h³) / h`= (108h + 18h² + h³) / h`= h² + 18h + 108

Answer: `h² + 18h + 108`

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Answer:

Y= 3/5-4

Step-by-step explanation:

What is slope-intercept form? Slope intercept form is an equation for graphing. It is y=mx+b. The "m" stands for the slope, or how much coordinates it takes to move to the next point. The "b" stands for the y-intercept, or where the line is perfectly on the y-line.

Step One: The first part of the equation is the slope, so let's figure that out. Since this one a graph, it is easy to tell the slope. The points are nicely marked, so we don't have to guess which points are visible. We are going up 3 jumps and then across 5 jumps. The slope is always "rise/run" where the "rise" is the y and "run" is x. So, the slope is 3/5x.

Step Two: For the last part, we need to know the y-intercept. It is clearly shown on the graph: -4. Because it is negative, we remove the plus sign because a plus with a negative is subtraction.

Step Three: We can combine both parts and that is the answer: y=3/5x-4.  

Answer:

4x plus 20y

Step-by-step explanation:

4 times x  plus 20xy

4x plus 20y

Each seat on the ferris wheel is at an angle of 24 degrees.

To determine the angle of each seat on a ferris wheel with 15 seats, we can use the concept of angles in a circle.

A circle has a total of 360 degrees. Since the ferris wheel has 15 seats evenly spaced around the circumference, we can divide 360 degrees by 15 to find the angle of each seat.

The calculation is as follows:

360 degrees ÷ 15 seats = 24 degrees per seat.

To visualize this, imagine drawing a circle and dividing it into 15 equal parts. Each part would represent a seat on the ferris wheel, and the angle between each part would be 24 degrees.

Note: The assumption here is that the seats are evenly spaced around the circumference of the ferris wheel. In practice, some ferris wheels may have seats arranged differently, so the angle per seat may vary.

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The correct answer is option c) infinitely many solutions..

To solve the system of equations using the substitution method, we'll substitute the value of y from the second equation into the first equation and solve for x.

Given:

-6x + 2y = 8 ---(1)

y = 3x + 4 ---(2)

Substitute equation (2) into equation (1):

-6x + 2(3x + 4) = 8

Simplify:

-6x + 6x + 8 = 8

8 = 8

We obtained a true statement (8 = 8), which means the two equations are equivalent. This solution shows that the system has infinitely many solutions.

Therefore, the correct answer is option c) infinitely many solutions..

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The 95% confidence interval to estimate the average beer consumption per cruise is from 79,440 bottles to 83,662 bottles.

The only assumption needed is that the population follows the Student's t-distribution; option B.

a. Construct a 95% confidence interval:

The formula for a confidence interval, CI, for the population mean (μ) is:

CI = sample mean ± (critical value * standard error)

Given:

Sample mean (x) = 81,551 bottles

Sample standard deviation (s) = 4,572 bottles

Sample size (n) = 15

Confidence level = 95%

With a confidence level of 95% and 15 degrees of freedom (n - 1), the critical value from the t-distribution is approximately 2.131.

Standard error (SE) = s / √n

SE = 4572 / √15

Lower limit of the confidence interval = x - (critical value * SE)

Upper limit of the confidence interval = x + (critical value * SE)

The confidence interval:

Lower limit = 81551 - (2.131 * (4572 / √15))

Upper limit = 81551 + (2.131 * (4572 / √15))

Lower limit ≈ 79440 bottles

Upper limit ≈ 83662 bottles

b. Assumptions about the population:

The only assumption needed is that the population follows the Student's t-distribution. This assumption is required when the population standard deviation is unknown, and we use the sample standard deviation as an estimate.

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