There is growing concern over a possible causal link between consumption of diet soda and obesity. In 2013, Gallup took a nationally representative sample of 2027 adults and asked them about their soda consumption. In the sample, 920 adults described themselves as overweight, and 300 of them said that they mostly drink diet soda. The remaining 1107 adults described themselves as about right weight, and 225 of them said that they mostly drink diet soda. We plan to test the following hypotheses: The pooled sample proportion of individuals who mostly drink diet soda is: a. 0.2491 b. 0.2033 c. 0.5000 d. 0.2590 e. 0.3261

Answer: 40 units

Step-by-step explanation: just did got it right.

Andres' job has an actual annual value of $43,400. This figure was obtained by summing his base salary, the company's health insurance contribution, and the company's retirement plan contribution.

To calculate the actual annual value of the job offer to Andres, we need to take into account his base salary, the company's contribution towards medical insurance, and the company's matching contribution to his retirement plan. Andres receives a base salary of $3,100 per month and gets paid semimonthly, which equates to an annual salary of $3,100 x 12 = $37,200.

The company pays half of Andres' $450 monthly medical insurance expense. So, that will be $450/2 = $225 per month, and over a year, that's $225 x 12 = $2,700.

Lastly, the company matches Andres' contribution to his retirement plan up to $3,500 annually.

To get the total value, add all these figures up: $37,200 (base salary) + $2,700 (health insurance contribution) + $3,500 (retirement contribution) = $43,400.

So, the actual annual value of Andres' job is $43,400.

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Answer:

A) (-2, 8), (4, 8)

B) See attachment.

C) 36 square units

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=x^2-2x\\g(x)=8\end{cases}[/tex]

To find the x-coordinates of the points where the two functions intersect, set the equations equal to each other and solve for x:

[tex]f(x)=g(x)\\\\x^2-2x=8\\\\x^2-2x-8=0\\\\x^2-4x+2x-8=0\\\\x(x-4)+2(x-4)=0\\\\(x+2)(x-4)=0\\\\\\x+2=0 \implies x=-2\\\\x-4=0 \implies x=4[/tex]

As points on the function g(x) have a y-coordinate of 8, the solutions to f(x) = g(x) are:

[tex]\Large\boxed{(-2,8)\;\textsf{and}\;(4,8)}[/tex]

[tex]\dotfill[/tex]

The function g(x) is a horizontal line parallel to the x-axis that intercepts the y-axis at (0, 8).

We are given that function f(x) is a concave up parabola with roots at (0, 0) and (2, 0). From Part A, we know that the parabola intersects g(x) at points (-2, 8) and (4, 8).

To help sketch the graph of function f(x), we can find its vertex and y-intercept.

The x-coordinate of the vertex of a quadratic function in the form y = ax² + bx + c is x = -b/2a. In this case, a = 1 and b = -2, so the x-coordinate of the vertex is:

[tex]x = -\dfrac{-2}{2(1)}=\dfrac{2}{2}=1[/tex]

To find the y-coordinate of the vertex, substitute x = 1 into f(x):

[tex]f(1)=(1)^2-2(1)=1-2=-1[/tex]

Therefore, the vertex of f(x) is at point (1, -1). The axis of symmetry of a parabola is the x-coordinate of the vertex, so in this case, the axis of symmetry is x = 1.

To find the y-intercept, substitute x = 0 into the function and solve for y:

[tex]f(0)=(0)^2-2(0)=0-0=0[/tex]

Therefore, the y-intercept of f(x) is the origin (0, 0).

[tex]\dotfill[/tex]

The area of the region R bounded by f(x) and g(x) on the interval [-2, 4] is given by the integral:

[tex]\displaystyle R = \int_{-2}^{4} \left[ g(x) - f(x) \right] \; dx[/tex]

Substitute g(x) = 8 and f(x) = x² - 2x:

[tex]\displaystyle R = \int_{-2}^{4} \left[8-(x^2-2x)\right] \; dx \\\\\\ R = \int_{-2}^{4} \left[8-x^2+2x\right] \; dx[/tex]

Evaluate the Integral

[tex]\displaystyle R = \left[8x-\dfrac{x^{2+1}}{2+1}+\dfrac{2x^{1+1}}{1+1}\right]^4_{-2} \\\\\\ R = \left[8x-\dfrac{x^{3}}{3}+x^2\right]^4_{-2} \\\\\\ R=\left(8(4)-\dfrac{(4)^{3}}{3}+(4)^2\right)-\left(8(-2)-\dfrac{(-2)^{3}}{3}+(-2)^2\right) \\\\\\ R=\left(32-\dfrac{64}{3}+16\right)-\left(-16+\dfrac{8}{3}+4\right) \\\\\\ R=\dfrac{80}{3}+\dfrac{28}{3} \\\\\\ R=\dfrac{108}{3}\\\\\\ R=36[/tex]

Therefore, the area of the region R bounded by f(x) and g(x) is:

[tex]\Large\boxed{\textsf{$36$ square units}}[/tex]

Answer:

The second option shows the correct translation of 3 units to the right and 1 unit down.

Answer:

5

Step-by-step explanation:

[tex]\sqrt{(2-(-2))^{2} + (6-(-3))^2}[/tex]

=[tex]\sqrt{4^{2} + 3^{2} } \\[/tex]

=[tex]\sqrt{25}[/tex]

=5

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

f(x) = (x + 2) (x − 5) (x − 6)

Step-by-step explanation:

f(x) = (x − (-2)) (x − 5) (x − 6)

f(x) = (x + 2) (x − 5) (x − 6)

Answer:

hjjjkkkkk(hmmmm jhhjjjjjjuu

Answer: x=15

Step-by-step explanation: use distributive property:

2x + 40=4x + 10

40=2x + 10

30= 2x

15=x

Answer:

The size of the sample should be at least 1037.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error of the interval is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

A level of confidence of 99% will be used and an error of no more than .04 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least

We need a sample size of at least n.

n is found when [tex]M = 0.04[/tex]

We don't know the proportion of the population, so we use [tex]\pi = 0.5[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.04 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.04\sqrt{n} = 2.575*0.5[/tex]

[tex]\sqrt{n} = \frac{2.575*0.5}{0.04}[/tex]

[tex](\sqrt{n})^{2} = (\frac{2.575*0.5}{0.04})^{2}[/tex]

[tex]n = 1036.03[/tex]

Rounding up

The size of the sample should be at least 1037.

Answer:

Step-by-step explanation:

a) you have that:

[tex]f'(x)=\frac{(x-2)(x+8)}{(x+1)(x-5)},\ \ x\neq -1,5[/tex]

The derivative of a function equals to zero allows you to find the critical points:

[tex]f'(x)=0\\\\(x-2)(x+8)=0\\\\x_1=2\\\\x_2=-8[/tex]

x=2,8 are the critical points

b) To know the behavior if f it is necessary to know where are f is indeterminated. The derivative give to you information about the slope of f. For x=-1,5 you have an infinite slope. Hence, for that values of x you have two indetermination s of f(x.)

However, if you see the atacched images you can obser that the original function (that is obtained with the intgegral) does not have available values for x<5 due to the logrithms. Hence, there are no critical points

The function only increases after x=5 from -infinity to +infinity

c) there are no local maximum neither local minimum

Answer:

4

Step-by-step explanation:

Garden area: 10 yd²

Each watermelon plant area: 2.5 yd²

No. of plants:

10/2.5 = 4

Answer:

Total length of the elastic band in this stretched position = 61.43 mm

Step-by-step explanation:

The complete Question with the image is attached to this solution

The second image shows the break down of the angle subtended by the elastic band over the crayons at the centre of the circle formed by the crayon's circular shape.

The elastic band extends over 3 of such length of an arc and covers a length of 2 × radius in the spaces between the contact with each crayon. This is also shown in the second attached image.

So, the length of the band will be a sum of 3 diameters and 3 of those arc lengths

Length of an arc is given by

L = (θ/360) × πD

θ = 120°

D = 10 mm

L = (1/3) × 10π = (10π/3) mm

But there are 3 of those, So, total length of the arcs = 3 × (10π/3) = (10π) mm

Length of those 3 diameter regions = 3×10 = 30 mm

Total length of the elastic band in this stretched position = 30 + 10π = 30 + 31.43 = 61.43 mm

Hope this Helps!!!

Answer:

672m

Step-by-step explanation:

L*W*H

8*6*14

672m

Answer:

15% of 8.95 is 1.3425

Step-by-step explanation:

Answer:

$1.34

Hope this helped :)

Answer:

size=13.80966

Step-by-step explanation:

Missing information:

size=13.80966

Since p-value of FP is less than 0.05 so it is significant to the model.

If all other things remain constant then a fire place add approximately $6476 to the selling price of the average house. So statement "A fireplace adds around $6476 to the selling price of the average house." is supported by the model.

It is impossible to definitively determine the correct statement without the actual regression output. While we can make educated guesses about the significance of the 'Fireplace' variable and its impact on the house's selling price, further information like t-values, p-values, and standard errors is required to make a detailed and accurate estimate.

With the information provided, it is impossible to definitively determine which of the four options are correct without the actual regression output. However, if it were provided and the p-value for the Fireplace's coefficient is higher than 0.05, we could say at α = .05, FP is not a significant predictor in a two-tailed test. If the regression coefficient for the Fireplace is $6,476 and it is significant, then a fireplace adds around $6476 to the selling price of the average house is correct. However, declaring that FP is a more significant predictor than Size or that a large house with no fireplace will sell for more than a small house with a fireplace, would require further information that goes beyond the coefficients themselves, including the standard errors, t-values, and p-values associated with each coefficient.

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Answer:

Zeros: x = 1 , − 2 , 2 End Behavior: Falls to the left and rises to the right.

Y-intercept: (0,4)

Step-by-step explanation:

mark me brainliest

Answer:

Option A  is correct.

Step-by-step explanation:  

The linear function that has the steepest slope is,

Explanation:

Slope intercept form: The general formula is,  where m is the slope and b is the y-intercept.

Option A:

According to slope intercept form:

Slope is -8

Similarly, for

Option B :

Slope is -2

Option C:

Slope is 7

Option D :

Slope is 6

Steepest slope defined as that is closest to being vertical.

This could be a line that is positive or negative slope respectively.

Therefore, the linear function that has the steepest slope is, option A

The steepest slope is in Option 4 with a slope of -4. Therefore, Option 4 has the steepest slope.

To determine which linear function has the steepest slope, we need to compare the slopes of the given options.

The slope of a linear function can be calculated using the formula:

[tex]\[ \text{Slope} = \frac{\text{change in } y}{\text{change in } x} \][/tex]

We will calculate the slopes for each option and compare them.

Option 1:

[tex]\[ \text{Slope} = \frac{-2 - 4}{1 - (-1)} = \frac{-6}{2} = -3 \][/tex]

Option 2:

[tex]\[ \text{Slope} = \frac{13 - 10}{6 - 3} = \frac{3}{3} = 1 \][/tex]

[tex]\[ \text{Slope} = \frac{16 - 10}{9 - 3} = \frac{6}{6} = 1 \][/tex]

[tex]\[ \text{Slope} = \frac{19 - 13}{12 - 9} = \frac{6}{3} = 2 \][/tex]

Option 3:

[tex]\[ \text{Slope} = \frac{-4 - 2}{-1 - 2} = \frac{-6}{-3} = 2 \][/tex]

Option 4:

[tex]\[ \text{Slope} = \frac{-12 - (-4)}{4 - 2} = \frac{-8}{2} = -4 \][/tex]

[tex]\[ \text{Slope} = \frac{-20 - (-12)}{6 - 4} = \frac{-8}{2} = -4 \][/tex]

[tex]\[ \text{Slope} = \frac{-28 - (-20)}{8 - 6} = \frac{-8}{2} = -4 \][/tex]

Comparing the slopes:

- Option 1: Slope = -3

- Option 2: Slopes = 1, 1, 2

- Option 3: Slope = 2

- Option 4: Slopes = -4, -4, -4

The steepest slope is the largest magnitude of slope, regardless of whether it's positive or negative. In this case, the steepest slope is in Option 4 with a slope of -4. Therefore, Option 4 has the steepest slope.

Answer:

The null and alternative hypothesis are:

[tex]H_0: \mu=110\\\\H_a:\mu\neq 110[/tex]

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the average room price in Atlanta is significantly different from $110 (P-value=0.317) .

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average room price in Atlanta is significantly different from $110.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=110\\\\H_a:\mu\neq 110[/tex]

The significance level is 0.05.

The sample has a size n=64.

The sample mean is M=112.

The standard deviation of the population is known and has a value of σ=16.

We can calculate the standard error as:

[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{16}{\sqrt{64}}=2[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{112-110}{2}=\dfrac{2}{2}=1[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as:

[tex]P-value=2\cdot P(z>1)=0.317[/tex]

As the P-value (0.317) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the average room price in Atlanta is significantly different from $110.

Answer:

[tex]t=\frac{15.5-18.7}{\frac{5.7}{\sqrt{11}}}=-1.862[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=11-1=10[/tex]  

The p value would be given by:

[tex]p_v =2*P(t_{(10)}<-1.862)=0.0922[/tex]  

We see that the p value is higher than the significance level so we don't have enough evidence to ocnclude that the true mean is different from 18.7 months in jail at 5% of significance.

Step-by-step explanation:

Information given

[tex]\bar X=15.5[/tex] represent the sample mean for the jail time

[tex]s=5.7[/tex] represent the sample standard deviation

[tex]n=11[/tex] sample size  

[tex]\mu_o =18.7[/tex] represent the value that we want to compare

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value for the test

System of hypothesis

We want to check the hypothesis if the true mean for the jail time is equal to 18.7 or no, the system of hypothesis are:

Null hypothesis:[tex]\mu = 18.7[/tex]  

Alternative hypothesis:[tex]\mu \neq 18.7[/tex]  

Since we don't know the population deviation the statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Rreplacing we got:

[tex]t=\frac{15.5-18.7}{\frac{5.7}{\sqrt{11}}}=-1.862[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=11-1=10[/tex]  

The p value would be given by:

[tex]p_v =2*P(t_{(10)}<-1.862)=0.0922[/tex]  

We see that the p value is higher than the significance level so we don't have enough evidence to ocnclude that the true mean is different from 18.7 months in jail at 5% of significance.

Answer:

Your answer would be Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A.

Explanation

B is a reflection of the x-axis.

But triangle C is not a reflection because if you fold the image with the y-axis line in the middle then you would see that triangle C doesnt match the placement of triangle A.

hope this helps

give brainliest if you please

Answer:

Without the picture of diagram, based on your description:

Triangle A is reflected across the x-axis to form triangle B.

Triangle A is rotated to form triangle C.

Option A: Triangle B is a reflection of triangle A across the x-axis.

It is correct because "Triangle A is reflected across the x-axis to form triangle B" => Triangle B is a reflection of triangle A across the x-axis

Option B: Triangle C is not a reflection of triangle A

It is correct because "Triangle A is rotated to form triangle C"

Option C: Triangle B is a reflection of triangle A across the y-axis

It is incorrect, because "Triangle A is reflected across the x-axis to form triangle B" => Triangle B is a reflection of triangle A across the x-axis, not y-axis.

Option D: Triangle C is a reflection of triangle A across the line y = x + 3

It is incorrect, because "Triangle A is rotated to form triangle C" => triangle C is a result of rotation, not reflection.

Hope this helps!

:)

Answer:

Step-by-step explanation:

You have to look up (google) the number of ml in a fluid ounce. It equals 29.57 ml approximately.

Next you must look up the number of mL in a teaspoon. The conversion factor turns out to be 4.93 mL = 1 teaspoon.

1 fluid ounce = 29.57 mL

20 fluid ounces = x mL

1/20 = 29.57 /x

x = 20*29.57

x = 591.4 mL

1 teaspoon = 4.93 mL

x teaspoons = 591.4

4.93 * x = 591.4

4.93 * x/4.93 = 591.4 / 4.93

x = 119.96

Answer:

-1/2

Step-by-step explanation:

Note the slope intercept form:

y = mx + b

y = (x , y)

m = slope

x = (x , y)

b = y-intercept.

In this case, the number that replaces the m (slope) is -1/2, which is your answer.

~

Answer:

m= -1/2

Step-by-step explanation:

This equation is in slope intercept form:

y=mx+b

where m is the slope and b is the y intercept

We have the equation:

y= -1/2x -3

If we compare the 2 equations:

y=-1/2x -3

y=mx+b

The slope must be -1/2, since x is being multiplied by -1/2

Answer:

Descriptive

Step-by-step explanation:

Descriptive statistics uses the data that helps to analyse, describe, and elaborate data accurately. It also provides information regarding the population through graphs or tables. Four types of descriptive statistics are measures of frequency, measures of central tendency, measures of dispersion, and measures of position.

The given example in question is descriptive statistics.

Answer:

bib

peep

ewe

kayak

racecar

level

noon

Answer:

6 cm

Step-by-step explanation:

3 is the radius

the radius is half of the diameter

to find the diameter from the radius you have to multiply it by 2

3×2

=6

Answer:

2100 Watt Hours

Step-by-step explanation:

600 Watt hours is consumed by the bulb every day.

3 Days and 12 Hours = 3 1/2 Days

To find how many Watt hours was consumed in 3 1/2 days we must multiply both of the numbers.

600 x 3 1/2 = 2100

Therefore, we can conclude that 2100 Watt Hours are consumed in 3 Days and 12 Hours.

Answer:-27/7

Step-by-step explanation:

f(x)=3/(x+2) -√(x-3)

f(19)=3/(19+2)-√(19-3)

f(19)=3/21 - √(16)

f(19)=1/7-4/1

f(19)=(1 x 1 - 7 x 4)/7

f(19)=(1-28)/7

f(19)=-27/7

To calculate f(19), we would substitute x with 19 in the function f(x) and simplify. However, the function provided is incomplete or incorrect, and therefore, a solution cannot be confidently provided.

To solve the problem f(19), we have to substitute the value of x with 19 into the provided function f(x). However, based on the question provided, the function seems to be incomplete or incorrectly stated.

If we had a correct form of the function f(x), the process would involve replacing any instance of x with 19 and simplifying the resulting expression according to the rules of arithmetic and algebra.

Example Process with Hypothetical Function

Let's assume the function is given correctly as f(x) = 3/(x+2) - √{x-3}. Then, we would calculate:

Step 1: Substitute x with 19: f(19) = 3/(19+2) - √{19-3}

Step 2: Simplify the expression: f(19) = 3/21 - √{16}

Step 3: Complete the calculations: f(19) = 1/7 - 4

Step 4: Find the common denominator and subtract: f(19) = -27/7

However, since we do not have the correct function, I am unable to confidently provide the solution to f(19).