The A.C. Nielsen Company collected data on the weekly TV viewing times, in hours, of 200 people. Suppose that the sample mean is 30.25, the sample standard deviation is 12.60, and that the histogram of the viewing times is bell shaped. Approximately what percent of the people in the study will have weekly TV viewing times between 17.65 and 42.85

Answers

Answer 1

Answer:

By the Empirical Rule, approximately 68% the people in the study will have weekly TV viewing times between 17.65 and 42.85

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell-shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 30.25

Standard deviation = 12.60

Approximately what percent of the people in the study will have weekly TV viewing times between 17.65 and 42.85

17.65 = 30.25 - 1*12.60

So 17.65 is one standard deviation below the mean.

42.85 = 30.25 + 1*12.60

So 42.85 is one standard deviation above the mean

By the Empirical Rule, approximately 68% the people in the study will have weekly TV viewing times between 17.65 and 42.85


Related Questions

What is the hinge Theorem in Geomatry

Answers

Answer:

In geometry, the hinge theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

Step-by-step explanation:

Answer:

In geometry, the  theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

Step-by-step explanation:

Easy 6th grade math ! Help please :)

Answers

Answer:

b 2.50 per 2 bottles of sprite

Step-by-step explanation:

Answer:

The answer is B.

2.50 per 2 bottles of sprite

Step-by-step explanation:

Every day, you take the elevator from the basement parking lot that is at level -2 . The elevator takes two seconds per level and you find that it takes 46 seconds to reach your floor.

Answers

Answer:

you live on the 21st floor

Step-by-step explanation:

46-4=42 (level -2 to ground level)

42÷2=21

A household goods manufacturer wants to increase the absorption capacity of a dish washing sponge. Based on past data, the average sponge could absorb 3.5 ounces. After the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge

Answers

Answer:

[tex]t=\frac{3.76-3.5}{\frac{0.241}{\sqrt{10}}}=3.407[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

And the p value using the alternative hypothesis is given by:

[tex]p_v =P(t_{(9)}>3.407)=0.0039[/tex]  

Since the p value is lower than the significance level provided of 0.10 we have enough evidence to reject the null hypothesis and we can conclude that the new design increased the absorption amount of the sponge

Step-by-step explanation:

Information provided

4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9

We can find the sample mean and deviation with the following formulas:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex] s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

[tex]\bar X=3.76[/tex] represent the sample mean

[tex]s=0.241[/tex] represent the sample standard deviation

[tex]n=10[/tex] sample size  

[tex]\mu_o =3.5[/tex] represent the value to check

[tex]\alpha=0.01[/tex] represent the significance level

t would represent the statistic

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

System of hypothesis

We want to test  if the new design increased the absorption amount of the sponge (3.5), the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 3.5[/tex]  

Alternative hypothesis:[tex]\mu > 3.5[/tex]  

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

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

Replacing the info given we got:

[tex]t=\frac{3.76-3.5}{\frac{0.241}{\sqrt{10}}}=3.407[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

And the p value using the alternative hypothesis is given by:

[tex]p_v =P(t_{(9)}>3.407)=0.0039[/tex]  

Since the p value is lower than the significance level provided of 0.10 we have enough evidence to reject the null hypothesis and we can conclude that the new design increased the absorption amount of the sponge

The is 2/3 of a pizza left. Wakami eats 1/4 of it. How much of the pizza did he eat?

Answers

Answer:

If you mean how much is left after he ate 1/4 from the 2/3 then 5/12 of the pizza is left.

Step-by-step explanation:

Final answer:

Wakami ate 1/6 of the entire pizza by consuming 1/4 of the 2/3 of the pizza that was left.

Explanation:

To find out how much of the pizza Wakami ate, we need to calculate 1/4 of the 2/3 of the pizza that was left. This requires multiplying the two fractions together:

2/3 of the pizza left times 1/4 that Wakami eats = 2/3 times 1/4

To multiply fractions, you simply multiply the numerators (top numbers) and then multiply the denominators (bottom numbers):

(2 times 1) / (3 times 4) = 2 / 12

Now we simplify the fraction by dividing both the numerator and the denominator by the greatest common divisor, which is 2:

2 / 12 = 1/6

So, Wakami ate 1/6 of the entire pizza.

How many 4 digit numbers can be formed if no two digits are the same?

Answers

i THINK its 4536... i may be wrong im sorry
4537 is the real answer with no digit repeating

In the study of population dynamics one of the most famous models for a growing but bounded population is the logistic equation dP dt = P(a − bP), where a and b are positive constants. Although we will come back to this equation and solve it by an alternative method in Section 3.2, solve the DE this first time using the fact that it is a Bernoulli equation.

Answers

Answer:

If  [tex]K[/tex] is a constant of integration, then

[tex]P = {\displaystyle \frac{1}{b/a + Ke^{-at}}}[/tex]

Step-by-step explanation:

According to the information of the problem we know that

[tex]{\displaystyle \frac{dP}{dt} = P(a-bP) }[/tex]

Remember that in general a Bernoulli equation is an equation of the type

[tex]y' + p(x)y = q(x)y^n[/tex]

And the idea to solve the equation is to substitute

[tex]{ \displaystyle v = y^{1-n}}[/tex]

Now for this case

[tex]{\displaystyle \frac{dP}{dt} - Pa = -bP^2}[/tex]

Then we substitute

[tex]v = P^{1-2} = P^{-1}[/tex]

Therefore

[tex]P = v^{-1}[/tex]

and if you compute the derivative of that you get that

[tex]{\displaystyle \frac{dP}{dt} = -v^{-2} \frac{dv}{dt}}[/tex]

Now you substitute that onto the original equation and get

[tex]{\displaystyle \frac{dP}{dt} - Pa = -bP^2}[/tex]

[tex]{\displaystyle -v^{-2} \frac{dv}{dt} - v^{-1} = -bv^{-2}[/tex]

If you multiply everything by  [tex]-v^2[/tex]  you get that

[tex]{\displaystyle \frac{dv}{dt} + v = b }[/tex]

That's a linear differential equation and the solution would be

[tex]v = {\displaystyle \frac{b}{a} + Ke^{-at}} = P^{-1}[/tex]

Where [tex]K[/tex] is a constant of integration, then

[tex]P = {\displaystyle \frac{1}{b/a + Ke^{-at}}}[/tex]

Final answer:

The given logistic equation is a Bernoulli equation, which can be solved using a substitution of variables method.

Explanation:

The given differential equation is a Bernoulli equation, which is a nonlinear first-order ordinary differential equation of the form dy/dx = P(x)y + Q(x)y^n, where n is a constant. To solve it, we can use a substitution of variables by setting y = u^(1-n). Applying this substitution to the logistic equation, we get du/dx = (1-n)a*u + (1-n)b*u^(2-n), which can be solved using separation of variables method.

Learn more about Logistic equation here:

https://brainly.com/question/33469987

#SPJ3

Time (hours) Number of Bricks
2 100
4 200
6 300
8 400

The time it takes a brick layer to lay bricks varies directly with the number of bricks. The brick layer's data is shown in the table. If x = time, and y = the number of bricks, which equation models the brick layer's direct variation?

Answers

Answer:

y=50x

Step-by-step explanation:

For every additional 2 hours (x), there are 100 bricks laid.

This means the slope is 50 (100/2)(200/4)etc.

50*2=100

50*4=200

50*6=300

50*8=400

Which statements about the ellipse are true? Check all that apply.


The center is located at (2, –1).

The major axis is 8 units long.

The minor axis is 3 units long.

The vertices are 4 units above and below the center.

The foci are units above and below the center.

The foci are located along a horizontal l

Answers

Answer:

The center is located at (2, –1).  

The major axis is 8 units long.

The vertices are 4 units above and below the centre.

The foci are √7 units above and below the centre.  

Step-by-step explanation:

Assume the ellipse looks like the one below.

The properties of a vertical ellipse are

[tex]\textbf{Vertical ellipse}\\\dfrac{ (x - h)^{2} }{b^{2}} + \dfrac{(y - k)^{2}}{a^{2}} = 1\begin{cases}\text{Centre} = (h,k)\\\text{Dist. between vertices} = 2a\\\text{Vertices} = (h, k\pm a)\\\text{Dist. between covertices} = 2b\\ \text{Covertices}= (h\pm b, k)\\c = \sqrt{a^{2} - b^{2}}\\\text{Dist. of foci from centre} = c\\\text{Foci} = (h, k\pm c)\\\end{cases}[/tex]

A. Centre

TRUE. The centre is at (2,-1).

B. Major axis

TRUE

Length of major axis = 3 - (-5) = 3 + 5 = 8

C. Minor axis

False

Length of minor axis = 5 - (-1) = 5 + 1 = 6

D. Vertices

TRUE

Distance between vertices = 8 = 2a

a - 8/2 = 4

Vertices at (h, k ± a) = (2, -1 ± 4)

E. Foci

TRUE

c² = a² - b² = 4² - 3² = 16 - 9 = 7

c = √7

The foci are √7 above and below the centre.

F. Foci

False.

The foci are on a vertical line.

 

A shipment to a warehouse consists of 500 PS4. The manager chooses a random sample of 50 PS4 and finds that 3 are defective. How many PS4 in the shipment are likely to be defective?

Answers

Answer:

30 PS4's

Step-by-step explanation:

The manager chose 50/500 PS4's to sample

3/50 were defective

To find how many were defective in all 500, we multiply the fraction by a number that makes the 50 (the sample), into a 500(the total).

That number is 10

Whatever multiplication you do to the bottom of a fraction, you do to the top

3*10 / 50*10

30 / 500 are likely to be defective

Answer:

30

Step-by-step explanation:

What do heating systems cooling systems and heat engines have in common

Answers

Answer:

is D

Step-by-step explanation:

for egny

Two-thirds of a number is equal to 20. What is the number?

Answers

Answer:

The number is 30

Step-by-step explanation:

Let x be the number

2/3 x = 20

Multiply each side by 3/2 to isolate x

3/2 *2/3x = 20*3/2

x = 30

f(x)=-3x+8, find f^-1(x) then state whether f^-1(x) is a function

Answers

Answer:

-3x + 8 = y

-3x = y - 8

3x = 8 - y

x = (8-y)/3

Now interchanging x and y:-

y = (8-x)/3

Here, y is inverse function i.e. f⁻¹(x)

Hence, f⁻¹(x) = (8-x)/3

Since f⁻¹(x) is a linear expression of x, therefore it is a function.

Step-by-step explanation:

Answer:

Look at the answer of the pic

A recent national survey found that high school students watched an average (mean) of 7.2 movies per month with a population standard deviation of 0.9. The distribution of number of movies watched per month follows the normal distribution. A random sample of 35 college students revealed that the mean number of movies watched last month was 6.2. At the 0.05 significance level, can we conclude that college students watch fewer movies a month than high school students?1. State the null hypothesis and the alternate hypothesis. A. H0: μ ≥ 7.2; H1: μ < 7.2B. H0: μ = 7.2; H1: μ ≠ 7.2C. H0: μ > 7.2; H1: μ = 7.2D. H0: μ ≤ 7.2; H1: μ > 7.22. State the decision rule.A. Reject H1 if z < –1.645B. Reject H0 if z > –1.645C. Reject H1 if z > –1.645D. Reject H0 if z < –1.6453. Compute the value of the test statistic.4. What is the p-value?

Answers

Answer:

1) A. H0: μ ≥ 7.2; H1: μ < 7.2

2) D. Reject H0 if z < –1.645

3) [tex]t=\frac{6.2-7.2}{\frac{0.9}{\sqrt{35}}}=-6.573[/tex]  

4) [tex]p_v =P(z<-6.573)=2,47x10^{-11}[/tex]  

Step-by-step explanation:

Information provided  

[tex]\bar X=6.2[/tex] represent the sample mean for the number of movies watched last month

[tex]\sigma=0.9[/tex] represent the population deviation

[tex]n=35[/tex] sample size selected

[tex]\mu_o =7.2[/tex] represent the value that we want to test    

[tex]\alpha[/tex] represent the significance level for the hypothesis test.    

t would represent the statistic

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

1) System of hypothesis

We want to check if college students watch fewer movies a month than high school students, and the best system of hypothesis are:

Null hypothesis:[tex]\mu \geq 7.2[/tex]      

Alternative hypothesis:[tex]\mu < 7.2[/tex]      

A. H0: μ ≥ 7.2; H1: μ < 7.2

2) Decision rule

For this case we are ocnduting a left tailed test so then we need to find a critical value in the normal standard distribution who accumulates 0.05 of the area in the left and we got:

[tex]z_{crit}= -1.645[/tex]

And the rejection zone would be:

D. Reject H0 if z < –1.645

3) Statistic

Since we know the population deviation the statistic is given by:

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

Replacing we got:

[tex]t=\frac{6.2-7.2}{\frac{0.9}{\sqrt{35}}}=-6.573[/tex]      

4) P value

We have a left tailed test then the p value would be:      

[tex]p_v =P(z<-6.573)=2,47x10^{-11}[/tex]  

Final answer:

The correct null and alternate hypotheses are H0: μ ≥ 7.2 and H1: μ < 7.2, respectively. Reject the null hypothesis if z < -1.645. The computed test statistic is approximately -7.378, suggesting a p-value near zero and thus, we can conclude that college students watch fewer movies on average.

Explanation:

In order to determine whether college students watch fewer movies a month than high school students, we should set up a hypothesis test comparing the college students' mean number of movies watched to the known population mean for high school students.

Step 1: State the null and alternate hypotheses.

The correct hypotheses would be A. H0: μ ≥ 7.2; H1: μ < 7.2 since we are testing if the college students watch fewer movies, which is a one-tailed test.

Step 2: State the decision rule.

The correct decision rule at the 0.05 significance level for a left-tailed test would be D. Reject H0 if z < – 1.645.

Step 3: Calculate the test statistic.

Using the formula for the z-test, z = (sample mean - population mean) / (population standard deviation / √ sample size), we calculate z = (6.2 - 7.2) / (0.9 / √35) ≈ – 7.378. Thus, the test statistic z is approximately -7.378.

Step 4: Find the p-value.

With a z-score as extreme as – 7.378, the p-value is near zero, implying strong evidence against the null hypothesis.

A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the 12311231 males​ surveyed, 190190 responded that they had at least one tattoo. Of the 10671067 females​ surveyed, 143143 responded that they had at least one tattoo. Construct a 9090​% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval. Let p 1p1 represent the proportion of males with tattoos and p 2p2 represent the proportion of females with tattoos. Find the 9090​% confidence interval for p 1 minus p 2p1−p2.

Answers

Answer:

[tex](0.154-0.134) - 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=-0.00402[/tex]  

[tex](0.154-0.134) + 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=0.044[/tex]  

We are confident at 95% that the difference between the two proportions is [tex]-0.00402 \leq p_1 -p_2 \leq 0.044[/tex]  

Since the confidence interval contains the value 0 we can conclude that at 10% of significance we don't have enough evidence to conclude that the true proportions for female and male with tattos differs

Step-by-step explanation:

Information given

[tex]p_1[/tex] represent the real population proportion of males with tattoos

[tex]\hat p_1 =\frac{190}{1231}=0.154[/tex] represent the estimated proportion of males with tattos

[tex]n_1=1231[/tex] is the sample size for males

[tex]p_2[/tex] represent the real population proportion of female with tatto

[tex]\hat p_2 =\frac{143}{1067}=0.134[/tex] represent the estimated proportion of females with tattos

[tex]n_2=1067[/tex] is the sample size of female

[tex]z[/tex] represent the critical value

Confidence intrval

The confidence interval for the difference of two proportions would be given by this formula  

[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]  

For the 90% confidence interval the value of [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2=0.05[/tex], and the critical value for this case would be:  

[tex]z_{\alpha/2}=1.64[/tex]  

Replacing the info given we got:

[tex](0.154-0.134) - 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=-0.00402[/tex]  

[tex](0.154-0.134) + 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=0.044[/tex]  

We are confident at 95% that the difference between the two proportions is [tex]-0.00402 \leq p_1 -p_2 \leq 0.044[/tex]  

Since the confidence interval contains the value 0 we can conclude that at 10% of significance we don't have enough evidence to conclude that the true proportions for female and male with tattos differs

A coral reef grows 0.16 meters ever week. How much does it grow in 7 weeks

Answers

Answer:

1.12 meters

Step-by-step explanation:

Answer:

1.12

Step-by-step explanation:

each week it grows 0.16 m

so,in 7 weeks it will grow 0.16*7m

A circle with radius 3 3start color #ff00af, 3, end color #ff00af has a sector with a central angle of 1 9 π 9 1 ​ πstart color #9d38bd, start fraction, 1, divided by, 9, end fraction, pi, end color #9d38bd radians . What is the area of the sector? Either enter an exact answer in terms of π πpi or use 3.14 3.143, point, 14 for π πpi and enter your answer as a decimal.


I will give as much points as possible

Answers

Answer:

  π/2 or 1.57 square units

Step-by-step explanation:

The area of a sector with central angle θ is given by the formula ...

  A = (1/2)r²θ

Filling in the given value, we find the area to be ...

  A = (1/2)(3²)(π/9) = π/2 . . . . square units

Using 3.14 for π, this is ...

  A = 3.14/2 = 1.57 . . . . square units

Listed below are student evaluation ratings of​ courses, where a rating of 5 is for​ "excellent." The ratings were obtained at one university in a state. Construct a confidence interval using a 99​% confidence level. What does the confidence interval tell about the population of all college students in the​ state?

3.6​, 3.1​, 4.0​, 4.9​, 3.0​, 4.3​, 3.6​, 4.6​, 4.6​, 4.0​, 4.4​, 3.6​, 3.3​, 4.2​, 3.7


What is the confidence interval for the population mean mu​?

_ < u < _

nothing ​(Round to two decimal places as​ needed.)

Answers

Answer:

[tex]3.93-2.977\frac{0.574}{\sqrt{15}}=3.49[/tex]    

[tex]3.93+2.977\frac{0.574}{\sqrt{15}}=4.37[/tex]

3.49 < u < 4.37

Step-by-step explanation:

Data provided

3.6​, 3.1​, 4.0​, 4.9​, 3.0​, 4.3​, 3.6​, 4.6​, 4.6​, 4.0​, 4.4​, 3.6​, 3.3​, 4.2​, 3.7

The sample mean and deviation can be calculated with the following formulas

[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex]

[tex]\bar X=3.93[/tex] represent the sample mean

[tex]\mu[/tex] population mean

s=0.574 represent the sample standard deviation

n=15 represent the sample size  

Confidence interval

The confidence interval for the true mean is given by:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom, given by:

[tex]df=n-1=15-1=114[/tex]

The Confidence is 0.99 or 99%, the significance is [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and the critical value would be[tex]t_{\alpha/2}=2.977[/tex]

Replacing we got:

[tex]3.93-2.977\frac{0.574}{\sqrt{15}}=3.49[/tex]    

[tex]3.93+2.977\frac{0.574}{\sqrt{15}}=4.37[/tex]

3.49 < u < 4.37

5 POINTS PLEASE HELP

Alan found the distance between point A(-8,-4) and point B(3,-4), his work is shown below.

-8 to the y-axis=8 units

3 to the y-axis = 3 units

(-8) - (3) = 5 units from A to B

What error did Alan make? What is the actual distnace from point A to point B?

Answers

Alan made an error in subtracting the x-coordinates without considering their signs. The correct method to find the distance between two points on the same horizontal line is taking the absolute value of the difference of the x-coordinates. Thus, the actual distance from point A to point B is 11 units.

Alan made an error in calculating the distance between point A(-8,-4) and point B(3,-4). The error is in the subtraction, as he should have taken the absolute value of the difference of the x-coordinates of points A and B because the y-coordinates are the same. To find the distance between two points on a coordinate plane, the correct formula when points lie on the same horizontal line (same y-coordinates) is the absolute difference of the x-coordinates. Therefore, the actual distance is calculated as follows:

|x2 - x1| = |3 - (-8)| = |3 + 8| = 11 units

So, the actual distance from point A to point B is 11 units.

MATHEMATICAL CONNECTIONS What value of x makes the quadrilateral a parallelogram?

3x + 10

***

Answers

Answer:

x = 5 (check the diagram included)

Step-by-step explanation:

The question is incomplete, I have included a diagram to aid the understanding of the question

Parallelograms are quadrilaterals which have their opposite sides parallel and equal. This also means that the opposite angles in a parallelogram are equal

From the attached figure, we have:

|FG| = 3x + 10, |HE| = 7x - 30

To calculate for the value of x that makes the quadrilateral a parallelogram, we have:

Remember the opposite sides of a parallelogram are equal

3x + 10 = 7x - 30

3x - 7x = 10 - 30

-4x = -20

x = 20 ÷ 4

x = 5

x = 5 makes the quadrilateral a parallelogram

Five friends are sharing 82 dollars they keep a record of what they do first they split up the ten bills

Answers

Answer:

82 divided by 5 = 16.4

Step-by-step explanation:

you divide 82 by 5 and get 16.4 or 82 divided by 10= 8.2

They do first they split up the ten bills and it is 8.0.

We have given that,

Five friends are sharing 82 dollars they keep a record

82 divided by 5

[tex]\frac{82}{5} = 16.4[/tex]

You divide 82 by 5 and get 16.4,

After the split up to ten bills is given by,

What is the split?

A split is a situation in a particular frame of a ten-pin bowling game where the player throws the ball and knocks the headpin

82 divided by 10

[tex]\frac{80}{10} =8.0[/tex]

They do first they split up the ten bills.

To learn more about the split visit:

https://brainly.com/question/1325044

#SPJ2

10×10 by the power of 2 equal​

Answers

Answer:

10,000

Step-by-step explanation:  

10 x 10 = 100 when you do the power of 2, you multiply that number by itself.

The area of a triangle is 1/2*(base)*(height) or base times height divided by two.

Answers

Answer:

both

Step-by-step explanation:

A punch recipe calls for twice as much lemonade as lime soda.
It calls for half as much ice cream as lime soda. If you use 2
gallons of line soda, how much lemonade will you need and
how much ice cream will you need? pls help!! :):):):):)

Answers

you will need

2 gallons lime soda

1 gallon icecream

and 4 gallons lemonade

Consider the following function. f(x) = (x + 5)2/3 (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) x = −5 (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing (−5,[infinity]) decreasing (−[infinity],−5) (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) relative maximum (x, y) = DNE relative minimum (x, y) = −[infinity],[infinity]

Answers

Answer:

See explaination

Step-by-step explanation:

Please kindly check attachment for detailed and step by step solution of the given problem.

a. The critical number of f is -5

b. The function is increasing on the interval (-5, infinity) and decreasing on the interval (-infinity, -5).

c.  There is no relative extremum at x = -5.

d. Since f(x) is increasing for x > -5 and decreasing for x < -5, there is no relative minimum or maximum in the interval (-infinity, infinity).

How to find the critical numbers

(a) To find the critical numbers of the function,  find where the derivative is 0 or undefined.

To find the derivative of f(x):

[tex]f'(x) = (2/3)(x + 5)^(-1/3)[/tex]

The derivative is undefined at x = -5, since[tex](x + 5)^(1/3)[/tex] would be 0 in the denominator.

So -5 is a critical number of f.

(b) To find the intervals on which the function is increasing or decreasing,  examine the sign of the derivative on each interval.

Since f'(x) is always positive (except at x = -5, where it is undefined),

The function is increasing on the interval (-5, infinity) and decreasing on the interval (-infinity, -5).

(c) To apply the First Derivative Test, look at the sign of the derivative near the critical point x = -5.

The derivative is undefined at x = -5, so the test is not applicable

Therefore, there is no relative extremum at x = -5.

Since f(x) is increasing for x > -5 and decreasing for x < -5, there is no relative minimum or maximum in the interval (-infinity, infinity).

Learn more on Function on https://brainly.com/question/11624077

#SPJ6

Determine what type of observational study is described. Explain. Vitamin D is important for the metabolism of calcium and exposure to sunshine is an important source of vitamin D. A researcher wanted to determine whether osteoperosis was associated with a lack of exposure to sunshine. He selected a sample of 250 women with osteoperosis and an equal number of women without osteoperosis. The two groups were similar in terms of​ age, diet,​ occupation, and exercise levels. Histories on exposure to sunshine over the previous twenty years were obtained for all women. The total number of hours that each woman had been exposed to sunshine in the previous twenty years was estimated. The amount of exposure to sunshine was compared for the two groups.

Answers

Answer: The type is Retrospective.

Step-by-step explanation: Observational Study is a type of research which measures determined characteristics of a population by studying individuals in a sample, without interfering or influencing the variables. There are 3 types of observational study:

Cross-sectional studies: colecting data at a certain point of time;Case-control studies: comparing individuals with a particular characteristics with others without it;Cohort studies: is the one where a group of individuals is selected to participate in the study;

According to the description given, the study above is a case-control study and the type is called Retrospective because it asks the individuals to tell about past habits, exposure to sunshine in this case. This type of study is not very reliable because it depends on the memory and the ability of the individuals to be honest and it can only prove association, not causation.

Final answer:

The type of observational study described in the question is a case-control study. The researcher selected women with and without osteoperosis, collected data on their exposure to sunshine, and compared the amount of exposure between the two groups.

Explanation:

The type of observational study described in the question is a case-control study. In a case-control study, the researcher selects subjects based on their disease status (in this case, women with or without osteoperosis) and compares their exposure to a risk factor (in this case, lack of exposure to sunshine). The researcher collected data on the exposure to sunshine over the previous twenty years for both groups and compared the amount of exposure between the two groups.

Learn more about Case-control study here:

https://brainly.com/question/33719932

#SPJ3

43. A beam rests against a wall, forming a 65º with the floor. Use the function y = 9 sec 8 to find the
length of the beam to the nearest tenth of a foot.

Answers

Answer:

 

[tex]Length\hspace{3}of\hspace{3}the\hspace{3}beam=y=21.3ft[/tex]

Step-by-step explanation:

Look the picture I attached you. As you can see the beam against the wall form a right triangle. The trigonometry functions on a right triangle are:

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\hspace{10}csc(\theta)=\frac{hypotenuse}{opposite}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\hspace{10}sec(\theta)=\frac{hypotenuse}{adjacent} \\\\tan(\theta)=\frac{opposite}{adjacent} \hspace{20}cot(\theta)=\frac{adjacent}{opposite}[/tex]

The problem give us the following data:

[tex]y=9sec(\theta)[/tex]

Using the previous information about the trigonometry functions on a right triangle and the data provided by the problem you can conclude:

[tex]y=Hypotenuse\\Adjacent=9\\\theta=65^{\circ}[/tex]

Therefore:

[tex]y=9sec(65^{\circ})=9*(2.366201583)=21.29581425\approx21.3ft[/tex]

The length of the beam for the given situation is 21.3 ft.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. Trigonometry is found all throughout geometry, as every straight-sided shape may be broken into as a collection of triangles.

Here, given function

y = 9. sec θ

put, θ = 65⁰

then, y = 9 X sec 65⁰

        y = 9 X 2.366

        y = 21.294 ft. ≈ 21.3 ft.

Thus, the length of the beam for the given situation is 21.3 ft.

Learn more about Trigonometry from:

https://brainly.com/question/13971311

#SPJ5

Kermit took out a 4 year loan for $5,500. He had to pay a total of $1,870 in interest payments. What rate did he pay for his loan?

Answers

Answer: 8.5%

Step-by-step explanation:

This is simple interest.

The formula fie finding simple interest is

I = principal × rate × time

-------------------------------

100

I = PRT/100

From the given values,

P = $5,500, T = 4years, R = ?, I = $1,870

Now we shall change the formula which is fundamental or in situ to suit the rate R.we now have

I = PRT

----

100

PRT = I × 100

R. = I × 100

---------

P × T

= 1,870 × 100

---------------

5,500 × 4

= 1,870 × 25

------------

5,500

= 187000/4

-----------

5500

= 46750/5500

= 8.5%

Therefore, the imtetest rate at which the loan was calculated is

8.5%.

Brandon poured what he estimated to be 32 ounces of oil into his car’s engine. From the markings on the container, he later determined that he had actually poured 36 ounces. What was the percent error in his estimate

Answers

Answer:

percentage error = 11.11 %

Step-by-step explanation:

Brandon poured w hat he estimated to be 32 ounces of oil into his car's engine . He later determined that he has actually poured 36 ounces from the marking on the container . The percentage error is computed below.

percentage error = approximate value - exact value/exact value × 100

approximate value = 32 ounces

exact value = 36 ounces

percentage error = |32 - 36| / | 36 | × 100

note we used the absolute value to eliminate negative signs

percentage error = 4/36 × 100

percentage error = 400/36

percentage error = 11.11 %

if £2000 is placed into a bank account that pays 3% compound interest per year how much will be in the account after 2 years

Answers

Principal Balance: 2000

Compound Interest: 3%

Type: Yearly

2000 x 1.03 = 2060

Year 1 : £2060

2060 x 1.03 = 2121.8

Year 2: £2121.8

There will be £2,121.80 in the account after 2 years.

Answer:okStep-by-step explanation:

Other Questions
What would happen if there was a sudden increase in the amount of greenhouse gases in Earth's atmosphere?Earth would suddenly cool down because more heat would leave the Earth system and go back to space.O Earth would suddenly cool down because solar radiation would not be able to flow through the atmosphere.O Earth would suddenly warm up because more heat from the atmosphere would be radiated toward Earth'ssurfaceO Earth would suddenly warm up because more heat from the Sun would be allowed to enter the atmosphere. A veterinarian surveys her clients and finds that 32 percent of the households have dogs, 25 percent have cats, and 11 percent have both dogs and cats. Let event C be choosing a client who has cats and let event D be choosing a client who has dogs. Which statements are true? Check all that apply. a 1/12b 36/1c 1/36d 1/6 What is mBC? A.70B.140C.28D.56What is mBCDA.168B.192C.220D.82 what is 1+234x9876-076+09x09.9876543212345678/8976543213456789.9876543 In Daniels fifth grade class, 37.5% of the 24 students walk to school. One-third of the walkers got a ride to school today from their parents. How many walkers got a ride to school from their parents today? A restaurant charged one customer $28.20 for 3 small dishes and 5 large dishes and charged another customer $23.30 for 4 small dishes and 3 large dishes. What will 2 small and 4 large dishes cost? //Add you starting comment block public class BubbleBubbleStarter //Replace the word Starter with your initials { public static void main (String[] args) { //Task 1: create an input double array list named mylist with some values pSystem.out.println("My list before sorting is: "); //Task 2: print the original list //Use println() to start and then replace with your printList() method after Task 4a is completed. p//Task 3: call the bubblesort method for mylist p//Task 4b: print the sorted list p} //Task 4a: create a method header named printlist to accept a formal parameter of a double array //create a method body to step through each array element println each element p//printList method header p//for loop p//println statement static void bubbleSort(double[] list) { boolean changed = true; do { changed = false; for (int j = 0; j < list.length - 1; j++) if (list[j] > list[j+1]) { //swap list[j] with list[j+1] double temp = list[j]; list[j] = list[j + 1]; list[j + 1] = temp; changed = true; } } while (changed); } } Why were posters of this kind produced during the war What was the battle where the Allies attacked Germany on the coast of France and pushed back the Germans Which field of study in the late nineteenth century was discussed in Robert Louis Stevenson's The Strange Case of Dr. Jekyll and Mr. Hyde? What is the mean for the data set?8 10 6 412 6 8 14 What were the Confederate soldiers trying to protect inManassas? If a dog is tied to a rope 15 feet long, how can it reach a bone30 feet away? The rope isn'tTE - TO - N - -HI-5.413.48.610.6 1.410 Read the lyrics from Natalie Merchant's song "Wonder." with love, with patience and with faith she'll make her way How might these words have inspired the author of the novel Wonder? They may have made the author decide that August's mother should have only two children, because raising a lot of children is hard work. They may have inspired the author to make August's character have to be homeschooled and his sister's character be able to go to a regular school. They may have made the author decide that August's character should be a boy to avoid any confusion between the novel and the song. They may have inspired the author to make August's character strong enough to face the challenges of a new school with the loving support of his family. Elliott Corp.'s transactions for the year ended December 31, 2020 included the following: Purchased real estate for $1,250,000 cash which was borrowed from a bank. Sold available-for-sale securities for $1,000,000. Paid dividends of $1,200,000. Issued 500 shares of common stock for $500,000. Purchased machinery and equipment for $250,000 cash. Paid $900,000 toward a bank loan. Reduced accounts receivable by $200,000. Increased accounts payable $400,000. Elliott's net cash used in investing activities for 2020 was a. $1,500,000 b. $ 500,000 c. $ 750,000 d. $ 250,000 What is the side length of a square with a perimeter of 52 meters According to economists, as a result of scarcity, people must __________. A.spend less money now so they have more in the futureB.realize that they can never have what they wantC.design ways to recycle more of what they ownD.make choices about how to use their resourcesPlease select the best answer from the choices providedABCD Computing Gross Profit The following data were taken from the accounts of Fluter Hardware, a small retail business. Sales $120,000 Sales returns and allowances 900 Sales discounts 650 Merchandise inventory, January 1 35,000 Purchases during the period 77,600 Purchases returns and allowances during the period 4,100 Purchases discounts taken during the period 2,300 Freight-in on merchandise purchased during the period 1,250 Merchandise inventory, December 31 32,000 Determine the gross profit. Please select the correct definition for the given word. glasnost Steam Workshop Downloader