what is the average rate of change for the function f(x)=x^2+4 for the domain of -2 to 4

Answer:

E) Because the interval contains 0, it is possible that there is no difference in mean carbonation levels.

Step-by-step explanation:

Hello!

The soda manufacturer claims that it's Cherry Fizz soda that has more carbonation than the competitor's Cherry Eclipse soda.

To test this claim they compared the carbonation by opening bottles of each soda, covered them with a balloon, and agitated the bottle to release the gas into the ballon. Later the balloon's diameter of each bottle of soda was measured.

Be the variables:

X₁: Diameter of a balloon filled with the gas of a Cherry Fizz soda bottle.

X₂: Diameter of a balloon filled with the gas of a Cherry Eclipse soda bottle.

X[bar]₁= 2.3 inches

X[bar]₂= 2.1 inches

The difference between the two means μ₁-μ₂ was estimated with a 90% CI, obtaining: [-0.8;1.2]inches

Usings 90% confidence level you can expect the interval [-0.8;1.2]inches to include the difference between the diameter of the balloons filled with the gas of the Cherry Fizz soda and the diameter of the balloons filled with the gas of the Cherry Eclipse soda.

The claims are:

A) Because 2.3 inches is larger than 2.1 inches, the manufacturer is correct, and Cherry Fizz has more carbonation.

INCORRECT, the given values are sample measures, you cannot reach any valid conclusions by simply comparing them.

B) Because the interval has more positive than negative values, Cherry Fizz has more carbonation.

INCORRECT, the confidence interval provides a range of values for the estimated parameter, it is equally probable that the parameter is closer to the lower bond, the upper bond, or in the middle of the interval.

C) Because 2.3 and 2.1 are very similar, there is no difference in the mean carbonation levels.

INCORRECT, same as in item A, you cannot reach any valid conclusion by just comparing the sample values, a propper hypothesis test is needed.

D) The interval cannot be interpreted because negative measurements are not possible.

INCORRECT, this interval vas made to estimate the difference between the two means, therefore if one value is less than the other it is possible to observe negative values.

If the CI was to estimate the value of the mean diameter of the balloons of one of the groups, then a negative measurement would be invalid.

E) Because the interval contains 0, there may be no difference in mean carbonation levels.

CORRECT

If you were to test the hypotheses

H₀: μ₁-μ₂=0

H₁: μ₁-μ₂≠0

Using a significance level, complementary to the confidence level used to construct the interval α: 0.1 you can decide whether or not the difference between population means are equal to zero or not.

If the interval contains the zero, then you do not reject the null hypotheses and there is no difference between the population means.

If the interval doesn't include the zero, then you reject the null hypothesis.

I hope this helps!

E) Because the interval contains 0, it is possible that there is no difference in mean carbonation levels.

The soda manufacturer claims that it's Cherry Fizz soda that has more carbonation than the competitor's Cherry Eclipse soda.

To test this claim they compared the carbonation by opening bottles of each soda, covered them with a balloon, and agitated the bottle to release the gas into the ballon. Later the balloon's diameter of each bottle of soda was measured.

Be the variables:

X₁: Diameter of a balloon filled with the gas of a Cherry Fizz soda bottle.

X₂: Diameter of a balloon filled with the gas of a Cherry Eclipse soda bottle.

X[bar]₁= 2.3 inches

X[bar]₂= 2.1 inches

The difference between the two means μ₁-μ₂ was estimated with a 90% CI, obtaining: [-0.8;1.2]inches

Usings 90% confidence level you can expect the interval [-0.8;1.2]inches to include the difference between the diameter of the balloons filled with the gas of the Cherry Fizz soda and the diameter of the balloons filled with the gas of the Cherry Eclipse soda.

The claims are:

A) Because 2.3 inches is larger than 2.1 inches, the manufacturer is correct, and Cherry Fizz has more carbonation.

B) Because the interval has more positive than negative values, Cherry Fizz has more carbonation.

C) Because 2.3 and 2.1 are very similar, there is no difference in the mean carbonation levels.

D) The interval cannot be interpreted because negative measurements are not possible.

If the CI was to estimate the value of the mean diameter of the balloons of one of the groups, then a negative measurement would be invalid.

E) Because the interval contains 0, there may be no difference in mean carbonation levels.

Using a significance level, complementary to the confidence level used to construct the interval α: 0.1 you can decide whether or not the difference between population means are equal to zero or not.

If the interval contains the zero, then you do not reject the null hypotheses and there is no difference between the population means.

If the interval doesn't include the zero, then you reject the null hypothesis.

Thus the interval contains 0, it is possible that there is no difference in mean carbonation levels.

To know more about null Hypothesis follow

https://brainly.com/question/15980493

Answer:

696.265 inches

Step-by-step explanation:

Radius = 27/2 = 13.5

2 semicircles + 2 lengths

(3.14 × 13.5²) + 2(62)

696.265 inches

Answer:

696

Step-by-step explanation:

Answer:

c= 5 yards.

Step-by-step explanation:

4*1.5=6

30/6= 5

Answer:

5/30

Step-by-step explanation:

5/30 = 1/6 =0.166666666...

The fraction equals a repeating decimal is 5/30.

A decimal numeral system is the standard system for denoting integer and non-integer numbers. The way of denoting numbers in the decimal system is often referred to as decimal notation.

Now the given fractions are,

30/50

13/25

5/30

13/10

Converting them into decimals we get,

30/50 = 0.6

13/25 = 0.52

5/30 = 0.1666..

13/10 = 1.3

Thus the repeating decimal is 0.1666..

So, the fraction with repeating decimal is 5/30 = 0.1666..

Thus, the fraction equals a repeating decimal is 5/30.

To learn more about fraction :

brainly.com/question/1301963

#SPJ2

Answer:

[tex]\dfrac{14}{29}[/tex]

Step-by-step explanation:

Let P(A) be the probability that goggle of type A is manufactured

P(B) be the probability that goggle of type B is manufactured

P(E) be the probability that a goggle is returned within 10 days of its purchase.

According to the question,

P(A) = 30%

P(B) = 70%

P(E/A) is the probability that a goggle is returned within 10 days of its purchase given that it was of type A.

P(E/B) is the probability that a goggle is returned within 10 days of its purchase given that it was of type B.

[tex]P(A \cap E)[/tex] will be the probability that a goggle is of type A and is returned within 10 days of its purchase.

[tex]P(B \cap E)[/tex] will be the probability that a goggle is of type B and is returned within 10 days of its purchase.

[tex]P(E \cap A) = P(A) \times P(E/A)[/tex]

[tex]P(E \cap A) = \dfrac{30}{100} \times \dfrac{5}{100}\\\Rightarrow P(E \cap A) = 1.5 \%[/tex]

[tex]P(E \cap B) = P(B) \times P(E/B)[/tex]

[tex]P(E \cap B) = \dfrac{70}{100} \times \dfrac{2}{100}\\\Rightarrow P(E \cap B) = 1.4 \%[/tex]

[tex]P(E) = 1.5 \% + 1.4 \% \\P(E) = 2.9\%[/tex]

If a goggle is returned within 10 days of its purchase, probability that it was of type B:

[tex]P(B/E) = \dfrac{P(E \cap B)}{P(E)}[/tex]

[tex]\Rightarrow \dfrac{1.4 \%}{2.9\%}\\\Rightarrow \dfrac{14}{29}[/tex]

So, the required probability is [tex]\dfrac{14}{29}.[/tex]

Answer:

3.508 kilograms

Step-by-step explanation:

This question can be solved using a rule of three.

We have that each kilogram is 1000 grams. How many kilograms are there for 3508 grams?

1kg - 1000g

xkg - 3508g

[tex]1000x = 3508[/tex]

[tex]x = \frac{3508}{1000}[/tex]

[tex]x = 3.508[/tex]

So the correct answer is:

3.508 kilograms

Answer:

35.800

Step-by-step explanation:

Answer:

It is x

Step-by-step explanation:

Answer:

The final percent would be (10/100) x (20/100) x (30/100) =  0.006 = 0.6%

Answer:3/500

Step-by-step explanation:

10% of 20% of 30%

10/100 of 20/100 of 30/100

1/10 x 1/5 x 3/10

(1x1x3)/(10x5x10)

3/500

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is

The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded.

Salesperson Before After

Sid Mahone $320 $340

Carol Quick 290 285

Tom Jackson 421 475

Andy Jones 510 510

Jean Sloan 210 210

Jack Walker 402 500

Peg Mancuso 625 631

Anita Loma 560 560

John Cuso 360 365

Carl Utz 431 431

A. S. Kushner 506 525

Fern Lawton 505 619

Solution:

Corresponding income of salespersons before and after form matched pairs.

The data for the test are the differences between the income is salespersons.

μd = the​ income before minus their income after.

Bedore after diff

320 340 -20

290 285 5

421 475 - 54

510 510 0

210 210 0

402 500 - 98

625 631 -6

569 560 0

360 365 - 5

431 431 0

506 525 - 19

505 619 - 114

Sample mean, xd

= (- 20 + 5 - 54 + 0 + 0 - 98 - 6 + 0 - 5 + 0 + - 19 - 114)/12 = - 25.92

xd = - 25.92

Standard deviation = √(summation(x - mean)²/n

n = 12

Summation(x - mean)² = (- 20 + 25.92)^2 + (5 - 25.92)^2 + (- 54 + 25.92)^2+ (0 + 25.92)^2 + (0 + 25.92)^2 + ( - 98 + 25.92)^2 + ( - 6 + 25.92)^2 + (0 + 25.92)^2 + (- 5 + 25.92)^2 + (0 + 25.92)^2 + (- 19 + 25.92)^2 + (- 114 + 25.92)^2 = 17784.5168

Standard deviation = √(17784.5168/12

sd = 38.5

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

1) The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 12 - 1 = 11

2) The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = ( - 25.92- 0)/(38.5/√12)

t = - 2.33

3) We would determine the probability value by using the t test calculator.

p = 0.02

4) Assume alpha = 0.05

Since alpha, 0.05 > than the p value, 0.02, then we would reject the null hypothesis. We can conclude that at 5% significance level, there is a significant increase in the typical salesperson’s weekly income due to the innovative incentive plan

Answer:

Step-by-step explanation:

If you meant " | ", as in |x|, that's "absolute value."  The domain of this function is "all real numbers," and the range is "all real numbers zero or greater."

Answer:

a) so the correct answer is that the probability that method A has been taught is 0.4737

b) the probability that B receives A is 0.5

Step-by-step explanation:

With the previous data we know that 3 methods teach an industrial skill and when putting into practice a worker does not learn, we have the failure rates like this:

method A fails 15%

method B fails: 5%

method C fails: 10%

usage percentages:

A: 30%

B: 40%

C: 30%

a) the probability that method A has been taught is as follows:

P (failure rate) = P (A) * P (failure rate A) + P (B) * P (failure rate B) + P (C) * P (failure rate C)

we replace the data obtaining:

P = 0.3 * 0.15 + 0.4 * 0.05 + 0.3 * 0.1 = 0.095

P ( failure rate A) = P (A) * P (failure rate A) / P (failure rate)

we replace the data obtaining:

 0.3 * 0.15 / 0.095 = 0.4737

so the correct answer is that the probability that method A has been taught is 0.4737

b) the probability that B receives A is as follows:

P (B | A) = P (B) = 0.50

Answer:

20x + 30y = 680

Step-by-step explanation:

Give me a good rating please!

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The equation represents the number of $20 and $30 gift cards bought.

20x + 30y = 680

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Number of gift cards for $20 = x

Number of gift cards for $30 = y

Total amount spend on gift card = $680

The equation represents the number of $20 and $30 gift cards bought.

20x + 30y = 680

Thus,

The equation represents the number of $20 and $30 gift cards bought.

20x + 30y = 680

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

Answer:1017.36 cm^3

Step-by-step explanation:

Diameter=18cm

Radius=r=18/2=9cm

Height=h=12cm

Volume of cone=1/3 x π x r^2 x h

Volume of cone=1/3 x 3.14 x 9^2 x 12

Volume of cone=1/3 3.14 x 9 x 9 x 12

Volume =(1x3.14x9x9x12) ➗ 3

Volume =3052.08 ➗ 3

Volume =1017.36

Volume of cone=1017.36 cm^3

Answer:

10 6

................

Answer:

~ 2 kilometers in length of the actual path ~

Step-by-step explanation:

Let us plan out our steps, and solve for each:

1. Given the information, let us create a proportionality as such:

        1       =           10,000      ⇒   x - centimeters in length of actual path

       20                    x

2. Now let us cross multiply, and solve through simple algebra for x:

10,000 * 20 = x,

x = 200,000 centimeters of the width of the item in reality

3. The answer demands in km, so let us convert 200,000 cm ⇒ km:

200,000/100,000 = 2 kilometers in length of the actual path

Answer:

The range in shelter A is 22, and the range in shelter B is 18.

Subtract 8 from 30 shelter A which gives you 22. Then subtract 10 from 28 which gives you 18 for Shelter B.

Answer:

The range in shelter A is 22, and the range in shelter B is 18.

Subtract 8 from 30 shelter A which gives you 22. Then subtract 10 from 28 which gives you 18 for Shelter B.

Step-by-step explanation:

Answer:12 months

Step-by-step explanation:

400+400=800 so  950-800=150 1800/150=12

Answer:

Step-by-step explanation:

y intercept is -3

x intercept is 4

Answer: x intercept = 4 and y intercept = -3

Step-by-step explanation:

In order to find the x intercept, set y=0 and solve the equation.

3x-4y-12=0

3x-4(0)-12=0

3x-12=0

add 12 to both sides

3x=12

divide both sides by 3

x = 4

The x intercept is 4.

To find the y intercept, set x = 0.

3x-4y-12=0

3(0)-4y-12=0

-4y-12=0

add 12 to both sides

-4y=12

divide both sides by -4

y = -3

The y intercept is -3.

Hope this helps! Have a great rest of your day :)

Answer:

Part A = 73.91%

Part B = 1/2 probability

Step-by-step explanation:

Part A - 90 + 20 + 80 + 40 = 230(total students)

90 + 80 = 170 students who like tv and reading

170/230 × 100 = 73.91%

Part B - 20(no read)/40(no tv) = 1/2 probability

Answer:

y=2x

Step-by-step explanation:

Every one x is two y.

Answer:

x = -2

y= -5

is the solution of the system of equations

Answer:

a) 5.37% probability that an individual distance is greater than 210.9 cm

b) 75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c) Because the underlying distribution is normal. We only have to verify the sample size if the underlying population is not normal.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 197.5, \sigma = 8.3[/tex]

a. Find the probability that an individual distance is greater than 210.9 cm

This is 1 subtracted by the pvalue of Z when X = 210.9. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{210.9 - 197.5}{8.3}[/tex]

[tex]Z = 1.61[/tex]

[tex]Z = 1.61[/tex] has a pvalue of 0.9463.

1 - 0.9463 = 0.0537

5.37% probability that an individual distance is greater than 210.9 cm.

b. Find the probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

Now [tex]n = 15, s = \frac{8.3}{\sqrt{15}} = 2.14[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 196. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{196 - 197.5}{2.14}[/tex]

[tex]Z = -0.7[/tex]

[tex]Z = -0.7[/tex] has a pvalue of 0.2420.

1 - 0.2420 = 0.7580

75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

The underlying distribution(overhead reach distances of adult females) is normal, which means that the sample size requirement(being at least 30) does not apply.

Answer:

[tex]0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570[/tex]

[tex]0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630[/tex]

The 95% confidence interval for the true proportion would be given by (0.570;0.630) .

And if we convert this into % we got (57.0%, 63.0%)

Step-by-step explanation:

The information given we have the following info given:

[tex] n = 1019[/tex] represent the sampel size

[tex] \hat p=0.6[/tex] represent the sample proportion of interest

The confidence level is 95%, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

The confidence interval for the mean is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

Replacing the info given we got:

[tex]0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570[/tex]

[tex]0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630[/tex]

The 95% confidence interval for the true proportion would be given by (0.570;0.630) .

And if we convert this into % we got (57.0%, 63.0%)

Answer:

y = -3

Step-by-step explanation:

y= 1/4x and x = -12

Substitute x=12 into the first equation

y = 1/4(-12)

y = -3

Answer:

-3

Step-by-step explanation:

1/4 x -12

As we solve we generate a succession of equivalent equations.

10t - 4t + 3t = 8

9t = 8

t = 8/9

Answer:

10t-4t+3t=8

t (10-4+3)=8

t (9)=8

9t=8

t=8/9

Step-by-step explanation:

In the question stated above, the common factor amongst the numbers with the variables is t, therefore we factorise the t out of the numbers, hence leaving t outside the bracket. After we solve the equation of the simple numbers of which the product is 9. After this we already know the 9 is to be multiplied by the t to make it 9t=8. We divide both side by the 9 and get a result of t=8/9

Answer: 346.4 in^3

Step-by-step explanation:

The pot can be thinked as a cylinder:

The volume of a cylinder is equal to:

V = (pi*r^2)*h

where h is the height, r is the radius and pi = 3.1416

Here we have that: r = 3.5in, h = 9in.

Then the volume is:

V = 3.1416*(3.5in)^2*9in = 346.4in^3

Answer:

60 ft^2

Step-by-step explanation:

6x10

get off of the bathrrom floor jean you sicko

Answer:

6 x 10 = 60 ft.^2

(A = b h)

Step-by-step explanation:

Why is he laying on his bathroom floor/tub/whatever-

Area is base times height. (length times width, if you will)

10 x 6

      =60

Answer:

(1, -1)

Step-by-step explanation:

To convert polar to rectangular coordinates, use these identities:

Here we were given the point [tex](\sqrt{2},-\frac{\pi}{4})[/tex] which is our (r, Ф) point

We can now plug these values into our x and y equations to convert to rectangular and find our (x, y) point

So our (x, y) point is (1, -1)