which expressions are equivalent to the one below? Check all that apply 10^x

The height of the shrubs is modeled by the function h(t) = 0.65t² + 2t + 17. After 7 years, the shrubs are 52.85 cm tall when they are sold.

The height (h) of a shrub after t years can be found by integrating the given growth rate function dh/dt = 1.3t + 2 with respect to time t. Given the initial height (or the initial condition), h(0) = 17 cm, the function turns out to be an integral taking initial condition into account:

h(t) = ∫ (1.3t + 2) dt + h(0)

After performing the integration, the function for height turns out to be:

[tex]h(t) = 0.65t^2 + 2t + 17[/tex]

Therefore, the height of the shrubs when they are sold (at t=7 years) can be found by substituting t=7 into the height function h(t).

[tex]h(7) = 0.65 * 7^2 + 2 * 7 + 17 = 52.85 cm[/tex]

So, the shrubs are 52.85 cm tall when they are sold.

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(a). The height of the shrub after t years is given by the function h(t) = (1.3/2)[tex]t^{2}[/tex] + 2t + 17.

(b). After 7 years, the shrubs reach a height of 62.85 cm.

Let's solve the given problem step-by-step:

(a)

The growth rate of the shrub is given by the differential equation dh/dt = 1.3t + 2. To find the height function h(t), we need to integrate this equation with respect to t.

1. We have:

dh/dt = 1.3t + 2

2. Integrating both sides with respect to t,

∫(dh) = ∫(1.3t + 2) dt

h(t) = (1.3/2)[tex]t^{2}[/tex]+ 2t + C

3. Where C is the constant of integration. To find C, we use the initial condition: h(0) = 17.

So:

17 = (1.3/2)[tex]0^{2}[/tex] + 2(0) + C

C = 17

4.Thus, the height function is:

h(t) = (1.3/2)[tex]t^{2}[/tex] + 2t + 17

(b)

To find the height after 7 years, we substitute t = 7 into the height function:

h(7) = (1.3/2)[tex]7^{2}[/tex] + 2(7) + 17

h(7) = (1.3/2)(49) + 14 + 17

h(7) = 31.85 + 14 + 17

h(7) = 62.85

Therefore, the shrubs are 62.85 cm tall when they are sold.

Final answer:

The point estimate for the population mean cholesterol level for adult males over the age of 55 years is 242.6 mg/dL, calculated by averaging the values from the given sample data.

Explanation:

The point estimate for the population mean is the average of the sample data. Here are the steps to calculate it:

So, the point estimate for the population mean cholesterol level for adult males over the age of 55 years is 242.6 mg/dL. This value is the best estimate for the mean cholesterol level based on the sample given.

Answer:

(x+1) (x^2+1)

Step-by-step explanation:

x^3+x^2+x+1

Factor by grouping

x^3+x^2           +x+1

Factor out x^2 from the first group  and 1 from the second group

x^2( x+1)  + 1( x+1)

Factor out (x+1)

(x+1) (x^2+1)

Answer:

a(1)=1

a(n)=a(n-1)+14

Step-by-step explanation:

The first term is 1, so a(1) = 1

Now, the second term, n=2 which means a(2)=a(1)+x

a(2)=1+x

also a(2)=15, then 1+x=15, and x=14

We can also check using a(3), a(4), and it fits.

The recursive formula of the arithmetic sequence is a(n) = a(n − 1) + 14.

There are two definitions for an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the same" or "each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term."

Given arithmetic sequence 1, 15, 29, 43, ....

the first term of the sequence is 1

a(1) = 1

and formula a(n) = a(n − 1) + x

the second term is 15

a(2) = 15 and n = 2

substitute in formula

a(n) = a(n − 1) + x

a(2) = a(2 - 1) + x

15 = a(1) + x

15 = 1 + x

x = 14

so formula is  a(n) = a(n − 1) + 14

check for n = 3

a(3) = a(3 - 1) + 14

a(3) = a(2) + 14

a(3) = 15 + 14 = 26

Hence the formula is  a(n) = a(n − 1) + 14

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Answer:

Step-by-step explanation:

Reduction to normal from using lambda-reduction:

The given lambda - calculus terms is, (λf. λx. f (f x)) (λy. Y * 3) 2

For the term, (λy. Y * 3) 2, we can substitute the value to the function.

Therefore, applying beta- reduction on "(λy. Y * 3) 2" will return 2*3= 6

So the term becomes,(λf. λx. f (f x)) 6

The first term, (λf. λx. f (f x)) takes a function and an argument, and substitute the argument in the function.

Here it is given that it is possible to substitute the resulting multiplication in the result.

Therefore by applying next level beta - reduction, the term becomes f(f(f(6)) (f x)) which is in normal form.

Answer:

In  2021 , the population of the country will be 1504 million

Step-by-step explanation:

We are given that

[tex]A=925.2e^{0.027t}[/tex]

Where A(in millions)

Time,t=After 2003

We have to find the population of the country will be 1504 million.

Substitute the values

[tex]1504=925.2e^{0.027t}[/tex]

[tex]e^{0.027t}=\frac{1504}{925.2}[/tex]

[tex]e^{0.027t}=1.626[/tex]

[tex]0.027t=ln(1.626)[/tex]

[tex]0.027t=0.486[/tex]

[tex]t=\frac{0.486}{0.027}[/tex]

[tex]t=18[/tex]

After 18 years means=2003+18=2021

In 2021 , the population of country will be 1504 million.

Answer:

a) 6,880

b) 4,059

c) Check Explanation

The number of expected votes for candidate A increases only in the first 3 weeks of mudslinging. The rate of weekly increase in those 3 weeks, is provided in the explanation. The number changes weekly for those 3 weeks with an average increase of 101 new votes per week.

Step-by-step explanation:

a. If the election were held today, how many people would vote?

b. How many of those would vote for candidate A?

c. How rapidly is the number of votes that candidate A will receive increasing at the moment?

There are 16,000 registered voters, 43% of whom are planning to vote, with 59% planning to vote for candidate A.

a) Number of registered voters planning to vote = 43% × 16000 = 6880

b) Number of registered voters that will vote and vote for candidate A

= 59% of registered voters planning to vote

= 59% × 6880 = 4059.2 ≈ 4059 people

c) Polls show that the percentage of people who plan to vote is increasing by 5 percentage points per week, and the percentage who will vote for candidate A is declining by 4 percentage points per week.

Since, the 'moment' isn't specified, we will check how much the number is increasing for the first 4 weeks after the mudslinging by candidate B began

Normally, 43% of registered voters want to vote, but now it is increasing at a rate of 5% per week. So, the percentage of registered voters that want to vote is now

43% + 5x% (where x = number of weeks after the mudslinging by candidate B started)

And the percentage of voting, registered voters that want to vote for candidate A is now (59% - 4x%)

After a week, percentage of registered voters that will vote = 48%

Number of registered voters that will vote = 48% × 16000 = 7680

percentage of voting, registered voters that want to vote for candidate A = 55%

Number of voting, registered voters that want to vote for candidate A = 55% × 7680 = 4224

Difference between the initial number of expected votes for candidate A between the beginning of the mudslinging and end of week 1

= 4224 - 4059 = 165

After week 2,

percentage of registered voters that will vote = 53%

Number of registered voters that will vote = 53% × 16000 = 8480

percentage of voting, registered voters that want to vote for candidate A = 51%

Number of voting, registered voters that want to vote for candidate A = 51% × 8480 = 4324.8 = 4325

Difference between the number of expected votes for candidate A between week 1 and week 2

= 4325 - 4224 = 101

After week 3,

percentage of registered voters that will vote = 58%

Number of registered voters that will vote = 58% × 16000 = 9280

percentage of voting, registered voters that want to vote for candidate A = 47%

Number of voting, registered voters that want to vote for candidate A = 47% × 9280 = 4361.6 = 4362

Difference between the number of expected votes for candidate A between week 2 and week 3

= 4362 - 4325 = 37

After week 4,

percentage of registered voters that will vote = 63%

Number of registered voters that will vote = 63% × 16000 = 10,080

percentage of voting, registered voters that want to vote for candidate A = 43%

Number of voting, registered voters that want to vote for candidate A = 43% × 10080 = 4334

Difference between the number of expected votes for candidate A between week 3 and week 4

= 4334 - 4362 = -28

The number of expected votes for candidate A begins to decline after the 4th week of mudslinging.

So, the required 'moment' should be within the first 3 weeks of mudslinging. And the rate of increase weekly is provided above with an average increase of 101 new voters per week.

Hope this Helps!!!

At the current moment, the number of votes that candidate A will receive is increasing at a rate of approximately 197 votes per week.

To determine how rapidly the number of votes that candidate A will receive is changing at this moment, we need to take into account the rate at which both the number of voters planning to vote and the percentage of voters supporting candidate A are changing.

Initial Conditions:

Weekly Changes:

Calculations:

⇒ 16,000 × 0.43 = 6,880

⇒ 6,880 × 0.59 = 4,059.2 (approximately 4059)

⇒ 16,000 × 0.05 = 800 voters/week

⇒ (800 × 0.59) + (16,000 × 0.43 × -0.04) = 472 - (6,880 × 0.04)

⇒ 472 - 275.2 = 196.8 voters/week

Thus, the number of votes that candidate A will receive is initially increasing at a rate of approximately 197 votes per week.

Answer:

Probability (Both fail)  = 0.001369

Probability (None fails) =0.927369

Probability (at least one fails)   = 0.072631

Step-by-step explanation:

given data

Probability (fail) P = 0.037

two alternators is  independent

solution

we get here first  probability that both will fail will be

Probability (Both fail) = 0.045²    ................1

Probability (Both fail)  = 0.001369

and

now we get probability that neither will fail

Probability (None fails) = (1-0.037)²              ...............2

Probability (None fails) =0.927369

and

now we get probability that at least one fails

Probability (at least one fails)  = 1 - Probability (non fails)     .................3

Probability (at least one fails)   = 1 - 0.927369

Probability (at least one fails)   = 0.072631

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 35

For the alternative hypothesis,

µ > 35

It is a right tailed test

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 16,

Degrees of freedom, df = n - 1 = 16 - 1 = 15

t = (x - µ)/(s/√n)

Where

x = sample mean = 42.7

µ = population mean = 32

s = samples standard deviation = 6

t = (42.7 - 32)/(6/√16) = 7.13

We would determine the p value using the t test calculator. It becomes

p = 0.00001

Since alpha, 0.01 > than the p value, 0.00001, then we would reject the null hypothesis. Therefore, At a 1% level of significance, there is sufficient data to conclude that children with a history of child care show significantly more behavioral problems than the average kindergarten child

b) Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

the information given, the from population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution,

Since confidence level = 90% = 0.95, α = 1 - CL = 1 – 0.90 = 0.1

α/2 = 0.1/2 = 0.05

the area to the left of z0.05 is 0.05 and the area to the right of z0.05 is 1 - 0.05 = 0.95

Looking at the t distribution table for t.95 and df = 15

z = 1.753

Margin of error = 1.753 × 6/√16

= 2.63

Confidence interval = 35 ± 2.63

Angle C in triangle ABC, where the angles form an arithmetic sequence with angle A at 23 degrees, is 97 degrees.

If the angles in triangle ABC form an arithmetic sequence and angle A = 23 degrees, then we can denote the angles of the triangle as A, A+d, A+2d, where d is the common difference between the terms of the arithmetic sequence. Since we know that the sum of angles in a triangle is 180 degrees, we can set up the equation:

23 + (23 + d) + (23 + 2d) = 180

Combining like terms, we get:

69 + 3d = 180

Subtracting 69 from both sides, we find:

3d = 111

Dividing by 3 gives us the common difference d:

d = 37 degrees

Therefore, angle C, being the third term in our arithmetic sequence, is:

angle C = A + 2d = 23 + (2 * 37) = 23 + 74 = 97 degrees

Answer:

Step-by-step explanation: All of the answers are correct for a square.

Opposite sides are congruent, all angles are congruent, opposite angles are congruent, diagonals congruent, and diagonals bisect are the correct answers for a rectangle.

Opposite sides are congruent, opposite angles are congruent, and diagonals bisect are the correct answers for a parallelogram.

All sides congruent, Opposite sides congruent, All angles congruent, Opposite angles congruent, Diagonals congruent and Diagonals bisect are the properties of square.

A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles

A square is a special type of quadrilateral that has the following properties:

All sides are congruent.

Opposite sides are parallel and congruent.

All angles are congruent and equal to 90 degrees.

Opposite angles are congruent.

Diagonals are congruent and bisect each other at right angles.

Hence, All sides congruent, Opposite sides congruent, All angles congruent, Opposite angles congruent, Diagonals congruent and Diagonals bisect are the properties of square.

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Answer:

50.265

Step-by-step explanation:

Sorry if its wrong

Answer:

I believe it's 188

Step-by-step explanation:

If there was a total of 564 and the cheeseburgers was three times the amount, you need to divide 564 by 3. 564 divided by 3 equals to 188. I am pretty sure this could be the correct answer!

Answer:

a) 0.4332 = 43.32% of the calls last between 3.6 and 4.2 minutes

b) 0.0668 = 6.68% of the calls last more than 4.2 minutes

c) 0.0666 = 6.66% of the calls last between 4.2 and 5 minutes

d) 0.9330 = 93.30% of the calls last between 3 and 5 minutes

e) They last at least 4.3 minutes

Step-by-step explanation:

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.

In this problem, we have that:

[tex]\mu = 3.6, \sigma = 0.4[/tex]

(a) What fraction of the calls last between 3.6 and 4.2 minutes?

This is the pvalue of Z when X = 4.2 subtracted by the pvalue of Z when X = 3.6.

X = 4.2

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

[tex]Z = \frac{4.2 - 3.6}{0.4}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a pvalue of 0.9332

X = 3.6

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

[tex]Z = \frac{3.6 - 3.6}{0.4}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a pvalue of 0.5

0.9332 - 0.5 = 0.4332

0.4332 = 43.32% of the calls last between 3.6 and 4.2 minutes

(b) What fraction of the calls last more than 4.2 minutes?

This is 1 subtracted by the pvalue of Z when X = 4.2. So

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

[tex]Z = \frac{4.2 - 3.6}{0.4}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a pvalue of 0.9332

1 - 0.9332 = 0.0668

0.0668 = 6.68% of the calls last more than 4.2 minutes

(c) What fraction of the calls last between 4.2 and 5 minutes?

This is the pvalue of Z when X = 5 subtracted by the pvalue of Z when X = 4.2. So

X = 5

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

[tex]Z = \frac{5 - 3.6}{0.4}[/tex]

[tex]Z = 3.5[/tex]

[tex]Z = 3.5[/tex] has a pvalue of 0.9998

X = 4.2

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

[tex]Z = \frac{4.2 - 3.6}{0.4}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a pvalue of 0.9332

0.9998 - 0.9332 = 0.0666

0.0666 = 6.66% of the calls last between 4.2 and 5 minutes

(d) What fraction of the calls last between 3 and 5 minutes?

This is the pvalue of Z when X = 5 subtracted by the pvalue of Z when X = 3.

X = 5

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

[tex]Z = \frac{5 - 3.6}{0.4}[/tex]

[tex]Z = 3.5[/tex]

[tex]Z = 3.5[/tex] has a pvalue of 0.9998

X = 3

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

[tex]Z = \frac{3 - 3.6}{0.4}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

0.9998 - 0.0668 = 0.9330

0.9330 = 93.30% of the calls last between 3 and 5 minutes

(e) As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 4% of the calls. What is this time?

At least X minutes

X is the 100-4 = 96th percentile, which is found when Z has a pvalue of 0.96. So X when Z = 1.75.

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

[tex]1.75 = \frac{X - 3.6}{0.4}[/tex]

[tex]X - 3.6 = 0.4*1.75[/tex]

[tex]X = 4.3[/tex]

They last at least 4.3 minutes

Answer:

[tex] P(\hat p>0.14)[/tex]

And using the z score given by:

[tex] z = \frac{\hat p -\mu_p}{\sigma_p}[/tex]

Where:

[tex]\mu_{\hat p} = 0.12[/tex]

[tex]\sigma_{\hat p}= \sqrt{\frac{0.12*(1-0.12)}{474}}= 0.0149[/tex]

If we find the z score for [tex]\hat p =0.14[/tex] we got:

[tex]z = \frac{0.14-0.12}{0.0149}= 1.340[/tex]

So we want to find this probability:

[tex] P(z>1.340)[/tex]

And using the complement rule and the normal standard distribution and excel we got:

[tex] P(Z>1.340) = 1-P(Z<1.340) = 1-0.9099= 0.0901[/tex]

Step-by-step explanation:

For this case we have the proportion of interest given [tex] p =0.12[/tex]. And we have a sample size selected n = 474

The distribution of [tex]\hat p[/tex] is given by:

[tex] \hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}}) [/tex]

We want to find this probability:

[tex] P(\hat p>0.14)[/tex]

And using the z score given by:

[tex] z = \frac{\hat p -\mu_p}{\sigma_p}[/tex]

Where:

[tex]\mu_{\hat p} = 0.12[/tex]

[tex]\sigma_{\hat p}= \sqrt{\frac{0.12*(1-0.12)}{474}}= 0.0149[/tex]

If we find the z score for [tex]\hat p =0.14[/tex] we got:

[tex]z = \frac{0.14-0.12}{0.0149}= 1.340[/tex]

So we want to find this probability:

[tex] P(z>1.340)[/tex]

And using the complement rule and the normal standard distribution and excel we got:

[tex] P(Z>1.340) = 1-P(Z<1.340) = 1-0.9099= 0.0901[/tex]

I suppose x should be π.

Recall the double angle identity for cosine:

[tex]\cos^2\dfrac x2=\dfrac{1+\cos x}2[/tex]

Then remember for [tex]0<x<\frac\pi2[/tex], we have [tex]\cos x>0[/tex].

Let [tex]x=\frac{7\pi}6[/tex]. Plugging this into the equation above gives

[tex]\cos^2\dfrac{7\pi}{12}=\dfrac{1+\cos\frac{7\pi}6}2[/tex]

Take the square root of both sides; this introduces two possible values, but we know [tex]\cos\frac{7\pi}{12}[/tex] should be positive, so

[tex]\cos\dfrac{7\pi}{12}=\sqrt{\dfrac{1+\cos\frac{7\pi}6}2}=\dfrac{\sqrt{2-\sqrt3}}2[/tex]

========================================================

Explanation:

One way to go about this is to list out all the perfect cubes. A perfect cube is the result of taking any whole number and multiplying it by itself 3 times.

1 cubed = 1^3 = 1*1*1 = 1

2 cubed = 2^3 = 2*2*2 = 8

3 cubed = 3^3 = 3*3*3 = 27

4 cubed = 4^3 = 4*4*4 = 64

and so on. We stop once we reach 1721, or if we go over. Ignore any values larger than 1721. You'll find that 11^3 = 1331 and 12^3 = 1728. So we stop here and exclude 1728 as that is larger than 1721.

A quick way to see where we should stop is to apply the cube root to 1721 and we get

[tex]\sqrt[3]{1721} = 1721^{1/3} \approx 11.98377[/tex]

The approximate result of 11.98377 tells us that 1721 is between the perfect cubes of 11^3 = 1331 and 12^3 = 1728

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

So effectively, we have 11 perfect cubes in the set {0, 1, 2, 3, ..., 1721} and this is out of 1722 numbers in that same set. Note how I added 1 onto 1721 to get 1722. I'm adding an extra number because of the 0. If 0 wasn't part of the set, then we would have 1721 values total inside.

In summary: There are 11 values we want (11 perfect cubes) out of 1722 values total.

Divide 11 over 1722 to get

11/1722 = 0.00638792102207

which rounds to 0.006388

The probability of randomly selecting a perfect cube from the set {0,1,2,...,1721} is calculated by finding the ratio of the number of favorable outcomes (perfect cubes in this range) to the total number of outcomes. We have 12 perfect cubes and 1722 total numbers, giving us a probability of approximately 0.006964.

The subject of this question is probability, a concept in mathematics. A perfect cube is a number that can be expressed as the cube of an integer.For instance, the numbers 1 (13), 8 (23), 27 (33), and so forth, are perfect cubes.

In this case, we need to find how many perfect cubes exist between 0 and 1721. The cube of 12 is 1728, which is greater than 1721 so, we can conclude that the largest whole number whose cube is less than 1721 is 11. This means there are 12 (perfect cubes) numbers from 0 to 1721 (0 included).

The total amount of numbers in this range is 1722 (from 0 to 1721 inclusive). Therefore, the probability of randomly selecting a perfect cube from this range is the ratio of the number of favorable outcomes (perfect cubes) to the total number of outcomes:

P(perfect cube) = Number of perfect cubes /Total numbers

P(perfect cube) = 12/1722 ≈ 0.006964.

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Answer:

5000m

12/3 = 4yd

2kg

8x16 = 128oz

9000ml

20qt

120+23 =143mins

Answer:

5000m

4yd

2kg

128oz

9000ml

20qt

143min

Answer: 3c^6 - 12c^5 + 9c^4

Step-by-step explanation:

The area of the rectangle is found by multiplying the height (3c^4) and the width (c^2 - 4c + 3), resulting in 3c^6 - 12c^5 + 9c^4.

To find the area of a rectangle, you use the formula Area = length x width. From your question, we are told that the height of the rectangle is 3c4, and the width is c2 - 4c + 3. So, to find the area, we need to multiply the height and the width. That will give us:

Area = 3c4(c2 - 4c + 3)

Which, upon multiplication, yields Area = 3c6 - 12c5 + 9c4.

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Answer:

[tex]z=\frac{25-24}{\frac{2}{\sqrt{16}}}=2[/tex]    

[tex]p_v =2*P(Z>2)=0.0455[/tex]  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean differs from 24 at 5% of significance

Step-by-step explanation:

Data given and notation  

[tex]\bar X=25[/tex] represent the sample mean

[tex]\sigma=2[/tex] represent the sample population deviation for the sample  

[tex]n=16[/tex] sample size  

[tex]\mu_o =24[/tex] represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is different from 24, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 24[/tex]  

Alternative hypothesis:[tex]\mu \neq 24[/tex]  

If we analyze the size for the sample is < 30 but we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

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

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]z=\frac{25-24}{\frac{2}{\sqrt{16}}}=2[/tex]    

P-value

Since is a two sided test the p value would be:  

[tex]p_v =2*P(Z>2)=0.0455[/tex]  

Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean differs from 24 at 5% of significance

A hypothesis test is used to determine if the average age of all the students at the university is significantly different from 24. The test statistic does not fall within the critical region, so we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean age is significantly different from 24.

In order to determine if the average age of all the students at the university is significantly different from 24, we can perform a hypothesis test.

Step 1: State the hypotheses:

Step 2: Set the significance level (α): α = 0.05.

Step 3: Calculate the test statistic:

Step 4: Determine the critical value(s): Since the test statistic follows a t-distribution, we need to find the critical values from the t-table. With a sample size of 16 and a significance level of 0.05, we have 15 degrees of freedom. The critical values are t = ±2.131.

Step 5: Make a decision: Since the test statistic (2) does not fall within the critical region (±2.131), we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean age is significantly different from 24.

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Answer:

Step-by-step explanation:

The null hypothesis is the hypothesis that is assumed to be true. It is an expression that is the opposite of what the researcher predicts.

The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected.

From the given situation,

Dr. Cawood states that 25% of the beads are purple. This is the null hypothesis.

Oliver, a student in Dr. Cawood's class believes that more than a quarter of the beads in the model box are purple. This is the alternative hypothesis.

Therefore, the correct null and alternative hypotheses are

H0: p = 0.25 and HA: p > 0.25

The null hypothesis, [tex]\(H_0\)[/tex], is that the proportion of purple beads in the bin is 25%, which can be written as [tex]\(H_0: p = 0.25\)[/tex]. The alternative hypothesis, [tex]\(H_1\)[/tex], is that the proportion of purple beads is greater than 25%, which can be written as [tex]\(H_1: p > 0.25\)[/tex].

In hypothesis testing, the null hypothesis represents the default position or the status quo, which in this case is Dr. Cawood's claim that 25% of the beads are purple. This is represented by the symbol [tex]\(H_0\)[/tex] and is often a statement of no effect or no difference. Here, it is stated as [tex]\(H_0: p = 0.25\)[/tex], where p is the proportion of purple beads in the bin.

The alternative hypothesis, denoted by [tex]\(H_1\)[/tex], represents the claim that is being tested against the null hypothesis. It is the hypothesis that the researcher or the student, in this case Oliver, believes to be true. Since Oliver believes that more than a quarter of the beads are purple, the alternative hypothesis is that the proportion of purple beads is greater than 25%. This is represented as [tex]\(H_1: p > 0.25\)[/tex].

It is important to note that the alternative hypothesis can also be one-sided (as in this case) or two-sided, depending on the context of the claim being tested. If Oliver believed that the proportion of purple beads was different from 25% (either more or less), the alternative hypothesis would be [tex]\(H_1: p \neq 0.25\)[/tex], indicating a two-sided test. However, since the claim specifies ""more than,"" a one-sided alternative hypothesis is appropriate.

Answer:

87.74

Step-by-step explanation:

Answer:

a) 729

b)0.0014

Step-by-step explanation:

(a) In order to determine number of possible answers, we'll use combination method

nPr= [tex](n)^{r}[/tex]

where,

n=3 and r=6

number of possible answers= [tex]3^{6}[/tex] => 729

(b) If Only one of the sets can contain all six correct answers.

probability of getting all five answers correct = 1/ 729 => 0.0014

The total number of possible answer sequences for the six questions is 729. The probability of guessing and getting all six answers correct is 1/729 or approximately 0.00137.

This question requires knowledge from probability and combinatorics, specific branches of Mathematics.

(a) Given that there are six questions on an exam and each question has three possible answers, the total number of possible answer sequences will be 3^6, also based on the rule of multiplication in probability theory. That gives us 729 possible answer sequences.

(b) If only one set of answers is correct, guessing each answer independently, the chances of getting the correct sequence is 1 in 729.

So, the probability of randomly guessing and getting all six answers correctly is 1/729, which is approximately 0.00137, or 0.137%.

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Answer:

k = -23

Step-by-step explanation:

-14=k+9

Subtract 9 from each side

-14-9 = k+9-9

-23 = k

Answer: k=23

Step-by-step explanation:

Answer:

14/1

Step-by-step explanation:

Answer:

The answer is 1. The next part of that same question should be 12n+8.

Step-by-step explanation:

G(x) = (16x − 7) cos³(4x) − 9 sin⁻¹(x)

A) Use product rule, power rule, and chain rule to take the derivative.

G'(x) = (16x − 7) (3 cos²(4x) (-4 sin(4x))) + 16 cos³(4x) − 9 / √(1 − x²)

G'(x) = (-192x + 84) cos²(4x) sin(4x) + 16 cos³(4x) − 9 / √(1 − x²)

Evaluate at x = 0.

G'(0) = (0 + 84) cos²(0) sin(0) + 16 cos³(0) − 9 / √(1 − 0)

G'(0) = 16 − 9

G'(0) = 7

B) Use point-slope form of a line to write the equation.

y − (-7) = 7 (x − 0)

y + 7 = 7x

y = 7x − 7

Answer:

1/12

Step-by-step explanation:

Probability is the result of the number of possible outcome divided by the number of total outcome.

Given that the box contains a red shirt, a blue shirt, a black trouser, and a red trouser, the number of total outcome is

= 1 + 1 + 1 + 1

= 4

The possibility of picking;

a black trouser is

= 1/4

then a red (without replacement, the total outcome drops to 3)

= 1/3

Hence, the probation choosing the black trouser and the red shirt without replacement

= 1/4 * 1/3

= 1/12

Step-by-step explanation:

Area, A = Length,x × Breadth,y

A=xy

When x and y are independent, E(xy) = E(x)E(y)

As x and y have the same distribution, U[L-A,L+A], they have the same mean.

We could argue by symmetry that E(x) = L and E(y) + L, also.

We can also reason this from the fact that, if X ~ U[L-A, L+A], f(x) = 1/(2A) from L-A to L+A

Therefore

[tex]E(x)= \int\limits {f(x)} \, dx \\\\=\int\limits^{(L+A)}_{(L-A)} {\frac{1}{2A}x } \, dx[/tex]

[tex]=\int\limits^{(L+A)}_{(L-A)} {\frac{1}{2A}x } \, dx \\\\=[\frac{1}{4A}x^2 ]\limits^{(L+A)}_{(L-A)}[/tex]

=1/(4A)(L+A)2 - 1/(4A)(L-A)2

= 1/(4A)(L2 + 2AL + A2) - 1/(4A)(L2 - 2AL + A2)

=1/(4A)(2AL+2AL)

= 1/(4A)(4AL)

= L

Thus, E(xy) = E(x)E(y) = L×L = L²

Answer:

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(58,21)[/tex]  

Where [tex]\mu=58[/tex] and [tex]\sigma=21[/tex]

The z score for this case is given by this formula:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

We know that the value of z = 1.78 and we want to estimate the value of X. If we solve for X from the z formula we got:

[tex] X= \mu +1.78 \sigma= 58 +1.78*21= 95.38[/tex]

So the corresponging weight for a z score of 1.78 is 95.38 grams

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(58,21)[/tex]  

Where [tex]\mu=58[/tex] and [tex]\sigma=21[/tex]

The z score for this case is given by this formula:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

We know that the value of z = 1.78 and we want to estimate the value of X. If we solve for X from the z formula we got:

[tex] X= \mu +1.78 \sigma= 58 +1.78*21= 95.38[/tex]

So the corresponging weight for a z score of 1.78 is 95.38 grams

A chicken egg with a z-score of 1.78 in a normal distribution model N(58, 21) will weigh approximately 95.38 grams.

The normal model N(58, 21) describes that weights of chicken eggs are normally distributed with a mean of 58 grams and a standard deviation of 21. Given a z-score of 1.78 for a randomly selected egg, we can calculate the egg's weight according to the Z-score formula, Z = (X - µ)/σ, where X is the value we want to find, µ is the mean, σ is the standard deviation, and Z is the z-score.

Let's apply the z-score value to the formula and solve for X:

Therefore, the weight of the egg with the z-score of 1.78 is approximately 95.38 grams.

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