Ximena spent 72 of the day
shopping at the mall. She spent
74 of this time trying on jeans.
What fraction of the day did
Charlotte spend trying on jeans?

Answer:

x=13

Step-by-step explanation: (8x-44)+(8x-44)+(8x-44)=180

24x-132=180

24x=312

312/24

x=13

Showing Proof

8(13)-44=60

60+60+60=180

Therefore the answer is x=13

In the triangle in the given diagram, the value of x is 13

In the diagram, the value of ∠C = (8x -44)°.

To determine the value of x, we will first determine the measure of ∠C.

From the question,

Triangle ABC is equilateral

Recall that, each interior angle of an equilateral triangle equals 60°.

∴ m ∠C = 60°

Since the measure of ∠C = 60°

Then, we can write that

(8x - 44)° = 60°

Now, we will solve the above equation for x

8x° - 44° = 60°

First, add 44° to both sides

8x° - 44° + 44° = 60° + 44°

8x° = 104°

∴ x = 104° ÷ 8°

x = 13

Hence, in the given triangle, the value of x is 13

Learn more here: https://brainly.com/question/23421311

Answer:

(a) P([tex]\bar X[/tex] [tex]\geq[/tex] 76) = 0.2327

(b) P(73 < [tex]\bar X[/tex] < 75) = 0.5035

(c) P([tex]\bar X[/tex] < 74.8) = 0.77035

Step-by-step explanation:

We are given that the mean of a population is 74 and the standard deviation is 16.

Assuming the data follows normal distribution.

Let [tex]\bar X[/tex] = sample mean

The z-score probability distribution for sample mean is given by;

                         Z = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 74

            [tex]\sigma[/tex] = standard deviation = 16

            n = sample size

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

(a) Probability that a random sample of size 34 yielding a sample mean of 76 or more is given by = P([tex]\bar X[/tex] [tex]\geq[/tex] 76)

   P([tex]\bar X[/tex] [tex]\geq[/tex] 76) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{76-74}{\frac{16}{\sqrt{34} } }[/tex] ) = P(Z [tex]\geq[/tex] 0.73) = 1 - P(Z < 0.73)

                                                 = 1 - 0.7673 = 0.2327

The above probability is calculated by looking at the value of x = 0.73 in the z table which has an area of 0.7673.

(b) Probability that a random sample of size 120 yielding a sample mean of between 73 and 75 is given by = P(73 < [tex]\bar X[/tex] < 75) = P([tex]\bar X[/tex] < 75) - P([tex]\bar X[/tex] [tex]\leq[/tex] 73)

   P([tex]\bar X[/tex] < 75) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{75-74}{\frac{16}{\sqrt{120} } }[/tex] ) = P(Z < 0.68) = 0.75175

   P([tex]\bar X[/tex] [tex]\leq[/tex] 73) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{73-74}{\frac{16}{\sqrt{120} } }[/tex] ) = P(Z [tex]\leq[/tex] -0.68) =1 - P(Z < 0.68)

                                                 = 1 - 0.75175 = 0.24825

Therefore, P(73 < [tex]\bar X[/tex] < 75) = 0.75175 - 0.24825 = 0.5035

The above probability is calculated by looking at the value of x = 0.68 in the z table which has an area of 0.75175.

(c) Probability that a random sample of size 218 yielding a sample mean of less than 74.8 is given by = P([tex]\bar X[/tex] < 74.8)

   P([tex]\bar X[/tex] < 74.8) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{74.8-74}{\frac{16}{\sqrt{218} } }[/tex] ) = P(Z < 0.74) = 0.77035

The above probability is calculated by looking at the value of x = 0.74 in the z table which has an area of 0.77035.

Answer:

20 feet

Step-by-step explanation:

Answer:

55%

Step-by-step explanation:

You could first find

10% of 1500=150

50%=750

25%=525

5%=75

750+75=825

The answer is 55% are female

The percentage of the audience that are female at the concert is 55%. This is calculated by dividing the number of females (825) by the total audience number (1500), and then multiplying that result by 100.

To calculate the percentage of women in the audience, we need to divide the number of women by the total number of people in the audience, then multiply by 100 to convert the decimal into a percentage.

Thus, the calculation would be as follows:

(825 / 1500) * 100 = 55%

So, the percentage of the audience that are female is 55%.

https://brainly.com/question/32197511

#SPJ3

Answer:

Jelly Bean price per pound = $3.25, Trail Mix price per pound = $1.25

Step-by-step explanation:

Let jb = price per pound of jelly beans

Let tm = price per pound of trail mix

equation 1 -> 6*jb + 2*tm = 22

equation 2 -> 3*jb + 5*tm = 16

simplify equation 1

6*jb + 2tm = 22

2*tm = 22 - 6*jb

divide by 2

tm = 11 - 3*jb

plug this into equation 2

3*jb + 5*tm = 16

3*jb + 5*(11-3*jb) = 16

3*jb + 55 - 15*jb = 16

-12*jb + 55 = 16

-12*jb = 16 - 55

-12*jb = -39

jb = -39/-12

jb = 3.25

then, plug the cost per pound of jelly beans back into the simplified equation 1

tm = 11 - 3*jb

tm = 11 - 3*3.25

tm = 1.25

Final answer:

The probability of more than 192 confidence intervals containing the true proportion when constructing 95% confidence intervals across 200 towns, which follows a binomial distribution.

Explanation:

When constructing confidence intervals for a proportion, if we state that we have 95% confidence, this means that if we were to take many samples and build a confidence interval from each sample, we would expect 95% of those intervals to contain the population proportion. In the case with 200 towns, 95% confidence suggests that approximately 190 out of 200 intervals would contain the true population proportion, as 95% of 200 is 190.

To find the probability that more than 192 of these intervals contain the true proportion, we would use the binomial distribution, where each interval has a 0.95 probability of containing the true proportion (success), and we are looking for the sum of the probabilities of 193, 194, ..., 200 successes out of 200 trials.

Answer:

257/2 degrees or 128.5 degrees

Step-by-step explanation:

radians to degrees is x radians * 180/π

[tex]\frac{257\pi }{360} * \frac{180}{\pi }= \frac{257}{2}[/tex]

it is 257/2 degrees or 128.5 degrees

Answer:

she would have $370.20

Step-by-step explanation:

24.68*15=370.2

The answer would be 320.2. 24.8 x 15= 320.5

Step-by-step explanation:

Answer:

Answer:

The first box plot.

Step-by-step explanation:

Step-by-step explanation:

In a box plot, the lower quartile is the right hand side of the box.  In the first plot, this is 3.

The upper quartile is the left hand side of the box.  In the first plot, this is 8.

The interquartile range is the difference between these two values:

8-3 = 5.

Answer:

  600

Step-by-step explanation:

As t gets very large, the exponential term goes to zero, and the expression nears the value ...

  P(∞) = 600/(1 +5·0) = 600

The maximum number of squirrels the park can support is modeled as being 600.

Answer:

wdym

Step-by-step explanation:

The equation 7/8 + 0 = 7/8 demonstrates the Identity Property of Addition, which states adding zero to any number leaves it unchanged. This property highlights zero's role as the addition identity element.

The property illustrated by the equation 7/8 + 0 = 7/8 is known as the Identity Property of Addition. This property states that adding zero to any number or fraction does not change its value. It's an essential property in mathematics, underlining the concept that zero is the identity element for addition. This implies that adding zero to a number does not contribute any new value, essentially leaving the original number unchanged.

In broader mathematical contexts, understanding such properties helps in simplifying expressions and solving equations more efficiently. The identity property, similar to the concept of identity in multiplication (where multiplying by 1 leaves a number unchanged), plays a crucial role in developing more complex algebraic concepts and operations.

Answer:

4 hours

Step-by-step explanation:

Answer:

The null hypothesis is represented as

H₀: p ≤ (3/4)

The alternative hypothesis is represented as

Hₐ: p > (3/4)

z = 1.65

p-value = 0.049471

The obtained p-value is less than the significance level at which the test was performed at. Hence, we reject the null hypothesis, accept the alternative hypothesis & say that there is significant evidence to conclude that more than (3/4) of the voting population would vote for the Democrat.

Step-by-step explanation:

The complete question is presented in the attached image to this answer.

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that random chance is responsible for the outcome or results of any experimental study/hypothesis testing.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that other than random chance, there are significant factors affecting the outcome or results of the experimental study/hypothesis testing.

For this question, the null hypothesis would be that there isn't significant evidence that that more than (3/4) of the entire voting population would vote for the Democrat. That is, the proportion of the entire voting population that would vote for the democrat is less than or equal to (3/4).

While the alternative hypothesis is that there is significant evidence that more than (3/4) of the voting population would vote for the Democrat.

Mathematically,

The null hypothesis is represented as

H₀: p ≤ (3/4)

The alternative hypothesis is represented as

Hₐ: p > (3/4)

To do this test, we will use the z-distribution because the sample size (1200) is large enough for the p-value for z-test statistic and the t-test statistic to approximately be equal.

So, we compute the z-test statistic

z = (x - μ)/σₓ

x = sample proportion of the surveyed registered voters that would vote for the democrat = (925/1200) = 0.77

μ = p₀ = The standard proportion that we're comparing against = (3/4) = 0.75

σₓ = standard error = √[p(1-p)/n]

where n = Sample size = 1200

σₓ = √[0.77×0.23/1200] = 0.01215

z = (0.77 - 0.75) ÷ 0.01215

z = 1.65

checking the tables for the p-value of this t-statistic

Significance level = 0.05

The hypothesis test uses a one-tailed condition because we're testing only in one direction (whether the proportion is greater than 0.75)

p-value (for z = 1.65, at 0.05 significance level, with a one tailed condition) = 0.049471

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.049471

0.171485 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is significant evidence to conclude that more than (3/4) of the voting population would vote for the Democrat.

Hope this Helps!!!

Answer:

a) X ~ exp ( 10 )

b) E(X) = 0.1 , Var (X) = 0.01

c)  P ( X < 0.07 ) = 0.00698

Step-by-step explanation:

Solution:-

- The spike train, used to study neural activity, the given time in between consecutive spikes (ISI) where the firing rate = 10 neurons per seconds.

- Denote a random variable "X"represent a single interspike interval (ISI) having an exponential distribution.

- Where X follows exponential distribution defined by event rate parameter i.e λ.

                               X ~ Exp ( λ )

- The event rate (λ) is the number of times an event occurs per unit time. Since we are studying a single interspike interval (ISI) - which corresponds to the firing rate. So, event rate (λ) = firing rate = 10 neurons per second. Hence, the distribution is:

                               X ~ Exp ( 10 )

- The expected value E(X) denotes the amount of time in which a single an event occurs; hence, the time taken for a single neuron.

                               E(X) = 1 / λ

                               E(X) = 1 / 10

                               E(X) = 0.1 s per neuron.

- The variance is the variation in the time taken by a single neuron to be emitted. It is defined as:

                               Var (X) = 1 / λ^2

                               Var (X) = 1 / 10^2

                               Var (X) = 0.01 s^2

- The probability that ISI is less than t = 0.07 seconds: P ( X < t = 0.07 s):

- The cumulative distribution function for exponential variate "X" is:

                                P ( X < t ) = 1 - e^(-λ*t)

- Plug the values and the determine:

                                P ( X < 0.07 ) = 1 - e^(-0.1*0.07)

                                                      = 1 - 0.99302

                                                      = 0.00698

Answer:

We accept H₀ we don´t have evidence of differences between the information from the sample and the population mean

Step-by-step explanation:

From data and excel (or any statistics calculator) we get:

X = 249,6 ml         and       s  1,26 ml

Sample mean and sample standard deviation respectively.

Population mean  μ₀  = 250 ml

We have a normal distribution but we dont know the standard deviation of the population. Furthermore we have a two tails test since we are finding if the sample give us evidence of differences ( in both senses ) when we compare them with the amount of water spec ( 250 ml )

Our test hypothesis are: null hypothesis       H₀    X = μ₀

Alternative Hypothesis                                 Hₐ     X ≠ μ₀

We also know that sample size is 8  therefore df  =  8 - 1   df = 7 , with this value and the fact that we are required to test at α = 0,05 ( two tails test)

t = 2,365

Then we evaluate our interval:

X ± t* (s/√n)   ⇒   249,6 ±  2,365 * ( 1,26/√8 )

 249,6 ±  2,365 * (1,26/2,83)  ⇒ 249,6 ±  2,365 *0,45

249,6 ± 1,052

P [ 250,652 ; 248,548]

Then the population mean 250 is inside the interval, therefore we must accept that the bottles have being  fill withing the spec. We accept H₀

Answer:

Because the p-value of 0.4304 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of water in all the bottles filled that day does not differ from the target value of 250 milliliters.

Step-by-step explanation:

Answer:

He would need 45,000 for his down payment. He would only have to come up with 9,000.

Step-by-step explanation:

10% times 450,000 is 45,000.

80% times 45,000 is 36,000. 45,000 minus 3600 is 9,000.

Answer:

$9,000

Step-by-step explanation:

10% of 450000

10/100 × 450000

= 45000

He has 80%, needs to arrange for 100-80 = 20% of the down payment

20/100 × 45000 = 9,000

We want to find the number of dollars Chi makes for every hour he cuts lawns. This proportion would be dollars/hour.

329.12 / 34 = 9.68

Chi's hourly wage is $9.68 per hour.

Hope this helps!! :)

Answer:

We conclude that the average attention span for teenage boys is less than 5 minutes.

Step-by-step explanation:

We are given that the mean time to distraction for teenage boys working on an independent task was 4 minutes.

Suppose that this mean was based on a random sample of 50 teenage Australian boys and that the sample standard deviation was 1.4 minutes.

Let [tex]\mu[/tex] = average attention span for teenage boys

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 5 minutes    {means that the average attention span for teenage boys is more than or equal to 5 minutes}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 5 minutes    {means that the average attention span for teenage boys is less than 5 minutes}

The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;

                    T.S.  = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean attention time span for teenage boys = 4 min

             s = sample standard deviation = 1.4 min

             n = sample of teenage boys = 50

So, the test statistics  =  [tex]\frac{4-5}{\frac{1.4}{\sqrt{50} } }[/tex]  ~  [tex]t_4_9[/tex]

                                     =  -5.051

Now at 0.01 significance level, the t table gives critical value of -2.405 at 49 degree of freedom for left-tailed test. Since our test statistics is less than the critical value of t as -2.405 > -5.051, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the average attention span for teenage boys is less than 5 minutes.

Answer:

a) N(A∩B) = 0.9

b) N(A∩B) = 4.9

c) N(A or B) = 4.2

Step-by-step explanation:

Given that A and B each randomly, and independently, choose 3 of 10 objects;

P(A) = P(B) = 3/10 = 0.3

P(A') = P(B') = 1 - 0.3 = 0.7

a) chosen by both;

Probability of being chosen by both;

P(A∩B) = 0.3 × 0.3 = 0.09

Expected Number of objects being chosen by both;

N(A∩B) = P(A∩B) × N(total) = 0.09×10

N(A∩B) = 0.9

b) not chosen by either A or B;

Probability of not being chosen by either A or B;

P(A'∩B') = 0.7 × 0.7 = 0.49

Expected Number of objects being chosen by both;

N(A'∩B') = P(A'∩B') × N(total) = 0.49×10

N(A∩B) = 4.9

c) chosen by exactly one of A and B.

Probability of being chosen by exactly one of A and B

P(A∩B') + P(A'∩B) = 0.3×0.7 + 0.7 × 0.3 = 0.42

Expected Number of objects being chosen by both;

N(A or B) = 0.42 × 10

N(A or B) = 4.2

The expected number of objects chosen by both A and B is 0.9. The expected number of objects not chosen by either A or B is 9.1. The expected number of objects chosen by exactly one of A and B is 4.2.

To find the expected number of objects chosen by both A and B, we can use the multiplication rule. Since A and B each independently choose 3 objects from a set of 10, the probability of choosing a specific object is 3/10 for both A and B. Therefore, the expected number of objects chosen by both A and B is (3/10)(3/10)(10) = 0.9.

To find the expected number of objects not chosen by either A or B, we can subtract the expected number of objects chosen by both A and B from the total number of objects. So, the expected number of objects not chosen by either A or B is 10 - 0.9 = 9.1.

To find the expected number of objects chosen by exactly one of A and B, we can use the addition rule. Since A and B each independently choose 3 objects, the probability of choosing a specific object is 3/10 for both A and B. Therefore, the expected number of objects chosen by exactly one of A and B is 2(3/10)(7/10)(10) = 4.2.

https://brainly.com/question/37190983

#SPJ11

Answer:

H₀: p = 0.20.

Hₐ: p ≠ 0.20.

Step-by-step explanation:

The question is:

The data in Nutrition Study include information on nutrition and health habits of a sample of 315 people. One of the variables is Smoke, indicating whether a person smokes or not (yes or no). Use technology to test whether the data provide evidence that the proportion of smokers is different from 20% given that 43 identify themselves as smokers. Clearly state the null and alternative hypotheses

In this case we need to test whether the proportion of smokers is different from 20%.

A one-proportion z-test can be used to determine the conclusion for this test.

The hypothesis defined as:

H₀: The proportion of smokers is 20%, i.e. p = 0.20.

Hₐ: The proportion of smokers is different from 20%, i.e. p ≠ 0.20.

The information provided is:

n = 315

X = number of people who identified themselves as smokers = 43

Compute the sample proportion of smokers as follows:

[tex]\hat p=\frac{X}{n}=\frac{43}{315}=0.137[/tex]

Compute the test statistic as follows:

[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.137-0.20}{\sqrt{\frac{0.20(1-0.20)}{315}}}=-2.80[/tex]

The test statistic is -2.80.

Compute the p-value as follows:

[tex]p-value=2\times P(Z<-2.80)\\=2\times [1-P(Z<2.80)]\\=2\times [1-0.99744]\\=0.00512[/tex]

*Use a z-table.

The p-value is 0.00512.

The p-value is quite small. So, the null hypothesis will be rejected at any significance level.

Thus, it can be concluded that the  proportion of smokers is different from 20%.

The null hypothesis is that the proportion of smokers is 20% and the alternative hypothesis is that the proportion of smokers is not 20%.

The null hypothesis simply means that there's no effect or relationship between the variables while the alternative hypothesis simply states that the prediction of the research has an effect

In this case, the null hypothesis is that the proportion of smokers is 20% and the alternative hypothesis is that the proportion of smokers is not 20%.

Learn more about hypothesis on:

https://brainly.com/question/15980493

Answer:

D) 4

Step-by-step explanation:

[tex]|3| + |-1| = 3 + 1 = 4 \\ [/tex]

Answer:

Step-by-step explanation:

1) The sample and the population of this study is the friends who replied his email which includes in his contact list. then, the number of the replied to his email are 9 friends.

population: the whole friends include in his contact list.

3) Type I error occurs when one incorrectly rejects the null hypothesis

Here there is possibility of type I error

Answer:

See explaination

Step-by-step explanation:

public class GaussElim{

private static final double eps = 1e-10; % set epsilon value

public static doublic[] fun(double[][] A,double[] b){

int n=b.length; %calculate length of vector b.

for( int j=0;j<n;j++){

int max=j; %find and swap pivot row.

for (int i=j+1;i<n;i++){

if(Math.abs(A[i][j])>Math.abs(A[max][j])){

max=i;

}

}

double[] t1= A[j]; %swap

A[j]=A[max];

A[max]=t1;

double t= b[j]; %swap

b[j]=b[max];

b[max]=t;

if(Math.abs(A[j][j])<=eps){

throw new ArithmeticException("Matrix is singular."); % if matrix A is a singular matrix then throw error.

}

for(int i=j+1;i<n;i++){

double alpha= A[i][j]/A[j][j];

b[i]=b[i]-alpha*b[j];

for(int k=j;k<n;k++){

A[i][k]=A[i][k]-alpha*A[j][k];

}

}

}

double[] x=new double[n]; % back substitution starts here

for(int i=n-1;i>=0;i--){

double sum=0.0;

for(int j=i+1;j<n;j++){

sum=sum+A[i][j]*x[j];

}

x[i]=(b[i]-sum)/A[i][i];

}

return x;

}

public static void main(String[] args){

int n=3;

double[][] A={{1,2,1},{4,2,0},{-1,5,-3}};

double[] b={5,3,21};

double[] x=fun(A,b);

for(int i=0;i<n;i++){

StdOut.println(x[i]);

}

}

}

Answer:

The answer is C) $197,263.70

Step-by-step explanation:

It's losing 6% PER year for the last 3 year.

You can do what I did and take $237,500 and times it 0.06. Which should give you 14,250, that is how much is lost in year one.

So subtract 14,250 from 237,500, you should have $223,250 now.

Repeat the first step with $223,250 now, you times it by 0.06 again and you should get 13,395, you subtract that from $223,250.

You have $209,855 now, once again times that by 0.06 and you get 12,591.30. Subtract 12,591.30 from 209,855 and you should end up with $197,263.70

It's a long, simple method and I'm sure there is another method of solving this question, but this is an easy way to get the answer.

Answer:

c

Step-by-step explanation:

because simple answer

Answer:

The slope is -1

Step-by-step explanation:

We can find the slope by using

m = (y2-y1)/(x2-x1)

   = (-3-5)/(6 - -2)

   = (-3-5)/(6+2)

   = -8/8

  -1

Answer:

a) (9/2)

b) (9/4)

Step-by-step explanation:

I = ∫¹₀ (x³ - 5x) dx = -(9/4)

a) ∫¹₀ (10x - 2x³) dx = -2 ∫¹₀ (x³ - 5x) dx

∫¹₀ (x³ - 5x) dx = -(9/4) from the given value for I

-2 ∫¹₀ (x³ - 5x) dx = -2 × (-9/4) = (9/2)

b) ∫¹₀ (5x - x³) dx = -1 ∫¹₀ (x³ - 5x) dx

∫¹₀ (x³ - 5x) dx = -(9/4) from the given value for I

-1 ∫¹₀ (x³ - 5x) dx = -1 × (-9/4) = (9/4)

Hope this Helps!!!

Answer:

a.

[tex]\int\limits_{0}^{1} 10x - 2x^3 \,dx = -2(\int\limits_{0}^{1} x^3 -5x\,dx) = -2*(-9/4) = 9/2[/tex]

b.

[tex]\int\limits_{0}^{1} 5x - x^3 \,dx = -1*(\int\limits_{0}^{1} x^3 -5x\,dx) = -1*(-9/4) = 9/4[/tex]

Step-by-step explanation:

According to the information given.

[tex]\int\limits_{0}^{1} x^3 - 5x \,dx = -9/4\\[/tex]

Now.

a.

[tex]\int\limits_{0}^{1} 10x - 2x^3 \,dx = -2(\int\limits_{0}^{1} x^3 -5x\,dx) = -2*(-9/4) = 9/2[/tex]

b.

[tex]\int\limits_{0}^{1} 5x - x^3 \,dx = -1*(\int\limits_{0}^{1} x^3 -5x\,dx) = -1*(-9/4) = 9/4[/tex]

Final answer:

To find the probability of selecting two male students from a class with 8 male and 7 female students, we multiply the individual probabilities. Hence, the answer is 4/15.

Explanation:

Probability of getting a male student in the first selection: 8/15

Probability of getting a male student in the second selection given the first is male: 7/14

Probability both selections are male students: (8/15) * (7/14) = 8/30 = 4/15

Answer:

[tex] {9}^{15} [/tex]

Step-by-step explanation:

[tex]( {9}^{3} ) \times ( {9}^{12} ) = 9 {}^{3 + 12} = {9}^{15} \\ [/tex]

Answer:

The degrees of freedom associated with the critical value is 25.

Step-by-step explanation:

The number of values in the final calculation of a statistic that are free to vary is referred to as the degrees of freedom. That is, it is the number of independent ways by which a dynamic system can move, without disrupting any constraint imposed on it.

The degrees of freedom for the t-distribution is obtained by substituting the values of n1​ and n2​ in the degrees of freedom formula.

Degrees of freedom, df = n1​+n2​−2

                                       = 15+12−2=27−2=25​

Therefore, the degrees of freedom associated with the critical value is 25.

Answer:

The population of the small community, 5 years into the future, after the initial 20-year period = 4268.

Step-by-step explanation:

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

The exponential function will look like

p = aeᵏᵗ

where a and k are constants.

Take the natural logarithms of both sides

In p = In aeᵏᵗ

In p = In a + In eᵏᵗ

In p = In a + kt

In p = kt + In a.

We then use linear regression to fit the data of In p against t to obtain k and In a.

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

In p | 4.605 | 5.298 | 6.109 | 6.856 | 7.601

In p = kt + In a.

y = mx + b

m = k and b = In a

Performing a linear regression analysis on the now-linear relationship between In p and t and also plotting a graph of the variables.

The regression equation obtained is

y = 0.151x + 4.584

The first attached image shows the equations necessary for the estimation of the linear regression parameters.

The second attached image shows the use of regression calculator and the plot of the function In p versus t.

Comparing

y = 0.151x + 4.584

With

In p = kt + In a.

y = In p

k = 0.151

x = t

In a = 4.584

a = 97.905

The exponential function relating p and t,

p = aeᵏᵗ now becomes

p = 97.905 e⁰•¹⁵¹ᵗ

So, to predict the population 5 years into the future, that is 5 years after the 20 year period.

we need p at t=25 years.

0.151 × 25 = 3.775

p(t=25) = 97.905 e³•⁷⁷⁵ = 4268.41 = 4268.

Hope this Helps!!!

To forecast another 5 years, an exponential growth model can be used. The growth rate 'r' can be estimated using linear regression on the natural log of population figures against time, and this rate can be used to compute the predicted population. However, such a model may not account for influences like resource depletion.

To predict the population 5 years into the future, we can use an exponential model and linear regression. The population growth described suggests it follows a sort of exponential process where population counts increase more rapidly as time progresses.

Exponential growth can be modeled using the equation P(t) = P0 * e^(rt), where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and e is the base of natural logarithms. To find 'r', we can plot the natural log of the population against time and apply linear regression. The slope of the regression line estimates the growth rate 'r'. Once we've estimated 'r', we can plug the estimated 'r', the current population P0, and the time (t=25, for 5 years into the future) into the formula to calculate the predicted population.

Though this approach gives an estimate, it's important to note that real-life population dynamics can be influenced by various factors not accounted for in a simple exponential model, such as carrying capacity and resource depletion. Thus, it's more of an optimistic estimate, assuming ideal conditions for continued growth.

https://brainly.com/question/12490064

#SPJ3