Billy has a von Neumann-Morgenstern utility function U(c) = c 1/2. If Billy is not injured this season, he will receive an income of 25 million dollars. If he is injured, his income will be only 10,000 dollars. The probability that he will be injured is .1 and the probability that he will not be injured is .9. His expected utility is

Answer:

$4.80

Step-by-step explanation:

Make a proportion

$12 for 2.5 pounds, and $x for 1 pound

12/2.5=x/1

x/1 is equivalent to x

12/2.5=x

Divide

x=4.8

So, one pound of peanuts costs $4.80

Answer:

4.8

Step-by-step explanation:

divide 12.00 by 2.5 to find the unit rate which is 4.8.

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.

To learn more on Quadrilateral click:

https://brainly.com/question/29934440

#SPJ5

Answer:

I)One to three roots.

ii)Two or zero extrema.

iii)One inflection point.

iv)Point symmetry about the inflection point.

v)Range is the set of real numbers.

vi)Three fundamental shapes.

vii)Four points or pieces of information are required to define a cubic polynomial function.

Roots are solvable by radicals.

Final answer:

The graph of a cube root function has several characteristics such as its domain, range, starting point, and symmetry.

Explanation:

A cube root function is represented by the equation y = ∛x. The graph of a cube root function has several characteristics:

Answer:

Yes,it is

Step-by-step explanation:

95's square root is 9.7467943448

10 is greater than 9.7 and so forth.

So the square root of 95 is less than 10.

The square root of 95 is approximately 9.74679434, thus the square root of 95 is less than 10. The question pertains to the mathematical operation of finding square roots that are indeed pivotal while solving various mathematical problems.

The student question asks if the square root of 95 is less than 10. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 95 is approximately 9.74679434, which is indeed less than 10. The concept of square roots comes from the realm of Mathematics, more specifically Algebra. It's crucial to understand this mathematical operation as it is frequently encountered in various mathematical problems, especially ones involving quadratic equations where an unknown variable is squared. Usually, these equations will yield two solutions, as both a positive and a negative number squared gives the same result. However, the context of a problem can sometimes restrict the solution to only one value, typically the positive.

As an example, let's consider an equation like x² = 49. The solutions to this are x = -7 and x = 7 because both (-7)² and 7² equals 49. But if this equation was describing a real-world scenario where negative values could not apply (like time or distance), the meaningful solution would only be x = 7.

For more about Square Root:

https://brainly.com/question/1540542

#SPJ3

Answer:

x = 16°, tan x = 0.3

Step-by-step explanation:

[tex]sin \: 2x = cos \: (3x + 10) \\ cos(90 - 2x) = cos \: (3x + 10) \\ 90 - 2x = 3x + 10 \\ 90 - 10 = 3x + 2x \\ 80 = 5x \\ x = \frac{80}{5} \\ \huge \red{ \boxed{x = 16 \degree }}\\ \\ tan \: x = tan \: 16 \degree \\ = 0.2867453858 \\ = 0.3[/tex]

Answer:

45?

Step-by-step explanation:

How would you not know this?

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:

(a) The 90 percent confidence interval for the population mean yearly premium is ($10,974.53, $10983.47).

(b) The sample size required is 107.

Step-by-step explanation:

(a)

The (1 - α)% confidence interval for population mean is:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]

Given:

[tex]\bar x=\$10,979\\s=\$1000\\n=20[/tex]

Compute the critical value of t for 90% confidence level as follows:

[tex]t_{\alpha/2, (n-1)}=t_{0.10/2, (20-1)}=t_{0.05, 19}=1.729[/tex]

*Use a t-table.

Compute the 90% confidence interval for population mean as follows:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]

     [tex]=10979\pm 1.729\times \frac{1000}{\sqrt{20}}\\=10979\pm4.47\\ =(10974.53, 10983.47)[/tex]

Thus, the 90 percent confidence interval for the population mean yearly premium is ($10,974.53, $10983.47).

(b)

The margin of error is provided as:

MOE = $250

The confidence level is, 99%.

The critical value of z for 99% confidence level is:

[tex]z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.58[/tex]

Compute the sample size as follows:

[tex]MOE= z_{\alpha/2}\times \frac{s}{\sqrt{n}}[/tex]

      [tex]n=[\frac{z_{\alpha/2}\times s}{MOE} ]^{2}[/tex]

         [tex]=[\frac{2.58\times 1000}{250}]^{2}[/tex]

         [tex]=106.5024\\\approx107[/tex]

Thus, the sample size required is 107.

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:

The sample proportion of successful procedures is 0.962.

Step-by-step explanation:

The sample proportion of successful procedures is the number of successfiç procedures divided by the total number of procedures.

In this problem:

158 procedures, of which 152 were successful. So

p = 152/158 = 0.962

The sample proportion of successful procedures is 0.962.

The sample proportion is the ratio of the number of successes to the total number of samples or trials, Hence, the sample proportion is 0.962

Given the Parameters :

The sample proportion can be calculated using the relation :

Sample proportion = 152/158 = 0.962

Hence, the sampling proportion of successful procedures is 0.962.

Learn more : https://brainly.com/question/18651667

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%.

https://brainly.com/question/22962752

#SPJ3

Answer:

a) we know that this is convergent.

b) we know that this might not converge.

Step-by-step explanation:

Given the [tex]\sum^\infty_{n=0}C_n8^n[/tex] is convergent

Therefore,

(a)  [tex]\sum^\infty_{n=0}C_n(-3)^n[/tex] The power series [tex]\sum C_nx^n[/tex] has radius of convergence at least as big as 8. So we definitely know it converges for all x satisfying -8<x≤8. In particular for x = -3

∴ [tex]\sum^\infty_{n=0}C_n(-3)^n[/tex]  is convergent.

(b) [tex]\sum^\infty_{n=0}C_n(-8)^n[/tex] -8 could be right on the edge of the interval of convergence, and so might not converge

The convergence of the series ∑ cn(−3)^n and ∑ cn(−8)^n depends on whether the original power series, ∑ cnxn, converges for these specific values of x i.e. x = -3 and x = -8. To determine this, one must apply the Ratio Test or Root Test.

This is a question about the convergence of a series in mathematics, particularly power series. For a power series like ∑ cnxn (from n = 0 to infinity), the series converges absolutely for certain values of x. When dealing with the two series in the question, ∑ cn(−3)^n and ∑ cn(−8)^n, we can observe that they are similar to the original power series, with x = -3 and x = -8, respectively.

Now, whether these series will converge or not, strictly depends on the radius of convergence of the original series. If the original series converges for x = -3 and x = -8, then these two series will also converge. Otherwise, they won't.

To determine the range or radius of convergence, you have to use the Ratio Test or Root Test in most cases. These are some standard mathematical methods used to determine whether a given series is convergent or not.

https://brainly.com/question/33953891

#SPJ11

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.

https://brainly.com/question/31665727

#SPJ3

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:

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:

[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]

Answer: [tex]x=9[/tex]

Divide both side by 5

[tex]5x/5=45/5\\x=9[/tex]

Answer:

[tex]x = 9[/tex]

Step-by-step explanation:

[tex]5x = 45 \\ \frac{5x}{5} = \frac{45}{5} \\ x = 9[/tex]

hope this helps you.....

Answer:

its d

Step-by-step explanation:

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.

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]

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: 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.

https://brainly.com/question/15218510

#SPJ3

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:

14/1

Step-by-step explanation:

Answer:

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

Answer:

Find the rate of change of temperature with respect to distance at the point (3, 9) in the x- direction.

(b) Find the rate of change of temperature with respect to distance at the point (3, 9) in the y-

Step-by-step explanation:

because 3 9 t 2 x y where t

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.

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:

a)We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.04 or no.:  

Null hypothesis:[tex]p \leq 0.04[/tex]  

Alternative hypothesis:[tex]p > 0.04[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

b) We need to use a z statistic

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.135 -0.04}{\sqrt{\frac{0.04(1-0.04)}{300}}}=8.396[/tex]  

Since is a right tailed test the p value would be:  

[tex]p_v =P(z>8.396) \approx 0[/tex]  

Step-by-step explanation:

Data given and notation

n=400 represent the random sample taken

X=54 represent the number of failures

[tex]\hat p=\frac{54}{400}=0.135[/tex] estimated proportion of adults that said that it is morally wrong to not report all income on tax returns

[tex]p_o=0.04[/tex] is the value that we want to test

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

z would represent the statistic (variable of interest)

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

Part a: Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.04 or no.:  

Null hypothesis:[tex]p \leq 0.04[/tex]  

Alternative hypothesis:[tex]p > 0.04[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Part b: Calculate the statistic  

We need to use a z statistic

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.135 -0.04}{\sqrt{\frac{0.04(1-0.04)}{300}}}=8.396[/tex]  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

[tex]p_v =P(z>8.396) \approx 0[/tex]  

So the p value obtained was a very low value and using the significance level for example [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of defectives is significantly higher than 0.04 or 4%

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:

50.265

Step-by-step explanation:

Sorry if its wrong