Arc Length and Radians question- please help! Will mark brainliest! Is 20pts!

The answer is shown but please give me an explanation so I can show my work!

a) Little book LTD earning per share is $1.118 per share.  

Explanation:

To calculate earning per share we will use following formula:[tex]\frac{NET INCOME}{WEIGHTED AVERAGE SHARE OUTSTANDING}[/tex]

Now to find net income we will take help of  asset turnover ratio :[tex]\frac{NET SALES}{TOTAL ASSET}[/tex]

NOTE :  LET x BE THE NET SALES DURING THE YEAR.

Asset turnover ratio = [tex]\frac{x}{860000}[/tex]

1.5 × $860000 = x

x (net sales) = $1290000

Outstanding shares = 75000 shares

So Net Income  = $1290000×.065

                         = $83850

Now Earning per share = [tex]\frac{83850}{75000}[/tex]

 Earning per share = $1.118

b)  Market to Book Ratio will be 1.2 for Little Book LTD.

Explanation:

Market to Book Ratio =[tex]\frac{MARKET CAPITALIZATION}{TOTAL BOOK VALUE}[/tex]

Market Capitalization = $ 75000× $ 12

                                   = $900000

So, Market To Book Ratio =[tex]\frac{900000}{750000}[/tex] =  1.2

    So , Market To Book Ratio is 1.2  for little book ltd.          

Answer:

(a) I attached a photo with the diagram.

(b) [tex]f(x) = \big( \frac{1}{2} \big)^{x-1}[/tex]

(c) 1/4

(d) 4

(e) [tex]k^2/2[/tex]

Step-by-step explanation:

(a) I attached a photo with the diagram.

(b) The easiest way to think about this part is in terms of combinatorics. Think about it like this.

To begin with, look at the three each level of the three represents a possible outcome of throwing the coin n-times. If you throw the coin 3 times at the end in total there are 8 possible outcomes. But The favorable outcomes are just 2.

 1  - Your first outcome is HEADS and all the others are different except the last one.

 2  - Your first outcome is TAILS and all the others are different except the last one.

Therefore the probability of the event is

[tex]f(x) = P(X=x) = \frac{2}{2^x} = \frac{1}{2^{x-1}} = \big( \frac{1}{2} \big)^{x-1}[/tex]

(c)

P(X = 0) = 0 because it is not possible to have two consecutive tails or heads.

[tex]E(X > 4) = 1 - P(X \leq 3) = 1 - ( P(X = 0 ) + P(X = 1) + P(X = 2) + P(X = 3))\\= 1 - ( \frac{1}{2} + \frac{1}{4} ) = \frac{1}{4}[/tex]

(d)

Remember that this is a geometric distribution therefore

[tex]E[X] = p/(1-p)[/tex], in this case  [tex]p = 1/2[/tex] so [tex]E[X] = 1[/tex] and

[tex]E[X+1]^2 = ( E[X] +1 )^2 = (1+1)^2 = 2^2 = 4[/tex]

Also

(e)

This is a geometric distribution so its variance is

[tex]Var(X) = \frac{1-p}{p^2} = 1/2 / 1/4 = 1/2[/tex]

And using properties of variance

[tex]Var(kX - k ) = Var(kX) = k^2 var(X) = k^2 /2[/tex]

To find the required answers, we create a tree diagram to visualize the possibilities of flipping a fair coin. Then, we determine the probability mass function (pmf) of X, finding the probabilities associated with each outcome. We find that P(X=0) is not possible and P(X>4) is 0. We also calculate E((X+1)^2) and Var(kX-k) using the formulas for expected value and variance of a discrete random variable.

To answer the question, we first need to understand the possibilities when flipping a coin. Let H represent a heads and T represent a tails. The possibilities are: HT, TH, and HH. Now, let's create a tree diagram to visualize the possibilities:

(b) To find the probability mass function (pmf) of X, we need to determine the probability of each outcome. Since the coin is fair, each outcome has a probability of 1/2. Therefore, the pmf of X is: P(X=1) = 1/2, P(X=2) = 1/4, P(X=3) = 1/4.

(c) (i) P(X=0) is not possible because we need to observe tails-heads in consecutive flips. (ii) P(X>4) is the probability of observing tails-heads after at least 4 flips, which is 0 since tails-heads can occur in the 2nd or 3rd flip.

(d) To find E((X+1)^2), we need to multiply each possible outcome by its corresponding probability, square it, and then sum them up. E((X+1)^2) = (0+1)^2 * P(X=1) + (1+1)^2 * P(X=2) + (2+1)^2 * P(X=3).

(e) Var(kX-k) = k^2 * Var(X), where Var(X) is the variance of X. Since X is a discrete random variable, Var(X) = E(X^2) - (E(X))^2.

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Answer:

0.75<p<0.85

Yes,the proportion of girls is significantly different from 0.5.

Step-by-step explanation:

We calculate the proportion of girls:

[tex]p=\frac{340}{425}\\\\\\\\=0.8[/tex]

#We then calculate the confidence interval as follows:

[tex]CI=p\pm z(ME)\\\\=p\pm z_{0.005}\sqrt{\frac{p(1-p)}{n}}\\\\=0.8+2.576\times \sqrt{\frac{0.8\times 0.2}{425}}\\\\=0.8\pm0.05\\\\=[0.75,0.85][/tex]

Hence, the proportion's confidence interval at 99% is 0.75<p<0.85

#We then state our hypothesis to validate the claim:

[tex]H_o:p=0.5\\H_a:p>0.5\\\\p=0.8(True \ mean)[/tex]

Since the confidence interval does not contain 0.5, which is the the 50% chance of having a girl, then it can be concluded the proportion of girls is significantly different from 0.5.

Answer:

Length=10 Inches

Width=10 Inches

Step-by-step explanation:

Volume of the box [tex]=800in^3[/tex]

Height=8 Inches

Base Perimeter =40 Inches

Volume of a box=lbh

SInce h=8 in, V=800.

Then:

8bl=800

bl=100

[tex]l=\frac{100}{b}[/tex]

Base Perimeter=40 Inches

Perimeter of the Base= 2(l+b)

Therefore: 2(l+b)=40

Substituting [tex]l=\frac{100}{b}[/tex]

[tex]2(\frac{100}{b}+b)=40\\\frac{100+b^2}{b}=20\\$Cross Multiply\\100+b^2=20b\\b^2-20b+100=0\\$Solving the quadratic equation \\b^2-10b-10b+100=0\\b(b-10)-10(b-10)=0\\(b-10)(b-10)=0\\b-10=0 (Twice)\\b=10 \:Inch[/tex]

Recall:

[tex]l=\frac{100}{b}=\frac{100}{10}\\l=10 Inch[/tex]

Therefore:

Length=10 Inches

Width=10 Inches

Answer:

[tex]4600-1.646\frac{800}{\sqrt{1800}}=4568.96[/tex]    

[tex]4600+1.646\frac{800}{\sqrt{1800}}=4631.04[/tex]    

We are confident at 90% that the true mean for the amount spent on medicines is between (4568.96 and 4631.04)

Step-by-step explanation:

Information given

[tex]\bar X=4600[/tex] represent the sample mean for the amount spent on medicines

[tex]\mu[/tex] population mean

s=800 represent the sample standard deviation

n=1800 represent the sample size  

Solution

The confidence interval for the true population mean is given by:

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

We can calculate the degrees of freedom with:

[tex]df=n-1=1800-1=1799[/tex]

We know that the Confidence level is 0.90 or 90%, the value of significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,1799)".And we see that [tex]t_{\alpha/2}=1.646[/tex]

Replcing in the formula for the confidence interval we got:

[tex]4600-1.646\frac{800}{\sqrt{1800}}=4568.96[/tex]    

[tex]4600+1.646\frac{800}{\sqrt{1800}}=4631.04[/tex]    

We are confident at 90% that the true mean for the amount spent on medicines is between (4568.96 and 4631.04)

Answer:

Combine the like terms

Step-by-step explanation:

2 + 7 = 2x + 5 - 43

The first step is to combine the like terms

9 = 2x - 38

Answer:

  yes, brother can go

Step-by-step explanation:

Apparently, you're not to think to deeply about this function. Rather, you are to take the question at face value. It is asking if the value of T(3) is more than 58.

Evaluation of polynomials is facilitated by writing them in "Horner form."

  T(x) = ((x -2)x +1)x^2 +27

  T(3) = ((3 -2)3 +1)9 +27 = (3 +1)9 +27 = 36 +27

  T(3) = 63

The coldest temperature is supposed to be 63 degrees, which is above 58 degrees. Baby brother can come along.

Answer:

yes, the little brother can go

Step-by-step explanation:

the lowest will be 63 degrees so the baby can go

Answer:

[tex]t=\frac{7.917-9.5}{\frac{1.501}{\sqrt{6}}}=-2.58[/tex]    

[tex]p_v =P(t_{5}<-2.58)=0.03[/tex]

If we compare the p value with a significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v < \alpha[/tex] so we can conclude that we can reject the null hypothesis, and there is enough evidence to conclude that the true mean is significantly lower than 9.5% at 0.05 of signficance

Step-by-step explanation:

Data given and notation    

Data: 6.6% 9.1% 7.0% 6.3% 8.5% 10.0%

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

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

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

[tex]\bar X=7.917[/tex] represent the sample mean

[tex]s=1.501[/tex] represent the sample standard deviation

[tex]n=6[/tex] sample size    

[tex]\mu_o =9.5[/tex] represent the value that we want to test  

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

t would represent the statistic (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 determine if the true mean os greater or not than 9.5%, the system of hypothesis would be:    

Null hypothesis:[tex]\mu \geq 9.5[/tex]    

Alternative hypothesis:[tex]\mu < 9.5[/tex]    

We don't know the population deviation, so for this case we can use the t test to compare the actual mean to the reference value, and the statistic is given by:    

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

t-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]t=\frac{7.917-9.5}{\frac{1.501}{\sqrt{6}}}=-2.58[/tex]    

Calculate the P-value    

The degrees of freedom are given by:

[tex] df = n-1 = 6-1=5[/tex]

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

[tex]p_v =P(t_{5}<-2.58)=0.03[/tex]

In Excel we can use the following formula to find the p value "=T.DIST(-2.58,5,TRUE)"  

Conclusion    

If we compare the p value with a significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v < \alpha[/tex] so we can conclude that we can reject the null hypothesis, and there is enough evidence to conclude that the true mean is significantly lower than 9.5% at 0.05 of signficance

The test statistic of the sampling will be -2.58.

The following can be deduced from the information:

Mean = 7.917

Degree of freedom = 6 - 1 = 5

P value = 0.975 > 0.05

The test statistic will be:

= (7.917 - 9.5) / (1.501 / ✓56)

= -2.58

In conclusion, the test statistic is -2.58.

Learn more about test statistic on:

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The question relates to a two-sample t-test in statistics, which compares the means of two processes. It involves calculating a t-score using sample data, and comparing this score to a critical value to determine if there is a significant difference between the two processes.

This question pertains to the field of statistics within mathematics. Specifically, it involves the use of a two-sample t-test to compare the means of two different processes. The two-sample t-test is used when the population standard deviations are unknown but assumed to be equal, which is the case here.

The process involves computing a t-score using the observed data (including sample mean, standard deviation, and sample size) and then comparing this score to a critical value from the t-distribution. If the observed t-score exceeds the critical value, there is evidence to suggest that there is a significant difference between the two processes.

In this case, you would calculate the t-score for Processes A and B using their respective sample means, standard deviations, and sample sizes. If the observed t-score is greater than the critical t-value at the chosen significance level (typically 0.05 or 0.01), we reject the null hypothesis that there is no difference between the two processes.

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To compare the number of artists with hit songs to the total number of artists signed, write a ratio using the two numbers. The ratio of artists with hit songs (10) to total artists signed (12) simplifies to 5:6 after dividing by the greatest common factor.

The student has asked to write a ratio comparing the number of artists with hit songs to the total number of artists signed by a music company in 2002. To do this, we take the number of artists with hit songs and place it in the numerator (top part) of the ratio and the total number of artists in the denominator (bottom part).

To write the ratio in its simplest form, we divide the numerator and the denominator by their greatest common factor if necessary. In this case, the ratio is already in the simplest form.

Step-by-Step Solution:

Number of artists with hit songs: 10

Total number of artists signed: 12

Write the ratio as 10:12

Simplify the ratio by dividing both numbers by 2, the greatest common factor, to get 5:6

So, the simplified ratio of the number of artists with hit songs to the total number of artists signed is 5:6.

Answer:

25 posts

Step-by-step explanation:

So the number of fence post would be the total length of the log divided by the length of each post. As the log is 16m and is corrected to the nearest metre, it could possibly be 16.499m. As for the post that is 70 cm long and corrected to the nearest 10cm, it may as well be 65 cm (or 0.65m) each post

So the max number of fence point once can possibly cut from the log would be

16.499 / 0.65 = 25 posts

Answer: D. 7 or 12

Step-by-step explanation: on edgenuity 2020 :))

Answer:

a) The standard error would be of 8.58 pounds.

b) The margin of error is 14.11 pounds.

c) The 90% confidence interval for the population mean is between 232.89 pounds and 261.11 pounds

Step-by-step explanation:

a.What is the standard error?

The standard error is

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample. So

[tex]s = \frac{47}{\sqrt{30}} = 8.58[/tex]

The standard error would be of 8.58 pounds.

b.What is the margin of error at 90% confidence?

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]

Now, find the margin of error M as such

[tex]M = z*s = 1.645*8.58 = 14.11[/tex]

The margin of error is 14.11 pounds.

c. Using my sample of 30, what would be the 90% confidence interval for the population mean?

Lower bound: Sample mean subtracted by the margin of error.

247 - 14.11 = 232.89 pounds

Upper bound

247 + 14.11 = 261.11 pounds

The 90% confidence interval for the population mean is between 232.89 pounds and 261.11 pounds

Answer:

a) The standard error would be of 8.58 pounds.

b) The margin of error is 14.11 pounds.

c) The 90% confidence interval for the population mean is between 232.89 pounds and 261.11 pounds

Step-by-step explanation:

Use log definition: if logₐ(b) = c then b = a^c

log₃(x) = 6 → x = 3⁶

x = 3⁶ → x = 726

Therefore, x = 726

Best of Luck!

Answer:

nothing

Step-by-step explanation:

nothing

Answer:

30 hours

Step-by-step explanation:

We can use ratios to solve

5 hours        x hours

-------------- = -------------

3 walls          18 walls

Using cross products

5*18 = 3x

Divide each side by 3

5*18/3 = 3x/3

30 =x

Answer:It will take Harold 30 hours to paint all 18 of the walls

Step-by-step explanation:Your multiplying the amount of walls he is painting by 6 so you do the same to the amount of hours he is painting

Answer: inverse operation

Step-by-step explanation:

here you go

Answer:

B is the correct answer.

Step-by-step explanation:

15 times 5 plus 450

= 525

25 times 5 plus 400

= 525

Answer:

Step-by-step explanation:

CB is the radius. It is equal to BD. So, the diameter CD is ...

  6 inches + 6 inches = 12 inches

The diameter is always twice the length of the radius.

The diameter of this cone is 12 inches.

Answer:

Estimate of the population proportion [tex]\mathbf{\widehat{(P)}}[/tex] = 0.147

Step-by-step explanation:

Given -

Wiley Publications has determined that out of a sample of 7,831 of its publications for 2012, 1,157 of them had been pirated online in some form.

Let x be the no of publication had been pirated online in some form.

x = 1157

n = 7831

Population proportion [tex]\boldsymbol{\widehat{P} = \frac{x}{n}}[/tex]

                                           =  [tex]\frac{1157}{7831}[/tex]

                                         =  0.147

Diego’s travel distance can be determined by first subtracting the pickup fee from the total fare and then dividing this result by the cost per mile. In this case, Diego traveled a total of 11 miles.

To calculate Diego’s travel distance, begin by subtracting the pickup fee from the total fare. The pickup fee is $2.75 and the total fare is $19.25, so this calculation gives us $19.25 - $2.75 = $16.50. Next, divide this result by the cost per mile to determine the total distance traveled. As City cabs charge $1.50 per mile, this calculation is $16.50 ÷ $1.50 = 11. So, Diego traveled 11 miles in the cab.

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Diego traveled 11 miles in the city cab, as calculated by subtracting the fixed pickup fee from the total fare and then dividing by the cost per mile.

City cabs charges a $2.75 pickup fee and $1.50 per mile traveled. If Diego's fare for a cross-town cab ride is $19.25, the question asks us to calculate how far he traveled in the cab. To solve this, we need to use the equation of the total fare which is:

Total fare = Pickup fee + (Cost per mile × Number of miles)

Let 'x' be the number of miles Diego traveled. Using the above equation and substituting the given values, we have:

$19.25 = $2.75 + ($1.50 × x)

To find 'x', we will subtract the pickup fee from the total fare and then divide the result by the cost per mile:

$19.25 - $2.75 = $1.50 × x

$16.50 = $1.50 × x

x = $16.50 / $1.50

x = 11

Therefore, Diego traveled 11 miles in the cab.

Answer:

350(1.137)^20=4563.28232

Answer:

Yes, there is  enough evidence to support the claim that ionizing radiation is beneficial in terms of marketability.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that ionizing radiation is beneficial in terms of marketability.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]

Being π1: the true proportion of treated bulbs that can be comercialized after 240 days, and π2: the true proportion of untreated bulbs that can be comercialized after 240 days.

The significance level is 0.05.

The sample 1, of size n1=180 has a proportion of p1=0.85.

[tex]p_1=X_1/n_1=153/180=0.85[/tex]

The sample 2, of size n2=180 has a proportion of p2=0.65.

[tex]p_2=X_2/n_2=117/180=0.65[/tex]

The difference between proportions is (p1-p2)=0.2.

[tex]p_d=p_1-p_2=0.85-0.65=0.2[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{153+117}{180+180}=\dfrac{270}{360}=0.75[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.75*0.25}{180}+\dfrac{0.75*0.25}{180}}\\\\\\s_{M_d}=\sqrt{0.001+0.001}=\sqrt{0.002}=0.0456[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.2-0}{0.0456}=\dfrac{0.2}{0.0456}=4.382[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]P-value=P(t>4.382)=0.000008[/tex]

As the P-value (0.000008) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is  enough evidence to support the claim that ionizing radiation is beneficial in terms of marketability.

Final answer:

The observed marketable rate of irradiated garlic bulbs suggests that ionizing radiation is beneficial to their marketability compared to untreated bulbs, and this could be statistically tested for significance.

Explanation:

The student's data indicates that irradiated garlic bulbs have a significantly higher rate of remaining marketable (85%) after 240 days compared to unirradiated bulbs (65%). Using a significance level of α = 0.05, we can infer a positive effect of ionizing radiation on the marketability of garlic bulbs. To statistically confirm this observation, one could perform a hypothesis test (such as a chi-squared test for independence) to determine if the difference in marketability between the treated and untreated groups is significant.

Answer:

18.59% probability that EXACTLY 10 will show that the above three food items were ordered

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they order the above food items, or they do not. The probability of a customer ordering these items is independent of other customers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Sixty percent of the customers of a fast food chain order the Whopper, french fries and a drink.

This means that [tex]p = 0.6[/tex]

If a random sample of 15 cash register receipts is selected, what is the probability that EXACTLY 10 will show that the above three food items were ordered

This is P(X = 10) when n = 15. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 10) = C_{15,10}.(0.6)^{10}.(0.4)^{5} = 0.1859[/tex]

18.59% probability that EXACTLY 10 will show that the above three food items were ordered

Answer:

The diameter is 3 inches

Step-by-step explanation:

If you are calculating a circle, one of the main rules you should know is that the diameter is double the radius. In this case the radius is 1.5 inches long. If you need the diameter, you need to double that figure; in this case the answer is 3 inches

Answer:

3 inches

Step-by-step explanation:

diameter is twice the length of the radius

1.5x2=3