what would be the value of $150 after eight years if you earn 12 %interest per year

Answer:

The answer is B, C, and E

Step-by-step explanation:

I hope this helps have a nice day! ❤

Answer:

a) As the claim is that the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup differs from 64% , the percentage can be significantly highly or lower. Then, the test is two-tailed and the null and alternative hypothesis are:

[tex]H_0: \pi=0.64\\\\H_a:\pi\neq 0.64[/tex]

b) P-value = 0.0166

c) At α= 0.05, the null hypothesis is rejected.

There is  enough evidence to support the claim that the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup differs from 64% .

d) No, as its brand is below the average when it comes to approval of the consumers.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup differs from 64% .

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.64\\\\H_a:\pi\neq 0.64[/tex]

The significance level is 0.05.

The sample has a size n=100.

The sample proportion is p=0.52.

[tex]p=X/n=52/100=0.52[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.64*0.36}{100}}\\\\\\ \sigma_p=\sqrt{0.0023}=0.048[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.52-0.64+0.5/100}{0.048}=\dfrac{-0.115}{0.048}=-2.3958[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as:

[tex]P-value=2\cdot P(z<-2.3958)=0.0166[/tex]

As the P-value (0.0166) 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 the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup differs from 64% .

Answer:

Step-by-step explanation:

Hello!

The manager of the store made a linear regression analysis to study if the amount of newspaper advertising (independent variable, X) significantly affects the sales (dependent variable, Y)

The coefficient of determination R² is a statistic that measures the percentage of the variability of Y that is explained by X in the context of the regression model. It also determines the ability of the model to replicate the results of the analysis.

The Excel output is attached below, the calculated determination coefficient is:

R²= 0.726

Interpretation

72.6% of the variability of the estimated average daily sales of the grocery store is explained by the amount of newspaper advertisement placed under the estimated model.

I hope this helps!

Answer: the answer is 14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Correct on edge 2021

Answer:

No

Step-by-step explanation:

If q=30​, L=5​, and K=15 is a point on the production function q=​f(L, ​K).

Production function is an equation that expresses the relationship between the quantities of factors of production used and the amount of product obtained under the assumption that the most efficient available methods of production are used.

The combination q=30​, L=5​, and K=16 cannot be a point because we assume production functions are efficient.

Answer:

option E is correct which states that cannot be a point because we assume production functions are efficient.

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:

C.

Step-by-step explanation:

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.

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Answer:

Step-by-step explanation:

Given that,

The square based prism has  dimensions is

6 by 6 by 10

Length = 6

Width = 6

Height = 10

Slant height of pyramid is given as

h = 10.6

Note: The base of the pyramid matches the top of the square prism, so it's square-based prism.

So, we are going to have

4 rectangular faces(i.e the square Base prism rectangular faces)

1 square face ( the based of the prism)

four triangular faces( the top pyramid)

So, area of the four face

It is a rectangular shape and it is calculated using

A = length × Breadth

Area of one face is

A = L × W

A = 6 × 10 = 60 Square units

And there are 4 similar rectangle

So, area of the four rectangles is

A' = 4 × 60 = 240 square unit

Now, area of the square base below can be calculated using

A = s²

A" = L² = 6² = 36 Square units

Now, area of the four triangle pyramid at the top

Area of triangle is given as

A = ½bh

A = ½ × 6 × 10.6

A = 31.8 square units.

The area of the four triangles becomes

A"' = 4 × 31.8

A"' = 126 square units

Then, the total area of the shape is

A(total ) = A' + A" + A"'

A(total) = 240 + 36 + 126

A(total) = 402 Square units

So, the total area of the solid shape is 402 Square units

Answer: D. 7 or 12

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

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:

  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:

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:

The angle between a line from 1 o'clock to 6 o'clock and a horizontal line is 150 degrees.

* The clock face has hours spaced 30 degrees apart.

* You want to find the angle between a line from 1 o'clock to 6 o'clock and a horizontal line.

1. **Finding the angle between consecutive hours:** Each hour on the clock face is 30 degrees apart from its neighbors. Therefore, the angle between 1 o'clock and 2 o'clock is 30 degrees, and the angle between 2 o'clock and 3 o'clock is also 30 degrees, and so on.

2. **Calculating the angle from 1 o'clock to 6 o'clock:** To get from 1 o'clock to 6 o'clock, we must move five hour marks counter-clockwise. Since each hour mark represents 30 degrees, moving five marks corresponds to an angle of 5 * 30 degrees = 150 degrees.

Therefore, the angle between a line from 1 o'clock to 6 o'clock and a horizontal line is 150 degrees.

Answer:

nothing

Step-by-step explanation:

nothing

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:

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:

[tex]438.53-2.12\frac{14.988}{\sqrt{17}}=430.82[/tex]    

[tex]438.53+2.12\frac{14.988}{\sqrt{17}}=446.24[/tex]    

So on this case the 95% confidence interval would be given by (430.82;446.24)    

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

[tex]\bar X[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

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

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

In order to calculate the mean and the sample deviation we can use the following formulas:  

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

[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)  

The mean calculated for this case is [tex]\bar X=438.53[/tex]

The sample deviation calculated [tex]s=14.988[/tex]

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=17-1=16[/tex]

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,16)".And we see that [tex]t_{\alpha/2}=2.12[/tex]

Now we have everything in order to replace into formula (1):

[tex]438.53-2.12\frac{14.988}{\sqrt{17}}=430.82[/tex]    

[tex]438.53+2.12\frac{14.988}{\sqrt{17}}=446.24[/tex]    

So on this case the 95% confidence interval would be given by (430.82;446.24)    

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 square root of 72 which is approximately 8.5

Step-by-step explanation:

When draw a line diagonally in a square you get 2 right triangles so you can do pathogream theorem on them so a squared plus b squared equals c squared. In this case 6^2 + 6^2 = c^2. By solving you get the answer

The length of the pipeline running diagonally across the square field is 8.485 kilometers.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the sides of the square field are each 6 kilometers long. Let's sides of the square as a, b, and c, where c is the length of the diagonal (the pipeline) and a and b are the sides of the square.

Using the Pythagorean theorem, we have:

c² = a² + b²

Since the square field is a square, all sides are equal, so a = b = 6 kilometers.

c² = 6² + 6²

c² = 36+ 36

c² = 72

c = 8.485 Km

Therefore, the length of the pipeline running diagonally across the square field is 8.485 kilometers.

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Answer:

see explaination

Step-by-step explanation:

Let mu1 be the mean for exclusively breaststroke

Let mu2 be the mean for individual medley

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

(a) H o: mu1=mu2 (i.e. null hypothesis)

Ha: mu1> mu2 (i.e. alternative hypothesis)

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

(b) Since both sample sizes are grearter than n=30, we can use normal distriubtion.

It is a one-tailed test.

Given a=0.01, the critical value is Z(0.01) =2.33 (from standard normal table)

So the rejection region is Z>2.33

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

(c) The test statistic is

Z=(xbar2-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(9017-5853)/sqrt(7162^2/130+1961^2/80)

=4.76

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

(d) Since Z=4.76 is larger than 2.33, we reject the null hypothesis.

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

(e) In conclusion there is sufficient evidence to indicate that the average number of meter per week spent practicing breaststroke is greater for exclusive breaststrokers than it is for those swimming individual medley

There is sufficient evidence to indicate that the mean number of breaststroke is greater for exclusive breaststrokers than for swimming individual medley.

In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

Let μ₁ be the mean for the exclusive breaststroke.

Let μ₂ be the mean for the individual medley.

For the null hypothesis, we have

H₀: μ₁ = μ₂

For the alternative hypothesis, we have

Hₐ: μ₁ > μ₂

The sample size of both is greater than 30, then the normal distribution will be

a = 0.01

The critical value is z(0.01) = 2.33 (From standard normal table)

So the rejection region is z > 2.33

The test statistic will be

[tex]z = \dfrac{\mu_2 - \mu_1}{\sqrt{s^2_1/n_1 + s^2_2/n_2}}\\\\\\z = \dfrac{9017 - 5853}{\sqrt{7162^2/130+1961^2/80}}\\\\\\z = 4.76[/tex]

Since the value of z is greater than 2.33, then we reject the null hypothesis.

More about the null hypotheses and alternative hypotheses link is given below.

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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:

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

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:

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:

associative property of addition

Step-by-step explanation:

The 5 is substituted into the parentheses and the 7 is taken out.

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