Toxic Pollution: In the first year of a study, health officials discovered toxic pollutants in the soil surrounding a factory. The initial measurement was 65 parts per million (ppm) of pollutant. They returned to take similar measurements for several years afterward, and uncovered a disturbing trend. The pollutant levels in the soil surrounding the factory were growing exponentially, at a rate of 4.5% each year. Which exponential model predicts the amount of pollutant in the soil t years from the first measurement?

Answer:

  A. 2(Pi)rh+2(Pi)r^2

Step-by-step explanation:

The surface area of a cylinder is the sum of the lateral area and the area of the two circular ends.

The lateral area is the product of the circumference of the cylinder and its height:

  lateral area = 2πrh

The area of the two ends is twice the area of each of those circles, so is ...

  total end area = 2(πr²)

Then the total surface area of a cylinder is ...

  SA = 2πrh +2πr²

Answer:

e) None of the above

Step-by-step explanation:

We are in posession of the sample's standard deviation, so we use the student t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 43 - 1 = 42

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 42 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0181

The margin of error is:

M = T*s = 2.0181*11.3 = 22.80

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 77.86 - 22.8 = 55.06

The upper end of the interval is the sample mean added to M. So it is 77.86 + 22.8 = 100.66.

So the correct answer is:

e) None of the above

Answer:

[tex]77.86-2.02\frac{11.30}{\sqrt{43}}=74.38[/tex]    

[tex]77.86+2.02\frac{11.30}{\sqrt{43}}=81.34[/tex]    

And for this cae none of the options satisfy the result so then the best option would be:

e) None of the above

Step-by-step explanation:

Information given by the problem

[tex]\bar X= 77.86[/tex] represent the sample mean for the score

[tex]\mu[/tex] population mean  

s=11.30 represent the sample standard deviation

n=43 represent the sample size  

Calculating the confidence interval

The confidence interval for the true mean of interest is given by:

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

For this case the degrees of freedom are:

[tex]df=n-1=43-1=42[/tex]

The Confidence is 0.95 or 95%, the significance then is [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the critical value for this case would be [tex]t_{\alpha/2}=2.02[/tex]

And replacing in equation (1) we got:

[tex]77.86-2.02\frac{11.30}{\sqrt{43}}=74.38[/tex]    

[tex]77.86+2.02\frac{11.30}{\sqrt{43}}=81.34[/tex]    

And for this cae none of the options satisfy the result so then the best option would be:

e) None of the above

hi

Here is the answer :

0.25 *140 = 35

Answer: 35

Step-by-step explanation: Well percent means over 100 so we can set up an equation for this problem by reading it from left to right.

What means x, is means equals, 25% is 25/100,

of means times, and 250 means 250.

So we have the equation x = 25/100 · 40.

Simplifying on the right side of the equation,

notice that 25/100 reduces to 1/4.

So we have x = 1/4 · 40.

Think of the 40 as 40/1.

So we can cross-cancel 140 and 4 to 35 and 1

and we have x = (1)(35) over (1)(1) or x = 35.

Now let's check our answer back in the

original problem to see if it makes sense.

We have (35) is 25% of 140.

Well we know that 100% of 140 would be 140.

So 25% of 250 should be a lot less than 140.

So 35 seems to make sense as a pretty good answer.

I have shown my work in the image attached.

Answer:

The answer would be 56.55ft please give brainliest :)

Answer:

55.65

Step-by-step explanation:

Answer:

[tex]a_{n}[/tex] = 8 *[tex]0.5^{n-1}[/tex]

Step-by-step explanation:

First find the common ratio

r = 4/8 = 1/2

and first term is 8

a_n = a_1 * r^(n-1)

a_n = 8 * (1/2)^(n-1)

[tex]a_{n}[/tex] = 8 *[tex]0.5^{n-1}[/tex]

Answer:

The mean of the total repair time is 150 minutes.

The variance of the total repair time is 725 minutes^2.

Step-by-step explanation:

To solve this problem, we have to use the properties of the mean and the variance. Our random variable is the sum of 3 normal variables.

In the case, for the mean, we have that the mean of the sum of 3 normal variables is equal to the sum of the mean of the 3 variables:

[tex]y=x_1+x_2+x_3 \\\\E(y)=E(x_1+x_2+x_3)=E(x_1)+E(x_2)+E(x_3)\\\\E(y)=50+60+40=150[/tex]

For the variance, we apply the property for the sum of independent variables (the correlation between the variables is 0):

[tex]V(y)=V(x_1)+V(x_2)+V(x_3)\\\\V(y)=s_1^2+s_2^2+s_3^2\\\\V(y)=15^2+20^2+10^2\\\\V(y)=225+400+100\\\\V(y)=725[/tex]

The product of each number and 3x in the set [-6, -11, -14, -9] is [-18x, -33x, -42x, -27x]. The term 'product' refers to the result of multiplication. This was calculated by individually multiplying each number in the set by 3x.

The question is asking what the product would be if you multiplied each number in the array by 3x. In mathematical terms, product refers to the result obtained from multiplying at least two numbers together.

Here's how we'd do this:

So, in conclusion, the set of numbers you get when you multiply the original set by 3x are: [-18x, -33x, -42x, -27x]. You calculate these one at a time, following the laws of multiplication. I hope that helps explain in detail what the term 'product' means in this mathematical context, and how to find it.

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Answer:8

Step-by-step explanation:

2x4=2x2x2

4x2=2x2x2

The greatest common factor is 2x2x2=8

1

2

0

x

+

120x+392

Step-by-step explanation:

Answer:

  n(A) = 2701

Step-by-step explanation:

If we subtract 299 from the numbers in the set, we get the counting numbers ...

  {1, 2, 3, ..., 2701}

The number of elements in the set is 2701:

  n(A) = 2701

n(A) is a notation used to denote the number of elements in a set. For the set A = {300, 301, 302, ..., 3000}, n(A) is calculated as 2701.

To find n(A) for the set A = {300, 301, 302, ..., 3000}, let's first understand that n(A) means. n(A) is a notation used in set theory to denote the number of elements in a set. In this case, it’s asking for the total number of integers from 300 to 3000.

You can calculate it by using the formula n = the last number - the first number + 1. Substituting the given values, we get n = 3000 - 300 + 1 = 2701. Therefore, n(A) for the set is 2701.

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Answer:

$0.11 (2 d.p.)

Step-by-step explanation:

Please see the attached picture for the full solution.

The cost of one pencil is 10.75 cents.

First, convert the total cost from dollars to cents.

As we know,

Since $1.29 is equal to 129 cents:

$1.29 * 100

= 129 cents.

Next,

divide 129 cents by 12 pencils to find the cost per pencil:

129 cents / 12 pencils

= 10.75 cents.

So, the cost of one pencil is 10.75 cents.

Answer:

The 95% confidence interval for the population proportion is (0.778, 0.884).

Step-by-step explanation:

We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.831.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.831*0.169}{195}}\\\\\\ \sigma_p=\sqrt{0.00072}=0.027[/tex]

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.027=0.053[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sisgma_p = 0.831-0.053=0.778\\\\UL=p+z \cdot \sisgma_p = 0.831+0.053=0.884[/tex]

The 95% confidence interval for the population proportion is (0.778, 0.884).

Answer:

d. can be equal to the value of the coefficient of determination (r2).

True on the special case when r =1 we have that [tex] r^2 = 1[/tex]

Step-by-step explanation:

We need to remember that the correlation coefficient is a measure to analyze the goodness of fit for a model and is given by:

[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]  

The determination coefficient is given by [tex] R= r^2[/tex]

Let's analyze one by one the possible options:

a. can never be equal to the value of the coefficient of determination (r2).

False if r = 1 then [tex] r^2 = 1[/tex]

b. is always larger than the value of the coefficient of determination (r2).

False not always if r= 1 we have that [tex] r^2 =1[/tex] and we don't satisfy the condition

c. is always smaller than the value of the coefficient of determination (r2).

False again if r =1 then we have [tex] r^2 = 1[/tex] and we don't satisfy the condition

d. can be equal to the value of the coefficient of determination (r2).

True on the special case when r =1 we have that [tex] r^2 = 1[/tex]

The correct answer is d. can be equal to the value of the coefficient of determination (r²).

The coefficient of correlation (r) and the coefficient of determination (r²) are related statistical measures used to describe the strength and direction of the linear relationship between two variables.

The coefficient of correlation (r) quantifies the strength and direction of this linear relationship, ranging from -1 to 1, where -1 represents a perfect negative correlation, 1 represents a perfect positive correlation, and 0 represents no linear correlation.

On the other hand, the coefficient of determination (r²) is simply the square of the coefficient of correlation and represents the proportion of variance in one variable that can be explained by the linear relationship with the other variable.

Since r² is the square of r, it's entirely possible for them to be equal. In fact, when r is either 1 or -1 (perfect correlations), r² will be equal to 1, indicating that 100% of the variance in one variable is explained by the linear relationship with the other variable.

Similarly, when r is 0 (no linear correlation), r² will be equal to 0, indicating that none of the variance in one variable is explained by the linear relationship with the other variable.

So, the relationship between r and r² depends on the strength of the linear correlation, and they can indeed be equal under certain conditions.

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Answer:

10

Step-by-step explanation:

When two numbers are placed together that close with parenthesis, you are most likely (99.9% of the time), going to be multiplying them.

Note that:

When you multiply two positive numbers, your result is positive.

When you multiply one negative and one positive number, your result will be negative.

When you multiply two negative numbers, your result will be positive.

Multiply -5 with -2: -5 * -2 = 10

10 is your answer.

~

Answer:

750000

Step-by-step explanation:

3 times 2.5 = 7.5 then to convert to grams times by 1000 which is 750000

Answer:

[tex]t=\frac{4917.5-5000}{\frac{450}{\sqrt{81}}}=-1.65[/tex]    

The degrees of freedom for this case are:

[tex]df=n-1=81-1=80[/tex]  

We need to find a critical value in the t distribution with 80 degrees of freedom who accumulates 0.05 of the area in the left and we got:

[tex] t_{cric}= -1.664[/tex]

Since the calculated value is not less than the critical value we don't have enough evidence to conlcude that the true mean is significantly lower than 5000 hours. Then the claim by the manufacturer (product lasts at least 5000 hours) makes sense.

Step-by-step explanation:

Information given

[tex]\bar X=4917.5[/tex] represent the sample mean

[tex]s=450[/tex] represent the sample standard deviation

[tex]n=81[/tex] sample size  

[tex]\mu_o =5000[/tex] represent the value to check

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic (variable of interest)  

System of hypothesis

We want to determine if product lasts at least 5000 hours, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 5000[/tex]  

Alternative hypothesis:[tex]\mu < 5000[/tex]  

The statistic for a one sample t testo for the true mean is given by:

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

Replacing the info given we got:

[tex]t=\frac{4917.5-5000}{\frac{450}{\sqrt{81}}}=-1.65[/tex]    

The degrees of freedom for this case are:

[tex]df=n-1=81-1=80[/tex]  

We need to find a critical value in the t distribution with 80 degrees of freedom who accumulates 0.05 of the area in the left and we got:

[tex] t_{cric}= -1.664[/tex]

Since the calculated value is not less than the critical value we don't have enough evidence to conlcude that the true mean is significantly lower than 5000 hours. Then the claim by the manufacturer (product lasts at least 5000 hours) makes sense.

Answer:

The total number of items to be counted each day ≈ 100

Step-by-step explanation:

Lindsay​ Electronics has 6,500 items in its inventory.

11​% of the items in inventory are A​ items

33% of the items in inventory are B items

56​% of the items in inventory are C items

A items are counted every 20 working​ days

B items are counted every 62 working​ days

C items are counted every 121 working​ days

How many items need to be counted each​ day?

First we will find the number of items of type A, B and C

Number of A​ items = 11​% of 6,500 = 0.11*6500 = 715

Number of B items = 33% of 6,500 = 0.33*6500 = 2145

Number of C items = 56% of 6,500 = 0.56*6500 = 3640

The number of A items to be counted each day is

A items = 715/20

The number of B items to be counted each day is

B items = 2145/62

The number of C items to be counted each day is

C items = 3640/121

The total number of items to be counted each day is

Total items = 715/20 + 2145/62 + 3640/121

Total items = 100.42

Rounding the answer to the nearest whole number yields,

Total items ≈ 100

Answer:

Square root of 1040.

Or decimal form - 32.249

Step-by-step explanation:

Answer:

The amount of money he has in the account after 3 years:

A = Money x (1 + rate)^year

  = 2000 x (1 + 4.3/100)^3

  =2269.3 dollar

Hope this helps!

:)

Answer:

Amount of money in the account:   $2,269.25

Interest: $269.25

Step-by-step explanation:

John starts out with $2000 in savings.

(I can't be bothered to find the formula for annual compound interest, so we'll do it manually based on yearly calculations.)

Because it is calculated annually, we must do yearly calculations.

2,000 x 1.043 = 2,086.00

After the first year, at 4.3% John's $2000 Savings account would mature into $2,086.00. (earning him $86.00 interest for the year)

2,086.00 x 1.043 = 2,175.70

After, the second year at 4.3%,  $2,086.00 becomes $2,175.70.  (making his interest $175.70 total, and $89.70 for the year.)

2,175.70 x 1.043 = 2,269.25

After the third, and final year, at 4.3%, $2,175.70 becomes $2,269.25. (making the interest $269.25 or $93.56 for the year.)

Answer:

[tex]z = \frac{4-4.25}{\frac{1.5}{\sqrt{40}}}= -1.054[/tex]

And we can find the following probability:

[tex] P(z<-1.054) = 0.146[/tex]

And the last probability can be founded using  the normal standard distribution or excel.

Step-by-step explanation:

For this case we define the random variable X as the ages of vehicles. We know the following info for this variable:

[tex]\bar X = 4.25[/tex] represent the mean

[tex]\sigma =18/12=1.5[/tex] represent the deviation in years

They select a sample size of n=40>30. And they want to find this probability:

[tex] P(\bar X<40)[/tex]

Since the sample size is large enough we can use the central limit theorem and the distribution for the sample mean would be:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) [/tex]

We can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score for 4 we got:

[tex]z = \frac{4-4.25}{\frac{1.5}{\sqrt{40}}}= -1.054[/tex]

And we can find the following probability:

[tex] P(z<-1.054) = 0.146[/tex]

And the last probability can be founded using  the normal standard distribution or excel.

Answer:

D.

Step-by-step explanation:

Density = mass / volume

Density= 3 , mass = 80

3 = 80 / volume

Volume = 80 / 3

Volume = 26.67 cubic inch

Now volume of a cube= 3 (side length)

26.67 = 3(side length)

Side length=26.67 /3

Side length=8.89 inches

Side length ≈ 9 inches

Answer:

Step-by-step explanation:

a) A test of H0​: p = 0.6 vs. HA​: p < 0.6 fails to reject the null hypothesis. Later it is discovered that p = 0.7.

Answer: No error has been made since there is not enough statistical evidence to reject the null.

b) A test of H0​: μ = 30 vs. HA​: μ > 30 rejects the null hypothesis. Later it is discovered that μ = 29.9. ​

A type I error has been made. Rejecting the null hypothesis when it is actually true.

c) A test of H0​: p = 0.4 vs. HA​: p /= 0.4 rejects the null hypothesis. Later it is discovered that p = 0.55.

A type I error has been made since the p value was greater than 0.4, one will fail to reject the null but in the case the null was rejected.

d) A test of H0​: p = 0.7 vs. HA​: p < 0.7 fails to reject the null hypothesis. Later it is discovered that p = 0.6.

A type II error has been made since the p value is less than 0.7 and it was expected that the null should be rejected but that ws not the case.

In situation a and d, a Type II error was made as the null hypothesis was not rejected but it should have been. In situation b, a Type I error was made as the null hypothesis was rejected but it shouldn't have been. In situation c, neither error was made as the null hypothesis was correctly rejected.

In each of the following situations, different types of errors are made. A type I error is made when the null hypothesis is true, but it is rejected. A type II error is the opposite, when the null hypothesis is false, but it isn't rejected.

   d) Type II error: The null hypothesis was not rejected, although the actual population proportion (0.6) was less than the hypothesized proportion (0.7).    

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Answer:

[tex]90\pi[/tex]

Step-by-step explanation:

The first step is to find the slant height of the cone. Using the pythagorean theorem, you can find that [tex]\sqrt{12^2+5^2}=13[/tex] cm. Plugging this into the equation, you get [tex]\pi \cdot 5 \cdot 13=90\pi[/tex]. Hope this helps!

Answer:

(D)117 Cubic Inches

Step-by-step explanation:

Dimensions of the box are:

Length[tex]=7\frac{1}{2}\:inch[/tex]

Width[tex]=4\frac{1}{3}\:inch[/tex]

Height[tex]=3\frac{3}{5}\:inch[/tex]

Volume of the Box =Length X Width X Height

[tex]=7\dfrac{1}{2}X4\dfrac{1}{3}X3\dfrac{3}{5}\\\\=\dfrac{15}{2}X\dfrac{13}{3}X\dfrac{18}{5}\\\\=\dfrac{15X13X18}{2X3X5}\\\\=\dfrac{3510}{30}[/tex]

=117 Cubic Inches

The volume of the box is 117 cubic inches.

Answer:

D) 117 cubic inches

Step-by-step explanation:

Have a wonderful day!

Answer: C 5/16

stay safe !!!

The probability that a randomly selected player on Team C 10 years old is 5/16.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

According to the table the total number of 10 years old players on Team C is 5 and the total number of all ages players (8, 9 and 10 years old) on Team C is 16,

So the probability that a randomly selected player on Team C is 10 years old is 5/16.

Therefore, the probability that a randomly selected player on Team C 10 years old is 5/16.

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Answer:

0.3

Step-by-step explanation:

Given: The odds of winning a contest are 3:7

To find: probability of winning the contest

Solution:

Probability refers to chances of occurrence of an event.

Odds are defined as (chances for success) : (chances against success)

Probability of winning = (chances for success) : (chances for success + chances against success)  

As odds of winning a contest are 3:7,

(chances for success) : (chances against success) = 3:7

So,

Probability of winning the contest = [tex]\frac{3}{3+7} =\frac{3}{10}=0.3[/tex]

Final answer:

To find the probability of winning a contest when given odds, add the two parts of the odds together and divide the favorable outcome by the total outcomes. For odds of 3:7, the probability of winning the contest is 3/10.

Explanation:

The odds of winning a contest are 3:7. What is the probability of winning the contest?

To find the probability from odds, you need to add the two numbers together to get the total possible outcomes. In this case, 3 + 7 = 10. Then, divide the favorable outcome by the total outcomes, so 3/10. This gives a probability of winning the contest as 3/10.

Answer:

I will answer a few questions so you can apply the same logic to the others

The volume of a sphere = [tex]\frac{4}{3}[/tex] π [tex]r^{3}[/tex]

1.

We can see that the radius of the sphere is 5cm

Substitute the value into the equation for volume and solve for V

V = [tex]\frac{4}{3}[/tex] * π * [tex]5^{3}[/tex]

V = 523.6 [tex]cm^{3}[/tex]

4.

The diameter is given to us as 6km. To find the radius we take half of this, 3km

Substitute the value into the equation for volume and solve for V

V = [tex]\frac{4}{3}[/tex] * π * [tex]3^{3}[/tex]

V = 113.1 [tex]km^{3}[/tex]

Hopefully that helps you with completing the rest!