f(x)= 2000 (2\(2^x\)

Answer:

The expression representing the perimeter of the platter will be:

P = 10/3x units

Hence, option (D) is true.

Step-by-step explanation:

Let the length l of a rectangular platter will be =  x

As the width of a rectangular platter is 2/3 its length.

so the width w of a rectangular platter will be = 2/3x

As the perimeter of the platter is defined as:

P=2(l+w)

where l is the length, and w is the width

substituting length l = x and width w = 2/3x

\(P=2\left(x\:+\:\frac{2}{3}x\right)\)

    \(=2\cdot \frac{5}{3}x\)             ∵ \(x\:+\:\frac{2}{3}x=\:\frac{5}{3}x\)

    \(=\frac{10x}{3}\) units

Therefore, the expression representing the perimeter of the platter will be:

P = 10/3x units

Hence, option (D) is true.

Answer:

D.

Step-by-step explanation:

The lateral surface area measures the area of the outside of the 3D shape. *Doesn't include the bases.

Since the measure of the outside of a cylinder is essentially a RECTANGLE, the formula for area is length x width. The length here would be the height, the width would be the circumference.

The selling price to earn $10 per Bible if 5,000 Bibles are printed when the fixed costs per print is $15,000 and variable costs are $25 per Bible, is $38.

The target profit is the profit that is expected by a manufacturer from the sale of its product.

The target profit can be established and used to determine the selling price.

When the target profit is added to the fixed cost per unit and the variable cost per unit, the resultant figure is the selling price.

Fixed costs per print = $15,000

Number of Bibles per print = 5,000

Fixed costs per Bible = $3 ($15,000/5,000)

Variable costs per Bible = $25

Expected profit per Bible = $10

The selling price = $38

Thus, the selling price to earn $10 per Bible if 5,000 Bibles are printed when the fixed costs per print is $15,000 and variable costs are $25 per Bible, is $38.

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Answer:

800

Step-by-step explanation:

800

Answer:

Length is 67

Step-by-step explanation:

For the show your work bit, your gonna wanna divide 4288 by 64 to get 67 as your length. Then draw your rectangle with the 64 square feet on one side and put a w next to it. Then on the next side write 67 square feet with an L next to it. Hope this helped!!

We are 90% confident that the true difference between the mean strengths of the two types lies between 0.015 and 0.105. The data does not show at the 0.05 level that the mean strengths are different, with a p-value of approximately 0.055. Therefore, we fail to reject the null hypothesis that the means are equal.

To find a 90% confidence interval for the difference in the mean strengths of the two types, we can use the two-sample t-test with pooled variance. The formula for the confidence interval is:

\($(\bar{x}_1 - \bar{x}2) \pm t{\alpha/2,\nu} \cdot s_p \cdot \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$\)

Plugging in the given values, we get:

\(\bar{x}1 = 3.18, \bar{x}2 = 3.24, n_1 = 5, n_2 = 7, s_p = \sqrt{\frac{ (n_1 - 1)s_1^2 + (n_2 - 1)s_2^2 }{ df }} = \sqrt{\frac{ (40.042^2 + 60.048^2) }{ 10 }} = 0.046, t{\alpha/2,\nu} = t{0.05/2,10} = 2.306$\)

Therefore, the 90% confidence interval for the difference between the mean strengths of the two types is:

\($(3.24 - 3.18) \pm 2.306 \cdot 0.046 \cdot \sqrt{\frac{1}{5}+\frac{1}{7}} = 0.06 \pm 0.045$\)

So the interval is (0.015, 0.105).

Thus, we are 90% confident that the true difference between the mean strengths of the two types lies between 0.015 and 0.105.

To test whether the mean strengths are different, we can use a two-tailed hypothesis test with a significance level of 0.05. The null hypothesis is that the means are equal, while the alternative hypothesis is that they are different. We can calculate the t-value as:

\($t = \frac{\bar{x}_1 - \bar{x}_2}{s_p \cdot \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} = \frac{3.18-3.24}{0.046 \cdot \sqrt{\frac{1}{5}+\frac{1}{7}}} = -2.13$\)

The degrees of freedom are the same as before, \($df = n_1 + n_2 - 2 = 10$\)

The p-value is the probability of getting a t-value at least as extreme as the observed one, assuming the null hypothesis is true. From a t-distribution table, we can find that the p-value for t = -2.13 with df = 10 is approximately 0.055. Since this is greater than the significance level of 0.05, we fail to reject the null hypothesis.

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Answer:

f(3) = 100

Step-by-step explanation:

Using the recursive formula and f(1) = 1 , then

f(2) = - 10 f(1) = - 10 × 1 = - 10

f(3) = - 10 f(2) = - 10  × - 10 = 100

Answer:

100

Step-by-step explanation:

Answer:

n = -2

Step-by-step explanation:

\(\frac{-5}{6}n-\frac{1}{6}=\frac{-1}{3}+\frac{11}{6}\\\\\frac{-5}{6}n=\frac{-1}{3}+\frac{11}{6}+\frac{1}{6}\\\\\frac{-5}{6}n=\frac{(-1)*2}{3*2}+\frac{11}{6}+\frac{1}{6}\\\\\frac{-5}{6}n=\frac{-2}{6}+\frac{11}{6}+\frac{1}{6}\\\\\frac{-5}{6}n=\frac{-2+11+1}{6}\\\\\frac{-5}{6}n=\frac{10}{6}\\\\n=\frac{10}{6}*\frac{6}{-5}\\\\n= -2\)

Answer:

Quadrant IV

Step-by-step explanation:

An angle whose measure is _302° is in standard position the terminal side of the angle fall in Quadrant IV

Answer:

I think its gonna be 162.860

Answer:

P(all female)= 1/2 x 1/2 x 1/2 = 1/8

P(all male ) = 1/2 x 1/2 x 1/2 = 1/8

P(all one gender) = P(all female) + P(all male) = 1/8 + 1/8 = 1/4

What is the probability that a three-child family is two girls and one boy?

Each possible birth order has P=1/8. That is, P(G,G,B)=P(G,B,G)=P(B,G,G)=1/8.

So, P(2G,1B)= 3/8 and P(1G,2B)= 3/8.

This allows us to write the overall gender probability distribution for families of three children as follows:

1/8 will be three girls

3/8 will be two girls and one boy

3/8 will be one girl and two boys

1/8 will be three boys

Adding it all up, we have 1/8 + 3/8 + 3/8 + 1/8 = 1 (100%)

Step-by-step explanation:

Based on the given linear equations, the number of 7th-grade students and 8th-grade students is 120 students and 150 students respectively. Hence, Mia's solution is correct.

The value of h in the given linear equation is determined as follows:

9 rectangles = 270 students

1 rectangle = 30 students

7 + h = 11

h = 11 - 7

h = 4

The number of 7th-grade students and 8th-grade students is then determined as follows:

7th-grade students:

4 * 30 = 120 students

8th-grade students:

5 * 30 = 150 students

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Answer:600kgms-1

Step-by-step explanation:

mass *velocity

60*10 =600

This correlation indicates that there is a strong negative relationship between students' level of optimism and their scores on the exam.

This correlation indicates that there is a strong negative relationship between students' level of optimism and their scores on the exam.

A correlation is a measure of the linear relationship between two variables. A correlation of -0.68 indicates that there is a strong negative relationship between the two variables, meaning that as the level of optimism increases, the exam scores decrease.

This correlation indicates that there is a strong negative relationship between students' level of optimism and their scores on the exam.

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Completely factored expressions are:

1. x² - 7x - 18 can be factored as:

(x - 9)(x + 2)

Expand the expression using FOIL:

(x - 9)(x + 2) = x² + 2x - 9x - 18 = x² - 7x - 18

2. p² - 5p - 14 can be factored as:

(p - 7)(p + 2)

Expand the expression using FOIL:

(p - 7)(p + 2) = p² + 2p - 7p - 14 = p² - 5p - 14

3. m² - 9m + 8 can be factored as:

(m - 1)(m - 8)

Expand the expression using FOIL:

(m - 1)(m - 8) = m² - 8m - m + 8 = m² - 9m + 8

Therefore, the completely factored expressions are:

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Answer:

Answer:

discovery of jupiter's mons which did not orbit earth

Step-by-step explanation:

The probability that Y=1 given X=2 and Z=3 is 1/3.

Given that X, Y, and Z have joint distribution as shown below:

\(f(x, y, z) = \frac{xy^2z}{180}, x=1,2,3;y=1,2;z=1,2,3\)

We need to find \(P(Y=1|X=2, Z=3)\).

Therefore, we can use the conditional probability formula:

\(P(Y = 1 | X = 2, Z = 3) = \frac{P(Y = 1, X = 2, Z = 3)}{P(X = 2, Z = 3)}\)

Now we find the numerator and denominator individually:

Numerator: \(P(Y = 1, X = 2, Z = 3)\)

Here, we fix X=2, Z=3 in the given probability distribution and find the value of Y=1.

\(P(Y = 1, X = 2, Z = 3) = f(2, 1, 3) = \frac{2(1)^2(3)}{180} \\= \frac{1}{15}\)

Denominator: \(P(X = 2, Z = 3)\)

We fix Z=3 in the given probability distribution and sum over all values of Y to get the probability of X=2 and Z=3.

\(P(X = 2, Z = 3) = \sum_{y=1}^{3} f(2,y,3)P(X = 2, Z = 3) = f(2,1,3) + f(2,2,3) + f(2,3,3)\\P(X = 2, Z = 3) = \frac{2(1)^2(3)}{180} + \frac{2(2)^2(3)}{180} + \frac{2(3)^2(3)}{180}\\P(X = 2, Z = 3) = \frac{1}{5}\)

Substituting these values in the conditional probability formula, we get:

\(P(Y = 1 | X = 2, Z = 3) = \frac{P(Y = 1, X = 2, Z = 3)}{P(X = 2, Z = 3)}\\P(Y = 1 | X = 2, Z = 3) = \frac{\frac{1}{15}}{\frac{1}{5}}\\P(Y = 1 | X = 2, Z = 3) = \frac{1}{3}\)

Therefore, the probability that Y=1 given X=2 and Z=3 is 1/3.

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The number of people surveyed is 20

In statistics, the sample size is the value of the number of individual samples used in an experiment. For example, if we are testing 100 samples of people who play cricket, then the sample size will be equal to 100.  

If a point of estimation is available then the formula for sample size n is given by      

Sample size n = p(1 - p)[ \(Z_{\alpha /2}\)/ E ]²    

Where p is the point of estimation

\(Z_{\alpha /2}\) is the critical value

E is the margin of error        

Here we have

51​% of the people polled answered yes to the question​ "Are you in favor of the death penalty for a person convicted of​ murder?"

Here estimated point p = 51% = 0.51

The margin of error E = 22​% = 0.22

The estimate was made with 95​% confidence.  

Then the critical value  \(Z_{\alpha /2}\) = 1.96  

Here we need to find how many people were​ surveyed        

From the above observations,

n = p(1 - p)[ \(Z_{\alpha /2}\)/ E ]²            

=>  0.51 (1 - 0.51) [ 1.96 / 0.22 ]²            

=>  0.51 (0.49) [ 8.91 ]²

=>  0.51(0.49) (79.3718)

=>  19.83    

=> 20   (approximately )                          

Therefore, the number of people surveyed is 20

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The Complete question:

In a​ poll, 51​% of the people polled answered yes to the question​ "Are you in favor of the death penalty for a person convicted of​ murder?" The margin of error in the poll was 22​%, and the estimate was made with 95​% confidence. At least how many people were​ surveyed?

The minimum number of surveyed people was?

The data source in this case is an advertisement, which is a form of secondary data.

Secondary data is information collected by someone other than the user. In this case, the television ad is promoting a specific car brand as being "considered to be the best" and suggesting that "now is the best time to replace your car". This information is not based on a sample or experimental data, but rather on the claims made by the car brand itself in their advertisement.

The data source in this case is secondary data, specifically an advertisement. This means that the information provided should be critically evaluated and further research should be conducted to verify its accuracy and reliability.

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Answer: y = 6x

Step-by-step explanation:

Since this is a direct proportion, we will introduce the constant of proportionality here and this will be:

y = kx

Since y = 30 and x= 5,

30 = 5 × k

30 = 5k

k = 30/5

k = 6

Therefore, the equation that connects y to x will be:

y = kx

y = 6x

The equation that connects y to x is y = 6x.

Answer:

0.12

Step-by-step explanation:

there are 128 fluid ounces in 1 gallon

15.36 / 128 = 0.12

Answer:

70 degrees

Opposite angles are equal to each other

Step-by-step explanation:

s = 3 and t = 2

= 2(8 + t)³ - 6

= 2(8 + 2)³ - 6

= 2(10)³ - 6

= 2(1.000) - 6

= 2.000 - 6

= 1.994

There have been numerous cases of athletes being accused of using performance-enhancing drugs, and the numbers may vary depending on the sport, country, and time period in question.

Additionally, determining how many athletes were using or not using performance-enhancing drugs would require specific information on individual cases.

Regarding the percentage of athletes falsely accused of using performance-enhancing drugs, it is difficult to determine an accurate figure without examining each case in detail. False accusations may occur due to various reasons, such as flawed testing procedures or contaminated supplements, and the percentage of false accusations may vary depending on the situation.

If you have a specific case or sport in mind, I can try to provide you with more information on that topic.

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Cathy would pay $42.12 for a bicycle helmet that costs $39 before tax.

To find out how much Cathy would pay for a bicycle helmet, we need to calculate the sales tax on the helmet and add it to the original price.

The sales tax rate remains the same, so Cathy would pay the same percentage of sales tax on the helmet as she did on the bicycle.

Sales tax on the bicycle = $12

Price of the bicycle = $150

Tax rate = Sales tax / Price of the bicycle = $12 / $150

To calculate the sales tax on the helmet, we multiply the tax rate by the price of the helmet:

Sales tax on the helmet = Tax rate * Price of the helmet = ($12 / $150) * $39

Now we can calculate the total cost of the helmet:

Total cost of the helmet = Price of the helmet + Sales tax on the helmet = $39 + ($12 / $150) * $39

To simplify the calculation, let's first evaluate ($12 / $150):

($12 / $150) = 0.08

Now we can calculate the total cost of the helmet:

Total cost of the helmet = $39 + (0.08 * $39)

Total cost of the helmet = $39 + $3.12

Total cost of the helmet = $42.12

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Answer:

Step-by-step explanation:

Look at the third line. The division would take place only if the 0 was ln(0). It isn't. It's just 0.

ln(x^2) = 2 * ln(x)

ln(3x) = ln3 + ln(x)

2 * ln(x) = ln(x) + ln(3)           Subtract ln(x) from both sides

ln(x) = ln(3)

This is the statistical question,  specifically hypothesis testing and type I and type II errors.

A "Red tide" is a bloom of poison-producing algae involving dinoflagellates that can cause shellfish, such as clams, to develop dangerous levels of paralysis-inducing toxins. The Division of Marine Fisheries (DMF) monitors toxin levels in shellfish to determine if harvesting should be banned in specific areas.

In this context, a Type I error occurs when the DMF incorrectly bans clam harvesting in an area where the mean toxin level is not actually above 800 μg/kg of clam meat. This is a false positive, as the decision to ban harvesting is based on the assumption that the toxin levels are too high, even though they are not.

A Type II error occurs when the DMF fails to ban clam harvesting in an area where the mean toxin level is actually above 800 μg/kg of clam meat. This is a false negative, as the decision to allow harvesting is based on the assumption that the toxin levels are safe, even though they are not.

In this situation, a Type II error has the greater consequence, as it allows for the harvesting and consumption of toxic clams, posing a significant risk to public health. A Type I error, while economically harmful to the clam industry, does not put consumers at risk.

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Distance formula:

\(d = \sqrt{(x_{2}-x_1)^2 +(y_2-y_1)^2}\)

Now replace the variables with the numbers (When you replace the numbers, it doesn't matter which is the first variable and second variable. Just do whatever is easiest).

\(d = \sqrt{(-1-(-7))^2+(5-(-1))^2}\\d = \sqrt{(-1+7)^2+(5+1)^2}\\d = \sqrt{6^2+6^2}\\d = \sqrt{36+36}\\d = \sqrt{72} \\d = 8.5\)

Thus, the distance between the two points is 8.5

The domain and ranges of the relations are;

3. Domain; {3, 5, -10, 9}

Range; {-4, 0, 6}

4. Domain; -2 ≤ x ≤ 4

Range; -2 ≤ y ≤ 4

The domain is the set of the set of the possible input values of the relation and the range is the set of the possible output values of the relation

3. {(3, -4), (5, -4), (3, 0), (-10, 6), (9, 6)}

The above ordered pair are presented in the form (x, y), where, the input values are the x-values and the output values are the y-values

The domain which is the set of the input values is therefore;

The range is therefore;

The x-value of 3 has two different y-values of -4 and 0. therefore, the relation is not a function

4. The relation is location of points on the circumference of a circle.

The input values are the x-values related to the graph, and the output values are the y-values related to the points on the circumference of the circle.

The diameter of the circle parallel to the x-axis extends from (-2, 1) to (4, 1)

The coordinates of locations on the diameter of the circle parallel to the y-axis are; (1, 4), and (1, -2)

The possible x-values, and therefore the domain are; -2 ≤ x ≤ 4

The possible y-values and therefore the range (vertical extension or reach of the circle) are; -2 ≤ y ≤ 4

The x-value of x = 1 has two y-values of -2 and 4, the relation between the x and y-values is therefore not a function.

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The answer is the second option which is : - 29

Answer:

29

Step-by-step explanation:

Answer:

The answer is 54

Step-by-step explanation:

Let us evaluate the exponent first

(3/4)^3 = 27/64

so we have

27/64 divided by 1/128

= 27/64 * 128/1 = 27 * 128/64

= 27 * 2 = 54