A cone has volume V, radius r, and a height of 12 cm.
Another cone has the same height and 1/3 times the
radius of the original cone. Write an expression for its
volume.

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Answer:

Step-by-step explanation:

Based on the number of hours that are there it look like each hour that it goes 50 adds on

1. The time goes up one hour each time

2. The number of pages go up by 50

So if there are 4 hours then this would happen

 1              2                   3                    4

50+50=  100+50=      150+50=       200

50 adds on as the hour goes up.

The area of streetlamp illuminates approximately 660.19 square meters of the street.

What is the area?

An area is a measure of the size or extent of a two-dimensional surface or region. It is the amount of space inside a flat, two-dimensional shape or figure. The area is typically measured in square units

The area of a circle is given by the formula A = πr², where r is the radius. In this case, the diameter (which is the same as the distance across the circle through the center) is 29 meters, so the radius is half of that, or 14.5 meters.

Using the formula for the area of a circle, we have:

A = πr²

A = 3.14 x 14.5²

A ≈ 660.19 square meters

Therefore, the streetlamp illuminates approximately 660.19 square meters of the street.

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Answer:

yes

Step-by-step explanation:

Answer:

yes y= 3 -2 is linear.

The values of the trigonometric identities are:

Sin X = 5/13

Cos X = 12/15

Tan X = 5/12

Sin M = 12/13

Cos M = 5/13

Tan M = 12/5

We have,

Sin = Perpendicular / Hypotenuse

Cos = Base / Hypotenuse

Tan = Perpendicular / Base

Now,

Sin X = 5/13

Cos X = 12/15

Tan X = 5/12

And,

Sin M = 12/13

Cos M = 5/13

Tan M = 12/5

Thus,

The values of the trigonometric identities are:

Sin X = 5/13

Cos X = 12/15

Tan X = 5/12

Sin M = 12/13

Cos M = 5/13

Tan M = 12/5

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Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that's supplementary to the third interior angle

2x - 2 = 45 + x

2x - x = 45 + 2

x = 47°

Answer:

x = 47

Step-by-step explanation:

Finding the third angle (y) of the triangle:

- Since angles on a straight line add up to 180:

2x -2 + y = 180

y = -2x + 2 + 180

= -2x + 182

Hence, the third angle of the triangle is -2x + 182.

Since all 3 angles of a triangle add up to 180°:

-2x + 182 + x + 45 = 180

-2x + x + 227 = 180

-2x + x = 180 - 227

-x = -47

x = 47

Hence, x = 47

Answer:

Exact Form: 3/2

Decimal Form: 1.5

Mixed Number Form: 1 1/2

Answer:

40.36

Step-by-step explanation:

= 26 + 14.36 = 40.36

Answer:

The answer is D 7 degrees F

Explanation - 7°F

39 + (-5) + 7 = 39 - 5 + 7 = 41

then, the low was 39 + (-5) = 34

thus, 41 - 34 = 7

so, 7°F above the low of 34°F

Hope this helps :D

Using the formula of area of a circle, about 226.08in² has been eaten

The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:

Area = π * r²

where π is approximately 3.14 and r is the radius of the circle.

Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.

Let's calculate the area of the entire pizza first:

Area = 3.14 * 12²

Area = 3.14 * 144

Area ≈ 452.16 square inches

Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:

Area of half of the pizza = 452.16 / 2

Area of half of the pizza ≈ 226.08 square inches

Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.

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If a group consists of 10 kids and 2 adults, the number of ways are there to form the line are 2 * 10!. So, correct option is C.

To form a line with an adult at the front and an adult at the back, we need to consider the positions of the 10 kids within the line. The two adults are fixed at the front and back, so we have 10 positions available for the kids.

To calculate the number of ways to arrange the kids in these positions, we can use the concept of permutations. Since each position can be occupied by a different kid, we have 10 options for the first position, 9 options for the second position, 8 options for the third position, and so on, until the last position, where only 1 kid remains.

Therefore, the number of ways to form the line is:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 10!

However, the problem also mentions that there are 2 adults, so we need to consider the arrangements of the adults as well. Since there are only two adults, there are 2 ways to arrange them in the line (adult at the front and adult at the back or vice versa).

Therefore, the total number of ways to form the line is:

2 x 10! = 2 * 10!

Hence, the correct option is b. 2 * 10!, which accounts for both the arrangements of the kids and the adults.

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The point estimate of the population is 0.415 round to the nearest thousandth as needed the margin error is 0.189.

In statistics, for point estimation, an unknown population parameter (e.g. population mean). More formally, it is applying a point estimator to data to obtain a point estimate.

Point estimation can be contrasted with interval estimation. Such interval estimates are usually confidence intervals for frequentist inference and confidence intervals for Bayesian inference. More generally, point estimators can be contrasted with set estimators. An example is the confidence rate or confidence rate. Point estimators can also be contrasted with distribution estimators. Examples include confidence distributions, randomized estimators, and Bayesian posterior distributions.

Based on the question,

The confidence  interval of Lower bound is 0.226.

The confidence interval of Upper bound is 0.604.

X - E = 0.226.                     --------------------------- (1)

X + E = 0.604                     ---------------------------(2)

Adding equation (1) and (2),

    2X = 0.83

⇒  X = 0.83/2

⇒ X = 0.415

Putting X = 0.415 in equation (1),

0.415 + E = 0.604

⇒ E = 0.604 - 0.415

⇒ E = 0.189

Thus, the point estimate of the population is 0.415 round to the nearest thousandth as needed the margin error is 0.189.

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Answer:

\({ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}\)

Answer:

8 and 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

What are the factors of 40? 8 * 5

8 + 5 = 13

To do it algebraically gives you a quadratic:

A + B = 13

AB = 40

A(13 - A) = 40

A2 - 13A + 40 = 0

(A - 8)(A - 5) = 0

A = 8 and B = 5

Answer:4.62x10^13

Step-by-step explanation:

5a) 3x3x13

b) 3x7x7

c)11x5x2x2

d)3x3x3x5x2

6a)2x2x2x131

7a)5x5x2x2

b) 3x2x17

c)5x2x2x2x2x2x2

d)5x5x5x3

e) 2x2x103

f)5x3x137

g) 2x2x2x2x2x2x2x2x2

h)5x5x7x7x3

It is more likely for them to make at least $5,000 in profit if they sell a larger quantity of treats. This can be achieved by implementing effective marketing strategies, setting an appealing price, and targeting a wide audience.

Let's say the team decides to sell the candy bars and sodas for $1 each. In this case, they will make $1 in revenue for each candy bar and can of soda sold.

Now, let's calculate the costs. The team spent $1000 to start the fundraiser, which is a fixed cost that does not depend on the number of treats sold. In addition, they spend $0.30 on each candy bar and can of soda sold.

To break even, the revenue needs to equal the total cost. Let's denote the number of treats they need to sell to break even as "x". The revenue from selling x treats would be $1 multiplied by x. The total cost would be the sum of the fixed cost and the cost per treat multiplied by the number of treats sold.

Equation to break even: Revenue = Cost

1x = $1000 + $0.30x

To solve for x, we can subtract $0.30x from both sides and then divide both sides by 0.70:

0.70x = $1000

x = $1000 / 0.70

x ≈ 1428.57

So, they need to sell approximately 1429 treats to break even.

To make at least $5,000 in profit, we need to calculate the revenue required to cover the costs and generate the desired profit. Let's denote the number of treats they need to sell to make this profit as "y".

Equation to make at least $5,000 in profit: Revenue = Cost + Profit

1y = $1000 + $0.30y + $5000

Simplifying the equation:

0.70y = $6000

y = $6000 / 0.70

y ≈ 8571.43

So, they need to sell approximately 8572 treats to make at least $5,000 in profit.

Whether it is likely for them to make at least $5,000 in profit depends on various factors, such as the demand for treats, the number of people attending the games, and the team's marketing efforts. If they can attract a large number of customers and successfully sell the treats, it is possible for them to make at least $5,000 in profit.

In general, it is more likely for them to make at least $5,000 in profit if they sell a larger quantity of treats. This can be achieved by implementing effective marketing strategies, setting an appealing price, and targeting a wide audience.

Additionally, if they can minimize their costs (such as by negotiating better deals for purchasing treats), they would have a better chance of reaching their profit goal.

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Given exponential expression is 1.05^(-3/i).

We can simplify this expression as follows:

1.05^(-3/i)

= [1 / (1.05^(3/i))]

= [1 / ((1.05^3)^(1/i))]

= [1 / (1.157625^(1/i))]

= 1.157625^(-1/i)

Thus, the given exponential expression is equivalent to 1.157625^(-1/i).

Since we don't know the value of i, we cannot find the exact value of the given exponential expression. However, we can evaluate the expression for some values of i.

For example, if we put i = 2, then 1/i = 1/2 = 0.5, and hence:

1.157625^(-1/i)

= 1.157625^(-1/2)

= 0.968

Therefore, the answer is option d. 0.968.

Note: We cannot evaluate the expression for i = 0 or any negative value of i because the expression will become undefined.

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Answer:

a,b,d

Step-by-step explanation:

a constant rate means it is constantly/repeatedly changing the same amount over time a,b,d keeps on changing (a is by 12% each year) (B is by 3 points each decade) (D is by 2.5% each year) C on the other hand changes every six months but stops at the end of the second year. therefore the answers are A,B and D

Answer:

First we need to write this in proper form:

\(\frac{f(x)}{g(x)} =\frac{x^{2}-6x-7}{x+1} \\Factor f(x)\\\\f(x)=(x-7)(x+1)\\\\\frac{f(x)}{g(x)} =\frac{(x-7)(x+1)}{x+1} \\\\\\X+1 cancels out\\\\\frac{f(x)}{g(x)} =x-7\)

Correct answer is B, f/g(x) = x-7

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

#Team Trees #Team Seas #PAW #Spread_Positivity

I hope this helps,

-Oceanbreeze24

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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Have a GREAT day!!!

Answer:

who friendhjcicivigigivigigogogig'g

Answer:

\(-\frac{15}{4}\)

Step-by-step explanation:

To find the slope or the gradient of a line you have to utilise the formula

\(\frac{y2-y1}{x2-x1}\)

Y₂ = -7

Y₁ = 8

X₂ = 7

X₁ = 3

So,

\(\frac{-7-8}{7-3}\)

→ Simplify

\(-\frac{15}{4}\)

By using the given points, we will see that the slope is -15/4.

If we know that a given line passes through two known points (x₁, y₁) and (x₂, y₂), then the slope can be written as:

\(s = \frac{y_2 - y_1}{x_2 - x_1}\)

Here the line passes through the points (3, 8) and (7, -7).

Using the above formula, we can see that the slope is:

\(s = \frac{-7 - 8}{7 - 3} = \frac{-15}{4}\)

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Suppose that F(x) = \(A0 + A1*x + A2*x^2 + A3*x^3 + A4*x^4 + ....\) If F(x) = 1/(1-x), A1000 = 1000!

The function F(x) can be expressed as a geometric series with a first term of 1 and a common ratio of x. Thus, we can write:

F(x) = \(1 + x + x^2 + x^3 + x^4 + ...\)
To find the coefficients A0, A1, A2, A3, A4, and so on, we can differentiate both sides of the equation with respect to x. This gives:
F'(x) = \(1 + 2x + 3x^2 + 4x^3 + 5x^4 + ...\)
Multiplying both sides by x, we get:
xF'(x) = \(x + 2x^2 + 3x^3 + 4x^4 + 5x^5 + ...\)
Now, we can differentiate both sides of this equation with respect to x again:
xF''(x) + F'(x) = \(1 + 4x + 9x^2 + 16x^3 + 25x^4 + ...\)
Multiplying both sides by x again, we get:
x(xF''(x) + F'(x)) = \(x + 4x^2 + 9x^3 + 16x^4 + 25x^5 + ...\)
Continuing this process, we get:
x^nFn(x) = \(n!x^n + n(n-1)!x^{(n+1)} + n(n-1)(n-2)!x^{(n+2)} + ...\)
Now, we can substitute x = 0 into this equation to find the coefficients. When we do this, all the terms except for the first one on the right-hand side disappear. Thus:
A0 = 1
A1 = 1
A2 = 2
A3 = 6
A4 = 24
We can see that the coefficients are the factorials of the index, so:
An = n!
Therefore, A1000 = 1000!

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To solve equations with fractions and variables in the denominator, we need to eliminate it by moving it to the other side. To do this, we multiply both sides of the equation by the term in the denominator. This will cancel out the fraction and leave us with a simpler equation to solve.

For example, suppose we have the equation (3 + x) / x = 2. To get rid of the fraction, we multiply both sides by x. This gives us: x * (3 + x) / x = x * 2. The x in the numerator and denominator cancel out, leaving us with:

3 + x = 2x. Now we can solve for x by subtracting x from both sides: 3 = x

This is the solution of the equation.

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Answer:  " 4 − 3a " .

________

Step-by-step explanation:

" 4 − a − a − a " ;

        = 4 − 1a − 1a − 1a " ;

        =  ?  " ;

________

Combine the "like terms" :

________

         →   " − 1a − 1a − 1a " ;

               = (− 1a − 1a) − 1a ;

               = ( − 2a) − 1a ;

               =  − 3a ;

________

Now, bring down the "4" ;

  and rewrite the expression:

________

        →  " 4 − 3a " ;

which cannot be simplified further.

________

The answer is:  " 4 − 3a " .

________

Hope this is helpful!

 Best wishes to you!

________

equation in slope-intercept form of the line that pae through the point (4, 7) and is parallel to the line represented by y = 2x - 5 is ( y - y1 ) = m( x - x1 ) => y - 7 = 2 (x-8) => 2x - y - 1 = 0

A number that specifies a line's direction and slope is known as the slope or slope of a line in mathematics. A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x).

equation is -

y = 2x - 5

since these are parallel to each other,

slope, m= 2

now the equation is -

( y - y1 ) = m( x - x1 )

y - 7 = 2 (x-8)

2x - y - 1 = 0

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1.1 The relationship between sampling distribution and confidence interval is that the sampling distribution helps us understand the distribution of sample statistics (such as the sample mean or proportion) when repeatedly sampling from a population.

The confidence interval, on the other hand, provides a range of values within which we can be confident that the true population parameter lies based on the sample data.

In other words, the sampling distribution gives us information about the variability and distribution of sample statistics, while the confidence interval uses this information to estimate the range of likely values for the population parameter.

1.2 To calculate the probability that the sample mean is between 9.0 and 11.0, we need to standardize the values using the z-score formula and then look up the corresponding probabilities from the standard normal distribution.

First, calculate the z-scores:

z1 = (9.0 - 10) / (3 / √40) = -1.8257

z2 = (11.0 - 10) / (3 / √40) = 1.8257

Next, look up the probabilities associated with these z-scores using a standard normal distribution table or a calculator. The probability that the sample mean is between 9.0 and 11.0 can be calculated as the difference between the two probabilities:

P(9.0 < x < 11.0) = P(z1 < Z < z2)

1.3 (a) To calculate the probability that the percentage of voters who support the candidate is between 40% and 45% in a sample of 200 voters, we can use the sampling distribution of sample proportions. Assuming the sample proportion follows a normal distribution, we can standardize the values using the z-score formula and then calculate the corresponding probabilities.

First, calculate the z-scores:

z1 = (0.40 - 0.40) / √[(0.40 * (1 - 0.40)) / 200] = 0

z2 = (0.45 - 0.40) / √[(0.40 * (1 - 0.40)) / 200]

Next, look up the probabilities associated with these z-scores using a standard normal distribution table or a calculator. The probability that the percentage of voters who support the candidate is between 40% and 45% can be calculated as the difference between the two probabilities:

P(40% < p < 45%) = P(z1 < Z < z2)

(b) To calculate the probability that the percentage of voters who support the candidate is more than 50%, we can again use the sampling distribution of sample proportions. We standardize the value using the z-score formula and calculate the corresponding probability.

Calculate the z-score:

z = (0.50 - 0.40) / √[(0.40 * (1 - 0.40)) / 200]

Look up the probability associated with this z-score using a standard normal distribution table or a calculator. The probability that the percentage of voters who support the candidate is more than 50% can be calculated as:

P(p > 50%) = P(Z > z)

1.4 To determine the 95% confidence interval for the true mean resistance, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

First, calculate the standard error:

Standard Error = population standard deviation / √(sample size)

              = 0.35 / √10

Next, find the critical value corresponding to a 95% confidence level from a t-distribution table with 9 degrees of freedom (n-1). The critical value for a 95% confidence level is approximately 2.

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a. The number of choices possible for each digit of the code is of: 10.

b. The total number of 4-digit passwords that Jess can create is of: 10,000.

c. The number of different ways to create even passwords is of: 5,000.

The Fundamental Counting Theorem states that if there are n independent trials, each with \(n_1, n_2, \cdots, n_n\) possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial, according to the rule presented as follows:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

Each digit can be between 0 and 9 inclusive, hence the number of outcomes possible for each digit of the password is given as follows:

10.

The password is composed of four digits, hence the total number of passwords possible is of:

N = 10 x 10 x 10 x 10 = 10,000.

Considering that Jess would like an even number, there are only five outcomes possible for the last digit (0, 2, 4, 6 or 8), hence the number of outcomes is of:

N = 10 x 10 x 10 x 5 = 5,000.

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Answer:

2/13

Step-by-step explanation:

In a standard deck of cards, there are 52 cards total, 4 kings, and 4 queens.

Probability is calculated by (number of favorable outcomes)/(number of possible outcomes), so our probability would be 8/52, which can be simplified to 2/13.

Hope this helps!