The square of T varies directly with the cube of a and inversely with the square of d; T = 2 when a = 2 and d = 4

The value of f(-2) is A: 3.


1. Given the function: f(x) = 24 / (3x - 2).
2. We need to find f(-2).
3. Substitute x with -2: f(-2) = 24 / (3(-2) - 2).
4. Perform the multiplication inside the parentheses: f(-2) = 24 / (-6 - 2).
5. Perform the subtraction inside the parentheses: f(-2) = 24 / (-8).
6. Divide 24 by -8: f(-2) = -3.


To find the value of f(-2) for the function f(x) = 24 / (3x - 2), we substitute the value of x with -2 and perform the necessary arithmetic operations. The resulting function becomes f(-2) = 24 / (3(-2) - 2), which simplifies to f(-2) = 24 / (-6 - 2). After performing the subtraction inside the parentheses, we have f(-2) = 24 / (-8). Finally, we divide 24 by -8, which results in f(-2) = -3.


For the given function f(x) = 24 / (3x - 2), the value of f(-2) is -3 (option C).

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Answer:

the Danyang–Kunshan Grand Bridge

The world's longest bridge is the Danyang–Kunshan Grand Bridge in China, part of the Beijing-Shanghai High-Speed Railway, according to Encyclopaedia Britannica (opens in new tab). The bridge, which opened in June 2011, spans 102.4 miles (165 kilometers)

Answer:

Danyang–Kunshan Grand Bridge

Step-by-step explanation:

The rate of inflating is r=30% per month.

The bill of food after three months can be determined as,

Thus, the bill after three months will be $263.64.

Answer

The average for the next test would be 60

Step-by-step explanation:

50+50+50+50+100= 300

then divide by 5 students

300/5 = 60

the probability of obtaining a sample mean within 500 of the population mean is approximately 0.6827.

To solve this problem, we need to use the central limit theorem which states that the distribution of the sample means will be approximately normal with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

Given that the population mean is 51800 and the population standard deviation is 4000, we can calculate the standard error of the mean as follows:

Standard error of the mean = 4000 / sqrt(64) = 500

We want to find the probability of obtaining a sample mean within 500 of the population mean. This can be written as:

P(51800 - 500 < X < 51800 + 500)

where X is the sample mean.

We can standardize this interval using the standard error of the mean:

P(-1 < Z < 1)

where Z is a standard normal variable.

Using a standard normal table, we find that the probability of Z being between -1 and 1 is approximately 0.6827.

Therefore, the probability of obtaining a sample mean within 500 of the population mean is approximately 0.6827.

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Answer:

43

Step-by-step explanation:

you find the answer then fart in a jar and throw it at ur grandma

Answer:   a square with side length 4 inches

a 2 inch by 8 inch rectangle

a heart-shaped base with an area of 16 square inches

Step-by-step explanation: The given height is 5. Any base with an area of 16 square inches will be an acceptable base.

For example, if the circular base had a radius of about 2.257 inches, its area would be 16 square inches

(2.257)² ≈ 5.093

5.093 × 3.1416 ≈ 16

16 × 5 = 80

The base for this prism should be like

a square with side length 4 inches.

a 2 inch by 8 inch rectangle.

a heart-shaped base with an area of 16 square inches.

Since

The given height is 5.

Any base with an area of 16 square inches should be considered as an acceptable base.

Like if the circular base had a radius of about 2.257 inches, its area would be 16 square inches

So, it be like

(2.257)² ≈ 5.093

Now

5.093 ( 3.1416) ≈ 16

16 ( 5) = 80

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Answer:

86.5 inches

Step-by-step explanation:

6228 / 72 = 86.5

Answer:

1) gradient  (00) (-2 4) = y2-y1 / 2-1 = 4/-2 = -2  m = -2/1  means = m = -2  (negative slope)   2)  gradient  y2-y1 / x2-x1 = 3-0 / 2-0  = 3/2 = (1 1/2)/1   m = 1 1/2  (positive slope) we use the formula y-values divided by the change in the x-values.    The equation of the gradient each goes like this 1) y = -2x   as y is at origin nothing else to add     The equation of the gradient each goes like this 2) y = 1  1/2x     The equation of the point formula  1) we take the y -y1 = m (x +x 1)  =  y-0 = -2x (x +0)  (as m = -2) y = -2(x +0)   and  The equation of the point formula  2)  y - 0 = m ( x +x1)     y - 0 = 1 1/2( x +0)  = y = 1 1/2( x +0)

Triangles ABC and DEF are: A. similar triangles.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar and the slopes of triangles ABC and DEF are equal;

Slope = rise/run

Slope of triangle ABC = AB/AC

Slope of triangle DEF = ED/DF

Slope of triangle ABC = Slope of triangle DEF

AB/AC = ED/DF

Similarly, the interior angles are congruent;

m∠B ≅ m∠E = 35°

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Both heteroskedasticity and the omission of an important explanatory variable can cause the usual OLS t-statistics to be invalid, while a high sample correlation coefficient between two independent variables can result in issues related to multicollinearity, affecting the standard errors and, consequently, the validity of the t-statistics.

(i) Heteroskedasticity: Heteroskedasticity refers to the situation where the variance of the error term in a regression model is not constant across different levels of the independent variables.

In the presence of heteroskedasticity, the usual Ordinary Least Squares (OLS) t-statistics can become invalid.

This is because heteroskedasticity violates one of the assumptions of the classical linear regression model, which assumes constant variance of the error term (homoskedasticity).

As a result, the estimated standard errors of the coefficients may be biased, leading to incorrect t-statistics and incorrect hypothesis testing.

(ii) A sample correlation coefficient of 0.95 between two independent variables that are in the model: The sample correlation coefficient measures the strength and direction of the linear relationship between two variables.

When two independent variables in a regression model have a high correlation, it can cause issues with multicollinearity. Multicollinearity refers to the situation where there is a high correlation between two or more independent variables.

In the presence of strong multicollinearity, the OLS estimators can still be unbiased, but their standard errors can be large. This can result in inflated standard errors and, consequently, invalid t-statistics.

(iii) Omitting an important explanatory variable: Omitting an important explanatory variable from a regression model can lead to omitted variable bias.

Omitted variable bias occurs when a relevant variable is left out of the model, and the remaining variables do not fully capture its effect on the dependent variable.

This can result in biased estimates of the coefficients for the included variables. In such cases, the OLS t-statistics can be invalid, as they are based on the assumption that the omitted variable has no effect on the dependent variable.

The omission of an important explanatory variable can lead to omitted variable bias and violate the assumptions of the classical linear regression model, resulting in incorrect hypothesis testing and potentially invalid t-statistics.

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The meteorologist needs to analyze approximately 164 air samples to be 80% certain that the error of estimate does not exceed 0.2 ppm.

A meteorologist aiming to estimate the nitrogen dioxide content in the air needs to consider the standard deviation and desired level of certainty. In this case, the known standard deviation is 2 ppm, and the desired certainty is 80%, with an error of estimate not exceeding 0.2 ppm.
To calculate the number of air samples needed, the meteorologist can use the formula:
n = (Z * σ / E)^2
Here, n represents the required sample size, Z is the z-score corresponding to the desired certainty level (80%), σ is the standard deviation (2 ppm), and E is the margin of error (0.2 ppm).
For 80% certainty, the z-score is approximately 1.28. Plugging the values into the formula, we get:
n = (1.28 * 2 / 0.2)^2 = (12.8)^2 ≈ 164
Thus, the meteorologist needs to analyze approximately 164 air samples to be 80% certain that the error of estimate does not exceed 0.2 ppm.

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The radius of the pipe is approximately 8.13 cm.

To find the radius of the pipe, we can use the formula for the volume of a cylinder, which relates the depth of the water, the width of the surface, and the radius of the pipe.

The volume of a cylinder is given by the formula V = π\(r^2\)h, where V is the volume, r is the radius, and h is the height or depth.

In this case, we are given the depth of the water as 18 cm and the width of the surface as 48 cm.

Since the width of the surface is equal to the diameter of the pipe, we can use the formula for the diameter of a circle, which is twice the radius.

Therefore, the radius is half of the diameter, or r = 48/2 = 24 cm.

Using the formula for the volume of a cylinder, we can write the equation as V = π\((24)^2\)(18), where V is the volume.

We know that the volume is equal to the cross-sectional area of the pipe multiplied by the depth of the water.

The cross-sectional area is given by the formula A = π\(r^2\).

Now we can solve for the radius.

Rearranging the equation V = π\((24)^2\)(18), we get

\((24)^2\) = V/(π(18))

Solving for \((24)^2\), we find that the radius is approximately 8.13 cm.

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Step 1: Write out the formula

Step 2: Write out the given values and substitute them into the formula

Let A be the event of "shopper reads the newspaper 1-2 times.

and

Let B be the event of "shopper remembered 1-3 cards".

n(A) = 15 + 10 = 25

n(B) = 8 + 15 = 23

n(U) = 8 + 15 + 9 + 10= 42

Therefore,

Hence,

Thus the probability that a randomly selected shopper reads the newspaper 1-2 times a week or remembered 1-3 cards is 11/14

The fraction of the group who had a score of 45 or more is 20/31

It is a method of graphical display of data where the data is displayed using  bars of various heights .

From the histogram , we can calculate by either determining the frequency value of group who had a score of 45 or more and divide it by total frequency or

By calculating the number of square in each group who had a score of 45 or more and dividing by the total number of squares.

There are total 31 squares

The health score for a group of people who had a score of 45 or more is 20

Therefore the fraction of the group who had a score of 45 or more is 20/31

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The probability that more than one woman will wear sunscreen when outside for more than one hour can be calculated using the binomial distribution.

The binomial distribution is a probability distribution that calculates the probability of a certain number of successes in a fixed number of independent trials. The binomial distribution is a discrete probability distribution that is characterized by two parameters: the probability of success in a single trial (p) and the number of trials (n).In this question, we need to find the probability that more than one woman will wear sunscreen when outside for more than one hour. Since we are dealing with more than one woman, we need to use the binomial distribution with the following parameters:p = probability that a woman wears sunscreen when outside for more than one hourn = number of womenLet's assume that p = 0.6 (60% chance that a woman will wear sunscreen when outside for more than one hour) and n = 3 (three women are outside for more than one hour).The probability that no woman will wear sunscreen is (1 - 0.6)^3 = 0.064.The probability that one woman will wear sunscreen is 3 × 0.6 × (1 - 0.6)^2 = 0.288.The probability that two women will wear sunscreen is 3 × 0.6^2 × (1 - 0.6) = 0.432.The probability that three women will wear sunscreen is 0.6^3 = 0.216.The probability that more than one woman will wear sunscreen is the sum of the probabilities that two or three women will wear sunscreen:P(X > 1) = P(X = 2) + P(X = 3) = 0.432 + 0.216 = 0.648Therefore, the probability that more than one woman will wear sunscreen when outside for more than one hour is 0.648 or 64.8%.
To accurately calculate the probability of more than one woman wearing sunscreen when outside for more than one hour, we would need more information, such as the total number of women and the individual probabilities of them wearing sunscreen.

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Answer:

Rajiv bought 23,382 balls.

Step-by-step explanation:

Given that Rajiv bought 1325 packs of red balls, 1238 packs of yellow balls and 1334 packs of green balls, and there were 6 balls in each pack, to determine how many balls did Rajiv buy the following calculation must be performed:

(1,325 + 1,238 + 1,334) x 6 = X

3.897 x 6 = X

23.382 = X

Therefore, Rajiv bought 23,382 balls.

Answer:

\(x \geqslant - 3\)

Step-by-step explanation:

\(x \geqslant - 3\)

Answer:

-5/2

Step-by-step explanation:

-7-3/10-6 = -10/4 which equals -5/2

Answer:

Hope it helps!~ (Sorry if you get it wrong or I got it wrong-)

Step-by-step explanation:

the state of being oriented. an introduction, as to guide one in adjusting to new surroundings, employment, activity, or the like: New employees receive two days of orientation. Psychology, Psychiatry. the ability to locate oneself in one's environment with reference to time, place, and people. This or ,

the determination of the relative position of something or someone (especially oneself).

"the child's surroundings provide clues to help in orientation"

the relative physical position or direction of something.

plural noun: orientations

"two complex shapes, presented in different orientations"

This-

~The Confuzzeled homan

Cylinder A -

Surface Area:

A = 2πrh + 2πr^2

A = 2 · π · 5 · 7.5 + 2 · π · 25 ≈ 392.69908

A = 392.7 cm^2

Volume:

V = πr^2h

V = π · 25 · 7.5 ≈ 589.04862

V = 589 cm^3

Cylinder B -

Surface Area:

A = 2πrh + 2πr^2

A = 2 · π · 3.5 · 5 + 2 · π · 12.25 ≈ 186.92476

A = 186.9 cm^2

Volume:

V = πr^2h

V = π · 12.25 · 5 ≈ 192.42255

V = 192.4 cm^3

Answer:

a) surface area: 125pi     volume: 187.5pi

b) (i dont know what you mean by "in terms of ." so ill give both)

surface area: 210pi or 659.734     volume: 61.25pi or 192.422

Step-by-step explanation:

a) surface area is this

2pirh+2pir^2

plug it in..

2pi(5)(7.5)+2pi(5)^2

simplify...

75pi+50pi

125pi

volume is this

pir^2h

plug it in...

pi(5)^2(7.5)

simplify...

187.5pi

b is basically same steps.

(i had to replace all the pi symbols with "pi" because it was inappropriate???)

Answer:

Jingle's breakeven point is achievable if 4000 units are sold.

Step-by-step explanation:

Answer:

\(8.11\)

Step-by-step explanation:

Rounded to nearest hundredth.

After Round to the nearest hundredth value of number is,

⇒ 8.11

We have to given that;

A number is,

⇒ 8.113

And, We an Round to the nearest hundredth.

Since, Rounding numbers refers to changing a number's digits such that it approximates a value.

Here, In number 8.113,

Digit in thousandth place is 3 which is less thn 5.

Hence, After Round to the nearest hundredth value of number is,

⇒ 8.11

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The amount of discount on the jacket is Birr 144.

We can use the following formula :

Discount amount = Original price - Discounted price

We must determine the original pricing of the jacket given that it has a discounted price of Birr 576 and the discount is 20%.

Assume "x" stands in for the original price.

The information provided indicates that the discounted price is 80% (100% - 20%) of the original cost:

Discounted price = 80% of the original price

576 = 0.8x

To find the original price, we can divide both sides of the equation by 0.8:

x = 576 / 0.8

x = 720

Now that we have the original price, we can calculate the amount of discount:

Discount amount = Original price - Discounted price

Discount amount = 720 - 576

Discount amount = Birr 144

Therefore, the amount of discount on the jacket is Birr 144.

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The integral of (x + 11) / (x^2 + 4x + 8) dx can be evaluated using partial fraction decomposition. The answer is  ln(|x^2 + 4x + 8|) + 2arctan[(x + 2) / √6] + C.

The integral of (x + 11) / (x^2 + 4x + 8) dx is equal to ln(|x^2 + 4x + 8|) + 2arctan[(x + 2) / √6] + C, where C is the constant of integration.

To explain the answer in more detail, we start by completing the square in the denominator. The quadratic expression x^2 + 4x + 8 can be rewritten as (x + 2)^2 + 4. We can then decompose the fraction using partial fractions. We express the given rational function as (A(x + 2) + B) / ((x + 2)^2 + 4), where A and B are constants to be determined.

By equating the numerators and simplifying, we find A = 1 and B = 10. Now we can rewrite the integral as the sum of two simpler integrals: ∫(1 / ((x + 2)^2 + 4)) dx + ∫(10 / ((x + 2)^2 + 4)) dx.

The first integral is a standard integral that gives us the arctan term: arctan((x + 2) / 2). The second integral requires a substitution, u = x + 2, which leads to ∫(10 / (u^2 + 4)) du = 10 * ∫(1 / (u^2 + 4)) du = 10 * (1 / 2) * arctan(u / 2).

Substituting back u = x + 2, we get 10 * (1 / 2) * arctan((x + 2) / 2) = 5arctan((x + 2) / 2). Combining the two integrals and adding the constant of integration, we obtain the final result: ln(|x^2 + 4x + 8|) + 2arctan[(x + 2) / √6] + C.

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The number of dishes the crispy clover has in his new menu can be expressed as  D + (1/5)D.

A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical operation enables the multiplication, division, addition, and subtraction operations.

Given data -

20% more dishes are available on the new menu than the old one.

D foods were on the previous menu.

As 20% more dishes are added,

Therefore we can also write it as (20/100)D

Now the total dishes in the new menu can be expressed as

= D + (20/100)D

= D + (1/5)D

Therefore the number of dishes the crispy clover has in his new menu can be expressed as  D + (1/5)D.

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The complete question is:

Crispy clover, a popular vegetarian restaurant, introduced a new menu that had 20% more dishes than the previous menu. The previous menu had D dishes. Which of the following expressions could represent how many dishes crispy clovers new menu has?

The points x ≤ 1 2/3 and x<-3/4 has plotted in the number line

A number line is a visual representation of the real number system. It is a straight line on which numbers are marked at equal intervals, with zero in the center and positive numbers to the right of zero and negative numbers to the left of zero

The line represents the set of all real numbers, with negative numbers to the left of zero and positive numbers to the right. The point marked with a circle (o) represents the value of x that satisfies both conditions, which is x ≤ 1 2/3 and x < -3/4. Since -3/4 is less than 1 2/3, any value of x that satisfies x ≤ 1 2/3 must also satisfy x < -3/4, so the two conditions are equivalent in this case.

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