Given that f(x)=6x+5 and g(x)=2x−7, what would be the composite function (f∘g)(x)?

Answer: 10

Step-by-step explanation:

Triangles have 3 sides. So each side is either equivalent or one side is short while the other two are equivalent.

The probability values are calculated and listed below

They are both black

Here, we have

Black = 3

Yellow = 5

Sice the balls are not replaced, we have

P(Both black) = 3/8 * 2/7

P(Both black) = 3/28

They are both yellow

Sice the balls are not replaced, we have

P(Both Yellow) = 5/8 * 4/7

P(Both Yellow) = 5/14

The first is yellow and the second is black

Sice the balls are not replaced, we have

P(Yellow and black) = 5/8 * 2/7

P(Both Yellow) = 5/28

One is yellow the other is black

Sice the balls are not replaced, we have

P(One Yellow and One black) = 5/8 * 2/7 * 2

P(One Yellow and One black) = 5/14

They are of the same colour​

Here, we have

P(Same) = 3/28 + 5/14

P(Same) = 13/28

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Answer:

I think that the middle one has the answer of 12, 24, 36, and 48.

Answer: i think the middle one is 24 ?

Step-by-step explanation:

Answer:

The first answer is correct

Step-by-step explanation:

< O Z Q = < O Z P  + < Q Z P

Given that,

< O Z Q = 12x - 4

< O Z P = 6x + 4

< Q Z P = 3x + 10

Let us solve it now.

< O Z Q = < O Z P  + < Q Z P

12x - 4 = 6x + 4 + 3x + 10

Combine like terms and make the x as the subject.

12x - 4 = 9x + 14

12x - 9x - 4  = 14

3x - 4 = 14

3x = 14 + 4

3x = 18

Divide both sides by 3.

x = 6

The slope of the trend line in the given scatter plot, using the two chosen points (236, 2855) and (248, 2865) is: 0.83.

The slope of a trend line is a measure of the direction and strength of the relationship between two variables. The slope can be positive, negative, or zero

The slope of a trend line = change in y/change in x.

Given the scatter plot, we can choose the following points, which we would use in finding the slope of the trend line:

(236, 2855) and (248, 2865).

Slope = (2865 - 2855)/(248 - 236)

Slope = 10/12

Slope = 0.83

Therefore, the slope of the trend line in the given scatter plot, using the two chosen points (236, 2855) and (248, 2865) is: 0.83.

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The scatterplot and trend line show the number of pass

attempts and passing yards a football team had during

seven seasons.

Because none of the data points lie on the trend line,

you must find two points on the line.

Point 1 can be

Point 2 can be

Using those twe (26, 2855) ope of theline is|

Football Passing Statistics

2875fy

2870

2865

2860

E2855

2850

2845

(233,2850)

(245, 2860)

230 233 238 239 242 245 248 251 254257

Answer:

B.

Step-by-step explanation:

All the possible outcomes are listed on choice B.

The event is a set of outcomes. if we flip three coins and obtain more tails than heads is E = {ttt, tth, tht, htt} option (B) is correct.

A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.

We have three coins.

As we know, in a coin there are two sides head and a tail.

If we flip three coins then the set of all the possible outcomes:

O = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}

The set of outcomes has more tails than heads.

E = {ttt, tth, tht, htt}

We can find the probability, the probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Probability = 4/8 = 1/2

Thus, the event is a set of outcomes. if we flip three coins and obtain more tails than heads is E = {ttt, tth, tht, htt} option (B) is correct.

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The probability that a table orders wine or dessert is 0.7075, or approximately 70.75%.

What is probability?

Probability is a measure or quantification of the likelihood or chance of an event occurring. It is a way to express how probable or likely an event is to happen, ranging from 0 (impossible) to 1 (certain).

What is Principle of inclusion-exclusion?

The principle of inclusion-exclusion is a fundamental concept in combinatorics and probability theory. It provides a method to count or calculate the probability of the union of multiple events.

The principle states that for any finite set of events, the probability of their union is equal to the sum of their individual probabilities minus the sum of the probabilities of their intersections.

To find the probability that a table orders wine or dessert, we can use the principle of inclusion-exclusion.

The probability of a table ordering wine is 0.35, and the probability of a table ordering dessert is 0.55. Since the events of ordering wine and ordering dessert are independent, we can calculate the probability of both events occurring by multiplying their individual probabilities:

P(wine) = 0.35

P(dessert) = 0.55

P(wine and dessert) = P(wine) * P(dessert) = 0.35 * 0.55 = 0.1925

Now, to find the probability of a table ordering wine or dessert, we need to consider the sum of the probabilities of ordering wine and dessert minus the probability of both events occurring:

P(wine or dessert) = P(wine) + P(dessert) - P(wine and dessert)

= 0.35 + 0.55 - 0.1925

= 0.7075

Therefore, the probability that a table orders wine or dessert is 0.7075, or approximately 70.75%.

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Answer:

103.5 i think if i read the question right

Answer:

Khalid should save 17.25 dollars each month.

Step-by-step explanation:

First, solve the equation: 112.75-18+8.75 to get 103.5.

Then, set up a proportion: 6m/6 = 103.5/6

Simplified, your answer should be 17.25.

I hope this helps :)

The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b)

This is incomplete question

Complete question is this:

With a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?

Choose the correct option:

Now, According to the question:

Hence, The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b).

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The required total amount of rainfall during two months is 5/6 inch of rain.

Given that,  a meteorologist recorded the rainfall in Silvergrove in two consecutive months.

In the first month, the amount of rainfall recorded is 1/4 inches.

In the second month, the amount of rainfall recorded is 7/12 inches.

To calculate the total amount of rainfall during two consecutive months, is by adding the amount of rainfall in each month.

That implies, sum = 1/4 + 7/12.

To calculate the sum of fraction of different denominator, take LCM of denominator of two fractions.

LCM of 4 and 12 is 12.

Multiply each fraction by 12/12 to make the fractions of the same denominators.

\(\frac{1}{4}\) × \(\frac{12}{12}\) = 3/12.

That implies, sum = 3/12+7/12.

Thus, sum = (3+7)/12 = 10/12.

On simplifying both numerator and denominator, gives,

Sum = 5/6.

Hence, the required total amount of rainfall during two months is 5/6 inch of rain.

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P(E) = 0.75 ( positive test), P(H) = 0.60 (intelligence)

P(E|H) = 0.98 (positive test given intelligence)

P(H|E) = 0.784 (intelligence given a positive test)

Let's break down the information given and identify the relevant probabilities:

P(E) represents the probability of a positive test, which is given as 75% or 0.75.

P(H) represents the probability of intelligence, which is given as 60% or 0.60.

P(E|H) represents the probability of a positive test given intelligence, which is given as 98% or 0.98.

We are interested in calculating P(H|E), which represents the probability of intelligence given a positive test.

Using Bayes' theorem, we can calculate P(H|E) as follows:

P(H|E) = (P(E|H) * P(H)) / P(E)

Substituting the given values:

P(H|E) = (0.98 * 0.60) / 0.75

P(H|E) ≈ 0.784

Therefore, the probability that Person A is intelligent, given a positive test result, is approximately 0.784 or 78.4%.

In summary, the probabilities are:

P(E) = 0.75 (Probability of a positive test)

P(H) = 0.60 (Probability of intelligence)

P(E|H) = 0.98 (Probability of a positive test given intelligence)

P(H|E) ≈ 0.784 (Probability of intelligence given a positive test)

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P(E) = 0.75 ( positive test), P(H) = 0.60 (intelligence)

P(E|H) = 0.98 (positive test given intelligence)

P(H|E) = 0.784 (intelligence given a positive test)

Let's break down the information given and identify the relevant probabilities:

P(E) represents the probability of a positive test, which is given as 75% or 0.75.

P(H) represents the probability of intelligence, which is given as 60% or 0.60.

P(E|H) represents the probability of a positive test given intelligence, which is given as 98% or 0.98.

We are interested in calculating P(H|E), which represents the probability of intelligence given a positive test.

Using Bayes' theorem, we can calculate P(H|E) as follows:

P(H|E) = (P(E|H) * P(H)) / P(E)

Substituting the given values:

P(H|E) = (0.98 * 0.60) / 0.75

P(H|E) ≈ 0.784

Therefore, the probability that Person A is intelligent, given a positive test result, is approximately 0.784 or 78.4%.

In summary, the probabilities are:

P(E) = 0.75 (Probability of a positive test)

P(H) = 0.60 (Probability of intelligence)

P(E|H) = 0.98 (Probability of a positive test given intelligence)

P(H|E) ≈ 0.784 (Probability of intelligence given a positive test)

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Answer:

b and d

Step-by-step explanation:

2(5x+2+x)=12x+4(b)

2(6x+2)=12x+4

First, solve the expression.

2(5x+2+x)

10x+4+2x

12x+4

So we know that one of the answers is B. and not A.

C. 2(5x+3)

10x+6

D. 2(6x+2)

12x+4

So the answers are B and D, or option B

---

hope it helps

If national savings is less than domestic investment, it means that the country is spending more than it is saving. This can result in a deficit in the current account balance.


1. National savings refers to the total amount of money that a country saves, which includes savings by households, businesses, and the government.
2. Domestic investment refers to the total amount of money that is being invested within the country, such as in infrastructure, businesses, and capital goods.
3. If national savings is less than domestic investment, it means that the country is not saving enough to cover its investment needs.
4. This situation can lead to a deficit in the current account balance, which is the difference between a country's exports and imports of goods and services, as well as other income and transfers.
5. When national savings is less than domestic investment, the country may have to rely on foreign sources of funds to finance its investment needs, which can result in a current account deficit.

6. A current account deficit means that the country is importing more than it is exporting and is relying on external financing to cover the gap.
7. A current account deficit can have both positive and negative implications. On the positive side, it can attract foreign investment and help finance economic growth. However, it can also make the country vulnerable to external shocks and lead to an increase in external debt.
8. To address a situation where national savings is less than domestic investment, the country can take measures to encourage saving, such as through tax incentives or promoting a culture of saving. Additionally, policies can be implemented to attract domestic and foreign investment to bridge the investment gap.

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Answer:

side = x-15 ft

Step-by-step explanation:

A = x²-30x+225

A = (x-15)(x-15)

Answer:

32 degrees

Step-by-step explanation:

180 - 116 = 64

64/2 = 32

Answer:

32°

Step-by-step explanation:

as it is an isosceles triangle from the sides mentioned above

so the other unknown angle is also x

interior angles of triangle sum up 180

so 116 + 2x = 180

2x = 180 -116

2x = 64

x = 32°

Answer:

The answer to the question provided is -27.

Answer:

-27

Step-by-step explanation:

Answer:

the question is missing

Step-by-step explanation:

Answer:

with what? there is nothing attached.

The work required to stretch the spring is 91.6 Ibs-inch

What is work?

Work is defined as force applied across a distance. Work examples include pushing an object against gravity, driving a car up a hill, and lowering a captive helium balloon. Work is the mechanical expression of energy.

Δx : displacement from equilibrium position

f = k Δ x (force due to spring = -kΔx)

where, k is the spring constant

Given,

f = 20ibs

Δx = 24 -18 Inches = 6 inches

∴ k = 20/6 ibs/inch

Now, PE stored in spring = 1/2 k (Δx)²

Δx : displacement from equilibrium position

Work done = change in PE

= 1/2K (Δx₂)² -1/2k (Δx₁)²

given,

Δx₁ = 21-18 inches = 3 inches

Δx₂ = 26-18 inches = 8 inches

∴work done = 1/2 * 20/6 (8² - 3²)Ibs-inches

=10/6 *5*11

work done = 91.6 ibs-inch

The spring must be stretched with 91.6 Ibs-inch of force.

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It will take about 30.56 minutes for the oven to reach 450 degrees Fahrenheit.

1. Let t be the time (in minutes) after turning on the oven. Let T(t) be the temperature (in degrees Fahrenheit) of the thermometer at time t. Then we can model the situation with the following equation:

T(t) = 72 + k(1 - e^(-rt))

where k is a constant related to the efficiency of the oven and the thermometer, and r is a constant related to the rate at which the oven heats up. We can use the information given in the problem to find values for k and r.

At t = 5, T(5) = 105, so we have:

105 = 72 + k(1 - e^(-5r))

And at t = 10, T(10) = 175, so we have:

175 = 72 + k(1 - e^(-10r))

Solving for k and r, we get:

k ≈ 55.384

r ≈ 0.163

So the equation that models the situation is:

T(t) = 72 + 55.384(1 - e^(-0.163t))

2. To find when the oven will reach 450 degrees Fahrenheit, we can set T(t) = 450 and solve for t:

450 = 72 + 55.384(1 - e^(-0.163t))

377.616 = 55.384e^(-0.163t)

ln(377.616/55.384) = -0.163t

t ≈ 30.56

So it will take about 30.56 minutes for the oven to reach 450 degrees Fahrenheit.

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The lower temperature is 200∘C for (a) and 353∘F for (b). In order to determine the lower temperature between two measurements given in different temperature scales, we need to convert them to a common scale.

The common scale we can use is the Kelvin scale, as it is an absolute temperature scale.

(a) To compare 273∘C and 273∘F, we need to convert them to Kelvin. The conversion formula for Celsius to Kelvin is K = C + 273.15, and for Fahrenheit to Kelvin, K = (F - 32) × 5/9 + 273.15.

- For 273∘C, we have K = 273 + 273.15 = 546.15K.

- For 273∘F, we have K = (273 - 32) × 5/9 + 273.15 ≈ 523.15K.

Since 523.15K is lower than 546.15K, the lower temperature is 273∘F.

(b) To compare 200∘C and 353∘F:

- For 200∘C, we have K = 200 + 273.15 = 473.15K.

- For 353∘F, we have K = (353 - 32) × 5/9 + 273.15 ≈ 423.15K.

Since 423.15K is lower than 473.15K, the lower temperature is 353∘F.

In summary, the lower temperature is 200∘C for (a) and 353∘F for (b).

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Answer:

16 science problems

26 math problems

Step-by-step explanation:

m = number of math problems

s = number of science problems

m = s + 10

m + s = 42

(s + 10) + s = 42

2s + 10 = 42

2s = 42 - 10 = 32

s = 32/2 = 16

m = s + 10 = 16 + 10 = 26

The given problem is about linear function with the following properties: f(-6) = -5 and the slope of fa is -5/4.

Step 1:The slope-intercept form of a linear equation is given by y = mx + b where m is the slope of the line and b is the y-intercept. Since the slope of fa is given by -5/4, we can write the equation of the function as: y = (-5/4)x + bFor a point (-6, -5) that lies on the line, we can substitute the values of x and y to solve for b.-5 = (-5/4)(-6) + b => -5 = 15/2 + b => b = -25/2Thus, the equation of the linear function is given by: f(x) = (-5/4)x - 25/2.This is the required solution. The value of 150 is not relevant to this problem.

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Answer:

Im gonna take a guess and say that the number of students is x and the $ collected is y

Step-by-step explanation:

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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a) It would take Anya approximately 4 years to accumulate $40,000 with an annual interest rate of 12%. b) Anya must earn an annual rate of return of approximately 12.6% to save $40,000 in 3 years.

a) To calculate the number of years it would take Anya to accumulate $40,000, we can use the future value formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Where:

Future Value = $40,000

Present Value = $25,000

Interest rate = 12% = 0.12

n = number of years

Substituting the given values into the formula, we have:

$40,000 = $25,000 * (1 + 0.12)ⁿ

Dividing both sides of the equation by $25,000, we get:

(1 + 0.12)ⁿ = 40,000 / 25,000

(1.12)ⁿ = 1.6

To solve for n, we can take the logarithm of both sides of the equation:

n * log(1.12) = log(1.6)

Using a calculator, we find that log(1.12) ≈ 0.0492 and log(1.6) ≈ 0.2041. Therefore:

n * 0.0492 = 0.2041

n = 0.2041 / 0.0492 ≈ 4.15

b) To calculate the required rate of return for Anya to save $40,000 in just 3 years, we can rearrange the future value formula:

Future Value = Present Value * (1 + interest rate)ⁿ

$40,000 = $25,000 * (1 + interest rate)³

Dividing both sides of the equation by $25,000, we have:

(1 + interest rate)³ = 40,000 / 25,000

(1 + interest rate)³ = 1.6

Taking the cube root of both sides of the equation:

1 + interest rate = ∛1.6

Subtracting 1 from both sides, we get:

interest rate = ∛1.6 - 1

Using a calculator, we find that ∛1.6 ≈ 1.126. Therefore:

interest rate = 1.126 - 1 ≈ 0.126

To express the interest rate as a percentage, we multiply by 100:

interest rate = 0.126 * 100 = 12.6%

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well, we know is an EQUIlateral triangle, so all 3 sides are equal,  so hmmm we can just get the distance between those two vertices and triple it for its perimeter.

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-8}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[3 - (-8)]^2 + [7 - (-5)]^2}\implies d=\sqrt{(3+8)^2 + (7+5)^2} \\\\\\ d=\sqrt{265}\implies \stackrel{triple~that}{3\sqrt{265}} ~~ \approx ~~ 48.84\)

Answer:

As engine size increases, highway mileage decreases.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan64° = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AB}\) = \(\frac{11}{c}\) ( multiply both sides by c )

c × tan64° = 11 ( divide both sides by tan64° )

c = \(\frac{11}{tan64}\) ≈ 5.4 ( to the nearest tenth )