Which of the following represents the area of a rectangle whose length is 5x − 3 and whose width is x + 7?

Answer: banana- 88

Orange-55

Apple-143

Step-by-step explanation:

220 divided by 5, times 2,

that’s the banana trees

220 divided by 4, that’s the oranges

Add the answers together

Take the answer away from 220 that’s the apples

The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

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Answer:

C. Neither

Step-by-step explanation:

The permutation is a selection of objects from a given sample in an ordered manner .

The combination is a selection of objects from a given sample irrespective of an order of arrangement.

The given line of people is neither an ordered arrangement of​ objects, nor a selection of objects from a group of objects So it fits neither of the combinations or permutations.

So the best answer is neither.

Answer:25 hours

Step-by-step explanation:

Answer:

i think its d

Step-by-step explanation:

cause i solved it and got the same answer

Answer:

4 students is 20% of 20 students.

Step-by-step explanation:

We can say that 20 students represent 100% and that 4 students represent x% of all students. Then we can use the proportion: 20 : 4 = 100 : x, or 20 / 4 = 100 / x. Then we will cross multiply: 20 x = 4 * 100, 20 x = 400, x = 400 : 20 , x = 20 %. Also we can say that 4 = 1/5 * 20 and 1/5 * 100 = 20 %

4 students are 20 percent of 20 students.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

We can say that 20 students represent 100% and that 4 students represent x% of all students.

Thus, we can use the proportion:

20 : 4 = 100: x, or 20 / 4 = 100 / x.

cross multiply

20 x = 4 * 100

20 x = 400

x = 400: 20

x = 20 %.

therefore, we can say that 4 students are 20 percent of 20 students.

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Answer:

gpaph C.

Step-by-step explanation:

graph 'C' represents the provided function. Its equation is

\(y=-\frac{5}{2}x +4.\)

Answer:

The value of x is 3

Step-by-step explanation:

∵ Quadrilateral ABCD is congruent to quadrilateral JKLM

∴ AB = JK and BC = KL

∴ CD = LM and AD = JM

∵ BC = 8x + 7

∵ KL = 31

∵ BC = KL

→ Equate their right sides

∴ 8x + 7 = 31

→ Subtract 7 from both sides

∵ 8x + 7 - 7 = 31 - 7

∴ 8x = 24

→ Divide both sides by 8 to find x

∴ \(\frac{8x}{8}\) = \(\frac{24}{8}\)

∴ x = 3

∴ The value of x is 3

Answer:

A (2,2) B (3,0) and C (1, -1)

Step-by-step explanation:

just ÷ everything by 3

6/3=2

6/3=2

9/3=3

0/3=0

3/3=1

-3/3=-1

From the triangle CDF, we can see that it is an isosceles triangle.

Bob can deduct a total of $2,210 on his Schedule C related to these expenses.

To determine the total amount Bob can deduct on his Schedule C related to these expenses, consider the specific categories that can be deducted. Based on the information provided, categorize the expenses as follows:

Course fees for continuing legal education: $1,400

Airfare and hotel room: $500

Meals provided by the hotel's restaurant: $300

Snacks from the newsstand: $10

To calculate the total amount that Bob can deduct, add up these expenses:

$1,400 + $500 + $300 + $10 = $2,210

Therefore, Bob can deduct a total of $2,210 on his Schedule C related to these expenses.

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Mean Absolute Deviation (MAD) is a measure of accuracy for a forecasting model.

It measures the average distance between the actual value and the predicted value, and can be calculated using the following formula: MAD = 1/n * Σ |Ai-F i |, where n is the number of data points, Ai is the actual value, and Fi is the forecasted value. MAD is often used to compare the accuracy of different forecasting models. A lower MAD value indicates that the model has a better accuracy in predicting future values. Additionally, MAD can also be used to measure the accuracy of a single forecasting model over time. If MAD increases, then the accuracy of the forecasting model is decreasing.

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Answer:

Step-by-step explanation:

This is a differential equation problem most easily solved with an exponential decay equation of the form

\(y=Ce^{kt}\). We know that the initial amount of salt in the tank is 28 pounds, so

C = 28. Now we just need to find k.

The concentration of salt changes as the pure water flows in and the salt water flows out. So the change in concentration, where y is the concentration of salt in the tank, is \(\frac{dy}{dt}\). Thus, the change in the concentration of salt is found in

\(\frac{dy}{dt}=\) inflow of salt - outflow of salt

Pure water, what is flowing into the tank, has no salt in it at all; and since we don't know how much salt is leaving (our unknown, basically), the outflow at 3 gal/min is 3 times the amount of salt leaving out of the 400 gallons of salt water at time t:

\(3(\frac{y}{400})\)

Therefore,

\(\frac{dy}{dt}=0-3(\frac{y}{400})\) or just

\(\frac{dy}{dt}=-\frac{3y}{400}\) and in terms of time,

\(-\frac{3t}{400}\)

Thus, our equation is

\(y=28e^{-\frac{3t}{400}\) and filling in 16 for the number of minutes in t:

y = 24.834 pounds of salt

We can write k(x) as the composition of g(x) and f(x).

k(x) = g(f(x))

A composition of two functions means that we need to evaluate one function in the other one.

Here we have the functions:

f(x)=  x²

g(x) = √(x - 1)

h(x) = 2x + 3

And we know that:

k(x) = √(x² - 1)

So we have a square root, then we need to evaluate g(x), and the argument is a square, then we need to evaluate in f(x), the composition is:

k(x) = g(f(x))

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Answer:

y maximum is at 1 for both the points (4,1) and (-4,1)

Step-by-step explanation:

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 50000\\ P=\textit{original amount deposited}\dotfill &\$23000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}\)

\(50000 = 23000\left(1+\frac{ ~~ \frac{r}{100} ~~ }{4}\right)^{4\cdot 7} \implies \cfrac{50000}{23000}=\left( 1+\cfrac{r}{400} \right)^{28} \\\\\\ \cfrac{50}{23}=\left( \cfrac{400+r}{400} \right)^{28}\implies \sqrt[28]{\cfrac{50}{23}}=\cfrac{400+r}{400} \\\\\\ 400\sqrt[28]{\cfrac{50}{23}}=400+r\implies 400\sqrt[28]{\cfrac{50}{23}}-400=r\implies \stackrel{ \% }{11.25}\approx r\)

Answer:

By using the value of cosine function relations, we can easily find the value of sin 120 degrees. Using the trigonometry formula, sin (90 + a) = cos a, we can find the sin 120 value. We know that the value of cos 30 degrees is √3/2. Therefore, sin 120° = √3/2

Step-by-step explanation:

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The z-score that has an area closest to 0.08 is -1.41.

To determine the z-score that has an area closest to 0.08 using the z-score table, we can find the z-score that corresponds  to an area of 0.08 to the left of it.

Using a standard normal distribution table, we can find the z-score that corresponds to an area closest to 0.08.

From the standard normal distribution table:

area closest to 0.08 = 0.07927

corresponding z-score = -1.41 (Check the attached image)

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Answer:

Using the z-score table, we look for the value closest to 0.08 in the body of the table. The closest value is 0.0793, which corresponds to a z-score of 1.41.

Therefore, the z-score that has an area closest to 0.08 is 1.41.

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer:

When it is 9am add 5 hours to it and you will get 2 pm

Step-by-step explanation:

Answer:

The teacher bought 113 crayons.

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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Answer:

2x^3-5x^2-28x+15 -------------------------expanded

2x^3-5x^2-28x+15--------------------simplified

Step-by-step explanation:

\left(2x-1\right)\left(x+3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

simplyfied

\left(2x^2+5x-3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

=2x^3-5x^2-28x+15

Answer:

a. 16

b. 343

hope this helps

Answer:

The temperature in °C is 35.

Step-by-step explanation:

To calculate the temperature in degree Celsius we need to use the following equation:

\(^{\circ} C = (^{\circ} F - 32) \times \frac{5}{9}\)    (1)

The given equation has an error. Equation (1) is the correct one.

Hence, the conversion of 95 °F to °C is:

\(^{\circ} C = (95 - 32) \times \frac{5}{9} = 35\)

Therefore, the temperature in °C is 35.

I hope it helps you!        

Answer: C. Trapazoid.

Step-by-step explanation:

Answer:

14 divided by 5

The quotient is 2, and the remainder is 4.

Let me know if this helps!

Answer:

quotient 2.8 , reminder 0

The missing figures in the question can be seen below.

The average retirement age = 56.1 years ...

The number of a  survey of retired citizen = 49

The standard deviation of the retirement age is 6 years.

Using alpha ∝ = 0.02

Answer:

Step-by-step explanation:

From the given options in the first question in the given information.

Type I error can take place when the researcher concludes the average retirement age increased, but the average retirement age did not increase.

A Type II error can take place when the researcher concludes that the average retirement age did not increase, but the average retirement age increased.

Recall that:

population mean = 56.1

sample size = 49

standard deviation = 6

At the level of significance of 0.02, using the Excel function (=Normsinv(0.02))

The critical value for z = 2.054

Standard error = \(\dfrac{\sigma}{\sqrt{n}}\)

=\(\dfrac{6}{\sqrt{49}}\)

= 6/7

= 0.857

The rejection region \(\overline X\) = \(\mu +Z_{\alpha/0.02}*\sigma_x\)

\(\overline X\) = \(56.1+2.05374891*0.857\)

\(\overline X\) = 57.86

P(Type II error) is as follows:

\(P(\overline X < 57.86| \mu = 57.4) = P( Z< \dfrac{\overline X - \mu }{\sigma_x})\)

\(= P( Z< \dfrac{57.86-57.4}{0.857})\)

\(= P( Z< 0.537)\)

From z tables;

P (Type II error) = 0.704

P(Type II error) is as follows:

\(P(\overline X < 57.86| \mu = 58.9) = P( Z< \dfrac{\overline X - \mu }{\sigma_x})\)

\(= P( Z< \dfrac{57.86-58.9}{0.857})\)

\(= P( Z<-1.214)\)

From z tables;

P (Type II error) = 0.1124

Answer:

\( \angle CBA = \frac{1}{2} \times \angle CAB\)

Step-by-step explanation:

\(\angle CAB = 2\times \angle CBA\\

\huge \red{ \boxed{\angle CBA = \frac{1}{2} \times \angle CAB}}\)