4x to the second power +5x when x=1

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

Let's consider that s be the length of a side of the regular pentagon.

The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm

Also,

we have the formula for the area of a regular pentagon as:

\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)

where a is the length of a side of the pentagon.

In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.

Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)

Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.

The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.

In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

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Answer:

65,760

Step-by-step explanation:

move decimal over two places to make a percent a decimal so .37

then multiply that times the 48000 to get 17,760 and then add that to the original 48000 to get 65,760

The inequality that represents all possible values of m, the number of miles Lola can travel in the car with the remaining gasoline in the tank is m ≤ 282.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Several types of inequalities are represented by a variety of notations, including:

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

Let the number of miles = m.

Given that, Lola’s car can travel no more than 445 miles on one full tank of gasoline.

m ≤ 445

After filling up the tank, she traveled 163 miles in the car.

Remaining distance is:

m ≤ 445 - 163

m ≤ 282

Hence, the inequality that represents all possible values of m, the number of miles Lola can travel in the car with the remaining gasoline in the tank is m ≤ 282.

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Step-by-step explanation:

Given

Number of Radio Stations=28

Number of College Radio Stations=12

\(required \: probabilty = \frac{number \: of \: college \: radio \: stations}{total \: number \: of \: radio \: stations} \)

Probability=12/28=3/7

Answer:

10,100,1000,-10,-100,-1000

Step-by-step explanation:

Answer:

first one is rough endoplasmic reticulum and the second is cell membrane

Answer:

y=3x^2+34

3x+y-10=0

Step-by-step explanation:

Answer: the answer is b or 6.48

Step-by-step explanation:

Using the given data and a significance level of 0.01, the p-value for the test of the hypothesis is approximately 0.0151.

To calculate the p-value using Excel, we can first find the test statistic, which follows a t-distribution with degrees of freedom calculated using the formula:

df = (s1^2/n1 + s2^2/n2)^2 / [ (s1^2/n1)^2 / (n1-1) + (s2^2/n2)^2 / (n2-1) ]

where s1 and s2 are the population standard deviations, and n1 and n2 are the sample sizes.

Using the given values, we find that the degrees of freedom are approximately 86.9. Next, we can calculate the test statistic using the formula:

t = (x1-bar - x2-bar) / sqrt(s1^2/n1 + s2^2/n2)

which gives us a value of approximately -1.906. Finally, we can find the p-value using the Excel function T.DIST.RT, which calculates the right-tailed probability of a t-distribution. The formula for the p-value is:

p-value = T.DIST.RT(t, df)

Using Excel, we can enter the formula =T.DIST.RT(-1.906, 86.9) to find that the p-value is approximately 0.0151.

In conclusion, based on the given data and a significance level of 0.01, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the true population mean of the first sample is less than the true population means of the second sample. The p-value of 0.0151 indicates that this conclusion is unlikely to be due to random chance alone.

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To answer the questions related to the probability of droplet sizes, we'll use the normal distribution with the given mean and variance. Let's solve each part of the question:

a. Probability that the size of a single droplet is less than 1500 μm:

To find this probability, we need to calculate the cumulative distribution function (CDF) of the normal distribution up to 1500 μm. We'll use the z-score formula:

z = (x - μ) / σ

Where:

x = droplet size (1500 μm)

μ = mean (1050 μm)

σ = standard deviation (square root of the variance, which is sqrt(22500 μm))

Calculating the z-score:

z = (1500 - 1050) / sqrt(22500)

= 450 / 150

= 3

Using the z-score table or a calculator, we can find that the cumulative probability corresponding to z = 3 is approximately 0.9987.

Therefore, the probability that the size of a single droplet is less than 1500 μm is approximately 0.9987.

b. Probability that the size of a single droplet is between 1000 and 1500 μm:

Similar to part (a), we need to calculate the cumulative probability for two values: 1000 μm and 1500 μm. Let's calculate the z-scores for both values:

For 1000 μm:

z_1000 = (1000 - 1050) / sqrt(22500)

For 1500 μm:

z_1500 = (1500 - 1050) / sqrt(22500)

Once we have the z-scores, we can find the corresponding cumulative probabilities using the z-score table or a calculator. Then, we subtract the probability for 1000 μm from the probability for 1500 μm to find the probability between the two values.

c. Characterizing the smallest 2% of all droplets:

To characterize the smallest 2% of droplets, we need to find the droplet size that corresponds to the 2nd percentile of the normal distribution. In other words, we need to find the value x such that the cumulative probability up to x is 0.02. We can use the z-score formula to solve for x:

z = (x - μ) / σ

We'll find the z-score corresponding to the cumulative probability 0.02 using the z-score table or a calculator. Then, we can rearrange the formula to solve for x:

x = z * σ + μ

d. Probability that at least one of five independently selected droplets exceeds 1500 μm:

To find this probability, we'll use the complement rule. The probability that none of the five droplets exceed 1500 μm is the complement of the probability that at least one of them exceeds 1500 μm. We can calculate this probability by subtracting the probability of none from 1. We'll use the probability obtained in part (a) for a single droplet.

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Answer:

55/7 in simplest form is 7 6/7

The proportional relationship has a constant of proportionality of 4.96

From the question,

The proportional relationship is given as

y = 4.96x

As a general rule

A proportional relationship is represented as y = kx

Where k represents the constant of proportionality

By comparing the y = 4.96x and y = kx, we have

k = 4.96

Hence, the constant of proportionality in the proportional relationship is k = 4.96

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Answer:

C

Step-by-step explanation:

The quotient of d minus 16 and 3 means that d - 16 is in the numerator and 3 is in the denominator. This equation is equal to 4, so the answer is:

(d - 16) / 3 = 4

I hope this helped and please mark me as brainliest!

Conceptually, the arithmetic and geometric average returns are different measures used to describe the performance of an investment or an asset over a specific period.

The arithmetic average return, also known as the mean return, is calculated by adding up all the individual returns and dividing by the number of periods. It represents the average return for each period independently.

On the other hand, the geometric average return, also called the compound annual growth rate (CAGR), considers the compounding effect of returns over time. It is calculated by taking the nth root of the total cumulative return, where n is the number of periods.

When to use each measure depends on the context and purpose of the analysis:

1. Arithmetic Average Return: This measure is typically used when you want to evaluate the average return for each individual period in isolation. It is useful for analyzing short-term returns, such as monthly or quarterly returns. The arithmetic average return provides a simple and straightforward way to assess the periodic performance of an investment.

2. Geometric Average Return: This measure is more suitable when you want to understand the compounded growth of an investment over an extended period. It is commonly used for long-term investment horizons, such as annual returns over multiple years.

The geometric average return provides a more accurate representation of the overall growth rate, accounting for the compounding effect and reinvestment of returns.

In summary, the arithmetic average return is suitable for analyzing short-term performance, while the geometric average return is preferred  evaluating long-term growth and the compounding effect of returns.

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The equation has infinite solutions which lie on the graph of this equation.

We have the following equation -

y = 8 - 2x

We have to solve for the possible values of x and y for which the equation is satisfied.

The rearrangement of a mathematical equation is process of expressing a variable in a equation in terms of other variables, constants etc.

According to the question, we have the following equation -

y = 8 - 2x

Rearranging the equation -

y = - 2x + 8

Now, plot the equation on graph - (Graph is attached at the end)

All the coordinates on this line satisfy the equation → y = 8 - 2x.

Hence, the equation has infinite solutions which lie on the graph of this equation.

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Step-by-step explanation:

8 + (-4) = 4

bcoz positive + negative you need to subtract it and copy the sign for the highest number

-5 + (-5) = - 10

bcoz of the its same negative you need to add

12 + 14 =26

-2/3 + - 5/6 = - 3/2

first you need to find the LCD and the lcd of 2 and 3 is 6 simplify it become - 4/6 + - 5/6 = - 9/6 find the GCF of 9 and 6 is 3 so - 9/6 divide by 3/3 is - 3/2

(8) (-4) = - 32

bcoz positive times negative is negative

(13) (7) = 91

kts positive coz they are both positive

(-9) (-12) = 108

its positive bcoz negative times negative is positive

(1/2) (2/5) = 1/5

bcoz 1/2 (1/5) = 2/10 find the GCF and its 2. so 2/10 ÷ 2/2 =1/5

(-3/8) (3/4) = - 9/32

The curve given by the vector-valued function r(t) = 5t^2i + 8t^3j is smooth on the open interval (-∞, +∞).

A vector-valued function is considered smooth when its components, i.e., the x and y components in this case, have continuous derivatives. The given function r(t) = 5t^2i + 8t^3j has the components x(t) = 5t^2 and y(t) = 8t^3.

Both x(t) and y(t) are polynomial functions, and polynomials are infinitely differentiable, meaning they have derivatives of all orders. Therefore, the derivatives of x(t) and y(t) exist for all real values of t.

Since the derivatives of x(t) and y(t) are continuous, the original vector-valued function r(t) = 5t^2i + 8t^3j is also smooth for all real values of t. Therefore, the curve described by the function is smooth on the open interval (-∞, +∞).

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Answer:

y = 3x + 4

Step-by-step explanation:

Given:

Coordinates

(-3 , -5)

Slope m = 3

Find;

Equation of slope

Computation:

Given, x1 = -3 and y1 = -5

Equation of slope = y - y1 = m(x - x1)

Equation of slope = y - (-5) = 3(x + 3)

Equation of slope = y + 5 = 3x + 9

Equation of slope = y = 3x + 9 - 5

Equation of slope = y = 3x + 4

y = 3x + 4

Answer:

Jacob got 18 votes.

Hope this helps :)

When the dimensions of a rectangular prism are doubled, the volume increases by a factor of 8.

A rectangular prism is a three-dimensional shape with six rectangular faces. The volume of a rectangular prism is calculated by multiplying the lengths of its three dimensions: length, width, and height. When these dimensions are doubled, each of the three dimensions is multiplied by 2.

Let's assume the original dimensions of the rectangular prism are length (L), width (W), and height (H). When these dimensions are doubled, the new dimensions become 2L, 2W, and 2H. To calculate the new volume, we multiply these new dimensions together: (2L) * (2W) * (2H) = 8LWH.

Comparing the new volume (8LWH) to the original volume (LWH), we see that the volume has increased by a factor of 8. This means that the new volume is eight times larger than the original volume. Doubling each dimension of a rectangular prism results in a significant increase in its volume.

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Answer:

B.  √5

Step-by-step explanation:

Given:

\(K=\sqrt{9-4\sqrt{5}}\)

Rewrite 9 as 5 + 4:

\(= \sqrt{5-4\sqrt{5}+4}+2\)

Rewrite 5 as (√5)², 4 as 2² and 4√5 as 2 · 2√5:

\(= \sqrt{(\sqrt{5})^2-2 \cdot 2\sqrt{5}+2^2}+2\)

Apply the perfect square formula  \(a^2-2ab+b^2=(a-b)^2\):

\(=\sqrt{(\sqrt{5}-2)^2}+2\)

Apply radical rule  \(\sqrt{a^2}=a\)

\(=\sqrt{5}-2+2\)

Simplify:

\(=\sqrt{5}\)

Answer:

1296cm².

Step-by-step explanation:

= 12×36×6÷2 ................

plz check weather correct or notn

Answer:

8/7

Step-by-step explanation:

(2,-5) (9,3)

3-(-5)=8 because you apply your keep change change

9-2=  7

so 8/7

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

5 groups ===> 1

1 group ====> 5

Step 02:

We must apply the algebraic rules to find the solution.

5 groups * 1 = 1 group * 5

5 * 1 = 1 * 5

5 = 5

The answer is:

Brent is correct

Answer:

y+x=1

y-x=1

Step-by-step explanation:

Well If x is 0, its pretty straight forward.

1+0=1

1-0=1

lol hope this helps

Answer:

Step-by-step explanation:

first lets find the total # of portions:

3+4+13=16+4=20

To make 4kg of this alloy you have to use:

nickel: (4/20)*3=12/20=6/10=0.6 kg

zinc: (4/20)*4=16/20=8/10=0.8 kg

copper: (4/20)*13=52/20=26/10=2.6 kg