Translate to an algebraic expression and simplify if possible:
The product of 5 and the sum of x and 7.
O 5x + 35
O None of these are correct
O 5x + 7
O 5(x + 7)

Answer and Step-by-step explanation:

Solution:

Given:

V = 2π cm3

We know that:

2π = πr2h

2π / πr2 = h

Which gives: h = 2 / r2

Minimize surface area = 2πrh + 2πr2

S = 2πrh + 2πr2

Put h = 2/ r2 in surface area, we get:

S = 2πr (2/ r2 ) + 2πr2

S = 4 π / r + 2πr2

Therefore, s(r) = 4 π / r + 2πr2

Differentiate concerning r, we have

S’(r) = -4π / r2 + 4πr

Again differentiate concerning r, we have:

S”(r) = 2 x 4 π/ r3 + 4π

For s’(r) = 0

0 = -4π / r2 + 4πr

-4π + 4πr3 = 0

r3 = 1

r = 1 cm

and s”(1) > 0 at r = 1 is point of minima.

So h = 2 π / π x1 x1

  = 2cm

Therefore minimum surface area the can should have a radius of 1cm and height of 2cm.

The higher R-squared value of the multiple regression model with the higher order independent variable implies that the linear model is not the best fit and that a more complex model is needed to better explain the data

1. Multiple regression models involve fitting a model that includes one or more independent variables to predict a dependent variable.

2.A value of X to a higher power, such as X squared, for an independent variable in a multiple regression model indicates that the relationship between the independent and dependent variables is not linear.

3. If this model produces a higher value of R-squared than a linear model, it means that it is a better fit for the data.

4. However, it does not necessarily imply that the linear model's residual plot is not randomly distributed around the zero line.

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The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

K=2h

k=0.5h

k=h + 1

k= 0.5h + 10

Answer:

\(x=3\)

Step-by-step explanation:

So we have the equation:

\(2x+7+2x=19\)

First, let's combine like terms on the left:

\((2x+2x)+7=19\)

Add:

\(4x+7=19\)

Subtract 7 from both sides:

\((4x+7)-7=(19)-7\)

The left side cancels. Subtract on the right:

\(4x=12\)

Now, divide both sides by 4:

\(\frac{4x}{4}=\frac{12}{4}\)

The left cancels. Divide on the right:

\(x=3\)

So, the value of x is 3.

Answer:

X=3

Step-by-step explanation:

2x+2x(=4x)=19-7

4x=12

X=12\4(divide)

x=3

Given :

The ratio of the amount of gold to the amount of silver is 2:5.

To Find :

The weight of gold in the alloy, if there are 80 g of silver.

Solution :

Let, amount of gold is x.

So, the ratio of amount of gold and silver is :

\(\dfrac{x}{80}=\dfrac{2}{5}\\\\x=32\ g\)

Therefore, the weight of gold in the alloy is 32 g.

Hence, this is the required solution.

Answer:

32

Step-by-step explanation:

do 80÷5=16 to get unit. Then do 16*2=32

The required coefficients are:4, -1, -11, and 7.

Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.

In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.

In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.

We need to consider the polynomial:

(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)

To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:

4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn

Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2

Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn

Taking the coefficients of the constant terms6 + 2 - 1 = 7

Therefore, the required coefficients are:4, -1, -11, and 7.

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Answer: 150

Step-by-step explanation:

You got it right, just divide 300 by 2 :)

Answer:

150

Step-by-step explanation:

50% is half if everything... half of 300 is 150

El supplemento y el complemento de cada ángulo son, respectivamente:

Caso A: m ∠ A' = 43°

Caso B: m ∠ A' = 31°

De acuerdo con la geometría, la suma de un ángulo y su complemento es igual a 90° and la suma de un ángulo y su suplemento es igual a 180°. Matemáticamente hablando, cada situación es descrita por las siguientes formulas:

Ángulo y su complemento

m ∠ A + m ∠ A' = 90°

Ángulo y su suplemento

m ∠ A + m ∠ A' = 90°

Donde:

Ahora procedemos a determinar cada ángulo faltante:

Caso A: Complemento

47° + m ∠ A' = 90°

m ∠ A' = 43°

Caso B: Suplemento

149° + m ∠ A' = 180°

m ∠ A' = 31°

El enunciado se encuentra escrito en español y la respuesta está escrita en el mismo idioma.

The statement is written in Spanish and its answer is written in the same language.

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Answer: The sum of the digits of 99 × n is 27 - 10 = 17.

Step-by-step explanation:

To find the sum of the digits of 99 × n, we can use the fact that 99 × n = 100 × n - n. The sum of the digits of 100 × n is simply n, since the hundreds digit is zero. Therefore, the sum of the digits of 99 × n is equal to the sum of the digits of n - n, which is simply zero.

For example, if n = 37, then 99 × n = 99 × 37 = 3,699. The sum of the digits of 3,699 is 3 + 6 + 9 + 9 = 27. The sum of the digits of 37 is 3 + 7 = 10. Therefore, the sum of the digits of 99 × n is 27 - 10 = 17.

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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∫ (3x^2 + 6x - 4) dx

like last time, but more

x^3 + 3x^2 - 4x + c

use the power rule, so for instance

∫ 3x^2

increase the exponent by 1

3x^3

now divide by the exponent

3x^3 / 3

simplify

x^3

∫ 6x

increase the exponent by 1, 1 + 1 = 2

6x^2

and divide by the exponent

6x^2 / 2

3x^2

Answer:

B. 5/144

5 can't go in 144 evenly. so its leading to 5/144

Step-by-step explanation:

The answer would be B.5/144

5 1 5

---- x ----- = -----

12 12 144

12 x 12 = 144

The capacity of the mug is 7/6 cups.

Given,

A mug is 3/7 full.

The mug contains 1/2 of a cup of water.

Solution:

Let x be the water.

Water the mug has = 3/7 of x

= 3/7x

Since the water in the mug is 1/2 cup,

3/7x = 1/2

x = 1/2 ÷ 3/7

= 1/2 × 7/3

= 7/6

Therefore,

The capacity of the mug is 7/6 cups.

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Hello, please consider the following.

We know that

\(a = p^{\frac{1}{3}}-p^{-\frac{1}{3}}\\\\=p^{\frac{1}{3}}-\dfrac{1}{p^{\frac{1}{3}}}\)

And we can write that.

\((p-\dfrac{1}{p})^3=(p-\dfrac{1}{p})(p^2-2+\dfrac{1}{p^2})\\\\=p^3-2p+\dfrac{1}{p}-p+\dfrac{2}{p}-\dfrac{1}{p^3}\\\\=p^3-\dfrac{1}{p^3}-3(p-\dfrac{1}{p})\)

It means that, by replacing p by \(p^{1/3}\)

\((p^{1/3}-\dfrac{1}{p^{1/3}})^3=p-\dfrac{1}{p}-3(p^{1/3}-\dfrac{1}{p^{1/3}})\\\\\\\text{ So }\\\\a^3=p-\dfrac{1}{p}-3a\\\\<=>\boxed{ a^3+3a=p-\dfrac{1}{p} }\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

106.76

Step-by-step explanation:

The formula to calculate the circumference if you know the radius is as follows: Circumference = 2 x Radius x π π = Pi = 3.14, thus, the math to calculate the circumference of a circle with a radius of 17 is: 2 x 17 x 3.14 = 106.76

We can use the formula for the monthly payment of a loan to calculate the amount we need to pay each month:

M = (P * r * (1+r)^n) / ((1+r)^n - 1)

Where:

M = the monthly payment

P = the principal (the amount borrowed)

r = the monthly interest rate (which is the annual interest rate divided by 12)

n = the total number of months in the loan term (which is the number of years multiplied by 12)

Plugging in the given values, we get:

P = $3825

r = 15% / 12 = 0.0125

n = 4 years * 12 = 48 months

M = ($3825 * 0.0125 * (1+0.0125)^48) / ((1+0.0125)^48 - 1)

M ≈ $94.87

Therefore, the monthly payment will be approximately $94.87.

Using both hoses will take 10 minutes to fill up the kiddie pool. Mary can fill up 1/3 of the pool using the front yard hose in 10 minutes and 1/6 of the pool using the backyard hose in 10 minutes.

To solve this problem, we need to use the concept of rates. Let's assume the rate of the hose in the backyard is x, so the rate of the hose in the front yard is 2x (because it is twice as fast as the other hose).

The combined rate of the two hoses is x + 2x = 3x, which means they can fill the pool in 30/3x = 10/x minutes.

We know that the area of the pool is 600 square feet and each small rock covers 20 square feet, so we need a total of 600/20 = 30 small rocks to cover the pool.

Since the mass of each rock is 20 grams, the total mass of all 30 rocks is 30 x 20 = 600 grams.

To find the density, we divide the total mass (600 grams) by the total volume of the rocks (30 x 20 cubic feet = 600 cubic feet)

Density = 600g / 600 cubic feet = 1g/cubic foot

Therefore, the answer is B. 10 minutes for the pool to fill up, and the density of the rocks is 1 gram per cubic foot.

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Answer:

x - (-8,0)

y - (0,8)

Step-by-step explanation:

To find the x-intercept, substitute in  0  for  y  and solve for  x . To find the y-intercept, substitute in  0 for  x  and solve for  y .

Answer: Choice A

Jackson likes earning rewards on his purchases.

=========================================================

Explanation:

Debit cards do not give out reward points for using them. Credit cards on the other hand do offer such a feature. So if Jackson wants reward points, he'll need to use a credit card. This is why choice A is the answer.

Choice B is ruled out because shopping locally could involve either type of card, or simply cash, depending the merchant's payment preferences. There's no incentive to use a credit card here.

Choice C is ruled out because a debit card is tied to a checking account. Blake making weekly transfers to this account seems to heavily imply he uses it a lot; therefore, he's likely using a debit card here.

Choice D is ruled out because Jena being careful with money would likely use a debit card. With debit cards, you use only the money in the checking account. No money is borrowed like with a credit card. This means there's no worry about going into debt when using a debit card.

Option d

...............

Answer:

D

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Using the general equation for depreciation which is y = A(1 – r)^t, The value of the car in 4 years is $12528.15

The value of the car is solved by using the formula for depreciation which is  y = A(1 – r)t

definition of variables

where

y = current value, = ?

A = original cost, = $24,000

r = rate of depreciation, = 15% and

t = time, in years. = 4 years

substituting the variables

current value, y = A(1 – r)t

current value, y = 24000 * (1 - 0.15)⁴

current value, y = 12528.15

the depreciation is $12528.15

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\( - 1 - ( - 8) \\ = - 1 + 8 \\ = 7\)

Hope it helps

ray4918 here to help

The plane containing point B and parallel to the plane CDH is plane ABF.

As, from the diagram we can see that there are two plane passing from point B; plane ABF and ABC.

But plane ABC is intersecting the given plane CDH, while plane ABF is not.

Thus, plane ABF is parallel to the plane CDH.

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She has the exact amount of fabric that she needs for this project.

We know that she is in charge of 40 campers, and she wants to make fabric-covered frames, such that each one needs 1/6 yards of fabric.

We know that he has a total of 6 + 2/3 yards to do this, and we need to see if that is enough.

Now, for each one of the 40 campers she needs 1/6 yards, so the total amount she needs is given by the product:

T = 40*(1/6 yards) = 40/6 yards = (36 + 4)/6 yards = (6 + 4/6) yards

T = (6 + 2/3) yards

So she has the exact amount of fabric that she needs for this project.

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Answer:

a. The expression that represents the number of cups of hot chocolate drunk per day as a function of degrees Celsius is

y = -30x + 3600 pr the equivalent y = 3600 - 30x

b. How many cups would they drink at 5 degrees Celsius?

x = 5 --> y = 3600 - 30 X 5 --> y = 3600 - 150 --> y = 3450

c. How many cups would they drink at 25 degrees Celsius?

x = 25 --> y = 3600 - 30 X 25 --> y = 3600 - 750 --> y = 2850

d. Write an equation to determine the temperature if 3000 cups of hot chocolate were consumed in a day.

y = 3000 --> 3000 = 3600 - 30x

e. Solve the equation to find the temperature if 3000 cups of hot chocolate were consumed in a day.

--> 3000 = 3600 - 30x --> 3000 - 3000 + 30x = 3600 - 30x - 3000 + 30x --> 30x + 600 --> 30x/30 = 600/30 --> x = 20

f. Is this answer reasonable? Explain.

It is very reasonable.

At 0 degree C. they drink 3600 cups.

As the temperature increases, hot chocolate consumption decreases.

At 5 degree C. they drink less hot chocolate: 3450 cups.

Since 20 degree C. is even warmer, they should drink even less at 20 degree C., but not as little as the 2850 cups they drink on those very warm 25 degree C. days.

Step-by-step explanation:

We need to name/define variables:

y = number of cups of hot chocolate consumed in a day in Fairbanks.

x = temperature in degrees Celsius

"For each rise of 1 degrees Celsius, their consumption decreases by 30 cups per day."

That tells you that y is a linear function of x, so we should be able to write it as

y=mx + b with some constants for slope, m, and y-intercept, b.

It also tells you that the slope is m=-30.

"People living in Fairbanks drink 3600 cups of hot chocolate per day when the temperature is 0 degrees Celsius."

That gives you the value of y when x=0, which is the y-intercept,

b=3600

Answer:

Step 1 Divide all terms by a (the coefficient of x2).

Step 2 Move the number term (c/a) to the right side of the equation.

Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.

hope this help

but this is little info dont worry i will answer your question just in a minute

Step-by-step explanation:

To find the mean of a set of numbers, you need to add up all the numbers and then divide by the number of numbers in the set.

In this case, the mean of the four numbers is 12, which means the sum of those four numbers is 4 × 12 = 48. The mean of the other six numbers is 22, which means the sum of those six numbers is 6 × 22 = 132. The sum of all ten numbers is therefore 48 + 132 = 180.

To find the mean of all ten numbers, we need to divide the sum by the number of numbers, which is \(\frac{180}{10}\) = 18. Therefore, the mean of all ten numbers is 18.