what is 2(27)=3y+8?
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The relationship between length and weight can be modeled by a power function.

The fact that the scatterplot of the natural logarithm of weight vs. the natural logarithm of length shows a more linear relationship suggests that the relationship between length and weight can be better modeled by a power function rather than an exponential function. This is because when the logarithms of both variables are taken, an exponential function becomes a linear function, while a power function remains a non-linear function.

In a power function, one variable is raised to a power that is not necessarily an integer, whereas in an exponential function, one variable is raised to a constant power. Therefore, it is more likely that the relationship between length and weight can be modeled by a power function.

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The missing Value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

The missing value that, when multiplied by 5/3^4, gives the result of 5^4, we can set up the equation:

(5/3^4) * x = 5^4

To solve for x, we can simplify both sides of the equation. First, let's simplify the right side:

5^4 = 5 * 5 * 5 * 5 = 625

Now, let's simplify the left side:

5/3^4 = 5/(3 * 3 * 3 * 3) = 5/81

Now we have:

(5/81) * x = 625

To solve for x, we can multiply both sides of the equation by the reciprocal of 5/81, which is 81/5:

(81/5) * (5/81) * x = (81/5) * 625

On the left side, the fraction (81/5) * (5/81) simplifies to 1, leaving us with:

1 * x = (81/5) * 625

Simplifying the right side:

(81/5) * 625 = 13125

Therefore, the missing value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

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Answer: -36

Step-by-step explanation:

13, 6, -1

to get from 13 to 6 and 6 to -1, you would subtract by 7 so keep subtracting by 7 until you get 8 different terms

13, 6, -1, -8, -15, -22, -29, -36

the eighth term would be -36

i hope that makes sense

Answer:

-18

Step-by-step explanation:

km

k= -3

m= 6

km = -3*6

km = -18

Answer:

The answer is -18.

Step-by-step explanation:

k×m

-3×6

-18

To solve the problem, we can let x be the number of cars washed and y be the number of SUVs washed. We have two equations based on the given information:

x + y = 105, since the total number of vehicles washed is 105.

10x + 20y = 1700, since the students made $1700 by washing cars and SUVs.

To simplify the second equation, we can divide both sides by 10:

x + 2y = 170

We can solve for one variable by subtracting the first equation from the second:

x + 2y - (x + y) = 170 - 105

This simplifies to:

y = 65

We can then substitute y = 65 into the first equation to find x:

x + 65 = 105

This simplifies to:

x = 40

Therefore, the students washed 40 cars and 65 SUVs to make $1700 at the fundraiser.

Answer: A≈1385.44m²

Step-by-step explanation:

A=πr2=π·212≈1385.44236m²

Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

Answer:

7.5

Step-by-step explanation:

Since we are given the price for 5 bags of dog food, we have to find the unit rate. Now to do that we divide the price by the amount.

12.50/5= 2.50

now since we have the unit rate, we take that and multiply the price of one by 3 to find the price of 3

2.50x3=7.50

Hope this helps!

Answer: 7.5 bags

Step-by-step explanation:

$12.50 divided by 5 bags= $2.5 per bag

$2.5*3 bags= $7.5

Answer:

The answer is (0,-6)

Answer:

b 16.4 ft

Step-by-step explanation:

To solve this problem using a graphing calculator, we need to plug in the value of q (which is given as 7) into the equation y = 2 csc e, and then graph the resulting equation.

First, we need to convert the angle e from degrees to radians, because the csc function takes its input in radians. We can use the conversion formula:

radians = degrees x (π/180)

So for e = 2, we have:

e (in radians) = 2 x (π/180) = 0.0349 radians

Now we can plug this value into the equation y = 2 csc e:

y = 2 csc(0.0349) ≈ 103.8 feet

This tells us that the length of the rafters needed to make the roof is approximately 103.8 feet. However, the question asks us to round to the nearest tenth of a foot, so the answer is:

y ≈ 103.8 feet ≈ 103.8 rounded to the nearest tenth of a foot

Therefore, the length of the rafters needed to make the roof for q 7" is approximately 103.8 feet, rounded to the nearest tenth of a foot.

So the correct answer is (b) 16.4 feet.

Using the graphing calculator, we find that the length of the rafters needed is approximately 16.4 feet, Therefore, the correct answer is option B, 16.4 feet.

To find the length of the rafters needed for the roof with an angle of 7 degrees, we'll use the given function y = 2 * csc(e), where e is the angle formed by the rafters and the top of the wall. Here's a step-by-step explanation:

1. Convert the angle from degrees to radians: e (in radians) = (7 degrees * π) / 180 ≈ 0.1222 radians.

2. Calculate the cosecant  (csc) of the angle e: csc(0.1222) ≈ 8.185.

3. Plug the value of csc(e) into the function: y = 2 * 8.185 ≈ 16.37.
Using a graphing calculator, we can input the function y = 2 csc e and graph it. Then, we can use the given angle of 2 to find the length of the rafters needed for a roof with a peak of 7 feet.

4. Round the length to the nearest tenth of a foot: 16.37 ≈ 16.4 feet.
When we graph the function, we can see that the length of the rafters is the distance between the x-axis and the point on the graph where y = 7.
So, the length of the rafters needed to make the roof for an angle of 7 degrees is approximately 16.4 feet (Option b).

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Answer: D

Step-by-step explanation:

Answer:p is r

Step-by-step explanation:

Answer: $4$

Step-by-step explanation:

The correct option is b) 3. The average processing time is 4 minutes. A denial of service probability of no more than 0.01 is desired. The average interarrival time is 10 minutes. The system need 3 servers.

To determine how many servers are needed in an Erlang loss system with an average processing time of 4 minutes, a denial of service probability of no more than 0.01, and an average interarrival time of 10 minutes, you can follow these steps:

1. Calculate the traffic intensity (A) using the formula: A = processing time / interarrival time. In this case, A = 4 minutes / 10 minutes = 0.4 Erlangs.

2. Use Erlang's B formula to find the number of servers (s) required to achieve a desired probability of denial of service (P): P = (\(A^s\) / s!) / Σ(\(A^k\) / k!) from k = 0 to s.

3. Iterate through the options provided (a: 2 servers, b: 3 servers, c: 4 servers, d: 5 servers) and find the first option that satisfies the desired probability of denial of service (P ≤ 0.01).

After performing the calculations, you'll find that option b) 3 servers satisfies the desired probability of denial of service. Therefore, the system needs 3 servers to achieve a denial of service probability of no more than 0.01.

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Answer:

ΔABC ~ ΔEDF

Step-by-step explanation:

ΔABC ~ ΔEDF

Given:

∠A = ∠E

∠B = ∠D

So,

We say that;

∠C = ∠F

By AAA;

Rule

ΔABC ~ ΔEDF

Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

Answer:

Step-by-step explanation:

Coins:

Equations:

Substitute q in the first equation:

Substitute p and q in the third equation:

Then, finding p and q:

So there are 30 quarters, 14 dimes and 29 pennies

Proof:

A random variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.

A random variable is defined as a variable that has posses a single numerical value, and determined for each outcome of an event. That is a variable whose value is either unknown or a function that assigns values to each of an experiment's outcomes. It can be either discrete (having specific values) or continuous (any value in a continuous range). Generally, random variables are represented by capital letters for example, X and Y. For example consider the tossing of coin event, then the values Heads = 0 and Tails= 1 and we have a Random Variable "X". Hence, required answer is random variable.

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Complete question:

a _______ variable is a variable that has a single numerical value, determined bychance, for each outcome of a procedure.

Answer:

The shadow is not the same image as the lady

Step-by-step explanation:

Had it in a test got it right

The lady’s shadow in the picture not a rigid transformation because the shadow is not the same image as the lady.

A rigid transformation (also called an isometry) is a transformation of the plane that preserves length.

In a rigid transformation the pre-image and image are congruent (have the same shape and sizes).

The transformation of a function may involve any change.

These can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

The lady’s shadow in the picture not a rigid transformation because the shadow is not the same image as the lady.

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Answer:

2t

Step-by-step explanation:

The expressions are not the same because different terms are negative. We can visualize the difference by rewriting the expressions as 13t + (-2t) and (-13t) + 2t. In the first expression, 13t-2t, the 2t is negative because it is being subtracted, and subtracting a number is the same as adding a negative.

The solution to the given differential equation is L⁻¹{Y(s)} = (b³ t sin 2t) / (2 (sin bt - bt cos bt))

To solve the differential equation using the convolution theorem, we'll follow these steps:

Take the Laplace transform of both sides of the differential equation.

Use the convolution theorem to simplify the resulting expression.

Take the inverse Laplace transform to obtain the solution in the time domain.

Let's start with step 1:

Given differential equation: d²y/dt² - 4y = t cos 2t

Taking the Laplace transform of both sides, we get:

s²Y(s) - sy(0) - y'(0) - 4Y(s) = L{t cos 2t}

Where Y(s) represents the Laplace transform of y(t), y(0) is the initial condition for y(t) at t = 0, and y'(0) is the initial condition for dy/dt at t = 0.

The Laplace transform of t cos 2t can be found using the Laplace transform table:

L{t cos 2t} = -Im{d/ds[1 / (s² - (2i)²)]}

= -Im{d/ds[1 / (s² + 4)]}

= -Im{(-2s) / [(s² + 4)²]}

= 2Im{(s) / [(s² + 4)²]}

Now let's simplify the expression using the convolution theorem:

The Laplace transform of the convolution of two functions, f(t) and g(t), is given by the product of their individual Laplace transforms:

L{f * g} = F(s) G(s)

In our case, f(t) = y(t) and g(t) = 2Im{(s) / [(s² + 4)²]}.

Therefore, F(s) = Y(s) and G(s) = 2Im{(s) / [(s² + 4)²]}.

Multiplying F(s) and G(s), we get:

Y(s) G(s) = Y(s) 2Im{(s) / [(s² + 4)²]}

Now, we can rewrite the left-hand side of the equation using the convolution theorem:

Y(s) * 2Im{(s) / [(s² + 4)²]} = L{t cos 2t}

Taking the inverse Laplace transform of both sides, we have:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = L⁻¹{L{t cos 2t}}

Simplifying the right-hand side using the inverse Laplace transform table, we get:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = t sin 2t / 4

Now, we can apply the convolution theorem to the left-hand side of the equation:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = L⁻¹{Y(s)} * L⁻¹{2Im{(s) / [(s² + 4)²]}}

The inverse Laplace transform of 2Im{(s) / [(s² + 4)²]} can be found using the inverse Laplace transform table:

L⁻¹{2Im{(s) / [(s² + 4)²]}} = 1 / 2b³ (sin bt - bt cos bt)

Therefore, we have:

L⁻¹{Y(s)} * 1 / 2b³ (sin bt - bt cos bt) = t sin 2t / 4

From this, we can deduce the inverse Laplace transform of Y(s):

L⁻¹{Y(s)} = (t sin 2t / 4) / (1 / 2b³ (sin bt - bt cos bt))

Simplifying further:

L⁻¹{Y(s)} = (b³ t sin 2t) / (2 (sin bt - bt cos bt))

This is the solution to the given differential equation.

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Answer:

x=2

Step-by-step explanation:

You have to subtract 8 from both sides.

-5x+8=-2

-8 -8

----------------

-5x= -10

now divide both sides by -5.

x=-10/-5

(And two negatives make a positive.)

x=10/5

now you have to simplify 10/5

10/5 simplified is 2

so the answer is:

x=2

I hope this helps. :)

The distance from the vector (1, 2, 3, 4) to the subspace of R^4 spanned by the vectors (1, -1, 1, 0) and (3, 2, 2, 1) can be calculated as the length of the orthogonal projection of (1, 2, 3, 4) onto the subspace.

To find the distance, we first need to determine the orthogonal projection of the vector (1, 2, 3, 4) onto the subspace spanned by (1, -1, 1, 0) and (3, 2, 2, 1).

The orthogonal projection of (1, 2, 3, 4) onto the subspace can be obtained by projecting (1, 2, 3, 4) onto each of the spanning vectors and then summing those projections. Using the projection formula, we find that the projection of (1, 2, 3, 4) onto the first spanning vector (1, -1, 1, 0) is (5/3, -5/3, 5/3, 0), and the projection onto the second spanning vector (3, 2, 2, 1) is (3/2, 1, 1, 1/2).

Next, we calculate the difference vector between (1, 2, 3, 4) and the sum of the two projections: (1, 2, 3, 4) - [(5/3, -5/3, 5/3, 0) + (3/2, 1, 1, 1/2)] = (2/6, 13/6, 7/6, 7/2).

Finally, we find the length of the difference vector, which represents the distance between (1, 2, 3, 4) and the subspace: √[(2/6)^2 + (13/6)^2 + (7/6)^2 + (7/2)^2] = √(242/9).

Therefore, the distance from the vector (1, 2, 3, 4) to the subspace of R^4 spanned by (1, -1, 1, 0) and (3, 2, 2, 1) is √(242/9).

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Answer:

X= -4

Answer:

1.5km of thread

Step-by-step explanation:

1 spool = 375 m

4 spools = 375 x 4 = 1500

1500 m = 1.5km

Answer:

-19

Step-by-step explanation:

Since we already have the values of the variables and the equation, all we have to do is plug in the numbers.

-b + 3x

-(4) + 3(-5)

-4 + (-15)

-4 - 15

-19

Answer:

\(\boxed {\boxed {\sf -19}}\)

Step-by-step explanation:

We are asked to evaluate the following expression.

\(-b+3x\)

We know the b is equal to 4, and x is equal to -5.

We can substitute the values into the expression.

\(-(4) + 3(-5)\)

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Multiply first. We multiply -1 and 4, then 3 and -5.

\([-1 *4] + 3(-5)\)

\(-4+ [3*(-5)]\)

\(-4+-15\)

Add.

\(-19\)

The expression -b+3x is equal to -19 when b equals 4 and x equals -5.

(a) The cost of 1 kg of turnips is £71.95, and

(b) The cost of 1 kg of mushrooms is £89.50.

To solve this problem, let's assign variables to the unknowns.

Let the cost of 1 kg of mushrooms be 'm' and the cost of 1 kg of turnips be 't'.

According to the given information:

Equation 1: 2m + 2.5t = 8.55

Equation 2: 3m + 4t = 13.10

We can solve these equations simultaneously to find the values of 'm' and 't'.

To eliminate the decimals, let's multiply both sides of Equation 1 by 10 and Equation 2 by 20:

20m + 25t = 85.50

60m + 80t = 262.00

Now, let's multiply Equation 1 by 12 and subtract Equation 2 multiplied by 5:

240m + 300t - (60m + 80t) = 1026.00 - 1310.00

180m + 220t = -284.00

We have a new equation:

180m + 220t = -284.00 ---(3)

Next, let's multiply Equation 1 by 18 and subtract Equation 2 multiplied by 4:

36m + 45t - (60m + 80t) = 154.35 - 524.00

-24m - 35t = -369.65

We have another new equation:

-24m - 35t = -369.65 ---(4)

Now, we have a system of linear equations with two variables. Let's solve this system by eliminating one variable.

Multiply Equation 3 by 35 and Equation 4 by 220:

6300m + 7700t = -9940.00 ---(5)

-5280m - 7700t = -81323.00 ---(6)

Adding Equations 5 and 6, we eliminate 't':

1020m = -91263.00

m = -91263.00/1020

m = -89.50

Substituting the value of 'm' back into Equation 3:

180(-89.50) + 220t = -284.00

-16110 + 220t = -284.00

220t = -284.00 + 16110

220t = 15826.00

t = 15826.00/220

t = 71.95.

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Using Trigonometric identities, the value of y = 11.49.

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence.

These are identities that, geometrically speaking, involve certain functions of one or more angles.

They are not to be confused with triangle identities, which are identities that may involve angles but may also involve side lengths or other lengths of a triangle.

Using Trigonometric Identities,

Cos θ = Base / Hypotenuse

Cos 29 = 10 / y

0.87 = 10 / y

y = 10 / 0.87

y = 11.49

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Answer:

\( \frac{y_ 2 - y_ 1 }{x_ 2 -x_ 1 } = \frac{y - y_ 1}{x - x_ 1} \\ \frac{10 - 7}{2 + 1} = \frac{y - 7}{x + 1} \\ \frac{y -7}{x + 1} = 1 \\ y -7 = x + 1 \\ x-y=-8\)

Answer:

\(x=\frac{1}{27}\)

Step-by-step explanation:

Solve for x.

We need to use the quotient property of logarithms.

Quotient Property of Logarithms: \(\log _{b} (x)-\log _{b} (y)=\log _{b} (\frac{x}{y} )\)

Apply the property to our equation.

\(\log(\frac{3}{x})=2\log(9)\)

Simplify the right side by moving the 2 inside the logarithm.

\(\log(\frac{3}{x})=\log(9^2)\)

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

\(\frac{3}{x}=9^2\)

Evaluate \(9^2\).

\(\frac{3}{x}=81\)

Multiply both sides of the equation by x.

\(\frac{3}{x}x=81x\)

Cancel the common factor of x on the left side.

\(3=81x\)

Divide both sides by 81.

\(\frac{3}{81} =\frac{81x}{81}\)

\(\frac{3}{81} =x\)

Simplify the fraction.

\(x=\frac{1}{27}\)