prove that the value of each expression is divisible by the given number 8^10-2^27 is divisible by 14

Without more information about the dimensions of the matrices involved, it is not possible to determine the values for the elements of the matrix z that represents the total text messages sent by sophomores, juniors, and seniors for a week using the matrix equation z = xy.

In general, the product of two matrices A and B is defined only if the number of columns in A is equal to the number of rows in B. If the dimensions of A are m x n, and the dimensions of B are n x p, then the resulting matrix C = AB will have dimensions m x p.

Therefore, we need to know the dimensions of the matrices x and y in order to determine the dimensions and values of the matrix z. Once we know the dimensions of x and y, we can use the matrix multiplication algorithm to calculate the elements of z.

Without this information, we cannot determine the values for the elements of the matrix z.

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Answer: x <- -8

x is less than negative eight.

Step-by-step explanation:

First, subtract 11 from both sides. Then divide both sides by 11. The arrow should be open and pointing to the left.

Answer:

x <- -8

Step-by-step explanation:

the area of the region enclosed by one loop of this curve is 6π square units.

The equation r = 4cos(30°) represents a polar curve. To sketch the curve, we'll plot points by evaluating r for different values of the angle θ.

First, let's convert the angle from degrees to radians:

30° = π/6 radians

Now, let's evaluate r for different values of θ:

For θ = 0°:

r = 4cos(30°) = 4cos(π/6) = 4(√3/2) = 2√3

For θ = 30°:

r = 4cos(30°) = 4cos(π/6) = 4(√3/2) = 2√3

For θ = 60°:

r = 4cos(60°) = 4cos(π/3) = 4(1/2) = 2

For θ = 90°:

r = 4cos(90°) = 4cos(π/2) = 4(0) = 0

For θ = 120°:

r = 4cos(120°) = 4cos(2π/3) = 4(-1/2) = -2

For θ = 150°:

r = 4cos(150°) = 4cos(5π/6) = 4(-√3/2) = -2√3

For θ = 180°:

r = 4cos(180°) = 4cos(π) = 4(-1) = -4

We can continue evaluating r for more values of θ, but based on the above calculations, we can see that the curve starts at r = 2√3, loops around to r = -2√3, and ends at r = -4. The curve resembles an inverted heart shape.

To find the area of the region enclosed by one loop of this curve, we can use the formula for the area of a polar region:

A = (1/2) ∫[α, β] (r(θ))^2 dθ

For one loop, we can choose α = 0 and β = 2π. Substituting the given equation r = 4cos(30°) = 4cos(π/6) = 2√3, we have:

A = (1/2) ∫[0, 2π] (2√3)^2 dθ

 = (1/2) ∫[0, 2π] 12 dθ

 = (1/2) * 12 * θ |[0, 2π]

 = 6π

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Answer:

  \(a_n=a_{n-1}-8;\ a_1=38\)

Step-by-step explanation:

The meaning of ...

  \(a_n=a_{n-1}-8\)

is that each term is 8 less than the one before. That is the description you're trying to match.

The meaning of ...

  \(a_1=38\)

Is that the first term is 38. Even if you don't know the first term, you do know that it is not 14. The fourth term is 14, as the problem statement tells you. Since each term is smaller than the one before, we know the first term is larger than the fourth term, so is larger than 14.

This information is sufficient to let you choose the correct answer.

  \(\boxed{a_n=a_{n-1}-8;\ a_1=38}\)

Answer:

No, because not all corresponding angles are congruent.

Step-by-step explanation:

In order for two triangles to be similar you must have that you know at least 2 corresponding angles are congruent which would also imply the third set of angles are also congruent. You can also tell if two triangles are similar based on their corresponding sides being proportional. Without even checking the proportionally part of corresponding sides, I see the 3 angles in the first triangle do not have the same measurement as the one in the second triangle. Therefore, the triangles cannot possibly by similar.

Hope this helped you love.

Answer:

C

Step-by-step explanation:

Answer:

Smaller number = 6

Larger number =  36

Step-by-step explanation:

Let the smaller number  be x

Larger number = 4x + 12

Sum of two numbers = 42

x + 4x + 12  = 42               {Add like terms}

    5x  + 12 = 42                {Subtract 12 from both sides}

             5x = 42 - 12

             5x = 30                   {Dive both sides by 5}

         5x/5 = 30/5

x = 6

Smaller number = 6

Larger number = 4*6 + 12 = 24 + 12 = 36

Answer:

Step-by-step explanation:

The value of the first card starts at $65 and decreases by $3 for each of x periods. Its value is ...

  65 -3x

The value of the second card starts at $55 and decreases by $2.50 for each of x periods. Its value is ...

  55 -2.5x

The equation that can be used to find x that makes the values equal is ...

  65 -3x = 55 -2.5x

__

The solution can be found by adding 3x-55 to both sides of this equation.

  10 = 0.5x

Multiplying by 2 gives ...

  20 = x

After 20 30-day periods. the cards will have the same value.

__

The value after 20 periods is ...

  65 -3×20 = 65 -60 = 5

Both cards will have a value of $5 when they have the same value.

Answer: 6336 ft.

Step-by-step explanation:

If you were asking what 1.2 miles equals in feet, your answer would be 6336 feet. Good luck on your test tomorrow!

Answer:

6336 feet

Step-by-step explanation:

each mile has 5280 feet. Simply multiply 1.2 by 5280 to get your answer

the ordered pair will be (3,-1) lies in the inverse function.

What is inverse function?

A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1

Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.

function g(x)=∛(x−4)

So the inverse of the function

g ¬(x) = x³+4

So the ordered pair will be (3,-1)

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The situation described represents an example of a Two-Sample t-test problem.

In this case, the researchers are interested in comparing the mean difference in risk-taking behavior between men and women. They have two independent groups, one consisting of 51 men and the other consisting of 55 women. The risk-taking behavior is measured on a scale from 0 to 100.

Since the researchers mention that the variance between the choices of both groups is very similar, it implies that the assumption of equal variances can be made. This assumption allows for the use of a pooled variance estimate when conducting the t-test.

To analyze the data and determine the confidence interval for the mean difference, the researchers can perform a Two-Sample t-test, which accounts for the difference in sample sizes and allows them to compare the means of the two independent groups.

The result of the Two-Sample t-test will provide information about whether there is a statistically significant difference in the mean risk-taking behavior between men and women, as well as a confidence interval for the true difference in means.

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(a) To determine how fast the population is growing when it reaches 5 million people, we can substitute P(t) = 5 into the differential equation P'(t) = 0.06P(t). This gives us P'(t) = 0.06(5) = 0.3 million people per year. Therefore, the population is growing at a rate of 0.3 million people per year when it reaches 5 million people.

(b) To determine the population size when it is growing at a rate of 700,000 people per year, we can set P'(t) = 700,000 and solve for P(t). From the given differential equation, we have 0.06P(t) = 700,000, which implies P(t) = 700,000/0.06 = 11,666,666.67 million people. Therefore, the population size is approximately 11.67 million people when it is growing at a rate of 700,000 people per year.

(c) To find a formula for P(t), we can solve the differential equation P'(t) = 0.06P(t). This is a separable differential equation, and integrating both sides gives us ln(P(t)) = 0.06t + C, where C is the constant of integration. By exponentiating both sides, we get P(t) = e^(0.06t+C). Using the initial condition P(0) = 3, we can find the value of C. Substituting t = 0 and P(0) = 3 into the equation, we have 3 = e^C. Therefore, the formula for P(t) is P(t) = 3e^(0.06t).

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The pizza from Jaco, Costa Rica, with a 27.8-centimeter diameter, has approximately 603.42 square centimeters of pizza.

To calculate the number of square centimeters of pizza, we need to determine the area of the circle using the formula A = πr^2, where A is the area and r is the radius of the circle.

Finding the radius:

The diameter of the pizza from Jaco, Costa Rica, is given as 27.8 centimeters. To find the radius, we divide the diameter by 2:

Radius = Diameter / 2 = 27.8 cm / 2 = 13.9 cm

Calculating the area:

Now that we have the radius, we can substitute it into the formula:

A = πr^2 = π * (13.9 cm)^2

Using the value of π (pi) as approximately 3.14159, we can calculate the area:

A ≈ 3.14159 * (13.9 cm)^2 ≈ 3.14159 * 192.21 cm^2 ≈ 603.42 cm^2

Therefore, the pizza from Jaco, Costa Rica, with a 27.8-centimeter diameter, has approximately 603.42 square centimeters of pizza.

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The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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The resulting electric field vector E() at a point z_0 far from the charge distribution is given by E = (ρ₀ × ρ) / (2ε₀εz_0)

Let's consider a cylindrical Gaussian surface of radius ρ and height z_0, centered at the origin and aligned with the z-axis.

The top and bottom surfaces of the cylinder do not contribute to the flux since the charge is uniformly distributed in the plane at z = 0.

Therefore, the only contribution comes from the curved surface of the cylinder.

By symmetry, the electric field D(P) is radially directed and has the same magnitude at every point on the curved surface.

We can express D(P) as D(P) = D(ρ), where ρ is the distance from the z-axis to the point P on the curved surface.

Now, let's calculate the electric flux Ψ(ρ) through the curved surface of the cylinder:

Ψ(ρ) = ∮S D · dA = D(ρ) × A

where A is the area of the curved surface, given by A = 2πρ× z_0.

Using Gauss's law, we can equate the flux to the enclosed charge divided by ε₀:

Ψ(ρ) = Q_enclosed / ε₀

Q_enclosed is simply the charge density (ρ₀) multiplied by the area of the cylinder's base:

Q_enclosed = ρ₀ × A_base

where A_base is the area of the circular base of the cylinder, given by A_base = πρ².

Combining the equations, we have:

D(ρ) × A = (ρ₀ × A_base) / ε₀

Substituting the expressions for A and A_base, we get:

D(ρ) × (2πρ × z_0) = (ρ₀ × πρ²) / ε₀

D(ρ) = (ρ₀ ×ρ) / (2ε₀z_0)

The electric field vector E can be obtained by dividing the electric displacement vector D(P) by the permittivity of the medium (ε):

E = D(P) / ε

Therefore, the resulting electric field vector E() at a point z_0 far from the charge distribution is given by:

E = (ρ₀ × ρ) / (2ε₀εz_0)

where ε is the relative permittivity (also known as the dielectric constant) of the medium surrounding the charge distribution.

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Answer:

64 (2) ^ n-1  

I hope that this helps!

Answer:

graph

Step-by-step explanation:

graph shown

intersected large curve

Answer:

18 centimeters.

Step-by-step explanation:

Since you already know the length (height) divide 20 by 5 = 4.

This gives you the width (4), add up all the sides ( 4 + 4 + 5 + 5).

The sum comes out to be 18.

The equation -5y + (7/3)y = -5 - (8/3)y - 4 gives no solution

An equation is an expression that shows the relationship between variables and numbers.

A linear equation is in the form:

y = mx + b

m is the rate of change and b is the initial y value

Given the equation: negative 5 times y plus seven thirds times y equals negative 5 minus eight thirds times y minus 4. This equates to:

-5y + (7/3)y = -5 - (8/3)y - 4

multiply through by 3:

-15y + 7y = -15 - 8y - 12

-8y = -27 - 8y

0 = -27

no solution

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No, the given data set is not a time series because it does not show changes or trends over time.

The data is grouped according to different educational levels and does not reflect any chronological progression. A time series data set is defined as a set of data points that are collected at regular intervals over a period of time.

The data set should reflect changes in a particular variable or set of variables over time.

Therefore, in order to be considered a time series, the data should be arranged in chronological order and represent changes over time, rather than grouped by different categories or variables.

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In a continuous probability distribution, a random variable can take any value in a specified range. (Option D)

A probability distribution refers to the mathematical function that provides the probabilities of occurrence of different possible outcomes for an experiment. Continuous probability distribution refers to a probability distribution with continuous types of data or random variables where the random variable can take on any value and is continuous. As there are infinite values that the variable can assume, the probability of the variable assuming any one specific value is zero. A continuous distribution is characterized by a range of values that are infinite, and therefore uncountable. The normal distribution is one example of a continuous distribution.

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Answer:

Answer is in photo

Step-by-step explanation:

160k

because if you take 8 + 8 its 16

Answer:   \(G(F(x)) = x^3-21x^2+147x-343\\\\\)

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

Work Shown:

\(G(x) = x^3\\\\G(F(x)) = \left(F(x)\right)^3\\\\G(F(x)) = \left(x-7\right)^3\\\\G(F(x)) = \left(x-7\right)\left(x-7\right)^2\\\\G(F(x)) = \left(x-7\right)\left(x^2-14x+49\right)\\\\G(F(x)) = x\left(x^2-14x+49\right)-7\left(x^2-14x+49\right)\\\\G(F(x)) = x^3-14x^2+49x-7x^2+98x-343\\\\G(F(x)) = x^3-21x^2+147x-343\\\\\)

Answer:

5 small greeting cards + 2 large greeting cards, it would cost 17.2$

a small greeting card + a large greeting card, 5.9$

dude this is easy, wait is my math right or not?

Answer:

14:6 is a ratio that would be equivalent to the ratio given.

I doubled 7 to 14, and 3 to 6. 21:12 or 28:18 could also be correct.

Final answer: 14:6

If there are answer choices that are not any of these ratios, I can help. xD