which of the following matrices has an inverse?

The equation of the sphere in standard form, one of whose diameters have (-5, 2, 9) and (3, 6, 1) as endpoints, is [tex]x^2 + y^2 + z^2 - 8x - 4y - 10z + 48 = 0[/tex]. Therefore, the correct option is (d) [tex]x^2 + y^2 + 7 + 2x + 8y - 10z - 6 = 0[/tex].

To find the equation, we start by finding the center of the sphere. The center of the sphere is the midpoint of the line segment connecting the given endpoints. Using the midpoint formula, we find the center to be [tex]((-5 + 3)/2,(2 + 6)/2,(9 + 1)/2) = (-1, 4, 5)[/tex].

Next, we find the radius of the sphere. The radius is half the length of the diameter, which is the distance between the two endpoints. Using the distance formula, we find the radius to be [tex]\sqrt{(-5 - 3)^2 + (2 - 6)^2 + (9 - 1)^2} = \sqrt{64 + 16 + 64} = \sqrt{144} = 12[/tex].

Finally, we substitute the center and radius into the equation of a sphere: [tex](x - h)^2 + (y - k)^2 + (z - l)^2 = r^2[/tex], where (h, k, l) is the center and r is the radius. Plugging in the values, we get [tex](x + 1)^2 + (y - 4)^2 + (z - 5)^2 = 12^2[/tex].

Expanding and simplifying, we arrive at the equation for sphere's standard form, [tex]x^2 + y^2 + z^2 - 8x - 4y - 10z + 48 = 0[/tex].

Therefore, the correct option is (d) [tex]x^2 + y^2 + 7 + 2x + 8y - 10z - 6 = 0[/tex].

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Answer:((2x^3)^4)/1x^2

Step-by-step explanation:

(2x^3)^4)=((2x)^4)(^3 times ^4)=16x^12

16x^12/1x^2=(16x/1x)(x^12-2)

Answer:

y= 3

x= -2

Step-by-step explanation:

..,............

Answer:

If the two alternate exterior angles are from two parallel lines cut by a transversal, angle 8 would be 30 degrees.

Explanation:

Alternate exterior angles resulting from two parallel lines cut by a transversal are congruent.

In Exhibit 34-1, the opportunity cost of one unit of Y in Country B is 2 units of X.

Opportunity cost refers to the value of the next best alternative that is forgone when making a choice. In this case, the opportunity cost of one unit of Y in Country B is being compared to the amount of X that could be produced instead.

The given information states that the opportunity cost of one unit of Y in Country B is 2 units of X. This means that for every unit of Y that Country B produces, it must give up the production of 2 units of X. In other words, the resources and efforts that could have been used to produce 2 units of X are instead allocated to producing one unit of Y.

This relationship indicates the relative trade-off between the production of X and Y in Country B. By sacrificing the production of 2 units of X, Country B can produce one unit of Y. The opportunity cost of producing Y is therefore 2 units of X.

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Answer:

it is 14

Step-by-step explanation:

Answer:

C) 14

Step-by-step explanation:

Volume of a Sphere:

V = 4/3πr³

V = 4/3(3.14)1.5³

V = 4/3(3.14)3.375

V = 14.13

14.13 ≈ 14

Answer:

V=141.3

Step-by-step explanation:

V=π*r2*h or V=B.h

V=3.14*(3*3)*5

V=3.14*9*5

V=141.3

The volume of a triangular prism with a base 8 cm and height of 4 cm, length of 20 cm = 0.32 liters.

To calculate the volume of a triangular prism, you multiply the area of the base triangle by the length of the prism. Given that the base triangle has a side length of 8 cm and a height of 4 cm, its area can be calculated as (1/2) * base * height = (1/2) * 8 cm * 4 cm = 16 cm².

Multiplying this by the length of the prism, which is 20 cm, we get the volume:

Volume = Base Area * Length = 16 cm² * 20 cm = 320 cm³.

To convert this volume to liters, we know that 1 liter is equal to 1000 cm³. Therefore, we can divide the volume in cm³ by 1000 to obtain the volume in liters:

Volume in liters = 320 cm³ / 1000 = 0.32 liters.

So, the volume of the triangular prism is 0.32 liters.

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Answer:

4.6

Step-by-step explanation:

3.. litteraly anything less than that

Answer:

0

Step-by-step explanation:

|4.7| = 4.7

Any number less than a positive 4.7 is less than |4.7|.

Answer:

64

Step-by-step explanation:

square= 16

triangle= 12

12*4 = 48+16 = 64

Answer:

64 m²

Step-by-step explanation:

Hello There!

The surface area is the total area of the figure

So in order to find the area we need to find the area of each shape

For the square:

the square has a length of 4 so we can simply find the area by squaring it

4 * 4 = 16

so the area of the square is 16 square meters

Now we need to find the area of the triangles

The formula for area of a triangle is

[tex]A=\frac{bh}{2}[/tex]

where b = base and h = height

The triangles dimensions are:

base - 4m

height - 6m

having found these dimensions we plug them in into the formula

[tex]A=\frac{4*6}{2} \\4*6=24\\\frac{24}{2} =12[/tex]

so the area of one of the triangles is 12 square meters

We want to find the total area of all of the triangles

To do so we multiply the area of one triangle by 4 (because there are four triangles)

12 * 4 = 48

So the total area of the four triangles is 48 square meters

Finally we add the two areas

48 + 16 = 64

so we can conclude that the total surface area of the pyramid is 64 m²

Answer:

x ≤ 21

Step-by-step explanation:

x/3 ≤ 7

x ≤ 21

Answer:

x ≤ 21

Step-by-step explanation:

With this problem, we have to solve for x, and to do that, we isolate the variable.

To do this, let’s get rid of the /3 from the x by multiplying both sides by 3

now we get x ≤ 7 times 3

finall, we get x≤21

Sherman's total return on his investment in Boca-Cola stock is $5,430.

The formula for the total return on an investment is as follows:

total return = capital gain + dividend yield

Initially, Sherman bought 150 shares of Boca-Cola stock for $15 a share.

Therefore, the initial investment (also known as the initial cost) is:

$15 x 150 = $2,250

Four years later, the stock price of Boca-Cola is $50 per share.

The capital gain is calculated as follows:

capital gain = final share price - initial share price

capital gain = $50 - $15

capital gain = $35

Therefore, the capital gain on Sherman's 150 shares is:

$35 x 150 = $5,250

Next, we need to calculate the total amount of dividends that Sherman received over the 4 years. The dividend per share is $0.30. Therefore, the total amount of dividends received is:

total dividends = dividend per share x number of shares x number of years

Sherman received dividends for 4 years, so:

total dividends = $0.30 x 150 x 4

total dividends = $180

The dividend yield is calculated as follows:

dividend yield = total dividends / initial cost

dividend yield = $180 / $2,250

dividend yield = 0.08 or 8%

Finally, we can calculate the total return:

total return = capital gain + dividend yield

total return = $5,250 + $180

total return = $5,430

Therefore, Sherman's total return on his investment in Boca-Cola stock is $5,430.

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Answer:

Eso es loca

Step-by-step explanation:

brainliest please??

Answer:

OK

Step-by-step explanation:

(a) The probability of success is 65% or 0.65, and the number of trials is 50.

(b) The probability as follows:

P(X ≤ 30) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 30)

(C) The probability as follows:

P(X ≥ 35) = P(X = 35) + P(X = 36) + P(X = 37) + ... + P(X = 50)

a. The probability of exactly 32 of the 50 IT businesses generating a profit in the next year can be calculated using the binomial distribution formula. In this case, the probability of success (a business generating a profit) is 65% or 0.65, and the number of trials is 50. Using the formula, we can calculate the probability as follows:

P(X = 32) = C(50, 32) * (0.65)^32 * (1 - 0.65)^(50 - 32)

where C(n, k) represents the binomial coefficient, equal to n! / (k! * (n - k)!). Calculating this expression gives us the probability that exactly 32 businesses will generate a profit.

b. To calculate the probability that at most 30 businesses will generate a profit, we need to find the cumulative probability from 0 to 30. We can calculate the probability as follows:

P(X ≤ 30) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 30)

The problem involves determining the probability that at most 30 out of 50 IT businesses will generate a profit in their first year. We can use the binomial distribution formula to calculate this probability. The formula is given by:

P(X ≤ k) = Σ (nCk * p^k * q^(n-k))

Where:

P(X ≤ k) is the probability of having at most k successes,

n is the number of trials (50 businesses),

k is the number of successes (profitable businesses),

p is the probability of success (65% or 0.65),

q is the probability of failure (35% or 0.35),

nCk is the combination formula (n choose k).

To find the probability that at most 30 businesses will generate a profit, we need to calculate the cumulative probability from 0 to 30. Using the binomial distribution formula, we can find the probability of each possible outcome (0, 1, 2, ..., 30) and sum them up. The cumulative probability can be calculated using software or statistical tables.

c. To calculate the probability that at least 35 businesses will generate a profit, we need to find the cumulative probability from 35 to 50. We can calculate the probability as follows:

P(X ≥ 35) = P(X = 35) + P(X = 36) + P(X = 37) + ... + P(X = 50)

These calculations can be performed using a statistical software package, spreadsheet software, or using statistical tables for the binomial distribution.

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The number of cellular phones in the US is projected to grow exponentially, reaching 5.071 million in 30 years and 420 million in 13.955 years. The growth factor is 1.32, which suggests that the number of cellular phones is increasing by approximately 32% each year.

a. To find N(30), we substitute t = 30 into the given exponential function:

[tex]\[N(t) = 0.05 * (1.32)^t\][/tex]

N(30) = 0.05 * (1.32)³⁰

You can calculate this value using a calculator or a computer software. The result is approximately 5.071 million.

In the context of the scenario, N(30) represents the estimated number of cellular phones in use in the United States, in millions, 30 years after 1990. It indicates the projected growth in the number of cellular phones over time based on the given exponential function.

b. To find t when N(0) = 420, we set N(t) equal to 420 and solve for t:

[tex]\[420 = 0.05 * (1.32)^t\][/tex]

Dividing both sides by 0.05:

[tex]\begin{equation}8400 = (1.32)^t[/tex]

To solve this equation for t, we can take the logarithm of both sides using the base 1.32:

log(8400) = t * log(1.32)

Now, solve for t by dividing both sides by log(1.32):

[tex]\begin{equation}t = \log(8400) / \log(1.32)[/tex]

You can calculate this value using a calculator or a computer software. The result is approximately 13.955 years.

In the context of the scenario, t represents the number of years after 1990 when the number of cellular phones in use in the United States reaches 420 million. It indicates the time it takes for the number of cellular phones to reach a specific value based on the given exponential function.

c. The value 1.32 in the equation N(t) = 0.05 * (1.32)^t represents the growth factor or the rate of exponential growth of the number of cellular phones. It indicates how much the number of cellular phones is multiplied by each unit of time (in this case, each year). In this scenario, the value 1.32 suggests that the number of cellular phones is increasing by approximately 32% each year.

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lets take number one for example,

When subtracting negative numbers, the (-) in the number (-20) cancels out the original minus sign, therefore, to answer the equation:

10 - (-20)

you would need to turn the equation into an addition problem, getting the equation:

10 + 20

and from there you can get the simple answer of:

30

(brainliest please)

Answer: 13750+262=14,012 ft^3

Step-by-step explanation:

Hello!!!

Find the volume of the bottom and top separately and then add them. Cylinder volume is the area of the bottom times the height (22/7)(5^2)•175=13750 ft^3

The volume of a sphere isV=(4/3)(22/7)r^3where r is the radius.  also 5 since it fits on the cylinder. Also we only want half the sphere so useV=(2/3)(22/7)•5^3=261.9 ft^3 round upto 262. Now add  together 13750+262=14,012 ft^3

Hope this helps~!!!!!

Answer:

The slope of the line is 2/3

Answer: 1.5

Step-by-step explanation:

I plugged it in STAT, but you can do rise over run, or use the formula, y2-y2/x2-x1

Answer:

0.65

Step-by-step explanation:

Just divide 13 by 20

The integral representation of the solution to the initial value ordinary differential equation (ODE) x'' - 8x' + 12x = f(t) with f(t) is given by x(t) = x₀ * δ(t) + x₁ * δ'(t) + ∫[a,b] G(t - τ) * f(τ) dτ.

The given ODE is a linear homogeneous second-order ODE with constant coefficients. To find the integral representation of the solution, we introduce the Dirac delta function, δ(t), and its derivative, δ'(t), as the basis for the particular solution.

To set up the integral representation for the solution of the initial value ODE x'' - 8x' + 12x = f(t), we first define the Green's function G(t - τ). The Green's function satisfies the homogeneous equation with the right-hand side equal to zero:

G''(t - τ) - 8G'(t - τ) + 12G(t - τ) = 0.

Next, we set up the integral representation as follows:

x(t) = x₀ * δ(t) + x₁ * δ'(t) + ∫[a,b] G(t - τ) * f(τ) dτ,

The integral represents the convolution of the forcing function f(τ) with the Green's function G(t - τ).

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Answer:

its 64 because 4x16= 64

Step-by-step explanation:

Answer:

Answer is B

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

The answer is B

Answer:

3

Step-by-step explanation:

Plug the coordinates into the distance formula to find that they are 3 units apart

Answer:

13 units

Step-by-step explanation:

sqrt (x2 - x1)^2 + (y2 - y1)^2

sqrt (-3 - (-3))^2 + (-8 -5)^2

sqrt (0)^2 + (-13)^2

sqrt 169

13

Answer:

C: -|x| + 3

Step-by-step explanation:

From the graph, we see that when y = 2, x is either +1 or -1

Also,when y = 1, x = +2 or -2

Thus,we can say that;

y = (-x) + 3 or -(x - 3)

So, we can write this in absolute value form as; y = -|x| + 3

Answer:

Debbie should have included 8 as a possible choice. The correct inequality is p < 9.

Step-by-step explanation:

Given

Passengers = Up to 8

Required

Determine why [tex]p < 8[/tex] is incorrect and make corrections

The inequality [tex]p < 8[/tex] means that the van can hold less than 8 passengers.

To make correction, the digit 8 has to be included in the inequality.

This can be written as:

[tex]p <9[/tex] or[tex]p \le 8[/tex]

Base on the given options, option (c) best answered the question.

The sampling distribution of x is N (µx = µ = 81, σx = 2.00).The probability of x > 84.9 is:P(x > 84.9) = P(z > 1.75) = 0.0401.The probability of 78.1 < x < 81 is:P(78.1 < x < 81) = P(-0.95 < z < 0) = 0.3289.

a)Sampling distribution of x

The sampling distribution of x is the probability distribution of all the possible sample means that can be drawn from a population under the same sampling method.

It represents the relative frequency of different values of x (sample mean) that can be obtained when samples of size n are taken from the population.

The sampling distribution of x is approximately normal when the sample size is sufficiently large, i.e. n ≥ 30. In this case, n = 49, which is sufficiently large to assume normality of sampling distribution of x.

The mean of the sampling distribution of x is µx = µ = 81, and the standard deviation is: σx = σ / √n = 14 / √49 = 2.00.

Hence, the sampling distribution of x is N (µx = µ = 81, σx = 2.00).

b)P(x > 84.9)

The z-score is:z = (x - µx) / σx = (84.9 - 81) / 2.00 = 1.75.

Using the standard normal distribution table, the probability of z > 1.75 is 0.0401.

Hence, the probability of x > 84.9 is:P(x > 84.9) = P(z > 1.75) = 0.0401

c)P(x ≤ 76.7)

The z-score is:z = (x - µx) / σx = (76.7 - 81) / 2.00 = -2.15

Using the standard normal distribution table, the probability of z ≤ -2.15 is 0.0150.

Hence, the probability of x ≤ 76.7 is:P(x ≤ 76.7) = P(z ≤ -2.15) = 0.0150d)P(78.1 < x < 81)

The z-score for x = 78.1 is:z1 = (x1 - µx) / σx = (78.1 - 81) / 2.00 = -0.95

The z-score for x = 81 is:z2 = (x2 - µx) / σx = (81 - 81) / 2.00 = 0

Using the standard normal distribution table, the probability of z1 < z < z2 is:P(z1 < z < z2) = P(-0.95 < z < 0) = P(z < 0) - P(z < -0.95) = 0.5000 - 0.1711 = 0.3289.

Hence, the probability of 78.1 < x < 81 is:P(78.1 < x < 81) = P(-0.95 < z < 0) = 0.3289.

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Answer:

17

Step-by-step explanation:

This means all students above 20, so 9 + 5 + 3 = 17

Answer:

17

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