Gilbert's weekly pay in dollars, D. can be represented by the function D = 13.5h, where h represents the number of hours
he works during a week.

Answer:

"35.84 years" is the appropriate solution.

Step-by-step explanation:

The given values are:

Rate of savings generation,

[tex]s'(t)=300e^{\frac{t}{20} }[/tex]

System cost to install,

= $30000

Now,

The total savings will be:

⇒  [tex]s(t)=\int\limits s'(t) \ dt[/tex]

On substituting the values, we get

⇒         [tex]= \int\limits 300e^{\frac{t}{20} } \ dt[/tex]

⇒  [tex]s(t)=\frac{300e^{\frac{t}{20} }}{\frac{1}{20} }+c[/tex]

When,

Savings = 0

t = 0, then

⇒  [tex]0=6000e^o+c[/tex]

⇒  [tex]c=-6000[/tex]

The formula will be:

⇒  [tex]s(t)=6000[e^{\frac{t}{20} }-1][/tex]

On putting the values in the above formula, we get

⇒  [tex]30000=6000(e^{\frac{t}{20} }-1)[/tex]

           [tex]5=e^{\frac{t}{20}}-1[/tex]

        [tex]e^{\frac{t}{20} }=6[/tex]

On taking log, we get

⇒  [tex]\frac{t}{20} =log \ 6[/tex]

      [tex]t=20 log 6[/tex]

        [tex]=35.84 \ years[/tex]  

The eigenvalues of the matrix -2 0 1 1 0 -1 0 1 -1 are λ₁ = -1, λ₂ = 1, and λ₃ = -1. The corresponding eigenspaces are E₁ = span{[-1, 1, 0]}, E₂ = span{[1, 1, 1]}, and E₃ = span{[-1, 1, 2]}.

Eigenvalues and eigenvectors play a fundamental role in linear algebra, particularly in the study of matrices.

The eigenvalues of a matrix are the values λ for which the equation A = λ has nontrivial solutions, where A is the given matrix and is a non-zero vector. The eigenspace associated with an eigenvalue is the set of all eigenvectors corresponding to that eigenvalue.

To find the eigenvalues of the matrix -2 0 1 1 0 -1 0 1 -1, we need to solve the characteristic equation det(A - λI) = 0, where A is the given matrix, λ is an eigenvalue, and I is the identity matrix.

The characteristic equation in this case is (-2 - λ)(λ² + 1) + (1 - λ)(-1) = 0. Simplifying this equation yields λ³ - 2λ² - 2 = 0. This is a cubic equation, and we can use a calculator or Wolfram Alpha to find its roots, which are λ₁ = -1, λ₂ = 1, and λ₃ = -1.

Once we have the eigenvalues, we can find the corresponding eigenvectors by solving the equation (A - λ) = 0 for each eigenvalue.

For λ₁ = -1, solving (A + ) = 0 gives us the eigenvector [-1, 1, 0]. For λ₂ = 1, solving (A - ) = 0 gives us the eigenvector [1, 1, 1].

Finally, for λ₃ = -1, solving (A + ) = 0 gives us the eigenvector [-1, 1, 2]. These eigenvectors span the eigenspaces E₁, E₂, and E₃, respectively.

In summary, the eigenvalues of the matrix -2 0 1 1 0 -1 0 1 -1 are λ₁ = -1, λ₂ = 1, and λ₃ = -1. The corresponding eigenspaces are E₁ = span{[-1, 1, 0]}, E₂ = span{[1, 1, 1]}, and E₃ = span{[-1, 1, 2]}.

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The radius of a circle is half of its diameter so the radius of a circle with a diameter of 240 mm is 120.00 mm. Option D is the correct answer.

To find the radius of a circle with a given diameter, you can follow these steps:

Given that the diameter is 240 mm, divide it by 2 to obtain the radius. Recall that the radius is half the length of the diameter.

Radius = Diameter / 2

In this case, Radius = 240 mm / 2 = 120 mm.

Therefore, the radius of the circle with a diameter of 240 mm is 120.00 mm.

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Answer:

yay

Step-by-step explanation:

yayyayyayyayyayyyayyayayayyayaya

Answer:

D. 5x2 + 28x + 21

Step-by-step explanation:

First you want to find the area of the white rectangle

Then find the area of the beings rectangle

Then subtract beings minus white.

                                     Sorry it’s +21. The first answer in your list

                                      then thats correct

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

5x^2+28x+21 confirmed from Cortez himself

Answer:

If you go to this link it'll give you a whole explanation and walk   how to get your answer:

https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-visualizing-equiv-frac/a/equivalent-fractions-common-denominator-review

Step-by-step explanation:

Hope that this helps! :)

Have a great rest of your day/night!

Answer:

= 15/20 + 1 10/20 + 4 4/20

= 5 29/20

= 6 9/20

Exact Form:

[tex]\frac{3}{4}[/tex]

Decimal Form:

6.45

Mixed Number Form:

6[tex]\frac{9}{12}[/tex]

Answer:

$36

Step-by-step explanation:

60-12 is 48 (20%)

And 75% Of 48 Is 36

The two types of incorrect decisions in a hypothesis test and the symbol used to represent the probability of making that type of error are as follows:

A. A Type 1 error is rejecting a true null hypothesis, whose probability is denoted α.

A Type II error is not rejecting a false null hypothesis, whose probability is denoted β.

A Type I error occurs when the null hypothesis is rejected, even though it is actually true.

The probability of committing a Type I error is denoted by α (alpha), which is the significance level of the test.

A Type II error occurs when the null hypothesis is not rejected, even though it is actually false.

The probability of committing a Type II error is denoted by β (beta).

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(a) The mgf of Y is M_Y(t) = exp (3.54t + 0.01632t²).

(b) The distribution of Y, the total weight of the three 1-kilo packs of cheese selected is Y ~ N(3.54, 0.216).

(c) The probability P(Y < W) = 0.2808.

(a) The moment generating function (mgf) of Y, the total weight of the three 1-kilo packs of cheese selected is given by:

M_Y(t) = M_X1(t) × M_X2(t) × M_X3(t)

= exp (µ_X1 t + ½ σ²_X1 t²) × exp (µ_X2 t + ½ σ²_X2 t²) × exp (µ_X3 t + ½ σ²_X3 t²)

= exp [(µ_X1 + µ_X2 + µ_X3) t + ½ (σ²_X1 + σ²_X2 + σ²_X3) t²]

Therefore, the mgf of Y is given by:

M_Y(t) = exp [(1.18 + 1.18 + 1.18) t + ½ (0.072 + 0.072 + 0.072) t²]

M_Y(t) = exp (3.54t + 0.01632t²)

(b) The total weight Y of the three 1-kilo packs of cheese is the sum of three independent and identically distributed random variables.

So, the distribution of Y is given by the following normal distribution: Y ~ N (µ_Y, σ²_Y), where µ_Y = µ_X1 + µ_X2 + µ_X3 and σ²_Y = σ²_X1 + σ²_X2 + σ²_X3.

Thus, µ_Y = 3 × 1.18

µ_Y = 3.54 and,

σ²_Y = 3 × 0.072

σ²_Y = 0.216

⇒ σ_Y = √0.216

⇒ σ_Y = 0.4649

Therefore, Y ~ N(3.54, 0.216).

(c) We need to find P(Y < W), where W is the weight of the 3-kilo pack of cheese.

Now, Y and W are independent normal random variables.

Therefore, Y - W is also a normal random variable with the following distribution: Y - W ~ N(µ_Y - µ_W, σ²_Y + σ²_W), where µ_W = 3.22 and σ²_W = 0.09².

We know that µ_Y - µ_W = 3.54 - 3.22

µ_Y - µ_W = 0.32 and,

σ²_Y + σ²_W = 0.216 + 0.09² = 0.301.

Therefore, σ_Y - W = √0.301

σ²_Y + σ²_W = 0.5486.

Now, we need to find P(Y - W < 0), which is equivalent to finding P(Z < -0.5799), where Z = (Y - W - (µ_Y - µ_W))/σ_Y - W.

Substituting the values, we get:

Z = (Y - W - 0.32)/0.5486

⇒ Y - W = -0.5799

Z = (Y - W - 0.32)/0.5486

⇒ Y - W < 0 is equivalent to Z < -0.5799.

Using a standard normal table or calculator, we get: P(Z < -0.5799) = 0.2808.

Hence P(Y < W) = P(Y - W < 0)

P(Y < W) = 0.2808.

Therefore, P(Y < W) = 0.2808, correct to four decimal places.

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Answer:

The domain of a function is the set of the possible input values of the function. For example: consider the function f(x) = cos x, the domain of the function is the set of possible values of x.

The cosine function takes x values from all real numbers.

Therefore, the domain of the cosine function is a real numbers.

Step-by-step explanation:

Answer:

Hours driven= 40 hours

Step-by-step explanation:

Giving the following information:

Variable income= $21.6 per hour

Fixed income= $250

Total income= $1,114

To calculate the number of hours driven, we need to use the following formula:

Total income= fixed income + hourly rate*number of hours

1,114 = 250 + 21.6*x

864 = 21.6x

864 / 21.6 = x

40=x

Hours driven= 40 hours

Answer:

I think that the answer is B , 337/5 i mean .

Good luck ^^

Answer:

400

Step-by-step explanation:

To evaluate the double integral over the region in the first quadrant enclosed by a circle and lines by changing to polar coordinates, we need to express the integral limits and the integrand in terms of polar coordinates.

The region in the first quadrant enclosed by a circle and lines can be defined as follows: The circle has a radius 'r' centered at the origin, and the lines are given by the equations θ = 0 and θ = π/4, where θ represents the angle in polar coordinates.

In polar coordinates, the limits of integration for 'r' would be from 0 to the radius of the circle, and the limits of integration for θ would be from 0 to π/4.

The integrand, which represents the function being integrated, would be expressed in terms of 'r' and θ.

To evaluate the double integral, we would integrate the function over the defined region using the limits of integration and the appropriate differential element in polar coordinates, which is r dr dθ.

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Answer:

True, false, true, true.

Step-by-step explanation:

The roots zeros of a quadratic function are the same as the factors of the quadratic function. This is true because your roots are your factors—>(x-3) is a factor, x=3 is the root.

The roots zeros are the spots where the quadratic function intersects with the y-axis. No! Those are called y-intercepts!

The roots zeros are the spots where the quadratic function intersects with the x-axis. True. X-intercepts are your solutions. (x-3) graphed would the (3,0). That’s a solution.

There are not always two roots/zeros of a quadratic function,​ True. No solution would be when your quadratic doesn’t intersect the x-axis. One solution would be when your vertex would be on the x-axis. Two solutions is when your quadratic intersects the x-axis twice. Can there be infinite solutions? No. It’s either 0, 1, or 2 solutions.

Answer:

B 3+ (7+ -2) = 3 +(-2+ 7)

Step-by-step explanation:

It shows that the answer is the same even if you switch the problem in the parentheses around

The option A is correct answer which is Normal distribution.

What is Normal distribution?

A sort of continuous probability distribution for a random variable with a real value is called a normal distribution or a Gaussian distribution in statistics.

When testing a population mean and the standard deviation with large sample size so we used Normal distribution.

Hence, the option A is correct answer which is Normal distribution.

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Answer:

8

Step-by-step explanation:

I just put it in the calculator thint

Answer:

the answer is d=20.5 hope this helped

Answer:

d= 20.5

Step-by-step explanation:

d/4+7/8=6

(we know that to add fractions, we have to have both denomiators the same number. We aslo know that that means 8. Using that information, we know that to top number must be 48. 48/8 = 6. We can substract)

48-7= 41

(we then need to divide by 2 as we would have had to already multiplyed 4 by 2.)

41/2 = 20.5

Answer:

The formula would be

((a+b) / 2)h = area

In this case a is one side of the base (top parralel or bottom line)

And b is the second one (top or bottom)

You can only choose one for each

You add those two up and divide that by 2

Now you multiply it by “h” or height.

Now you have the area

The pool's hydrostatic force is 1,500 pounds at the shallow end, 4,500 pounds at the deep end, 1,500 pounds on each side from shallow to deep, and 0 pounds at the bottom.

(a) To compute the pressure the water exerts at that depth and multiply it by the shallow end's surface area, we must first measure the hydrostatic force on the shallow end. The equation P = gh, pressure is P, is the fluid's density, acceleration from gravity is g, the depth is h, determines the pressure that a fluid exerts at a given depth.

In this case, the depth of the shallow end is 3 ft. The weight density of water is given as 62.5 lb/ft³.

Plugging in these values, we have,

P = (62.5 lb/ft³) * (32.2 ft/s²) * (3 ft)

P = 1,500 lb/ft².

To find the hydrostatic force, we multiply this pressure by the surface area of the shallow end, which is the width times the length,

Hydrostatic force = 1,500 lb/ft² * (20 ft * 40 ft)

Hydrostatic force = 1,500 lb. Therefore, the hydrostatic force on the shallow end is 1,500 lb.

(b) Using the same method as in part (a), we find that the pressure exerted by the water at the depth of the deep end, which is 9 ft, is ,

P = (62.5 lb/ft³) * (32.2 ft/s²) * (9 ft)

P = 4,500 lb/ft².

Multiplying this pressure by the surface area of the deep end (20 ft * 40 ft), we get the hydrostatic force on the deep end,

Hydrostatic force = 4,500 lb/ft² * (20 ft * 40 ft)

Hydrostatic force = 4,500 lb.

Therefore, the hydrostatic force on the deep end is 4,500 lb.

(c) The depth of the side is varying linearly from 3 ft to 9 ft. Taking the average depth, we have (3 ft + 9 ft) / 2 = 6 ft.

Using the formula,

P = (62.5 lb/ft³) * (32.2 ft/s²) * (6 ft),

We find that the pressure is 3,000 lb/ft².

Multiplying this pressure by the surface area of the side (20 ft * 6 ft), we get the hydrostatic force,

Hydrostatic force = 3,000 lb/ft² * (20 ft * 6 ft)

Hydrostatic force = 1,500 lb.

(d) Since the bottom of the pool is horizontal, the depth remains constant throughout, which is 3 ft. Plugging this value into the formul,

P = (62.5 lb/ft³) * (32.2 ft/s²) * (3 ft),

p =  1,500 lb/ft², we find that the pressure is 1,500 lb/ft². However, since the bottom is horizontal, the surface area facing upward cancels out the surface area facing downward, resulting in a net force of 0 lb.

Therefore, the hydrostatic force on the bottom of the pool is 0 lb.

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Answer:

it would be 64-81  than answer devide by 6.

Answer:

what are we rounding? like what is your question?

Step-by-step explanation:

**if you answer you have my promise and i'll go back and provide an actual answer**

The y-intercept of the graph of the function f(d) would represent 7 and a reasonable domain to plot the growth function is 0 ≤ d ≤ 18 because the number of days is a whole number.

Part A: When the biologist concluded her study, the radius of the algae was approximately 13,29 mm.

What is a reasonable domain to plot the growth function?The given equation is,f(d) = 7(1.06)d

The radius of the algae was approximately 13.29 mm, which is the value of f(d).Thus, f(d) = 13.29

Substitute this value in the equation to find the value of d.13.29 = 7(1.06)dlog(13.29/7)/log(1.06) = dd = 17.19

Hence, a reasonable domain to plot the growth function is 0 ≤ d ≤ 18 because the number of days is a whole number.

Part B: What does the y-intercept of the graph of the function f(d) represent?The y-intercept of the graph of the function f(d) represents the initial value of the function when x = 0. The given function is,f(d) = 7(1.06)d

Substitute 0 in the above function and solve for f(0).f(0) = 7(1.06)0f(0) = 7

Hence, the y-intercept of the graph of the function f(d) represents 7.

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Answer:

Step-by-step explanation:

Find the diagram attached

The sum of the two adjacent angles is 180 degrees. Hence;

8x-9 + 53 = 180

8x + 44 = 180

Subtract 44 from both sides of the equation

8x + 44 - 44 = 180 - 44

8x = 136

Divide both sides by 8

8x/8 = 136/8

x = 17

Hence the value of x is 17

Using the midpoint rule with the given value of n, we can approximate the integral. The answer, rounded to four decimal places, will be explained in the following paragraphs.

The midpoint rule is a numerical method used to approximate definite integrals. It involves dividing the interval of integration into n subintervals of equal width and evaluating the function at the midpoint of each subinterval. The approximated value of the integral is obtained by summing the products of the function values at the midpoints and the width of each subinterval.

To calculate the integral using the midpoint rule, we need to know the value of n, which determines the number of subintervals. The larger the value of n, the more accurate the approximation becomes. However, increasing n also requires more computational effort.

Once we have determined the value of n, we divide the interval of integration into n subintervals of equal width. Then, we evaluate the function at the midpoint of each subinterval and multiply it by the width of the subinterval. Finally, we sum up all these products to obtain the approximate value of the integral.

Rounding the answer to four decimal places ensures that the approximation is presented with a reasonable level of precision. It is important to note that while the midpoint rule provides a reasonable estimate, it may not always yield an exact result due to the inherent limitations of numerical methods for integration.

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Answer:

KISS THEY BESTFRIEND AND THEY BOTH WANNA CUDDLE

Step-by-step explanation:

Answer:

expressing how you feel even if it comes off wrong because sometimes we understand this based off of a boys actions for example say he gets an attitude because your talking to everyone except him at a party and he came there with you well you have to understand that it could come off as awkward because he standing around looking lonely because your not admiring his presence when he's there with you and 9 times out of 10 your his girl friend

Step-by-step explanation:

The vertices of the ellipse are (12, -1) and (4, -1), and the co-vertices are (8, 1) and (8, -3).

To find the vertices and co-vertices of the given ellipse, we can use the equation of an ellipse in standard form:

((x-h)²/a²) + ((y-k)²/b²) = 1

Comparing this with the given equation ((x-8)²/(16)) + ((y+1)²/(4)) = 1, we can identify the values of h, k, a, and b.

From the equation, we can see that the center of the ellipse is at (h, k) = (8, -1). The value of a is the square root of the denominator of the x-term, which is 4, so a = 4. Similarly, the value of b is the square root of the denominator of the y-term, which is 2, so b = 2.

The vertices of the ellipse are located at a distance of a units from the center along the major axis, which is the x-axis. Therefore, the vertices are (8+a, -1) and (8-a, -1), which simplifies to (12, -1) and (4, -1).

The co-vertices of the ellipse are located at a distance of b units from the center along the minor axis, which is the y-axis. Therefore, the co-vertices are (8, -1+b) and (8, -1-b), which simplifies to (8, 1) and (8, -3).

Hence, the correct answer is: The vertices are (12, -1) and (4, -1). The co-vertices are (8, 1) and (8, -3).

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Answer:

-8.8829646e+20

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remark

94737638 x -9376383889483

The exact answer can be found by using the calculator that comes with windows (windows 7 if you are using that. Windows 10 for sure.). It can give exact answers up to 18 digits (or that's what I thought. This question is an astonishing 21 digits). The answer to this question is

-888,296,462,670,872,461,154

I don't know if Apple has a calculator that comes with its operating system. I would think so, but I don't know. I use a PC.