Sorry i am very confused on this pls help

Answer:

The width is 3

Step-by-step explanation:

the formula is l×w

If two angles are complementary, it means that their sum is 90 degrees. This means that

angle FGJ + angle JGH = 90

From the diagram, angle JGH = 24.4

Thus,

angle FGJ + 24.4 = 90

angle FGJ = 90 - 24.4

angle FGJ = 65.6 degrees

Answer:

option 4 (2,-15)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

9 1/2 ÷20

9/1 +1/2 ÷20 ( convert to an improper frqction)

18/2 + 1/2 ÷20 ( Multiply 9/1 by 2/2)

19/2 ÷20 ( add 18/2 and 1/2)

19/2 ×1/20 (dividing by 20 is the same as multiplying by 1/20)

19/40

0.475

The formula to calculate the conditional probability of A given B is given to be:

If French is represented by F, and males by M, the formula to calculate the probability of a student speaking French given they are male is given to be:

The probability formula is given to be:

Therefore, we have:

and

Therefore, the conditional probability is:

The probability is 0.167 or 1/6

Answer:

y = 3x+3

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The derivative of the function h(x) = 19x^(3/2) - 8x is h'(x) = 57x^(1/2) - 8.

To find the derivative of the function h(x) = 19x^(3/2) - 8x, we can use the power rule and the constant multiple rule. First, let's rewrite the function by substituting x^(1/2) for x:

h(x) = 19(x^(1/2))^3 - 8(x^(1/2)

Now, applying the power rule, we have:

h'(x) = 19 * 3(x^(1/2))^(3-1) - 8 * 1(x^(1/2))^(1-1)

h'(x) = 57x^(1/2) - 8(x^(0))

Since x^(0) is equal to 1 for any nonzero x, we have:

h'(x) = 57x^(1/2) - 8(1)

h'(x) = 57x^(1/2) - 8

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The derivative of the function h(x) = 19x^3 - 8√x is h'(x) = 57x^2 - 4√(x). To find the derivative of the function h(x) = 19x^3 - 8√x, we can apply the power rule and chain rule of differentiation.

First, let's rewrite the function as h(x) = 19x^3 - 8x^(1/2).

To differentiate this function, we need to apply the power rule and chain rule. The power rule states that the derivative of x^n with respect to x is nx^(n-1).

Using the power rule, we differentiate each term of the function separately:

h'(x) = d/dx (19x^3) - d/dx (8x^(1/2))

For the first term, the power rule gives us:

d/dx (19x^3) = 3 * 19x^(3-1) = 57x^2

For the second term, we need to use the chain rule. The chain rule states that if we have a composite function, such as f(g(x)), the derivative is given by f'(g(x)) * g'(x).

In our case, the function is f(x) = -8x^(1/2), and g(x) = x. The derivative of f(x) with respect to g(x) is f'(g(x)) = -4√(x), and the derivative of g(x) with respect to x is 1.

Applying the chain rule, we have:

d/dx (8x^(1/2)) = -4√(x) * 1 = -4√(x)

Now we can substitute the derivatives back into the original expression:

h'(x) = 57x^2 - 4√(x)

Therefore, the derivative of the function h(x) = 19x^3 - 8√x is h'(x) = 57x^2 - 4√(x).

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The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\)

Option D is the correct answer.

We have,

In this equation, the variable x represents the number of times the square is cut in half, and y represents the surface area of the square.

As x increases, the exponent of 1/2 decreases, causing the value of y to decrease.

This exponential decay accurately represents the idea that the surface area becomes less and less but never reaches zero units²

Thus,

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\).

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The correct equation that would help model the surface area of a square piece of paper as it is repeatedly cut in half is:  \(\(y=36(\frac{1}{2})^x\)\)

As the square is cut in half, the side length of the square is divided by 2, resulting in the area being divided by \(\(2^2 = 4\)\).

Therefore, the equation \(y=36(\frac{1}{2})^x\)\)accurately represents the decreasing surface area of the square as it is repeatedly cut in half.

and, \(\(y=x^2+4x-16\)\)is a quadratic equation that does not represent the decreasing nature of the surface area.

and, \(\(y=-25x^2\)\) is a quadratic equation with a negative coefficient.

and, \(\(y=9(2)^x\)\)represents exponential growth rather than the decreasing nature of the surface area when the square is cut in half.

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The function  \(f(x) = x^3 / (x^2 - 49)\)has a vertical asymptote at x = 7 and x = -7. There are no slant asymptotes. To find the vertical asymptotes of the function f(x), we need to identify the values of x for which the denominator becomes zero, as division by zero is undefined.

In this case, the denominator is (x² - 49). To determine when it equals zero, we set it equal to zero and solve for x:

x² - 49 = 0

This equation can be factored as the difference of squares:

(x - 7)(x + 7) = 0

Setting each factor equal to zero, we find that x = 7 and x = -7. Therefore, the function has vertical asymptotes at x = 7 and x = -7.

On the other hand, to determine if there are any slant asymptotes, we need to check if the degree of the numerator (x³) is greater than the degree of the denominator \((x^2 - 49)\). In this case, the degree of the numerator is 3, while the degree of the denominator is 2. Since the degree of the numerator is greater, there are no slant asymptotes for this function.

In summary, the function \(f(x) = x^3 / (x^2 - 49)\) has vertical asymptotes at x = 7 and x = -7. There are no slant asymptotes.

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Answer:

Yes

Step-by-step explanation:

Since the lines cross over each other, yes, they do bisect each other.

~theLocoCoco

The solution to the system of linear equations is:x = -18, y = -3, z = -7

The method of back-substitution is used to solve a system of linear equations. This method can be used to calculate the values of one variable at a time. In this method, the variable with the highest power is calculated first, and the values of other variables are calculated by substituting the already calculated variables' values. The method of back-substitution is a straightforward method of solving linear equations, and it is an essential tool for solving more complicated equations, such as those found in engineering, physics, and economics. Back-substitution can be used to solve any linear equation system, whether it is a homogeneous or non-homogeneous system.

To solve the given system of linear equations using back-substitution, we are required to find the values of x and y.

2x+3y-3z = -4-8y-7z = 73

Z = -7

Substituting the value of z = -7 in equation 2, we get:

-8y-7(-7) = 73

-8y + 49 = 73

-8y = 73 - 49

-8y = 24

y = -3

Substituting y = -3 in equation 1, we get:

2x + 3(-3) - 3(-7) = -4

Simplifying: 2x - 9 + 21 = -42

x + 12 = -42

x = -42 - 12

x = -18

Hence, the solution to the system of linear equations is:

x = -18

y = -3

z = -7

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Answer:

70 miles

Step-by-step explanation:

15 + 35 + (35 - 15) = 15 + 35 + 20 = 70

Answer:

Step-by-step explanation:

Let the height be x

1. It is the opposite side

2. The ratio of the opposite side to the adjacent side is called the tangent

3. As per definition of the tangent we got:

ANSWER :

The zeros are 1/2 and -5

EXPLANATION :

From the problem, we have the function :

The zeros of the function are the values of x when f(x) = 0

Using quadratic formula with a = 2, b = 9 and c = -5

The magnitude of vector F is 29.73.\(\( \vec{A}=5 \hat{i}-2 \hat{j}, \vec{B}=-3 \hat{i}+4 \hat{j} \),\) and\(\( \vec{F}=2 \vec{A}-4 \vec{B} \).\)

We need to find the magnitude of \(\( \vec{F} \)\).The magnitude of a vector is defined as the square root of the sum of squares of its components.

It can be mathematically represented as
,\(\[\left | \vec{A} \right | = \sqrt{\vec{A}\cdot \vec{A}}\]\)
Using this formula, we can find the magnitude of vector F as

\(,\[\vec{F}=2 \vec{A}-4 \vec{B} \]\[\vec{F}=2 (5 \hat{i}-2 \hat{j})-4 (-3 \hat{i}+4 \hat{j})\]\[\vec{F}=10\hat{i}-4\hat{j}+12\hat{i}-16\hat{j}\]\[\vec{F}=22\hat{i}-20\hat{j}\]\)

The magnitude of the vector F is
,\(\[\left | \vec{F} \right | = \sqrt{\vec{F}\cdot \vec{F}}\]\[\left | \vec{F} \right | = \sqrt{(22\hat{i})^2+(-20\hat{j})^2}\]\[\left | \vec{F} \right | = \sqrt{484+400}\]\[\left | \vec{F} \right | = \sqrt{884}\]\[\left | \vec{F} \right | = 29.73\]\)

Therefore, the magnitude of vector F is 29.73.

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A block weighing 90lb rests on a 35° incline. Find the magnitude of the components of the​ block's weight perpendicular and parallel to the incline.

Solution:

Here, the given data is:

Weight of the block = 90 lb

The angle of incline = 35°

We need to find the following:

Perpendicular component Parallel component

First, let us draw a diagram of the given scenario:

From the above diagram, we can see that the weight of the block is acting in a direction perpendicular to the incline and a direction parallel to the incline.

Hence, we will consider the given angle of 35° as our reference angle for all calculations.

Let W be the weight of the block.

Then,

W sin θ gives the perpendicular component of the weight.

W cos θ gives the parallel component of the weight.

Using the given data, we get:

W = 90 lbθ = 35°

Perpendicular component,

W sin θ= W sin 35°= 90 lb x sin 35°= 51.83 lb (approx)Therefore, the magnitude of the component of the block's weight perpendicular to the incline is 51.83 lb (approx).

Parallel component,

W cos θ= W cos 35°= 90 lb x cos 35°= 73.39 lb (approx)Therefore, the magnitude of the component of the block's weight parallel to the incline is 73.39 lb (approx).

Hence, we get the following results:

Perpendicular component = 51.83 lb (approx)Parallel component = 73.39 lb (approx)

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a) By strong induction, any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

b) By strong induction, any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

c) By strong induction, any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

a. Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

Base case: For postage worth 8 cents, we can use two 4-cent stamps, which can be made using a combination of one 3-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 8, can be made from 3-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 8, we can use the induction hypothesis to make k cents using 3-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with a 5-cent stamp to get the same value. If the last stamp we added was a 5-cent stamp, we can replace it with two 3-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3-cent or 5-cent stamps.

b. Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

Base case: For postage worth 24 cents, we can use three 8-cent stamps, which can be made using a combination of one 7-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 24, can be made from 7-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 24, we can use the induction hypothesis to make k cents using 7-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 5-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with three 5-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 7-cent or 5-cent stamps.

c. Prove that any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

Base case: For postage worth 12 cents, we can use one 3-cent stamp and three 3-cent stamps, which can be made using a combination of two 7-cent stamps.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 12, can be made from 3-cent or 7-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 12, we can use the induction hypothesis to make k cents using 3-cent or 7-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with one 3-cent stamp and two 7-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3

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Answer:  205,209

Step-by-step explanation:

We want to find a perfect cube that is closest to the number N = 205,632

A perfect cube number is a number such that the square root is a whole number.

Now, to search this number we must take the square root of N:

n = √(205,632) = 453.47

Now, we can round it down or up and get whole numbers, and the squares of those whole numbers will be perfect squares that are near 205,632, lets start with rounding down.

n = 453

the square of 453 is:

453^2 = 205,209

If instead we round up the  453,47, we would get:

n = 454

and the square will be

n = 454^2 = 206,116

Now, to see which one is closser to N, we can take the differences:

205,632 -  205,209 = 423

206,116 - 205,632 = 484

so if we take n = 453 we are closser no N, then the perfect square that is closest to 205,632 is 205,209

Answer:

D

Step-by-step explanation:

bc it starts with -square root of 20 and then - square root of 6 and the 3.14 and then square root of 8 and then square root of 18

Answer:

8 visits

Step-by-step explanation:

The height of the starting point needs to be about 25.76 feet higher than the height of the ending point.

We have,

To find the slope, we can use the given ratio of vertical change to horizontal change:

slope = 6/100 x 130/2 = 4.68

Since the slope is less than 8/100, it is within the constraints.

To find the height difference between the starting and ending points, we need to consider several factors.

First, we need to add the height of the rider, the harness, and the brake above the cable to the height of the cable above the ground:

= 4 + 3 + 16/175 x 16

= 7.74 feet

Next, we need to add the 5% slack in the cable:

= 7.74 + 0.05 x 130

= 14.24 feet

Finally, we need to add the height of the starting tree and subtract the height of the ending tree:

= 40 - 14.24

= 25.76 feet

Therefore,

The height of the starting point needs to be about 25.76 feet higher than the height of the ending point.

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a. The amount of the quarterly deposit is approximately $5,573.39.

b. The accumulated amount in the account after the 15th deposit is approximately $128,523.79.

a. To find the amount of the quarterly deposit, we can use the formula for the future value of an ordinary annuity. The formula is:

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

Where:
A = Accumulated amount
P = Quarterly deposit
r = Interest rate per compounding period
n = Number of compounding periods

In this case, the interest is compounded every 3 months, so the interest rate per compounding period is 9.6% / 4 = 2.4%.

a. To find the quarterly deposit, we need to solve the formula for P. Rearranging the formula, we have:

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

Substituting the given values:
A = $350,000 (the desired accumulated amount)
r = 2.4% (0.024 as a decimal)
n = 5 years * 4 quarters per year = 20 quarters

P = $350,000 * 0.024 / ((1 + 0.024)^20 - 1)
P ≈ $5,573.39

Therefore, the amount of the quarterly deposit is approximately $5,573.39.

b. To find the accumulated amount after the 15th deposit, we can use the future value of an ordinary annuity formula but with a different value for n. Since the interest is compounded every 3 months, the number of compounding periods is 15 quarters.

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

Substituting the given values:
P = $5,573.39 (the calculated quarterly deposit)
r = 2.4% (0.024 as a decimal)
n = 15 quarters

A = $5,573.39 * ((1 + 0.024)^15 - 1) / 0.024
A ≈ $128,523.79

Therefore, the accumulated amount in the account after the 15th deposit is approximately $128,523.79.

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Answer:

y = 4

Step-by-step explanation:

I think you meant

2(4y - 9 ) = 14

Multiply:

2 ×4y = 8y

2× 9 = 18

Thus, we have

8y-18 = 14

Now add 18 to both sides

8y-18+18=14+18

Simplify

8y  = 32

Solution:

y = 4

Hence y = 4.

Kavinsky

Factors of the polynomial are: (x - 3)(x + 3)(x - 5).

What if factoring polynomial?

A polynomial with coefficients in a certain field or in integers is expressed as the product of irreducible factors with coefficients in the same domain by the process of factorization of polynomials, also known as polynomial factorization.

Given:  

We have to show tat x - 5 is a factor of the polynomial and to find the factor of the polynomial.

First to show x - 5 is a factor of the given polynomial.

We know that,

If x - 5 is the factor of the given polynomial then by factor theorem x - 5 = 0.

So, x = 5

Plug x = 5 in t(x).

t(5) = 0

That means 5 is the zero of the polynomial t(x).

Therefore, x - 5 is the factor of the polynomial.

Now, to factor the polynomial.

Therefore, after factoring the polynomial we get, .

Answer:

The steps on how to show that the binomial is a factor of the polynomial and then factor the polynomial completely are:

1. Set the binomial equal to 0.

x - 5 = 0

2. Solve for x.

x = 5

3. Substitute the value of x into the polynomial.

t(5) = 5^3 - 5(5^2) - 9(5) + 45

t(5) = 125 - 125 - 45 + 45

t(5) = 0

4. Since the value of the polynomial is 0 when x = 5, the binomial (x - 5) is a factor of the polynomial.

5. To factor the polynomial completely, we can use the difference of squares factorization.

t(x) = (x - 5)(x^2 + 9)

The complete factorization of the polynomial is:

t(x) = (x - 5)(x^2 + 9)

To find the area of the surface given by z = f(x, y) above the region R, we can integrate the function f(x, y) over the region R. In this case, the function is f(x, y) = 13 + 4x - 3y and the region R is a square with vertices (0, 0), (2, 0), (0, 2), and (2, 2).

To calculate the area, we need to integrate the function f(x, y) over the region R. The integral represents the sum of infinitesimally small areas over the region. In this case, we integrate the function f(x, y) = 13 + 4x - 3y over the square region R.
The integral is given by:
A = ∫∫R f(x, y) dA
where dA represents the infinitesimal area element.
Since R is a square, we can set up the integral using Cartesian coordinates:
A = ∫0^2 ∫0^2 (13 + 4x - 3y) dxdy
Evaluating the integral, we get:
A = ∫0^2 (13x + 2x^2 - 3xy)dy
Simplifying further, we integrate with respect to y:
A = ∫0^2 (13x + 2x^2 - 3xy)dy = (13x + 2x^2 - 3xy) * y |0^2
Substituting the limits of integration, we get:
A = (13x + 2x^2 - 6x) - (0) = 13x + 2x^2 - 6x
Simplifying the expression, we have:
A = 2x^2 + 7x
Therefore, the area of the surface above the region R is given by the function A = 2x^2 + 7x.

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The polynomial equation kx^2 - 2x^4 = 0 has no real solutions, for any non-zero value of k.

The equation kx^2 - 2x^4 = 0 has the form of a polynomial equation, where k and x are variables. To find the nonzero value of k that will cause the equation to have 2 real solutions, we need to analyze the roots of the equation.

The roots of the equation are the values of x that make the equation equal to zero. To find the roots, we can set each factor of the polynomial equal to zero and solve for x:

kx^2 = 0 and 2x^4 = 0

The first equation gives us x = 0, which is not a valid solution, because it is not a real number.

The second equation gives us x^4 = 0, then x = 0. But x = 0 is not a valid solution for this equation, as it is not a real number.

Therefore, the polynomial equation kx^2 - 2x^4 = 0 has no real solutions, for any non-zero value of k.

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Answer:

f = 2

Step-by-step explanation:

10 = 6 + 2f

subtract 6 from both sides

4 = 2f

divide both sides by 2

2 = f

Eight people skiing downhill in a race can finish in 40,320 different orders.

Calculating probabilities for a set of possibilities keeping in account the order they are in is called permutation (\({n}_P_{r}\)).

If we overlook the order, it becomes a problem of combination (\({n}_C_{r}\)).

Permutation plays an important role in probability problems where the order of the possible outcomes is concerned. It does not allow repetition of outcomes.

Mathematically, permutation can be represented as:

\({n}_P_{r}=\frac{n!}{(n-r)!}\)

where 'n' represents the total objects/values/instances and 'r' represents our selected number of objects/values/instances.

In this case, we have total 8 drivers (n=8) and 8 positions we are selecting i.e. the order skiing people finish in (r=8);

\({n}_P_{r}=\frac{8!}{(8-8)!}=\frac{8!}{0!}=\frac{40320}{1}\)

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Answer:

your answer is (B) -2 & -3

(A) Algorithms are mathematical formulas placed in software that performs an analysis on a data set.

Therefore, (A) algorithms are mathematical formulas placed in software that performs an analysis on a data set.

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