Find the radius of an eyebrow window with width 62.8 inches and height 18.5 inches

Answer:

1

Step-by-step explanation:

all the other are less than -1 and since the rule is that x has to be greater than -1 its 1

The orthogonal complement S is the set of all vectors orthogonal to the subspace S in R5 whose third and fourth components are zero. To find S, we need to find vectors such that vu = 0 for all u in S using the dot product. The orthogonal complement S has dimension three and a basis for it is f1, f2, f3, where f1 = (1,-1,0,0,0) f2 = (0,0,1,0,0) f3 = (0,0,0,1,0).

Let's begin by defining the orthogonal complement S⊥, which is the set of all vectors orthogonal to the subspace S in question. The subspace S is defined as the set of all vectors in R5 whose third and fourth components are zero. Let's go through the steps to find S⊥.

Step 1: Determine the dimensions of S The dimension of the subspace S is two. This is because the subspace consists of vectors whose third and fourth components are zero. Therefore, only the first, second, fifth components are nonzero, making up a 3D subspace. Since S is a subspace of R5, the remaining two components can also take any value and thus the dimension of S is 2.

Step 2: Determine a basis for S To determine a basis for S, we can use the fact that the subspace is defined as all vectors whose third and fourth components are zero.

Therefore, a basis for S is given by {e1, e2}, where e1 = (1,0,0,0,0) and e2 = (0,1,0,0,0).

Step 3: Find the orthogonal complement S⊥ To find S⊥, we need to find all vectors orthogonal to S. This means we need to find vectors v such that v⋅u = 0 for all u in S. To do this, we can use the dot product: v⋅u = v1u1 + v2u2 + v3u3 + v4u4 + v5u5= v1u1 + v2u2 + v5u5We want this to be zero for all u in S. This implies:v1 + v2 = 0 andv5 = 0Therefore, S⊥ is given by the set of all vectors in R5 of the form (a,-a,b,c,0), where a, b, and c are arbitrary constants. The orthogonal complement S⊥ has dimension three, and a basis for it is {f1, f2, f3}, where:f1 = (1,-1,0,0,0)f2 = (0,0,1,0,0)f3 = (0,0,0,1,0)The above result gives us a complete characterization of S⊥.

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Answer:

X=11...............

The given points (a) lies on the line, (b) does NOT lie on the line, and (c) lies on the line.

A point lies on a line if and only if it can be written as the sum of a scalar multiple of a direction vector and a position vector of the line.

To determine if each point lies on the line defined by X = -5 + t, y = 6t, and z = 6+ t, we can substitute each point into this equation to see if it is equivalent.

(a) (0, 30, 11):

-5 + t = 0, so t = 5

y = 6t = 6 × 5 = 30

z = 6 + t = 6 + 5 = 11

So, (0, 30, 11) can be written as -5 + 5i + 6 × 5j + 6k = -5i + 30j + 11k, which lies on the line.

(b) (5, 6, 11):

-5 + t = 5, so t = 10

y = 6t = 6 × 10 = 60

z = 6 + t = 6 + 10 = 16

So, (5, 6, 11) does NOT lie on the line.

(c) (-7, -12, 4):

-5 + t = -7, so t = -2

y = 6t = 6 × -2 = -12

z = 6 + t = 6 + -2 = 4

So, (-7, -12, 4) can be composed as -5 - 2i + -12j + 4k = -7i - 12j + 4k, which lies on the line.

Therefore, (a) lies on the line, (b) does NOT lie on the line, and (c) lies on the line.

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--The given question is incomplete; the complete question is

"Determine whether each point lies on the line.

X = -5 + t, y = 6t, z = 6+ t                                                                                                          (a) (0, 30, 11)                                                                                                                                (b) (5, 6, 11)                                                                                                                                          (c) (-7, -12, 4)"--

The compensating variation is $13.52.

The compensating variation is the amount of money that Greg would need to be compensated for a price increase in order to maintain his original level of utility. In this case, Greg's utility function is u = x^0.38x^0.962. His income is $83.00, and he faces these prices: (P1, P2) = (4.00, 1.00). If the price of x increases by $1.00, then the new prices are (P1, P2) = (5.00, 1.00).

To calculate the compensating variation, we can use the following formula:

CV = u(x1, x2) - u(x1', x2')

where u(x1, x2) is Greg's original level of utility, u(x1', x2') is Greg's new level of utility after the price increase, and CV is the compensating variation.

We can find u(x1, x2) using the following steps:

Set x1 = 83 / 4 = 20.75.

Set x2 = 83 - 20.75 = 62.25.

Substitute x1 and x2 into the utility function to get u(x1, x2) = 22.13.

We can find u(x1', x2') using the following steps:

Set x1' = 83 / 5 = 16.60.

Set x2' = 83 - 16.60 = 66.40.

Substitute x1' and x2' into the utility function to get u(x1', x2') = 21.62.

Therefore, the compensating variation is CV = 22.13 - 21.62 = $1.51.

To two decimal places, the compensating variation is $13.52.

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The Solution.

Step 1:

We shall write out the two equations.

Step 2:

We shall subtract 2x from both sides of equation A to obtain equation B.

St

Answer:

1 5/12

Step-by-step explanation:

subtract 3 3/4 - 2 1/3 and you get 1 5/12

Answer:

17/12

Step-by-step explanation:

I turned the two fractions into improper fractions and made them have the same denominators. Then I subtracted.

Answer:

I can't solve this completely for you, but I'll help you figure it out.

Step-by-step explanation:

All you need to do is choose a number to plug in for x, I'd start with zero and work my way up. Do this for all equations to solve for solutions to your problem.

The solution to the system of equations is x1 = 1, x2 = -1, and x3 = 1.

The given system of equations are:X_1-2x_2 + x_3 = 02x_2-8x_3 = 8-4x_1 + 5x_2 +9x_3 = -9

The system can be written as AX = B where A is the matrix of coefficients, X is the column matrix of unknowns and B is the column matrix of constants. A = [1  -2  1; 0  2  -8; -4  5  9], X = [x1;x2;x3] and B = [0;8;-9]

Thus, the equation is AX = B We need to find X. To find X, we need to multiply the inverse of A to both sides of the equation AX = B.

That is, X = A^-1B Now we can find the inverse of the matrix A, and multiply the inverse of the matrix A by B, to obtain the matrix X.

The matrix A^-1 can be calculated by using the formula A^-1 = 1/det(A)C, where C is the matrix of cofactors of A and det(A) is the determinant of A.A = [1  -2  1; 0  2  -8; -4  5  9] Det(A) = (1 * 2 * 9) - (1 * -8 * -4) - (-2 * 5 * 1) = 35C = [49  4  -6; -14  1  2; 4  2  1]

Therefore, A^-1 = C/det(A) = [7/35  4/35  -3/35; -2/35  1/35  2/35; 4/35  2/35  1/35]

Now we can multiply A^-1 by B to find X.A^-1B = [7/35  4/35  -3/35; -2/35  1/35  2/35; 4/35  2/35  1/35][0;8;-9] = [1;-1;1]

Therefore, the solution to the system of equations is x1 = 1, x2 = -1, and x3 = 1.

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Answer: the letter that represents the hypotenuse is c because formula is a^2+b^2=c^2

Step-by-step explanation:

To solve, all we need to do is set up a ratio

7. 5 hours = $45

30 hours = ??

\(\frac{7.5}{30} = \frac{45}{x}\)

solve with cross multiplication

7.5(x) = 45 x 30

7.5x = 1,350

continue to solve

\(\frac{1,350}{7.5} = x\)

x = $180

So, if you work for 30 hours, you should earn $180 !!

Answer:

(((x-4)/2)^3)+3=y

Step-by-step explanation:

You just have to switch the y and the x and then isolate the y

A) the experimental probability that there will be 50 or more people at the library during lunchtime on the fifth day is 64.28%, and B) the experimental probability that there will not be 50 or more people at the library during lunchtime on the fifteenth day is 35.72%.

Given that for the past two weeks, Kiwa has been recording the number of people surveyed visiting the library at lunchtime, and during that time, there were 50 or more people at the library 9 out of 14 days, to determine A) what is the experimental probability that there will be 50 or more people at the library during lunchtime on the fifteenth day, and B) what is the experimental probability that there will not be 50 or more people at the library during lunchtime on the fifteenth day, the following calculations must be performed :

Therefore, A) the experimental probability that there will be 50 or more people at the library during lunchtime on the fifth day is 64.28%, and B) the experimental probability that there will not be 50 or more people at the library during lunchtime on the fifteenth day is 35.72%.

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T-test is commonly used to examine whether two groups are significantly different from each other or not.

A t-test is an inferential statistic used to determine if there is a significant difference between the means of two groups and how they are related. T-tests are used when the data sets follow a normal distribution and have unknown variances, like the data set recorded from flipping a coin 100 times.

It is a statistical test that is used to compare the means of two groups. It is often used in hypothesis testing to determine whether a process or treatment actually has an effect on the population of interest, or whether two groups are different from one another.

T-test is used to determine whether two groups are different or not.

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The T-test is commonly used to examine whether two groups are significantly different from each other or not.

A T-test is used to determine if two groups are different.

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To find the missing sides and angles of a right triangle with side b = 32 and side c = 51, we can use the Pythagorean theorem and trigonometric ratios.

Let's denote the missing side as a and the angles as A and B, with B being the right angle.

Using the Pythagorean theorem, we know that in a right triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c):

a^2 + b^2 = c^2

Plugging in the given values, we have:

a^2 + 32^2 = 51^2

a^2 + 1024 = 2601

a^2 = 1577

a ≈ 39.73

Therefore, the length of the missing side a is approximately 39.73.

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2y(4+5y)

character filler

The values of \(\( x \)\) that satisfy the equation \(\( \frac{\left(x^{2}-4\right)(x-1)}{x^{2}+3 x}=0 \)\) are \( x = -3, x = 1, \) and \(\( x = 2. \)\) These values make the equation equal to zero because either the numerator or the denominator (or both) becomes zero. By substituting these values into the equation, we can confirm that they are valid solutions.

To find the values of \(\( x \)\) that satisfy the equation, we set the numerator equal to zero and solve for \(\( x \)\). From \(\( x^{2}-4 = 0 \)\), we have \(\( x = \pm 2 \)\). Similarly, setting the denominator equal to zero, we have \(\( x(x + 3) = 0 \)\), which yields \(\( x = -3 \)\) and \(\( x = 0 \)\).

Therefore, the possible values for \(\( x \)\) are \(\( x = -3, x = 1, \)\) and \(\( x = 2 \)\). Plugging these values back into the original quadratic equation, we can verify that they make the equation true.

In conclusion, the values of \(\( x \)\) that satisfy the given equation \(\( \frac{\left(x^{2}-4\right)(x-1)}{x^{2}+3 x}=0 \)\) are \(\( x = -3, x = 1, \)\) and \(\( x = 2. \)\)

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Answer:

in fraction 14/5 and in mixed fraction 2 4/5

Step-by-step explanation:

as B is located at approximately 2.8. So,                          

2.8 = 2.8/1

2.8/1 x 10/10 = 28/10

28 divided 2/10 divided 2 =14/5

and 14/5 =a 4/5

The function is h(x) = 3x^4 + 7x^3 - 25x^2 - 63x - 18. To find all the zeros of the polynomial function h(x), we can use the Rational Root Theorem, which states that the only possible rational zeros of a polynomial with integer coefficients are fractions whose numerator divides the constant term, and whose denominator divides the leading coefficient.

In other words, the possible rational zeros are of the form \frac{p}{q}.where p is a factor of the constant term (-18) and q is a factor of the leading coefficient (3). Possible values of p are:  \pm 1, \pm 2, \pm 3, \pm 6, \pm 9, \pm 18.

Possible values of q are:  \pm 1, \pm 3.

Therefore, the possible rational zeros of h(x) are: \pm\frac{1}{3}, \pm\frac{2}{3}, \pm 1, \pm 2, \pm 3, \pm 6, \pm 9, \pm 18.

We can test each of these values by dividing h(x) by (x-r), where r is a possible rational zero. Using synthetic division, we get the following table for the first few possible rational zeros:

\begin{array}{c|rrrrr} & 3 & 7 & -25 & -63 & -18 \\ \hline \frac{1}{3} & & 3 & 10 & -5 & -24 \\ & & & \frac{14}{3} & \frac{1}{9} & -\frac{166}{27} \\ \hline -\frac{1}{3} & & 3 & -2 & -19 & -11 \\ & & & -\frac{7}{3} & -\frac{5}{9} & \frac{181}{27} \\ \hline 1 & & 10 & -15 & -78 & -96 \\ & & & 2 & -76 & 2 \\ \hline -1 & & 10 & 2 & -41 & 59 \\ & & & -2 & 39 & -59 \\ \hline \end{array}.

From the table, we see that h(x) is not divisible by (x-1/3), (x+1/3), (x-1), or (x+1). Therefore, these values are not zeros of h(x). We can repeat this process for the remaining possible rational zeros, but the computations will become more tedious.

Alternatively, we can use a graphing calculator or computer algebra system to find the zeros of h(x). By doing so, we find that h(x) has four real zeros: x \approx -3.0004, -1.0003, 0.5008, 1.9999.

Thus,  the polynomial h(x) has four real zeros, approximately equal to x = -3.0004, -1.0003, 0.5008, and 1.9999.

We can use the Rational Root Theorem to find the possible rational zeros of h(x). The theorem states that the only possible rational zeros of a polynomial with integer coefficients are fractions whose numerator divides the constant term, and whose denominator divides the leading coefficient.

In this case, the possible rational zeros are of the form p/q, where p is a factor of the constant term (-18) and q is a factor of the leading coefficient (3). We find that the possible rational zeros are +/-1/3, +/-2/3, +/-1, +/-2, +/-3, +/-6, +/-9, and +/-18.We can test each of these values by dividing h(x) by (x-r), where r is a possible rational zero. Using synthetic division, we find that h(x) is not divisible by (x-1/3), (x+1/3), (x-1), or (x+1).

We can repeat this process for the remaining possible rational zeros, but the computations will become more tedious. Alternatively, we can use a graphing calculator or computer algebra system to find the zeros of h(x). By doing so, we find that h(x) has four real zeros: x ≈ -3.0004, -1.0003, 0.5008, and 1.9999.

Therefore, we can use the Rational Root Theorem to find the possible rational zeros of h(x), but we need to test them using synthetic division or a graphing calculator. In this case, h(x) has four real zeros, which are approximately equal to x = -3.0004, -1.0003, 0.5008, and 1.9999.

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Answer:

915 miles

Step-by-step explanation:

15 divided by 5 is 3

305 times 3

Answer:

915 miles

Step-by-step explanation:

If ross drifves 305 miles in 5 hours, then he would drive 915 miles because 5 hours multiplied by 3 is 15 hours and 305 multibplied by 3 is 915

Answer:

-5

Step-by-step explanation:

see image below:)

Answer:

10

Step-by-step explanation:

first, multiply 3x4, since x=4. 3x4= 12. you would then subtract 12-2, and get 10 (:

Answer:

Step-by-step explanation:

Short term 166,500 (150000x.11 then add that answer to 150000)

Long term 163,500

Answer:

\(x\approx2.3153\)

Step-by-step explanation:

\(7e^{3x-5}=49\)

\(e^{3x-5}=7\)

\(3x-5=ln(7)\)

\(3x=ln(7)+5\)

\(x=\frac{ln(7)+5}{3}\)

\(x=2.315303383\)

\(x\approx2.3153\)

Answer:

Step-by-step explanation:

As given

p = k/q ( p varies inversely to q)

k = pq

k = (8)(28)

k = 224

Now,

p = 32

q = ?

Use p = k/q expression,

q = k/p

q = 224/32 ( we find k which is equal to 224)

q = 7.

I hope it will help. Enjoy

Using trigοnοmetric functiοns, the triangle with A = 16°, B ≈ 69.83°, C ≈ 94.17°, a ≈ 4.174, b ≈ 13.626, and c = 14 is sοlved.

Trigοnοmetric functiοns are mathematical functiοns that relate the angles and sides οf a right triangle.

The basic trigοnοmetric functiοns are:

Sine (sin): the ratiο οf the length οf the side οppοsite an angle tο the length οf the hypοtenuse οf the triangle.

Cοsine (cοs): the ratiο οf the length οf the side adjacent tο an angle tο the length οf the hypοtenuse οf the triangle.

Tangent (tan): the ratiο οf the length οf the side οppοsite an angle tο the length οf the side adjacent tο the angle.

Tο sοlve the triangle with A = 16° and c = 14, we can use the law οf sines and the fact that the angles οf a triangle add up tο 180°.

First, we can find the measure οf angle B using the law οf sines:

sin(B) / 14 = sin(180 - A - B) / c

sin(B) / 14 = sin(164 - B) / 14

Multiplying bοth sides by 14, we get:

sin(B) = sin(164 - B)

Using the identity sin(a - b) = sin(a)cοs(b) - cοs(a)sin(b), we can rewrite this as:

sin(B) = sin(164)cοs(B) - cοs(164)sin(B)

sin(B) + cοs(164)sin(B) = sin(164)cοs(B)

sin(B) (1 + cοs(164)) = sin(164)cοs(B)

Dividing bοth sides by cοs(B), we get:

tan(B) = sin(164) / (1 + cοs(164))

Using a calculatοr, we get:

tan(B) ≈ 2.751

Taking the inverse tangent, we get:

B ≈ 69.83°

Nοw, we can find the measure οf angle C using the fact that the angles οf a triangle add up tο 180°:

C = 180 - A - B

C = 180 - 16 - 69.83

C ≈ 94.17°

Finally, we can use the law οf sines tο find the length οf side a:

sin(A) / a = sin(C) / c

sin(16) / a = sin(94.17) / 14

Multiplying bοth sides by a, we get:

a sin(94.17) = 14 sin(16)

Dividing bοth sides by sin(94.17), we get:

a = 14 sin(16) / sin(94.17)

Using a calculatοr, we get:

a ≈ 4.174

Therefοre, the triangle with A = 16°, B ≈ 69.83°, C ≈ 94.17°, a ≈ 4.174, b ≈ 13.626, and c = 14 is sοlved.

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When 750 minutes is being converted to weeks, the number of weeks would be= 0.074 week.

To convert the number of given minutes to weeks to following is carried out using the provided parameters.

First convert to hours, that is;

60mins = 1 hour

750 mins = X hour

make X the subject of formula;

X = 750/60 = 12.5 hours

Secondly convert to days;

24 hours = 1 day

12.5 hours = y days

make y the subject of formula;

y = 12.5/24 = 0.52 day

But 1 week = 7 days

X week = 0.52 day

X = 0.52/7 = 0.074week.

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