A 29- m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 33 . Find the length of the shadow. If necessary, round your answer to the nearest tenth.

Answer:

Step-by-step explanation:

Two-digit multiples of 4 with one digit being 2 are:

So there are 7 possible options out of 9

Answer:

it matters what word came first

Step-by-step explanation:

The order of the items in a ratio is very important, and must be respected; whichever word came first in the ratio (when expressed in words), its number must come first in the ratio.

4:3. The order of numbers in a ratio is important. ...

numerator / denominator. A fraction is another way of expressing one number divided by another. ...

24 / 56 = 0.42857.

Answer:

∠1 = 52

∠2 = 128

∠4 = 128

Step-by-step explanation:

∠3 and ∠1 are vertical angles

As we now vertical angles are congruent

So if ∠3 = 52°, then ∠1 also equals 52°

∠3 and ∠4 are supplementary angles

supplementary angles add up to equal 180

Thus, ∠3 + ∠4 = 180

If ∠3 = 52°

Then 52 + ∠4 = 180

180 - 52 = 128

Hence, ∠4 = 128

∠4 and ∠2 are vertical angles

Like stated previously vertical angles are congruent

So if ∠4 = 128 then ∠2 also equals 128

a) To factor the quadratic expression x^2 - x - 20, let's first check if there is a greatest common factor (GCF) that can be factored out. In this case, there is no common factor other than 1.

Next, we need to find two numbers whose product is -20 and whose sum is -1 (coefficient of the x-term). By inspecting the factors of 20, we can determine that -5 and 4 satisfy these conditions.

Therefore, we can rewrite the quadratic expression as follows: x^2 - x - 20 = (x - 5)(x + 4)

b) For the quadratic expression x^2 - 13x + 42, let's again check if there is a GCF that can be factored out. In this case, there is no common factor other than 1.

Next, we need to find two numbers whose product is 42 and whose sum is -13 (coefficient of the x-term). By inspecting the factors of 42, we can determine that -6 and -7 satisfy these conditions.

Therefore, we can rewrite the quadratic expression as follows: x^2 - 13x + 42 = (x - 6)(x - 7)

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Answer:

49pi m^2

Step-by-step explanation:

Area of circle=pi r^2

D=2r=14

r=7

Area of circle =7^2pi=49pim^2

Answer:

Step-by-step explanation:

The diameter = 14m

r = d/2

r = 14/2

r = 7

Area = pi * r * r

Area = 7 * 7 * pi

Area = 49 pi

Answer:

Discretionary expenses are Optional and Can be reduced to help save money. For example, a Magazine Subscription is a discretionary expense.

Step-by-step explanation:

Fits the definition of a discretionary expense and the example matches too because it is Optional.

Answer:

c

Step-by-step explanation:

9,603.75 cm² is the area of the given triangle.

So, the perimeter of the triangle is 392 cm.

Then, let the rest 2 sides be x, where x = x.

Now, we know that the rest 2 equal sides are of length 98.5 cm.

Now, calculate the area as follows:

Therefore, 9,603.75 cm² is the area of the given triangle.

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Answer:

both

Step-by-step explanation:

op confirmed :)

Answer:

Both

Step-by-step explanation:

uh A and B are both correct

Answer:

Julia had 120 peas to start .

Answer:

  120 peas

Step-by-step explanation:

Before Julia gave Vlada 15 peas, the ratio of their numbers was 3:2. Afterward, Julia still had 10 more peas. You want to know the number Julia started with.

Let j represent the initial number of peas Julia had. Then Vlada had 2/3j peas. After the transfer, the difference was ...

  (j -15) -(2/3j +15) = 10

  1/3j -30 = 10

  1/3j = 40

  j = 120

Julia had 120 peas at first.

__

Additional comment

The transfer of peas decreases the difference by 30, so if it remains 10 it must have originally been 40. The difference in initial ratio units is 3-2 = 1, so Julia's initial 3 ratio units represent 3·40 = 120 peas.

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Answer:

I think its 238.00

Step-by-step explanation:

(a) To convert the complex number from polar form to standard form, we use the formula:
x = r cos(theta)
y = r sin(theta)
where r is the magnitude of the complex number and theta is the angle in radians.

In this case, we have:
r = 6
theta = 300 degrees = (5/6) pi radians (using the conversion 180 degrees = pi radians)

So,
x = 6 cos((5/6) pi) = -3
y = 6 sin((5/6) pi) = 3 sqrt(3)

Therefore, the complex number 6(cos 300° + i sin 300°) is equal to -3 + 3 sqrt(3) i in standard form.

(b) Using the same formula as before:
r = 5
theta = 0 degrees = 0 radians

So,
x = 5 cos(0) = 5
y = 5 sin(0) = 0

Therefore, the complex number 5(cos 0° + i sin 0°) is equal to 5 + 0i, or simply 5, in standard form.

(a) To write the complex number 6(cos 300° + i sin 300°) in standard form, we use the polar to rectangular conversion formula:

x = r*cos(θ)
y = r*sin(θ)

where r is the magnitude (6 in this case) and θ is the angle (300°).

x = 6*cos(300°)
y = 6*sin(300°)

Now, evaluate the trigonometric functions:

x = 6*(-1/2)
y = 6*(-√3/2)

x = -3
y = -3√3

So, the standard form is:

-3 - 3√3i

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The coordinate of the triangle after the dilation is (3, 3), (6, 3), (3, 6)

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

(5, 5), (10,5), (5, 10)

Scale factor = 3/5

The coordinate of the triangle after the dilation is calculated as

Image' = triangle * Scale factor

Substitute the known values in the above equation, so, we have the following representation

(5, 5), (10,5), (5, 10) * 3/5

Evaluate

(3, 3), (6, 3), (3, 6)

Hence, the image is (3, 3), (6, 3), (3, 6) and it is attached

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The answer is 16/15, don’t ask ok, used a calculator

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. The value of r ranges from -1 to +1, where a value of -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

The correlation coefficient's sign will not change when the order of the variables in a correlation study is changed, but the coefficient's numerical value might. This is due to the symmetry of the correlation coefficient with regard to the two variables under comparison.

For instance, if you calculate the correlation coefficient between X and Y and the result is r = 0.7, it indicates that Y tends to rise as X does. The correlation coefficient between the variables Y and X will have the same sign (+ or -) but a different numerical value if the variables are computed in a different order.

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The equation has infinite solution.

The equation is as follows:

2(x + 4) = 2x + 8

Let's open the bracket of the left side of the equation

2x + 8 = 2x + 8

Therefore, the equation has both sides equal to each other.

Hence, the solution of the equation is infinite.

An infinite solution has both sides equal.

Therefore, the equation has infinite solution.

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Answer: -1 1/2 to -1: -1 1/3 and -5/4

-1 to -1/2: -2/3, -3/4, -6/7, -5/6

-1/2 to 0: -1/3 and -3/8

0 to 1/2: 1/5, 1/10, 3/12, 3/8, 3/7, 1/3

1/2 to 1: 4/5, 6/10, 7/8, 7/9, 3/4, 8/10

1 to 1 1/2: 1 5/12, 9/8

Step-by-step explanation:

1)The pdf of U is f(u) = (1/(2√u)) exp(-u/2) for u > 0 and f(u) = 0 otherwise.

2)U follows a gamma-distribution with parameter a = 3/2 or a = 1/2.

3)x = (y²/2) and dx = y dy using exponential distribution

We can rewrite the integral as:

I(1/2) = ∫₀^∞ y exp(-y²) dy

       = 1/2 ∫₀^∞ exp(-u/2) du

This is the same as the integral for f(u) when u = 1/2.

Therefore, we have:

I(1/2) = V1

(1) For U = Z², we can use the method of transformations.

Let g(z) be the transformation function such that

U = g(Z)

   = Z².

Then, the inverse function of g is given by h(u) = ±√u.

Thus, we can apply the transformation theorem as follows:

f(u) = |h'(u)| g(h(u)) f(u)

     = |1/(2√u)| exp(-u/2) for u > 0 f(u) = 0 otherwise

Therefore, the pdf of U is given by:

f(u) = (1/(2√u)) exp(-u/2) for u > 0 and f(u) = 0 otherwise.

(2) We are given that f(1/2) = VT, where V is a constant.

We can substitute u = 1/2 in the pdf of U and equate it to VT.

Then, we get:VT = (1/(2√(1/2))) exp(-1/4)VT

                            = √2 exp(-1/4)

This gives us the value of V.

Now, we can use the pdf of the gamma distribution to find the parameter a such that the gamma distribution matches the pdf of U.

The pdf of the gamma distribution is given by:

f(u) = (u^(a-1) exp(-u)/Γ(a)) for u > 0 where Γ(a) is the gamma function.

We can use the following relation between the gamma and the factorial function to simplify the expression for the gamma function:

Γ(a) = (a-1)!

Thus, we can rewrite the pdf of the gamma distribution as:

f(u) = (u^(a-1) exp(-u)/(a-1)!) for u > 0

We can now equate the pdf of U to the pdf of the gamma distribution and solve for a.

Then, we get:

(1/(2√u)) exp(-u/2) = (u^(a-1) exp(-u)/(a-1)!) for u > 0 a = 3/2

Therefore, U follows a gamma distribution with parameter

a = 3/2 or equivalently,

a = 1/2.

(3) We need to show that I(1/2) = V1.

Here, I(1) = ∫₀^∞ exp(-x) dx is the integral of the exponential distribution with rate parameter 1 and V is a constant.

We can use the change of variables y = √(2x) to simplify the expression for I(1/2) as follows:

I(1/2) = ∫₀^∞ exp(-√(2x)) dx

Now, we can substitute y²/2 = x to obtain:

x = (y²/2) and

dx = y dy

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Answer: A, B, D

it can’t be “C” because that would be equal to 40%

The correct option is c. 33%.

The job rate of industry’s percent increase from 2003 to 2013 is 33%.

The percentage increase would be the change between the final and initial values given as a percentage. We need the initial value and the enhanced (new) value to calculate the percentage.

In other words, % growth is a measurement of percent change that indicates the amount by which a quantity increases in magnitude, strength, or value.

If the % rise is negative, we might conclude that there is corresponding proportion reduction. Let's look at the percentage growth calculation now.

Now, according to the question;

Total Number of years = 10 years

Total number of new jobs created = 2.65 thousand x 10

                                                         = 26.5 thousand

                                                         = 26,500

Number of jobs in 2013 = 78,900 + 26,500

                                       = 105,400

Percentage increase = (105,400 - 78,900)/78,900 x 100

                                   = 26,500/78,900 x 100

                                   = 0.3359 x 100

                                    = 33.59%

Percentage increase = 33% (approx)

Therefore, the percentage increases in the job between 2003 and 2013 is 33%.

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Answer:

C

Step-by-step explanation:

Answer:

Each single entertainment segment is 4.5 minutes.

Step-by-step explanation:

Out of the 20 minute show there are two blocks of time that are ads. The ads are each 13/4 minutes long.

13/4 = 13 ÷ 4 = 3.25

minutes.

Let's take away the time used for ads from the 20 minite total.

20 - 3.25 - 3.25

= 13.5

Without ads the show's actual runtime is 13.5 minutes.

Now we'll divide that 13.5 into three equal parts.

13.5 ÷ 3 = 4.5

Each of the three equal entertainment segments is 4.5 minutes long.

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

We assume that G is a connected planar graph with no vertex of degree <= 5. We will use e <= 3v - 6 to prove that G is not a planar graph. By handshaking lemma, we know that 2e = sum of degrees of all vertices. Let d be the maximum degree of G.

Qa. Contrapositive of an implication is a new implication formed by negating both the hypothesis and the conclusion.

The contrapositive of the implication "If G is a connected planar graph, then G has at least one vertex of degree <= 5" is "If G has no vertex of degree <= 5, then G is not a connected planar graph."

Qb. Proof: We assume that G is a connected planar graph with no vertex of degree <= 5.

We will use e <= 3v - 6 to prove that G is not a planar graph. By handshaking lemma, we know that 2e = sum of degrees of all vertices.

Let d be the maximum degree of G. Since G has no vertex of degree <= 5, then d >= 6.

Thus, the sum of degrees of all vertices in G is greater than or equal to 6v/2, which is equal to 3v.

Hence, 2e >= 3v.

Substituting this inequality in e <= 3v - 6, we get 2e >= 3e - 6, which implies that e >= 6.

Since e >= 6, it follows that G is not planar.

Qc. Proof: We use proof by induction on the number of vertices of G. For a graph with one vertex, the statement is trivially true.

For a graph with n > 1 vertices, assume that every planar graph with at most n - 1 vertices can be colored with 6 (or less) colors.

Let G be a planar graph with n vertices.

By part (a), there exists a vertex v of G with degree <= 5.

We remove v and all its edges from G to get a new graph G' with n - 1 vertices.

By the induction hypothesis, we can color G' with 6 (or less) colors.

We add back v and its edges to G.

Since v has degree <= 5, at most 5 colors are used on its adjacent vertices.

We use a new color for v.

Thus, G can be colored with 6 (or less) colors.

Therefore, by induction, the statement is true for all planar graphs.

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Answer:

D

Step-by-step explanation:

because it makes sense75 would be what he deposits in his bank account each month because x is the number of deposits

and 50 would be his birthday money he received

Answer: D, an enlargement

Step-by-step explanation:

i got the same question

\(\text{The imaginary unit,}~ i = \sqrt{-1}\\\\\sqrt{-2} ~ \text{can be written as.}\\\\\sqrt{-2}\\\\=\sqrt{-1 \cdot 2}\\\\=\sqrt{-1} \sqrt{2}\\\\=i\sqrt 2\\\\=\sqrt 2 i\)

Answer: they dont have the same numbers

Step-by-step explanation:

Answer:

Function A is 2

Function B is 5

Difference is -3

Step-by-step explanation:

The y intercept is the rate of change or the value of zero

Answer:

Yes, because -18/6 is -3, which is a higher value than -4 :)

The rate at which the diameter decreases when the diameter is 10 cm is -0.00798 cm/min.

To find the rate at which the diameter decreases, we can use the relationship between the surface area and the diameter of a sphere.

The surface area of a sphere is given by the formula:

A = \(4\pi r^2\), where A is the surface area and r is the radius (which is half the diameter).

Differentiating both sides of the equation with respect to time t, we get:

dA/dt = 8πr(dr/dt).

We are given that the surface area decreases at a rate of \(1 cm^2/min\), so dA/dt = \(-1 cm^2/min\). We want to find dr/dt when the diameter is 10 cm, which means the radius is r = 10/2 = 5 cm.

Substituting these values into the equation, we have:

-1 = 8π(5)(dr/dt).

Simplifying, we get:

-1 = 40π(dr/dt).

Now, solving for dr/dt:

dr/dt = -1 / (40π).

Using a calculator, this evaluates to approximately -0.00798 cm/min.

Therefore, when the diameter is 10 cm, the rate at which the diameter decreases is approximately -0.00798 cm/min. Note that the negative sign indicates the decrease in diameter.

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