Find the angle of elevation of the sun if a building 135 feet tall casts a shadow 150 feet long. Round to the nearest degree

Answer:

y= -x+5

Step-by-step explanation:

The slope of the two parallel lines is equal

so, the slope of

y=-x-3 is -1

slope=y2-y1/x2-x1=-3-15/8--10=-1

the equation of the line is

y-15= -1(x--10)

y= -x-10+15

y= -x+5

Considering the expression of a line and parallel lines, you obtain, the correct answer is third option: the equation of the line that passes through the pair of points (-10,15) and (8, -3) is y= -x +5.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:

\(m=\frac{y2-y1}{x2-x1}\)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

Parallel lines are two lines that always maintain the same distance and if they were extended to infinity they would never touch.

That is, parallel lines are two or more lines that never intersect.

Parallel lines are characterized by having the same slope.

So, in this case, being (x1,y1)= (-10,15) and (x2,y2)= (8,-3), the slope m can be calculated as:

\(m=\frac{-3-15}{8-(-10)}\)

\(m=\frac{-18}{18}\)

m=-1

So, being y= -1x + b and considering point 1, you obtain:

15= -1×(-10) +b

15= 10 + b

15-10=b

5= b

So, the equation of the line is y=-1x + 5= -x +5

To know if this line is parallel to y +4= -(x - 1), in first place you must rearrange this second equation of a line:

y +4= -x +1

y=-x +1 -4

y= -x-3

You can see that both equations of a line have -1 as the slope value m.

Finally, the correct answer is third option: the equation of the line that passes through the pair of points (-10,15) and (8, -3) is y= -x +5.

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Polar curves are a type of curve defined by the relationship between a point in the Cartesian plane and a particular point (or set of points) in the polar coordinate system. In this context, the slope of the tangent line is the rate at which the curve changes at a particular point on the curve. To find the slope of the tangent line to polar curve

r = 2 sin at the point 2√3 (21³, 3), we must first convert the polar equation to Cartesian coordinates .Using the following formulas for converting polar coordinates to Cartesian coordinates:

x = r cosθ, y = r sinθ,  where r represents the distance from the origin and θ represents the angle measured from the positive x-axis, we get:

x = 2sinθ cosθ = sin(2θ)y = 2sinθ sinθ = (1/2)sin(2θ)   The derivative of y with respect to x is given by:

dy/dx = (dy/dθ) / (dx/dθ) To find the slope of the tangent line at the point (21³, 3), we must evaluate the derivative at this point. Since x = 2√3, we can write:cosθ = x/r = 2√3 / 2 = √3sinθ = y/r = 3 / 2Using the chain rule, we get:

dy/dθ = (dy/dr) / (dθ/dr) = (cosθ)sinθ + r cosθdx/dθ = (dx/dr) / (dθ/dr) = (cosθ)cosθ - r sinθSubstituting the values of cosθ and sinθ, we get:dy/dθ = √3/2dx/dθ = -1/2Therefore, the slope of the tangent line at the point (21³, 3) is:

dy/dx = (dy/dθ) / (dx/dθ) = (-√3/2) / (1/2) = -√3Therefore, the slope of the tangent line to polar curve r = 2 sin at the point 2√3 (21³, 3) is -√3.

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Answer:

Choice B

Step-by-step explanation:

As we know that

1 pound = 16 ounces

So for choice A

it is given that

2 pound would cost $3.90

i.e. 32 ounces would cost $3.90

So per ounce it would be

= $3.90 ÷ 32

= 0.121875

Now for choice B

It is given that

36 ounces would cost for $3.05

So per ounces it would be

= $3.05 ÷ 36

= 0.08472

So here the per ounces would be less for choice B so the same would be considered

Step 1:State the full and alternative hypotheses for the testNull Hypothesis: H0: μ = 1 cm (bolts are 1 cm long when they come off the assembly line)Alternative Hypothesis: Ha: μ ≠ 1 cm (bolts are not 1 cm long when they come off the assembly line)

The null hypothesis and alternative hypothesis can also be written as follows:Null Hypothesis: H0: μ - 1 = 0 (bolts are 1 cm long when they come off the assembly line)Alternative Hypothesis: Ha: μ - 1 ≠ 0 (bolts are not 1 cm long when they come off the assembly line)Explanation:Given that a manufacturer must test that his bolts are 1.00 cm long when they come off the assembly line.

He must recalibrate his machines if the bolts are too long or too short. After sampling 49 randomly selected bolts off the assembly line, he calculates the sample mean to be 1.08 cm. there is not sufficient evidence to show that the manufacturer needs to recalibrate the machines.

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In Step 1, she incorrectly factored out 1/2. She should have written y=1/2(x^2−4x+6).

Answer

A m2=m23

Step-by-step explanation:

cause you have to look at a way so you can find the anser to it

Answer:

A

Step-by-step explanation:

w = 12500p + 250

250 is a fixed number of words.

12500 is the slope

For each dollar the price increases, the number of words increases by 12,500.

Answer: A

Solution

By definition

Graphically, what |y| represents is

If y = x -5

The correct option is D.

To have a better understanding of it lets graw its graph

Yes, the function f(x) = x / (x + 2) satisfies the hypotheses of the mean value theorem on the given interval [1, 4]. This is because f is continuous on [1, 4] and differentiable on (1, 4).

Given f(x) = x/ x + 2

We are asked to check whether the function satisfies the hypotheses of the mean value theorem on the given interval [1, 4].

Mean Value Theorem: If f(x) is continuous on the closed interval [a, b] and is differentiable on the open interval (a, b), then there exists a number c in (a, b) such that: f(b) − f(a) / b − a = f'(c)

For the given function, we have the interval [1, 4]. The function is continuous on [1,4].

Also, the function is differentiable on (1,4).

Therefore, the given function satisfies the hypotheses of the mean value theorem on the given interval [1, 4]. Hence, the correct option is Yes, f is continuous on [1,4] and differentiable on (1,4).

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Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The attached figure shows several kinds of quadrilaterals. The sum of angles of a quadrilateral is 360°. A pair of sides will be parallel if the sum of consecutive angles between them is 180°.

Trapezium/Trapezoid

By definition, a trapezium/trapezoid has exactly one pair of parallel sides.

Concave quadrilateral

This is a quadrilateral with a reflex angle (one that measures more than 180°). Such an angle demands that no consecutive pair of internal angles have a total of 180°. Hence no two sides can be parallel.

Convex quadrilateral

If a simple quadrilateral is not concave, it is convex. Since the sum of angles is 360°, there exists the possibility for at least one adjacent pair of angles to total 180°. That would make at least one pair of sides be parallel.

In the attached figure, all of the quadrilaterals shown, except the "dart" at upper left, are convex quadrilaterals. Most of them, except the "kite" at lower left, have at least one pair of parallel sides.

There is no assurance that a convex quadrilateral will have no parallel sides.

Kite

A kite has two pairs of congruent adjacent sides. It cannot have any parallel sides.

Rhombus

A rhombus has all four sides of equal length. It is a parallelogram with two pairs of parallel sides.

The two figures on the list that have no pairs of parallel sides are ...

These are shown in the left column of the attached figure.

The integral ∫(a to 0) x^2 dx can be evaluated using the concept of infinite Riemann sums, leading to the result of a^3.

1. Divide the interval [0, a] into n equal subintervals. The width of each subinterval is Δx = a/n.

2. Choose a sample point xi in each subinterval. For the ith subinterval, let xi be the right endpoint of the subinterval. So xi = iΔx.

3. Approximate the area under the curve y = x^2 within each subinterval by the rectangle with width Δx and height (xi)^2 = (iΔx)^2.

4. Calculate the sum of the areas of all the rectangles: S = (Δx)^2(1^2 + 2^2 + 3^2 + ... + n^2).

5. Rewrite the sum in terms of the sample point xi: S = (a/n)^2(1^2 + 2^2 + 3^2 + ... + n^2).

6. Simplify the sum of squares: 1^2 + 2^2 + 3^2 + ... + n^2 = n(n + 1)(2n + 1)/6.

7. Substitute this result into the sum: S = (a/n)^2(n(n + 1)(2n + 1)/6).

8. Simplify further: S = a^2(n + 1)(2n + 1)/(6n).

9. Take the limit as n approaches infinity: lim(n→∞) a^2(n + 1)(2n + 1)/(6n).

10. Simplify the limit: lim(n→∞) a^2(2 + 1/n)(n + 1)/(6).

11. Recognize that lim(n→∞) (2 + 1/n) = 2, and lim(n→∞) (n + 1)/n = 1.

12. Substitute these values into the limit: lim(n→∞) a^2(2)(1)/(6) = a^2/3.

13. The result of the infinite Riemann sum is a^2/3.

14. Finally, notice that the integral ∫(a to 0) x^2 dx is equivalent to the infinite Riemann sum, so the result is a^2/3.

15. Since the original integral is ∫(a to 0) x^2 dx, we need to reverse the limits: ∫(0 to a) x^2 dx.

16. Apply the property of definite integrals: ∫(0 to a) x^2 dx = -∫(a to 0) x^2 dx.

17. Negate the result of the infinite Riemann sum: -a^2/3.

18. Combine the two results: ∫(a to 0) x^2 dx = a^2/3 = a^3.

Therefore, using the concept of infinite Riemann sums, we have shown that ∫(a to 0) x^2 dx = a^3.

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The coordinates of R between points Q and R are (5/4, -2)

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

Q(9, -5) and S(-10, 3)

We have the partition to be

m : n = 3 : 5

The coordinate is then calculated as

R = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

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

R = 1/8 * (3 * -10 + 5 * 8, 3 * 3 + 5 * -5)

Evaluate

R = (5/4, -2)

Hence, the coordinate is (5/4, -2)

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Answer:

To solve the inequality:

-10 - 66h ≥ -3

We can begin by isolating the variable h on one side of the inequality. First, we can add 10 to both sides:

-10 + 10 - 66h ≥ -3 + 10

Simplifying, we get:

-66h ≥ 7

Next, we can divide both sides by -66, remembering to reverse the inequality since we are dividing by a negative number:

h ≤ -7/66

Therefore, the solution to the inequality is h ≤ -7/66.

Step-by-step explanation:

Answer: Approx. 323

Step-by-step explanation:

By subtracting 56% (known percentage) - 100%, it will give us the unknown percentage

100% - 56% = 44%

Now, we can multiply that by 0.44 (44%)

0.44 x 224 = 98.56 (99)

Now add the unknown to known amount of cupcakes.

99 + 224 = 323 total cupcakes

Answer:

323 Total Cupcakes

Step-by-step explanation:

100% - 56% = 44%

0.44 x 224 = 98.56 (99)

99 + 224 = 323

To complete the square for the equation x2 - 16x + 60 = -12, add 64 to each side of the equation. This will give us x2 - 16x + 124 = 52.

Then, factor out the coefficient of x2 (1) and the coefficient of x (16). This will give us (x - 8)2 = 52. Finally, subtract 52 from both sides to get (x - 8)2 = 0. Solving for x yields x = 8.

Equations are mathematical statements that express the equality of two expressions. They involve one or more unknowns that are represented by variables and involve numbers, constants, and operators. An equation states that the expressions on either side of the equal sign have the same value.

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The area of quadrilateral OBEC is 16m - 8, which depends on the slope of line CD

To solve this problem, we can use the fact that the two lines intersect at point E(4,4).

We know that line AB has a slope of -2,

so its equation is y = -2x + b,

where b is the y-intercept.

Since it passes through point B(0,b), we can solve for b by substituting x = 0 and y = b:

b = -2(0) + b

b = b

So the equation of line AB is,

⇒ y = -2x + b.

We also know that it passes through point A(a,0), so we can substitute these coordinates into the equation to solve for a:

0 = -2a + b

b = 2a

Substituting b = 2a back into the equation for line AB, we get

y = -2x + 2a.

Now we need to find the equation of the second line CD.

We know that it passes through point C(8,0), so we can use point-slope form to find its equation:

y - 0 = m(x - 8)

where m is the slope of line CD.

To find the slope, we know that it passes through point D(0,d), so we can substitute these coordinates into the equation:

d - 0 = m(0 - 8)

d = -8m

Substituting d = -8m back into the equation for line CD, we get

y = -8/(-1/m)x = 8mx.

Now we can find the coordinates of point D by substituting x = 0:

D = (0, 8m)

To find the coordinates of point O, we need to find where lines AB and CD intersect.

Setting their equations equal to each other and solving for x, we get:

-2x + 2a = 8mx

x = 2a/(4m+1)

Substituting x back into either equation, we get:

y = -2(2a/(4m+1)) + 2a = -4am/(4m+1) + 2a

y = 8m(2a/(4m+1)) = 16am/(4m+1)

Either way, we now have the coordinates of point O(a, -4am/(4m+1)) or (2a/(4m+1), 0).

Finally, we can find the area of quadrilateral OBEC by subtracting the areas of triangles OEB and CED from the area of rectangle OCBD:

Area(OBEC) = Area(OCBD) - Area(OEB) - Area(CED)

                  = (8)(8m) - (1/2)(4)(4) - (1/2)(8-4)(8m-d)

                  = 64m - 8 - 16m + 4d

                  = 48m + 4d - 8

Substituting d = -8m, we get:

Area(OBEC) = 64m - 8 - 16m - 32m = 16m - 8

So, the area of quadrilateral OBEC is 16m - 8, which depends on the slope of line CD.

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The scientist started with around 16 bacteria in the petri dish.

Each hour, the number of bacteria increases by about 80%.

To describe the model in more detail:

The equation Y = 16 x 1.8ˣ represents an exponential growth model for the bacteria population in the petri dish.

The initial population of bacteria at the start of the experiment is approximately 16.

As time progresses, represented by the variable x (the number of hours), the number of bacteria increases exponentially.

The term 1.8ˣ in the equation represents the exponential growth factor. With each passing hour, the number of bacteria multiplies by a factor of 1.8.

This indicates that the bacteria population experiences rapid growth, increasing by 80% per hour.

Exponential growth models are characterized by a constant relative growth rate the population size grows at an increasingly faster pace over time.

The bacteria population in the petri dish exhibits such growth dynamics, with the number of bacteria multiplying by 1.8 every hour.

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The coordinates of the point that divides the line segment from (6, 2) to (8, -10) into a ratio of 1 to 3 are (7, -1).

To find the coordinates of the point on the directed line segment that partitions it into a ratio of 1 to 3, we can use the concept of section formula.

The section formula states that if we have two points A(x₁, y₁) and B(x₂, y₂) dividing a line segment in the ratio of m₁ : m₂, then the coordinates of the dividing point P are given by:

Px = (m₁ * x₂ + m₂ * x₁) / (m₁ + m₂)

Py = (m₁ * y₂ + m₂ * y₁) / (m₁ + m₂)

In this case, the ratio is 1:3, which means m₁ = 1 and m₂ = 3. The given points are A(6, 2) and B(8, -10). Substituting these values into the formula, we can calculate the coordinates of the dividing point P:

Px = (1 * 8 + 3 * 6) / (1 + 3) = 7

Py = (1 * -10 + 3 * 2) / (1 + 3) = -2/2 = -1

Therefore, the coordinates of the point that divides the line segment from (6, 2) to (8, -10) into a ratio of 1 to 3 are (7, -1).

To find the coordinates of the point that divides the line segment between (6, 2) and (8, -10) in a 1:3 ratio, we can use the section formula. Applying the formula, where m₁ is 1 and m₂ is 3, the point P(x, y) can be determined.

By substituting the values into the formula, the x-coordinate is calculated as (1 * 8 + 3 * 6) / (1 + 3) = 7, and the y-coordinate is (1 * -10 + 3 * 2) / (1 + 3) = -1. Thus, the coordinates of the point that partitions the line segment into a ratio of 1 to 3 are (7, -1).

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Answer: A

Step-by-step explanation:

Looks like A, since it's the altitude.

Answer:

(3×6)÷5

Step-by-step explanation:

We are given the following expression:

(3/5)*6

The 6 can also be written as a fraction(6/1).

So we have a multiplication of fractions, is which we multiply the numerators and denominators.

So

(3*6)/5

The fraction sign means division

So the answer is:

(3×6)÷5

In a perfectly symmetrical distribution with a mean (µ) of 30, there is no specific mode because all values occur with equal frequency.

In a perfectly symmetrical distribution, such as a symmetric bell-shaped curve or a uniform distribution, each value occurs with the same frequency. This means that there is no value that occurs more frequently than others, resulting in multiple modes or no mode at all.

The mode is typically used to identify the most common value in a dataset, but in a perfectly symmetrical distribution, all values have equal frequency, and there is no single mode. Instead, the distribution is characterized by its symmetry around the mean (µ). The mean represents the central tendency of the distribution, indicating the balance point of the data. In this case, with a mean of 30, the distribution is centered around this value, with equal numbers of observations on either side.

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On solving the provided question, we can say that By percentage, the amount that will be covered in the insurance = $749

A percentage in mathematics is a figure or ratio that is stated as a the fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

By percentage.,

35% 0f 2140 =

35/100 X 2140 = 0.35*2140 = $749

the amount that will be covered in the insurance = $749

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The probability that the article will have no errors is approximately 0.0233.

To solve this problem, we can use the formula for the probability of an event, which is the number of favorable outcomes divided by the total number of outcomes.

Let's first find the probability that the article is typed by the first typist. Since the article is equally likely to be typed by either typist, this probability is 1/2.

Now, we need to find the probability that the article has no errors given that it is typed by the first typist. We know that the average number of errors per article typed by the first typist is 3.5, so the probability that an article typed by the first typist has no errors is given by the Poisson distribution with λ = 3.5:

P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-3.5) * 3.5^0 / 1 = e^(-3.5) ≈ 0.0302

Similarly, we can find the probability that the article has no errors given that it is typed by the second typist. This probability is given by the Poisson distribution with λ = 4.1:

P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-4.1) * 4.1^0 / 1 = e^(-4.1) ≈ 0.0164

Finally, we can use the law of total probability to find the probability that the article has no errors:

P(X = 0) = P(X = 0 | typed by first typist) * P(typed by first typist) + P(X = 0 | typed by second typist) * P(typed by second typist)

= 0.0302 * 1/2 + 0.0164 * 1/2

= 0.0233

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Answer:

b) b=a/h

Step-by-step explanation:

A=bh

Dividing both side by h,

or, b=A/h

OR,

A=bh

or, b=A/h

Answer:

b

Step-by-step explanation:

uhm

Start by changing the -4x to + -4x.

So we have 3x + 2a + -4x.

To simplify, we can only combine what are called our like terms and in this problem, we have a pair of like terms in our x terms.

3x + -4x simplifies to -x.

So our answer is -x + 2a.

Note that if you wrote your answer as -1x + 2a, it means the same thing. However, as we move farther into math, we usually tend to drop the -1 or 1 that is in front of a variable since it's implied

Answer:

Miranda. Because she earns $10 per hour while Tommy earns $8 per hour.

Step-by-step explanation:

y = 10x <--- 10 is the amount she earns per every x, which is the number of hours she works.

Tommy's equation is y = 8x

Because if you plug in his values of time (x) and total cash earned (y) you get:

32=?4

Read the above ^ as " 32 = blank multiplied by four "

subtract both sides by four to find blank

Our blank equals 8, which is the amount Tommy makes per hour.