What is the area, in square centimeters, of the trapezoid below?
11.7 cm
5.5 cm
6.5 cm

Therefore, the players are 6.84 meters apart from each other.

An item that is propelled by the application of an external force and then travels freely while being affected by gravity and air resistance is referred to as a projectile. Projectiles are generally used in sports and combat, despite the fact that every item traveling through space is a projectile.

The straight line that traverses a point with a slope equal to the derivative of the curve at that location is said to be the tangent line to a plane curve at that point in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

If we let x be the distance between the players, then we can use the tangent function to relate the angle of elevation to the distance between the player and the basket:

tan(40°) = 3.5/x

tan(50°) = 3.5/(x+1)

We can solve for x in both equations, and set them equal to each other, we get x= 6.84m

Therefore, the players are 6.84 meters apart from each other.

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The smaller sample's margin of error will be almost twice as great as the larger sample's margin of error.

Calculating the margin of error for a given sample from a population:

Let the level of significance be   and the standard deviation of the population be σ and the sample size be n, then we have:

MOE(Margin of Error)=  [tex]z_{a/2}\times\frac{\sigma}{\sqrt n}[/tex]

Using the above formula to calculate the margin of errors for two specified samples

For first sample:

Sample size = n(1) = 1000

MOE(1) = [tex]z_{a/2}\times\frac{\sigma}{\sqrt {1000}}[/tex]

For second sample:

Sample size = n(2) = 4000

MOE(2) = [tex]z_{a/2}\times\frac{\sigma}{\sqrt {4000}}[/tex]

(since it was given that they have same point estimates, so same standard deviation)

Their ratios are given by

MOE(2)/MOE(1) = [tex]\frac{z_{a/2}\times\frac{\sigma}{\sqrt {4000}}}{z_{a/2}\times\frac{\sigma}{\sqrt {1000}}}[/tex]

MOE(2)/MOE(1) = [tex]\sqrt{\frac{1000}{4000}}[/tex]

MOE(2)/MOE(1) = 1/2

MOE(1) = 2*MOE(2)

Thus, the margin of error from the smaller sample will be about double of the margin of error from the larger sample.

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Answer:

[tex] \frac{-5}{28} [/tex]

Step-by-step explanation:

Given:

[tex] \frac{-1}{5} * (\frac{3}{4} + \frac{1}{7}) [/tex]

Required:

Solve

Solution:

[tex] \frac{-1}{5} * (\frac{3}{4} + \frac{1}{7}) [/tex]

Apply distributive property by multiplying each reaction in the box by -⅕

[tex] (\frac{-1}{5} * \frac{3}{4}) + (\frac{-1}{5} * \frac{1}{7}) [/tex]

[tex] \frac{-3}{20} + \frac{-1}{35} [/tex]

Add together. Common denominator is 140. Therefore:

[tex] \frac{-21 + (-4)}{140} [/tex]

[tex] \frac{-25}{140} [/tex]

Simplify further

[tex] \frac{-5}{28} [/tex]

Step-by-step explanation:

4x-0.5=x+7

4x-x=7+0.5

3x=7+0.5

3x=7.5

x=2.5

hope this helps

Answer:

Simple, [tex]1/8=2/5x[/tex] so [tex]1/8/2/5=x[/tex] would become [tex]x=1/20[/tex], which is equal to 2/40 :)

Step-by-step explanation:

Answer:

Our goal is to understand how range and interquartile range describe data. To do this, we have to define the range and interquartile range of a given set of data, we have to be able to calculate the range and interquartile a range of a given set of data, and then we want to be able to determine how range and interquartile range are impacted by outliers.

So how can you describe data with range and interquartile range? Range tells us if data is grouped closely together or spread far apart. Interquartile range tells us if data is grouped closely around the median. The key concepts. Range is the difference of the maximum and minimum values.

So if we wanted to calculate the range of this particular data set here, we would say 20 minus 1 and get a range of 19. Interquartile range is the difference of the upper and lower quartiles. In order to do this, we first have to find the median to find those upper and lower quartiles. The median of this data set, the value in the middle, is 6. The lower quartile is the median of the lower half, the middle value then of these three data points being 3.

The upper quartile would be the middle of this data set, and that would be 8. So if we wanted to find the interquartile range, we'd subtract those values. 8 minus 3 gives us an interquartile range of 5. Interquartile range describes the spread of data around the median.

A small interquartile range means that most of the data, the middle half, is clustered tightly around the median, whereas a large interquartile range would mean that that data that's in the middle is more spread out. And finally, outliers impact the range, but have little impact on the interquartile range. If we consider our data set here, we see that we have an outlier of 20, but it really only impacts the range.

It does not play a significant role on the interquartile range.

Step-by-step explanation: also brainleist

Hence your answer will be D

Answer:

A ≈ 25.1 cm²

Step-by-step explanation:

The area (A) of the shaded region is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{\frac{4\pi }{9} }{2\pi }[/tex]

   = π × 6² × [tex]\frac{\frac{4\pi }{9} }{2\pi }[/tex] ← cancel π and 2π by π

   = 36 × [tex]\frac{\frac{4\pi }{9} }{2}[/tex]

   = 18 × [tex]\frac{4\pi }{9}[/tex]

   = 2 × 4π

   = 8π ≈ 25.1 cm² ( to 1 dec. place )

Answer:

Hope it helps you!...............

The order of the quantities in an inequality matters. Therefore, it is true.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.

When resolving an inequality, you can do one of the following: Add the same amount to each side; Subtract the same amount from each side; Multiply or divide each side by the same positive amount. You must flip the inequality symbol if you multiply or divide each side by a negative number.

Therefore, the order matters.

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Answer:

A translation is a type of transformation that moves each point in a figure the same distance in the same direction.

Step-by-step explanation:

Translations are often referred to as slides. You can describe a translation using words like "moved up 3 and over 5 to the left" or with notation.

The inequality to represent each situation is Harry > 60 inches, Sherry ≠ 4 years, and Hank ≥ $7.50.

a) Harry: This inequality states that Harry is taller than 60 inches. This is likely referring to Harry's height, as most people measure height in inches. This inequality can also be written as Harry ≥ 60 inches, emphasizing that Harry is at least 60 inches tall.

b) Sherry: This inequality states that Sherry is not equal to 4 years. This could be referring to Sherry's age, as it is common to measure age in years. This inequality can also be written as Sherry ≠ 4 years, emphasizing that Sherry is not exactly 4 years old.

c) Hank: This inequality states that Hank is greater than or equal to $7.50. This is likely referring to Hank's amount of money, as it is common to measure money in dollars. This inequality can also be written as Hank ≥ $7.50, emphasizing that Hank has at least $7.50.

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The composite function is the result of first applying the function (x^2 - 1) to the input and then applying the function (5x + 2) to the result. The final result of the composite function is 5x^3 + 2x - 3.

Step 1: Apply (x^2 - 1) to the input:

(x^2 - 1) = x^2 - 1

Step 2: Apply (5x + 2) to the result:

(5x + 2)(x^2 - 1)

= 5x^3 - 5x + 2x - 2

Step 3: Simplify:

5x^3 - 5x + 2x - 2

= 5x^3 + 2x - 3

A composite function is the result of applying two or more functions in succession. The order of operations for a composite function is to first apply the first function, then apply the second function to the result of the first, and so on. In the example given, the composite function

f(x) = (5x + 2) ∘ (x^2 - 1)

is the result of first applying the function

(x^2 - 1)

to the input and then applying the function (5x + 2) to the result. The calculation can be broken down into three steps: Step 1 is to apply (x^2 - 1) to the input to get x^2 - 1, Step 2 is to apply (5x + 2) to the result to get 5x^3 - 5x + 2x - 2,

and Step 3 is to simplify the result to get the final answer of

5x^3 + 2x - 3.

To summarize, the composite function

f(x) = (5x + 2) ∘ (x^2 - 1)

is the result of first applying the function (x^2 - 1) to the input, and then applying the function (5x + 2) to the

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Answer:

9m^8 n^2

Step-by-step explanation:

Open up the parenthesis and simplify to find your answer.

Therefore , the solution of the given problem of tractable problem comes out to be  the halting problem is undecidable for Turing machines.

a process that completes a manageable task in a polynomial amount of time. The polynomial upper bound is used. If an issue cannot be resolved in a polynomial amount of time, it is referred to as being intractable. The bound's minimum is exponential.

Here,

Alan Turing proved in 1936 that a general algorithm running on a Turing

machine that solves the halting problem for all possible program-input

pairs necessarily cannot exist.

the halting problem is undecidable for Turing machines.

Therefore , the solution of the given problem of probability comes out to be  the halting problem is undecidable for Turing machines.

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The statement that best represents the function must be identified by reading the graph.

A) When  x < 0, the function is negative.

This is accurate; as you can see, the function is negative for x < 0 because it is below the horizontal axis.

We shall see that choice A is the proper one. "When x < 0, the function is negative."

The function tends to infinity on the positive side at an x close to zero.

The function tends to negative infinity at x close to zero on the negative side.

The function tends to zero as x's absolute value grows.

So we can conclude that this is an inverse function similar to:

y = f(x) = 1/x

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Answer:

Step-by-step explanation:

We know that : Percentage means 'divided by 100'

therefore, 1/2 percent = 1 / 2 ÷ 100 = 0.5 ÷100 = 5÷1000= 0.005

The two spaceships will meet in 8 hours if the second spaceship is traveling at 90. 000 km/hr.

To calculate the time it will take for the two spaceships to meet, you must use the equation Distance = Rate x Time. Since the first spaceship has a higher rate of speed, it will reach the second spaceship in less time than it would take the second spaceship to reach the first.

This means that the time it takes for the two spaceships to meet will be equal to the time it takes for the first spaceship to travel the distance between the two space stations. We can use the equation to solve for time: Time = Distance/Rate. In this case, the distance is 710,000 km and the rate is 110,000 km/hr, so the time is 6.45 hours.

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Two supplementary angles equal 180 degrees.

Let the first angle = x

The second angle is 30 degrees more so this would be x + 30

Now add the two angles together to equal 180:

X + x+ 30 = 100

Combine like terms:

2x + 30 = 180

Subtract 30 from both sides:

2x = 150

Divide both sides by 2:

X = 75

One angle = x = 75

The other angle is x + 30 = 75 + 30 = 105

The smaller angle is 75 degrees.

The equation 11 = −4x²−x³ is a cubic polynomial.

Polynomial:

A polynomial is an algebraic expression containing indefinites and constants. Polynomials can be thought of as dialects of mathematics. They are used to represent numbers in almost all areas of mathematics, and are used in specific areas of mathematics such as mathematics  Critical analysis. For example, 2x + 9 and x2 + 3x + 11 are polynomials.

Cubic Polynomial:

The cubic polynomial is the polynomial with the largest exponent of the variables. H. Order of variables as 3. Based on the degree, polynomials are divided into four types: zero polynomials, linear polynomials, second order polynomials, and third order polynomials. The general form of a cubic polynomial is p(x): ax³ + bx² + cx + d, where a ≠ 0. where a, b, and c are coefficients and d is a constant, all of which are real numbers. An equation involving a cubic polynomial is called a cubic equation. Examples of cubic polynomials are p(x): x³ − 5x² + 15x − 6 and

r(z): πz³ + (√2)10.

Now,

A cubic polynomial is a polynomial of degree 3. A cubic polynomial has the form f(x)=a₃x³ +a₂x² +a₁ x+ a₀

​Here, the polynomial 11 = −4x² −x³

or x³+4x² +11 = 0 is a polynomial of degree 3 with coefficients a₁ = 0,

a₂ =4, a₃​ =1 and constant a₀= 11.

Hence, 11 = −4x² −x³  is a cubic polynomial.

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Answer:

of g(x) is the set of all real numbers

The independent variable is h (the number of hours Neil works) and the dependent variable is B (the amount of Neil's bonus).

In this scenario, the amount of Neil's bonus (B) is dependent on the number of hours he works (h). The number of hours he works is the input or independent variable, while the amount of bonus he receives is the output or dependent variable. It can be said that the number of hours he works is the cause and the amount of bonus is the effect.

The equation is B = f(h) where f is the function that relates the two variables.

Thus, the independent variable is h (the number of hours Neil works) and the dependent variable is B (the amount of Neil's bonus).

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Complete Question is-

Neil works as a consultant at a software company and the amount of his annual bonus is based on the number of hours he works, which variable is independent and which is dependent? With B as the amount of Neil's bonus, and h as the number of hours Neil works.

Answer:

14 minutes

Step-by-step explanation:

We can represent Xavier's running in the following ratio using the given information:

distance : time

13 miles  :  182 minutes

To get the answer to this problem, all we have to do is divide both sides of the ratio by 13, so that the left side is 1 mile.

[tex]13 \textrm{ miles} : 182\textrm{ minutes}\\\overline{\ \ \ \ 13 \ \ \ \: } \ \ \: \overline{\ \ \ \ \ \ \, 13 \ \ \ \ \ \ }[/tex]

1 mile     :   14 minutes

It takes Xavier 14 minutes to run 1 mile.

Therefore after using the Pythagorean Theorem and the properties of chords in a circle we got 626 when m+n is divided by 1000.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse.

Let M and N be the midpoints of chords AB and CD, respectively.

Let X and Y be the foot of the perpendicular from P to chord AB and CD respectively.

Since X,Y are on the circle and P is the midpoint of XY,

OP = PX = PY = radius = 25

Now, using the Distance Formula:

(XM)^2 + (YN)^2 = (12)^2

By the Pythagorean Theorem, on triangle PXN and PYM,

(25)^2 + (YN)^2 = (PN)^2 = (14/2)^2 and

(25)^2 + (XM)^2 = (PX)^2 = (30/2)^2

OP^2 = 625 = 25^2

thus m+n = 625 + 1 = 626

and remainder when m+n is divided by 1000 is 626 % 1000 = 626

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Answer:

80%

Step-by-step explanation:

First we find the percentage she got wrong:

[tex]\frac{18}{90}[/tex] Is the fraction she got wrong, now we convert this into a percentage by divding 18 by 90 and multiplying by 100

18÷90×100=20

so to find the remaining percent we subtract 20 from 100

100-20=80

And our answer is 80

Answer:

80%

Step-by-step explanation:

10%= 9

20%= 18

18= how many they got wrong

90=total questions

90= 100%

18= 20%

100%=20%=80%

Answer:

Your answer is wrong, H is the correct answer.

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. Note: This rule must be satisfied for all 3 conditions of the sides.

Answer:

B) 81 and 20°

Step-by-step explanation:

In any triangle, the sum of the measures of the three angles is 180°. Therefore, if two angles in a triangle have measures of 79° and 81°, the third angle must have a measure of 180 - 79 - 81 = 20°. Therefore, the answer is B) 81 and 20°.

Answer:

B

Step-by-step explanation:

Answer:

its G

Step-by-step explanation:

Answer:

8x^3

Step-by-step explanation:

(2x)^3

=(2x)^3

=2x*2x*2x

=8x^3