Complete the following statements.
In general, ________% of the values in a data set lie at or below the median.

________% of the values in a data set lie at or below the third quartile (Q3).

If a sample consists of 2100 test scores, ________ of them would be at or below the second quartile (Q2).

If a sample consists of 2100 test scores, ________ of them would be at or above the first quartile (Q1).

The values of {m} that is greater than 4.6 represent the solution of the given inequality.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

The given inequality is -

5m - 7 > 16

Adding 7 on both sides, we get -

5m - 7 + 7 > 16 + 7

5m > 23

m > 23/5

m > 4.6

Therefore, the values of {m} that is greater than 4.6 represent the solution of the given inequality.

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Answer:

-6x² - 11x - 3

Step-by-step explanation:

This represents the product of the two functions.

(-2x-3)(3x+1) = -(2x+3)(3x+1) = -(6x² + 11x + 3) = -6x² - 11x - 3

Answer:

The area of triangle is 28 ft².

Step-by-step explanation:

Here's the required formula to find the area of triangle :

\(\star{\underline{\boxed{\sf{Area_{(\triangle)}= \dfrac{1}{2}bh}}}}\)

Substituting all the given values in the formula to find the area of triangle :

\({\implies{\sf{Area_{(\triangle)}= \dfrac{1}{2}bh}}}\)

\({\implies{\sf{Area_{(\triangle)}= \dfrac{1}{2} \times b \times h}}}\)

\({\implies{\sf{Area_{(\triangle)}= \dfrac{1}{2} \times 7 \times 8}}}\)

\({\implies{\sf{Area_{(\triangle)}= \dfrac{1}{\cancel{2}} \times 7 \times \cancel{8}}}}\)

\({\implies{\sf{Area_{(\triangle)}= 1 \times 7 \times 4}}}\)

\({\implies{\sf{Area_{(\triangle)}=7 \times 4}}}\)

\({\implies{\sf{\underline{\underline{Area_{(\triangle)}=28 \: {ft}^{2}}}}}}\)

Hence, the area of triangle is 28 ft².

\(\rule{300}{2.5}\)

Answer:

Charlotte's age = 30 years

Olivia's age = 50 years

Step-by-step explanation:

Present ages of Charlotte & Olivia = 6:10.

Then, their present ages are:

Charlotte = 6x

Olivia = 10x

Now, in 10 years, their ratio = 4:6

Then,

Ratio of Charlotte's & Olivia's present age + 10 years each = Ratio of their ages in 10 years

\(\frac{6x + 10}{10x + 10} = \frac{4}{6} \\6(6x + 10) = 4 (10x + 10) \: \: \: \: [\mathrm{cross\: multiplication}]\\36x + 60 = 40x + 40\\36x - 40x = 40 - 60\\4x = 20\\\boxed{\bf\:x = 5}\)

So,

Charlotte's present age \(= 6x = 6(5) = {\boxed{\bf\:30 \:years}\)

Olivia's present age = \(10x = 10(5) = \boxed{\bf\:50 \: years}\)

\(\rule{150pt}{2pt}\)

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

B. 8 x 12

Step-by-step explanation:

First of all, it has an area of 96

So lets find the multiplication pair that equals 96.

10 x 10 = 100        NO

6 x 16 = 96           YES

8 x 12 = 96           YES

Now we have two equations: 8 x 12 and 6 x 16

Perimeter of 40 means:

2(a+b) = 40

Lets input the two equations:

2(8+12) = 2 x 20 = 40

2(6+16) = 2 x 22 = 44

So the dimensions that works is 8 x 12

If my answer is incorrect, pls correct me!

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Answer:

third option

Step-by-step explanation:

under a counterclockwise rotation of 90° about the origin

a point (x, y ) → (y, - x )

Then

A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )

B (2, - 2 ) → (- 2, - 2 )

C (1, - 4 ) → (- 4, - 1 )

The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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

The figure,

Where, we have

A = (-1, -2)

B = (2, -2)

C = (1, -4)

The rule of 90 degrees counterclockwise is

(x, y) = (-y, x)

Using the above as a guide, we have the following:

A = (2, -1)

B = (2, 2)

C = (4, 1)

Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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(a) The algebraic expression, -5x - 2 + 5x + 2 is simplified as 0.

(b) The algebraic expression, 5x -2  - (5x + 2) is simplified as -4.

The given algebraic expression is simplified by adding similar terms together, as it will make the expression to be in simplest form.

The given algebraic expressions are;

-5x - 2 + 5x + 2

5x -2  - (5x + 2)

The first algebraic expression is simplified as follows;

-5x - 2 + 5x + 2

collect similar terms;

(-5x + 5x) + (-2 + 2)

= 0 + 0

= 0

The second algebraic expression is simplified as follows;

5x - 2 - (5x + 2)

= 5x - 2 - 5x - 2

collect similar terms;

= (5x - 5x) + (-2 - 2)

= 0 - 4

= - 4

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Answer:

neither

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

the formula for distance is √(X2-X1)^2 + (y2-y1)^2

=√(5-0)^2 + (12-0)^2

=√5^2 + 12^2

=√25+144

=√169

=13

For any line passing through the points (x1,y1) and (x2,y2), its slope is given by:

a = (y2 - y1)/(x2 - x1)

And its intercept is given by:

b = y1 - ax1 = y2 - ax2

And the equation of this line, in the slope-intercept form, is y = ax + b

Then, for a line passing through the points (3,4) and (-6,5), we have:

a = (5 - 4)/(-6 - 3) = -1/9

Then, the intercept is:

b = 4 + 3/9 = 13/3

Therefore, the equation of the line is given by:

y = -x/9 + 13/3

Answer:

Viewed as a right angled triangle

tan

(

x

)

=

5

12

can be thought of as the ratio of opposite to adjacent sides in a triangle with sides

5

,

12

and

13

(where

13

is derived from the Pythagorean Theorem)

So

sin

(

x

)

=

5

13

and

cos

(

x

)

=

12

13

Step-by-step explanation:

Answer:

Therefore, x is 1 and 2.

Step-by-step explanation:

As you plot both equations on the same graph, you will get something like this, shown in the graph.

Then, you have to find the x solutions where they intersect.

So, both equations intersect at x = 1 and 2.

The length of the arc intercepted by a central angle of 3 radians in a circle of radius 76 is 228 and the length of the arc intercepted by a central angle of 2 radians in a circle of radius 15 is 30.

Explain:

The following formula determines the length of an arc that a circle's central angle intercepts:

Arc length is equal to (central angle / 2) 2r r r

where r denotes the circle's radius. We can determine the length of the two arcs using the following formula:

For the first circle, with a radius of 76 and a center angle of 3 radians:

Arc length = 3 x 76 = 228

Therefore, in a circle with a radius of 76, the length of the arc that is intercepted by a central angle of 3 radians is 228.

For the second circle, whose radius is 15, and whose center angle is 2 radians:

Arc length = 2 x 15 = 30

As a result, the length of the arc in a circle with a radius of 15 is 30 when it is intercepted by a central angle of 2 radians.

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Answer:

This is valid I'm pretty sure

Step-by-step explanation:

The is is because Bugs Bunny is disproved and he finds that it is not duck season, so it would be valid. I hope I'm right.

Answer:

The argument would be valid

Step-by-step explanation:

Let p = "It is duck season"

Let q = "My name is Bugs Bunny"

The formation would be:

p ∨ q

~ p

∴ ~q

If you made a truth value table, the critical row (means where the premises are true, in this case it would be ~p) has true premise and a true conclusion. Thus the argument is valid.

Work Shown:

Complementary angles add to 90 degrees.

A+B = 90

(3x+18)+(2x+17) = 90

5x+35 = 90

5x = 90-35

5x = 55

x = 55/5

x = 11

Then we can determine each angle:

As a check: A+B = 51+39 = 90 to confirm the answer.

The area of the rectangle is 81 square units. (option a)

To find the area of a rectangle, we need to know its length and width. We can determine these values by looking at the difference between the x-coordinates and the y-coordinates of the vertices.

In this case, we have the following coordinates: (-4,5), (5,5), (-4,-4), and (5,-4).

The length of the rectangle is the difference between the x-coordinates of the left and right vertices:

=> 5 - (-4) = 9.

The width is the difference between the y-coordinates of the top and bottom vertices:

=> 5 - (-4) = 9.

To find the area of the rectangle, we multiply its length by its width:

=> 9 x 9 = 81.

So, the correct answer is the (a), 81 square units.

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A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function.

A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. Accordingly, the likelihood of any specific outcome of y is the same, and the likelihood of any range of outcomes is equal to the length of the range. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function. Accordingly, the length of the range multiplied by the likelihood of any specific occurrence yields the cumulative probability of any range of outcomes. Since the likelihood of any specific result in that range is 1 and the range's length is 0.5, for instance, the cumulative probability of 0 y 0.5 is 0.5. Since the likelihood of any given result within that range is still 1, but the range's length is 0.5, the cumulative probability of 0.5 y 1 is 0.75. The chance of any range of outcomes for y1 and y2 if they are independent random variables both having the uniform(0,1) distribution is just the sum of their respective cumulative probabilities.

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hello how are you? I am fine

Answer:

x = 10

Step-by-step explanation:

We know that it's a right triangle and it's two sides, which are 6 and 8

So we can find the third side, the Hypotenuse or x, using the Pythagoras Theorem

6² + 8² = Hypotenuse ²

36 + 64 = Hypotenuse²

100 = Hypotenuse²

Hypotenuse = root100

Hypotenuse = 10

Therefore x = 10

Answer:

x is -7.5 or -14/2 or -7½

Step-by-step explanation:

- Supposing y varies directly with x

\( { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} \)

[k is a constant of proportionality (k ≠ 0)]

- When y is 6, x is -2

\( \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}\)

- Therefore, the equation is;

\({ \boxed{ \tt{y = - 2x}}}\)

- What is x when y is 15

\({ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}\)

The value of x is -5

The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:

                                        k = y/x

                                        k = 6/-2

                                        k = -3

Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation

                                15 = -3x

Then solve x,

                       x = \(\frac{-15}{3}\)

                        x = -5

Therefore, when y = 15, x = -5.

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The function can be defined as  price = 6x

It will cost $150 to buy 25 reams of paper.

The domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.

The range of the function is all non-negative real numbers, since the price cannot be negative.

Fir 25 items, price = 6(25) = $150

It will cost $150 to buy 25 reams of paper.

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1.  Rewrite one side (or both) by combining like terms. Option C

2. Yes, the equations are equivalent. Option A

1.

Equation A ;  2x -1  = 5x

Equation B ; -1 = 3x

To get equation B from equation A

2x - 1 = 5x

Collect like terms

-1 = 5x -2x

Subtract the like terms

-1 = 3x

Thus, rewrite one side (or both) by combining like terms. Option C

2. 2x - 1 = 5x ...... equation A

Solution ;

2x -5x = 1

-3x = 1

x = -1/3

-1 = 3x

Solution;

x = -1/3

Thus, the equations are equivalent. Option A

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The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?

To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.

The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.

The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.

That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)

The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.

That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,

the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°

The negative sign indicates that the angle is measured below the horizontal line.

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The runners can finish in 362880 possible results

What is Permutation?

Permutation is the different number of arrangements that can be formed by taking r things from the n available things.

The formula  n! = 1 × 2 × 3 × 4 × .......× n.

To get the order the runners could possibly finish,

= 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 326880

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Answer:

5

can be done by multiplication multiplicative property

Step-by-step explanation:

2/3 * (3/2 * 5)

1st = 2/3 * 3/2 * 5

2nd = 2 * 3 * 5

             3 * 2

3rd = 3 * 5

            3

therefore

the answer = 5

Answer:

\(\Large \boxed{\mathrm{associative \ property \ of \ multiplication}}\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

The associative property of multiplication can be use to make the problem easier to solve.

In associative property of multiplication, when we multiply a bunch of numbers, we can group the numbers in any combination.

\(a \times (b \times c) = (a \times b) \times c\)

\(\rule[225]{225}{2}\)

Answer:

A a house in that market that sells for ​$300,000 is unusual.

Step-by-step explanation:

Let the random variable X denote the price of a house and the random variable Y denote the living area of a house.

The number of houses surveyed by the real estate agent is, n = 1057.

Assume that both the random  variables, X and Y are approximately normally distributed.

That is,

\(X\sim N(\$169400,\ \$68438)\\\\Y\sim N(2058\ \text{sq. ft.},\ 790\ \text{sq. ft.})\)

To compute the probability of a Normal distribution we first need to convert the raw scores to z-scores.

\(z=\frac{\text{Raw score}-\mu}{\sigma}\)

A z-score higher than 1.96 and lower than -1.96 are considered unusual. The values having these z-scores are considered as outliers.

(1)

Compute the z-score for X = 300000 as follows:

\(z=\frac{X-\mu}{\sigma}\\\\=\frac{300000-169400}{68438}\\\\=2.70\)

(2)

Compute the z-score for Y = 3000 as follows:

\(z=\frac{Y-\mu}{\sigma}\\\\=\frac{3000-2058}{790}\\\\=1.19\)

The z-score for a house in that market that sells for ​$300,000 is more than 1.96.

This implies, that the price $300,000 is unusually high.

The complete statement is:

The house that sells for ​$300 comma 000 has a​ z-score of 2.70 and the house with 3000 sq ft has a​ z-score of 1.19.

Reason:

We cannot divide by zero. This means the denominator cannot equal zero. If it was zero, then,

2x+10 = 0

2x = -10

x = -10/2

x = -5

Follow that chain in reverse to see that x = -5 causes the denominator 2x+10 to be zero. This is why we kick -5 out of the domain. Any other x value is valid.

Answer:

y=2/3

Step-by-step explanation:

2y+4y=6-3y

⇔ 2y+4y+3y=6

⇔ 9y=6

⇔ y=6/9=2/3

The answer is:

y = 2/3

Work/explanation:

For now, I focus on the left side and combine the like terms:

\(\bf{2y+4y=6-3y}\)

\(\bf{6y=6-3y}\)

Add 3y to each side

\(\bf{6y+3y=6}\)

Combine like terms

\(\bf{9y=6}\)

Divide each side by 9

\(\bf{y=\dfrac{6}{9}}\)

\(\bf{y=\dfrac{2}{3}}\)

Hence, the answer is 2/3.