Calculate the range and interquartile range for the following set of scores from a continuous variable: 5, 1, 6, 5, 4, 6, 7, 12. Identify the score that corresponds to the 75th percentile and the score that corresponds to the 25th percentile. Why is the interquartile range a better description of variability in the data than the S range?

The value of x is 5, while the value of y is 24

In order to get the value of x we would first have to find the value of y

The sum of angles on a straight line = 180

hence we would have:

5y + 2y + 12 = 180

7y = 180 - 12

7y = 168

y = 24 degrees

The angle that is made at R is 90 degrees

we would have

2y + 12 + 5x = 90

y = 24

2 * 24 + 12 + 5x = 90

60 + 5x = 90

5x = 90 - 60

5x = 30

x = 30 / 6

x = 5

Hence the value of x is 5

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The surface area of a horse with the mass  is 4.5 x 10^6 square centimeters,

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

S = 10mi

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

m =  4.5 x 10^5 grams

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

S =10 * 4.5 x 10^5

So, we have

S =4.5 x 10^6

Hence, the surfave area is 4.5 x 10^6

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Answer:

6

Step-by-step explanation:

(1.3 + 0.2) / 5 + 2.7

1) 1.3 + 0.2 = 1.5

2) 1.5 / 5 = 0.3

3) 0.3 + 2.7 = 6

The given expressions {4x^3+2x^2+6x+7}/{2x+1} and 2x^2+3+(4/{2x+1}) are equal at x = 10, they are not equal at x = -1/2, and they are equal for all x other than -1/2.

Substitute x = 10 in the given expressions, we get

{4x^3+2x^2+6x+7}/{2x+1}

= (4000+200+60+7)/21

=203.19

2x^2+3+(4/{2x+1}.)

200+3+4/21

=203.19

Hence, the given expressions are equal when x = 10

Now substitute x = -1/2 in the given expressions

={4x^3+2x^2+6x+7}/{2x+1}

=(4*-1/8+2*1/4+6*-1/2+7)/0

2x^2+3+(4/{2x+1}.)

=2*1/4+3+4/0

When we substitute the value x= -1/2 then it divide by 0 and value will be infinite and hence we can say that the values are not equal at x = -1/2

2x^2+3+(4/{2x+1}.) take LCM

{4x^3+2x^2+6x+7}/{2x+1} here both expression are equal and  we can't able find the value at x = -1/2 but for other value of x they are equal.

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The required angle of the elevation at point C to A is given as ∠C = 31°.

The angle of elevation is the angle between a horizontal line of sight and a line of sight that is directed upwards to an object or point. In other words, it is the angle between the horizontal and an observer's line of sight to an object above the observer

Here,
A figure has been shown, Consider triangle ABC, where ∠A = 59, ∠B = 90°,
Since the sum of the angle in the triangle should be 180°.
∠A + ∠B + ∠C = 180
∠C + 90 + 59 = 180
∠C = 90 - 59
∠C = 31°

Thus, the required angle of the elevation at point C to A is given as ∠C = 31°.

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The solution to the equation is x = 3.5.

What is an equation?

An equation is a mathematical statement that says two expressions are equal. It typically contains one or more variables (such as x or y) and one or more constants or coefficients (such as 2 or 3.5). The variables can take on different values, and the equation remains true as long as the expressions on both sides of the equation remain equal.

In the example given, "4x+11=25" is an equation. It says that the expression "4x+11" is equal to the expression "25". We can solve the equation by isolating the variable x on one side of the equation, as shown in the previous answer:

4x + 11 - 11 = 25 - 11

4x = 14

4x/4 = 14/4

x = 3.5

Hence, The solution to the equation is x = 3.5.

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The option B is a linear function. The solution has been obtained by using the properties of a linear function.

What is a linear function?

A function is referred to as linear if it can be represented on a graph as a straight line. Typically, the highest degree of this polynomial function is 1 or 0. Despite the fact that linear functions can be expressed in both calculus and linear algebra.

We are given four functions.

It is clearly visible that option A is not a linear function because the degree of the function is 2.

Option B is a linear function because we obtain a straight line on the graph.

Also, option C is not a linear function because the degree of the function is greater than 1.

Similarly, option D is also not a linear function because it's graph is not a straight line.

Hence, option B is a linear function.

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Answer:

Step-by-step explanation:

The sum of interior angles in a quadrilateral is 360°, from the picture we have a 90°, 160° and 70°.

so

take off from 360° the know angles and we will find the angle "?"

360 - 90 - 160 - 70 =

40° (your answer)

Answer:

Step-by-step explanation:

Note that the pattern in the table is that the perimeter of a square with area x is four times the square root of x. We can express this relationship as:

f(x) = 4 * √(x)

We know that the area of a square is calculated as the square of its side length, which means that the side length of a square with area x is the square root of x. Therefore, the length of the side of the square can be expressed as:

s = √(x)

To calculate the perimeter of the square, we simply add up the lengths of all four sides:

P = 4s = 4 * √(x)

So, the function f(x) in the table represents the perimeter of a square with area x, which can be calculated using the equation:

f(x) = 4 * √(x)

To verify this, let us take these examples:

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The angle measure m<T is equivalent to 78 degrees

Similar triangles are triangles that have similar sides and angles.

From the given triangle

<A = <R

<B = <S

<C = <T

Since the sum of angle in a triangle is 180 degrees, hence;

<A + <B + <T = 180

24 + 78 + <T = 180

102 + <T = 180

<T = 180 - 102
<T = 78 degrees

Hence the measure of m<T from the triangle is 78 degrees

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Rounded to the nearest hundredth of an inch, the distance is 310.91 inches.

How far apart or how far away items or locations are from one another is measured numerically as distance. A physical quantity, it is typically stated in terms of meters, kilometers, miles, or feet. Given that it simply has magnitude and no direction, distance is a scalar quantity.

Usually, a formula is used to determine the distance between two points. One example is the distance formula in Euclidean geometry, which includes computing the square root of the sum of the squares of the coordinate differences between the two points.

Distance can be measured in a variety of contexts, including physics, where it is used to describe an object's displacement through time, and geography, where it is used to define the separation between two points on the surface of the Earth. It is also frequently used in daily life when people go for walks or runs or when they drive from one area to another to calculate the distance they travel.

There are no holes in the first and last 2 inches of the metal strip, leaving 3410 inches (3414 - 2 - 2) as the remaining length.

We can divide the total remaining length by the number of gaps between the holes to determine the distance between the centers of two adjacent holes. The distance between the 12 holes is determined by the fact that there are 11 gaps between them.

distance = (total length - length of 2 end pieces) / (number of gaps)

distance = (3410 in.) / 11

distance ≈ 310.91 in.

Rounded to the nearest hundredth of an inch, the distance is 310.91 inches.

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Answer:

He can eat 6 pies in 198 seconds.

Step-by-step explanation:

Divide

132÷4=33

Divide

198÷33=6 pies in 198 seconds

The statement that all numbers that have 5 as a factor also have 2 as a factor is false, as numbers ending in 5 have five as a factor but are odd numbers, meaning that they do not have two is a factor.

The factors of a number are the numbers by which the number is divisible.

Hence the numbers that have 2 and 5 as factors as the multiples, given as follows:

Numbers that finish in 5 are odd, meaning that they do not have 2 is a factor, hence the statement is false.

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Answer:

35y^(10)z^(4)

Step-by-step explanation:

Solution Given:

(-5y^(4)z)(-7y^(6)z³)

Here while opening bracket

If their is like terms they can be multiplied ,divided,subtracted as well as added.

So

Here

opening bracket and keeping in serially

-5*-7*y^(4)*y^(6)*z*z^(3)

here if their is like terms their power is added.

And solving remaining one.

35y^(4+6)z^(1+3)

Here -5*-7=35

Again

Solving it.

35y^(10)z^(4)

Answer:

[tex]35y^{10}z^4[/tex]

Step-by-step explanation:

Given expression:

[tex](-5y^4z)(-7y^6z^3)[/tex]

Apply the rule:  (-a) · (-b) = ab

[tex]\implies 5y^4z \cdot 7y^6z^3[/tex]

Multiply the numbers:  5 · 7 = 35

[tex]\implies 35y^4zy^6z^3[/tex]

Collect like terms:

[tex]\implies 35y^4y^6z^3z[/tex]

[tex]\textsf{Apply exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\implies 35y^{(4+6)}z^{(3+1)}[/tex]

Simplify the exponents:

[tex]\implies 35y^{10}z^4[/tex]

Suppose that the functions q and r are defined as q(x) = 2x+2 and r(x) = x² +1, the function  (r * q)(4) =(q * r)(4) and they are equal to 170.

Which is the commutative law?

commutative law, in mathematics, is either of two laws relating to number operations of addition and multiplication that are stated symbolically as a + b = b + a and ab = ba. From these laws, it follows that any finite sum or product is unaltered by reordering its terms or factors.

Given the following functions:

q(x) = 2x+2

r(x) = x² +1

Taking the product

q(x)*r(x) = (2x + 2)(x² +1)

Note that according to the communatative law, (r * q)(x) = (q * r)(x)

(r * q)(4) =(q * r)(4)  = (2(4)+2)((4)² +1)

(r * q)(4) =(q * r)(4)  = (10)(16+1)

(r * q)(4) =(q * r)(4)= 10(17)

(r * q)(4) =(q * r)(4) = 170

Hence, the function  (r * q)(4) =(q * r)(4) and they are equal to 170.

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Answer:

The answer to your question is, 0.484

Step-by-step explanation:

The actual chances of an event occurring are defined by a probability. Probability has several uses in games, and in business to create probability-based forecasts which bascially how it works.

Lets graph it out:

Let A signify that the selected employee participates to a workplace retirement savings plan. Let P stand for the male employes.

P(A∩P) the intersection of male & female.

P(A\P)  is the probability that a randomly picked worker participates to a workplace retirement savings plan is the option male

The probability that a randomly selected worker contributes to a retirement savings plan at work is male is found in this formula :

P(A\P)=P(A∩P)/A(P)

P(A\P)=(121/500)/(250/500)

P(A\P)=0.484

Thus, the probability that a randomly selected worker contributes to a retirement savings plan at work that is male will be,

0.484.

If a bundle of strip flooring has 25 sq ft and 30% extra is provided for side and end matching, 12.2 bundles of strip flooring are required to cover a rectangle floor space 16 ft by 14 ft 6 in size.

Once the length and breadth of a rectangle are determined, the area is computed. The area of a rectangle may be calculated by multiplying its length and width.

In this question, because the rectangular floor has an area of 16 ft by 14 ft 6 in, we can compute the total area of the floor by multiplying 16 ft by 14 ft 6 in, which is 234 [tex]ft^{2}[/tex]. We also know that a strip flooring bundle comprises 25 square feet. As a result, we must determine how many bundles of strip flooring are required to cover the floor.

We must account for side and end matching, which is computed by increasing the total floor area by 30%. To determine the extra space required for side and end matching, multiply 234 ft2 by 0.3. This equates to 70.2 [tex]ft^{2}[/tex].

We can now compute the total area required to cover the floor. This is 234 [tex]ft^{2}[/tex] + 70.2 [tex]ft^{2}[/tex] = 304.2 [tex]ft^{2}[/tex].

Because each strip flooring bundle includes 25 square feet, we can divide 304.2 [tex]ft^{2}[/tex] by 25 to determine the total number of bundles required to cover the floor.

This corresponds to 12.2 bundles.

Therefore, 12.2 bundles of strip flooring are needed to cover a rectangular floor area 16 ft by 14 ft 6 in size, with 30% extra for side and end​ matching.

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Answer: A) 6

Step-by-step explanation:

This is geometry. The two angles are corresponding angles, because they are both cut by the same **transversal line**. When that occurs, corresponding angles are created.

now importantly: corresponding angles are equal to each other, or **congruent**. Knowing this, we can set them equal to each other.

17x+11=19x-1

Solve...

11=2x-1

12=2x

x=6

hope this helps

MM

======================================================

Explanation:

If we plugged x = 4 into the expression, then we'll have 0 in the denominator. This causes a division by zero error.

Luckily the numerator factors to (x-4)(x-2)^2. This is found by using the Rational Root Theorem, along with either synthetic division or polynomial long division. I'll skip these steps unless you need me to write them out.

Once we know the numerator factors this way, we can then write the following steps:

[tex]L = \displaystyle \lim_{\text{x}\to4}\frac{\text{x}^3-8\text{x}^2+20\text{x}-16}{\text{x}-4}\\\\\\L = \displaystyle \lim_{\text{x}\to4}\frac{(\text{x}-4)(\text{x}-2)^2}{\text{x}-4}\\\\\\L = \displaystyle \lim_{\text{x}\to4}(\text{x}-2)^2\\\\\\L = (4-2)^2\\\\\\L = 4\\\\\\[/tex]

Therefore,

[tex]\displaystyle \lim_{\text{x}\to4}\frac{\text{x}^3-8\text{x}^2+20\text{x}-16}{\text{x}-4}=4\\\\\\[/tex]

You can use graphing software like Desmos or GeoGebra to confirm the answer is correct. WolframAlpha is another good choice.

The conclusion is that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

The test statistic for this hypothesis test can be calculated as follows:

t = (μ1 - μ2) / sqrt(s1^2 / n1 + s2^2 / n2)

Plugging in the values, we get:

t = (1090 - 485) / sqrt(403^2 / 5 + 382^2 / 8) = 4.36

Next, we need to find the critical value for a two-tailed test at a significance level of 0.10 using a t-distribution table or using a t-distribution calculator.

Using a t-distribution table or calculator, we find the critical value for a two-tailed test at a significance level of 0.10 and df = 9.57 is ±1.833.

Since the calculated t-value (4.36) is greater than the critical value (1.833), we reject the null hypothesis and conclude that there is evidence to suggest that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

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Answer:

So the answer is 1535 with a remainder of 18.

Step-by-step explanation:

  63

96431

-----

96431 - 54249 = 42182

-----

42182

 4218

-----

  420

  ---

   18

   ---

Answer:

Step-by-step explanation:

y = 2x - 6

Answer: a) ZY = 27

b) WY = 27

c) RX = 27

d) mWRZ = 90 degrees

e) mXYZ = 90 degrees

f) mZWY = 90 degrees

Step-by-step explanation:

The x-components  and y-components of the vector [tex]\mathbf{\hat v}[/tex] are -3.0 cm/s and 0 cm/s, respectively.

In mathematics, an axis is a reference line used to locate points in space. It is often used to define a coordinate system, which is a system for representing points and geometric shapes in space using numbers or coordinates.

To find the x- and y-components of the vector [tex]\mathbf{\hat v}[/tex] = (3.0 cm/s, −x-direction), we need to determine the direction of the vector. The notation "-x-direction" means that the vector points in the opposite direction of the positive x-axis. Therefore, the angle between the vector and the negative x-axis is 180 degrees.

The magnitude (or length) of the vector is given by the first component, which is 3.0 cm/s.

The x-component of the vector can be found by multiplying the magnitude by the cosine of the angle:

x-component = magnitude x cos(angle) = 3.0 cm/s x cos(180°) = -3.0 cm/s

The negative sign indicates that the x-component is in the opposite direction of the positive x-axis.

The y-component of the vector can be found by multiplying the magnitude by the sine of the angle:

y-component = magnitude x sin(angle) = 3.0 cm/s x sin(180°) = 0 cm/s

Therefore, the x-components  and y-components of the vector [tex]\mathbf{\hat v}[/tex] are -3.0 cm/s and 0 cm/s, respectively.

Expressed as an ordered pair, the components are (-3.0 cm/s, 0 cm/s).

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