Scores for a civil service exam are normally distributed with a mean of 75 and a standard deviation of 6.5. what score marks the difference between the bottom 10% and the top 90%?

For the expression (x - 8)(x + 8), using the arithmetic operation the value for x is x = 8.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The given expression is - (x - 8)(x + 8)

Use the arithmetic operation of multiplication -

(x - 8)(x + 8)

x(x + 8) - 8(x + 8)

x² + 8x - 8x -64

Now, use the arithmetic operation of addition and subtraction -

x² + 8x - 8x -64

x² - 64

Now, collect the like terms on each side -

x² = 64

x = √64

Now, solve the radical form to get the value of x -

x = √64

x = 8

Therefore, the value of x is obtained as x = 8.

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So, on solving the provided question, we can say that coefficient of the variable in the expression 2 − 5x − 4 8 is 5

A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include:  The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example  Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.

here,

coefficient of the variable in the expression 2 − 5x − 4 8 is 5

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Answer: 2 and 3

Step-by-step explanation:

On solving the provided question we can say that the value of trigonometry value is - [tex](sin^2x - cos^2x )( 1- sin^2xcos^x)\\[/tex]

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

[tex]sin^6 x - cos^6x\\(sin^3x)^2 - (cos^3x)^2\\(sin x - cosx)(sinx + cosx)(1 + sinx cosx)(1 - sinx cosx)\\(sin^2x - cos^2x )( 1- sin^2xcos^x)\\[/tex]

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AAA(Angle angle angle) Theorem can be used to prove given triangles as similar.

As we know we have to show all three angles equally.

so we have to show the similarities between T(DNM) and T(DFE) ....

(T Means Triangle.)

(A Means Angle)

As  D is a common vertex in both the triangles

by equations 1, 2, and 3 we can conclude that all three angles of T(DFE) =  T(DNM)

SO By the AAA rule, we can say that the two Triangles are similar.

Now we can say all the sides of T(DFE) will be in all propositions of T(DNM).

Like DN/DF=DM/DE=NM/FE

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The student's error is that 16 has to be prime factorized as (2)⁴ or 2 × 2 × 2 × 2.

Prime factorization is defined as the method of writing a number as the product of two or more prime numbers.

Prime numbers are numbers which has only two factors, 1 and the number itself.

Given number is 16.

We have to factorize 16 as a product of prime factors.

Student wrote it as,

16 = 2 × 8

The error here is that 8 is not a prime number. We have to again factorize 8 to get the required factored form.

8 = 2 × 4

4 = 2 × 2

So combining all these,

16 = 2 × 2 × 2 × 2

So 16 can be prime factorized as 16 = 2 × 2 × 2 × 2.

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Answer: x=1,y=3

Step-by-step explanation:

Given,

y - 1 =2x

y = 2x + 1-----(i)

Again,

We have,

y = 2x + 1

Now replacing the value of y from (i)

2x + 1= -x +

or, 2x + x= 3

or,3x= 3

So x=1

Now,

y=2x +1

or, y=2×1+1

so y=

Answer:

x=1, y=3. (1, 3).

Step-by-step explanation:

2y-2=4x

y=-x+4

----------

2y-2=4x implies 2(y-1)=2(2x), so y-1=2x.

(-x+4)-1=2x

-x+4-1=2x

-x+3=2x

3=2x-(-x)

3=2x+x

3=3x

x=3/3

x=1

y=-1+4=3

The total cost of the move when hiring movers for 35 hours is $1221, and the total cost of the move when hiring movers for 10 hours is $546.

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Enlarging or contracting a figure's size is known as dilatation. In other words, a scale factor is used to either enlarge or diminish the image while maintaining similarity between the preimage and the image.

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Answer:

y = 7

Step-by-step explanation:

The equation of a horizontal line is worth memorizing. It is:

y = anumber

(and just in case for future reference the equation of a vertical line is

x= anumber)

Well, you are given one point (3,7).That is in the form (x,y). So x is 3 and y is 7.

y is 7

y = 7

(if it helps...horizontal lines have 0 slope. So m = 0. The equation in point-intercept form is

y = mx + b

y = 0x + b

y = b this is the y= anumber) originally mentioned here)

Answer:

Step-by-step explanation:

104 units

Answer:

[tex]27)x {}^{3} + 3x {}^{2} - 10x - 24 \\ 28)x {}^{3} - 9 {}^{2} + 8x + 60[/tex]

Step-by-step explanation:

Greetings!!

[tex]27)(x - 3)(x + 2)(x + 4)[/tex]

Expand; (x-3)(x+2): x^2-x-6

Apply FOIL method: (a+b) (c+d) = ac+ad+bc+bd

[tex](x - 3)(x + 2) = x.x + x.2 - 3.x - 3.2[/tex]

simplify

[tex]x {}^{2} - x - 6[/tex]

[tex]x {}^{2} - x - 6.(x + 4)[/tex]

distribute parentheses

[tex] = x {}^{2} .x + x {}^{2} .4 - x.x - x.4 - 6.x - 6.4 \\ = x {}^{3} + 4x {}^{2} - x {}^{2} - 6x - 24[/tex]

simplify/ Add similar elements

[tex]x {}^{3} + 3x {}^{2} - 10x - 24[/tex]

Thus, use the same format for question number 28 and you will get the value

[tex]x {}^{3} - 9x {}^{2} + 8x + 60[/tex]

If you have any questions or there is sth unclear tag me on comment box

Hope it helps!!

On solving the provided question, we can say that Volume of cuboid = 2x(3x+4)(3x-4)

Volume = [tex]18x^3 + 48x^2 + 32x[/tex]

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

here,

we have a cuboid

Volume of cuboid = 2x(3x+4)(3x-4)

Volume = [tex]18x^3 + 48x^2 + 32x[/tex]

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 Answer:

If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal. When you solve an equation, you find the value of the variable that makes the equation true. In order to solve the equation, you isolate the variable.

Step-by-step explanation:

Answer: 36

Step-by-step explanation:

80% or 200 is 16

16+20=36

The midpoint formula is a mathematical formula used to find the midpoint of a line segment, given the coordinates of the two endpoints of the segment. In class 11, it is defined as:

Midpoint = ( (x1 + x2)/2 , (y1 + y2)/2 )

Where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment, and (x, y) are the coordinates of the midpoint of the segment.

For example, if the two endpoints of a line segment are (5,6) and (9,11)

Midpoint = ( (5 + 9)/2 , (6 + 11)/2 )

Midpoint = (7,8.5)

The midpoint of the line segment with endpoints (5,6) and (9,11) is (7,8.5)

It's worth noting that this formula can be adapted for three-dimensional points, where the midpoint formula would be

((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)

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Answer:

7.5

Step-by-step explanation:

10 + ( 7 × 1.5) = 20.5

6 + ( 7 × 13 ) = 13

20.5 - 13 = 7.5

Triangle ABC is dilated by a scale factor of 1/2, the line A”B” equals Line AB divided by two

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Translation is the movement of a point up, down, left or right in the coordinate plane.

Dilation is the increase or decrease in the size of a figure.

Triangle A”B”C” is formed using the translation (x+2, y+0) and the dilation by a scale factor of 1/2 from the origin.

Since there is a dilation by a scale factor of 1/2, hence:

A"B" = AB * 1/2

A"B" = AB/2

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The graph solution is in the attached images, for all the systems of inequalities.

What is the graph of a function?

The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.

The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.

we have the following inequalities:

i)

y > 3x - 17,

y ≤ -4x +11.

ii)

4x - 4y > -40,

-5x + 5y < 10.

iii)

x + 3y ≥ 31,

4x - 2y ≥ -2,.

iv)

5x + y < 3,

5x + y > 37

Hence, the graph solution is in the attached images, for all the systems of inequalities.

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positive number to the power negative 1 is a number that is always less than 1.

Explanation: a-m = 1/am. when calculate have the result when a positive number is raised to the power of -1, we always get a number that is less than one; for example, 2-1 = 1/2 < 1.

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The numeric value for the logarithmic expressions is given as follows:

1. [tex]\log_{6}{\left(\frac{5}{8}\right)} = -0.263[/tex]

2. [tex]\log_6{40} = 2.059[/tex]

3. [tex]\log_6{64} = 2[/tex]

4. [tex]\log_6{125} = 2.694[/tex]

a. [tex]\log_{5}{\left(\frac{11}{30}\right)} = -0.623[/tex]

b. [tex]\log_5{330} = 3.603[/tex]

c. [tex]\log_5{121} = 2.98[/tex]

For the first expression, we have that the logarithm of the quotient is the subtraction of the logarithms, hence:

[tex]\log_{6}{\left(\frac{5}{8}\right)} = \log_6{5} - \log_6{8} = 0.898 - 1.161 = -0.263[/tex]

The same rule is applied for item a, hence:

[tex]\log_{5}{\left(\frac{11}{30}\right)} = \log_5{11} - \log_5{30} = 1.49 - 2.113 = -0.623[/tex]

For the second expression, we apply the logarithm of the product, which is the sum of the logarithms, hence:

[tex]\log_6{40} = \log_6{5 \times 8} = \log_6{5} + \log_6{8} = 0.898 + 1.161 = 2.059[/tex]

For item b, we have that:

[tex]\log_5{330} = \log_5{11 \times 30} = \log_5{11} + \log_5{30} = 1.49 + 2.113 = 3.603[/tex]

For the third expression, we have that the exponent is equals to the base, hence we just take the lower term, as follows:

[tex]\log_6{64} = \log_6{2^6} = 2[/tex]

For the fourth term, we have the rule for the logarithm of an exponent, hence:

[tex]\log_6{125} = \log_6{5^3} = 3\log_6{5} = 3 \times 0.898 = 2.694[/tex]

The same rule is applied for item c, as follows:

[tex]\log_5{121} = \log_5{11^2} = 2\log_5{11} = 2 \times 1.49 = 2.98[/tex]

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Answer:

the awsner is 20 I believe so don't trust me or trust me i don't care

Step-by-step explanation:

I don't know

Answer:

9/64

Step-by-step explanation:

1 3/4 x (15/4-3 1/2) divided by 1 1/3

2   3/4x1/4 divided by 4/3

3    3/16 divided by 4/3

4     3/16x3/4=9/64

The trend line equation to estimate the hiker's elevation after 150 minutes is 2033 feet.

Given that,

A trend line's equation for the hiker's elevation is y = 9.16x + 659.

We must determine,

The trend line equation is used to calculate the hiker's elevation after 150 minutes.

In response to the question,

A trend line's equation for the hiker's elevation is y = 9.16x + 659.

Where x is the number of minutes and y is the elevation of the hiker in feet.

Substitute the value of x = 150minute in the given equation to find the trend line to estimate the hiker's elevation after 150minutes.

Therefore,

y = 9.16x + 659

x = 150

y = 9.16(150) + 659

y = 1374 + 659

y = 2033

As a result, the trend line equation for estimating the hiker's elevation after 150 minutes is 2033 feet.

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The number of shares that Ade and Ola possess will be 1500 and 2500, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Ade and Ola share a sum of 4000.00 in a ratio of 3:5.

Let 'x' and 'y' be the number of shares that Ade and Ola have, respectively. Then the equations are given as,

x / y = 3 / 5            ...1

x + y = 4000        ...2

From equations 1 and 2, then we have

(3/5)y + y = 4000

(8/5) y = 4000

y = 2500

Then the value of the variable 'x' is calculated as,

x + 2500 = 4000

x = 1500

The number of shares that Ade and Ola possess will be 1500 and 2500, respectively.

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By replacing the values of the point in the quadratic equation, we can see that it is not a solution.

Here we have the quadratic equation:

y = 3x^2 + 5

And we want to see if the point 3x^2 + 5 is a solution of the quadratic equation.

To check that, we need to replace the values of the point in the equation and see if the equation is true.

We need to replace:

x = 5

y = 0

We will get:

0 = 3*5^2 + 5

0 = 3*25 + 5

0 = 75 + 5

0 = 80

This is a false equation, then (5,0) is not a solution.

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The correct option for the area of rectangle is A: 7(x + 2) sq in.

The characteristics of a rectangle were just as follows:

An area is the amount of space a rectangle takes up.By calculating the product of a rectangle's length and breadth, one can get the area of the shape.

So,

Area of a rectangle = Length × Width

Dimension are-

So,

Area of a rectangle = 7 × (x + 2) sq in..

Thus, the expression represents area of a rectangle is 7 × (x + 2) sq in.

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The complete question is-

The dimensions of a rectangle are 7 in by (x+2)in. Which expression represents its area?

A: 7(x + 2) sq in..

B: 7 + (x + 2) sq in..

Answer: The fundamental theorem of algebra states that the equation 2x^2+8x+14=0 has at least one complex root, which means that there are numbers that can be plugged into x that make the equation equal to zero. ✅

PLEASEEEE GIVE BRANLIEST

Step-by-step explanation:

The fundamental theorem of algebra states that for any non-constant polynomial equation with real or complex coefficients, there is at least one complex root (or solution).

In the case of the equation 2x^2+8x+14=0, the theorem guarantees that this equation has at least one complex root, which means that there are numbers that can be plugged into x that will make the equation equal to zero.

So, the fundamental theorem of algebra guarantees that for the equation 2x^2+8x+14=0, there exists at least one complex solution that makes the equation true. In this case, the solutions are x = -1+i and x = -1-i ✅