Practice Problems
1. The absolute value of a number is its distance from 0 on the
number line (no sign, just value). Compare the absolute value of
7 and -7.

The 87th percentile is the value [tex]x_{0.87}[/tex] such that 87% of the distribution lies below [tex]X=x_{0.87}[/tex], i.e.

[tex]P(X \le x_{0.87}) = 0.87[/tex]

Transform [tex]X[/tex] to the standard normal random variable [tex]Z[/tex], then solve for [tex]x_{0.87}[/tex] using the inverse CDF of [tex]Z[/tex].

[tex]P(X\le x_{0.87}) = P\left(\dfrac{X-60}{12} \le \dfrac{x_{0.87}-60}{12}\right) = P\left(Z \le \dfrac{x_{0.87}-60}{12}\right) = 0.87[/tex]

[tex]\implies \dfrac{x_{0.87}-60}{12} = F_Z^{-1}(0.87) \approx 1.12369[/tex]

[tex]\implies \boxed{x_{0.87} \approx 73.5167}[/tex]

Answer:

Center of the Sphere is a fixed point in its interior which is equidistant from each point on sphere. Option A is not right because it says center is line segment. Option B is right as it says it is fixed and equidistant from point of surface.

Step-by-step explanation:

Answer:

x=-6

Step-by-step explanation:

-6+4=-2
Give brainliest please

Answer:

Step-by-step explanation:

9w^{321+15+6}

9w^{342}

The average monthly salary of the female employees is $900.

An equation is a mathematical statement that equates algebraic expression  to other algebraic expressions or constants by an equal sign that helps to determine the value of unknown variables.

It is given that

the average of the monthly salary of female and male employees is $ 2000

Let the average monthly salary of the female employees is $b

It is again given that

The average monthly salary of the male employees is $(b +200)

so , the equation can be formed as

b + b + 200  = 2000

2b + 200 = 2000

2b = 2000 - 200

2b = 1800

b = $900

The average monthly salary of the female employees is $900.

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Answer:

-2 3/8

Step-by-step explanation:

since point A is left of 0, it means it is a negative value.

so, the positive answer options are automatically out.

then we see that point A is 2 full units and a little bit left of 0.

that means it has to be lower than -2 but higher than -3.

-22/7 = -3 1/7

so, that is too low.

-3 7/8 is too low.

so, that leaves -2 3/8 (confirmed also by the fact that A is a little bit higher than half between -2 and -3, which is the case for -2 3/8).

Answer:

8 * sqrt2

Step-by-step explanation:

the area of a square can be found by squaring the length of the diagonal and then dividing it by 2. 16^2 / 2 = 128. if the area of a square is 128, each side is sqrt 128 = 8 * sqrt2

For the given right triangle, we have:

Here we have a right triangle, remember that the sum of the internal angles of a triangle must be 180°, then:

N + M + L = 180°

We can see that:

N = 37°

M = 90°

Then:

L = 180° - N - M = 180° - 37° - 90° = 53°

Also, if we step on N, the adjacent cathetus measures 6 units, then we can use the relations:

tan(37°) = (opposite cathetus)/(adjacent cathetus)

tan(37°) = ML/6

tan(37°)*6 = ML = 4.5

cos(37°) = (adjacent cathetus)/(hypotenuse)

cos(37°) = 6/NL

NL = 6/cos(37°) =  7.5

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The effective tax rate based on the assumed information is 2.5%.

Let's assume that the figures are:

Income tax expense = $50

Income before tax = $2000

It should be noted that tax rate is calculated as:

= Income tax expense / Income before tax

= 50/2000

= 0.025

= 2.5%

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Answer:

1) a
2) b

Step-by-step explanation:

1) Lets check all the options

a) Cannot be simplified

b) [tex](6^2)^5=6^{10}[/tex] because [tex](a^m)^n=a^{mn}[/tex]

c) [tex](2\times3)^{10}=6^{10}[/tex] fairly self-explanatory because [tex]2\times3=6[/tex]

d) [tex]2^{10}\times3^{10}=6^{10}[/tex] because [tex]a^m\times b^m=ab^m[/tex]

Hence a is the answer.

2) [tex]25\frac12\div\frac12=\frac{51}2\times\frac21=51[/tex]

Hence b is the answer

The function g(x) is [tex]g(x) = (x + 7)^3[/tex]

The function f(x) is given as:

[tex]f(x) = \sqrt[3]{x} - 7[/tex]

If f(g(x)) = g(f(x)) = x, then the functions are inverse functions.

So, we have:

[tex]f(x) = \sqrt[3]{x} - 7[/tex]

Rewrite as:

[tex]y = \sqrt[3]{x} - 7[/tex]

Swap x and y

[tex]x = \sqrt[3]{y} - 7[/tex]

Add 7 to both sides

[tex]x + 7 = \sqrt[3]{y}[/tex]

Take the cube of both sides

[tex]y = (x + 7)^3[/tex]

This implies that

[tex]g(x) = (x + 7)^3[/tex]

Hence, the function g(x) is [tex]g(x) = (x + 7)^3[/tex]

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The equation of the segments perpendicular bisector is; y = -¹/₂x + 2

i) Since it is a perpendicular bisector, hence point M is the midpoint. Thus;

Midpoint (AB) = [(x₁ + x₂)/2], [(y₁ + y₂)/2] = (x_m, y_m)

Slope AB will be;

m₁ = ((x₁ - x₂)/(y₁ - y₂))

Slope of perpendicular bisector is;

m₂ = -1/m₁

Equation of perpendicular bisector is;

(y - y_m) = m₂(x - x_m)

ii) Midpoint (AB) = [(-2 + 6)/2], [(3 - 1)/2] = (2, 1)

Slope AB will be;

m₁ = ((6 + 2)/(-1 - 3)) = -2

m₂ = -1/-2 = 1/2

Equation of perpendicular bisector is;

(y - 1) = -¹/₂(x - 2)

y - 1 = -¹/₂x + 1

y = -¹/₂x + 2

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The value of the Z-score will be equal to 2.

The z score indicates how many standard deviations your score is from the mean.

At the mean position, the standard deviation is 0 now the z score is the measure of the data which is how far from the mean. So the given data is at two standard deviations to the right of the mean so the Z-Score will be 2.

Therefore the value of the Z-score will be equal to 2.

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Step-by-step explanation:

gfyiaycoeayclpb tydivh.

hellooo

Step-by-step explanation:

so sine is 0 and (-1/3 isnt gonna positive out on the other side no is positive so ur last answer E is it

The truth values of the propositions are false, true and false

The Boolean variables are given as:

p = false

r = false

q = true

s = true

The truth values of the propositions are as follows:

1. (s → (p ∧ ¬ r)) ∧ ((p → (r ∨ q)) ∧ s)

As a general rule:

∧ means and

¬ not

∨ or

So, we have:

(true → (false ∧ ¬ false)) ∧ ((false → (false ∨ true)) ∧ true)

¬ false= true.

So, we have:

(true → (false ∧ true)) ∧ ((false → (false ∨ true)) ∧ true)

false ∧ true = false and false ∨ true = true

So, we have:

(true → false) ∧ ((false → true) ∧ true)

false → true = true and true → false = false

So, we have:

(false) ∧ (true ∧ true)

true ∧ true = true

So, we have:

false ∧ true

Lastly

false ∧ true = false

Hence, the truth value of (s → (p ∧ ¬ r)) ∧ ((p → (r ∨ q)) ∧ s) is false

2. ((p ∧ ¬ q) → (q ∧  r)) → (s ∨ ¬q)

This means

((false ∧ ¬ true) → (true ∧  false)) → (true ∨ ¬true)

Using the established rules in (1), we have:

((false ∧ false) → (true ∧  false)) → (true ∨ false)

This gives

((false → false)) → true

This gives

true → true

Lastly, we have:

true

Hence, the truth value of ((false ∧ ¬ true) → (true ∧  false)) → (true ∨ ¬true) is true

3. (p → q) ∧ (q → r)

This gives

(false → true) ∧ (true → false)

Using the established rules in (1), we have:

true ∧ false

This gives

false

Hence, the truth value of (p → q) ∧ (q → r) is false

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Answer:

D(t)=60+23*sin(2*pi*t/24)+26*cos(2*pi*t/24)

Step-by-step explanation:

The temperature at any time t can be represented as:

D(t)=A+B*sin(2*pi*t/T)+C*cos(2*pi*t/T)

where A is the average temperature, B is the amplitude of the sine wave, C is the amplitude of the cosine wave, and T is the period.

In this case, we are given that the average temperature is 60, the high temperature is 73, and the low temperature is 47. We can therefore calculate that the amplitude of the sine wave is 23 and the amplitude of the cosine wave is 26. The period is 24 hours. Therefore, the equation for the temperature in terms of time is:

D(t)=60+23*sin(2*pi*t/24)+26*cos(2*pi*t/24)

The solution of the given Inequality is; D: x ≤ 6

We want to find the solution to the Inequality;

5x - 9 ≤ 21

Using Addition property of equality, add 9 to both sides to get;

5x ≤ 30

Using division property of equality, divide both sides by 5 to get;

x ≤ 6

All real numbers less than or equal to 6

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Answer:

Step-by-step explanation:

10.

[tex]\left \{ {{x-2y=4} \atop {4x+2y+6}} \right.[/tex]

The y values cancel out if you add the equations

5x = 10

x = 2

plug in x

2 - 2y = 4

-2y = 2

y=-1

Answer: C. (2, -1)

11.

[tex]\left \{ {{6x-2y=-4} \atop {-4x+3y=-4}} \right.[/tex]

In order to get terms to cancel out, multiply the top by 3 and bottom by 2

[tex]\left \{ {{18x-6y=-12} \atop {-8x+6y=-8}} \right.[/tex]

The y values cancel out if you add the equations

10x = -20

x = -2

plug in x

6(-2) - 2y = -4

-12 - 2y = -4

-2y = 8

y = -4

Answer: B. (-2, -4)

Answer:

It should look like a v with the origin at +0.5

Step-by-step explanation:

The equation for the distance d from Dallas, in terms of h, the number of hours Joe has traveled is d = 320 - 69h. Hence, option B is the right choice.

The total distance that Joe needs to cover to travel to Dallas = 320 miles {As he lives 320 miles away from Dallas}.

The distance that Joe covers after traveling for h hours at an average speed of 69 miles per hour = 69h {as Distance = Speed*Time}

Therefore, the distance left to cover by Joe, that is the distance from Dallas d can be written as the difference between the total distance needed to be covered and the distance Joe already covered.

Thus the equation is d = 320 - 69h.

Thus, the equation for the distance d from Dallas, in terms of h, the number of hours Joe has traveled is d = 320 - 69h. Hence, option B is the right choice.

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Answer:

the MEAN for class a is 72.6

the MEAN for class b is 84.0

if you take these means and compare them, you can see that on average, class B performed better.

the MEDIAN for class a is 72

the MEDIAN for class b is 85

Step-by-step explanation:

The measure of <2 is 60.

The tangent is defined as a line touching circles or an ellipse at only one point.

given:

VU = 80° and ST = 40°

By using theorem,

The measure of the internal angle is the semi- sum of the arcs comprising it and its opposite.

<2= 1/2 (80+ 40)

<2= 60

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The most suitable viewing window to solve the system is -20 ≤ x ≤ 20 and -15 ≤ x ≤ 15 option fourth is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two linear equations:

0.02x - 0.05y =  -0.38

0.03x + 0.04y = 1.04

We can write above equations as follows:

2x - 5y = -38

3x + 4y = 104

After solving with the substitution method:

x = 16

y = 14

-20 ≤ x ≤ 20

-15 ≤ x ≤ 15

Thus, the most suitable viewing window to solve the system is -20 ≤ x ≤ 20 and -15 ≤ x ≤ 15 option fourth is correct.

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Answer:

20x^2 + 47x + 24

Step-by-step explanation:

The area of a rectangle is LENGTH * WIDTH. From the diagram, we see that  LENGTH = 4x + 3 and WIDTH = 8 + 5x. Therefore the area is:

A = LENGTH*WIDTH

  = (4x+3)(5x+8)

  = 20x^2 + 32x + 15x + 24

  = 20x^2 + 47x + 24

Answer: C. 20x²+47x+24

Step-by-step explanation: Use the FOIL Method (First, Outer, Inner, Last). Equation: (5x+8) (4x+3). Hope this helps!

Using a system of equations, it is found that it would take 2 servings of macaroni and 8 servings of broccoli to get the desired amount.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Researching the problem on the internet, each serving of macaroni has 3 grams of protein, while each serving of broccoli has 2 grams. Since 22 grams of protein are needed, we have that:

3M + 2B = 22.

Each serving of macaroni has 16 grams of carbohydrates, while each serving of broccoli has 4 grams. Since 64 grams of carbohydrates are needed, we have that:

16M + 4B = 64

Simplifying by 4:

4M + B = 16 -> B = 16 - 4M

Replacing in the first equation:

3M + 2B = 22

3M + 2(16 - 4M) = 22

5M = 10

M = 10/5

M = 2.

B = 16 - 4M = 16 - 8 = 8

2 servings of macaroni and 8 servings of broccoli are needed.

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For systems A and B we have:

1) Change the first equation in A by a multiple of itself. (the multiple is 1/3).

2) Yes, the systems are equivalent.

Here we have the systems of equations:

A:

-3x + 12y = 15

7x - 10y = -2

B:

-x + 4y = 5

7x - 10y = -2

Notice that the second equation is the same in both systems, so we only need to work with the first ones.

If we take the first equation in system A:

-3x + 12y = 15

If we divide both sides by 3, we get:

-x + 4y = 5

Which is the first equation of B.

So we just need to replace the first equation in system A by a multiple of itself to get system B.

Because of that, we conclude that both systems are equivalent (because are made of the same equations) which means that both systems have the same solutions.

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Answer: C), Yes

Step-by-step explanation:

Answer:

Therefore the slope is 13

Step-by-step explanation:

Using Slope intercept formula y = mx + b.

Note : m is the slope ( the number near x).

y+6=13(x−4)

y+6 = 13x - 52

Add -6 to both sides

y+ 6- 6 = 13x- 52- 6

y= 13x -58

Therefore the slope is 13

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the slope of the line y+6=13(x-4)

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

The slope of this particular graph is: the constant multiplied by the parentheses.

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

            [tex]\bf{=Slope \:13}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

The statement that's is likey true about the population of the town is that most likely about 40% to 60% of the people Jon the health club yearly.

It should be noted that a dot plot simply gives a pictorial representation of the information given.

In this case, the population of the town is that most likely about 40% to 60% of the people Jon the health club yearly.

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Answer: Most likely, about 40% to 60 % of the people in the town join a health club yearly.

Step-by-step explanation:

The point that is labeled H on this graph is that at 25th second, Josiah is 60 meter distance from the starting line.

Note that At the point H, there is  found to be an intersection between the distance taken by both people involve so:

Y (a)= 10 + 2x ------ Josiah

Y (0) = 3x   ----- Chana

If  Y (a)= Y (0)

Then:

10 + 2x = 3x

x = 10

F = x = 20

Y (o) = 60

If x = 20

= then Y(0) = 3 x 20

= 60

Therefore, The point that is labeled H on this graph is that at 25th second, Josiah is 60 meter distance from the starting line.

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