Gracie earns 17.25/h for a 37.5h week, plus extra for overtime. During store inventory she worked 48.5h. Her gross earnings were $1,471.88. What is Gracie’s overtime rate of pay? show work please

The expected length of the arc containing the point (1,0) is; π

First of all, it is pertinent to note that the lengths of the four arcs in which the circle is divided by the three points and (1, 0) have identical distributions.

The problem is same as dividing a circle of length 2π at four points chosen at random, and labelling one of them (1, 0). Now, let us make L₁, L₂, L₃, L₄ to be the lengths of the four arcs determined by those four points.

Thus, we have;

L₁ + L₂ + L₃ + L₄ = 2π

Whereas, the expected value of several random variables is additive as;

E[ L₁ + L₂ + L₃ + L₄] =  [EL₁] + [EL₂] + [EL₃] + [EL₄]

By symmetry the lengths have the same probability distribution and as such; [EL₁] = [EL₂] = [EL₃] = [EL₄] and the sum must be 2π. Thus, we can say that each expected value is 2π/4 = π/4.

Finally, the expected value of the arc containing the point (1, 0) is the sum of the expected values of the two arcs that are adjacent to (1, 0), i.e.,

π/2 + π/2 = π

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Answer:

(0.5,2) and (-3,3)

Step-by-step explanation:

Answer:

Y = 4x -2 is (0.5,2)

y = x +3 is (-3,3)

Answer:

- 15

Step-by-step explanation:

1) Simplify 15 - 2 to 13.

39/13  - 2 × 9

2) Simplify 39/13 to 3.

3 - 2 × 9

3) Simplify 2 × 9 to 18.

3 - 18

4) Simplify.

- 15

Using the cosine rule, the equation to use to solve for x is: x = √(4.0² + 4.7² − 2(4.0)(4.7) × cos(41)) ≈ 3.1 cm.

The cosine rule is given as, c = √(a² + b² − 2ab × cos(C))

Given the following:

Plug in the values:

x = √(4.0² + 4.7² − 2(4.0)(4.7) × cos(41))

x ≈ 3.1 cm

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An inequality that can be used to describe the possible values of x is; C. 0 < x < 14

From the given image, let us first use sine rule to find the angles in the triangle with sides 12, 6 and 7 and angle 120°. Thus;

7/sin α = 12/sin 102

sin α = (7/12) * sin 102

sin α = 0.570586

α = sin⁻¹0.570586

α = 34.8°

We know that sum of angles in a triangle is 180°. Thus;

34.8° + 90° + (7x + 4) = 180°

124.8 + 7x + 4 = 180

7x = 180 - 128.4

x = 51.6/7

x = 7.37

Looking at the given options, x cannot be negative and that rules out the first option. x is greater than 8/7 and that rules out the second option but x is greater than 0 and less than 14 and so option C is correct.

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To solve a one-variable-inequality, isolate the variable on one side of the inequality. This can be done by using the four mathematical operations.

What is the four mathematical operations?

The four mathematical operations include the following:

These operations can be used to solve equations, inequalities, and more.

Given inequality:

As stated in the previous section, let's isolate the variable (c) using the four mathematical operations. Clearly, we have to add both sides by 12 of the inequality as "c" is being subtracted by 12. Therefore, we get:

Simplify the right-hand-side to obtain the simplified inequality:

Therefore, option B is the correct/best choice.

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Answer:

Both of the two unknown sides of the triangle are 23.32 cm

Step-by-step explanation:

"Isosceles" means that the triangle has two equal sides. It is quite symmetrical. If we draw in the height, the base will be cut right in half by it. See image.

First use area formula:

A = 1/2bh

to find the measure of the height (Area and base were both given)

Then use the Pythagorean Theorem to solve for the hypotenuse, which is the side of the triangle. See image.

Answer:

4x+5 ≤29. Answer = $6 or less

Step-by-step explanation:

1. x= the price of the rice bowl

2. 4x= price of 4 rice bowls

3. So we get 4x+5(The total amount of their purchase)

4. Kara has only $29 so she can spend that much

5. The inequality 4x+5≤29 represents how much can she spend on each rice bowl.

6. The answers include $6,$5,$4,$3,$2, and $1 or less.

Answer:

3 seconds

Step-by-step explanation:

When the ball hits the ground, the height will be 0. Therefore, you can substitute 0 in for the value of f(t), hence the equation will be:

0 = -16t^2 + 32t + 48

You can then factor out -16:

0 = t^2 - 2t - 3

Factor:

0 = (t-3)(t+1)
t = 3, -1

However -1 is an extraneous solution because time cannot be negative. Therefore, the answer is 3 seconds.

This chart represents a proportional relationship. The rate of change will be 4.

Firstly, there is a proportional relationship.

Two values x  and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.

The constant k is called the constant of proportionality.

Given;

x y

1 4

2 8

3 12

4 16

Here, x = ky

put the first value

k = 1/4

This chart represents a proportional relationship.

So the rate of change will be

[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}\\\\Rate = \dfrac{8 - 4}{2 - 1}\\\\Rate = 4[/tex]

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Circumference

Area

Answer:

Ig u have forgotten about the figure u need to ask it again but with figure

Answer:

12 Vanilla Frosted Cupcakes

Step-by-step explanation:

30 Cupcakes.

1/5 Of 30 is 6.

30 - 6 = 24.

24/2 = 12.

The area bounded by the curves y = 8x – x² and y = 7 will be 36 square units.

The complete question is given below.

When the two curves intersect then they bound the region is known as the area bounded by the curve.

The curves are given below.

y = 8x – x²

y = 7

By solving the equations 1 and 2, then we have

       8x – x² = 7

x²  – 8x + 7 = 0

(x – 1)(x – 7) = 0

                 x = 1, 7

Then the area bounded by the curves y = 8x – x² and y = 7 will be

[tex]A = \int _1^7 [(8x - x^2) - 7] \ dx\\\\A = \left [ 4x^2 - \dfrac{x^3}{3} - 7x \right ]_1^7\\\\A = \left [ 4 * 7^2 - \dfrac{7^3}{3} - 7*7 \right ] - \left [ 4*1^2 - \dfrac{1^3}{3} - 7*1 \right ]\\\\[/tex]

On further solving we have

A = 32.667 + 3.333

A = 36 square units

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Answer:

D

Step-by-step explanation:

The product of the slopes of two perpendicular lines is -1.

If the slopes of the diagonals are 1 and -1, then their product is -1, and they are perpendicular.

Answer: D

A sentence that describes what Talia should do to show that the diagonals of the square are perpendicular is: D. show that the slope of SQ is 1 and the slope of PR is -1.

In order for a quadrilateral to be a square, the two (2) pairs of its sides must be equal (congruent) and perpendicular to each other.

Therefore, we would have to calculate the slope of each side by using this mathematical equation:

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m₁) of SQ = (a - 0)/(a - 0)

Slope (m₁) of SQ = a/a = 1.

Slope (m₂) of PR = (a - 0)/(0 - a)

Slope (m₂) of PR = -a/a = -1.

Based on the condition for two (2) perpendicular lines, we have:

m₁ × m₂ = -1

1 × -1 = -1

-1 = -1

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Answer:

Common difference:  30

General term formula:   [tex]a_n=30n-9[/tex]

52nd term:  1551

Step-by-step explanation:

Given sequence:

21, 51, 81, 111

Calculate the difference in terms:

[tex]21 \underset{+30}{\longrightarrow} 51 \underset{+30}{\longrightarrow} 81 \underset{+30}{\longrightarrow} 111[/tex]

The sequence is increasing by 30 each time, so as there is a common difference, this is an arithmetic sequence with a common difference of 30.

General form of an arithmetic sequence

[tex]a_n=a+(n-1)d[/tex]

where:

Given:

Substitute the given values into the formula to find the general term formula:

[tex]\implies a_n=21+(n-1)30[/tex]

[tex]\implies a_n=21+30n-30[/tex]

[tex]\implies a_n=30n-9[/tex]

To find the 52nd term, simply substitute n = 52 into the found general term formula:

[tex]\implies a_{52}=30(52)-9[/tex]

[tex]\implies a_{52}=1560-9[/tex]

[tex]\implies a_{52}=1551[/tex]

Answer:

6.6 cm and 14.6 cm

Step-by-step explanation:

(a)

the length of arc AB is calculated as

AB = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{95}{360}[/tex]

     = 2π × 4 × [tex]\frac{95}{360}[/tex]

     = 8π × [tex]\frac{95}{360}[/tex]

     = [tex]\frac{8\pi (95)}{360}[/tex]

     ≈ 6.6 cm ( to the nearest tenth )

(b)

the perimeter (P) of sector AOB is

P = r + r + AB = 4 + 4 + 6.6 = 14.6 cm

Step-by-step explanation:

3.

the circumference of a circle is

2×pi×r

r = 4 cm

so, we know, the full circle circumference is

2×pi×4 = 8×pi = 25.13274123... cm

a.

the arc length of AB is the part of the whole circumference that corresponds to 95° out of the full 360° of a whole circle.

arc AB = 8×pi × 95/360 = pi × 95/45 = pi × 19/9 =

= 6.632251158... cm

b.

the perimeter of OAB (the "pie slice") is then the arc AB plus 2 radius lengths (from the end points on the arc to the center of the circle) :

pi × 19/9 + 2×4 = pi×19/9 + 8 = 14.632251158... cm

Answer:

its right there.

Step-by-step explanation:

Based on the data, the true statement about the people surveyed is: option B.

A two-way frequency table is a table that's used to graphically the represent frequencies or relative frequencies that are associated with two categorical variables such as role model and level of education.

By critically observing the data provided in this two-way frequency table, we can infer and logically deduce that a person whose role model is a stranger is more likely to have high school (0.4 or 40&) than some college as their highest level of education.

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Answer:

B

Step-by-step explanation:

14%start color #11accd, 14, percent, end color #11accd of the people whose role model is a family member have an advanced degree, but only \maroonD{12\%}12%start color #ca337c, 12, percent, end color #ca337c of people whose role model is a friend or acquaintance have an advanced degree.

This statement is false.

40%start color #1fab54, 40, percent, end color #1fab54 of people who role model is a stranger have high school as their highest level of education, while only \purpleC{23\%}23%start color #aa87ff, 23, percent, end color #aa87ff have some college as their highest level.

This statement is true.

We only know the column relative frequencies, not the row relative frequencies, so we cannot make this claim.

If there were an equal number of people with family members and strangers as role models, then the statement would be true. However, suppose this data came from a sample where 100100100 people have a family member as a role model and 400400400 people have a stranger as a role model.

Family member: 0.23(100)=230.23(100)=230, point, 23, left parenthesis, 100, right parenthesis, equals, 23 would have a bachelor's degree as their highest level of education

Stranger: 0.14(400)=560.14(400)=560, point, 14, left parenthesis, 400, right parenthesis, equals, 56 would have a bachelor's degree as their highest level of education

Without knowing the total number of people in each group, or the row relative frequencies, we can't say this statement is true.

We only know the column relative frequencies, not the row relative frequencies, so we cannot make this claim.

If there were an equal number of people with friends or acquaintances and strangers as role models, then the statement would be true. However, suppose this data came from a sample where 400400400 people have a friend or acquaintance as a role model and 200200200 people have a stranger as a role model.

Friend or acquaintance: 0.12(400)=480.12(400)=480, point, 12, left parenthesis, 400, right parenthesis, equals, 48 would have finished less than high school

Stranger: 0.19(200)=380.19(200)=380, point, 19, left parenthesis, 200, right parenthesis, equals, 38 would have finished less than high school

Without knowing the total number of people in each group, or the row relative frequencies, we can't say this statement is true.

Based on this data, the statement which must be true is, "A person whose role model is a stranger is more likely to have high school than some college as their highest level of education. "

Answer:

x=79/5 or 15.8

Step-by-step explanation:

....................

Answer:

[tex]\frac{79}{5}[/tex]

Step-by-step explanation:

Combine [tex]\frac{1}{3}[/tex] and x.

[tex]\frac{x}{3} +\frac{11}{15}=6[/tex]

Move all terms not containing x to the right side of the equation.

[tex]\frac{x}{3}=\frac{79}{15}[/tex]

Multiply both sides of the equation by 3.

3[tex]\frac{x}{3}[/tex]=3([tex]\frac{79}{15}[/tex])

Then 3 cancels out on the left side so all is left is 3.

On the right side, you need to multiply.

3 times 79 is 237.

Now simplify and you get:

79/5

Hope this helped!

Answer: 7/8

What you have to do here is to find the highest number which can be divided by both. Or you have to divide both the numerator and denominator until it can not be divided by any number anymore. You can do this by finding the highest common factor (HCF) of both the number, 35 and 40.

Highest Common Factor: HCF of two or more numbers is the greatest factor that divides the numbers. For example, 2 is the HCF of 4 and 6.

So, the highest number which divides 35 and 40, is 5. Now 35 divided by 5 is 7 and 40 divided by 5 is 8. The final answer is 7/8 and there is no more numbers which can divide both of them by a specific number.

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   hope it helped
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The sample space of event A would be {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

An experimenter does some random experiments which have a fixed set of outputs. That set of all possible outputs of that experiment is called sample space.

Using two six-sided number cubes, each labeled with the numbers 1 through 6.

Event A is defined by rolling a sum greater than 8.

Then the sample space of event A would be;

{(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

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Answer:

{(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

proof in pic

Answer:

B

Step-by-step explanation:

We see the graph of y=x², so eliminate A.

Since the second graph opens downwards, the coefficient of x² must be negative, so eliminate C.

Also, the axis of symmetry is x = 0, so eliminate D.

This leaves us with B

Answer:

A. Vertex is ( -1, 16)

B. Do they mean y-intercept for vertical intercept? That is (0,14)

C. X-intercepts are

(-3.838, 0) and (1.828, 0)

Step-by-step explanation:

plug the equation into desmos. It will graph and give you the info.

To find y-int, plug in 0 for x. This gives you the point 0, 14.

You can also use the quadratic equation to find the x-intercepts.

Answer:

see explanation

Step-by-step explanation:

A

given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

f(x) = - 2x² - 4x + 14 ← is in standard form

with a = - 2, b = - 4 , then

x = - [tex]\frac{-4}{-4}[/tex] = - 1

substitute x = - 1 into f(x) for corresponding y- coordinate

f(- 1) = - 2(- 1)² - 4(- 1) + 14 = - 2 + 4 + 14 = 16

vertex = (- 1, 16 )

B

to find the y- intercept let x = 0

f(0) = - 2(0)² - 4(0) + 14 = 0 - 0 + 14

y- intercept = (0, 14 )

C

to find the x- intercepts let f(x) = 0 , that is

- 2x² - 4x + 14 = 0 ( divide through by - 2 )

x² + 2x - 7 = 0 ( add 7 to both sides )

x² + 2x = 7

using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(1)x + 1 = 7 + 1

(x + 1)² = 8 ( take square root of both sides )

x + 1 = ± [tex]\sqrt{8}[/tex] ( subtract 1 from both sides )

x = - 1 ± [tex]\sqrt{8}[/tex]

then

x = - 1 - [tex]\sqrt{8}[/tex] ≈ - 3.83 ( to 2 dec. places )

x = - 1 + [tex]\sqrt{8}[/tex] ≈ 1.83 ( to 2 dec. places )

that is x- intercepts are (- 3.83, 0 ) , (1.83, 0 )

Answer:

-x - 3

Step-by-step explanation:

1) Distribute

(3x+3)-(4x+6)

3x + 3 - 4x - 6

2) Subtract the numbers

3x + 3 - 4x - 6

3x - 3 - 4x

3) Combine like terms

3x - 3 - 4x

-x - 3

Equation 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p has the same soltion as the provided equation option second and third are correct.

It is defined as the combination of constants and variables with mathematical operators.

We have an equation:

2.3p – 10.1 = 6.5p – 4 – 0.01p

Combine like terms:

2.3p – 10.1 = 6.49p – 4

Or in the equation 2.3p – 10.1 = 6.5p – 4 – 0.01p mulitply by 100 on both sides.

We get:

230p – 1010 = 650p – 400 – p

Thus, equation 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p has the same soltion as the provided equation option second and third are correct.

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Answer:

[tex]\boxed {54^{o}}[/tex]

Step-by-step explanation:

By Inscribed Angle Theorem, the value of an inscribed angle enclosed by an arc is the half the value of that arc.

⇒ ∠RPQ = 108°/2

⇒ ∠RPQ = 54°

Considering the direction of the wind, it is found that the plane's speed needs to be of 520 knots.

The ground speed, considering that the wind is flowing from Kansas City to Washington, and the trip is Washington to Kansas City, is given by:

G = Plane speed - Wind speed.

Hence:

450 knows = Plane speed - 70 knots.

Plane speed = 520 knots.

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Answer:

75 km

Step-by-step explanation:

(50km/h)(1.5h) = 75km