Sharlene works 8 hours a day on Monday, Wednesday and Friday and 6 hours a day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $ 324 a week. How much does she earn in dollars per hour?

10. The missing conversion is 20.32 inches

11. Total number of red cars is 34

12. Total number of blue cars is 36

13. Total number of silver cars is 70

Ratio is the number of times a quantity is contained more  or less than another in a whole.

Analysis:

10. If 1 inch = 2.54cm

     Then 8 inches = 8 x 2.54cm = 20.32 cm

     First car park: Total number of cars = 60

     ratio of red:blue:silver = 1:2:3

     Total ratio = 1+2+3 = 6

     number of red cars = 1/6 x 60 = 10

     number of blue cars = 2/6 x 60 = 20 cars

     number of silver cars = 3/6 x 60 = 30

   second car park: Total number of cars = 80

    ratio of blue: red: silver = 2:3:5

    total ratio = 2+3+5 = 10

    number of red cars = 3/10 x 80 = 24

    number of blue cars = 2/10 x 80 = 16

    number of silver cars = 5/10 x 80 = 40

11.  Total number of red cars = 10+24 = 34

12.  Total number of blue cars = 20+16 = 36

13.  Total number of silver cars = 30+40 = 70

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The domain and range of this square root function y = 5/2√(-5x + 1) - 87 are as follows;

Domain = {x|x ≤ 1/5}.

Range = {y|y ≥ -87}.

The domain and range of this square root function y = -315√(11x - 3) - 15/88 are as follows;

Domain = {x|x ≥ 3/11}.

Range = {y|y ≤ -15/88}.

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached below for the given square root function y = 5/2√(-5x + 1) - 87 and y = -315√(11x - 3) - 15/88, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, 1/5} or {x|x ≤ 1/5}.

Range = {-87, ∞} or {y|y ≥ -87}.

Domain = {3/11, ∞} or {x|x ≥ 3/11}.

Range = {-∞, -15/88} or {y|y ≤ -15/88}.

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Answer:

0.011865211

Step-by-step explanation:

5.9/497.252 =0.011865211

Answer:

84.28

Step-by-step explanation:

Reason:

The largest sin(x) can get is 1, and the same goes for sin(3x).

Consequently, the largest 2sin(3x) can get is 2.

You can visually verify these claims by graphing each function with a tool like Desmos. Take note of the y coordinate of the highest points. See below.

Therefore, the largest f(x) = 2sin(3x)+C can get is 2+C or C+2

The statement "using the quadratic terms to account for curvature and one or more interaction terms to handle particular combinations of predictors is an example of a second-order model" is True.

A second-order model is the one that comprises quadratic terms that account for curvature and one or more interaction terms to handle particular combinations of predictors. It includes polynomial regression that involves polynomials of order two or greater to predict a response variable. The second-order model refers to a polynomial regression model that has a power of 2 on at least one predictor. The second-order model is a method to represent the quadratic relationship between two variables. The model can be represented as follows:

y = α + β1x + β2x2 + e where, y represents the dependent variable, α represents the intercept, x represents the independent variable, β1 represents the slope, β2 represents the curvature term, and e represents the residual error.

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The answer is 96.96

From the question, we have

60.60 increased by 60%

= 60.60 + 60.60 * 60/100

= 96.96

Percentage:

Use the percentage formula to express a number or percentage in terms of 100. % simply indicates one out of one hundred. An expression for a number between 0 and 1 can be made using the percentage formula. It is a number that is represented as a fraction of 100. The sign % is used to denote it and it is mostly used to compare and calculate ratios. The formula for percentage increases is the ratio of the increased value to the original value multiplied by 100. It is described in percentage form. If anything is valued more highly, both its value and proportion will rise.

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When the person retires at age 65, the IRA will contain approximately $161,666.68. This amount is significantly higher than the total deposits made over the time period.    

To calculate the final value of the IRA, we can use the formula for the future value of an ordinary annuity:

\[FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)\]

Plugging in the given values, we have:

\[FV = 30 \times \left( \frac{(1 + 0.06/12)^{47 \times 12} - 1}{0.06/12} \right)\]

Solving this equation, we find that the IRA will contain approximately $161,666.68 when the person retires at age 65.

This final amount is much greater than the total deposits made over the time period, which would be $30 multiplied by the number of months (47 years multiplied by 12 months per year), resulting in $16,920. Therefore, the person benefits from the compounded interest earned on their IRA contributions over the years of saving for retirement.          

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Answer:

35 divided by 4 is 8.75 so one movie ticket should be $8.75

Step-by-step explanation:

Answer:d

Step-by-step explanation:

The answer is d. None of the above is true.

To calculate velocity, we need to use the equation:

Velocity = M * P / Y

Given:

M = 1,000

P = 2.25

Y = 2,000

Plugging in the values:

Velocity = 1,000 * 2.25 / 2,000

Simplifying:

Velocity = 2.25 / 2

The result is:

Velocity = 1.125

Therefore, the correct answer is: d. None of the above is true.

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The dimensions of the rectangle =  6 ft

Along with arithmetic, geometry is among the oldest subfields of mathematics. It is concerned with spatial characteristics like the separation between objects, their shape and size, and their relative positions. Geometer is the term used to describe a mathematician who specializes in geometry.

At a fundamental level, geometry is essential to understand because it lays the groundwork for learning more complex mathematical concepts. Raj Valli, the founder of Thinkster Math, notes that algebra and geometry frequently overlap. In science and math classes, it introduces crucial formulas like the Pythagorean theorem.

length = 2w - 1

We know that the area:

Area = length * width

Area = 2w - 1 * width

A= 2w^2 -w = 21

2w^2 - w -21 = 0.  Solve for w using quadratic formula.  

[-b±√(b2 - 4ac)]/2a

[1± √((-1)^2 - 4*2*(-21))]/(2*2)

[1± √(1+168)]/4

w = 3.5 ft

length = 2w - 1

= 2*3.5 - 1

= 6 ft

The dimensions of the rectangle =  6 ft.

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The p-value is 0.01, which means that it is very rare to observe a test statistic that is equal to or more extreme than the one that was actually observed. SO the option a is correct.

In the given question, in a hypothesis test for population proportion, we calculated the p-value is 0.01 for the test statistic, we have to find which statement of the p-value is correct.

The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

If the null hypothesis is correct, the p-value is the likelihood that a test statistic will be equal to or more extreme than the one that was actually observed. Given that the null hypothesis is correct in this situation, the p-value of 0.01 indicates that it is extremely unusual to see a test statistic as dramatic as the one that was actually seen. This shows that the alternative hypothesis is more likely to be correct and that the null hypothesis is probably not true.

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Answer:

How is this number written in scientific notation? A. 1.429 x 10.

The number 0.001429 is written in scientific notation as \(1.429*10^{-3}\).

Here, the density of oxygen is 0.001429 grams per cubic centimeter.

What is scientific notation method?

Scientific notation is a way of writing very large or very small numbers.

A number is written in Scientific notation when a number between 1 and 10 is multiplied by a power of 10.

The value of 0.001429 in scientific notation is written as;

⇒\(0.001429 = 1.429*10^{-3}\)

The number 0.001429 is written in scientific notation as \(1.429*10^{-3}\).

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Answer:

\(y = \frac{3}{2} x + 2\)

Step-by-step explanation:

\(2y - 3x = 4\)

\(y - \frac{3}{2} x = 2\)

\(y = \frac{3}{2} x + 2\)

While flood recurrence and probability graphs can provide valuable information on the frequency and severity of major floods, it is important to consider the impact of urbanization and other factors that can affect the accuracy of these predictions.

Urbanization can have a significant impact on the reliability of using flood recurrence and probability graphs to calculate the frequency and severity of major floods. As cities expand and become more developed, the natural landscape is altered in various ways, including the creation of impervious surfaces such as pavement and buildings, which reduce the amount of water that can be absorbed into the ground. This can lead to increased runoff during heavy rainfall events and higher flood peaks.

Furthermore, urbanization can also change the flow patterns of rivers and streams, as well as affect the drainage systems and infrastructure of cities. As a result, the historic records used to create flood recurrence and probability graphs may no longer accurately reflect the current and future flood risks in urban areas.

In addition, climate change can further complicate the reliability of using these graphs, as it can lead to changes in precipitation patterns, sea level rise, and other factors that can affect the frequency and severity of floods.

Therefore, while flood recurrence and probability graphs can provide valuable information on the frequency and severity of major floods, it is important to consider the impact of urbanization and other factors that can affect the accuracy of these predictions.

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What is Midsegment Theorem ?

The Midsegment Theorem, also known as the Midline Theorem or the Triangle Midsegment Theorem, states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half its length.

Explanation:
Here is the complete flowchart with the missing statements and reasons filled in:

Statement 1: Measure of angle ADE is 68 degrees.

Reason 1: Given.

Statement 2: Measure of angle DAE is 90 degrees.

Reason 2: Definition of right angle.

Statement 3: Measure of angle AED is 22 degrees.

Reason 3: Angle sum of triangle ADE is 180 degrees.

Statement 4: Segment DE joins the midpoints of segment AB and AC.

Reason 4: Given.

Statement 5: Segment DE is parallel to segment BC.

Reason 5: Midsegment theorem.

Statement 6: Angle ECB is congruent to angle AED.

Reason 6: Corresponding angles formed by parallel lines.

Statement 7: Measure of angle ECB is 22 degrees.

Reason 7: Substitution property.

So, statements 3 and 6, and reasons 3 and 6, respectively, can be used to fill in the blank spaces numbered 3 and 6, and statement 5 and reason 5 can be used to fill in the blank spaces numbered 4 and 5. Finally, statement 7 and reason 7 can be used to fill in the blank space numbered 7.

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Answer:

42y-48

Step-by-step explanation:

6 x 7

6 x 8

The perimeter of the hexagon with 7 congruent circles of radius 4 are packed into it, so hexagon sides are tangent to 6 circles is -

6s, or approximately 60.72.

Let's begin by drawing a diagram:

       ______

    /        \

   /    o     \

  /            \

 /     o o o    \

/     o o o o    \

\     o o o o    /

 \     o o o    /

  \            /

   \__________/

Each circle is tangent to two sides of the hexagon, so the distance between two opposite vertices of the hexagon is equal to the diameter of a circle, which is 8.

Let's call the side length of the hexagon "s".

Then we can draw a right triangle with legs of length s/2 and s/4, and hypotenuse of length 8.

Using the Pythagorean theorem, we can solve for s:

(s/2)^2 + (s/4)^2 = 8^2

5s^2/16 = 64

s^2 = 102.4

s = sqrt(102.4) = 10.12 (rounded to two decimal places)

Therefore, the perimeter of the hexagon is 6s, or approximately 60.72.

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1. Correct option D. y= 4/5x-9/5

2. option C. (4, 0) is a solution.

3. option B, is the correct answer.

4. option B. (11, 1), is a solution.

5. option A, "(1,7) and (7,1)" is a correct answer.

A statement proving the equality of two mathematical expressions is known as an equation.

1. Solve the equation for y:  4x - 5y = 9  

⇒ 5y = 4x - 9

⇒ y = 4/5 x - 9/5  (correct option D)

2. Solution of this equation:  7a - 5b = 28

from the given options we simply substitute the values of a and b into the equation and check if the equation holds true.

option C. (4, 0);

Substituting a=4 and b=0 into the equation 7a-5b=28, we get:

7(4) - 5(0) = 28, which is equal to 28. So (4, 0) is a solution.

3. we simply substitute the values of x and y into the equation and check if the equation holds true.

Substituting x=2 and y=-9 into the equation 5x-y/3=13, we get:

5(2) - (-9)/3 = 10 + 3 = 13, which is equal to 13. So (2,-9) is a solution.

Substituting x=3 and y=-6 into the equation 5x-y/3=13, we get:

5(3) - (-6)/3 = 15 + 2 = 17, which is not equal to 13. So (3,-6) is not a solution.

Therefore, option B, "The first is a solution, but the second is not" is the correct answer.

4. we simply substitute the values of x and y into the equation and check if the equation holds true.

option B. (11, 1), Substituting x=11 and y=1 into the equation (x+3)y=14, we get: (11+3)(1) = 14(1) = 14, which is equal to 14. So (11,1) is a solution.

5. we substitute each pair into the equation and check if it holds true.

option A. (1,7) and (7,1); Substituting x=1 and y=7 into the equation 4xy+8=36, we get: 4(1)(7) + 8 = 28 + 8 = 36, which is equal to 36. So (1,7) is a solution.

Substituting x=7 and y=1 into the equation 4xy+8=36, we get:

4(7)(1) + 8 = 28 + 8 = 36, which is equal to 36. So (7,1) is also a solution.

Therefore, option A, "(1,7) and (7,1)" is a correct answer.

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The answers of the given equations are

1. option D

2.option C

3. option B

4.option B

5.option A.

What is equation?

Equation is basically a mathematical statement where two expressions are connected by a equal sign. It contains atleast one variable that has be determined.

1) Given equation is 4x- 5y= 9

To solve this equation at first we subtract 4x from both sides

                         -5y= 9-4x

Multiplying by '-' sign to the both sides of the equation we get,

                         5y= 4x-9

Dividing by 5 on the both sides of equation we get,

                      y= (4/5)x - (9/5)

Hence option D is correct.

2) Given equation is 7a-5b = 28----------(1)

putting a=4 and b=0  in equation (1) we get,

                  7× 4- 5×0=28

Hence the ordered pair ( 4,0) is the solution of the equation as the value of a and b satisfies the right side of equation (1). option C.

3) Given equation is 5x- y/3= 13-----------(2)

Putting (2,-9) in equation (2) we get,

  10+3=13 which is the RHS of equation (2)

Putting (3,-6) in equation (2) we get,

  15+2=17 which is not the RHS of equation (2)

So the first is a solution of the equation but the second is not.

Option B.

4) Given equation is (x+3)y=14---------(3)

Putting the values (11,1) in equation (3) we get,

(11+3)×1= 14 which is the RHS of the equation (3).

So the ordered pair is (11,1).

Option B.

5) Given equation is 4xy+8=36

It can be deduced to,

                      4xy+8=36

                       4xy= 36-8

                        4xy= 28

                           x y= 7-------(4)

Putting (1,7) and (7,1) in equation (4) we get,

                      1×7=7×1=7 which is the RHS of equation (4)

So the pair is (1,7) and (7,1). Option A.

Hence, the answers are

1. option D

2.option C

3. option B

4.option B

5.option A.

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Complete Question:

Alejandro jumped from a cliff into the ocean in Acapulco while vacationing with some friends.

\(h(t)=-16t^2 + 16t + 480\)

Where t is the time in seconds and h is the height in feet

(a) How long did it take for Alejandro to reach his maximum height

(b) What was the highest point Alejandro reached

(c) Alejandro hits the water after how many seconds

Answer:

(a) 0.5 seconds

(b) 484 feet

(c) 6 seconds

Step-by-step explanation:

Given

\(h(t)=-16t^2 + 16t + 480\)

Solving (a): Time to reach maximum height

This is the maximum of the function and it is calculated using:

\(t = -\frac{b}{2a}\)

Where

\(a = -16; b = 16; c =480\)

So:

\(t = -\frac{16}{2*-16}\)

\(t = \frac{16}{32}\)

\(t = 0.5\)

Solving (b): Highest point reached

Time to reach the highest point is 0.5.

So, the highest point is: h(0.5)

\(h(t)=-16t^2 + 16t + 480\)

\(h(0.5) = -16 * 0.5^2 + 16 * 0.5 + 480\)

\(h(0.5) = 484\)

Solving (c): Time he hits water.

At this point, h(t) = 0

So;

\(h(t)=-16t^2 + 16t + 480\)

\(-16t^2 + 16t + 480 = 0\)

Factorize

\(-16(t^2 - t -30) = 0\)

Divide both sides by -16

\(t^2 - t -30 = 0\)

Expand

\(t^2 + 5t - 6t - 30 = 0\)

Factorize

\(t(t + 5)-6(t + 5) =0\)

\((t -6)(t + 5) =0\)

\(t =6\ or\ t = -5\)

Time can't be negative.

So:

\(t = 6\)

The objective function formula that is nonlinear is - 2xy/2xy + z

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

- 2xy/2xy + z

- x + y + z

- 3x - 2y + z

A linear function is a function that has a degree of 1

Other functions with other degrees are nonlinear

Using the above as a guide, we have the following functions with a degree of 1

- x + y + z

- 3x - 2y + z

Hence, the objective function formulas that is nonlinear is - 2xy/2xy + z

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Therefore, the sales price is $151.25. So, the answer is (C) $151.25.

Sale price refers to the price of a product or service that has been reduced from its original or regular price. It is usually offered as a discount or promotion to attract customers and increase sales. The sale price can be expressed as a percentage or a dollar amount off the regular price. For example, a shirt with a regular price of $50 might be put on sale for 20% off, making the sale price $40.

To find the sales price, we need to apply the discount to the original price:

Discount amount = 45% of $275 = 0.45 x $275 = $123.75

\(Sales price = Original price - Discount amount\)

\(Sales price = $275 - $123.75 = $151.25\\)

Therefore, the sales price is $151.25. So, the answer is (C) $151.25.

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The correlation coefficients and security returns provided suggest a relationship between security 1 and security 2.

The given information includes security returns and correlation coefficients between different securities. Based on the data, it is evident that there is a relationship between security 1 and security 2. The correlation coefficient P12 is -1, indicating a perfect negative correlation between the two securities. This means that when security 1's returns increase, security 2's returns decrease, and vice versa.

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Answer:

Step-by-step explanation:

∠B and ∠D are same side interior angles and are supplementary angles ( they add up to 180°) because AB ║CD are cut by transversal BD

5x +4x = 180

9x =180

x= 20

∠B = 5*20 =100°

∠D =4*20 =80°

At a = √25/π^2 - 0.04 revolutions will the circular helix r = acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis.

In the given question, we have to find how many revolutions will the circular helix r = acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis.

r = acosti + asintj + 0.2tk, length = 10 unit

So |r| = \(\int^{2\pi}_{0}\sqrt{(dx/dt)^2+(dy/dt)^2+(dz/dt)^2}dt\)

From the given equation,

x = acost, y = asint, z = 0.2t

dx/dt = -asint, dy/dt = acost, dz/dt = 0.2

10 = \(\int^{2\pi}_{0}\sqrt{(-a\sin t)^2+(a\cos t)^2+(0.2)^2}dt\)

10 = \(\int^{2\pi}_{0}\sqrt{a^2\sin^2 t+a^2\cos^2t+0.04}dt\)

As we know that sin^2x+cos^2x = 1. So

10 = \(\int^{2\pi}_{0}\sqrt{a^2+0.04}dt\)

10 = \(\sqrt{a^2+0.04}\int^{2\pi}_{0}dt\)

10 = \(\sqrt{a^2+0.04}\cdot[t]^{2\pi}_{0}\)

10 = √(a^2+0.04)∙[2π-0]

2π√(a^2+0.04) = 10

Divide by 2π on both side, we get

√(a^2+0.04) = 5/π

Taking square on both side, we get

a^2+0.04 = 25/π^2

Subtract 0.04 on both side, we get

a^2 = 25/π^2 - 0.04

taking square root on both side, we get

a = √25/π^2 - 0.04

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The right question is:

How many revolutions will the circular helix

r = acosti + asintj + 0.2tk

make in a distance of 10 units measured along the z-axis?

Answer:

sqrt53

Step-by-step explanation:

So here I'm assuming you need to know the hypotenuse of the triangle. Since it is a right triangle, we are able to use Pythagorean's theorem which is a^2 + b^2 = c^2.

We can set a = 2, b = 7, and solve for c.

2^2 + 7^2 = c^2

4 + 49 = c^2

53 = c^2

c = sqrt53

The area of the swimming pool cover is approximately 159.27 square feet, rounded to the nearest hundredth.

To find the area of the swimming pool cover, we can calculate the area of the rectangle and the area of the semicircle separately.

Area of the rectangle:

The length of the rectangle is 12 feet and the width is 10 feet. The formula to calculate the area of a rectangle is:

Area_rectangle = length × width

Area_rectangle = 12 × 10

Area_rectangle = 120 square feet

Area of the semicircle:

The radius of the semicircle is half the distance between the parallel lines, which is 10/2 = 5 feet. The formula to calculate the area of a semicircle is:

Area_semicircle = (π × radius²) / 2

Area_semicircle = (π × 5²) / 2

Area_semicircle = (π × 25) / 2

Area_semicircle ≈ 39.27 square feet

The total area of the swimming pool cover:

To find the total area, we add the area of the rectangle and the area of the semicircle:

Total_area = Area_rectangle + Area_semicircle

Total_area = 120 + 39.27

Total_area ≈ 159.27 square feet

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The vertex form of the give quadratic equation is f(x) = (x+1)² + 2

The standard vertex form of a quadratic equation is expressed as

y = a(x -h)² + k

where (h, k) is the vertex

Given the quadratic equation

f(x) = x^2 + 2x + 3

Complete the question

f(x) = (x^2+2x) + 3

f(x) = (x^2+2x+1)-1 + 3

f(x) = (x+1)² + 2

Hence the vertex form of the give quadratic equation is f(x) = (x+1)² + 2

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