Kim ran a 26-mile marathon.
She ran 1/7 of the marathon during
the first hour. How many miles did
Kim run during the first hour?

Answer: 5.66

Step-by-step explanation:

The perimeter of the square being 32, the sides are 8 units. The diameter of the circumscribing circle is the diagonal of the square which is 8 sec 45 = 11.3 units. Hence, the radius of the circle = 5.66 units.

Answer:

11

Step-by-step explanation:

plz watch all steps in pic

Using a system of equations, it is found that the lengths of the sides of the triangle are given as follows:

5.29 feet, 2.43 feet, 5.79 feet.

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 the lengths, that are x, y and z.

The length of one side of a triangle is 2 feet less than three times the length of its second side, hence:

x = 3y - 2.

The length of the third side is 3/4 of the sun of the lengths of the first two sides, hence:

z = 0.75(x + y).

Find the lengths of all three sides if the perimeter of the triangle is 17.5 feet, hence:

x + y + z = 17.5.

3y + 2 + y + 0.75(3y - 2 + y) = 17.5

4y + 0.75(4y - 2) = 15.5.

7y = 17

y = 2.43 feet.

Hence:

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89,170,326

millions is the place value of 9

hope that helps :)

Reason: The two line segments CF and AH point in the same direction, and they never intersect. Therefore, we consider them parallel.

Skew lines are ones that point in different directions. An example of a pair of skew lines would be AB and DE. Skew lines never intersect, but we don't consider them parallel.

Answer:

3/8

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

36 ÷ 4 = 9

36 ÷ 9 = 4

Answer:

9

Step-by-step explanation:

All three approaches yield the same result: AED4,600,000 (Expenditure Approach), AED1,600,000 (Income Approach), and AED1,800,000 (Production Approach). This consistency demonstrates that the three approaches provide equivalent measures of GDP.

To calculate the contributions to GDP of the given transactions, we can use the three approaches: the expenditure approach, income approach, and production approach. Let's calculate the GDP using each approach and demonstrate that they give the same answer.

Expenditure Approach:

GDP is calculated as the sum of all final expenditures. In this case, the final expenditures are the sales of the supercomputers.

GDP = Sales of supercomputers

= (3 * AED1,000,000) + (1 * AED800,000)

= AED3,800,000 + AED800,000

= AED4,600,000

Income Approach:

GDP can also be calculated by summing up all the incomes earned during production. In this case, the incomes include wages, interest, and taxes.

GDP = Wages + Interest + Taxes

= (Labour costs for ABC + Labour costs for Jumbo) + (Interest on debt for ABC) + (Taxes for ABC + Taxes for Jumbo)

= (AED1,000,000 + AED200,000) + AED100,000 + (AED200,000 + AED100,000)

= AED1,200,000 + AED100,000 + AED300,000

= AED1,600,000

Production Approach:

GDP can also be calculated by summing the value added at each stage of production. In this case, the value added is the sales price minus the cost of components purchased.

GDP = Sales price of supercomputers - Cost of components

= (3 * AED1,000,000) + (1 * AED800,000) - (4 * AED500,000)

= AED3,000,000 + AED800,000 - AED2,000,000

= AED1,800,000

As we can see, all three approaches yield the same result: AED4,600,000 (Expenditure Approach), AED1,600,000 (Income Approach), and AED1,800,000 (Production Approach). This consistency demonstrates that the three approaches provide equivalent measures of GDP.

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Answer: Right , Scalene

Step-by-step explanation: the picture shows that it is a right triangle. It also has side lengths of 8.66, 7, and 5.1 which are all different making it a scalene triangle.

Answer:

43,200

Step-by-step explanation:

25,000x .20=5,000

30,000 x .20=6,000

36,000x.20=7,200

43,200x.20=8,640

51,840x.20=10,368

Answer:

85/4 = 21 ,remainder =1

so

21  1/4

Step-by-step explanation:

"Problem:

Jenny earns a base pay of $1000 per month plus a 5% commission on all sales. Last month she sold $8000 worth of products. What was her total earnings for the month?

Solution:

Jenny's commission for the month is 5% of $8000, which can be calculated as:

Commission = 5% of $8000 = (5/100) * $8000 = $400

Her total earnings for the month can be found by adding her base pay and commission:

Total Earnings = Base Pay + Commission

Total Earnings = $1000 + $400

Total Earnings = $1400

Therefore, Jenny's total earnings for the month were $1400." (ChatGPT, 2023)

The translation rule that matches the transformation for congruent angles is given as follows:

(x,y) -> (x + 4, y - 5).

The translations are movements to the triangle in each of these directions:

There were two translations in this problem, listed as follows:

For the first translation, the triangle was moved down five units, hence the rule is given as follows:

y -> y - 5.

For the second translation, the triangle was moved right four units, hence the rule is given as follows:

The complete translation, obtained by the combination of each translation, is given as follows:

(x,y) -> (x + 4, y - 5).

Meaning that the first option is the correct option.

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Let u = tan⁻¹x, then du/dx = 1/(1+x²).

Using the formula for the derivative of inverse tangent, we have:

tan(u) = x

sec²(u) du/dx = 1

du/dx = cos²(u)

Substituting into the original expression, we get:

∫(tan⁻¹x × e^tan⁻¹x)/(1+x²) dx = ∫(tan⁻¹x × e^u × cos²(u)) du

Using integration by parts with u = tan⁻¹x and dv = e^u × cos²(u) du, we get:

v = (1/2) e^u (sin(u) + u cos(u))

∫(tan⁻¹x × e^u × cos²(u)) du = (1/2) e^u (sin(u) + u cos(u)) tan⁻¹x - ∫[(sin(u) + u cos(u)) / (1+x²)] dx

Substituting back u = tan⁻¹x, we get:

∫(tan⁻¹x × e^tan⁻¹x × cos²(tan⁻¹x)) dx = (1/2) e^tan⁻¹x (x sin(tan⁻¹x) + cos(tan⁻¹x)) tan⁻¹x - ∫[(x cos(tan⁻¹x) + sin(tan⁻¹x)) / (1+x²)] dx

Using the identity sin(tan⁻¹x) = x / √(1+x²) and cos(tan⁻¹x) = 1 / √(1+x²), we simplify the expression to:

∫(tan⁻¹x × e^tan⁻¹x × cos²(tan⁻¹x)) dx = (1/2) x e^tan⁻¹x + (1/2) ∫[e^tan⁻¹x / (1+x²)] dx

The remaining integral can be solved using another substitution with v = tan⁻¹x, which results in:

∫(tan⁻¹x × e^tan⁻¹x × cos²(tan⁻¹x)) dx = (1/2) x e^tan⁻¹x + (1/2) ln(1+x²) + C, where C is the constant of integration

9/18

Divide by 9

9/9=1

18/9=2

Answer : 1/2

The solution of the given equation are,

\(x=\frac{\pi }{2}+2n\pi , x = -0.33983 + 2n\pi , x = \pi +0.33983+2n\pi\)

What is solution of the equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other terms, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transform the equation into an equality.

Consider, the given equation

\(2-3cos^2(x)=2sin(x)\)

⇒ \(2-3cos^2(x) - 2sin(x)=0\)

Since, \(cos^2(x) = 1-sin^2(x)\)

Plug this value in the above equation.

\(2-3(1-sin^2(x))-2sin(x)=0\\2-3+3sin^2(x)-2sin(x)=0\\-1+3sin^2(x)-2sin(x)=0\\3sin^2(x)-2sin(x)-1=0\\\)

Substitute \(sin(x) = u\)

⇒

\(3u^2-2u-1=0\\3u^2-3u+u-1=0\\3u(u-1)+1(u-1)=0\\(u-1)(3u+1)=0\)

⇒

\((u-1)=0, (3u+1)=0\\u=1, u=-\frac{1}{3}\)

Back substitute: u = sin(x)

⇒

\(sin(x) = 1\\sin(x) = -\frac{1}{3}\)

For,

\(sin(x)=1 , x = \frac{\pi }{2}+2n\pi \\ sin(x)=-\frac{1}{3}, x = arcsin(-\frac{1}{3} )+2n\pi , x = \pi +arcsin(\frac{1}{3})+2n\pi\)

Combine all solutions, the we get

\(x=\frac{\pi }{2}+2n\pi , x = -0.33983 + 2n\pi , x = \pi +0.33983+2n\pi\)

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Complete question:

Solve the equation for x, 2 - 3 cos²(x) = 2 sin(x)

The number of people aged 31-50 years old are cell phone users in the tri-County area are 26,767,650.

A pie chart, also known as a circle chart, is a method of summarizing a set of numeric variables or displaying the variables of a given factor (e.g. percentage distribution).

For the given question;

The total population = 72,345,000.

The total percentage between 31-50 years old = 23% + 14% (see from graph).

Let x be the total number of people between aged between 31 -50 years who are cell phone users.

(23% + 14%) of  72,345,000 = x

x = 37× 72,345,000 / 100

x = 26,767,650.

Therefore, the number of cell phone users aged between 31 to 50 are 26,767,650.

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Answer: 4



Step-by-step explanation:

Answer:

The answer to the question is C

Step-by-step explanation:

as the question state that 1.9 is subtracted from the 7.4×3 so tge 1.9 will be removed ffrom it .

Answer: 24

Step-by-step explanation:

To find the area of the composite figure, we need to find the area of the sector and the area of the triangle and then add them together.

Area of sector = (θ/360) * π * r^2, where θ is the angle of the sector in degrees, r is the radius of the circle.

The angle of the sector can be found by subtracting the angle of the triangle from 360 degrees. The radius of the circle can be found by dividing the length of the arc by the angle of the sector.

Length of the arc = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 4 = 4.19

Radius of the circle = 4.19/60 = 0.07

Angle of sector = 360 - 60 = 300 degrees

Area of sector = (300/360) * 3.14 * 0.07^2 = 0.0041

The area of the triangle can be found using the formula:

Area of triangle = (1/2) * base * height = (1/2) * 8 * 6 = 24

Therefore, the total area of the composite figure is:

0.0041 + 24 = 24.0041

Rounding to the nearest hundredth, the area of the composite figure is approximately 24.00.

Answer:yes

Step-by-step explanation:

a) The pattern of yo-yo dieting can be described as an oscillating feedback loop.

What is  feedback loops?

The process of using a system's outputs as inputs again is known as a feedback loop.

a) The pattern of yo-yo dieting can be described as an oscillating feedback loop. In this situation, the person's weight serves as the feedback variable, and the person's diet and exercise habits serve as the input variables that influence the feedback variable. When the person's weight increases, it provides negative feedback that prompts the person to diet and exercise more in order to lose weight. When the person's weight decreases, it provides positive feedback that reinforces the person's diet and exercise habits. This feedback loop continues to oscillate, with the person's weight fluctuating between high and low levels.

b) To help such a person stabilize their weight, it may be helpful to modify the input variables in the feedback loop. One approach could be to focus on adopting a healthy and balanced diet that is sustainable in the long term, rather than going on extreme diets that are difficult to stick to.

     Additionally, engaging in regular physical activity and developing healthy habits such as eating slowly and avoiding distractions while eating can also help to stabilize weight. It may also be helpful to seek support from a healthcare professional or a registered dietitian, who can provide guidance and support for making sustainable lifestyle changes.

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9514 1404 393

Answer:

  7.0 cm

Step-by-step explanation:

The relationship between radius and area of a sphere is ...

  A = 4πr²

Then the radius as a function of area is ...

  r = √(A/(4π)) = (√(A/π))/2

For an area of 616 cm², the corresponding radius is ...

  r = (√(616/π))/2 ≈ 7.0 cm . . . . radius of the orange

Hope you could understand.

If you have any query, feel free to ask.

A linear pair of angles is formed when two lines intersect. That's why it's said that these angles are supplementary because they sum 180 degrees.

Statement Reason.

1. Angle 1 and 2 are a linear pair. Given.

2. Angle 2 = 115. Given.

3. Angle 1 + Angle 2 = 180. Definition of linear pairs.

4. Angle 1 + 115 = 180. By statement 2.

5. Angle 1 = 180-115 = 65 Subtracting on both sides by 115.

Answer:

25 meters per minute

150 in 6 minutes

Step-by-step explanation:

Answer:

1.62i

Step-by-step explanation:

Collect like terms by subtracting their coefficients.

(6.29-5.3) x i

Subtract the numbers.

1.62i

Was this the answer you were looking for?

Answer:

A

Step-by-step explanation:

A

Answer:

Q9 -  Option 1---- A -  15.6 Square Units

Q10 --Option --- (B) RECTANGLE

Step-by-step explanation:

Q9 --

we know area of triangle  = 1/2 ab sin theta

Where theta is the angle included between sides A and side B

A  = 5.2

B = 7

theta  = 121 degrees

1/2 * 5.2 * 7 * sin 121 degrees = 15.6 Square Units

Conclusion

The area of the triangle is 15.6 Square Units

Option --- (B) RECTANGLE

Hope this helps!

a) The number alive after 7 years is given as follows: 48.

b) The percentage of herd that dies each year is of 10%.

The exponential function in the context of this problem is defined as follows:

N(t)=100(0.9)^t.

The parameters of the function are defined as follows:

The amount of herd alive after 7 years is found with the numeric value at t = 7, replacing the lone instance of t in the function by 7, hence:

N(7) = 100 x (0.9)^7 = 48.

(rounding to the nearest whole number).

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