Algebra 2 semester 1

Answer:

The population of city A is [tex]74\%[/tex] of the population of city B

Step-by-step explanation:

Let

y------> population of the city A

x-----> population of city B

we know that

[tex](100\%-26\%)=74\%=\frac{74}{100}=0.74[/tex]

so

[tex]y=0.74x[/tex]

therefore

The population of city A is [tex]74\%[/tex] of the population of city B

Ivan has 24 minutes of New Orleans jazz on his MP3 player.

To find out how much of an hour of New Orleans jazz Ivan has, we use the following steps:

1. We know that Ivan has an hour of jazz music on his MP3 player.

2. We are given that 2/5 of this jazz music is by musicians from New Orleans.

3. To find out how much of New Orleans jazz music that is, we calculate 2/5 of 1 hour.

Here's the calculation:

[tex]\( \frac{2}{5} \times 1 \text{ hour} = \frac{2}{5} \times 60 \text{ minutes} \)[/tex]

[tex]\( \frac{2}{5} \times 60 = \frac{120}{5} \text{ minutes} \)[/tex]

[tex]\( \frac{120}{5} = 24 \text{ minutes} \)[/tex]

Therefore, Ivan has 24 minutes of New Orleans jazz on his MP3 player.

complete question given below:

Answer:

The measure of DE is 108°. What is the measure of ZDEF, the tangent-chord angle?

54

Step-by-step explanation:

The result of 4,816.40625 cubic inches is rounded to 4,816 cubic inches to the nearest cubic inch.

To find the volume of Miguel's aquarium, which is in the shape of a rectangular prism, we use the formula for the volume of a rectangular prism:

Volume = length * width *  height

In this case, the length is 30.25 inches, the width is 12.5 inches, and the height is 12.75 inches.

So, the calculation for the volume would be:

Volume = 30.25 inches * 12.5 inches * 12.75 inches
= 4,816.40625 cubic inches.

Rounding to the nearest cubic inch, the volume of the aquarium is 4,816 cubic inches.

Subtract p² - 4p from p² + p - 6 to get 5p - 6. To obtain p - 9, subtract 15 from 5p - 6.

Let's break it down step by step:

1. Subtracting p² - 4p from p² + p - 6:

  Start by writing down the expression p² + p - 6.

  Now, subtract p² - 4p from it term by term.

  (p² + p - 6) - (p² - 4p)

2. Expand and Simplify:

  Distribute the subtraction across each term inside the parentheses:

  p² + p - 6 - p² + 4p

  This simplifies to: (p² - p²) + (p + 4p) - 6

  = 0 + 5p - 6

  = 5p - 6

3. Now, to get p - 9:

  We want to manipulate 5p - 6 to p - 9.

  Subtracting 15 from 5p - 6 gives:

  5p - 6 - 15

  = 5p - 21

Therefore, subtracting 5p - 21 from 5p - 6 results in p - 9.

Answer:  7.1 inches

Step-by-step explanation:

Given: One leg of isosceles right triangle = 5 inches

Since in isosceles right triangle , two sides have same side length , therefore the length of the other leg should be 5 inches.

Let H be the hypotenuse of the isosceles right triangle

Now, by Pythagoras Theorem , we have

[tex]H^2=5^2+5^2=25+25=50\\\\\Rightarrow\ H=\sqrt{50}=5\sqrt{2}\\\\\Rightarrow\ H==5\times(1.41421356237)\\\\\Rightarrow\ H==7.07106781187\approx7.1\ inches[/tex]

Hence, the approximate length of the hypotenuse = 7.1 inches

Answer: C

Step-by-step explanation: 7.1 inches

If silvio earns 10% for each car sale he makes while working at a used car dealership then he earns $200 as commission for selling car for $2,000.

percentage, a relative value indicating hundredth parts of any quantity.

Given that silvio earns 10% for each car sale he makes while working at a used car dealership.

silvio sells a used car for $2,000.

We have to find the commission earned by Silvio.

We have to calculate 10% of $2000 to find the commission.

Convert 10% to decimal value by dividing with 100.

commission = 10% of $2000

commission = 0.1 x $2000

commission = $200

Hence, if silvio earns 10% for each car sale he makes while working at a used car dealership then he earns $200 as commission for selling car for $2,000.

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Final answer:

To find BD, we can use the fact that the opposite sides of a parallelogram are equal in length. The length of BD is 4.8 units.

Explanation:

In the given problem, we have a parallelogram ABCD with m∠A = 60º. BK is perpendicular to AD and AK = KD. The perimeter of ABCD is 24. To find BD, we can use the fact that the opposite sides of a parallelogram are equal in length. Since AK = KD, the length of AD is twice the length of AK.

Let AK = x. Then AD = 2x. The perimeter of ABCD is given by P = AB + BC + CD + AD. Substituting the given values, we have 24 = AB + BC + CD + 2x. We know that AB = CD, so the equation becomes 24 = 2AB + 2BC + 2x. Rearranging the terms, we get AB + BC + x = 12.

Using the fact that opposite sides of a parallelogram are equal in length, we can deduce that BC = AB. Substituting this into the equation, we have 2AB + AB + x = 12. Simplifying, we get 3AB + x = 12. Since AK = KD, we have x = KD. Substituting this into the equation, we have 3AB + KD = 12. Since AK = KD, we have 3AB + AK = 12. Since AK = KD, we have 3AB + 2AK = 12. Simplifying, we get 3AB + 2AB = 12. Combining like terms, we get 5AB = 12. Dividing both sides by 5, we get AB = 12/5. Since AB = CD, we have CD = 12/5. Since opposite sides of a parallelogram are equal in length, we have BD = AD = 2x = 2(12/5) = 24/5 = 4.8.

We have been given a Venn diagram in which U = {students in 10th grade at Lee High School}. We are asked to find how many students have chosen to participate in the painting class.

We  can see from our Venn diagram that 3 students are participating in chorus and painting. 2 students are participating in chorus, theater and painting. 4 students are participating in painting and theater.

To find total students who have chosen to participate in the painting class we will add all the students who are participating in other activities with painting.

[tex]\text{Students participating in painting class}=8+3+2+4[/tex]

[tex]\text{Students participating in painting class}=17[/tex]

Therefore, 17 students have chosen to participate in painting class.

Answer:

17

Step-by-step explanation:

Answer:

6% of a pound does not weigh more than 1 ounce.

Step-by-step explanation:

First, we will calculate 6% (0.06) of 1 pound.

0.06 × 1 lb = 0.06 lb

1 pound is equal to 16 ounces. 0.06 pounds, expressed in ounces is:

0.06 lb × (16 oz/ 1 lb) = 0.96 oz

6% of a pound = 0.96 oz

0.96 oz < 1 oz

Due to the transitive property, we can affirm that 6% of a pound does not weigh more than 1 ounce.

Answer : The measurement of a central angle is, [tex]140^o[/tex]

Step-by-step explanation :

Formula used for angle subtended by an arc is:

[tex]s=\frac{\pi r\theta}{180}[/tex]

where,

s = arc length = [tex]\frac{7}{3}\pi m[/tex]

r = radius = [tex]\frac{diameter}{2}=\frac{6m}{2}=3m[/tex]

Now put all the given values in the above formula, we get:

[tex]s=\frac{\pi r\theta}{180}[/tex]

[tex]\frac{7}{3}\pi=\frac{\pi \times (3)\times \theta}{180}[/tex]

[tex]\theta =140^o[/tex]

Thus, the measurement of a central angle is, [tex]140^o[/tex]

The values of x that satisfy the absolute value equation |x – 3| = 40 are 43 and -37. These are derived from solving the two possible scenarios for absolute value equations, resulting in a positive and a negative solution.

To find which values of x will make the absolute value equation |x – 3| = 40 true, we need to consider both the positive and negative scenarios that can result from the absolute value. The absolute value of a number equals the number itself if it is positive or zero, and it equals the negative of the number if it is negative.

So, we set up two equations:

Solving the first equation for x, we add 3 to both sides:

x = 40 + 3

x = 43

Solving the second equation for x, we add 3 to both sides:

x = -40 + 3

x = -37

Therefore, the values of x that will satisfy the equation are 43 and -37. Option D is the correct answer.

Final answer:

The values of x that make the absolute value equation true are 43 and -37.

Explanation:

To solve the equation |x-3| = 40, we need to consider two cases:

1. x-3 = 40: In this case, we add 3 to both sides to isolate x and get x = 43.

2. -(x-3) = 40: In this case, we distribute the negative sign and add 3 to both sides to isolate x, which gives x = -37.

Therefore, the values of x that make the absolute value equation true are {43, -37}.

Final answer:

To solve the problem, a system of equations is set up with the second number as 'x' and the first as 'x + 124.' The equations are simplified to find 'x = 106,' which makes the first number '230.' The two numbers are 106 and 230.

Explanation:

To find the two numbers that add to 336 and where the first number is 124 larger than the second, we need to set up a system of equations based on the information given:

Let the second number be x.

Then the first number will be x + 124 since it is 124 bigger than the second.

The sum of the two numbers is 336, so we can write the equation x + (x + 124) = 336.

Simplifying this equation, we get 2x + 124 = 336.

Subtract 124 from both sides to isolate the term with x, yielding 2x = 212.

Divide both sides by 2 to find x, which gives x = 106.

Since the first number is 124 larger, we add 124 to 106, resulting in the first number being 230.

Therefore, the two numbers are 106 and 230.

Final answer:

The percent error of the estimated distance from your house to school is 15.8% when rounded to the nearest tenth.

Explanation:

To find the percent error of your estimate, you use the formula:

Error = (|Estimated value - Actual value| / Actual value) × 100

Plugging the values from your question:

Error = (|1.6 miles - 1.9 miles| / 1.9 miles) × 100

Error = (|-0.3 miles| / 1.9 miles) × 100

Error = (0.3 miles / 1.9 miles) × 100

Error = 0.15789473684 × 100

Error = 15.789473684%

When rounded to the nearest tenth of a percent, the percent error is 15.8%.

Final answer:

Tran must calculate the surface area of the hemisphere, including the base, to determine the amount of paint needed, which is the sum of half the surface area of the sphere and the area of the base.

Explanation:

The question is asking what Tran would compute when using π to determine the amount of paint required for a hemisphere. First, Tran needs to calculate the surface area of the sphere to determine the paint needed. Given the circumference C = 18.84 cm, the radius r can be found using C = 2πr, which gives us a radius of r = C / (2π). Once we have the radius, we can find the surface area A of the sphere using A = 4πr², which is necessary to determine the paint needed for the outer surface.

However, when the sphere is cut into two hemispheres, the flat face of each hemisphere (base) also needs paint. The area of the base is a circle with an area of πr². Thus, the total surface area that Tran would need to paint for one hemisphere, including the base, is πr² + 2πr² (half of the sphere's surface area).

Final answer:

Option  D.) Tran found the minimum amount of paint needed to cover both hemispheres.

Explanation:

Tran found the minimum amount of paint needed to cover both hemispheres. To calculate the amount of paint needed to cover a hemisphere, we need to find the surface area of the hemisphere. The formula for the surface area of a sphere is 4πr², where r is the radius.

Given that the circumference of the sphere is 18.84 centimeters, we can use the formula C = 2πr to solve for the radius. Plugging in the value for C, we get 18.84 = 2πr.

Simplifying the equation, we find that the radius of the sphere is approximately 3 centimeters.

The surface area of a hemisphere is half the surface area of a sphere, so the surface area of one hemisphere is 2πr²/2 = πr².

Substituting the value of r, we find that the surface area of one hemisphere is approximately 9π square centimeters.

Since Tran cut the sphere in half and created two identical hemispheres, the minimum amount of paint needed to cover both hemispheres would be twice the surface area of one hemisphere, which is approximately 18π square centimeters.