A straight slide in a playground design makes an isosceles triangle with the

ground and its platform, with area 32 square feet. What is the length of the slide?

A 412 feet 32 © 8/2 feet 126

B 8 feet 6

0 16 feet 256

Answer:

Step-by-step explanation:

The equation is:

          [tex]P = PV\times \frac{i}{1-(1 + i)^{-n}}[/tex]

Where,

For example, to calculate the montly payment of a $30,000 loan to be paid in 10 years, at 8% compounded monthly, you use>

Hence, n represents number of periods over which interest is calculated on the loan.

Answer:

to sum it up its A

Step-by-step explanation:

Answer:

there is no table :)

Step-by-Step Explanation:

y = 1/4x +1

X        Y

4        2

8        3

12       4

Answer:

a. Triangular prism

b. (Perimeter of base×height) +2(base area)

c. Total surface area

[tex] = 11(3 + 4 + 5) + 2( \frac{1}{2} )(3)(4) \\ = 11(12) + 3(4) \\ = 132 + 12 \\ = 144 \:{cm}^{2} [/tex]

The reason why we multiply the perimeter of the base by the height is because we are trying to find the area of each of the rectangular sides of the prism. (length×breadth)

Answer: 12 minutes

Step-by-step explanation: Since there are 2 people and 24 minutes total, you have to divide the total time by the amount of people. The equation will be 24=2x, so divide 24 by 2 and you get 12

Answer:

The absolute value of 13 is (-13)

Step-by-step explanation:

It just is lol

Answer: 13

Explanation: The absolute value of an integer it its distance from zero on a number line. Since 13 is 13 units from zero, the absolute value of 13 is 13.

To represent the absolute value of a number, we use a vertical bar on either side of the number so we say that |13| = 13.

I have drawn a number line and also showed you in the image attached.

Answer:

$7300

Step-by-step explanation:

Loretta's taxable income in 2009 is $42,540. Calculation involves subtracting allowable deductions from gross income.

Loretta's taxable income can be calculated by subtracting her allowable deductions from her gross income. As Head of the Household, Loretta is eligible for a higher standard deduction compared to single individuals. For tax year 2009, the standard deduction for Head of the Household was $8,350. Loretta can also claim deductions for herself and her two children. The personal exemption for each individual was $3,650 in 2009. Therefore, Loretta's total deductions would be $8,350 (standard deduction) + $3,650 (personal exemption for herself) + $3,650 (personal exemption for child 1) + $3,650 (personal exemption for child 2) = $19,300.

To find Loretta's taxable income, we subtract her total deductions from her gross income: $61,840 - $19,300 = $42,540. Therefore, Loretta's taxable income is $42,540 in 2009.

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Answer:

Fred is 31 years old and Natalie is 14 years old.

Step-by-step explanation:

Given:

If you add Natalie's age and Fred's age, the result is 45.

If you add Fred's age to 3 times Natalie's age, the result is 73.

Now, to find the age of Fred and Natalie.

Let the age of Fred be [tex]x.[/tex]

And the age of Natalie be [tex]y.[/tex]

As, given If you add Natalie's age and Fred's age, the result is 45.

[tex]x+y=45[/tex]    ......(1)

Now, if you add Fred's age to 3 times Natalie's age, the result is 73.

[tex]x+3y=73[/tex]   ......(2)

So, to solve the equations by using elimination method.

Now, subtracting both the equations (1) and (2):

[tex]x+y-(x+3y)=45-73[/tex]

[tex]x+y-x-3y=-28[/tex]

[tex]-2y=-28[/tex]

Dividing both sides by -2 we get:

[tex]y=14.[/tex]

Natalie's age = 14 years.

Now, to get the age of Fred by substituting the value of [tex]y[/tex] in equation (1):

[tex]x+y=45\\\\x+14=45[/tex]

Subtracting both sides by 14 we get:

[tex]x=31.[/tex]

Fred age = 31 years.

Therefore, Fred is 31 years old and Natalie is 14 years old.

These are 16 questions and 16 answers

Answer:

Explanation:

From 1 to 10, find the sale price to the nearest cent:

1. $239 television; 10% discount

   [tex]Sale\text{ }price=Orignal\text{ }price-discount\\ \\ Sale\text{ }price=\$239-10\%\times \$239=\\\\ Sale\text{ }price=\$239-0.10\times \$239=\\\\ Sale\text{ }price=\$239-\$23.9=\$215.10[/tex]

2. $72 game; 20% discount

You can also multiply by the factor (1 - % discount);

For instance for 20% discount, the factor is 1 - 20% = 1 -0.20 = 0.80. Which means that you can multiply the original price by the factor 0.80 to get the sale price:

              [tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$72\times(1-0.20)=\\\\ Sale\text{ }price=\$72\times0.80=\\\\ Sale\text{ }price=\$57.60[/tex]

3. $18.95 football; 15% discount

             [tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$18.95\times(1-0.15)=\\\\ Sale\text{ }price=\$18.95\times0.85=\\\\ Sale\text{ }price=\$16.11[/tex]

4. $10.99 CD; 25% discount

            [tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$10.99\times(1-0.25)=\\\\ Sale\text{ }price=\$10.99\times0.75=\\\\ Sale\text{ }price=\$8.24[/tex]

5. $149 MP3 player; 40% discount

            [tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$149\times(1-0.40)=\\\\ Sale\text{ }price=\$149\times0.60=\\\\ Sale\text{ }price=\$89.40[/tex]

6. $213 ski jacket; 30% discount

            [tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$213\times(1-0.30)=\\\\ Sale\text{ }price=\$213\times0.70=\\\\ Sale\text{ }price=\$149.10[/tex]

7. $595 refrigerator; 20% discount

            [tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$595\times(1-0.20)=\\\\ Sale\text{ }price=\$595\times0.80=\\\\ Sale\text{ }price=\$476.00[/tex]

8. $64 video game; 25% discount

          [tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$64\times(1-0.25)=\\\\ Sale\text{ }price=\$64\times0.75=\\\\ Sale\text{ }price=\$48.00[/tex]

9. $119 croquet set; 50% discount

You should not have problems with this: 50% discount means that you will pay half the price.

Hence, the sale price is:

           [tex]Sale\text{ }price=Orignal\text{ }price/2 \\\\ Sale\text{ }price=\$59.50[/tex]

10. $14.99 clock; 10% discount

            [tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$14.99\times(1-0.10)=\\\\ Sale\text{ }price=\$14.99\times0.90=\\\\ Sale\text{ }price=\$13.49[/tex]

11. A radio is on sale for $50. If this price represents a 10% discount from the original price, what is the original price to the nearest nickel? Hint: need to use a proportion to find the whole.

First note that if the discount is 10%, the sale price is 100% - 10% = 90% of the original price.

Let's set the proportion that represents the proportionality between the two ratios, starting with the fact that $ is the 90% and original price is the 100% (the whole part):

             [tex]\$50/90=x/100[/tex]

              [tex]x=100\times\$50/90=\$55.55[/tex]

Hence, the original price is $55.55

12. A box of laundry detergent is on sale for $6.50. If this price represents a 40% discount from the original price, what is the original price to the nearest cent?

Use the same hint used in the question above: set a proportion.

Remember a 40% discount means that the sale price is 60% of the original price:

              [tex]\$6.50/60=x/100\\ \\ x=100\times\$6.50/60=\$10.83[/tex]

13. Determine the price of a $35 basketball that is on sale for 50% off the regular price.

Again, 50% discount means that the sale price will be half of the original price, or the original price will be double of the sale price.

Here, the original price is $35, hence the sale price is $35/2 = $17.50

14. Dominic bought a new alarm clock that was on sale for $18.75. If this price represents a 30% discount from the original price, what is the original price to the nearest cent?

Since the price is after a 30% discount, the sale price is a 70% of the original price, and you set the proportion:

          [tex]\$18.75/70=x/100[/tex]

Solve for x:

           [tex]x=100\times\$18.75/70=\$26.79[/tex]

15. Michael bought a new fishing rod. The regular price of the fishing rod was $125.99. He bought it on sale with a 15% discount. Sales tax of 3% is applied to the discounted total. What was the sale price with tax of Michael’s fishing rod to the nearest cent?

           [tex]\$125.99\times(1-0.15)=\$125.99\times0.85=\$107.09[/tex]

          [tex]\$107.09\times1.03=\$110.30[/tex]

Hence, the sale price with tax is $110.30

The last answer (# 16) is in the attached file, since this already exceeds the number of characters allowed.

Answer:

20 hours

Step-by-step explanation:

We can change the 3 hours and 20 minutes to "minutes" instead of hours:

1 hour is 60 minutes. So 3 hours is 60 * 3 = 180 minutes.

Add the 20 : 180 + 20 = 200 minutes for one costume.

Multiply by 6 for 6 costumes: 200 * 6 = 1200.

So 1200 minutes or 1200/60 = 20 hours to make 6 costumes

Answer:

Option A, b + 5

Step-by-step explanation:

Step 1:  Determine the equation to find the amount of boys

b + (b + 5) = 27

b:  represents boys

b + 5:  represents girls where they equal 5 more than boys

Answer: Option A, b + 5

Answer:

31+2+48=31+50

30+50+1=81

Step-by-step explanation:

Ms. Killikelly is trying to add two 2-digits numbers by making the groups of tens

So she first tried to make 48 as 50 (i.e. group of five tens) by adding digit 2 of the number 33 to the number 48.

Now she needs to add 31 and 50. She needs to add three groups of tens (i.e. 30) with five groups of tens (i.e. 50) and then add 1(i.e. the remaining 1 of 31) as following

:

[tex]10+10+10+10+10+10+10+10+1=30+50+1=81[tex]  

(because 30=10+10+10 and 50=10+10+10+10+10)

OR simply as follow

30+50+1=81

Step-by-step explanation:

[tex] \frac{1}{4} \: log_4 16 \\ \\ = \frac{1}{4} \: log_4 {4}^{2} \\ \\ = \frac{1}{4} \times 2\: log_4 {4} \\ \\ = \frac{1}{4} \times 2\: \times 1 \\ \\ = \frac{1}{2} \\ \\ \huge \blue{ \boxed{\therefore \: \frac{1}{4} \: log_4 16= \frac{1}{2} }}\\ [/tex]

Answer: - 0.2727

Step-by-step explanation:

Answer:

[tex]Speed\ of\ car=38\ km/h[/tex]

Step-by-step explanation:

Distance Covered by Horse:

[tex]Speed\ of\ horse=50\ km\h=50\times \frac{1000}{60}\ meter/ minute\\\\Speed\ of\ horse=\frac{2500}{3}\ meter/minute\\\\Distance\ covered\ in\ 4\ minutes=speed\times time=\frac{2500}{3}\times 4\\\\Distance\ covered\ in\ 4\ minutes=\frac{10000}{3}\ meters\\\\[/tex]

Distance covered by Car:

[tex]Let\ speed\ of\ car=x\ meter/minute\\\\time=4\ minutes\\\\Distance\ covered=speed\times time=4\times x=4x[/tex]

[tex]Distance\ covered\ by\ horse=Distance\ covered\ by\ car+800\\\\\frac{10000}{3}=4x+800\\\\4x=\frac{10000}{3}-800\\\\4x=\frac{7600}{3}\\\\x=\frac{7600}{3\times 4}\ meter/minute\\\\x=\frac{7600}{3\times 4}\times \frac{60}{1000}\ km/h\\\\x=38\ km/h[/tex]

Final answer:

Jones' horse travels at 833.33 meters per minute, and in 4 minutes it covers 3333.32 meters. The car travels 2533.32 meters in the same time, giving it a speed of 633.33 meters per minute or 38 km/h.

Explanation:

To find out how fast the car was moving, we can begin by converting Jones' speed into meters per minute because the distance is given in meters and time in minutes. Jones moves at 50 km/h which is approximately 833.33 meters per minute (since 50,000 meters in 60 minutes).

Jones catches up to the car in 4 minutes, which means he covers the 800-meter gap plus however far the car travels in that same time. In 4 minutes, Jones travels 4 minutes * 833.33 meters/minute = 3333.32 meters. Therefore, the car must have traveled 3333.32 meters - 800 meters = 2533.32 meters in 4 minutes.

We can then calculate the car's speed by dividing the distance it traveled by the time it took: 2533.32 meters / 4 minutes, which gives us 633.33 meters per minute. To convert this back into kilometers per hour, we multiply by 60 minutes and divide by 1000 meters to get the speed of the car in km/h. This results in 38 km/h as the car's speed.

Any decimal number that lies between 0.15 and 0.7 meets the criteria, such as 0.6, 0.20 or 0.30. In mathematics, there can be infinite possibilities between these values as you can always add more digits after the decimal point.

In mathematics, a decimal number greater than 0.15 and less than 0.7 could be any number that falls within these two boundaries.  For example, 0.6 is a decimal number that would meet these criteria. Alternatively, a number like 0.20 or 0.30 would also satisfy the conditions specified in the question.

Remember, a decimal between two numbers can have infinite possibilities. That's because you can always add more digits after the decimal point (for example, 0.601, 0.602, 0.603, ..., and so on).

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Answer:

86.666666 or 0.01153846153

Answer:

0.0115

Step-by-step explanation:

Answer:

[tex]Final\ grade=79.5[/tex]

Step-by-step explanation:

[tex]Homework\ grade=92\\\\quiz\ grade=68\\\\Test\ grade=81\\\\Final\ Grade=10\%\ of\ homework\ grade+20\%\ of\ quizzes\ grade+70\%\ of\ test\ grade\\\\Final\ Grade=\frac{10}{100}\times 92+\frac{20}{100}\times 68+\frac{70}{100}\times 81\\\\Final\ grade=0.1\times 92+0.2\times 68+0.7\times 81\\\\Final\ grade=9.2+13.6+56.7\\\\Final\ grade=79.5[/tex]

Final answer:

The final grade, calculated by weighting the individual grades for homework, quizzes, and tests, and then applying standard rounding rules, would be a rounded grade of 80.

Explanation:

To calculate the final grade based on the given weights, multiply each individual grade by its respective percentage and then add the results together. Here's a step-by-step calculation:

Homework: 92 (weight 10%) -> 92 x 0.10 = 9.2

Quizzes: 68 (weight 20%) -> 68 x 0.20 = 13.6

Tests: 81 (weight 70%) -> 81 x 0.70 = 56.7

Add these results together to get the final grade:

9.2 (Homework) + 13.6 (Quizzes) + 56.7 (Tests) = 79.5

Using standard rules for rounding, 79.5 would be rounded to 80, which is typically a 'B' grade.

Answer:173.5

Step-by-step explanation:87.9+85.6 =173.5

you have to use absolute value to turn them both positive

Hope this helps

First divide the commission by the number sold:

225/5 = 45

300/8 = 37.5 since the commission is a different amount it is not just multiplication so the last two answers are not correct.

Since for 5 the commission was 45 but for 8 it was less than 45, the equation can’t use 45 as a multiplier

The answer has to be E= 25s + 100

Answer:

Step-by-step explanation:

Simple interest I = P×R×T/100

P = $575

T = 1year

R = 5%

I = $(575 × 5 × 1)/100

I = $ 28.75

Answer:

Baked Potato

Step-by-step-explanation:

      Go ahead to the nearest grocery or supermarket, and buy a plain potato, go back home and take the plastic off of it, put it in the microwave on it's side for around 6 or 7 minutes, depending how burnt you like it, 6 is normal, 7 is a little bit burnt. Take it out with an oven mitt, as it will be very hot, and flip it over on the other side and put it in the microwave on the side for that many minutes as you did before. After the timer, take it out with something on your hands to protect them, then slit the middle with a knife, and add some butter and mash it around, and enjoy!

Answer:

76

Step-by-step explanation:

Given that in one morning, a diner chef had 176 breakfast orders.

Now, a circular graph shows the types of orders and it shows that 43% of the total labeled as the Eggs order.

We have to find the number of orders were there for eggs.

Now, it will be 43% of total breakfast orders i.e. 176.

Hence, it was [tex]176 \times \frac{43}{100} = 75.68[/tex] ≈ 76 (Answer)

To find the quantity of egg orders, we multiply the total number of orders (176) by the percentage of orders for eggs (43%). The result, 75.68, is rounded to the nearest whole number to get 76 orders.

The question is about calculating a certain percentage of the total number of breakfast orders. Given that the total number of orders is 176 and the percentage of orders that were for eggs is 43%, we can calculate the number of egg orders by multiplying 176 by 43% (or 0.43 as a decimal).

To calculate this, take the total number of breakfast orders and multiply it by the percentage of orders that were for eggs. In this case, that would be 176 (the total orders) multiplied by 0.43 (the percentage of orders made up of eggs).

Here's how to calculate it: 176 * 0.43 = 75.68 Because we can't really have a fraction of an order, we'll round to the nearest whole number, which gives us 76 orders.

Therefore, the answer is c) 76.

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Answer:

Step-by-step explanation:

1/2x-33/2=1/2(x-33)

The process of factoring 1/2 out of the equation 1/2x - 33/2 involves dividing each term in the expression by 1/2. This process yields the result x - 33.

To factor 1/2 out of the expression 1/2x - 33/2, you perform the factoring by dividing every term in the expression by 1/2. In mathematics, factoring is a crucial concept and is widely used in simplifying expressions, solving quadratic equations, and multiple other scenarios. So, the factoring works as follows:

Hence, when you factor 1/2 out of 1/2x - 33/2, the result is x - 33.

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Answer:

The value in decemal form would be 14.66287829 or 14.66287

Step-by-step explanation:

√ 215