A baseball diamond is a square with corners at home plate, first base, second base, and third base. The distance between home plate and first base is 30 yards. What is the area of a baseball diamond?
A.
900 square yards
B.
120 square yards
C.
90 square yards

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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[tex]\frac{1}{7} -3(\frac{3}{7}h -\frac{2}{7}) = \frac{7-9h}{7}[/tex]

Solution:

Given expression is:

[tex]\frac{1}{7} -3(\frac{3}{7}h -\frac{2}{7})[/tex]

We have to combine the like terms

From given expression,

[tex]\frac{1}{7} -3(\frac{3}{7}h -\frac{2}{7})[/tex]

By distributive property,

The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

a(b + c) = ab + bc

Therefore,

Solve for brackets using distributive property

[tex]\frac{1}{7} - (3 \times \frac{3}{7}h) + (3 \times \frac{2}{7})\\\\\frac{1}{7} - \frac{9h}{7} + \frac{6}{7}[/tex]

Add 1/7 and 6/7

[tex]\frac{1}{7} + \frac{6}{7} -\frac{9h}{7}\\\\\frac{1+6}{7} -\frac{9h}{7}\\\\Simplify\\\\\frac{7}{7}-\frac{9h}{7}\\\\1-\frac{9h}{7}\\\\Simplify\\\\\frac{7-9h}{7}[/tex]

Thus the equivalent expression is found

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:

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.

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.

When constructing a triangle with given side lengths, the possible range for the third side can be determined by adding and subtracting the lengths of the existing sides. Side lengths of 4, 10, and 14 inches are not possible choices for the third side length.

The third side of a triangle must be less than the sum but greater than the difference of the other two sides. Given sides of 6 inches and 8 inches:

Therefore, the lengths of the sides 4, 10, and 14 inches are not possible.

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:

£28+£16(each half hour)

£28+£48= £76

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

Answer:

Judy

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:

86.666666 or 0.01153846153

Answer:

0.0115

Step-by-step explanation:

Answer: - 0.2727

Step-by-step explanation:

Answer:

Andy had 3 apples, and his mom surprised him with x apples. His mom told him that he had 8 apples in total. As he counted the apples he found out his mom gave him 5 apples By subtracting 8 and 3.

Step-by-step explanation:

The inequality is:

[tex]70+6x\geq 150[/tex]

You must do more than 14 sales to get at least $ 150

Solution:

Given that,

As a salesperson you are paid $70 per week plus $6 per sale

Let "x" be the number of sales

This week you want your pay to be at least $150

We have to frame a inequality to represent the number of sales you need to make to achieve your goal

This week he must earn at least $ 150

Thus, he can spend $ 150 or more then 150 also

So we have to use "greater than or equal to" symbol

From given,

[tex]70 + 6(\text{number of sales})\geq 150[/tex]

[tex]70+6x\geq 150[/tex]

Thus the inequality is found

Solve the inequality

[tex]70+6x\geq 150\\\\Subtract\ 70\ from\ both\ sides\\\\6x\geq 150-70\\\\6x\geq 80\\\\Divide\ both\ sides\ by\ 6\\\\x\geq 13.3\\\\Thus\ approximately\ we\ get\\\\x\geq 14[/tex]

So he must do more than 14 sales to get at least $ 150

Number of adults = 264

Number of children= 127

Step-by-step explanation:

Let the number of adults be......x

Let the number of children be.....y

The total number of people that used the public swimming pool is given as 391. This means

x+y=391

The total cost per the receipt is : $752.75

This means, 2.25 x+ 1.25 y = 752.75

The two equations are;

x+y=391  ...........(i)

2.25 x+ 1.25 y = 752.75...........(ii)

Making the x variable equal to eliminate x

2.25x + 2.25 y = 879.75

2.25x + 1.25 y = 752.75

Apply subtraction as

1.00 y = 127.00

y=127

Use the value of y in equation (i)

x+y=391

x+127=391

x=391-127=264

Number of adults = 264

Number of children= 127

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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:

Apply the distributive property.

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Simplify by adding terms.

Tap for fewer steps...

Subtract  

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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.

A. Inverse

Basically, inverse Property of Addition states that if you add any number added to its opposite the result will be equal zero. So, here we have the following equation:

[tex]x + 12 = 47[/tex]

Adding -12 to both sides we get:

[tex]x + 12 - 12= 47-12 \\ \\ \\ But \ 12+(-12)=0 \\ \\ \\ So: \\ \\ x + 0= 35 \\ \\ Finally: \\ \\ \boxed{x=35}[/tex]

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Answer:

A. Inverse

Step-by-step explanation:

The given equation is [tex]x+12=47[/tex]

To solve this equation, we use the inverse property of addition.

We add the additive inverse of 12 to both sides to get:

[tex]x+12-12=47-12[/tex]

We then simplify to obtain:

[tex]x+0=35[/tex]

This gives us  x=35.

The correct answer is A

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:

Anya spend the most money

Answer:

look at the picture shown

Answer:

22

Step-by-step explanation: