. Zalia meets her friend at the science museum to see a special exhibition. The admission to the museum is $12.50 plus tax. Zalia pays for herself and her friend. They have lunch at the museum’s cafe. Zalia has a sandwich for $5.95, an apple for $1.25 and a drink for $1.69. She is charged tax and also tips her server 15%. If tax is 7.25%, how much did Zalia pay all total for her day at the science museum?
a.
$41.43
b.
$37.68
c.
$36.35
d.
$24.27

Answer:

Songs cost the same at both stores.

Step-by-step explanation:

Line QR bisects angle PQS. Solve for x and find measure PQS:
m<PQS = 4x - 6, m<PQR = x + 11 ...?

 m<PQR  = (1/2) (m<PQS) = (1/2)( 4x - 6)

    so  x + 11 = 2x - 3 implies x =14

and then m<PQS = 4x - 6 =50°

The total distance Joel walked is 3/4 of a mile.

To find the total distance, we add up the individual distances:

To add these fractions, they must have a common denominator. The least common denominator for 5, 10, and 20 is 20. So we convert the fractions:

Now we add the fractions:

8/20 + 6/20 + 1/20 = 15/20

Finally, we can simplify 15/20 by dividing both the numerator and the denominator by 5:

15/20 = 3/4

Therefore, the total distance Joel walked is 3/4 of a mile.

To find the cost of production for 170 units, consider both fixed costs and variable costs (the integral of the marginal cost function). The cost of producing 171 units can be estimated by adding the marginal cost for the additional unit.

The quantity of interest is C(170), the total cost to produce 170 units. To estimate this value, you can calculate the fixed costs plus the integral of the marginal cost from 1 to 170 (the number of items produced).

So, first, calculate the fixed costs which is given as $13000.

Next, estimate the total variable costs, which is the integral of the marginal cost function over the range from 1 to 170 units. Given marginal cost function is C'(q) = 0.006q^2-q+50. Use the power rule to integrate the function, then evaluate it at q=1 and q=170 and subtract.

The value of C'(170) is simply the value of the marginal cost function at q=170.

After finding the value of C(170) and C'(170), the total cost to produce 171 units, C(171), is approximately the total cost to produce 170 units plus the marginal cost to produce the 171st unit.

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The total is: $ 1345.5

It is given that:

I would like to purchase 20 products at a cost 65.00 per product.

This means that the cost of 20 products will be:

[tex]20\times 65=\$\ 1300[/tex]

Also, there is a sales tax of 3.5%

This means that a person has to pay a extra 3.5% on the total cost of the items he purchased.

i.e. he need to pay 3/5% on $ 1300

This means that the amount of tax he need to pay is: 3.5% of 1300

                                                                              =  3.5%×1300

                                                                             = 0.035×1300

                                                                            = $ 45.5.

Hence, the total cost is: $ 1300+$ 45.5

This means that the total cost is: $ 1345.5

The perimeter of the rectangle is 35.0 meters, and the area is 66.0 square meters, using the formulas for perimeter (2(length + width)) and area (length × width).

To calculate the perimeter and area of a rectangle, we apply the formulas: Perimeter = 2(length + width) and Area = length × width. In this case, the rectangle has a length of 5.50 m and a width of 12.0 m.

Calculating the Perimeter

Perimeter = 2(5.50 m + 12.0 m) = 2(17.5 m) = 35.0 m

Calculating the Area

Area = 5.50 m × 12.0 m = 66.0 m²

The perimeter of this rectangle is 35.0 meters, and the area is 66.0 square meters.

The conversion of fahrenheit to degree celsius for  f = 113 is 45 degree celsius

What is a mathematical expression?

When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression.

Given, formula of temperature conversion of degree celsius to fahrenheit

c=5/9(f-32)

If f = 113

then putting the value on the equation, we get

c = 5/9(113-32)

c = 5/9(81)

c = 5*9

c = 45 degree celsius

Therefore, The conversion of fahrenheit to degree celsius for  f = 113 is 45 degree celsius

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The answer for #5 is C.

Answer: if 3 for every 1000 students quit due serious health issues, then you can see the proportion doing the quotient between this numbers. This is:

3/1000 = 0.003

Then if you choose a random student, you have a 0.003 probability of choosing one who can have a health issue.

and a 0.997 probability to choose a student with no health issues.

Now, the company wins  $50 for the healthy students, and lose ($50 - $8000)  = -$7950 for each student that is sick (because they initially pay the 50$ and latter get the $8000).

Then the insurance company should expect to make in average:

0.997*$50 - 0.003*($7950) = $26

So the company should expect to make 26 dollars per student in a year.

20 is 50 percent of the number 40.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Let 20 is 50% of the number x.

Now, 50% of x=20

0.50×x=20

0.5x=20

x=20/0.5

x=40

Therefore, 20 is 50 percent of the number 40.

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Answer:

The complete factored form of given polynomial  [tex]21x^3+35x^2+9x+15[/tex] is [tex](7x^2+3)(3x+5)[/tex]

Step-by-step explanation:

Given polynomial  [tex]21x^3+35x^2+9x+15[/tex]

We have to factorize the given polynomial completely.

Consider the given polynomial  [tex]21x^3+35x^2+9x+15[/tex]

We will solve it by grouping of terms,

Grouping is collecting terms having some factors common

Taking [tex]7x^2[/tex] common from first two term and 3 from last two terms , we have,

[tex]21x^3+35x^2+9x+15[/tex]

[tex]\Rightarrow 7x^2(3x+5)+3(3x+5)[/tex]

Now taking (3x +5) common from both terms , we have,

[tex]\Rightarrow (7x^2+3)(3x+5)[/tex]

Thus, the complete factored form of given polynomial  [tex]21x^3+35x^2+9x+15[/tex] is [tex](7x^2+3)(3x+5)[/tex]

The converse of the statement “If an angle is a right angle, then it measures 90 degrees” is “If an angle measures 90 degrees, then it is a right angle.”

The converse of the statement “If an angle is a right angle, then it measures 90 degrees” is “If an angle measures 90 degrees, then it is a right angle.” The converse of a conditional statement swaps the hypothesis and conclusion of the original statement. In this case, the original statement states that if an angle is a right angle (hypothesis), then it measures 90 degrees (conclusion). The converse states that if an angle measures 90 degrees (hypothesis), then it is a right angle (conclusion).

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Answer:

{-4, 2} Original poster forgot to add the + sign

Step-by-step explanation:

Solve (x + 6)(x - 4) = -16

{-4, 6}

{-4, 2}

{-12, 22}

Odyssey

Answer:

y is -8 and 4.

Step-by-step explanation:

then d= 44/3.14 

r= 22/3.14

Answer: Martha will earns for 2.5 hours of baby sitting [tex]\approx\$8.13[/tex]

She will earns for 4.0 hours of baby sitting =[tex]\$13[/tex]

She will earns for 5.5 hours of baby sitting =[tex]\approx\$17.88[/tex]

Step-by-step explanation:

Given: Martha earns for each hour of baby sitting = $3.25

Then, Martha will earns for 2.5 hours of baby sitting =[tex]2.5\times3.25=\$8.125\approx\$8.13[/tex]

She will earns for 4.0 hours of baby sitting =[tex]4.0\times3.25=\$13[/tex]

She will earns for 5.5 hours of baby sitting =[tex]5.5\times3.25=\$17.875\approx\$17.88[/tex]

Answer:

1gm/ cm^3

Step-by-step explanation: