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Naddik [55]
3 years ago
12

Heather Johnson bought a new set of tires for $436.00 and a car seat for $22.85. The state tax rate is 6%, the county tax rate i

s 1.5%, and the city tax rate is 0.5%. What is the total purchase price?
Mathematics
1 answer:
Papessa [141]3 years ago
5 0

Answer:

$495.56

Step-by-step explanation:

Tax increases the price paid for a good or service. So, the total price paid for the goods would increase by the total amount of tax

Sum of the three taxes = 6% + 1.5% + 0.5% = 8%

Total cost of items purchased = $436 + $22.85 = $485.85

Total purchase price = Total cost of items purchased x (1 + total tax)

$485.85 x (1.08) = $495.56

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Mr. Garcia has been asked to give 6 desks to Mrs. Johnson. He needs to keep at least 17 desks for his students. He created a mod
kumpel [21]

Answer:

The inequality which represents the model for this situation is x-6\geq 17.

Step-by-step explanation:

Let Mr. Garcia has x number of desks initially.

He has been asked to give 6 desks to Mrs. Johnson.

Also, he needs to keep at least 17 desks for his students.

So, after giving 6 desks to Mrs. Johnson from the total number of desks he has, he must have at least 17 desks for his students.

Therefore, the inequality is: x-6\geq 17.

Hence, the inequality which represents the model for this situation is x-6\geq 17.

8 0
2 years ago
The school district does not have to pay the 8% sales tax on the $2,992.50 purchase. Estimate the amount of sales tax the distri
grigory [225]

Answer:

$239.40

Step-by-step explanation:

$2,992.50 × 0.08

$239.40

I arrived at this estimate based on my work shown above.

4 0
3 years ago
WILL GIVE BRAINLIEST PLEASE HELP<br> Write the equation and show work. Find 'x" and ' TK'
marishachu [46]

Answer:

x=6

TK=72

Step-by-step explanation:

Because there are two smaller lines drawn in lines TA and AK, it means that the length of TA is the same as AK.

Hence, 6x=4x+12

Subtract 4x from both sides:

6x-4x=4x+12-4x

2x=12

Divide both sides by 2:

\frac{2x}{2}=\frac{12}{2}

x=6

To find TK,

6x+4x+12=10x+12=10\times 6+12=60+12=72

4 0
3 years ago
A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi
mestny [16]

Answer:

  • Base Length of 84cm
  • Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, V=x^2h=296352

h=\dfrac{296352}{x^2}

Surface Area of the box = Base Area + Area of 4 sides

A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}

Step 2: Find the derivative of A(x)

If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}

Step 3: Set A'(x)=0 and solve for x

A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42

Therefore, the dimensions that minimizes the box surface area are:

  • Base Length of 84cm
  • Height of 42 cm.
5 0
3 years ago
A car depreciated $2000 each year it was owned and driven. What type of depreciation is this?
Greeley [361]
Straight line depreciation, the value of the car is given by the following equation, where V is the value of the car, and O is the original value of the car, and x is the number of years since buying the car. V=O-2x This equation follows the form of a straight line, that is: y=mx+b
3 0
3 years ago
Read 2 more answers
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