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puteri [66]
2 years ago
7

Sales tax on an item is directly proportional to the cost of the item purchased. If the tax on a $600 item is $42, what is the s

ales tax on a $930 item?
Mathematics
1 answer:
Dafna11 [192]2 years ago
4 0
Answer: $65.10

Step-by-step work:

1.Set the ratio
\frac{600}{42}  =  \frac{930}{x}
2.Cross-multiply
600x = 930(42)
600x = 39060
3.Divide to single out x
600x \div 600 = 39060 \div 600
x = 65.10


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terrence made a sphere out of modeling clay. the sphere had a radius of 2 inches. approximately how much modeling clay did terre
navik [9.2K]

Amount of clay used = volume of the sphere

It is given that the radius of the sphere is 2 inches.

Volume of the sphere = \frac{4}{3} \pi r^{3}

=\frac{4}{3} \pi (2^{3} )

=\frac{4}{3} \pi (8)

=\frac{32}{3} \pi

Hence, the amount of modeling clay Terrence used =\frac{32}{3} \pi cubic inches.


5 0
1 year ago
Roberto wants to display his 18 sports cards in an album. Some pages hold 2 cards and others hold 3 cards. How many different wa
Ratling [72]
<span>65 = number of different arrangements of 2 and 3 card pages such that the total number of card slots equals 18. 416,154,290,872,320,000 = number of different ways of arranging 18 cards on the above 65 different arrangements of page sizes. ===== This is a rather badly worded question in that some assumptions aren't mentioned. The assumptions being: 1. The card's are not interchangeable. So number of possible permutations of the 18 cards is 18!. 2. That all of the pages must be filled. Since the least common multiple of 2 and 3 is 6, that means that 2 pages of 3 cards can only be interchanged with 3 pages of 2 cards. So with that said, we have the following configurations. 6x3 card pages. Only 1 possible configuration. 4x3 cards and 3x2 cards. These pages can be arranged in 7!/4!3! = 35 different ways. 2x3 cards and 6x2 cards. These pages can be arranged in 8!/2!6! = 28 ways 9x2 card pages. These can only be arranged in 1 way. So the total number of possible pages and the orders in which that they can be arranged is 1+35+28+1 = 65 possible combinations. Now for each of those 65 possible ways of placing 2 and 3 card pages such that the total number of card spaces is 18 has to be multiplied by the number of possible ways to arrange 18 cards which is 18! = 6402373705728000. So the total amount of arranging those cards is 6402373705728000 * 65 = 416,154,290,872,320,000</span>
7 0
2 years ago
Marco has drawn a line to represent the perpendicular cross-section of the triangular prism. Is he correct? Explain. triangular
evablogger [386]

Answer:

The correct option is;

Yes, the line should be perpendicular to one of the rectangular faces

Step-by-step explanation:

The given information are;

A triangular prism lying on a rectangular base and a line drawn along the slant height

A perpendicular bisector should therefore be perpendicular with reference to the base of the triangular prism such that the cross section will be congruent to the triangular faces

Therefore Marco is correct and the correct option is yes, the line should be perpendicular to one of the rectangular faces (the face the prism is lying on).

8 0
1 year ago
Read 2 more answers
A juice drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of drink on an average. Any overfill
ozzi

Answer:

d. The average is equal to 12 ounces.

Step-by-step explanation:

In this problem, the drink filling machine must be perfectly calibrated at 12 ounces since it needs to be shut down in cases of overfilling (mean > 12 ounces) and underfilling (mean < 12 ounces). Therefore, the correct approach would be to test if the mean is 12 ounces and the correct set of hypothesis would be:

H_0:\mu=12\\H_a:\mu\neq 12

The correct alternative is d. The average is equal to 12 ounces.

5 0
2 years ago
Suppose we have two thermometers. One thermometer is very precise but is delicate and heavy (X). We have another thermometer tha
makvit [3.9K]

Answer:

Step-by-step explanation:

(a)   H0: μ_D=0

      Ha: μ_D ≠ 0

b) Find attached the solution

(c)  By technology,

p - value = 0.4437

Hence, the p-value is 0.4437

8 0
1 year ago
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