write 171 miles in 3 hours as a unit rate

Final answer:

There are 27,405,5040 different ways the medals can be awarded to the 32 students.

Explanation:

In this problem, we need to find the number of different ways the 6 medals can be awarded to the 32 students. To solve this, we can use the concept of permutations. There are 32 students competing for the first medal, so there are 32 choices for that medal. Once the first medal is awarded, there are 31 students remaining to compete for the second medal, so there are 31 choices for that medal. We continue this process until all 6 medals have been awarded. Therefore, the total number of different ways the medals can be awarded is 32 * 31 * 30 * 29 * 28 * 27 = 27,405,5040.

The statement is option (A) ∠ ADB and ∠CBD satisfies the alternate interior angle theorem.

A rectangle is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. It is four-sided polygon in which the opposite sides are parallel and equal to each other.

For the given situation,

The diagram below shows the rectangle ABCD.

The diagonals AC and BD are drawn.

From the diagram,

According to alternate interior angle theorem, [tex]\angle ADB[/tex] and [tex]\angle CBD[/tex] are alternate interior angles .

Hence we can conclude that the statement is option (A) ∠ ADB and ∠CBD satisfies the alternate interior angle theorem.

Learn more about the rectangles here

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Final answer:

Kara will pay $55.68 for the dress after a 15% discount is applied to the original price of $65.50.

Explanation:

Kara wants to buy a dress with an original price of $65.50, and there is a 15% discount on it.

To find out how much Kara will pay for the dress after the discount, we first need to calculate the amount of the discount.

To do this, we convert the percentage to a decimal by dividing by 100 (15% = 0.15) and then multiply it by the original price of the dress.

The amount of the discount is:

$65.50 × 0.15 = $9.825.

To find out the final price that Kara pays, we subtract the discount from the original price:

$65.50 - $9.825 = $55.675.

However, stores usually round the price to the nearest cent, so Kara would pay $55.68 for the dress after the discount is applied.

Answer:

40

Step-by-step explanation:

because its just easy trust me it is !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! i just need points but fr fr its 40

Answer:  The correct option is (D) 147 sq. units.

Step-by-step explanation:  We Re given to find the area of the polygon shown in the figure.

Let us divide the given polygon in two rectangles A and B as shown in the attached figure below.

The dimensions of rectangle A are

length, l = 10 units  and  breadth, b = 3 units.

So, the area of rectangle A is given by

[tex]AREA_A=l\times b=10\times3=30~\textup{sq. units}.[/tex]

And, the dimensions of rectangle B are

length, l' = 13 units  and  breadth, b' = 12 - 3 = 9 units.

So, the area of rectangle B is given by

[tex]AREA_B=l'\times b'=13\times9=117~\textup{sq. units}.[/tex]

Therefore, the area of the polygon is

[tex]AREA=AREA_A+AREA_B=30+117=147~\textup{sq. units}.[/tex]

Thus, the required area of th given polygon is 147 sq. units.

Option (D) is CORRECT.

The greatest number of weights the trainer can purchase is 17.

To find the maximum number of weights the trainer can purchase, we need to divide the trainer's total budget by the cost of each weight.

Step 1: Find the cost of weights per trainer's budget: $156 - $78 = $78

Step 2: Divide the cost of weights by the cost of each weight: $78 / $4.50 = 17.33

Since you cannot purchase a fraction of a weight, the trainer can purchase a maximum of 17 weights.

Final answer:

To determine a fair price for a lottery ticket, calculate the expected value by adding the product of the probabilities and outcomes of all prizes. In the given raffle scenario, the fair price would be $0.35, which is the expected value of a ticket.

Explanation:

The question pertains to the concept of expected value in probability, which is often used to determine a fair price for lottery tickets. Expected value is calculated by multiplying the probability of each outcome by the payout of that outcome and then summing these products. In a raffle with 250 prizes of $5, 50 prizes of $25, and 10 prizes of $100, with 10,000 tickets sold, we can calculate the expected value as follows:

Expected value from $5 prizes = (250 prizes * $5) / 10,000 tickets = $0.125

Expected value from $25 prizes = (50 prizes * $25) / 10,000 tickets = $0.125

Expected value from $100 prizes = (10 prizes * $100) / 10,000 tickets = $0.100

Adding these up, the expected value of a ticket is $0.125 + $0.125 + $0.100 = $0.35. Therefore, a fair price for a ticket would be $0.35 to break even.

The probability of getting exactly 3 tails when flipping a fair coin 5 times is 0.3125, or [tex]\( 31.25\% \)[/tex]. This means that in about 31.25% of the cases, when flipping a fair coin 5 times, exactly 3 of those flips will result in tails.

To find the probability of getting exactly 3 tails when flipping a fair coin 5 times, we can use the binomial probability formula. In a binomial experiment like this, where there are only two possible outcomes (heads or tails) and each trial is independent and has the same probability of success (50% for a fair coin), we can use the binomial probability formula:

[tex]\[ P(X = k) = \binom{n}{k} \times p^k \times (1-p)^{n-k} \][/tex]

Where:

- P(X = k) is the probability of getting exactly k successes (tails, in this case).

- n is the number of trials (5 flips).

- k is the number of successes (3 tails).

- p is the probability of success on each trial (0.5 for a fair coin).

- (1-p) is the probability of failure on each trial.

Substituting the given values into the formula:

[tex]\[ P(X = 3) = \binom{5}{3} \times (0.5)^3 \times (1-0.5)^{5-3} \][/tex]

[tex]\[ P(X = 3) = \binom{5}{3} \times 0.5^3 \times 0.5^2 \][/tex]

[tex]\[ P(X = 3) = \frac{5!}{3!(5-3)!} \times 0.5^3 \times 0.5^2 \][/tex]

[tex]\[ P(X = 3) = \frac{5 \times 4}{2 \times 1} \times 0.125 \times 0.25 \][/tex]

[tex]\[ P(X = 3) = 10 \times 0.125 \times 0.25 \][/tex]

[tex]\[ P(X = 3) = 0.3125 \][/tex]

So, the probability of getting exactly 3 tails when flipping a fair coin 5 times is 0.3125, or [tex]\( 31.25\% \)[/tex].

This means that in about 31.25% of the cases, when flipping a fair coin 5 times, exactly 3 of those flips will result in tails.

(X+3)^2-x^2=39  x^2+6X+9-x^2=39 6x+9=39. 6x=30 x =5 x+3=8

2x+2 + 5x+3 = 180

7x+5 = 180

7x = 175

x = 175/7 = 25

x = 25