In triangle ABC, the measure of angle B is 90 degrees, BC=16, and AC=20. triangle DEF is similar to triangle ABC, where vertices D, E, and F corresponds to vertices A, B, and C, respectively, and each side of triangle DEF is 1/3 the length of the corresponding side of triangle ABC. what is the value of sinF?(please show your work)

Answers

Answer 1

Answer: The third side of triangle ABC is AB. Using the Pythagorean Theorem, its length is 12.
12² + 16² = 20²

∠F is congruent to ∠C and so the sin(∠F) = sin(∠C)

The sin(∠C) = opposite/hypotenuse
= |AB| / |AC|
= 12/20
= 3/5
= 0.6

So the answer is 0.6.

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Perry can fill a sorter with oranges from the conveyer belt in 10 minutes. While Perry fills the sorter, Gillian takes oranges out of the sorter and puts them in shipping crates. With Gillian taking oranges out of the sorter, it takes 25 minutes for Perry to fill the sorter.Which of the following can be used to determine the amount of time it takes for Gillian to empty the sorter if Perry does not add oranges? A) 1 over 10 minus 1 over x equals 1 over 25 B) 1 over 10 minus 1 over 25 equals 1 over x C) 1 over 25 minus 1 over x equals 1 over 10 D) 1 over 10 minus 1 over x equals x over 25
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Isabel bought a new jacket for $48 before tax. She paid 6.5% in sales tax. How much was the sales tax?A)$2.68
B)$2.92
C)$3.12
D)$3.08

Answers

Basing on the data provide above, if Isabel bought the jacket for $48.00 and sales tax is equal to 6.5% which is basically 0.065, we can multiply 0.065 * 48.00 which will be equal to $3.12. So going back to the options the answer is C. which is $3.12.

Owen’s grandmother put some money into his savings account on the day he was born. Today, Owen turns 18 years old, and he’s discovered that he has earned $225 in simple interest on his grandmother’s money. If the yearly interest rate was 5%, how much money did his grandmother deposit at the time of his birth?

Answers

Answer:

Step-by-step explanation:

The formula for simple interest is prt = I, where p is the initial investment (our unknown in this case), r is the interest rate in decimal form, t is the time in years, and I is the interest earned. That is NOT the same as the amount of money in the account t years later.

For us,

p = ??,

r = .05,

t = 18, and

I = 225.

Filling in:

p(.05)(18) = 225 and

.9p = 225 so

p = 250

Answer:

The answer is $250.

Step-by-step explanation:

First, the money that his grandmother deposited is called the principal, P. Substitute the given values into the formula, interest equals principal times rate times time, and solve for P. Here, I is 225 dollars and t is 18 years.

Next, the percent given represents the interest rate, r, but first it must be changed to a decimal. To change it, move the decimal point 2 places to the left.

Now, multiply point 0, 5, and 18 to simplify the right side of the equation. The product is point nine.

Finally, divide both sides of the equation by .9 . The result is P equals $225 The principal, or original deposit, is $250.

HELP PLEASE!!!1.) True or False: "The sum of all the probabilities of outcomes of an event is equal to 100.

2.) If I roll a fair die 100 times, about how many times would I roll a 4?
A.) 25 times
B.) 67 times
C.) 17 times
D.) There is not enough information to answer.

Answers

Answer:

1. false

2. 17 times

Step-by-step explanation:

The sum of all the probabilities of outcomes of an event is equal to 1

2. A die has 1,2,3,4,5,6

P(4) = number of 4's/ total numbers

= 1/6

Multiply the number of roll's by the probability of getting a 4

100 *1/6 = 50/3 = 16 2/3

This is approximately 17

What is the value of x in the equation of 8x - 5 = 6x + 1

Answers

Answer:

Step-by-step explanation:

8x - 5 = 6x + 1

2x - 5 = 1

2x = 6

x = 3

Answer: X = 3

Step-by-step explanation: 8x - 5 = 6x + 1

+5 +5

8x = 6x + 6

-6x -6x

2x = 6

2x/2= 6/2

X = 3

Help plz i will make u a brainllest 24.Can you use the SSS Postulate or the SAS Postulate to prove abd=dca? 26 28

Answers

Answer: 24) C. SSS only

26) D. DH = HF

Step-by-step explanation:

24.

Statement Reason

1. BD = CA 1. Given

2. AB = CD 2. Given

3. AD = AD 3. Reflexive Property

4. ΔABD = ΔDCA 4. SSS Congruency Theorem

We have no information about the angles so cannot use SAS Theorem.

26. G H F

E H D

Line up the letters to find the congruent sides:

⇒ GH = EH

HF = HD

GF = ED

Bob and Mark talk about their families. Bob says he has 3 kids, the product of their ages is 72. He gives another clue: the sum of the ages of his children. Mark points out that there is still not enough information to accurately guess. Finally, Bob says, "My youngest child called Justice." Mark can then correctly determine the ages of Bob's children. What are the ages?

Answers

I have answered this question before.

Given:
Bob has three kids whose ages has the product of 72. I will only be able to give you a set of 3 numbers to represent the ages. Had the sum of the ages been given, the specific ages would be provided.

I just did a prime factorization of 72.

72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 =   9
9 ÷ 3 = 3
3 ÷ 3 = 1

1 x 2 x 2 x 2 x 3 x 3 = 72   ⇒ 2³ x 3²

There are a lot of possible combinations, here are a few.

1 x 8 x   9 = 72    ⇒ 1 + 8 + 9 = 18
1 x 4 x 18 = 72 ⇒ 1 + 4 + 18 = 23
2 x 4 x   9 = 72 ⇒ 2 + 4 + 9 = 15

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