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3 years ago

Triangle RSV is congruent to triangle TVS. Find y

Mathematics

2 answers:

arlik [135]3 years ago

4 0

Triangle RSV is congruent to triangle TVS.

So,

|RS|=|TV|

|SV|=|VS|

|VR|=|ST| (They are hypotenuses of the congruent triangles).

|VR|=25

|ST|=4y-2

25 = 4y - 2

4y=27

y=27/4=6.75

y=6.75

diamong [38]3 years ago

3 0

ΔRSV ≡ ΔTVS

⇒ Line ST ≡ Line RV

<u>Solve y:</u>

4y - 2 = 25

4y = 27

y = 6.75

Answer: y = 6.75

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Write an equation that represents the data in the table x 5,10,15,20 y 17,22,27,32

maks197457 [2]

They go up by 12
17-5=12
22-10=12
27-15=12
32-20=12

6 0

3 years ago

In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 11% of voters a

Radda [10]

Answer:

a) 0.0214 = 2.14% probability that none of the people are Independent.

b) 0.8516 = 85.16% probability that fewer than 6 are Independent.

c) 0.8914 = 89.14% probability that more than 2 people are Independent.

Step-by-step explanation:

For each people, there are only two possible outcomes. Either they are independent, or they are not. For each person asked, the probability of them being Independent voters is the same. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

It is believed that 11% of voters are Independent.

This means that $p = 0.11$

A survey asked 33 people to identify themselves as Democrat, Republican, or Independent.

This means that $n = 33$

A. What is the probability that none of the people are Independent?

This is P(X = 0). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{33,0}.(0.11)^{0}.(0.89)^{33} = 0.0214$

0.0214 = 2.14% probability that none of the people are Independent.

B. What is the probability that fewer than 6 are Independent?

This is

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{33,0}.(0.11)^{0}.(0.89)^{33} = 0.0214$

$P(X = 1) = C_{33,1}.(0.11)^{1}.(0.89)^{32} = 0.0872$

$P(X = 2) = C_{33,2}.(0.11)^{2}.(0.89)^{31} = 0.1724$

$P(X = 3) = C_{33,3}.(0.11)^{3}.(0.89)^{30} = 0.2202$

$P(X = 4) = C_{33,4}.(0.11)^{4}.(0.89)^{29} = 0.2041$

$P(X = 5) = C_{33,5}.(0.11)^{5}.(0.89)^{28} = 0.1463$

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0214 + 0.0872 + 0.1724 + 0.2202 + 0.2041 + 0.1463 = 0.8516$

0.8516 = 85.16% probability that fewer than 6 are Independent.

C. What is the probability that more than 2 people are Independent?

This is:

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{33,0}.(0.11)^{0}.(0.89)^{33} = 0.0214$

$P(X = 1) = C_{33,1}.(0.11)^{1}.(0.89)^{32} = 0.0872$

$P(X < 2) = 0.0214 + 0.0872 = 0.1086$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1086 = 0.8914$

0.8914 = 89.14% probability that more than 2 people are Independent.

8 0

3 years ago

Are 2a and 2b like terms ? explain .

djyliett [7]

Answer:

Nope

Step-by-step explanation:

Since they both have different variables they aren’t like terms

4 0

3 years ago

Read 2 more answers

On a map, San Francisco is 7.5 inches from San Diego. The actual distance is 500 miles. The same map shows that Fresno is 3.3 in

Strike441 [17]

If 500 miles is represented by 7.5 inches:
Divide 500 by 7.5
500/7.5 = 66.666
Multiply this by 3.3
66.666*3.3 = 220

The answer is 220 miles

6 0

3 years ago

Read 2 more answers

Complete the recursive formula of the geometric sequence -0.56\,,-5.6\,,-56\,,-560,...−0.56,−5.6,−56,−560,...Minus, 0, point, 56

pentagon [3]

Answer:

The recursive formula is:

Cn = 10C(n-1)

Step-by-step explanation:

Given the geometric sequence.

-0.56, -5.6, -56, -560, ...

The common ratio is

-5.6/-0.56 = -56/-5.6 = -560/-56 = ... = 10

The recursive formula is easily

Cn = C(n-1) × 10

That is a number is ten times the preceding number.

7 0

3 years ago