Please help me and take a picture and show your work

dybincka [34]

Answer:

The information we need is that the angle between the sides (that is, angle TVU for triangle TVU and angle WVX for triangle WVX) need to be equal.

These angles are vertically opposite angles, because they are formed by two lines crossing, so these angles are equal.

Step-by-step explanation:

The SAS Congruence Theorem says that if two triangles have 2 equal sides and the angle between these sides are also equal, the triangles are congruent.

In this question, we know that the sides UV and VW are congruent, as V is the midpoint of UW. We also know that TV = VX, so now we have two equal sides for each triangle.

The information we need is that the angle between the sides (that is, angle TVU for triangle TVU and angle WVX for triangle WVX) need to be equal.

These angles are vertically opposite angles, because they are formed by two lines crossing, so these angles are equal.

Now we can conclude that the triangles are congruent.

7 0

2 years ago

Jasmin has 50 marbles in a bag.20% of the marbles are blue.How many marbles are blue

Minchanka [31]

20% of 100 is 20. divide that by 2 to get 20% of 50. 20/2 is 10. 20% of 50 is 10. There are 10 blue marbles.

Hope it helped :)
Ali

6 0

3 years ago

34% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and a

finlep [7]

Answer:

a) There is a 18.73% probability that exactly two students use credit cards because of the rewards program.

b) There is a 71.62% probability that more than two students use credit cards because of the rewards program.

c) There is a 82% probability that between two and five students, inclusive, use credit cards because of the rewards program.

Step-by-step explanation:

There are only two possible outcomes. Either the student use credit cards because of the rewards program, or they use for other reason. So, we can solve this problem by the binomial distribution.

Binomial probability

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

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

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

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

And $\pi$ is the probability of X happening.

In this problem, we have that:

10 student are sampled, so $n = 10$

34% of college students say they use credit cards because of the rewards program, so $\pi = 0.34$

(a) exactly two

This is P(X = 2).

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

$P(X = 2) = C_{10,2}.(0.34)^{2}.(0.66)^{8} = 0.1873$

There is a 18.73% probability that exactly two students use credit cards because of the rewards program.

(b) more than two

This is $P(X > 2)$ .

Either a value is larger than two, or it is smaller of equal. The sum of the decimal probabilities must be 1. So:

$P(X \leq 2) + P(X > 2) = 1$

$P(X > 2) = 1 - P(X \leq 2)$

In which

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

So

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

$P(X = 0) = C_{10,0}.(0.34)^{0}.(0.66)^{10} = 0.0157$

$P(X = 1) = C_{10,1}.(0.34)^{1}.(0.66)^{9} = 0.0808$

$P(X = 2) = C_{10,2}.(0.34)^{2}.(0.66)^{8} = 0.1873$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0157 + 0.0808 + 0.1873 = 0.2838$

$P(X > 2) = 1 - P(X \leq 2) = 1 - 0.2838 = 0.7162$

There is a 71.62% probability that more than two students use credit cards because of the rewards program.

(c) between two and five inclusive

This is:

$P = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

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

$P(X = 2) = C_{10,2}.(0.34)^{2}.(0.66)^{8} = 0.1873$

$P(X = 3) = C_{10,3}.(0.34)^{3}.(0.66)^{7} = 0.2573$

$P(X = 4) = C_{10,4}.(0.34)^{4}.(0.66)^{6} = 0.2320$

$P(X = 5) = C_{10,5}.(0.34)^{5}.(0.66)^{5} = 0.1434$

$P = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.1873 + 0.2573 + 0.2320 + 0.1434 = 0.82$

There is a 82% probability that between two and five students, inclusive, use credit cards because of the rewards program.

6 0

3 years ago

Prove that the statement (ab)^n=a^n * b^n is true using mathematical induction.

mamaluj [8]

Answer:

see below

Step-by-step explanation:

(ab)^n=a^n * b^n

We need to show that it is true for n=1

assuming that it is true for n = k;

(ab)^n=a^n * b^n

( ab) ^1 = a^1 * b^1

ab = a * b

ab = ab

Then we need to show that it is true for n = ( k+1)

or (ab)^(k+1)=a^( k+1) * b^( k+1)

Starting with

(ab)^k=a^k * b^k given

Multiply each side by ab

ab * (ab)^k= ab *a^k * b^k

( ab) ^ ( k+1) = a^ ( k+1) b^ (k+1)

Therefore, the rule is true for every natural number n

5 0

3 years ago

Read 2 more answers

Pls help this is probably super easy but not for me

san4es73 [151]

Answer:

A. 29 feet

Step-by-step explanation:

Use cos to find the hypotenuse

cos = adj/hp

0.64 = 20/hyp

hyp = 20/0.64

hyp = 31.25

---------------------------

Use Pythagorean Theorem to find the height of tree above eyes

a² + b² = c²

a² + 20² = 31.25²

a² = 31.25² - 20²

a² = 576.5625

a = 24 (to the nearest foot)

-------------------------------

Finally add in the eye height

h = 24 + 5

h = 29 feet

3 0

2 years ago

Read 2 more answers

Please help me and take a picture and show your work​

Please help me and take a picture and show your work