Explain how you can use the Triangle Sum Theorem to find the measures of the angles in an equilateral triangle.The angles of an equilateral triangle are . Let the measure of each angle be x. Then, by the Triangle Sum Theorem, x + x + x = 3x = °_. Solving for x gives x = °.

Answers

Answer 1

Answer:

Answers:

The first blank is 180

The second blank is 60

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The triangle sum theorem basically says that adding up all three angles of any triangle always leads to 180 degrees. So that's why

(angle1)+(angle2)+(angle3) = 180

x+x+x = 180

3x = 180

Divide both sides of that last equation by 3. This is to undo the multiplication of 3 done to x.

3x = 180

3x/3 = 180/3 ... divide both sides by 3

x = 60

Each angle of this equilateral triangle is 60 degrees. In an equilateral triangle, all three sides are the same length. Also in an equilateral triangle, all three angles are the same measure and always 60 degrees.

Answer 2

Answer:

Final answer:

The Triangle Sum Theorem says that all angles in a triangle add up to 180 degrees. In an equilateral triangle, all angles are equal. Hence, each angle is 60 degrees.

Explanation:

The Triangle Sum Theorem states that the sum of the measures of the angles in a triangle is always 180 degrees. Now, in an equilateral triangle, all angles are equal. Let's denote the measure of each angle with x. According to the theorem, the sum of these measures is x + x + x = 180. Simplifying this gives 3x = 180. Hence, solving for x, which refers to the measure of each angle in the equilateral triangle, we get x = 180 / 3 = 60 degrees. Thus, each angle in an equilateral triangle measures 60 degrees.

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true

Step-by-step explanation:

Answer:

true?

Step-by-step explanation:

If x - 10 = -15, then find the value of 5x - 30 *

Answers

Answer:

The value is -55

In the equation x-10=-15, x is equal to -5.

Therefore, the value of x is plugged into the second equation and the value found is -55.

Answer:

x = -55

Step-by-step explanation:

We know that x - 10 = -15 and we want to find the value of 5x - 30 but our first step would be to find the value x so then we can can substitute that back into the expression so

x - 10 = -15

⇔ Add -10 to both sides to isolate x

x = -5

So now we know that value of 'x' is -5 we can substitute it back into the expression 5x - 30 so

5x - 30

→ Substitute x = -5 back into it

5 × -5 - 30

→ Simplify

-25 - 30 = -55

If x - 10 = -15, then find the value of 5x - 30 the value of x is -55

Answer below
5*____= 1

Answers

Answer:

Step-by-step explanation:

just keep the first number and flip the sign and it would be 1 i think idrk

50 pts Alessandro wrote the quadratic equation -6=x^2+4x-1 in standard form. What is the value of c in his new equation? c= -6 c= -1 c= 5 c= 7

Answers

Answer:

Step-by-step explanation: c on edg

Answer: c=5

Step-by-step explanation:

C on edg got 100%

In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random and without replacement. Suppose that six of the tanks contain material in which the viscosity exceeds the customer requirements. a. What is the probability that exactly one tank in the sample contains high-viscosity material?
b. What is the probability that at least one tank in the sample contains high-viscosity material?
c. In addition to the six tanks with high viscosity levels, four different tanks contain material with high impurities. What is the probability that exactly one tank in the sample contains high-viscosity material and exactly one tank in the sample contains material with high impurities?

Answers

Answer:

a) P(A) = 0,4607 or P(A) = 46,07 %

b) P(B) = 0,7120 or 71,2 %

c) P(C) = 0,2055 or P(C) = 20,55 %

Step-by-step explanation:

We will use two concepts in solving this problem.

1.- The probability of an event (A) is for definition:

P(A) = Number of favorable events/ Total number of events FE/TE

2.- If A and B are complementary events ( the sum of them is equal to 1) then:

P(A) = 1 - P(B)

a) The total number of events is:

C ( 24,4) = 24! / 4! ( 24 - 4 )! ⇒ C ( 24,4) = 24! / 4! * 20!

C ( 24,4) = 24*23*22*21*20! / 4! * 20!

C ( 24,4) = 24*23*22*21/4*3*2

C ( 24,4) = 24*23*22*21/4*3*2 ⇒ C ( 24,4) = 10626

TE = 10626

Splitting the group of tanks in two 6 with h-v and 24-6 (18) without h-v

we get that total number of favorable events is the product of:

FE = 6* C ( 18, 3) = 6 * 18! / 3!*15! = 18*17*16*15!/15!

FE = 4896

Then P(A) ( 1 tank in the sample contains h-v material is:

P(A) = 4896/10626

P(A) = 0,4607 or P(A) = 46,07 %

b) P(B) will be the probability of at least 1 tank contains h-v

P(B) = 1 - P ( no one tank with h-v)

Again Total number of events is 10626

The total number of favorable events for the ocurrence of P is C (18,4)

FE = C (18,4) = 18! / 14!*4! = 18*17*16*15*14!/14!*4!

FE = 18*17*16*15/4*3*2 = 3060

Then P = 3060/10626

P = 0,2879

And the probability we are looking for is

P(B) = 1 - 0,2879

P(B) = 0,7120 or 71,2 %

c) We call P(C) the probability of finding exactly 1 tank with h-v and t-i

having 4 with t-i tanks is:

reasoning the same way but now having 4 with t-i (impurities) number of favorable events is:

FE = 6*4* C(14,2) = 24 * 14!/12!*2!

FE = 24* 14*13*12! / 12!*2

FE = 24*14*13/2 ⇒ FE = 2184

And again as the TE = 10626

P(C) = 2184/ 10626

P(C) = 0,2055 or P(C) = 20,55 %

Final answer:

These problems relate to the field of probability and specifically utilize the Hypergeometric Distribution. By plugging data into the appropriate formula, we can find the probabilities. For instance, the joint probability of independent events can be used to find the chance of exactly one tank having high viscosity and one tank having high impurities.

Explanation:

This question is asking us to solve probability problems. It specifically related to the Hypergeometric Distribution, which is used when we're interested in success/failure outcomes (in this case, tanks with high or acceptable viscosity), and when we're sampling without replacement.

For part a, we are looking for the probability of picking exactly one tank with high-viscosity. We would calculate this using the hypergeometric distribution formula:

P(X=k) = (C(K, k) * C(N-K, n-k)) / C(N, n)

where K is the total number of success states in the population (6 tanks with high viscosity), k is the number of success states in the sample (1 tank), N is the population size (24 tanks), and n is the number of samples (4 tanks). Plugging these numbers in, we can find the answer.

For part b, to find the probability that at least one tank in the sample contains high-viscosity material, we can either sum the probabilities P(X=1), P(X=2), P(X=3), and P(X=4), or find the complement of the probability that none of the tanks have high viscosity, i.e., 1- P(X=0).

For part c, with the addition of 4 tanks with high impurities, we can use the joint probability of independent events, which is the product of the probabilities of the two independent events. Here, the probability that exactly one tank has high viscosity and exactly one tank has high impurities would be the product of the two individual probabilities calculated in a similar manner.

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A study conducted at a certain college shows that 54% of the school's graduates move to a different state after graduating. Find the probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

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Answer:

99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they move to a different state, or they do not. The probability of a graduate moving to a different state is independent of other graduates. So 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.

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