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3 years ago

From the diagram below, Is m∠A = 105? and Is ∠B = 75?

Mathematics

2 answers:

PilotLPTM [1.2K]3 years ago

7 0

$LINES \: \: AND \: \: ANGLES \\ \\ \\\\In \: the \: attached \: figure \: , \\ \\ Angles \: \: \: a \: \: \: and \: \: \: b \: \:, \: As \: shown \: above \: \\ are \: called \: Co - interior \: angles \\ \\ a \: + \: b \: = \: 180 \: ( \: True \: for \: all \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Co - interior \: angles \: ) \\ \\ In \: the \: given \: question \: \: A \: \: and \: \: 105 \: \: \\ are \: Co - interior \: angles \\ \\ A \: \: + \: \: 105 \: \: = \: \: 180 \\ \: \: \: \: || \: \: A \: \: = \: \: 75 \: degrees \: \: \: || \: \: \: \: \: \: Ans. \\ \\ B \: \: and \: \: 75 \: \: are \: also \: \: Co - interior \: \\ angles\\ \\ B \: \: + \: \: 75 \: \: \: = \: \: 180 \\ \: \: \: \: || \: \: B \: \: = \: \: 105\: degrees \: \: || \: \: \: \: \: \: \: Ans.$

frutty [35]3 years ago

3 0

It is the other way around. Angle A = 75° and angle B = 105°.

105° and A are what they call allied/co-interior angles. They must add up to 180°. A= 180°-105° = 75°.

75° and B must also add up to 180°. 180°-75° = 105°.

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Solve for C.<br> 5/4= -4c + 1/4

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5/4= -4c + 1/4

Inverse operation

$\frac{5}{4} = -4c + \frac{1}{4}$

- 1/4 -1/4

5/4 - 1/4 = 4/4

$\frac{4}{4} = -4c$
-4c/-4 = 4/4 ÷ -4/1

4/4 *- 1/4 = c
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Answer: $c = - \frac{1}{2}$

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2 years ago

1/5 divided by 3 is what

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Answer:

the answer would be 1/15, or approximately 0.067.

Step-by-step explanation:

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2 years ago

What is the minimum value for g(x)=x2−10x 16? enter your answer in the box.

motikmotik

The minimum value for g(x)=x² - 10x + 16 is -9

<h3>How to determine the minimum value?</h3>

The function is given as:

g(x)=x² - 10x + 16

Differentiate the function

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Set the function 0

2x - 10 = 0

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2x = 10

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2 years ago

C) Millennium Park has an outdoor concert theater. Before a concert, the area reserved for special seating is roped off in the s

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Answer:

The converse of Pythagorean Theorem states:

If the square length of the longes side of a triangle is equal to the sum of the squares of the other two sides, then it's a right triangle.

We use the converse of Pythagorean Theorem to prove that a triangle is a right triangle. It's like the inverse use of the theorem. Often, this theorem is used to find the length of a side of a triangle when we already know it's a right triangle. However, when we don't know that is a right triangle, we use the converse to prove it.

Step-by-step explanation:

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2 years ago

Due to a manufacturing error, two cans of regular soda were accidentally filled with diet soda and placed into a 18-pack. Suppos

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Answer:

a) There is a 1.21% probability that both contain diet soda.

b) There is a 79.21% probability that both contain diet soda.

c) $P(X = 2)$ is unusual, $P(X = 0)$ is not unusual

d) There is a 19.58% probability that exactly one is diet and exactly one is regular.

Step-by-step explanation:

There are only two possible outcomes. Either the can has diet soda, or it hasn't. So we use the binomial probability distribution.

Binomial probability distribution

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

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

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.

A number of sucesses $x$ is considered unusually low if $P(X \leq x) \leq 0.05$ and unusually high if $P(X \geq x) \geq 0.05$

In this problem, we have that:

Two cans are randomly chosen, so $n = 2$

Two out of 18 cans are filled with diet coke, so $\pi = \frac{2}{18} = 0.11$

a) Determine the probability that both contain diet soda. P(both diet soda)

That is P(X = 2).

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

$P(X = 2) = C_{2,2}(0.11)^{2}(0.89)^{0} = 0.0121$

There is a 1.21% probability that both contain diet soda.

b)Determine the probability that both contain regular soda. P(both regular)

That is P(X = 0).

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

$P(X = 0) = C_{2,0}(0.11)^{0}(0.89)^{2} = 0.7921$

There is a 79.21% probability that both contain diet soda.

c) Would this be unusual?

We have that $P(X = 2)$ is unusual, since $P(X \geq 2) = P(X = 2) = 0.0121 \leq 0.05$

For P(X = 0), it is not unusually high nor unusually low.

d) Determine the probability that exactly one is diet and exactly one is regular. P(one diet and one regular)

That is P(X = 1).

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

$P(X = 1) = C_{2,1}(0.11)^{1}(0.89)^{1} = 0.1958$

There is a 19.58% probability that exactly one is diet and exactly one is regular.

8 0

3 years ago