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postnew [5]
3 years ago
10

In ∆ABC, m<A = 72 and m<B = 83. What is the measure of <C?​

Mathematics
2 answers:
mart [117]3 years ago
7 0

Answer:

25

Step-by-step explanation:

<em>Theorem:</em>

<em>The sum of the measures of the interior angles of a triangle is 180 degrees.</em>

The theorem is can be written as the equation below.

m<A + m<B + m<C = 180

We know the measures of angles A and B, so we substitute the values for those measures, and we solve for the measure of angle C.

72 + 83 + m<C = 180

Add like terms on the left side.

155 + m<C = 180

Subtract 155 from both sides.

m<C = 25

Answer: m<C = 25

Anna007 [38]3 years ago
3 0

Answer:

25 degrees.

Step-by-step explanation:

The 3 angles in a triangle  add up to 180 degrees therefore:

m < C = 180 - 72 - 83

=  180 - 155

= 25 degrees.

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In a population where 77% of voters prefer Candidate A, an organization conducts a poll of 19 voters. Find the probability that
Rus_ich [418]

Answer:

P(X=14)=(19C14)(0.77)^{14} (1-0.77)^{19-14}=0.1928

Then the probability that 14 of the 19 voters will prefer Candidate A is approximately 0.1928 or 19.28%

Step-by-step explanation:

We can define X the random variable of interest "number of voters that will prefer Candidate A", since we have a sample size given and a probability of success we can use the binomial distribution to model the random variable. And on this case we can assume the following distribution:

X \sim Binom(n=19, p=0.77)

The probability mass function for the Binomial distribution is given by:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

For this problem we want to find this probability:

P(X=14)

And usign the probability mass function defined before we got:

P(X=14)=(19C14)(0.77)^{14} (1-0.77)^{19-14}=0.1928

Then the probability that 14 of the 19 voters will prefer Candidate A is approximately 0.1928 or 19.28%

3 0
3 years ago
Keira , larry and gita picked apples at an orchard. keira picked twice as many pounds as larry and 3 times as many as gita. the
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Hope this helps
6 0
3 years ago
Determine whether f(x) and g(x) are inverses. Show your work.
MrMuchimi
Answer:

f(x) and g(x) are inverses

Explanation:\begin{gathered} f(x)\text{ = }\frac{1}{x-5}+8 \\ g(x)\text{ = }\frac{1}{x\text{ - 8 }}\text{ + 5} \end{gathered}

To find:

To determine whether f(x) and g(x) are inverses

For two function to be inverse of ech other, f(g(x))) = x and g(f(x)) = x. We will find the value/expression of f((g(x)) and g(f(x))

\begin{gathered} f(g(x))\text{ = }\frac{1}{\frac{1}{x\text{ - 8}}+\text{ 5 -5}}+8 \\  \\ f(g(x))\text{ = }\frac{1}{\frac{1}{x\text{ - 8}}}\text{ + 8 = 1 }\times\frac{x-8}{1}\text{ + 8} \\  \\ f(g(x))\text{ = x - 8 + 8} \\ f(g(x))\text{ = x} \end{gathered}\begin{gathered} g(f(x))\text{ = }\frac{1}{\frac{1}{x\text{ - 5}}+8-8}\text{+ 5} \\ g(f(x))\text{ = }\frac{1}{\frac{1}{x-5}}+5 \\ g(f(x))\text{ = x - 5 + 5} \\ g(f(x\text{\rparen\rparen = x} \end{gathered}

Since f(g(x)) = x and g(f(x)) = x

Then f(x) and g(x) are inverses

6 0
1 year ago
THE DOTS SHOWN REPRESENT WHAT KIND OF SEQUENCE?
Juli2301 [7.4K]
The dots are getting bigger so i would say the third or last option.
5 0
3 years ago
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