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skelet666 [1.2K]
3 years ago
10

Find the measure of the missing angle using the exterior angle sum theorm.

Mathematics
1 answer:
Sliva [168]3 years ago
6 0

Answer:

85°

Step-by-step explanation:

The exterior angle of a triangle is=sum of the opposite interior angles

So

? °=45°+40°

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Deanna gets 3 problems incorrect on her math quiz and scores 85%. How many questions were on the quiz?
katrin2010 [14]

Answer:

There were 20 questions on the quiz

Step-by-step explanation:

In this question, we are concerned with knowing the number of questions on a quiz, given that Deana had a certain percentage after scoring an amount of marks.

We proceed as follows;

Let the number of questions on the quiz be X.

Now, she got 85% by making 3 incorrect choices. This means the percentage of questions she got incorrectly would be 100-85 = 15%

what we are saying is that it is just 15% of her questions that were wrong.

This mathematically;

15% of x = 3

15/100 * x = 3

15x = 3 * 100

15x = 300

x = 300/15

x = 20

5 0
3 years ago
If p is a polynomial show that lim x→ap(x)=p(a
Lostsunrise [7]

Let p(x) be a polynomial, and suppose that a is any real number. Prove that

lim x→a p(x) = p(a) .

 

Solution. Notice that

 

2(−1)4 − 3(−1)3 − 4(−1)2 − (−1) − 1 = 1 .

 

So x − (−1) must divide 2x^4 − 3x^3 − 4x^2 − x − 2. Do polynomial long division to get 2x^4 − 3x^3 − 4x^2 – x – 2 / (x − (−1)) = 2x^3 − 5x^2 + x – 2.

 

Let ε > 0. Set δ = min{ ε/40 , 1}. Let x be a real number such that 0 < |x−(−1)| < δ. Then |x + 1| < ε/40 . Also, |x + 1| < 1, so −2 < x < 0. In particular |x| < 2. So

 

|2x^3 − 5x^2 + x − 2| ≤ |2x^3 | + | − 5x^2 | + |x| + | − 2|

= 2|x|^3 + 5|x|^2 + |x| + 2

< 2(2)^3 + 5(2)^2 + (2) + 2

= 40

 

Thus, |2x^4 − 3x^3 − 4x^2 − x − 2| = |x + 1| · |2x^3 − 5x^2 + x − 2| < ε/40 · 40 = ε.

3 0
3 years ago
The soccer team at your school wants to spray paint a design on the middle of the
balandron [24]
Gdassduhhrjjdhdudjdhhdjdjdjsj I’m bout a dead man just got hit by the fire pit I’m bout a man I’m going to get
6 0
2 years ago
you have 8 kinds of writing paper and 5 envelope colors. how many parings of one kind of writing paper and one envelop color is
Arada [10]
5 pairs

one kind of writing paper for each coloured envelope
the last three papers would have to be in envelope colours that were already use so they cant be counted.
4 0
3 years ago
A hospital claims that the proportion, p, of full-term babies born in their hospital that weigh more than 7 pounds is 36%. In a
Natali [406]

Answer:

Claim :The proportion, p, of full-term babies born in their hospital that weigh more than 7 pounds is 36%.

n =  170

x = 56

We will use one sample proportion test  

\widehat{p}=\frac{x}{n}

\widehat{p}=\frac{56}{170}

\widehat{p}=0.3294

The proportion, p, of full-term babies born in their hospital that weigh more than 7 pounds is 36%.

H_0:p \neq 0.36 \\H_a:p= 0.36

Formula of test statistic =\frac{\widehat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}

                                       =\frac{0.3294-0.36}{\sqrt{\frac{0.36(1-0.36)}{170}}}

                                        =−0.8311

Now refer the p value from the z table

P-Value is .202987 (Calculated by online calculator)

Level of significance α = 0.05

Since p value < α

So we reject the null hypothesis .

Hence the claim is true

6 0
3 years ago
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