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2 years ago

1. What is the value of x? Show your work to justify your answer. (2 points)

Mathematics

2 answers:

Anarel [89]2 years ago

8 0

Answer:

Step-by-step explanation:

mafiozo [28]2 years ago

4 0

Answer:

1. 56°

2. 116°

Step-by-step explanation:

We are given the figure PQR having ∠PQR = x° and ∠QPR = 60°. Also, the exterior angle ∠R = (2x+4)°

1. It is required to find the value of x.

Now, we use the 'Exterior Angle Property of a Triangle' which states that 'the sum of two adjacent interior angles of a triangle is equal to the exterior angle of the triangle'.

So, according to our question,

∠PQR + ∠QPR = ∠R

i.e. x + 60° = (2x+4)°

i.e. x = 56°

Hence, the value of x is 56°.

2. As we know that the value of the exterior angle is (2x+4).

So, we substitute the value of x, which gives 2x+4 = 2×56°+4 = 112°+4 = 116°

Hence, the value of exterior angle is 116°

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A random sample of 12 recent college graduates reported an average starting salary of $54,000 with a standard deviation of $6,00

Marianna [84]

Answer: a.) $50188 to $57812

Step-by-step explanation: Confidence Interval (CI) is an interval of values in which we are confident the true mean is in.

The interval is calculated as

x ± $z\frac{s}{\sqrt{n} }$

a. For a 95% CI, z-value is 1.96.

Solving:

54,000 ± $1.96.\frac{6000}{\sqrt{12} }$

54,000 ± $1.96\frac{6000}{3.464}$

54,000 ± 1.96*1732.102

54,000 ± 3395

This means the interval is

50605 < μ < 57395

With a 95% confidence interval, the mean starting salary of college graduates is between 50605 and 57395 or from 50188 to 57812$.

b. The mean starting salary for college students in 2017 is $50,516, which is in the confidence interval. Therefore, since we 95% sure the real mean is between 50188 and 57812, there was no significant change since 2017.

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2 years ago

What are both of these shaded as?

Sedaia [141]

Answer:

1 whole and 15/100= 1.15

Step-by-step explanation:

The first box is 1 whole, in total there are 100 squares. All u need to do is count the number of squares

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2 years ago

You are going to make 5 assemblies, where each assembly requires the use of 1 Type A Bolt. You have a container of bolts that co

OverLord2011 [107]

Answer:

Step-by-step explanation:

You are to make 5 assemblies.

Each assembly requires the use of 1 Type A bolt.

To make the 5 assemblies, you need 5 Type A bolts.

The container of bolts has a total of 60 bolts.

The focus - Type A bolts - is 20 out of this 60.

The probability of obtaining a Type A bolt at all, is 20/60, which is = 1/3

(A) What is the probability of taking the exact number of Type A bolts you need for your 5 assemblies, if you randomly take 10 bolts from the container?

- The exact number of Type A bolts you need for the 5 assemblies is 5

1/3 × 5/10 = 5/30 = 1/6 = 0.167

(B) What is the probability of taking/having less than 5 Type A bolts out of the randomly selected 10 bolts? The solution is to sum up the following:

1/3 × 4/10 = 0.133

1/3 × 3/10 = 0.1

1/3 × 2/10 = 0.067

1/3 × 1/10 = 0.033

1/3 × 0/10 = 0

TOTAL = 0.333