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Olin [163]
3 years ago
8

Δ ABC is isosceles. If m∠A = 100°, m∠B = (12x + 4)°, and m∠C = (14x - 2)°, find x.

Mathematics
1 answer:
valentina_108 [34]3 years ago
8 0
Since the sum of the angles of a triangle is 180 degrees, we simply have to add all the angles and equate it to 180 to solve for x. So:
100 + 12x + 4 + 14x - 2 = 180
26x = 78
x = 3

So, x is equal to 3.
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The director of a state agency believes that the average starting salary for clerical employees in the state is less than ​$35 c
MrRissso [65]

Answer:

There is not enough evidence to conclude that  average starting salary for clerical employees in the state is less than ​$35,000 per year.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 35,000 dollars per year

Sample mean, \bar{x} = 34,700 dollars per year

Sample size, n = 100

Alpha, α = 0.10

Population standard deviation, σ = 3,500 dollars per year

First, we design the null and the alternate hypothesis

H_{0}: \mu = 35,000\text{ dollars per year}\\H_A: \mu < 35,000\text{ dollars per year}

We use one-tailed z test to perform this hypothesis.

Formula:

z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }

Putting all the values, we have

z_{stat} = \displaystyle\frac{34700 - 35000}{\frac{3500}{\sqrt{100}} } = -0.8571

Now, z_{critical} \text{ at 0.10 level of significance } = -1.28

Since,  

z_{stat} > z_{critical}

We fail to reject the null hypothesis and accept the null hypothesis.

Thus, there is not enough evidence to conclude that  average starting salary for clerical employees in the state is less than ​$35,000 per year.

3 0
3 years ago
{1,2,3,...,75,76,78} how many numbers in the set above have 2 as a factor but not have 10 as a factor
Alinara [238K]

Answer:

<h2>A) 32</h2>

Step-by-step explanation:

From 1 to 10 we have 4 numbers which are {2,4,6,8}

From 10 to 20 we have 4 numbers which are {12,14,16,18}

.

.

.

From 70 to 78 we have 4 numbers which are {72,747,6,78}

<em><u>conclusion:</u></em> we 4×8 number = 32

5 0
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erik [133]

Answer:

In a discrete probability distribution of a random variable X, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value x of X and its probability p(x), and then adding all these products together, giving. .

Step-by-step explanation:

I really hope this helps have a wonderful day

7 0
3 years ago
Shelly spent 10 mintues jogging and 20 mintues cycling and burned 300 calories. The next day, shelly swapped times and did 20 mi
ratelena [41]
She burned 30 calories for each minute of jogging and 15 calories for each minute of cycling because 300 divided by 10 is 30 and 300 divided by 20 is 15
6 0
2 years ago
Write four decimals with the 4 digit in a different place in each --- ones tenths hundreds and thousandths.Then write a statemen
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4 .04 .004 .0004
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