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Umnica [9.8K]
10 months ago
14

Given that △ABC ≅ △DEF , m∠E=3y+20, m∠B= 10 +5y, and m∠A=5y , answer the following:

Mathematics
1 answer:
Vinvika [58]10 months ago
8 0

Answer:

y=5

m<A= 25

m<E= 35

Step-by-step explanation:

since <E equals <B due to CPCTC the equation:

3y+20=10+5y

is the equation

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You want to put a fence around your yard that is 35 feet by 41 feet. How much fencing do you need?
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Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. 5x+7=2y and
Luda [366]

Answer:

The correct option is option B. It has one solution, and it's x=-3

Step-by-step explanation:

We have the following system of equations:

5x+7 = 2y                        (1)

y-9x=23                            (2)

Step 1: Solve for 'y' in equation (2):

y-9x = 23

y = 9x + 23

Step 2: Substitute in equation (1):

5x + 7 = 2y

5x + 7 = 2(9x + 23)

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Suppose the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 5 million dollars
GuDViN [60]

Answer:

Probability that a randomly selected firm will earn less than 100 million dollars is 0.8413.

Step-by-step explanation:

We are given that the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 5 million dollars. Also, incomes for the industry are distributed normally.

<em>Let X = incomes for the industry</em>

So, X ~ N(\mu=95,\sigma^{2}=5^{2})

Now, the z score probability distribution is given by;

         Z = \frac{X-\mu}{\sigma} ~ N(0,1)

where, \mu = mean income of firms in the industry = 95 million dollars

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So, probability that a randomly selected firm will earn less than 100 million dollars is given by = P(X < 100 million dollars)

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Therefore, probability that a randomly selected firm will earn less than 100 million dollars is 0.8413.

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