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Softa [21]
3 years ago
10

Please help with this problem

Mathematics
2 answers:
jeka943 years ago
5 0

Answer:

measure of angle B: 75

measure of angle A: 105

Step-by-step explanation:

this is a parallelogram. so, that means that adjacent angles are equal. that means that angle B is equal to angle D. that means that we can label angle B as 75 degrees. and, we know that a square is 360 degrees. so, if we take the 150 degrees of angle B and angle D combined, then we have 210 degrees to work with. but, since it is a parallelogram, we can divide 210 in half and get both angles. so, each angle is 105 degrees. and that is how we got the answer.

Alchen [17]3 years ago
3 0
If i am not mistaken,

B = 75 degree

A = 180 - 75 = 105 degree
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Find the other endpoint of the line segment with the given endpoint and midpoint.
Shtirlitz [24]

Answer:

endpoint is (29, -13)

Step-by-step explanation:

Formula for midpoint is (\frac{x_{1} + x_{2} }{2} ,\frac{y_{1} + y_{2}  }{2} )

So, let (x_{2} , y_{2} ) be the coordinates of the endpoint you are looking for.

x_{1} = -9  and y_{1}  = 7

(\frac{-9 + x_{2} }{2} , \frac{7 + y_{2} }{2} ) = (10, -3)

\frac{-9 + x_{2} }{2}  = 10           \frac{7 + y_{2} }{2}  = -3

-9 + x_{2} = 20         7 + y_{2}  = -6

x_{2}  =  29                    y_{2}  = -13

endpoint is (29, -13)

6 0
3 years ago
What is the volume of this right prism?<br><br> 96 in³<br><br> 60 in³<br><br> 48 in³<br><br> 44 in³
yulyashka [42]

Answer:

96 in³

Step-by-step explanation:

Volume = 2(BHD) / 2

The 2s cancel out

Volume = 3(8)4

Volume = 96

4 0
2 years ago
2. The time between engine failures for a 2-1/2-ton truck used by the military is
OLEGan [10]

Answer:

A truck "<em>will be able to travel a total distance of over 5000 miles without an engine failure</em>" with a probability of 0.89435 or about 89.435%.

For a sample of 12 trucks, its average time-between-failures of 5000 miles or more is 0.9999925 or practically 1.

Step-by-step explanation:

We have here a <em>random variable</em> <em>normally distributed</em> (the time between engine failures). According to this, most values are around the mean of the distribution and less are far from it considering both extremes of the distribution.

The <em>normal distribution</em> is defined by two parameters: the population mean and the population standard deviation, and we have each of them:

\\ \mu = 6000 miles.

\\ \sigma = 800 miles.

To find the probabilities asked in the question, we need to follow the next concepts and steps:

  1. We will use the concept of the <em>standard normal distribution</em>, which has a mean = 0, and a standard deviation = 1. Why? With this distribution, we can easily find the probabilities of any normally distributed data, after obtaining the corresponding <em>z-score</em>.
  2. A z-score is a kind of <em>standardized value</em> which tells us the <em>distance of a raw score from the mean in standard deviation units</em>. The formula for it is: \\ z = \frac{x - \mu}{\sigma}. Where <em>x</em> is the value for the raw score (in this case x = 5000 miles).
  3. The values for probabilities for the standard normal distribution are tabulated in the <em>standard normal table</em> (available in Statistics books and on the Internet). We will use the <em>cumulative standard normal table</em> (see below).

With this information, we can solve the first part of the question.

The chance that a truck will be able to travel a total distance of over 5000 miles without an engine failure

We can "translate" the former mathematically as:

\\ P(x>5000) miles.

The z-score for x = 5000 miles is:

\\ z = \frac{5000 - 6000}{800}

\\ z = \frac{-1000}{800}

\\ z = -1.25

This value of z is negative, and it tells us that the raw score is 1.25 standard deviations <em>below</em> the population mean. Most standard normal tables are made using positive values for z. However, since the normal distribution is symmetrical, we can use the following formula to overcome this:

\\ P(z

So

\\ P(z

Consulting a standard normal table available on the Internet, we have

\\ P(z

Then

\\ P(z1.25)

\\ P(z1.25)

However, this value is for P(z<-1.25), and we need to find the probability P(z>-1.25) = P(x>5000) (Remember that we standardized x to z, but the probabilities are the same).

In this way, we have

\\ P(z>-1.25) = 1 - P(z

That is, the complement of P(z<-1.25) is P(z>-1.25) = P(x>5000). Thus:

\\ P(z>-1.25) = 1 - 0.10565

\\ P(z>-1.25) = 0.89435  

In words, a truck "<em>will be able to travel a total distance of over 5000 miles without an engine failure</em>" with a probability of 0.89435 or about 89.435%.

We can see the former probability in the graph below.  

The chance that a fleet of a dozen trucks will have an average time-between-failures of 5000 miles or more

We are asked here for a sample of <em>12 trucks</em>, and this is a problem of <em>the sampling distribution of the means</em>.

In this case, we have samples from a <em>normally distributed data</em>, then, the sample means are also normally distributed. Mathematically:

\\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})

In words, the samples means are normally distributed with the same mean of the population mean \\ \mu, but with a standard deviation \\ \frac{\sigma}{\sqrt{n}}.

We have also a standardized variable that follows a standard normal distribution (mean = 0, standard deviation = 1), and we use it to find the probability in question. That is

\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}

\\ z \sim N(0, 1)

Then

The "average time-between-failures of 5000" is \\ \overline{x} = 5000. In other words, this is the mean of the sample of the 12 trucks.

Thus

\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}

\\ z = \frac{5000 - 6000}{\frac{800}{\sqrt{12}}}

\\ z = \frac{-1000}{\frac{800}{\sqrt{12}}}

\\ z = \frac{-1000}{230.940148}

\\ z = -4.330126

This value is so low for z, that it tells us that P(z>-4.33) is almost 1, in other words it is almost certain that for a sample of 12 trucks, its average time-between-failures of 5000 miles or more is almost 1.

\\ P(z

\\ P(z

\\ P(z

The complement of P(z<-4.33) is:

\\ P(z>-4.33) = 1 - P(z or practically 1.

In conclusion, for a sample of 12 trucks, its average time-between-failures of 5000 miles or more is 0.9999925 or practically 1.

7 0
3 years ago
I need help with this.
luda_lava [24]

Answer:

12 mm

Step-by-step explanation:

Use Pyth Theor

9^2 + b^2 = 15^2

81 + b^2 = 225

b^2 = 144

sqrt 144 = 12

b = 12

5 0
2 years ago
Read 2 more answers
Lena found a 5/8
DENIUS [597]

Answer:

Naomi had the correct measurement the ring weighed 0.625 carats

Step-by-step explanation:

* The diamond ring weighed 5/8 carats

- To know who is right lets change the fraction 5/8 to a decimal number

∵ 5/8 means 5 ÷ 8

- 5 is smaller than 8 so we will multiply it by 10 and

 insert decimal point in the quotient (answer of division)

∴ It will be 50 ÷ 8 = 6 and remainder 2/8 ⇒ 1/4

∴ The quotient = 0.6 and remainder 1/4

- 1 is smaller than 4 so we will multiply it by 10

∴ It will be 10 ÷ 4 = 2 and remainder 2/4 ⇒ 1/2

∴ The quotient = 0.62 and remainder 1/2

- 1 is smaller than 2 so we will multiply it by 10

∴ It will be 10 ÷ 2 = 5 without remainder

∴ The quotient = 0.625

* Naomi had the correct measurement the ring weighed 0.625 carats

8 0
3 years ago
Read 2 more answers
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