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VladimirAG [237]
3 years ago
10

What is the area of a triangle with vertices at (−4, 1) , ​ (−7, 5) ​ , and ​ (0, 1) ​?

Mathematics
1 answer:
artcher [175]3 years ago
3 0
The answer to this is 8.
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Mallory needs to go to the airport. It takes her 120 minutes to get there by car. This
sergeinik [125]

Answer:

120(3)=x

120*3=360

x=360 min to go to the Airport by train.

Step-by-step explanation:

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3 years ago
Abbot is paid weekly for every hour he works. He worked 6 hours each day for 5 days last week. He earned $408, before taxes. Wri
Contact [7]

Answer:

p=13.6h

Step-by-step explanation:

if he works 6 hours a day for five days that's 30 hours. $408 divided by 30 hours is $13.6 per hour.

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3 years ago
Suppose you pay back $575 on a $525 loan you had for 75 days. What was your simple annual interest rate? State your result to th
KengaRu [80]

The <em>simple annual interest</em> rate for the $ 525 loan is equal to 46.35 %.

<h3>What is the interest rate behind a pay back?</h3>

In this situation we assume that the loan does not accumulate interests continuously in time. Hence, the <em>interest</em> rate for paying the loan back 75 days later is:

575 = 525 · (1 + r/100)

50 = 525 · r /100

5000 = 525 · r

r = 9.524

The loan has an <em>interest</em> rate of 9.524 % for 75 days. <em>Simple annual interest</em> rate is determine by rule of three:

r' = 9.524 × 365/75

r' = 46.350

The <em>simple annual interest</em> rate for the $ 525 loan is equal to 46.35 %.

To learn more on interests: brainly.com/question/26457073

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7 0
2 years ago
You have 6 dollars +12 pennies +to quarters + 4 dimes=2 nickels how much do you have
alina1380 [7]
You may have $26 I not a genius but this is easy
3 0
3 years ago
Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true
IgorLugansk [536]

Answer:

(a) 95% confidence interval for the true average porosity of a certain seam is [4.52 , 5.18].

(b) 98% confidence interval for the true average porosity of a another seam is [4.12 , 4.99].

Step-by-step explanation:

We are given that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.75.

(a) Also, the average porosity for 20 specimens from the seam was 4.85.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                      P.Q. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample average porosity = 4.85

            \sigma = population standard deviation = 0.75

            n = sample of specimens = 20

            \mu = true average porosity

<em>Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>

<u>So, 95% confidence interval for the true mean, </u>\mu<u> is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                     of significance are -1.96 & 1.96}  

P(-1.96 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.96) = 0.95

P( -1.96 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} < 1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

P( \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ]

                                            = [ 4.85-1.96 \times {\frac{0.75}{\sqrt{20} } } , 4.85+1.96 \times {\frac{0.75}{\sqrt{20} } } ]

                                            = [4.52 , 5.18]

Therefore, 95% confidence interval for the true average porosity of a certain seam is [4.52 , 5.18].

(b) Now, there is another seam based on 16 specimens with a sample average porosity of 4.56.

The pivotal quantity for 98% confidence interval for the population mean is given by;

                      P.Q. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample average porosity = 4.56

            \sigma = population standard deviation = 0.75

            n = sample of specimens = 16

            \mu = true average porosity

<em>Here for constructing 98% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>

<u>So, 98% confidence interval for the true mean, </u>\mu<u> is ;</u>

P(-2.3263 < N(0,1) < 2.3263) = 0.98  {As the critical value of z at 1% level

                                                   of significance are -2.3263 & 2.3263}  

P(-2.3263 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 2.3263) = 0.98

P( -2.3263 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} <  2.3263 ) = 0.98

P( \bar X-2.3263 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+2.3263 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.98

<u>98% confidence interval for</u> \mu = [ \bar X-2.3263 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+2.3263 \times {\frac{\sigma}{\sqrt{n} } } ]

                                            = [ 4.56-2.3263 \times {\frac{0.75}{\sqrt{16} } } , 4.56+2.3263 \times {\frac{0.75}{\sqrt{16} } } ]

                                            = [4.12 , 4.99]

Therefore, 98% confidence interval for the true average porosity of a another seam is [4.12 , 4.99].

7 0
3 years ago
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