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FromTheMoon [43]
3 years ago
13

Answer as quickly as you possibly can

Mathematics
1 answer:
klemol [59]3 years ago
5 0

Answer:

m = 3/2

Step-by-step explanation:

You want to find the slope, or the change in y coordinates over change in x-coordinates.

The first given point is E(-2, -4)

The second point is F(2, 2)

Coordinates are given in (x, y), so following the equation and computing the  x and y coordinates of E - F for both the numerator and denominator:

\frac{y_2 - y_1}{x_2-x_1}  =  \frac{-4 -2}{-2 -2} = \frac{-6}{-4} = \frac{3}{2}

You could also have went the other way and calculated F - E for the numerator and denominator and get the same answer.

Finally, to check you can also look at the graph through the rise over run (rise/run) method and see that from E, you go up 3 (rise) and to the right 2 (run) to get to the next point on the line.

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A couple has a 400 acre farm that they want to leave to their future grandchildren. They decide to give each grandchild 12% of t
ruslelena [56]

Answer:

48

Step-by-step explanation:

5 0
2 years ago
The score on an exam from a certain MAT 112 class, X, is normally distributed with μ=78.1 and σ=10.8.
salantis [7]

a) X

b) 0.1539

c) 0.1539

d) 0.6922

Step-by-step explanation:

a)

In this problem, the score on the exam is normally distributed with the following parameters:

\mu=78.1 (mean)

\sigma = 10.8 (standard deviation)

We call X the name of the variable (the score obtained in the exam).

Therefore, the event "a student obtains a score less than 67.1) means that the variable X has a value less than 67.1. Mathematically, this means that we are asking for:

X

And the probability for this to occur can be written as:

p(X

b)

To find the probability of X to be less than 67.1, we have to calculate the area under the standardized normal distribution (so, with mean 0 and standard deviation 1) between z=-\infty and z=Z, where Z is the z-score corresponding to X = 67.1 on the s tandardized normal distribution.

The z-score corresponding to 67.1 is:

Z=\frac{67.1-\mu}{\sigma}=\frac{67.1-78.1}{10.8}=-1.02

Therefore, the probability that X < 67.1 is equal to the probability that z < -1.02 on the standardized normal distribution:

p(X

And by looking at the z-score tables, we find that this probability is:

p(z

And so,

p(X

c)

Here we want to find the probability that a randomly chosen score is greater than 89.1, so

p(X>89.1)

First of all, we have to calculate the z-score corresponding to this value of X, which is:

Z=\frac{89.1-\mu}{\sigma}=\frac{89.1-78.1}{10.8}=1.02

Then we notice that the z-score tables give only the area on the left of the values on the left of the mean (0), so we have to use the following symmetry property:

p(z>1.02) =p(z

Because the normal distribution is symmetric.

But from part b) we know that

p(z

Therefore:

p(X>89.1)=p(z>1.02)=0.1539

d)

Here we want to find the probability that the randomly chosen score is between 67.1 and 89.1, which can be written as

p(67.1

Or also as

p(67.1

Since the overall probability under the whole distribution must be 1.

From part b) and c) we know that:

p(X

p(X>89.1)=0.1539

Therefore, here we find immediately than:

p(67.1

7 0
3 years ago
Please help with algebra problem
kumpel [21]
Number of weekend minutes used: x
Number of weekday minutes used: y

This month Nick was billed for 643 minutes:
(1) x+y=643

The charge for these minutes was $35.44
Telephone company charges $0.04 per minute for weekend calls (x)
and $0.08 per minute for calls made on weekdays (y)
(2) 0.04x+0.08y=35.44

We have a system of 2 equations and 2 unkowns:
(1) x+y=643
(2) 0.04x+0.08y=35.44

Using the method of substitution
Isolating x from the first equation:
(1) x+y-y=643-y
(3) x=643-y

Replacing x by 643-y in the second equation
(2) 0.04x+0.08y=35.44
0.04(643-y)+0.08y=35.44
25.72-0.04y+0.08y=35.44
0.04y+25.72=35.44

Solving for y:
0.04y+25.72-25.72=35.44-25.72
0.04y=9.72

Dividing both sides of the equation by 0.04:
0.04y/0.04=9.72/0.04
y=243

Replacing y by 243 in the equation (3)
(3) x=643-y
x=643-243
x=400

Answers:
The number of weekends minutes used was 400
The number of weekdays minutes used was 243
6 0
3 years ago
Complete the coordinate proof for the quadrilateral determined by the points A(7, 9), B(9, 4) , C(4, 2), D(2, 7) . Prove that AB
seraphim [82]

Answer:

its B

Step-by-step explanation:

8 0
3 years ago
The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h.
Mila [183]

Answer:

a =  \frac{a - 12bh}{12a}

4 0
3 years ago
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