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3 years ago

Can somebody help me with (a) and (b)? Thanks! :D

Mathematics

2 answers:

Pachacha [2.7K]3 years ago

6 0

Answer:

PART A:

Line m: 1/2x + 6

Line n: 1/2x - 3

PART B:

The slope is the same in both lines

MakcuM [25]3 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

Since the lines are parallel they have the same slopes

Calculate the slope of line m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (2, 7) ← 2 points on the line

m = $\frac{7-6}{2-0}$ = $\frac{1}{2}$

Note the line crosses the y- axis at (0, 6) ⇒ b = 6

Thus

y = $\frac{1}{2}$ x + 6 ← equation of line m

Note for line n the line crosses the y- axis at (0, - 3) ⇒ b = - 3

Thus

y = $\frac{1}{2}$ x - 3 ← equation of line n

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4. Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean

Karo-lina-s [1.5K]

Answer:

Yes, Tom must be admitted to this university.

Step-by-step explanation:

We are given that the scores on national test are normally distributed with a mean of 500 and a standard deviation of 100.

Also, we are provided with the condition that Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test.

Let, X = score in national test, so X ~ N( $\mu=500 , \sigma^{2} = 100^{2}$ )

The standard normal z distribution is given by;

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

Now, z score of probability that tom scores 585 is;

Z = $\frac{585-500}{100}$ = 0.85

Now, proportion of students scoring below 85% marks is given by;

P(Z < 0.85) = 0.80234

This shows that Tom scored 80.23% of the students who took test while he just have to score more than 70%.

So, it means that Tom must be admitted to this university.

4 0

4 years ago

*99 POINTS*The science club sponsor is ordering caps and shirts for the boys and girls in the science club.There are 45 science

zhuklara [117]

for every member to get a shirt you would need to order 9 packages of shirt (because 5 times 9 is 45) and for caps the minimum to order would be 15 packages of caps

explanation

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15 is the total packages of hats needed to order

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4 years ago

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justin needs to take a taxi to the airport. it will coast $1.75 for the first mile and $0.50 for each additional 1/4 of a mile .

lora16 [44]

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4 years ago

Solve 2x + 3y = 16 4x+10y = 40

Aleksandr-060686 [28]

Answer:

x = 5, y = 2

Step-by-step explanation:

First, find the value of x in respect to y:

2x + 3y = 16
2x = 16 - 3y

x = 8 - 3/2y

Then, substitute this expression into the second equation (Since we've established x is equal to 8 - 3/2y, we can put that in place of x):

4(8 - 3/2y) + 10y = 40

Then, distribute and solve for y:

32 - 6y + 10y = 40
32 + 4y = 40
4y = 8
y = 2

Now that we know what y equals, we can substitute the value of y in the equation to find x:
2x + 3(2) = 16
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2x = 10

x = 5

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3 years ago

231 is 75% of what number?

Margarita [4]

231 ------> 75
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7 0

4 years ago

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