Two Step Equations<br><br> 9=5- 9/3

A certain standardized test's math scores have a bell-shaped distribution with a mean of 530 and a standard deviation of 119. Co

kumpel [21]

Answer:

a) 68.2%

b) 31.8%

c) 2.3%

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 530

Standard Deviation, σ = 119

We are given that the distribution of math scores is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(test scores is between 411 and 649)

$P(411 \leq x \leq 649)\\\\= P(\displaystyle\frac{411 - 530}{119} \leq z \leq \displaystyle\frac{649-530}{119})\\\\= P(-1 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -1)\\= 0.841 - 0.159 = 0.682 = 68.2\%$

b) P(scores is less than 411 or greater than 649)

$P(x < 411 < x, x > 649)\\=1 = P(411 \leq x \leq 649)\\=1 - 0.682\\=0.318 = 31.8\%$

c) P(score greater than 768)

P(x > 768)

$P( x > 768) = P( z > \displaystyle\frac{768 - 530}{119}) = P(z > 2)$

$= 1 - P(z \leq 2)$

Calculation the value from standard normal z table, we have,

$P(x > 768) = 1 -0.977 = 0.023 = 2.3\%$

5 0

3 years ago

A line has a slope of -3 and a y-intercept of 3.

vladimir1956 [14]

Answer:

y = -3x + 3

Step-by-step explanation:

If ... A line has a slope of -3 and a y-intercept of 3, then the equation of that line is y = mx + b => y = -3x + 3. You don't need the table of values.

3 0

3 years ago

My lawn is 17ft wide and 20ft long, each square foot of lawn gets 1350 new snowflakes per min how much snow in kilograms accumul

Alina [70]

Answer:

46.818 kg

Step-by-step explanation:

First, find the surface area of your yard. This is found by multiplying the length and width.

The equation for this is (l*w)=sa

So,

l=20ft

w=17ft

(20*17)= 340 square feet.

So, if each square foot gets 1350 new flakes per minute, you are going to find how much the entire yard gets in a minute by multiplying the surface area by 1350.

So,

(340*1350)= 459000 flakes for the entire yard in one minute.

Since there is 60 minutes in an hour, multiply 459,000 by 60.

459,000*60= 27,540,000 new flakes in the yard per hour.

Now, to find the weight in milligrams:

27,540,000*1.7= 46,818,000 mgs

Finally, because a kilogram is equal to one million milligrams (mg),

46,818,000/1,000,000= 46.818 kg

7 0

3 years ago

Help I’ll give you 30 points

Gnesinka [82]

Answer:

a) 16.25 centimeters

b) 6.8 centimeters

Step-by-step explanation:

We can set up a proportion for both of these problems.

a) Look at the longest side of each triangle. We can set up a fraction: 7.2/18. We can also set up a fraction for XZ and PR:

6.5/x

x represents the length you're trying to find.

Since the triangles are similar, we have an equation:

7.2/18=6.5/x

Cross multiply

16.25

XZ is 16.25 centimeters long.

b)

We can do same thing:

7.2/18=x/17

Cross multiply

6.8

QR is 6.8 centimeters long.

Hope this helps!

6 0

3 years ago

Read 2 more answers

Select all the statements that are true for the graph shown.

Yuki888 [10]

Answer:

The relationship is proportional.

The relationship is linear.

The equation of the line is y = –3x.

Step-by-step explanation:

The line in the question passes through origin and (4,-12).

The rate of change of the line is

$m=\dfrac{-12-0}{4-0}\\\Rightarrow m=\dfrac{-12}{4}\\\Rightarrow m=-3$

The rate of change of the line or slope of the line is -3

Equation of the line is given by

$(y-0)=-3(x-0)\\\Rightarrow y=-3x$

This means that the relationship is linear.

If we take any value of x then there will be only one value of y this means that the relationship is proportional.

So the following statements are true

The relationship is proportional.

The relationship is linear.

The equation of the line is y = –3x.

3 0

3 years ago

Read 2 more answers

Two Step Equations 9=5- 9/3