Find the x intercept and the y intercept of the line 3x-6y=6.

If g(x)=2(x-4), find the value of x if g(x) =20 A. 32 B. 12 C. 14 D. 10

SOVA2 [1]

I think it is 32, bc the value of x is 20 so your problem would look like this; 2 ( (20) - 4 )

5 0

3 years ago

Scores on a test are normally distributed with a mean of 81.2 and a standard deviation of 3.6. What is the probability of a rand

Misha Larkins [42]

Answer:

The probability of a randomly selected student scoring in between 77.6 and 88.4 is 0.8185.

Solution:

Given, Scores on a test are normally distributed with a mean of 81.2

And a standard deviation of 3.6.

We have to find What is the probability of a randomly selected student scoring between 77.6 and 88.4?

For that we are going to subtract probability of getting more than 88.4 from probability of getting more than 77.6

Now probability of getting more than 88.4 = 1 - area of z – score of 88.4

$\mathrm{Now}, \mathrm{z}-\mathrm{score}=\frac{88.4-\mathrm{mean}}{\text {standard deviation}}=\frac{88.4-81.2}{3.6}=\frac{7.2}{3.6}=2$

So, probability of getting more than 88.4 = 1 – area of z- score(2)

= 1 – 0.9772 [using z table values]

= 0.0228.

Now probability of getting more than 77.6 = 1 - area of z – score of 77.6

$\mathrm{Now}, \mathrm{z}-\text { score }=\frac{77.6-\text { mean }}{\text { standard deviation }}=\frac{77.6-81.2}{3.6}=\frac{-3.6}{3.6}=-1$

So, probability of getting more than 77.6 = 1 – area of z- score(-1)

= 1 – 0.1587 [Using z table values]

= 0.8413

Now, probability of getting in between 77.6 and 88.4 = 0.8413 – 0.0228 = 0.8185

Hence, the probability of a randomly selected student getting in between 77.6 and 88.4 is 0.8185.

4 0

3 years ago

A paper cup is a perfect cylinder that is 6.4 cm tall and 3 cm across. Find the total area of paper needed to make the cup, to t

NNADVOKAT [17]

Hey there! I'm happy to help!

We want to find how much paper we need to make the cup. So, we need to find the surface area of the cylinder, which is basically the "walls and floors" of the cup. So, this is the circle on the bottom and the surrounding stuff that goes up. There is no circular top to this cup, which will be important when finding the total area of paper.

So, first we need to find how much paper we need to make the bottom circle. The formula for the area of a circle is A=πr². This r represents the radius, or the distance from the center of the circle to the edge. We are given that the cup is 3 cm completely across, and the radius is be half of that, so the radius is 1.5 cm. Let's find the area. We will use 3.14 for π.

π×1.5²=7.065

Now, we need to find the area of the walls of the cup. The wall is a rectangle that is basically wrapped around the circle. The height of the rectangle is the height of the cup and the length of the rectangle is the circumference (perimeter) of the bottom circle because the length of the rectangle wraps completely around the circle.

First, let's find the circumference of the circle. The circumference is the diameter (distance across the circle, so 3 cm) multiplied by π. We will use 3.14 for π.

3π=9.42

So, this means that the long side of the rectangle is 9.42 cm, and now we multiply this by the height.

9.42×6.4=60.288

Now, we add the rectangle area and the bottom circle area.

60.288+7.065=67.353

But, they want us to round to the nearest centimetre, so we will just say 67 square centimetres.

An important thing to note is that this is not the area of a normal cylinder (one with a top and a bottom circle) because it is a cup so it does not have a top. If you have a cylinder with a top and a bottom, you would just multiply the area of the circle by two, so then you have the top and bottom. If that were the case, the area of our cylinder would be 74 cm with the numbers we have been given here.

Have a wonderful day!

3 0

3 years ago

URGENT PLEASE HELP!!!

Ira Lisetskai [31]

Answer:

1) -17x-9

Step-by-step explanation:

1)

(-2x^3+x-5)+(x^3-3x-4)

Combine like terms using P.E.M.D.A.S:

(-2x^3+x-5)+(x^3-3x-4)

(-9x-5)+(-8x-4)

Combine like terms:

(-2x^3+x-5)+(x^3-3x-4)

(-9x-5)+(-8x-4)

-17x-9

I hope this helps a bit!☺

8 0

2 years ago

what was the interest rate if your balance on an investment of 857 dollars at the end of six years is 1268.36 dollars

Mumz [18]

<h3>The interest rate is 8 % if your balance on an investment of 857 dollars at the end of six years is 1268.36 dollars</h3>

Solution:

Given that,

Principal = $ 857

Amount = $ 1268.36

Number of years = 6

Rate of interest = ?

Simple Interest = Amount - principal

Simple Interest = 1268.36 - 857

Simple Interest = 411.36

Use the formula,

$Simple Interest = \frac{ p \times n \times r}{100}\\\\411.36 = \frac{ 857 \times 6 \times r}{100}\\\\41136 = 5142 \times r\\\\r = \frac{41136}{5142}\\\\r = 8 \%$

Thus the interest rate is 8 %

3 0

3 years ago

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