Simplify:<br> 1) (3x2y3)2

What is the unknown fraction

Veseljchak [2.6K]

Answer: B. 8/100

Let's give 5/10 a denominator of 100 since 58/100 does, so they have common denominators:

5/10 * 10 = 50/100

Now, we can subtract 50/100 from 58/100 to find the unknown fraction:

58/100 - 50/100 = 8/100

This gives us an answer of,

B. 8/100

6 0

2 years ago

On a certain standardized test used for college entrance purposes, the mean score was 21 and the standard deviation was 5. The d

Fiesta28 [93]

Answer:

A

Step-by-step explanation:

Carlos' score was 2 standard deviations from the mean, so his z-score was 2.0. You can either use the empirical 68-95-98.5 rule, or you can plug it into your calculator as <u>normalcdf(-999, 2) = .977</u>

So 97.7% of people had a score lower than Carlos!

.977 * 1.5 million = 1,465,500 people

5 0

4 years ago

9.01 prove that the two circles are similar

il63 [147K]

Answer:

see the procedure

Step-by-step explanation:

we know that

Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another.

In this problem to prove circle C and circle A are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another.

we have that

Circle C is centered at (0,-1) and has a radius of 2 units

Circle A is centered at (3,4) and has a radius of 5 units

step 1

Move the center of the circle C onto the center of the circle A

the transformation has the following rule

(x,y)--------> (x+3,y+5)

so

(0,-1)------> (0+3,-1+5)-----> (3,4)

center circle C is now equal to center circle A

The circles are now concentric (they have the same center)

step 2

A dilation is needed to increase the size of circle C to coincide with circle A

scale factor=radius circle A/radius circle C-----> 5/2=2.5

radius circle C will be=2*scale factor-----> 2*2.5=5 units

radius circle C is now equal to radius circle A

therefore

A translation, followed by a dilation will map one circle onto the other, thus proving that the circles are similar

4 0

4 years ago

Try It #2

storchak [24]

Answer:

The population in year 2014 is 41100.

Step-by-step explanation:

In the question, it is given that the city's population is growing linearly. In 2008 , population was 28200 and in 2012 , it is 36800 .

It is required to predict the population in 2014 .

To do so, use the population given in two years as two points on a line and find the equation of population and year. Then, find the population in year 2014 .

Step 1 of 2

The population in 2008 was 28200 and in 2012 it was, 36800 .

The equation relating population and year is,

$\begin{aligned}&y-28200=\left(\frac{36800-28200}{2012-2008}\right)(x-2008) \\&y-28200=\left(\frac{8600}{4}\right)(x-2008) \\&y-28200=2150(x-2008)\end{aligned}$

Step 2 of 2

The population in year 2014 can be determined by substituting 2014 for x,

$\begin{aligned}&y-28200=2150(2014-2008) \\&y-28200=2150(6) \\&y-28200=12900 \\&y=41100\end{aligned}$

6 0

2 years ago

Use SOH CAH TOA to identify the Tangent Z.

NeX [460]

SOH = Sine Opposite Hypotenus

CAH = Cosine Adjacent Hypotenus

TOA = Tangent Opposite Adjacent

Based on the key I wrote above, TOA is what you will use. Starting from angle Z look at the opposite side and adjacent side. (Opposite = 21 and Adjacent = 20) Make sure you're not looking at the hypotenus which is the side that is always across from the 90° angle.

Going by opposite over adjacent, that would be 21/20

The answer is the first choice 21/20

3 0

3 years ago

Simplify: 1) (3x2y3)2