If the difference (3x ^ 2 - 2x + 5) - (x ^ 2 + 3x - 2) is multiplied by 3x ^ 2 , what is the result, written in standard form?

aron lei is making identical balloon arrangements for a party. He has 32 maroon balloons and 24 white balloons, he wants each ar

alexandr402 [8]

Answer:

The greatest number of arrangements that he can make if every balloon is used is 8.

Step-by-step explanation:

The greatest number of arrangements will be the greatest common factor between 24 and 32.

GCF of 24 and 32:

We keep factoring both numbers by prime factors, while they can both be divided by the same number. So

24 - 32|2

12 - 16|2

6 - 8|2

3 - 4

There is no factor for which we can divide both 3 and 4. So the GCF is 2*2*2 = 8.

This means that the greatest number of arrangements that he can make if every balloon is used is 8.

5 0

3 years ago

The distance between two cities on a map is 3.5 centimeters. The map uses a scale in which 1 centimeter represents 20 kilometers

USPshnik [31]

Answer:

70

Step-by-step explanation:

20 km times 3 plus 10 km

4 0

3 years ago

Angle Pairs Relationships HW

WITCHER [35]

Answer:

Step-by-step explanation:

1. A = 68

B = 112

c = 68

2. A = 127

3. A = 70

B = 55

C = 25

7 0

2 years ago

Mr. Green teaches mathematics and his class recently finished a unit on statistics. The student scores on this unit are: 40 47 5

Harrizon [31]

Answer:

Mean = 64.46, Median = 62 and Mode = Bi-modal (50 and 62)

Range of the data is 55.

Step-by-step explanation:

We are given that Mr. Green teaches mathematics and his class recently finished a unit on statistics.

<u>The student scores on this unit are:</u> 40, 47, 50, 50, 50, 54, 56, 56, 60, 60, 62, 62, 62, 63, 65, 70, 70, 72, 76, 77, 80, 85, 85, 95.

We know that Measures of Central Tendency are: Mean, Median and Mode.

Mean is calculated as;

Mean = $\frac{\sum X}{n}$

where $\sum X$ = Sum of all values in the data

n = Number of observations = 24

So, Mean = $\frac{40+ 47+ 50+ 50+ 50+ 54+ 56+ 56+ 60 +60+ 62+ 62+ 62+ 63+ 65+ 70+ 70+ 72+ 76+ 77+ 80+ 85+ 85+ 95}{24}$

= $\frac{1547}{24}$ = 64.46

So, mean of data si 64.46.

For calculating Median, we have to observe that the number of observations (n) is even or odd, i.e.;

If n is odd, then the formula for calculating median is given by;

Median = $(\frac{n+1}{2})^{th} \text{ obs.}$

If n is even, then the formula for calculating median is given by;

Median = $\frac{(\frac{n}{2})^{th}\text{ obs.} +(\frac{n}{2}+1)^{th}\text{ obs.} }{2}$

Now here in our data, the number of observations is even, i.e. n = 24.

So, Median = $\frac{(\frac{n}{2})^{th}\text{ obs.} +(\frac{n}{2}+1)^{th}\text{ obs.} }{2}$

= $\frac{(\frac{24}{2})^{th}\text{ obs.} +(\frac{24}{2}+1)^{th}\text{ obs.} }{2}$

= $\frac{(12)^{th}\text{ obs.} +(13)^{th}\text{ obs.} }{2}$

= $\frac{62 + 62 }{2}$ = $\frac{124}{2}$ = 62

Hence, the median of the data is 62.

A Mode is a value that appears maximum number of times in our data.

In our data, there are two values which appear maximum number of times, i.e. 50 and 62 as these both appear maximum 3 times in the data.

This means our data is Bi-modal with 50 and 62.

The Range is calculated as the difference between the highest and lowest value in the data.

Range = Highest value - Lowest value

= 95 - 40 = 55

Hence, range of the data is 55.

5 0

3 years ago

the measure of angle a is 16 degrees greater than the measure of angle b. the tow angles are complementary. find the measure of

Fudgin [204]

This is a system of equations problem. Set up the 2 equations like so: If the angles are complementary then they add up to 90, therefore, a + b = 90. We also know that a is 16 more than b. The word "is" means equals and "more" is addition. Therefore, a is 16 more than b is "a = b + 16". Now sub in that value of a (b + 16) into the first equation and solve for b. Then back-substitute to solve for a. (b + 16) + b = 90 so 2b + 16 = 90 and 2b = 74. So b = 37. If b = 37, then a + 37 = 90 and a = 53. Check yourself to make sure that 37 + 53 add up to equal 90 (they do, just get used to checking yourself for accuracy).

4 0

3 years ago