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7 1/4 - 3/4 = 6 5/4 - 3/4 = 6 2/4

6 2/4 ÷ 3 = 26/4 ÷ 3 = 26/4 x 1/3 = 2 1/6

**Answer: 2 1/6 yd**

6 2/4 ÷ 3 = 26/4 ÷ 3 = 26/4 x 1/3 = 2 1/6

Question

Yun is making some investments in the stock market. Stock for Company A has a 30% chance of losing $12,000, a 45% chance of breaking even, and a 25% chance of earning Yun $11,000. Assuming Yun would like the odds to be in favor of her gaining money, should she invest in Company A? Explain. a. no, 7,700 > 3,600
b. yes, 7,700 > 3,600
c. yes, 3,600 > 2,750
d. no, 3,600 > 2,750

Solution 1

We have been given that company A has a 30% chance of losing $12,000.

Let us calculate the amount that Yun can loose.

Now, 45% chance of breaking even. It means neither loss nor profit.

Then, 25% chance of earning Yun $11,000.

Let us calculate the amount of profit

Since, 3,600 > 2,750. It means that Yun will be in loss on investing in the company.

**Hence, she will not invest in the company A.**

d is the correct option.

d. no, 3,600 > 2,750

Solution 2

D. no, 3,600 > 2,750.

Question

A lawn roller is 1 m wide and 80 cm high. What area is covered in each revolution

Solution 1

The area for each revolution is given by:

A = 2 * pi * r * l

Where,

r: roller radius

l: roller width

We have then:

A = 2 * 3.14 * (0.80 / 2) * 1

A = 2.512 m ^ 2

**Answer:**

**The area that is covered in each revolution is:**

**A = 2.512 m ^ 2**

A = 2 * pi * r * l

Where,

r: roller radius

l: roller width

We have then:

A = 2 * 3.14 * (0.80 / 2) * 1

A = 2.512 m ^ 2

Question

The graph of y = f(x − 3) is a _____ of the graph of y = f(x).

Solution 1

shift

These are common types of transformations of functions. Many functions have graphs that are simple transformations of the parent graphs, that are the most basic functions. In this way, we can use **vertical and horizontal shifts **to sketch graphs of functions. These are** rigid transformations** because the basic shape of the graph is unchanged. Therefore is a **Horizontal Shift, **so the graph of the function **has been shifted 3 units to the right.**

Solution 2

**Answer: shifted 3 units to the right.**

**Step-by-step explanation:**

Question

Divide 969 by 26.
A. 32 r 6
b. 29 r 17
C. 37 r 7
D. 28 r 5

Solution 1

On **dividing **969 by 26 will get **quotient **= 37 and **remainder **= 7

**Division **is the process of **splitting **a number or an amount into equal parts, **division **is one of the four basic operations of arithmetic, the ways that numbers are **combined **to make new numbers, it is used for **splitting **into equal parts or groups, It is **breaking **a number up into an equal number of parts.

Given that, we are asked to **divide** 969 by 26.

969 / 26

Since, 26 is a two** digits number**, we will first take the first **two digits** of the number given,

The number which we can **multiply **with 26 to get the **closest** number from 96 is 3, 26 × 3 = 78

96-78 = 18

Now,

18 + the **remaining **number 9, will make a number = 189

189 / 26

Since, 18 is less than 26, and 189 is less than 260 (10 times 26) that means a number which is closest to 189 in the table of 26 is between 1 times 26 to 10 times 26, therefore, we will consider the whole number 189,

7 times 26 = 182, which is closest to 189,

189-182 = 7

Since, first we get 3 and now 7

Therefore, the **quotient **will be 37 and the **remainder **is 7

Hence, on **dividing **969 by 26 will get **quotient **= 37 and **remainder **= 7

Learn more about **division**, click;

#SPJ5

Solution 2

**Answer:**

**The Answer is =37 r 7**

**Step-by-step explanation:**

969 / 26

26 * 37 = 962

969 - 962 = 7

969 / 26 = **37 R 7.**

Question

A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. One flower is chosen at random and given to a woman. Another flower is then chosen at random and given to a different woman. What is the probability that both flowers are pink roses?

Solution 1

Total flowers = 5 + 4 + 6 = 15

Pink roses = 4

P(two pink roses) = (4/15)(3/14) = 2/35

**Answer: 2/35**

Pink roses = 4

P(two pink roses) = (4/15)(3/14) = 2/35

Solution 2

Question

A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. One flower is chosen at random and given to a woman. Another flower is then chosen at random and given to a different woman. What is the probability that both flowers are pink roses?

Solution 1

4/15·3/14 = 0.057 so it's b.) 0.057

Solution 2

5+4+6=15 2/15=.133333 or 13% or 2/15

Question

What is 4log1/2^w(2log1/2^u-3log1/2^v written as a single logarithm?

Solution 1

Given:

4log1/2^w (2log1/2^u-3log1/2^v)

Req'd:

Single logarithm = ?

Sol'n:

First remove the parenthesis,

4 log 1/2 (w) + 2 log 1/2 (u) - 3 log 1/2 (v)

Simplify each term,

Simplify the 4 log 1/2 (w) by moving the constant 4 inside the logarithm;

Simplify the 2 log 1/2 (u) by moving the constant 2 inside the logarithm;

Simplify the -3 log 1/2 (v) by moving the constant -3 inside the logarithm:

log 1/2 (w^4) + 2 log 1/2 (u) - 3 log 1/2 (v)

log 1/2 (w^4) + log 1/2 (u^2) - log 1/2 (v^3)

We have to use the product property of logarithms which is log of b (x) + log of b (y) = log of b (xy):

Thus,

Log of 1/2 (w^4 u^2) - log of 1/2 (v^3)

then use the quotient property of logarithms which is log of b (x) - log of b (y) = log of b (x/y)

Therefore,

log of 1/2 (w^4 u^2 / v^3)

and for the final step and answer, reorder or rearrange w^4 and u^2:

**log of 1/2 (u^2 w^4 / v^3) **

4log1/2^w (2log1/2^u-3log1/2^v)

Req'd:

Single logarithm = ?

Sol'n:

First remove the parenthesis,

4 log 1/2 (w) + 2 log 1/2 (u) - 3 log 1/2 (v)

Simplify each term,

Simplify the 4 log 1/2 (w) by moving the constant 4 inside the logarithm;

Simplify the 2 log 1/2 (u) by moving the constant 2 inside the logarithm;

Simplify the -3 log 1/2 (v) by moving the constant -3 inside the logarithm:

log 1/2 (w^4) + 2 log 1/2 (u) - 3 log 1/2 (v)

log 1/2 (w^4) + log 1/2 (u^2) - log 1/2 (v^3)

We have to use the product property of logarithms which is log of b (x) + log of b (y) = log of b (xy):

Thus,

Log of 1/2 (w^4 u^2) - log of 1/2 (v^3)

then use the quotient property of logarithms which is log of b (x) - log of b (y) = log of b (x/y)

Therefore,

log of 1/2 (w^4 u^2 / v^3)

and for the final step and answer, reorder or rearrange w^4 and u^2:

Solution 2

**Answer:**

**Step-by-step explanation:**

**Given :** Expression

**To write : **As a single logarithm?

**Solution :**

**Remove parenthesis,**

**Simplify each term by applying logarithmic property,**

**Use the product property of logarithms,**

**Use the quotient property of logarithms,**

**Therefore, **

Question

Change 5/8 to a percentage.
A. 87.5%
B. 62.5%
C. 92.5%
D. 37.5%

Solution 1

5/8 = 5 ÷ 8 = .625

move decimal 2 places to right for %

.625 = 62.5%

move decimal 2 places to right for %

.625 = 62.5%

Question

The height reached by amal's rocket was 1/4 of the height reached by min's rocket. Amal's rocket REAched a height of 15 meters. Which equation could be used to find the height reached by min's rocket

Solution 1

To solve this problem you must keep on min the information given in the problem shown above:

1- You have that

- The height reached by amal's rocket was 1/4 of the height reached by min's rocket.

- Amal's rocket REAched a height of 15 meters.

2. Therefore, let's call "x" to the height reached by min's rocket. Then, you have:

(1/4)x=15

x/4=15

Which equation could be used to find the height reached by min's rocket?

** The answer is: x/4=15**

1- You have that

- The height reached by amal's rocket was 1/4 of the height reached by min's rocket.

- Amal's rocket REAched a height of 15 meters.

2. Therefore, let's call "x" to the height reached by min's rocket. Then, you have:

(1/4)x=15

x/4=15

Which equation could be used to find the height reached by min's rocket?

Question

Marina correctly simplified the expression (-4a^-2 b^4)/(8a^-6b^-3) assuming that a does not equal 0 and b does not equal 0. Her simplified expression is below. -1/2a^4b^
The exponent of the variable b in Marina’s solution should be...

Solution 1

For this case we have the following expression:

(-4a ^ -2 b ^ 4) / (8a ^ -6b ^ -3)

We can rewrite the expression using properties of exponents.

We have then:

(-4/8) * ((a ^ (- 2 - (- 6))) (b ^ (4 - (- 3))))

Rewriting we have:

(-2/4) * ((a ^ (- 2 + 6)) (b ^ (4 + 3)))

(-1/2) * ((a ^ 4) (b ^ 7))

-1 / 2a ^ 4b ^ 7

**Answer:**

**The exponent of the variable b in Marina's solution should be 7**

(-4a ^ -2 b ^ 4) / (8a ^ -6b ^ -3)

We can rewrite the expression using properties of exponents.

We have then:

(-4/8) * ((a ^ (- 2 - (- 6))) (b ^ (4 - (- 3))))

Rewriting we have:

(-2/4) * ((a ^ (- 2 + 6)) (b ^ (4 + 3)))

(-1/2) * ((a ^ 4) (b ^ 7))

-1 / 2a ^ 4b ^ 7

Solution 2

**Answer:**

7 is correct!

**Step-by-step explanation:**

hope that this helps. Peace and Love

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