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2 days ago

Which expressions are equivalent to StartFraction 1 Over 81 EndFraction? Check all that apply.

Mathematics

1 answer:

tester [10.7K]2 days ago

7 0

The available options are

$(A)8^{-1} (B)9^{-2} (C)\dfrac{9^8}{9^4} (D)\frac{9^8}{9^{10}} (E)9^{-6}\cdot 9^3 (F)9^5 \cdot 9^{-7$

Answer:

$(B)9^{-2} \\ (D)\frac{9^8}{9^{10}} \\ (F)9^5 \cdot 9^{-7$

Step-by-step explanation:

Given the fraction $\dfrac{1}{81}$

$\dfrac{1}{81}=\dfrac{1}{9^2}=9^{-2$

Any option that renders a form equivalent to any of the above is valid.

Option B= $9^{-2}$ which is equivalent

In Option D: $\frac{9^8}{9^10}=9^{8-10}=9^{-2}$

In Option F: $9^5 \cdot 9^{-7}=9^{5-7}=9^{-2}$

Thus, Options B, D, and F are equivalent.

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Mary wrote a book of 1536 pages. She numbered all pages by hand. How many times did she write the digit 6?

lawyer [11215]

Response:

404 instances

Detailed breakdown:

8 0

1 month ago

In three hours, Company ABC can make X ball bearings. Company DEF can make X ball bearings in 4 hours. Company GHI can make X ba

AnnZ [10913]

Answer:

X ball bearings can be produced in 1 hour and 20 minutes

Step-by-step explanation:

Proportions

Proportions serve as an essential method for solving various common challenges. We understand that:

Company ABC manufactures X ball bearings in 3 hours.

Company DEF produces X ball bearings in 4 hours.

Company GHI generates X ball bearings in 6 hours.

In a single hour, each company is capable of producing:

ABC: X/3 ball bearings

DEF: X/4 ball bearings

GHI: X/6 ball bearings

By collaborating, they can produce

$\displaystyle \frac{X}{3}+\frac{X}{4}+\frac{X}{6}$

ball bearings. Operating together

$\displaystyle \frac{4X+3X+2X}{12}=\frac{9X}{12}=\frac{3X}{4}$

If their output is 3/4 of a ball bearing in one hour, then it will take

$\displaystyle \frac{4}{3}$ hours to create one complete ball bearing. This translates to 1 hour and 20 minutes.

X ball bearings can be produced in 1 hour and 20 minutes

8 0

1 month ago

What's the verbal expression for the algebraic expression 1/8y .?

Leona [11148]

The given expression is $\frac{1}{8}y$

Thus, in verbal form, we can express it as one eighth of a number.

5 0

1 month ago

1 kilogram is equivalent to about 2.2 pounds. An orangutan weighs 142 pounds. What is its mass in kilograms? Round your answer t

AnnZ [10913]

The weight of an orangutan is 64.5 kilograms

Solution:

It is stated that the orangutan's weight is 142 pounds

Additionally,

1 kilogram is approximately 2.2 pounds

We will now convert 142 pounds into kilograms

1 kilogram = 2.2 pounds

$\text{1 pound } = \frac{1}{2.2} \text{ kilograms }$

As a result, 142 pounds translates to

$142 \text{ pound } = \frac{1}{2.2} \times 142 \text{ kilogrmas }$

$\rightarrow \frac{1}{2.2} \times 142 = 64.545 \text{ kilograms }$

When rounding to the nearest tenth, we obtain 64.5 kilograms

Therefore the mass of the orangutan is 64.5 kilograms

3 0

14 days ago

At what rate would you need to invest $12000 and make $2880 after 8 years?

PIT_PIT [11049]

Answer:

$3\%$

Step-by-step explanation:

We start with the fact that

The formula for simple interest is represented by

$I=P(rt)$

where:

I denotes the Final Interest Value

P indicates the Principal amount to be invested

r specifies the interest rate

t refers to the Number of Time Periods

For this scenario, we have

$t=8\ years\\ P=\$12,000\\I=\$2,880\\r=?$

We can substitute these values into the formula mentioned above

$2,880=12,000(8r)$

Next, we solve for t

$2,880=96,000(r)$

$r=2,880/96,000$

$r=0.03$

Convert to a percentage format

$0.03*100=3\%$

4 0

28 days ago