All categories

3 years ago

Simplify the expression. [(11 - 4)^3]^2 ÷ (4 + 3)^5

Mathematics

1 answer:

MAXImum [283]3 years ago

5 0

Answer:

Step-by-step explanation:

$\left[\left(11\:-\:4\right)^3\right]^2\:\div \left(4\:+\:3\right)^5\\\\\frac{\left(\left(11-4\right)^3\right)^2}{\left(4+3\right)^5}\\\\\mathrm{Subtract\:the\:numbers:}\:11-4=7\\\\=\frac{\left(7^3\right)^2}{\left(4+3\right)^5}\\\\\mathrm{Add\:the\:numbers:}\:4+3=7\\\\=\frac{\left(7^3\right)^2}{7^5}\\\\\left(7^3\right)^2=7^6\\\\=\frac{7^6}{7^5}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\\frac{7^6}{7^5}=7^{6-5}\\\\\mathrm{Subtract\:the\:numbers:}\:6-5=1\\\\=7$

You might be interested in

A mail order company charges 4.5% for shipping and handling. If the total order is 54.34 how much was the order total before shi

Andrews [41]

Answer:

$52

Step-by-step explanation:

Given that :

Amount charged for shipping and handling = 4.5%

Let cost of order = x

Total amount charged = 54.34

However,

total. Amount charged = (total cost + handling and shipping)

54.34 = x + 0.045x

54.34 = 1.045x

Order total before shipping = 54.34 / 1.045

Order total before shipping = 52

6 0

3 years ago

A cone shaped paper water cup has a height of 12 cm and a radius of 6 cm. If the cup is filled with water to half its height, wh

monitta

Answer:

The portion of the volume of the cup that is filled with water is $\frac{1}{8}$

Step-by-step explanation:

step 1

Find the volume of the paper water cup

The volume of the cone is equal to

$V=\frac{1}{3}\pi r^{2}h$

we have

$r=6\ cm$

$h=12\ cm$

substitute

$V=\frac{1}{3}\pi (6)^{2}(12)$

$V=144\pi\ cm^{3}$

step 2

If the cup is filled with water to half its height, find out what portion of the volume of the cup is filled with water

Remember that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

In this problem the similar cone has half the height of the complete cone

The scale factor is equal to 1/2

therefore

The volume of the cup that is filled with water is equal to the volume of the complete cup by the scale factor elevated to the cube

$V=(1/2)^{3}(144\pi)=(1/8)144\pi\ cm^{3}$

therefore

The portion of the volume of the cup that is filled with water is

$\frac{1}{8}$

8 0

3 years ago

Read 2 more answers

What is the converse statement of ~c → p?

pychu [463]

Answer:

p -> ~c

Step-by-step explanation:

Converse is when you change the order.

If a, then b

If b, then a

5 0

4 years ago

Vicki made a fruit tart and cut it into six equal pieces . vicki, silvia,and Elena each took 2 pieces of the tart home. vicki sa

frez [133]

Yes, Vicki's statement is true.
The fruit tart was split into 6 pieces and to find what 1/3 of 6 is, you'd have to divide 6/3 which equals 2. So, 1/3 of 6 is 2 and each girl took home 2 pieces (1/3) of the tart home

4 0

3 years ago

Using fluorescent imaging techniques, researchers observed that the position of binding sites on HIV peptides is approximately N

konstantin123 [22]

Answer:

The values is

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 2.45$