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3 years ago

4. Simplify : (4 a4b 5 ) ✕ (2 a3b)2

Mathematics

1 answer:

Darina [25.2K]3 years ago

6 0

Answer:

$8a^{10}b^{7}$

Step-by-step explanation:

$($ $4a^{4}$ $b^{5}$ $)$ × $($ $2$ $a^{3}$ $b$ $)^{2}$

$(4a^{4} b^{5} )$ × $(2a^{6}b^{2})$

$8a^{4}b^{5}a^{6}b^{2}$

$8a^{10}b^{7}$

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There are 320 students in a school. 16 come to school by car. 96 walk to school. Estimate the probability that a particular stud

lorasvet [3.4K]

Answer:

a. The probability that a particular student arrives by car is $\frac{1}{20}$ = 0.05, which equals 5%.

b. The probability that a particular student walks to school is $\frac{3}{10}$ = 0.3, which equals 30%.

c. The probability that a particular student does not walk to school is $\frac{7}{10}$ = 0.7, which equals 70%.

d. The probability that a particular student does not walk or come by car is $\frac{13}{20}$ = 0.65, which equals 65%.

Step-by-step explanation:

Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

$P(A)=\frac{number of favorable cases}{number of possible cases}$

In this case, the number of possible cases is always the same, which is equal to the total number of students. So the number of possible cases is 320 students. The number of favorable cases varies as follows:

a. Number of favorable cases= number of students that arrive by car= 16

So: $P(A)=\frac{16}{320}$

P(A)= $\frac{1}{20}$ = 0.05, which equals 5%

The probability that a particular student arrives by car is $\frac{1}{20}$ = 0.05, which equals 5%.

b. Number of favorable cases= number of students that walk to school= 96

So: $P(A)=\frac{96}{320}$

P(A)= $\frac{3}{10}$ = 0.3, which equals 30%

The probability that a particular student walks to school is $\frac{3}{10}$ = 0.3, which equals 30%.

c. Number of favorable cases= number of students that do not walk to school = 320 students - number of students that walk to school= 320 students - 96 students= 224 students

So: $P(A)=\frac{224}{320}$

P(A)= $\frac{7}{10}$ = 0.7, which equals 70%

The probability that a particular student does not walk to school is $\frac{7}{10}$ = 0.7, which equals 70%.

d. Number of favorable cases= number of students that do not walk or come by car= 320 students - number of students that walk to school - number of students that arrive by car= 320 students - 96 students - 16 students= 208 students

So: $P(A)=\frac{208}{320}$

P(A)= $\frac{13}{20}$ = 0.65, which equals 65%

The probability that a particular student does not walk or come by car is $\frac{13}{20}$ = 0.65, which equals 65%.

6 0

3 years ago

If 5 friends buy a package of 38 balloons, how should they divide them?

Nastasia [14]

All you have to do is divide 38 divided by 5 which = 7 r 3

I hope this helps.

Have a awesome day. :)

7 0

3 years ago

Read 2 more answers

A rectangle school banner has a length of 44 inches, a perimeter of 156 inches , and an area of 1496 square inches. The cheerlea

Andrej [43]

Based on the lengths, the cheerleaders' banner is scaled down by a factor of 4.

So, 44 ÷ 4 = 11.

For the perimeter, 156 ÷ 4 is 39.

For the area, you have to do A=bh
(Area = base × height)

The base (length) is 11 inches, multiply that by two to get 22 inches which is the amount for both lengths. If the total perimeter is 39, you have to subtract 22 from that to get the remaining inches which is 17.
17÷2= 8.5 inches. The height is 8.5.

Now you can plug them in
A=bh
A=(11)(8.5)
A=93.5 in^2

The final answer is:
Area = 93.5 in^2
Length = 11 in
Perimeter = 39 in

I hope that helps!

7 0

3 years ago

Find the values of the variables for which ABCD must be a parallelogram

sleet_krkn [62]

Answer:

y=5 and x=4

Step-by-step explanation:

So,the diagonals of a parallelogram bisect each other..

therefore,we have our two eqn

4x-2=3y-1------------(i)

3y-3=3x

or,y-1=x----------(ii)

Now,simply substitute value of x in eqn (i)

4(y-1)-2=3y-1

or,4y-4-2=3y-1

or,y=5

Again,substitute y=5 in eqn (ii)

5-1=x

therefore,

x=5

Hope it helps you!!!

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4 years ago

How do I find the value of x?? please help

Snowcat [4.5K]

Add the two angles and then subtract from 180* to find the missing angle

So,

145* + 15* = 160*

180* - 160* = 20*

Answer: x = 20*

4 0

3 years ago

4. Simplify : (4 a4b 5 ) ✕ (2 a3b)2​

4. Simplify : (4 a4b 5 ) ✕ (2 a3b)2