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Murljashka [212]

1 year ago

11

Simplify the expression to a form in which 2 is raised to a single integer power. fraction numerator open parentheses 2 to the p

ower of 10 close parentheses cubed 2 to the power of short dash 10 end exponent over denominator 2 to the power of short dash 7 end exponent end fraction

1 answer:

anzhelika [568]1 year ago

5 0

Answer:

2^27

Step-by-step explanation:

Given the following expression:

[(2^10)^3 x (2^-10)] ÷ 2^-7

This can be easily simplified. Let us simplify the numerator first. To do that, we have

(2^10)^3 making use of the power rule of indices that says:

(A^a)^b = A^ab where a and b are powers, we have:

2^(10x3) = 2^30

Therefore the numerator becomes:

2^30 x 2^-10. Also making use of the multiplication rule that says:

A^a x A^b = A^(a + b), we have

2^30 x 2^-10 = 2^(30 – 10) = 2^20.

Now we have:

(2^20) ÷ (2^-7)

To simplify this, we need the division rule of indices which says:

A^a ÷ A^b = A^(a – b)

Therefore we have:

(2^20) ÷ (2^-7) = 2^[20 – (–7)] = 2^(20+7) = 2^27

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Which describes how to graph h (x) = negative RootIndex StartRoot x + 8 EndRoot by transforming the parent function?

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Answer:

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Step-by-step explanation:

The given function is

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Since there is a negative multiply the transformed function, there is a reflection in the x-axis.

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1 year ago

Tim Tradesman estimates his taxable income will be $7,500. He is paid every two weeks or 26 times a year.

alisha [4.7K]

Given:
Taxable income: 7,500
Paid every two weeks or 26 weeks in a year

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8 0

1 year ago

Read 2 more answers

The gas tank of a car is filled with a nozzle that discharges gasoline at a constant flow rate. Based on unit considerations of

Cloud [144]

Answer:

It is going 84.12s = 1 minute and 24.12 seconds to fill the tank.

Step-by-step explanation:

The filling time of a gas tank can be given by a first order function in this format:

$F(t) = V - r*t$

In which $F(t)$ is the current amount of fuel in the tank(in L), $V$ is the volume of the tank(in L), $r$ is the discharge rate of the tank(in L/s) and t is the time in seconds.

Finding the values of the parameters:

The tank is completly empty, so $F(t) = 0$ .

The volume of the tank is 14 gallons. However, the problem states that the volume of the tank is measured in liters.

Each gallon has 3.78L.

So $V = 14*3.78 = 53L$

The discharge rate for the gas is 38.0 l/min. However, the problem states that the discharge rate is in L/s. So, to find the value of r, we solve the following rule of three.

38 L - 60s

r L - 1s

$60r = 38$

$r = \frac{38}{60}$

$r = 0.63$

Solving the equation:

$F(t) = V - r*t$

$0 = 53 - 0.63t$

$0.63t = 53$

$t = \frac{53}{0.63}$

$t = 84.12s$

It is going 84.12s = 1 minute and 24.12 seconds to fill the tank.

6 0

1 year ago

Out of five men and five women, we form a committee consisting of four different people. Assuming that each committee of size fo

masha68 [24]

Answer:

1. 10/21

2. 11/42

3. 41/42

4. 2/15

Step-by-step explanation:

Probability defines the ratio of the number of favorable outcomes to the total number of outcomes.

Combination Operations

$5C2 = \frac{5! }{2! (5-2)!} = \frac{5*4*3! }{2! 3!} =\frac{5*4 }{2*1} =\frac{20}{2}= 10$

$10C4 = \frac{10! }{4! (10-4)!} = \frac{10*9*8*7*6! }{4! 6!} =\frac{10*9*8*7 }{4*3*2*1} =\frac{5040}{24}= 210$

$5C3 = \frac{5! }{3! (5-3)!} = \frac{5*4*3! }{3! 2!} =\frac{5*4 }{2*1} =\frac{20}{2}= 10$

$5C1 = \frac{5! }{1! (5-1)!} = \frac{5*4! }{1! 4!} =\frac{5 }{1} = 5$

$8C2 = \frac{8! }{2! (8-2)!} = \frac{8*7*6! }{2! 6!} =\frac{8*7 }{2*1} = 4*7= 28$

$5C4 = \frac{5! }{4! (5-4)!} = \frac{5*4! }{4! 1!} =\frac{5 }{1} = 5$

$5C0 = \frac{5! }{0! (5-0)!} = \frac{5! }{0! 5!} = 1$

1. Probability of forming a committee consisting of two men and two women

= $\frac{5C2 * 5C2}{10C4} =\frac{10*10}{210} =\frac{10}{21}$

2. Probability of forming a committee that has more women than men

(NOTE: Since the committee desired has only 4 members, forming a committee that has more women than men can only be possible if we have 4 women, 0 men or 3 women 1 man)

= $\frac{5C3 * 5C1 + 5C4*5C0}{10C4} = \frac{10 * 5 + 5*1 }{210} = \frac{50 + 5}{210}=\frac{55}{210} = \frac{11}{42}$

3. Probability of forming a committee that has at least one man

(NOTE: at least one man implies the committee must not have all women members )

= $1 - \frac{5C4}{10C4} = 1 - \frac{5}{210} = 1 - \frac{1}{42} = \frac{41}{42}$

4. Probability of forming a committee with both Alice and Bob are members of the committee (NOTE: If Alice and Bob are compulsory member of the committee, there are only two more people to join the committee from the remaining 8 people)

$=\frac{8C2}{10C4} =\frac{28}{210} =\frac{2}{15}$

it be like a coin toss ut a little more complicated. For every toss we have 4 outcomes from 210 possililities

6 0

2 years ago