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4 years ago

Write 2^100 as an exponent with a base of: 32

Mathematics

1 answer:

jeka944 years ago

8 0

Answer:

32^20

Step-by-step explanation:

Here you can either:

Convert to logarthmic format and use base changing formula.

Simply do 2^100=32^x, find x.

I chose option 2 because its quicker here. However, it will not always work.

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Find the missing coefficent. (5d - 7)(5d - 6) = 25d2 + d + 42

Tcecarenko [31]

25d^2-30d-35d+42=25d^2-65d+42.

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4 years ago

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A box holds 8 red and 4 blue beads. Three beads are taken from the box and not replaced. Determine: The probability that all thr

zubka84 [21]

Answer: $\dfrac{14}{55}, \dfrac{13}{55}$

Step-by-step explanation:

Given

There are 8 red and 4 blue beads

Three beads were taken from the box

(i)No of ways of choosing three red beads out of 12 beads is $^8C_3$

Total no of ways $^{12}C_3$

Probability is

$P=\dfrac{^8C_3}{^{12}C_3}=\dfrac{8\times 7\times 6}{12\times 11\times 10}=\dfrac{2\times 7}{11\times 5}\\P=\dfrac{14}{55}$

(ii)atleast two beads refers to minimum two beads

There can be two possibilities (2B,1 R), (3B, 0R)

$\Rightarrow P=\dfrac{^4C_2\times ^8C_1}{^{12}C_3}+\dfrac{^4C_3}{^{12}C_3}\\\\\Rightarrow P=\dfrac{6\times 8}{220}+\dfrac{4}{220}=\dfrac{52}{220}\\\\\Rightarrow P=\dfrac{13}{55}$

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3 years ago

A 5 pack of clay pots cost $14.25. What is the unit price?

cupoosta [38]

Answer:4.25

Step-by-step explanation: you divide the cost by the materials I believe (I’m sorry if it’s wrong)

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2 years ago

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The graph shows two polygons ABCD and A′B′C′D′.

stellarik [79]

Answer:

Translate ABCD down 1, then reflect it over the y-axis

and

Reflect ABCD over the y-axis, then translate down 1

Step-by-step explanation:

First of all, the two steps are the same, just in a different order

Second, if you look at the instructions you can see what would happen to the quadrilateral. Reflecting over the y-axis would make the shape flip horizontally (left to right), as shown in the image. This means the points on the left move to the right, and the points on the right move to the left. Top and bottom points stay the same. And the "translation" just means to slide. In both the answers, it says "translate 1 unit down", which just means "move 1 unit down", which is exactly what happens in the image

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3 years ago

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there are multiple chickens and rabbits in a cage. There are 72 heads and 200 feet inside the cage. How many chickens are in the

mezya [45]

44 chicken and 28 rabbits

Given:
chicken head + rabbit head = 72 heads
chicken feet + rabbit feet = 200 feet

c + r = 72
2c + 4r = 200

find the value of c using the 1st equation:
c = 72 - r

substitute c by its value in the 2nd equation:
2c + 4r = 200
2(72-r) + 4r = 200
144 - 2r + 4r = 200
2r = 200 - 144
2r = 56
r = 56/2
r = 28

c = 72 - r
c = 72 - 28
c = 44

c = 44 ; r = 28

To check:
2c + 4r = 200
2(44) + 4(28) = 200
88 + 112 = 200
200 = 200

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4 years ago