Find the GCF of each expression. Then factor the expression. 25b^2 - 20b

Answers

Answer 1

Answer: Hello!

The prime factors of these two numbres are :

$25b^2 = 5^2* b^2\n 20b = 5* 2^2 * b$

The GCF can be calculated by multiplying common primes factors :
$5* b = 5b$

So the GCF is 5b and the expression can be factored this way :
$25b^2 - 20b = 5b* 5b - 4* 5b = 5b\left(5b-4\right)$

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A grocery store will only accept yellow onions that are at least 2.75 in. in diameter. A grower has a crop of onions with diameters that are normally distributed, with a mean diameter of 3.25 in. and a standard deviation of 0.25 in. What percent of the onions will be accepted by the grocery store?A. 16%
B. 2.5%
C. 97.5%
D. 34%

Answers

Answer:

C. 97.5%

Step-by-step explanation:

For identify the percent of the onions that will be accepted by the grocery, we need to standardized the minimum diameter accepted.

Standardized is to find the equivalent number of 2.75 in a normal distribution with mean 0 and standard deviation 1. This is calculate as:

$Z=(2.75-3.25)/(0.25)=-2$

Where z is the equivalent value of 2.75 in the standard normal distribution, 3.25 is the mean and 0.25 is the standard deviation.

So, 2.75 in a normal distribution with mean 3.25 and standard deviation of 0.25 is equivalent to have a -2 in standard normal distribution.

A standard normal distribution is a normal distribution with mean 0 and standard deviation 1.

Finally the percent of the onions that will be accepted by the grocery store is calculate as the probability of z to be bigger that -2 in a standard normal distribution. That is:

P(Z>-2)=0.9772

This value can be found in a table of standard normal distribution that given a z, it show you the area on the right of this number.

So, the percent of onions that are going to be accepted is approximately 97.5%

it has to be C.........

One half of the birds at the pet store are yellow. Tara buys one of the yellow birds. Then one third of the birds at the store are yellow. How many yellow birds were at the pet store before Tara bought one? Explain

Answers

$x - all\ birds\n \n (1)/(2) x \ -\ the\ yellow\ birds\n \n (1)/(2) x-1=(1)/(3) x\ \ /\cdot6\n \n 3x-6=2x\n \nx=6\ \ \ \Rightarrow\ \ \ (1)/(2) x=(1)/(2) \cdot 6=3\n \n Ans.\ 3\ yellow\ birds$

Well, y=ny
2(y-1)=ny
(where ny is not-yellow)
You get y=2y-2 or y=2. You had two yellow birds and two other types.

a piece of licorice is to be cut into 10 equal size pieces. if the length of the piece of licorice is 2/3 yard, how long will each piece of licorice be?

Answers

Sooo, 2/3 of a yard is 2 feet because a yard is 3 feet. If you need 10 of the same pieces and you convert feet to inches you would have 24 inches. 24/10= 2.4. Each piece of licorice would need to be 2.4 inches long if you wanted the same length.

A baseball is thrown into the air from a height of 5 feet. The ball reaches a maximum height of 43.5 feet and spends a total of 3.2 seconds in the air. Write the equation that models the height of the baseball? Assume that acceleration due to gravity is –16 ft/s2

Answers

Answer:

h(t) = -16t2 + 49.64t + 5 (which is letter C )

Step-by-step explanation:

Got it correct

h = 5 + ut - 16t^2
When the balls falls back to the ground, h = 0
0 = 5 + 3.2u - 16(3.2)^2
0 = 5 + 3.2u - 163.84
0 = 3.2u - 158.84
3.2u = 158.84
u = 158.84/3.2 = 49.6 ft/s

Required equation is
h = 5 + 49.6t - 16t^2

A store is selling lemons at 2 for $3. Each lemon yields 2 tablespoons of lemon juice. How much will it cost to buy enough lemons to make a 9-inch lemon pie requiring 1/2 cup of lemon juice?

Answers

Answer:

It will cost $6 to buy enough lemons.

Step-by-step explanation:

Consider the provided information.

To make a 9-inch lemon pie requiring 1/2 cup of lemon juice.

1 cup = 16 tablespoons

1/2 cup = 8 tablespoons

That means we only need 8 tablespoons.

Each lemon yields 2 tablespoons of lemon juice.

Number of lemon required =8 ÷ 2 = 4

That means we need only 4 lemon.

Store is selling lemons at 2 for $3 that means 4 lemons for $6.

Hence, it will cost $6 to buy enough lemons.

Answer:

6 dollars to buy enough lemons

Step-by-step explanation:

Does the following equation have an answer?2n²=m √m=o {n ∈ N*} {o ∈ N*} {m ∈ N*}
It had wondering for days...

Answers

We see that n is in the set of natural numbers (1,2,3,4,5,...), so of course m should be in the natural numbers. However, we see that 2n^2, when square rooted, is $n√(2)$ . With n in the natural numbers, the square root of m, or o, can never be a natural number but is always an irrational number. Therefore, this equation has no solutions.

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