In 1906 Americans consumed an average of 26.85 gallons of whole milk per year. By 1998 the average consumption was 8.32 gallons. What is the percent decrease in consumption of whole milk?

Answers

Answer 1

Answer:

Answer: 69.01%

Step-by-step explanation:

In 1906 Americans consumed an average of 26.85 gallons of milk per year while by 1998 the average consumption was 8.32 gallons.

To get the percent decrease in consumption of whole milk goes thus:

We first find the amount of decrease in the milk consumed. This will be:

= 26.85 - 8.32

= 18.53

Percentage decrease

= 18.53/26.85 × 100

= 0.6901 × 100

= 69.01%

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Find b, given that a = 20, angle A = 30°, and angle B = 45° in triangle ABC

Answers

Answer:

b = 20√2

Step-by-step explanation:

Given: ΔABC

a = 20 , m∠A = 30° and m∠B = 45°

To find: value of b.

We use Sine result, which state that

$(a)/(sin\,A)=(b)/(sin\,B)$

Substituting given values we, get

$(20)/(sin\,30^(\circ))=(b)/(sin\,45^(\circ))$

we know that $sin\,30^(\circ)=(1)/(2)\:and\:sin\,45^(\circ)=(1)/(√(2))$ , we get

$(20)/((1)/(2))=(b)/((1)/(√(2)))$

$20{*2}=b*√(2)$

$b*√(2)=40$

$b=(40)/(√(2))$

$b=20√(2)$

Therefore, b = 20√2

The side b is opposite to the angle B, applying the law of the sines, we have:

$(a)/(sinA) = (b)/(sinB)$
$(20)/(sin30^0) = (b)/(sin45^0)$
$(20)/( (1)/(2) ) = (b)/( ( √(2) )/(2) )$
$20* ( √(2) )/(2) = b* (1)/(2)$
$(20 √(2) )/(2) = (b)/(2)$
$2*b =2*20 √(2)$
$2b = 40 √(2)$
$b = (40 √(2) )/(2)$
$\boxed{b = 20 √(2) }$

A spinner with 10 equally sized slices has 2 red slices, 4 yellow slices, and 4 blue slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a red slice?

Answers

The probability that the dial stops on a red slice, when it is spun and stops on a slice at random is 1/5.

How to get probability of an event?

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

A spinner with 10 equally sized slices has 2 red slices, 4 yellow slices, and 4 blue slices.

The total number of slices is 10 and the total number of favorable outcome to get a red slice is 2. Thus, the probability that the dial stops on a red slice is,

$P=(2)/(10)\nP=(1)/(5)$

Thus, the probability that the dial stops on a red slice, when it is spun and stops on a slice at random is 1/5.

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#SPJ2

Answer: 5

Step-by-step explanation: with these problems you're supposed to add all the numbers and then you divide it by the number you're asking to find the probability of so 10/2=5

Suppose you want to factor the expression x2 + 2xn+n?. Given that n>0, what are the factors? Explain.Select the correct answer below and, if necessary, fill in the answer box to complete your choice.

O A. The value of n can be any positive integer resulting in the same factor

O B. The value of n can be any positive integer resulting in the distinct factors

(Use a comma to separate answers as needed.)

O C. The value of n can be any prime integer resulting in the same factor

O

D. The value of n can be any prime integer resulting in the distinct factors

(Use a comma to separate answers as needed.)

O E. The expression cannot be factored for the given values of n.

Answers

Answer:

A. The value of n can be any positive integer resulting in the same factor

Step-by-step explanation:

Given

$x^2 + 2xn + n^2$ --- the right expression

$n > 0$

Required

Possible values of n

$x^2 + 2xn + n^2$

Expand

$x^2 + 2xn + n^2 = x^2 + xn+xn + n^2$

Factorize

$x^2 + 2xn + n^2 = x(x + n)+n(x + n)$

Factor out $x + n$

$x^2 + 2xn + n^2 = (x + n)(x + n)$

From the expression above, we can see that the result has the same factor. This means that options (b), (d) and (e) are not possible

$x^2 + 2xn + n^2 = (x + n)^2$

The above also shows that n can take any positive value.

Hence: (a) is correct

Solve this equation: –9h – 6 + 12h + 40 = 22. A. h = 24 B. h = – 4 C. h = 4 D. h = –4/7

Answers

In the equation: -9h - 6 + 12h + 40 = 22, collecting like terms gives: -9h + 12h = 22 + 6 - 40 which gives 3h = -12. They we divide both sides of the equation by 3 to get 3h / 3 = -12 / 3 which gives h = -4. Therefore, the solution to the given equation is h = -4 (option B).

A cross product is an equation which states that two ratios are equal.
True
False

Answers

It is true that a cross product is an equation that states that two ratios are equal. For example, if a player's batting average is 400 out of 1000, and you wanted to know how many times they will hit every 50 times batting, then you would set the equation up at 400/1000 and equal that to X/50, then you would use cross product to find the answer.

Let f(x) = 12 over the quantity of 4 x + 2. Find f(−1).

Answers

The value of f(-1) is -6

what is function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Given:

f(x) = 12/ (4x +2)

for x=-1

then,

f(-1) = 12/ ( 4(-1) + 2)

f(-1) = 12/ (-4 + 2)

f(-1) = 12/(-2)

f(-1) = -12/2

f(-1) = -6

Hence, the value of f(-1) is -6

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