An answer and explanation on how to solve this would be most appreciated.

An equation is formed of two equal expressions. The amount of 20% milk and 12% milk that is needed to be mixed is 7.5 gallons and 12.5 gallons, respectively.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the amount of 20%milk mixed be represented by x, while the amount of 12% milk mixed is represented by y. Therefore, the two-equation can be written as,

x+y=20 gallons

0.20x + 0.12y = (0.15×20)

Solve the first equation for x, therefore,

x = 20 - y

substitute the value of x in the second equation,

0.20(20-y) + 0.12y = 3

4 - 0.2y +0.12y = 3

-0.08y = -1

y = 12.5 gallons

substitute the value of y in the first equation,

x + 12.5 = 20

x = 7.5 gallons

Hence, the amount of 20% milk and 12% milk that is needed to be mixed is 7.5 gallons and 12.5 gallons, respectively.

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The equations in options B and D are the polynomials other equations are not polynomial.

Polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

The exponent of the polynomial should be always a whole number like {0,1,2,3,4,5,6,.........}

Here in the option, only two equations are polynomials that are

(2/3)x²+x+1  and   x³+2x+√2

Hence the equations in options B and D are the polynomials other equations are not polynomial.

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Answer:

A, C and D

Step-by-step explanation:

Answer:

a) P(1 and tails) = 1/10 = .1

b) P(even and heads) = 1/5 = .2

Step-by-step explanation:

The spinner has 5 outcomes: 1-5.

The coin has 2 outcomes: Heads or Tails.

We want to find the probability of P(1 ∩ T) and P(2,4 ∩ H).

Spinning the spinner and flipping the coin are independent events; therefore, getting one outcome has no effect on the outcome of another.

For independent events, the multiplication rule is:

If we use this formula for A, we get that:

The probability of getting a 1 on the spinner is P(1) = 1/5.

The probability of getting tails on the coin toss is P(tails) = 1/2.

We can now multiply these probabilities together:

The probability of getting a 1 on the spinner and tails on the coin toss is P(1 and tails) = 1/10 or .1.

There are two even numbers between 1 and 5: 2 and 4.

The probability of getting an even number on the spinner is 2/5.

The probability of getting heads on the coin toss is 1/2.

We can multiply these probabilities together:

The probability of getting an even number on the spinner and heads on the coin toss is P(even and heads) = 1/5 or .2.

Step-by-step explanation:

let the big cube side be b

small cube side be s

s = 2/3 * b

bv + sv = 118.125

b^3 + 8/9 b^3= 118.125

17 b^3/8 = 118.125

b^3 = 55.58

b = 3.816in

s = 2.544in

Answer:

D. 188/250

Step-by-step explanation:

Total number attending concert is 250

Total number of adults AND tickets purchased in advance:

48 + 100 + 40 = 188

Divide by 250:

[tex]\frac{188}{250}[/tex]

The probability that the randomly selected person attending the concert is an adult or has purchased the ticket in advance is 188/250.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given a table which shows when the tickets for a concert are sold and the types of tickets that are sold.

The probability of A or B can be calculated as,

P(A or B) = P(A) + P(B) - P(A and B)

Let A denote the people is an adult.

Let B denote the people who has purchased the ticket in advance.

P(A) = 148/250

P(B) = 140/250

P(A and B) = 100/250

Probability that a randomly selected person attending the concert is an adult or has purchased the ticket in advance is,

P(A or B) = 148/250 + 140/250 - 100/250

              = 288/250 - 100/250

               = 188/250

Hence the required probability is 188/250.

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Answer:

132 m²

Step-by-step explanation:

Split the figure into 2 parts :

Area (Triangle)

Area (Rectangle)

Area (Figure)

Answer:

It would take 10 weeks to buy the laptop so she could cover the price of the laptop and tax.

Step-by-step explanation:

Answer:

a = b + 6

b = 8

Step-by-step explanation:

a = b + 6

b = 8

Answer:

I don't think there is a way the values can be determined...

If a and b are in different triangles then the true option is that values of a and b can't be determined.

A triangle is a two dimensional figure having three sides and three angles.

Sum of angles of a triangle is equal to 180° whether it is a right angled or not.

In first triangle one angle is x°, second is 75° and third one is a° and in second triangle one angle is 60°, second is y°, third one is b°.

Sum of angles in first triangle is x+75+a=180

Sum of angles in second triangle is y+60+b=180

because any relationship between x and y is not given in the questions so values of a and b cannot be determined.

Hence the correct option is D which is that values of a and b cannot be determined.

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Answer: both

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

(I think ) sorry it it's wrong

Answer:
(x,y)
(-5,28)
(-1,4)
(0,-2)
(1,-8)

Step-by-step explanation:

You just have to plug in the values of x into the function rule to get all the values. Hope this helps!

Answer:

A 2/6

Step-by-step explanation:

1/3

x 2/2

2/6

Step-by-step explanation:

If you are solving for y :

[tex] \: [/tex]

[tex]x < 3y - 18[/tex]

[tex]x + 18 < 3y[/tex]

[tex] \frac{x + 18}{3} < \frac{3y}{3} [/tex]

[tex]y > \frac{3}{x} + 6[/tex]

Answer:

95

Step-by-step explanation:

19 DVDs for 10 dollars and he has 50 dollars well 50 dollars is just 5 groups of 10 so just 19 x 5 = 95

Answer:

median = 535

mode = 540

mean = 538.75

Step-by-step explanation:

To find the median, place the scores in order from smallest to largest, then find the middle score:

390, 460, 480, 480, 500, 510, 520, 530, 540, 540, 540, 580, 620, 630, 650, 650

As there is an even number of scores (16), the median is the average (mean) of the two middle scores (highlighed above).

Therefore, the median is 535

The mode is the number that appears the most.

Therefore, the mode is 540.

The mean is the total of the scores divided by how many scores there are.

Mean = (390 + 460 + 480 + 480 + 500 + 510 + 520 + 530 + 540 + 540 + 540 + 580 + 620 + 630 + 650 + 650) ÷ 16

⇒ Mean is 538.75

[tex]area = 24 \: {cm}^{2} [/tex]

[tex]height = 8 \: cm[/tex]

the volume of the given prism.

[tex]v = area \: of \: cross \: section \times height[/tex]

[tex]v = 24 \times 8[/tex]

[tex]v = 192 \: {cm}^{3} [/tex]

hence, the volume of the prism is 192 cubic centimeters.

The volume of the roof is 10667 cube feet and the volume of the entire house, including the roof, is 58667 cube feet.

To find the volume of the composite figures, follow the steps listed below:,

A pyramid-shaped hip roof is a good choice for a house in an area with many hurricanes. The volume of the roof is:

[tex]V=\dfrac{1}{3}(\text{length x width x height})\\V=\dfrac{1}{3}40\times40\times20\\V\approx10667\rm\; ft^3[/tex]

The volume of the room is:

V=length x width x height

V=40 x 40 x 30

V=48000 ft³

The volume of the entire house, including the roof, is,

V=10667+48000

V=58667 ft³

Thus, the volume of the roof is 10667 cube feet and the volume of the entire house, including the roof, is 58667 cube feet.

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The equation of the line that is parallel to x = 3 and goes through (4, -3) is: x = 4).

The slopes or parallel lines are always the same.

Given the equation of a vertical line, x = 3, the slope is undefined. So also, the slope of the line that is parallel to x = 3 is undefined.

If the line passes through the point (4, -3), it means it intercepts the x-axis at x = 4.

Therefore, the equation of the line that passes through (4, -3) and is parallel to x = 3 is: x = 4.

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Answer:

Step-by-step explanation:

A triangular pyramid has 6 edges, 4 vertices, and 1 base

The surface area of the square pyramid is 96 sq. mi.

Given:

side length (s) = 6 mi

slant height (l) = 5 mi

*image of a typical square pyramid is shown in the attachment below.

Recall:

Formula for surface area of square pyramid (SA) = [tex]A+\frac{1}{2}Pl[/tex]

Where,

[tex]A=[/tex] area of the base = [tex]s^2=6^2=36[/tex] sq mi

[tex]P=[/tex] perimeter of the base = [tex]4(s)=4*6=24[/tex]  mi

[tex]l=[/tex] slant height = 5 mi

Plug in the values

[tex]SA=36+\frac{1}{2} *24*5[/tex]

[tex]SA=36+60[/tex]

[tex]SA=96[/tex]

The surface area(SA) of the square pyramid is 96 sq. mi

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A trapezoid has an area of 10 square units. The scale factor would be 3  to dilate the trapezoid to have an area of 90 square units.

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor.

Let the linear scale factor be k.

The area scale factor is [tex]k^2[/tex]

We'll multiply the old area (10) by the area scale factor ([tex]k^2[/tex] ) to get the area of 90 square units

[tex]10 \times k^2 = 90\\\\k^2 = \frac{90}{10} \\\\k^2 = 9\\\\k = \sqrt{9} \\\\k = 3[/tex]approximately

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Answer:

6

Step-by-step explanation:

Median = (n+1) ÷ 2

Median = total frequency which is 55 + 1 = 56 ÷ 2 = 28th term.

So to find this term you add the frequencies until you get 28 or a number higher than 28.

3+1+10+15 = 29.

We got 29 when we got to the column of shoe size 6. So the Median is in shoe size 6.

Answer:

97.7 %

Step-by-step explanation:

TWO standard deviations above the mean

  z - score = 2   corresponds to .9772    97.7 %

Answer:

10,200

Step-by-step explanation:

P(1-r)^n

r = decimal form of the interest rate percent

n = amount of years

principal times (1 - decimal form of the interest rate percent) to the (amount of years) power

12000 (1-.05)^3

use PEMDAS

12000 times (.95)^3

12000 times .857375 =

ANSWER:

10288.5

Answer:

$341.80

Step-by-step explanation:

Value after 1 year :

Value after 2 years :

Value after 3 years :

Answer:

2/3 X 12 =8

Step-by-step explanation:

2.

-----. X 12 =2 x 12= 24 Which is 24/3 =8

3