Dawn is having a party. She wants to make punch and the recipe calls for 4 pints of orange juice, 5 cups of apple juice, 1/2 gallon of lemonade, and 2 quarts of pineapple juice. When she mixes this altogether, how many gallons of punch did Dawn make?

This is equivalent to y = 3x+4 (slope intercept form)

By "standard form", I mean the form Ax+By+C = 0.

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Explanation:

Let's solve the first equation for y

x+3y-4 = 0

x+3y = 4

3y = 4-x

3y = -x+4

y = (-x+4)/3

y = (-x/3) + (4/3)

y = (-1/3)x + (4/3)

The equation is now in y = mx+b form, aka slope intercept form, with m = -1/3 as the slope and b = 4/3 as the y intercept. We'll focus on the slope.

Apply the negative reciprocal to this so that we go from -1/3 to +3/1 or simply 3. Flip the fraction and the sign. Note how -1/3 and 3 multiply to -1. Perpendicular slopes always multiply to -1, assuming neither line is vertical.

So this mystery perpendicular line we're after has a slope of 3.

It has the same y intercept as 2x+5y-20 = 0. Plug in x = 0 and solve for to determine the y intercept.

2x+5y-20 = 0

2(0)+5y-20 = 0

5y-20 = 0

5y = 20

y = 50/5

y = 4

The y intercept of 2x+5y-20 = 0 is y = 4, so it's also the y intercept of our final answer. Let b = 4.

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We found that:

So we know that,

y = mx+b

y = 3x+4

is the slope intercept form of the answer. Since your teacher gave you the equations in standard form (one version of it anyway), let's convert y = 3x+4 to that form as well

y = 3x+4

y-3x = 4

-3x+y = 4 .... one way to express standard form

-3x+y-4 = 0 .... another standard form

Some math textbooks use Ax+By = C as standard form, while others use Ax+By+C = 0. Unfortunately, it's a bit confusing because the same phrasing is used.

Answer:

7.96 cm

Step-by-step explanation:

radius of bottom: 19/2 = 9.5

area of bottom = pi * r^2 = 283.53

height * base area = volume

Answer:

(a) Attached to this response.

(b)

(i) 0 cups = 0.275

(ii) 4 cups = 0.125

(iii) 8 cups = 0.025

Step-by-step explanation:

(a) The frequency and relative frequency table has been attached to this response.

i. The first column, labelled x, is the number of cups of coffee consumed per day.

ii. The second column, labelled f, is the number of people that consumed x cups of coffee per day. It is found by counting the number of occurrences (i.e frequency) of the numbers of the first column, x, in the given data.

For example, 0 in first column appears 11 times in the given data. Also, 5 in the first column appears 4 times in the given data.

iii. The third column, labelled r, is the relative relative frequency of the number of cups of coffee. It is calculated by dividing the frequency of the cups of coffee by the total number of people that consumed it. As shown on the table, it is calculated by dividing the each of the values on the second column by the sum of the values on that same column (second column).

For example, the relative frequency of 2 cups of coffee is given by:

r = 7  ÷ 40 = 0.175

Also, the relative frequency of 4 cups of coffee is given by;

r = 5 ÷ 40 = 0.125

(b) The probability (Pₓ) that a randomly selected person consumed x cups of coffee is given by;

Pₓ = frequency of x ÷ total frequency

This is also the relative frequency of x

Therefore,

(i) The probability (P₀) that a randomly selected person consumed 0 cups of coffee is given by;

the relative frequency of 0 = 0.275

(ii) The probability (P₄) that a randomly selected person consumed 4 cups of coffee is given by;

the relative frequency of 4 = 0.125

(iii) The probability (P₈) that a randomly selected person consumed 8 cups of coffee is given by;

the relative frequency of 8 = 0.025

Answer:

V = 696.91

Step-by-step explanation:

Volume of a sphere formula:

V = 4/3πr³

Given:

d = 11

r = d/2

r = 5.5

Work:

V = 4/3πr³

V = 4/3π(5.5)³

V = 4/3π(166.375)

V = 696.91

Answer:

The answer is below

Step-by-step explanation:

The model is a tile with length 1/4 in. and width 1/6 in while the actual tile has length 1/6 ft. and width 1/9 ft.

Firstly we have to convert the model length and width from inches to feet.

1 feet = 12 inches

model length =  1/4 in. = 1/4 in * (1/12) ft./in = 1/48 ft.

model width =  1/6 in. = 1/6 in * (1/12) ft./in = 1/72 ft.

Therefore:

Ratio of model length to actual length of tile = (1/48 ft.) / (1/6 ft.) = 1 / 8

Ratio of model length to actual length of tile = (1/72 ft.) / (1/9 ft.) = 1 / 8

Area of model tile = length * width = 1/48 ft. * 1/72 ft. = 1/3456 ft²

Area of actual tile = length * width = 1/6 ft. * 1/9 ft. = 1/54 ft²

Ratio of model area to actual area of tile = (1/3456 ft²) / (1/54 ft²) = 1 / 64

Answer:

2.77

Step-by-step explanation:

39.50x.07=2.77

Answer:

20

Step-by-step explanation:

Answer:

Step-by-step explanation:

convert either gram into kg or kg into gram

lets convert kg into g

1 kg=1000g

20kg=1000*24g

=20000g

450/20000*100%

450/200%

2.25%

first convert 450 g to kg = 0.45 kg

Now 0.45 kg as a. percentage of 20 kg = 0.45/20×100= 2.25%

Answer:

The third one

Step-by-step explanation:

Answer:

the third one

Step-by-step explanation:

Answer:

Girl i dont know im so sorry

Step-by-step explanation:

good luck on ur assignment tho xoxo

Answer:

326.73cm²

Step-by-step explanation:

=

2

π

r

h

2

π

r

2

=

2

π

4

9

2

π

4

2

≈

326.72564cm²

Answer:

It would be 125 fish.

Step-by-step explanation:

This is because since there are 10 crustaceans for every 25 fish, there are 2.5 times more fish than crustaceans. Therefore, if there were 50 crustaceans, you would do 50 * 2.5 to get 125 fish.

Answer:

p = 4

Step-by-step explanation:

Given the expression x ^ 2-px + 3 = 0

If x = 0 is a solution

Substitute into the expression

0² - 0p + 3 = 0

-0p = -3

p = 3/0

p cannot be determined for this root

If x = 1

1² - 1p + 3 =0

1 - p + 3 = 0

-p+4 = 0

-p = -4

p = 4

Hence the va;ue of p is 4

Answer:

SR=1/2*PO

5x-38=1/2*7x-49

2(5x-38)=7x-49

10x-76=7x-49

10x-7x=-49+76

3x=27

x=27/3

x=9

substitute the value of x in RS

5x-38

5*9-38

45-38

7

Step-by-step explanation:

Answer:

RS = 7

Step-by-step explanation:

Given a segment joining the midpoints of 2 sides of a triangle then it is half the length of the third side, that is

5x - 38 = [tex]\frac{1}{2}[/tex] (7x - 49) ( multiply both sides by 2 to clear the fraction )

10x - 76 = 7x - 49 ( subtract 7x from both sides )

3x - 76 = - 49 ( add 76 to both sides )

3x = 27 ( divide both sides by 3 )

x = 9

Then

RS = 5x - 38 = 5(9) - 38 = 45 - 38 = 7

Answer:

6 x 5 x 1/2(divide by 2) = 15, 15 x 2(two triangles) = 30

27 x 6 = 162 (area of base)

27(width) x 6(height) x 2(two rectangles on both slanted sides) = 324

Add given areas:

30 + 162 + 324 = 516 ft2 is your answer.

Answer:

(2,-7)

Step-by-step explanation:

Answer:

1.0

2.undefined

Step-by-step explanation:

Answer:1) 0, 2) is undefined

Step-by-step explanation:

Answer:

68

Step-by-step explanation:

A P E X

Answer:

11h +5x

Step-by-step explanation:

6h + 5(x + h)

Distribute

6h + 5x+ 5h

Combine like terms

11h +5x

Answer:

12barras

Step-by-step explanation:

Hoy vamos a hacer una excursión con la escuela y tuvimos que hacer sándwiches para toda la clase. Si gastamos 2 hogazas de pan para hacer sándwiches para mis 4 hermanos, ¿cuántas hogazas de pan necesitaremos para hacer sándwiches para los 24 estudiantes de la clase?

De la pregunta anterior:

4 personas = 2 barras de pan

24 personas = x

Multiplicar cruzada

4 × x = 24 × 2 barras de pan

x = 24 × 2 barras de pan / 4

x = 12 barras de pan

Answer:

150.7

Step-by-step explanation:

Formula to the find volume of a pyramid:

V=1/3 (B)(h)

V=1/3 (19) (23.8)

Answer:

7 feet i think? i may be wrong tho

Step-by-step explanation:

Answer:

Q1. A. 209.8

Q2. B. 313.6

Q3. 448.22 (not in ur options)

Step-by-step explanation:

Answer:

Tip = $9

Step-by-step explanation:

Bill amount to nearest ten dollars = $60

[tex]tip = 15\% of 60 = \frac{15}{100} \times 60 = 9[/tex]

Answer:

X = -2

Step-by-step explanation:

Hope this helps

Answer:

Step-by-step explanation:

take theta as reference angle

using sin rule

sin theta=opposite/hypotenuse

sin theta=3/5

sin theta=0.60

theta=sin 37 degree

therefore the value of theta is 37 degree.

Answer:  a is 21 b is 45 and c is yes more people are going above because the median is above the speed limit

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

An input can only have one output.

Answer: 3.9047 rounded to the nearest thousandth is 3.9050, or 3.905.

Step-by-step explanation:

You round 47 up to 50, which gets you to 3.9050, which you can then reduce it to 3.905.