Suppose an apple picker in China earns an average wage of 45 cents per hour. An apple picker can harvest about 2.0 bushels of apples each hour. One gallon of apple juice requires 40 apples. Each bushel contains about 126 apples. What is the labor cost of one gallon of apple juice in dollars?

Answer:

(66.3-14.62)/0.6-0.22

(51.68)/0.6-0.22

(51.68/0.6)-0.22

(86.14667)-0.22

85.92667

Answer:

$96.00

Step-by-step explanation:

Perimeter formula, 2w+2l

2(23)+2(25)=96 feet

1$ per foot

96 feet,

so $96

Answer:

I think it 96.00

Step-by-step explanation:

Answer:

Step-by-step explanation:

the upper left graph is the correct answer

because "... or equal to" always represents a filled dot, while just "greater/less than" represents blank dot

Answer:

Step-by-step explanation:

Cassava = 1/3 of his land

Remaining after planting Cassava = 1 - 1/3 = 2/3 of his land

Maize = 2/5 x 2/3 = 4/15 of his land

Vegetables = 2/3 - 4/15 = 2/5 of his land

If vegetables = 10 acres

2/5 of his land = 10 acres

1/5 of his land = 10 ÷ 2 = 5 acres

5/5 of his land = 5 x 5 = 25 acres

Greetings from Brasil...

Here we have application of Trigonometry

COS β = adjacent side ÷ hypotenuse (H)

bringing to our problem....

COS A = AC ÷ H

But we dont have AC.... We have to use Pitagoras:

AB² = AC² + BC²

AC² = AB² - BC²

AC = √(AB² - BC²)

AC = √(10² - 8²)

AC = √(100 - 64)

AC = √36

So

COS A = AC ÷ H  ⇔ COS A = AC ÷ AB

COS A = 6/10

Answer: B) 3/5

Step-by-step explanation:

Cos = adjacent/hypotenuse

Thus, the cos is AC/AB.

Because of Pythagorean Theorem, AC^2=AB^2-BC^2.  Let AC be x.

[tex]x^2=10^2-8^2\\x^2=100-64\\x^2=36\\x=6[/tex]

Thus, the cos is 6/10, or 3/5

Answer:

2

-5

49

-6

3

Step-by-step explanation:

Coefficient is a number, value or item that serves as a measure of some property or characteristic.

or in other words a number that is added in front of a term.

Hope this helps ;) ❤❤❤

Answer:

y + c ÷ m = x

Step-by-step explanation:

You start of with:

y = mx - c

We can get rid of the + c by putting it on the other side. When a number goes to the other side it does the opposite, so the - will become a +. It will end up as:

y + c = mx

We just need x on itself so we need to get ride of m. In this sum, mx means that they are multiplying together, we need to make that divide. So we take m on the other side and make it divide. This brings us to x on itself.

(y+c) ÷ m = x

Hope this helps.

x can be changed into the subject of the formula as x = (y + c) / m.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Subject of an equation is that variable we are going to find out.

The given equation is y = mx - c.

Here y is the subject.

We need to rewrite the equation to make x the subject.

y = mx - c

Adding c on both sides,

y + c = mx - c + c

y + c = mx

Dividing both sides by m, we get,

(y + c) / m = mx / m

(y + c) / m = x

Hence the given formula y = mx - c can be rewritten to make x the subject as x = (y + c) / m.

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Answer:

1. a. b = - 8

b. x = 8

c. x = 11

d. x = 5

2. 12 soccer balls and 8 basketballs can be purchased.

Step by step explanation

a. [tex] - 14 + 6b + 7 - 2b = 1 + 5b[/tex]

Calculate the sum

[tex] - 7 + 6b - 2b = 1 + 5b[/tex]

Collect like terms

[tex] 7 + 4b = 1 + 5b[/tex]

Move variable to L.H.S and change it's sign

Similarly, Move constant to R.H.S and change its sign

[tex]4b - 5b = 1 + 7[/tex]

Collect like terms

[tex] - b = 8[/tex]

Change the signs on both sides of the equation

[tex]b = - 8[/tex]

-----------------------------------------------------------------

b. [tex] \frac{5x + 10}{ - 6} = - 5[/tex]

Apply cross product property

[tex]5x + 10 = - 5 \times ( - 6)[/tex]

Multiply the numbers

[tex]5x + 10 = 30[/tex]

Move constant to R.H.S and change its sign

[tex]5x = 30 - 10[/tex]

Calculate the difference

[tex]5x = 20[/tex]

Divide both sides of the equation by 5

[tex] \frac{5x}{5} = \frac{20}{5} [/tex]

Calculate

[tex]x = 4[/tex]

----------------------------------------------------------------

c. [tex] - 15 = \frac{ - 8x - 17}{7} [/tex]

Apply cross product property

[tex] - 15 \times 7 = - 8x - 17[/tex]

Multiply the numbers

[tex] - 105 = - 8x - 17[/tex]

Swap the sides of the equation

[tex] - 8x - 17 = - 105[/tex]

Move constant to R.H.S and change its sign

[tex] - 8x = - 105 + 17[/tex]

Calculate

[tex] - 8x = - 88[/tex]

Change the signs on both sides of the equation

[tex]8x = 88[/tex]

Divide both sides of the equation by 8

[tex] \frac{8x}{8} = \frac{88}{8} [/tex]

Calculate

[tex]x = 11[/tex]

------------------------------------------------------------------

D. [tex]5 = 6x + 5(x - 10)[/tex]

Distribute 5 through the parentheses

[tex]5 = 6x + 5x - 50[/tex]

Collect like terms

[tex]5 = 11x - 50[/tex]

Swap both sides of the equation

[tex]11x - 50 = 5[/tex]

Move constant to R.H.S and change its sign

[tex]11x = 5 + 50[/tex]

Calculate the sum

[tex]11x = 55[/tex]

Divide both sides of the equation by 11

[tex] \frac{11x}{11} = \frac{55}{11} [/tex]

Calculate

[tex]x = 5[/tex]

------------------------------------------------------------------

2.

Solution,

No.of students in soccer = x

No.of students in basketball = y

Total no.of students = 20

i.e x + y = 20 → equation ( i )

Cost of soccer ball = $ 7

Cost of basketball = $ 10

Total budget = $ 164

i.e 7x + 10 y = 165 → equation ( ii )

In equation ( i ),

x + y = 20

Move 'y' to R.H.S and change its sign

x = 20 - y

Put the value of x in equation ( i )

[tex]7(20 - y) + 10y = 164[/tex]

[tex]140 - 7y + 10y = 164[/tex]

[tex]3y = 164 - 140[/tex]

[tex]3y = 24[/tex]

[tex]y = \frac{24}{3} [/tex]

[tex]y = 8[/tex]

Now, put the value of y in equation ( i ) ,

x + y = 20

[tex]x + 8 = 20[/tex]

[tex]x = 20 - 8[/tex]

[tex]x = 12[/tex]

Hence, 12 soccer balls and 8 basketballs can be purchased.

Hope this helps...

Best regards!!

Answer:

1. b = -8

2. x = 8

3. x = 11

4. x = 5

hope that helpwd

Answer:

x=1/4c+1/4k

Step-by-step explanation:

4x-c=k

move c over

4x=c+k

then divide by 4

x=1/4c+1/4k

hope this helps

Answer:

12.65

Step-by-step explanation:

In the case of the blue triangle, to calculate the rise, which would be the increase, therefore it would be the hypotenuse formed by the arrow.

We have to Pythagoras is:

h ^ 2 = a ^ 2 + b ^ 2

In this case:

a (x-axis) = 4

b (y-axis) = 12

replacing:

h ^ 2 = 4 ^ 2 + 12 ^ 2

h ^ 2 = 160

h = 12.65

Which means that the rise in the blue triangle is 12.65 units

Answer:

5.65%

Step-by-step explanation:

Principal=$600

Time=20 years

FV=600*3=$1800

n=1

r=?

r= n[(A/P)^1/nt - 1]

=1{(1800/600)^ 1/1*20 - 1}

={(3)^1/20-1}

=3^0.05-1

=1.0565-1

=0.0565

rate=0.0565*100

=5.65% to the nearest hundredth percent

Answer: A) 2.95 units

Step-by-step explanation:

The diameter of a circle is twice the radius.  Thus, simply do 5.9/2 to get that the radius is 2.95 units long.

Hope it helps <3

Answer:

your answer would be A-2.95

5.9/2=2.95

Step-by-step explanation:

Answer:

0.2

Step-by-step explanation:

it works out to be 0.2 as a decimal and 20% as a percentage.

Answer:

.2

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find x we use cosine

That's

cos ∅ = adjacent / hypotenuse

From the question

The adjacent is x

The hypotenuse is 28

So we have

cos 43 = x / 28

x = 28 cos 43

x = 20.477

x = 20 to the nearest tenth

Hope this helps you

Answer:

Step by step explanation

1. [tex] \frac{1}{1 - x} + \frac{x}{ {x}^{2} - 1} [/tex]

Use [tex] \frac{ - a}{b} = \frac{a}{ - b} = - \frac{a}{b} [/tex] to rewrite the fractions

[tex] - \frac{1}{x - 1} + \frac{x}{(x - 1)(x + 1)} [/tex]

Write all numerators above the Least Common Denominator ( X - 1 ) ( X + 1 )

[tex] \frac{ - (x + 1) + x}{(x - 1)(x + 1)} [/tex]

When there is a ( - ) in front of an expression in parentheses , change the sign of each term in the expression

[tex] \frac{ - x - 1 + x}{(x - 1)(x + 1)} [/tex]

Using [tex](a - b)(a + b) = {a}^{2} - {b}^{2} [/tex] , simplify the product

[tex] \frac{ - x - 1 + x}{ {x}^{2} - 1 } [/tex]

Since two opposites add up to zero, remove them from the expression

[tex] \frac{ - 1}{ {x}^{2} - 1} [/tex]

So, Option A is the right option.

___________________________________

2.

[tex] \frac{ {x}^{2} - x - 12}{ {x}^{2} - 16} - \frac{1 - 2x}{x + 4} [/tex]

Write - X as a difference

[tex] \frac{ {x}^{2} + 3x - 4x - 12 }{ {x}^{2} - 16 } - \frac{1 - 2x}{x + 4} [/tex]

Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex] , factor the expression

[tex] \frac{ {x}^{2} + 3x - 4x - 12 }{(x - 4)(x + 4)} - \frac{1 - 2x}{x + 4} [/tex]

Factor the expression

[tex] \frac{x(x + 3) - 4(x + 3)}{(x - 4)(x + 4)} - \frac{1 - 2x}{x + 4} [/tex]

Factor out X+3 from the expression

[tex] \frac{(x + 3)(x - 4)}{(x - 4)(x + 4)} - \frac{1 - 2x}{x + 4} [/tex]

Reduce the fraction with x-4

[tex] \frac{x + 3}{x + 4} - \frac{1 - 2x}{x + 4} [/tex]

Write all the numerators above the common denominator

[tex] \frac{x + 3 - ( 1- 2x)}{x + 4} [/tex]

When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression

[tex] \frac{x + 3 - 1 + 2x}{x + 4} [/tex]

Collect like terms

[tex] \frac{3x + 3 - 1}{x + 4} [/tex]

Subtract the numbers

[tex] \frac{3x + 2}{x + 4} [/tex]

Undefined at,

X + 4 = 0

Move constant to R.H.S and change its sign

[tex]x = 0 - 4[/tex]

Calculate

[tex]x = - 4[/tex]

So, the answer is :

[tex] \frac{3x + 2}{x + 4} [/tex] , undefined at X = -4 and 4

Hope this helps..

Best regards!!

Answer:

f(x) = 2(x –3)²

Step-by-step explanation:

f(x) = 2x² – 12x + 18

The vertex form of the above expression can be obtained as follow:

f(x) = 2x² – 12x + 18

Factorise

f(x) = 2(x² – 6x + 9)

Next, we shall simplify x² – 6x + 9 by factorisation method.

This is illustrated below:

x² – 6x + 9

Multiply the first term i.e x² and last term i.e 9 together. The result is 9x².

Next, find two factors of 9x² such that their sum will result to the 2nd term i.e –6x in the expression above.

The factors are –3x and –3x

Next, replace –6x with –3x and –3x in the equation above as shown below:

x² – 6x + 9

x² – 3x –3x + 9

Factorise

x(x – 3) –3(x –3)

(x –3)(x –3)

(x –3)²

f(x) = 2x² – 12x + 18

f(x) = 2(x² – 6x + 9)

f(x) = 2(x –3)²

Therefore, the vertex form of the function f(x) = 2x² – 12x + 18 is

f(x) = 2(x –3)²

Answer:

3z/4

Step-by-step explanation:

Here, we start by calculating the 50% of z

mathematically, that would be 50/100 * z = 50z/100 = z/2

Now we want to calculate the 150% of this.

That would be 150/100 * z/2 = 150z/200 = 3z/4

Answer:

80

Step-by-step explanation:

t is important to note that a square of any non-zero integer is positive, and therefore there is no advantage in using negative integers instead of positive integers to attain the greatest difference of squares. So we will not consider negative integers.

The greatest value of a^2 - b^2 occurs when a^2 is at its largest and b^2 is at its smallest.

The larger a, the larger a^2:

8 ^ 2 = 64

9 ^ 2 = 81

10 ^ 2= 100

Since a^2 can have at most two digits, a=10 is too large, and so a=9 is the largest integral value of a we can use.

Now, b^2 is at its smallest when b is closest to zero on the number line (the further b gets from zero, the larger its square becomes):

2 ^ 2 = 4

1 ^ 2 =1

0 ^ 2 = 0

Remember to go back to the original problem sometimes, to make sure you are taking everything into account. It states b doesn't =0, and therefore the b=1 is the closest b can get to zero as an integer. So, the greatest difference between b^2 and a^2 is when b=1 and a=9, giving the result:

a^2-b^2 =9^2-1^2 =81-1= 80.

So, 80 is your answer.

Answer:

Shaded area: 70cm^2

Step-by-step explanation:

Whole=120cm^2

White Square=

10-2.5-2.5=5

12-1-1=10

5✖️10=50cm^2

Whole-white=70cm^2

Answer:

$3.25

Step-by-step explanation:

To get the price of one cup of coffee without including Dax's two dollar tip, the first step is to subtract 2 from 18.25.

18.25 - 2= 16.25

16.25 is price of the five cups of coffee that Dax bought without the two dollar tip. The final step is to get the price of one cup of coffee which is basically:

16.25 ÷ 5 = 3.25

The cost of each cup of coffee is $3.25.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

To get the price of one cup of coffee without including Dax's two-dollar tip, the first step is to subtract 2 from 18.25.

18.25 - 2= 16.25

16.25 is the price of the five cups of coffee that Dax bought without the two-dollar tip. The final step is to get the price of one cup of coffee which is basically:

16.25 ÷ 5 = $3.25

Hence, the cost will be $3.25.

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Answer:

last answer

Step-by-step explanation:

P' (2, -4)

Q' (-2, -5)

R' (1, -8)

Answer:

C. P'(2, -4) Q'(-2, -5) R'(1, -8)

Step-by-step explanation:

When you reflect something across the y-axis you change (x,y) to (-x,y).

For each point, change the x to a negative x.

P(-2, -4) --> P'(2, -4)

Q(2, -5) --> Q'(-2, -5)

R(-1, -8) --> R'(1, -8)

Hope this helps. If you have any follow-up questions, feel free to ask.

Have a great day! :)

Answer:

r=9

EF = 55

Step-by-step explanation:

CF = ED

9r - 6 = 8r+3

Subtract 8r from each side

9r-8r - 6 = 8r-8r+3

r-6 =3

Add 6 to each side

r-6+6 = 3+6

r = 9

EF= CD = 4r+19

            = 4*9+19

              =36+ 19

               =55

Answer:

x = 30

(30, 0)

Step-by-step explanation:

The x-intercept is when the graph crosses the x-axis when y = 0. In that case, simply plug in 0 for y:

x + 6(0) = 30

x + 0 = 30

x = 30

Answer: (30,0)

Step-by-step explanation:

x-intercept can be found in the form x = my + b, where b is the x-intercept. Thus, simply turn x+6y=30 into x-6y+30, to find that the x-intercept is (30,0)

Hope it helps <3

Answer:

[tex]n^6[/tex].

Step-by-step explanation:

[tex]n^4 * \frac{n^7}{n^5}[/tex]

= [tex]n^4 * n^{7 - 5}[/tex]

= [tex]n^4 * n^2[/tex]

= [tex]n^{4 + 2}[/tex]

= [tex]n^6[/tex].

Hope this helps!

Answer:

There are four possible outcomes for each spin: red, blue, yellow, green.

Answer:

5400 cycles

Step-by-step explanation:

You have the following function:

[tex]V(t)=220sin(180\pi t)[/tex]

where t is in seconds.

In order to find the number of cycles in 1 minute, you first  calculate the frequency of the function, which is given by:

[tex]f=\frac{180\pi}{2\pi}=90s^{-1}[/tex]

The number of cycles is then given by:

[tex]n=ft=(90s^{-1})(60s)=5400\ cycles[/tex]

There are 5400 cycles in 1 minute

Answer:

(3x + 20)° + 70° = 180°

Step-by-step explanation:

Answer:

10% off

Step-by-step explanation:

When $70 is discounted to $63, you can multiply 70 times 0.1 to get 7 which 70-63=7. To make 0.1 to a percentage, multiply by 100 to get 10%.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer: £4

Step-by-step explanation:

From the question, we are informed that when the normal price of a book is reduced by 30%, then the sale price of the book is £2.80.

Since the normal price of a book is reduced by 30%, that means the book is sold at (100% - 30%) = 70% of its normal price.

Let the normal price of the book be y.

70% of y = £2.80

70/100 × y = £2.80

0.7 × y = £2.80

0.7y = £2.80

y = £2.80/0.7

y = £4

The normal price of the book is £4.

Answer:

a. True, because they are corresponding angles.

b. False, because angles 1 and 2 are supplementary, meaning that they add up to 180 degrees, but 125 + 65 = 190 degrees.

c. True, because they are corresponding angles.

d. True, becuase they are two angles that add up to 180 degrees.

e. True, because they are both interior angles on opposite sides of the transversal.

Answer:

a. True.

b. False.

c. True.

d. True.

e. True.

Step-by-step explanation:

a. This statement is true because angles 6 and 8 are vertical angles. That means they are congruent.

b. This statement is false because Elm Street is a straight line, which means that angles 1 and 2 are supplementary angles and their measures will add up to be 180 degrees. 65 + 125 = 190, which is not equal to 180.

c. This statement is true because angles 5 and 1 correspond to each other.

d. This statement is true because angles 7 and 8 form a straight line.

e. This statement is true because they are interior angles that are alternate.

Hope this helps!