A candy distributor needs to mix a 40% fat-content chocolate with a 50% fat-content chocolate to create 100 kilograms of a 41% fat-content chocolate. How many kilograms of each kind of chocolate must they use? A) Write an equation that uses the information as it is given above that can be used to solve this problem. Use x as your variable to represent the quantity of 40% fat-content chocolate. Equation: B) Answer: They must mix ?Kilograms of the 40% chocolate and ?Kilograms of the 50% chocolate.

Answer:

(3, 6)

Step-by-step explanation:

1. If any factors can be cancelled out, then this indicates that there are holes in the graph.

2. To find the x-coordinate of the hole, set the factor equal to zero and solve for x.

3. Find the y-coordinate by substituting the x-coordinate back into the "reduced" function.

Here are the steps:

[tex]f(x) = \dfrac{ { x }^{ 2 } -9 }{ x-3 }[/tex]

Factor the top part of the function

x² - 9

Since both terms are perfect squares, factor using the difference of squares formula, a² - b² = (a + b) (a - b) where a = x and b = 3

(x + 3) (x - 3)

Now that we have the top part of the function factored, we can solve the rest of the problem:

[tex]f \left( x \right) = \dfrac{ \left( x+3 \right) \left( x-3 \right) }{ x-3 }[/tex]

Set the factor "x - 3" equal to zero and solve for x

x - 3 = 0

Add 3 to both sides

x - 3 + 3 = 0 + 3

Simplify

x = 3

Now we need to solve for "y"

[tex]f \left( x \right) = \dfrac{ \left( x+3 \right) \left( x-3 \right) }{ x-3 }[/tex]

We change "f(x)", to "y"

[tex]y = \dfrac{ \left( x+3 \right) \left( x-3 \right) }{ x-3 }[/tex]

The two "x - 3" cancel out

y = x + 3

Substitute the x-value into the equation

y = 3 + 3

Add 3 and 3

y = 6

Now that we have our coordinates, we can write it as:

(x, y) = (3, 6)

So the answer is (3, 6)

Answer:

1,000g:60sec

or 10 gram every singular second.

Step-by-step explanation:

Answer:

35.283

Step-by-step explanation:

Let's put it in a vertical format;

35

0.283

35 plus 0 = 35, and the rest will remain same, so the answer is 35.283

Answer:

-2

Step-by-step explanation:

4x:3=6:5.

4x/3=6/5

4x × 5=6×3

20 X=18

X=18-20

X=-2

Answer:

5+6 +(3*3)

Step-by-step explanation:

If you are allowed to mix the numbers then

5 + 6 + (3*3)

5+6 = 11

3*3 = 9

11+9 = 20

Hope this helps

Answer:

7

Step-by-step explanation:

there is 2k pounds per ton, so it would just be 14/7

Answer:

7

Step-by-step explanation:

GIven;

A truck delivers 14,000 pounds of gravel.

To FInd;

How many tons are in 14,000 pounds?

Note;

Pound to Ton = Formula: Divide the mass value by 2

Solve;

Hence, 14/2 = 7

~Learn with Lenvy~

Answer:

Dave had most fun for 1.5 minutes.

explanation:

Let the "fun time" be f

total time * portion of time fun  = fun time

[tex]\sf t * p = f[/tex]

[tex]\sf 6 \ * \frac{1}{4} = f[/tex]

[tex]\sf \frac{6}{4} = f[/tex]

[tex]\sf f = 1.5 \ minutes[/tex]

Question was for how many minutes, Dave had fun, so he had fun for 1.5 minutes

Let that half be x

So

[tex]\\ \rm\Rrightarrow x(4)=6min[/tex]

[tex]\\ \rm\Rrightarrow x=6/4[/tex]

[tex]\\ \rm\Rrightarrow x=1.5min[/tex]

Answer:

Use a simple random sampling technique.

Step-by-step explanation:

Sampling is a procedure applied in statistical analysis where a fixed number of data (observations or individuals) are selected from a superior population. The approach used to select a sample from a population is determined on the basis of the type of analysis being executed.

To test for defective bulbs the store manager has to select a sample. She can select a sample of size n from the 1000 bulbs using the simple random sampling technique.

A simple random sample is a part of a statistical population in which every individual of the population has an equal probability of being selected.

Assigning each individual of the population a unique number and using a computer or random number generator for selection is a procedure to select a simple random sample.

Answer:

it will travel 9 hour in 600miles

it will take 4 men to weed the same compound in 2 days

it will take 2 men to now a large piece of law in 3 days

Step-by-step explanation:

it

Answer:

Well i don't have a notebook but i can tell you how to graph it

Step-by-step explanation:

First of all its dotted lines since ther arent less than/greater than or equal to

then the first equation is shaded down with a y intercept of -1 and a slop of 1

the second equation opens up has a slope of -1 and a y intercept of 2

To answer your question no it's not.

Answer:

3

Step-by-step explanation:

2y - 6y = 5 - 17

-4y = -12

y = 3

Answer:

Derrick receive $11268.25 from his grandparents on his 18th birthday

Step-by-step explanation:

We are given  Derrick turned 15, his grandparents put $10,000 into an account that yielded 4% interest, compounded quarterly.

When Derrick turns 18, his grandparents will give him the money to use toward his college education.

Principal = $ 10000

Time = 18-15 = 3 years

Rate of interest = [tex]4\% = 0.04[/tex]

No. of compounds per year = 4

[tex]Amount = P(1+\frac{r}{n})^{nt}\\Amount=10000(1+\frac{0.04}{4})^{4 \times 3}\\Amount =11268.25[/tex]

Hence  Derrick receive $11268.25 from his grandparents on his 18th birthday

Answer:

7.3 years.

Step-by-step explanation:

A = P(1 + i)^n

9500 = 7500(1 + 0.033)^n     where n = number of years.

1.033^n = 9500/7500

n log 1.033 = log(9500/7500)

n =  log(9500/7500)/log 1.033

n = 7.28 = 7.3.

Answer:

-3/2

Step-by-step explanation:

use slope formula

y1-y2/x1-x2

Answer:

In equation form the answer is x=0y=10/3 but in point form the answer is (0,10/3)

Step-by-step explanation:

Answer:

C. 3 3/8

Steps:

1/8-(-5+3/4)= x + 1

1/8 - (-20+3/4) = x+ 1

1/8 - (-17/4)=x+1

1/8 +17/4= x + 1

1+17x2 /8= x+1

1+34 /8= x+1

35/8 = x + 1

x= 35/8 -1

x= 35-8 /8

x=27/8

x=3 3/8

Answer:

98 cm

Step-by-step explanation:

sum the parts of the ratio , 2 + 4 + 7 = 13 parts

divide perimeter by 13 to find the value of one part of the ratio.

182 ÷ 13 = 14 cm ← value of 1 part of the ratio , then

2 parts = 2 × 14 = 28 cm

4 parts = 4 × 14 = 56 cm

7 parts = 7 × 14 = 98 cm

the longest side is 98 cm

Answer:

ok

Step-by-step explanation:

Answer:

30%

Step-by-step explanation:

4320 - 288 = 4032

4032/12 =336 per copies

So, he sold them in 5760

5760 - 4032 = 1728

(1728/5760)*100 = 30%

Answer: a) y= 2,170,000(1+0.04)^10
b)  3,212,130 U.S. workers working at home.

Step-by-step explanation:

Step-by-step explanation:

initial amount: 2,170,000

rate of growth: 4%, or 0.04

time: 10 years

Using this information we can use the formula y=a(1+r)^t to figure out the answer.

After plugging in the amounts, we end up with the equation: 2,170,000(1+0.04)^10

Now, all that's left is to calculate. The final amount is 3,212,130

Answer:

A. 3680.32 inches³

Step-by-step explanation:

To find the volume of this shape, all we have to do is multiply the length width and height together:

v = l × w × h = 15.5 × 11.2 × 21.2 = 3680.32 inches³

Hope this helps!

Answer:

Step-by-step explanation:

Circumference: Pi(D)

Circumference: 3.14x30

Circumference: 94.2

Area: Pi(R)^2

Area: 3.14x15^2

Area: 3.14x225

Area: 706.5

Answer:

d) 168 in.³

Step-by-step explanation:

volume = length × width × height

volume = 6 in. × 4 in. × 7 in.

volume = 168 in.³

Answer: d) 168 in³

Step-by-step explanation:

        The volume of a right rectangular prism can be found by multiplying the base (the length times the width) by the height. Since we are given all the values needed, we can multiply them all together and find our answer.

                 V = length * width * height

                 V = 4 in * 6 in * 7 in

                 V = 168 in³

  This gives us an answer of "d) 168 in³"

The answer is given is explanation

Answer:

Step-by-step explanation:

Given the exponential function:

P(t) = 500,000 * e^(-0.099t)

P(t) = population t years later

When population will be one-half the initial amount

Half the initial amount = 500000/2 = 250,000

250000 = 500000 * e^(-0.099t)

250000/50000 = e^(-0.099t)

0.5 = e^(-0.099t)

Take the In of both sides

In(0.5) = - 0.099t

−0.693147 = - 0.099t

0.693147 / 0.099 = t

t =

Answer:

8cm

Step-by-step explanation:

The circumference of a circle= π×diameter(d)

= πd= 8π cm

d=8π/π =8cm

Answer:

3/2

Step-by-step explanation:

"Negative" means take the opposite sign.

"reciprocal" means flip it over.

Answer:

a is the answer................. :P

Step-by-step explanation:

slope = rise/run

rise=2

run=4

rise/run= .5

and it intercepts y-axis at -5

Answer:

Step-by-step explanation:

Sum = -14

Product = - 32

So, the factors = -16 , 2

When we add -16 +2 = -12 and when we multiply it is -32

w⁴ - 14w² - 32 =  w⁴ - 16w² + 2w² - 16 * 2

                      = w²(w² - 16) + 2(w² - 16)

                      = (w² - 16)(w² + 2)

                      = (w² - 4²)(w² + 2)

                      = (w + 4)(w - 4)(w² + 2)

Step-by-step explanation:

Replace w^2 with any other variable for eg: w^2=a

so that will make the equation:

a^2-14a-32

now factorize this equation and u can find the value of a

a^2-16a+2a-32

a(a-16)+2(a-16)

so factors= (a+2) (a-16)

since a was w^2 so replace them with w^2 and u got factors of the equation

you can also directly factorize the whole equation through middle term breaking

w^4-16w^2+2w^2-32

w^2(w^2-16)+2(w^2-16)

(w^2+2)(w^2-16)

you get the same answer