A candy distributor needs to mix a 10% fat-content chocolate with a 40% fat-content chocolate to create 100 kilograms of a 16% fat-content chocolate. How many kilograms of each kind of chocolate must they use?

Answers

Answer 1

Answer: $x-how\ many\ kilograms\ of\ 10\%\ fat-content\ chocolate\n \n10\%\cdot x+40\%\cdot(100-x)=16\%\cdot 100\n \n 0.10x+0.4(100-x)=0.16\cdot 100\n \n0.1x+40-0.4x=16\n \n-0.3x=-24\ /:(-0.3)\n \nx= (24)/(0.3) \n \nx=80\ \ \ \Rightarrow\ \ \ 100-x=100-80=20\n \nAns.\ 80\ kg\ -of\ 10\%\ fat-content\ chocolate;\ \n20\ kg-of\ 40\%\ fat-content\ chocolate$

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Write the denominator of the fractiona 7/20 as the product of prime factors

Answers

Answer:

Step-by-step explanation:

prime factors of 20 = 2 * 2 * 5

$(7)/(20)=(7)/(2*2*5)$

Final answer:

The denominator of the fraction 7/20 can be written as the product of prime factors: 2 x 2 x 5.

Explanation:

The denominator of the fraction 7/20 can be written as the product of prime factors by finding the prime factorization of 20.

Start by dividing 20 by the smallest prime number, which is 2. 20/2 = 10.
2 is a prime factor, so we continue to divide 10 by 2. 10/2 = 5.
5 is a prime number, so we have found the prime factorization of 20: 2 x 2 x 5 = 20.

Therefore, the denominator of the fraction 7/20 can be written as 2 x 2 x 5.

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A sample with which of these variances has a standard deviation that is greater than the variance?A. 2.25
B. 1.75
C. 0.75
D. 1.25

Answers

By using relation between standard deviation and variance we got that sample with 0.75 variance has a standard deviation that is greater than the variance

What is standard deviation?

Standard deviation is a number used to tell how measurements for a group are spread out from the average (mean), or expected value

Here we have to find a sample with standard deviation greater than the variance.

We know that Standard deviation is the square root of the variance so if we want a sample with greater Standard deviation than the variance then it's variance should be less than one as we know that if

$0 < x < 1 \Rightarrow \sqrt x > x$

And here given variances are

2.25, 1.75,0.75 and 1.25

Hence 0.75 is correct answer

By using relation between standard deviation and variance we got that sample with 0.75 variance has a standard deviation that is greater than the variance

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Standard deviation is the square root of the variance. For the square root of a number to be greater than the number, the number must be between 0 and 1.
Hence, for the standard variation to be greater than the variance, the variance must be between 0 and 1.

Answer: C [0.75]

The table and the graph each show a different relationship between the same two variables, x and y:A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 3,180 and 4,240 and 5,300 and 6,360. On the right of this table is a graph. The x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis values on the graph are from 0 to 350 in increments of 70 for each grid line. A line passing through the ordered pairs 2, 70 and 4, 140 and 6, 210 and 8, 280 is drawn.

How much more would the value of y be in the table than its value on the graph when x = 11?

110
150
215
275

Answers

Answer:

The value of y be in the table is 275 more than its value on the graph when x = 11.

Step-by-step explanation:

The slope represent the changer is y with respect to change in x.

$Slope=(y_2-y_1)/(x_2-x_1)$

From the table it is noticed that the value of y increased by 60 as the value of x increased by 1. Therefore the slope of the function is 60. It is also calculated by the formula. The two points from the table are (3,180) and (4,240).

$Slope=(240-180)/(4-3)=60$

The point slope form is,

$y-y_1=m(x-x_1)$

The equation of function is,

$y-180=60(x-3)$

$y-180=60x-180$

$y=60x$

Put x=11

$y=60* 11=660$

Therefore the value of table is 660 at x=11.

The two points from the graph are (2,70) and (4,140).

$Slope=(140-70)/(4-2)=35$

The equation of line is,

$y-70=35(x-2)$

$y-70=35x-70$

$y=35x$

Put x=11

Therefore the value of line is 385 at x=11.

The difference between values of y at x=11 is,

$660-385=275$

Therefore the value of y be in the table is 275 more than its value on the graph when x = 11.

Answer:

the answer is 275.

i got it right on my test.

Harrison mows lawns and rakes leaves for his summer and fall weekend jobs. He gets $10 an hour to mow lawns and $8 an hour to rake leaves. If, during September, Harrison mows for m hours and rakes for 12 hours, which expression represents the amount of money he makes

Answers

The expression which represents the amount of money he makes is 10m + 96

How to be write mathematical expression?

Amount earned per hour for lawns = $10
Amount earned per hour to rake leaves = $8
Number of hours mowed = m
Number of hours raked = 12 hours

Total amount of money earned = (10 × m) + (8 × 12)

= 10m + 96

Therefore, the expression which represents the amount of money he makes is 10m + 96

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10m+8(12)

Harrison mowes lawns for 11 hours, so m=11. How Much money does he make in September? He makes 206 $.

Mark was thinking of a number. Mark doubles it and gets an answer of 64. What was the original number?

Answers

Answer:

Step-by-step explanation:

32x2=64

Answer:

Step-by-step explanation:

64/2=32

What is the slope-intercept equation for the line below?

Answers

Answer: D

Step-by-step explanation:

If we look at the graph we can see that the line intercepts the y-axis at (0,-4), so the intercept must be -4.

If we use the rise-over-run formula for (0,-4) and (4,1) we would get:

$(1--4)/(4) \n\n=(5)/(4)$

Since the line is going upwards, the equation must be positive.

Therefore, the equation in slope-intercept form is y=5/4x-4.

Answer is D

First, we can eliminate option b and c because they are negative, and the line in the graph is goin up.
Then you count and get that the m is 5/4, put it together: y=5/4x-4

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