The table shows the number of candies packed by Machine J. The equation shows the number of candies packed by Machine K. In both representations, x is a measure of the number of minutes and y is a measure of the number of candies packed. Machine J Candy Packing
x
(minutes) y
(candies)
3 90
6 180
9 270
12 360

Machine K: y = 26x

How many more candies could machine J pack than machine K in 11 minutes?
30
44
90
330

Answers

Answer 1

Answer: To find out the answer, treat both machines as lines. The answer can be found when you have equations for each machine. The first step of that would be to make an equation for "line" J, so find the slope using two sets of its given coordinates, I'll use (3,90) and (6,180).

$(y_2 - y_1)/(x_2 - x_1)$ Substitute in the x and y values
$(180 - 90)/(6 - 3)$ Subtract
$(90)/(3)$ Divide
30

Now that you know 30 is the slope, you can plug that and one set of coordinates, I'll use (3,90) into point-slope form.

y - y_1 = m(x - x_1) Substitute in your x and y coordinates and slope
y - 90 = 30(x - 3) Use the Distributive Property
y - 90 = 30x - 90 Add 90 to both sides
y = 30x

Now you have the equations for both machines. You want to find out how many candies each machine packages in 11 minutes, and x represent minutes, so plug 11 into the x value for both equations.

Machine J

y = 30x Substitute
y = 30 (11) Multiply
y = 330

Machine J packs 330 candies in 11 minutes.

Machine K

y = 26x Substitute
y = 26 (11) Multiply
y = 286

Machine K packs 286 candies in 11 minutes.

Finally, to find out how many more candies Machine J packs than Machine K, subtract the two values.

330 - 286 = 44

Machine J can pack 44 more candies than Machine K in 11 minutes.

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In right triangle ABC, the right angle is A and m b=46°. what is m_c?

Answers

Interpretation: In triangle ABC, A is the right angle, angle B measures 46 degrees. Find the measure of angle C.

Assuming correct interpretation,
We know there are 180 degrees in a triangle.
A right angle is 90 degrees. So together, A and B measure 90 + 46 = 136 degrees. This means the last angle must be 180 - 136 = 44 degrees

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Answers

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How many times greater is 70,000,000 ( 70 million) than 7,000,000 (7 million) ?

Answers

70,000,000 is 10 times greater than 7,000,000

Julia works at a music store. One of her jobs is to stock new CDs on the shelf. A recent order arrived with 215 classical CDs, 125 jazz CDs, and 330 soft rock CDs. Part A
julia needs to place the CDs on the sale racks wth 5 CDs in each group. Write two different equations that can be used to show how many groups, g Julia will use to arrange all the CDS.
Equation:

Answers

Solution:

Total Number of CD's=215 classical CD's + 125 jazz CD's, and 330 soft rock CD's

=215+125+330

=340+330

=670 CD's

Number of CD's that Julia want to place in each group = 5 CD's

There are two ways in which 5 CD's can be placed in a group, either 5 CD's in a row or 5 CD's in a Column.

Let number of rows that contain 5 CD's in a group in the shelf = x

And, Number of Columns which contain 5 CD's in a group in the shelf= y

Equation containing number of groups containing 5 CD's can be written as

→5 x=670

→5 y= 670

Total number of groups in either case will be

$=(670)/(5)\n\n=154$

Equation: {[(215+125)+330)]/5} /is divided by.

To solve the equation for x by completing the square what equation is equivalent to x^2-x-2=0here are options for both blanks (The equivalent equation (x-Blank)^2=Blank

-1/4
1/4
-1/2
1/2
-9/4
9/4
-3/2
3/2

Answers

so to complete the square in
ax^2+bx+c=d form

make sure a=1
subtract c from both sides
take 1/2 of b and square it
add that to both sides
factor perfect square

1x^2-1x-2=0
a=1
move c to other side
add 2 to oth sides
x^2-1x=2
take 1/2 of b and square it
1/2 of -1=-1/2
squaer it
1/4
add that to both sides
x^2-1x+1/4=2+1/4
factor left side
(x-1/2)=2+1/4

first blank is 1/2

2+1/4=8/4+1/4=9/4

blanks are
1/2 and 9/4

In a survey, 70 out of 84 people from the north prefer professional football over college football. 120 people from the south were asked the same question. In order for favorite type of football and region to be independent, how many people in the south would have to prefer professional football

Answers

Answer: Around 100 people will answer that they prefer professional football.

Step-by-step explanation:

In the north, 70 out of 84 prefer professional football, then the relative frequency is

p = 70/84 = 0.83

Now, in the south, they asked to 120 people, and we can assume that the relative frequency will be about the same than in the north (because the relation is independent, which means that the region does not affect on the answer to the question of if they prefer professional or college football), so we have that if X people prefer professional football, we have:

p = X/120 = 0.83

X = 120*0.83 = 100

So around 100 people will answer that they prefer professional football.

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