What is the solution to the system of equations?
{2x + 3y = 6
x+y=1

Answer:

10.

Step-by-step explanation:

X is often associated with the value of "independent variable"

y=20-2(5)

y=20-10

y=10

The amount of fabric used to make the headband is 16.13 inches. The amount of fabric used to make the wristband is 9.64 inches.

In order to determine the amount of fabric used to make the accessories, the total inches used would be divided by the total number of people the accessory was made for.

The amount of fabric used to make headband for a player = total quantity of fabrics used / total number of people

677.46 / (38 + 4)

677.46 / 42

= 16.13 inches

The amount of fabric used to make wristband for a player = total quantity of fabrics used / total number of players

366.32 / 38 = 9.64 inches

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Answer:12 accorns

Step-by-step explanation:

If they each hid the same number of acorns, although the squirrel needed 4 fewer holes, the chipmunk hid 3 acorns in each hole

Let's assume the number of holes the chipmunk dug is 'c', and the number of acorns it hid in each hole is 'x'. Similarly, let's assume the number of holes the squirrel dug is 's', and the number of acorns it hid in each hole is 'y'.

According to the information provided, the chipmunk hid 3 acorns in each of the holes it dug, so x = 3. The squirrel hid 4 acorns in each of the holes it dug, so y = 4.

Both the chipmunk and squirrel hid the same number of acorns, so cx = sy.

Also, the squirrel needed 4 fewer holes, so s = c - 4.

Now, we can use the information to set up a system of equations:

cx = sy

c - 4 = s

Substitute the value of s from the second equation into the first equation:

c(c - 4) = 3(c - 4)

Expand the equation:

c² - 4c = 3c - 12

Now, bring all terms to one side of the equation:

c² - 4c - 3c + 12 = 0

Combine like terms:

c² - 7c + 12 = 0

Now, factor the quadratic equation:

(c - 3)(c - 4) = 0

Now, set each factor to zero and solve for 'c':

c - 3 = 0 => c = 3

c - 4 = 0 => c = 4

Since the chipmunk hid 3 acorns in each hole, the correct answer is The chipmunk hid 3 acorns.

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The area of the forest in square yards is [tex]9.3 \times 10^6[/tex]

The area of the forest in square miles is given as:

[tex]Area = 3mi^2[/tex]

To convert the area to square yards from square miles, we multiply the area by 3.098 * 10^6.

So, we have:

[tex]Area = 3 \times 3.098 \times 10^6yd^2[/tex]

Evaluate the product

[tex]Area = 9.294 \times 10^6yd^2[/tex]

Approximate

[tex]Area = 9.3 \times 10^6yd^2[/tex]

Hence, the area of the forest in square yards is [tex]9.3 \times 10^6[/tex]

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Answer:

Step-by-step explanation:

Let the number of quarters be x and nickels be y.

Given:

We have equations:

Solve the system by elimination, subtract 5 times the first equation from the second one:

Find the value of y:

Verify:

Answer: 3050.8877551

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

5 x 4 = 20

Answer: 20 slices of pizza

Step-by-step explanation:

you multiply 5 times 4

Answer:

c. $324

Step-by-step explanation:

The solution is,

A) 83/400= 0,2075

B) 100/400=0,25

C) 42/400= 0,105

D) 42/100= 0,42

E) The special training program was effective.

Division can be stated as the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

Explanation:

Total population= 400 salespeople

Received a bonus last year= 83 salespeople

Attended a special sales training program= 100 salespeople

Both attended sales training and received a bonus= 42 salespeople

a) You need to calculate the number of salespeople that receive a bonus over total population

83/400= 0,2075 The proportion of salespeople that receive a bonus is 0,2075

b) You need to calculate the number of salespeople that attended a special program over total population

100/400= 0,25 The proportion of salespeople that attended a special program is 0,35

c) 42/400= 0,105  The proportion of salespeople that receive a bonus and attended a special program is  0,105

d) You need to calculate the proportion of people that having attended received a bonus.

42/100= 0,42  The proportion of salespeople that receive a bonus having attended a special program is  0,42

e) The special training program was effective. The proportion of people that receive a bonus over the total population that didn't attend the program (41/300=0,14) is inferior to the proportion of salespeople that attend the program and receive a bonus. Meaning that there are more chances of receiving a bonus taking a training program.

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Complete question:

A company employs 400 salespeople. Of these, 83 received a bonus last year, 100 attended a special sales training program at the beginning of last year, and 42 both attended the special sales training program and received a bonus. (Note: the bonus was based totally on sales performance.) a) What proportion of the 400 salespeople received a bonus last year? b) What proportion of the 400 salespeople attended the special sales training program at the beginning of last year? c) What proportion of the 400 salespeople both attended the special sales training program and received a bonus? d) What proportion of the salespeople who attended the special sales training program received a bonus? e) Based on your answers to parts a and d, does the special sales training program seem to have been effective? Explain your answer.

See picture for solution.

Answer:

Yes Jeff is the correct answer

Step-by-step explanation:

Answer:

  more than 1100

Step-by-step explanation:

The contribution margin for each package sold is ...

  $6.50 -3.00 = $3.50

The number of packages that must be sold to cover fixed costs is ...

  3.50n > 3850

  n > 1100 . . . . . . . divide by 3.50

The company will generate a profit if more than 1100 packages are produced and sold each week.

_____

Additional comment

If exactly 1100 packages are sold, then costs are covered, but profit is 0. In order for profit to be positive, more than 1100 packages must be sold.

Answer:

Step-by-step explanation:

Answer:

4.5 ounces

Step-by-step explanation:

18/4=4.5

Answer:

80

Step-by-step explanation:

25 percent is equal to 1/4

1/4 of 80 is 20

Answer:

80

Step-by-step explanation:

Recall that for two vector x and y making an angle θ with each,

x • y = ||x|| ||y|| cos(θ)

If we replace y with x, we see that

x • x = ||x|| ||x|| cos(0) = ||x||²   ⇒   ||x|| = √(x • x)

Using the last identity, the magnitude of w is

||w|| = √(w • w)

but since w = u + v, we have

w • w = (u + v) • (u + v)

The dot product distributes over sums and is commutative, so

w • w = (u • u) + (u • v) + (v • u) + (v • v)

… = ||u||² + 2 (u • v) + ||v||²

… = ||u||² + 2 ||u|| ||v|| cos(θ) + ||v||²

If u has a direction of 45° with the positive x-axis, v has a direction of 150°, then the angle between u and v is |45° - 150°| = 105°. So,

||w|| = √(||u||² + 2 ||u|| ||v|| cos(150°) + ||v||²)

… = √(10² + 2 • 10 • 13 cos(150°) + 13²)

… ≈ 14.2

Using the parallelogram rule for vector addition (see attached sketch), the sum of the angle between w and u and 45° is equal to the direction of w.

If φ is the angle between w and u, then

w • u = ||w|| ||u|| cos(φ)

… = 14.2 • 10 • cos(φ)

but we also have

w • u = (u + v) • u

… = (u • u) + (v • u)

… = ||u||² + ||u|| ||v|| cos(105°)

… = 10² + 10 • 13 • cos(105°)

… ≈ 66.4

Then

14.2 • 10 • cos(φ) ≈ 66.4

cos(φ) ≈ 0.467

φ ≈ 62.1°

and so the direction of w is 62.1° + 45° ≈ 107.1°.

Answer:

whats the question, tell me it and i'll help you

Step-by-step explanation:

Answer:

x =-27

Step-by-step explanation:

X/3= -9

or,X=-9×3(cross multiplication)

or, X=-27

Answer:

9b+10s

Step-by-step explanation:

you are trying to find an expression for total cost after an unknown amount of hours. you need to multiply the number of hours (defined as b and s in this example) by the cost per hour given ($9/hr for the bike and $10/hr for the scooter).

this would result in the following expression: total cost=9b+10s

Answer:

a) f(n) = 11 + f(n - 1)

Step-by-step explanation:

f(2) = 11 + 4 = 15

f(3) = 11 + 15 = 26

f(4) = 11 + 26 = 37

f(5) = 11 + 37 = 48

Answer:

(8,-9)

Step-by-step explanation:

using the principle of vectors, you match each number to their coordinates and add them

so we have (7+1,-12+3)

which is equal to (8,-9)

Answer:

5/2

Step-by-step explanation:

Formula: y2-y1/x2-x1

Labeled:

(1,3)

1 = x2

3 = y2

(7,-12)

7= x1

-12 = x1

In order:

3+12 / 1-7

=15/6

which is simplified to 5/2

so when trying to find the slope of two points you want to use a certent formula which is y2 minus y1 over x2 minus x1 and if the x1 or y1 is negative it will be plus.

first you need to label them and then put them in the order you labeled them to the formula. After subtract or add and if you can simplify it then simplified it to get your answer.

this is the best way I can explain it, sorry

:(

Answer:

∠4 = 135°

Step-by-step explanation:

∠4 = the sum of the two remote angles in the triangle.  (remote angles are the angles not  next to ∠4

∠4 = 80° + 55°

∠4 = 135°

Answer:

<4 = 135

Step-by-step explanation:

I took this test

Answer:

Multiply each side by −5, add 25 to each side.

Step-by-step explanation:

Answer:

43 messages

Step-by-step explanation:

Given:

146 messages = $21.90

x messages = $6.45

Finding x by cross-multiplication:

x = 146*6.45/21.90 = 43

Hope this helps! :)

Answer: b

Step-by-step explanation: graph b is correct hope it helps

Answer:

i would say A. if its not a its B.

Step-by-step explanation: