The PTA prepared 10 gallons of punch to serve at their first meeting. If each serving is eight ounces, how many people can be served?

The next correct step of the following elimination method is (C) subtract to eliminate 'x'

So, the next correct step of the elimination method:

Then, option (A) and option (D) is incorrect.

Thus, the correct option will be an option (C).

Therefore, the next correct step of the following elimination method is (C) subtract to eliminate 'x'

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The blue ribbon is 2.2 times longer than the orange ribbon

From the information given, we have that;

Now, lets convert the mixed fractions to improper fractions;

Length of orange ribbon = 95/12

Length of blue ribbon = 209/12

The ratio is expressed as;

Length of blue ribbon/length of orange ribbon

Substitute the values, we have;

= 209/12 ÷ 95/12

Take the inverse of the divisor and multiply

= 209/ 12 × 12/95

= 2. 2 times

Hence, it is 2.2 times longer.

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Answer:

The answer to your question is: 6 units

Step-by-step explanation:

Data

A (-4, 0)

B (-3,1)

C (0,-2)

D (-1,-3)

Formula

d = √((x2 - x1)² + (y2 - y1)²)

Process

dAB = √((x2 - x1)² + (y2 - y1)²)                 dAC = √((0 + 4)² + (-2 + 0)²)

      = √((-3 + 4)² + (1 - 0)²)                      dAC = √((4)² + (-2)²)

      = √((1)² + (1)²)                                    dAC = √(16 + 4)

      = √1 + 1                                             dAC = √20

dAB = √2  = dCD

dAD = √((-1 + 4)² + (-3 - 0)²)                    

dAD = √((3)² + (-3)²)

dAD = √9 + 9

dAD = √18 = dBC

reactangle's area = base x height = √18 x √2 = √18 x 2 = √36

                                                       = 6 units

Answer:d

Step-by-step explanation:

The answer after its estimation will be 3,00,00,000.

Here, the 53,320 will be estimated to 50,000 and 599 will be estimated to 600.

So, on multiplying, we get;

50,000×600 = 3,00,00,000

To offer an estimated, projected result rather than an exact result, we employ approximations in our calculations. Calculations are easier to handle when they are estimated using round numbers.

The result of rounding 109 to the closest ten is 110. and 100 is the nearest hundred. 2) Round the number downward if it is followed by the digits 0, 1, 2, 3, or 4. 102, for instance, is 100 when rounded to the closest ten.

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The division equation that represents number of 3/8 in 5/4 is 10/3 = x.

Given,

Fractions : 3/8 and 5/4

We have to find a division equation for number of 3/8 in 5/4

Number of 3/8 in 5/4 = x

Now,

Number of a in b = b/a

So here,

Number of 3/8 in 5/4, x = 5/4 / 3/8

Number of 3/8 in 5/4, x = 5/ 3/2

Number of 3/8 in 5/4, x = 5 × 2 / 3

Number of 3/8 in 5/4, x = 10/3

That is,

The division equation that represents number of 3/8 in 5/4 is 10/3 = x.

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Answer: Multiply 102 by 8.82 = 899.64x

Answer: b=116, c=64

Step-by-step explanation:

In an observational study, we measure or survey members of a sample without trying to affect them. In an experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.

This is clearly an observational study

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Answer:

it would be 89

Step-by-step explanation:

The measure of the acute angles in the triangle are 7.5 and 82.5

From the question, we have the following parameters:

One acute angle is 11 times the measure of the other acute angle.

Let the acute angles be x and y

Such that

y = 11x

The sum of the acute angles in a right triangle is 90

So, we have

x + y = 90

This gives

x + 11x = 90

So, we have

12x = 90

Divide by 12

x = 7.5

Recall that y = 11x

So, we have

y = 11 x 7.5

Evaluate

y = 82.5

Hence, the acute angles are 7.5 and 82.5

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It is a completely randomized design.

What is completely randomized design ?

Completely randomized designs are used in experiment design to explore the effects of a single primary factor without taking additional nuisance variables into account. This article describes single-factor, entirely randomized designs. On the basis of the various levels of that primary factor, the experiment compares the values of a response variable. The levels of the main factor are given at random to the experimental units in fully randomized designs.

Objects or subjects are assigned to groups in a completely random design at random. Labeling each subject before choosing from the labeled participants in a table of random numbers is one common practice for allocating subjects to treatment groups. Computers can be used to accomplish this as well.

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The distance between the two points is 10 units and the slope of the line is -78/25

To find the distance between two points, we can simply use the formula of distance between two which is given as

[tex]d=\sqrt{(y_2-y_1)^2 + (x_2 - x_1)^2}[/tex]

Let's substitute the values and solve for the distance.

[tex]d=\sqrt{(y_2-y_1)^2 + (x_2 - x_1)^2}\\d = \sqrt{(1-7)^2 + (-3 - 5)^2} \\d = 10[/tex]

2)

The slope of the line can be found using the two points given.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\[/tex]

let's substitute the values and solve.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\\\m = -\frac{78}{25}[/tex]

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The unknown angles are as follows:

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, linear angles, alternate angles etc.

Therefore,

∠1 = 110 degrees

∠2 = 180 - 110 (sum of angles on a straight line)

∠2 = 70°

∠3 = ∠1 (vertically opposite angles)

Vertically opposite angles are congruent. vertically opposite angles share the same vertex

Therefore,

∠3 = 110°

∠2 = ∠4 (vertically opposite angles)

∠4 = 70°

∠1 = ∠5 (corresponding angles)

Corresponding angles are congruent

∠5 = 110°

∠6 = ∠4(alternate angles)

Alternate angles are congruent.

∠6 = 70°

∠1 = ∠7 (alternate exterior angles)

∠7 = 110°

∠2 = ∠8(alternate exterior angles)

∠8 = 70°

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Answer: 25 + 12.5v ≥ 170

Step-by-step explanation:

We already have the 25 reward points; it also gives the information that she gets 12.5 points for each visit. Because we don't know the amount she has gone to the theater or will go we have to use a variable; 12.5v. When we add them, we get 25 + 12.5v. The inequality we use is ≥ because it says "at least". When this is used that means it has to be equal to or greater and that is why use that sign and get the full equation;

5 + 12.5v ≥ 170

Answer:

55

Step-by-step explanation:

Answer:

y = -1/2x + 6.

Step-by-step explanation:

The line perpendicular to y = 2x + 3 has slope of - 1/2 so we can write it as

y = -1/2x + c

When x = -4, y = 8 so we substitute:

8 = -1/2 (-4) + c

8 = 2 + c

c = 8-2 = 6

So, the answer is

y = -1/2x + 6.

Answer:

y = -1/2x + 6.

Step-by-step explanation:

Step-by-step explanation:

[tex] \frac{5}{6} (a) - 3 = \frac{5}{8} \\ lcd = 48 \\ \\ \frac{5}{6} (a)(48) - 3(48) = \frac{5}{8} (48) \\ 40a - 144 = 30 \\ 40a = 30 + 144 \\ 40a = 174 \\ \frac{40a}{40} = \frac{174}{40} \\ a = 4\frac{14}{40} \\ a = 4 \frac{7}{20} [/tex]

I FIRST FOUND THE LCD AFTER THAT MULTIPLY EACH AND EVERY TERM IN THE EQUATION BY IT TO HET RID OF THE FRACTIONS AND SOLVE FOR a.

Answer:

b -3

Step-by-step explanation:

t-3(4-t)=-24 multiply

t-12+3t=-24 simplify

4t-12=-24 plus 12 on both side

4t=-12 divide 4 on both side

t=-3

The cost of each ticket is 8.9 dollars.

What is cost price?

In mathematics, the term cost price can be explained with the help of profit which states, as the amount which is on the commodity and in the form of standard price called cost price. For the profit, the amount of the commodity can be designed by the shopkeeper which is bigger amount as per the cost price.

According to the question, the Jason bought 4 tickets for basket ball game. He paid a total cost of $42.10 for the tickets and for parking as $6.50

The paid amount for the 4 tickets is: $42.10.

And the parking cost is: $6.50

Total cost price without parking is: $42.10 - $6.50 = $35.60

Therefore, to calculate the cost of each ticket is: 35.60/4 = 8.9 dollars

Hence, the cost of each ticket is 8.9 dollars.

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Our strategy to win $200 is to use $100 in just one chance. It is the best bet for winning $200.

Given that we start with $100 at a casino and can bet any amount of that particular money to play a game to any amount of times where we have a 40% chance of winning in each game. If we win, we will gain the amount we bet and return the amount that we bet. If we lose, we will lose our bet.

It has been asked that what should be our strategy to win get $200.

We can write from the given information that:

Probability of wining = 40 % = 0.4

Probability of losing = 1 - 0.4 = 0.6

The best bet to win $200 is to bet $100 in one go itself.

For the above bet chance of winning $100 is 0.4

But let us assume that we are betting $50 two times,

Then L-Lose and W-Win

There will be 4 rational possible cases (WW,WL,LW,LL)

Probability of all the 4 above given cases will be as follows:

Probability of (WW) = 0.4 X 0.4 = 0.16

Probaility of (WL) = 0.4 X 0.6 = 0.24

Probability of (LW) = 0.6 X 0.4 = 0.24

Probability of (LL) = 0.6 X 0.6 = 0.36

Now for winning $100 we need to win both the bets of $50.

But the probability of winning both the bets = 0.16 ( very less than 0.4)

Hence the best bet would be to use $100 in one chance itself.

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Our strategy to win $200 is to use $100 in just one chance. It is the best bet for winning $200.

It has been asked that what should be our strategy to win get $200.

We can write from the given information that:

Probability of wining = 40 % = 0.4

Probability of losing = 1 - 0.4 = 0.6

The best bet to win $200 is to bet $100 in one go itself.

For the above bet chance of winning $100 is 0.4

But let us assume that we are betting $50 two times,

Then L-Lose and W-Win

There will be 4 rational possible cases (WW,WL,LW,LL)

Probability of all the 4 above given cases will be as follows:

Probability of (WW) = 0.4 X 0.4 = 0.16

Probability of (WL) = 0.4 X 0.6 = 0.24

Probability of (LW) = 0.6 X 0.4 = 0.24

Probability of (LL) = 0.6 X 0.6 = 0.36

Now for winning $100 we need to win both the bets of $50.

But the probability of winning both the bets = 0.16 ( very less than 0.4)

Hence the best bet would be to use $100 in one chance itself.

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The equation that represents the value of d is d = b + kc

The graph that completes the question is added as an attachment

The equation of the graph is given as

y = kx

Because the graph shows a direct variation, the equation can be illustrated as

y = mx

Where m represents the slope of the line

By comparing the equation y = mx and y = kx, we can conclude that

m = k

This means that the slope of the equation y = kx is k

From the graph, we have the points

(x, y) = (a, b) and (a + c, d)

The slope of a line is calculated using

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

Slope = k

(x₁, y₁) = (a, b) and (x₂, y₂) = (a + c, d)

So, we have

k = (d - b)/(a + c - a)

Evaluate the like terms

k = (d - b)/(c)

Multiply both sides by c

d - b = kc

Add b to both sides

d = b + kc

Hence, the value of d is d = b + kc

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Answer:

5;3

Step-by-step explanation:

Problem

Juanita wants to buy a computer. She needs to earn at least 400 dollars. If she makes 9 dollars an hour and has already saved 40 dollars, how many hours does she need to work?

Solution

Let x the number of hours required we can set up the following inequality:

40 + 9x > 400

And now we can solve for x we can subtract 40 and we got:

9x > 360

And then we got:

x> 40

So then Juanita needs to work at least 40 hours

And the graph of the inequality is given by:

Answer:

3 5/14 (second choice)

Step-by-step explanation:

c = -3 1/7

d = 6.5 (6 1/2 as fraction)

-3 1/7 as improper fraction: -22/7

6 1/2 as improper fraction: 13/2

Now put both fractions into a common denominator

-22/7 = -44/14

13/2 = 91/14

Now add:

-44/14 + 91/14 = 47/14

Change 47/14 back to fraction

47/14 = 3 5/14

Answer: The answer is the $42 T-Shirts

Step-by-step explanation: 42 divided by 4 is 10.5 dollars per t-shirt.

25 divided by 2 would mean 12.5 dollars per t shirt. There is only a 2 dollar difference, but it is clear that the 4 t-shirt deal is the best.

The total pounds of apples that Chris must pick before Pam’s orchard is cheaper that David's is 14.

The first step is to determine the total cost of picking apples from both orchards.

Cost of picking apples from David's Orchard : (10 x $2) + [(x - 10) x $1]

$20 + $x - $10

= $10 + $x

Cost of picking apples from Pam's Orchard : $10 + ($10 x $1.5) + [(x - 10) x 0.75]

$10 + $15 + 0.75x - 7.5

= $17.50 + 0.75x

When  Pam's Orchard is cheaper, the equation becomes :

$10 + $x  > $17.50 + 0.75x

$x - 0.75x > $17.50 - $10

0.25x > $7.50

x > $7.50 / 2.5

x > 3

Total pounds should be greater than 3, so it can be 4.

Total pounds = 10 + 3 = 14

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Using an arithmetic sequence, the number of design that the artist should use is:

b. Design 6.

In an arithmetic sequence, the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the rule presented as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term of the sequence.

The sequence for the number of circles is:

(4, 6, 8, ...)

Hence the common difference is given by:

d = 8 - 6 = 6 - 4 = 2.

Then the rule for the nth term is:

[tex]a_n = 4 + 2(n - 1)[/tex]

As the first term is of 4.

The maximum number is of 15 shaded circles, hence:

4 + 2(n - 1) ≤ 15

4 + 2n - 2 ≤ 15

2 + 2n ≤ 15

2n ≤ 13

x ≤ 6.5.

Hence the maximum number is of 6, meaning that Design 6 is chosen, given by option b.

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The club has to send 57 coupons to existing members.

Given,

The number of coupons sent out by a new club to boost sales for next year's membership = 152

They provide 3 times as many to potential members than to existing members

We have to find the number of coupons they send to existing members;

Here,

x be the number of coupons to existing members.

Then,

3x = 152

Now,

x = 152/3 = 50.66 ≈ 57

That is,

The club has to send 57 coupons to existing members.

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Answer:

6.5°

Step-by-step explanation:

We know that both XYZ and LMN are complementary angles.

Complementary angles add up to 90°.

So,

we can simply add both of the expressions and set it equal to 90 (degrees).

(3x+14) + (5x+24) = 90

-> add the variables and constants

8x+38=90

-> subtract the 38 from both sides (90-38)

8x=52

-> divide out the coefficient to isolate the variable

x=6.5

So, the answer is 6.5 degrees.

Hope this helped :)