Rubber Bands
Juan wants to buy small bag and
I medium bag of rubber bands. Will
that give him more rubber bands
than a large bag? Explain.
No-Because, 25+45=70
2. Make Sense What information is given?
What do you need to find?
4. Explain If Juan buys I small bag and
I medium bag of rubber bands, will he
have more rubber bands than a large
bag has? Make a math argument.
Number of Rubber Bands in a Bag
Small
25
Medium
45
Large
70
3. Reasoning Juan wants to use counters to
solve the problem. Do you think Juan's tool
choice is a good one? Why or why not?

The comparison of the equations are

From the question, we have the following equation that can be used in our computation:

-x + 4y = 32

Add x to both sides of the equation

So, we have the following representation

4y = x + 32

Divide through by 4

So, we have

y = 1/4x + 32/4

Evaluate

y = 1/4x + 8

A linear equation is represented as

y = mx + c

Where

Slope = m

As a general rule, linear equations that have the same slope are parallel

This means that the equation y = 1/4x + 1 is parallel to y = 1/4x + 8

Also;

The slopes of perpendicular lines are opposite reciprocals

This means that the equation 4x + y = -3 is perpendicular to y = 1/4x + 8

Lastly, the third equation would neither parallel not perpendicular to the line.

This is because the first equation is parallel and the second equation is perpendicular

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The set of side measurements could be used to form a triangle is 7, 13 and 16.

If a, b and c are the sides of the triangle

Then

a+b > c

b+c > a

c+a > b

The first set of side measurements = 2, 6 and 10

2+6 > 10

8 < 10

This is not the side measurements of a triangle

The second set of side measurements = 3, 18 and 22

3+18 > 22

21 < 22

The is not the side measurements of a triangle

The third set of side measurements = 7, 13, 16

7+13 > 16

20 > 16

13+16 > 7

29 > 7

7+16 > 12

23 >12

This is the side measurements of a triangle

The fourth set of side measurements = 8, 7  and 19

8+7 > 19

15 < 19

This is not the side measurements of a triangle

Hence, the set of side measurements could be used to form a triangle is 7, 13 and 16

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Answer:

C. 7, 13, 16

Step-by-step explanation:

In order to be a triangle, the two smaller sides need to add up and be greater than the 3rd side.

In all the other sides they end up shorter:

2 + 6 = 8

8 < 10

3 + 18 = 21

21 < 22

8 + 7 = 15

15 < 19

BUT

7 + 13 = 20

20 > 16

The value of f(12) in the arithmetic sequence is 30.

Arithmetic sequence formula can be represented as follows;

aₙ = a + (n - 1)d

where

Therefore,

f(3) = - 3

f(6) = 8

Hence, let's find f(12).

-3 = a + 2d

8 = a + 5d

3d = 11

d = 11 / 3

a = -3 - 2(11 / 3)

a = - 3 - 22 / 3

a = - 31 / 3

Hence,

a₁₂ = a + 11d

a₁₂ = - 31 / 3 + 11(11 / 3)

a₁₂ = - 31 / 3 + 121 / 3

a₁₂ = 90 / 3

a₁₂ = 30

Therefore,

f(12) = 30

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Answer:

34

Step-by-step explanation:

I will need a lot more info then that but i think it'll be 34

y do i have to write so much for a small answer the answer is 12.5

Answer: One ticket would cost $12.50

Step-by-step explanation:

If 6 tickets cost $75, to find the cost of one ticket, we need to divide.

$75 divided by 6 is $12.5.

$12.5 is not a valid answer, so we need to show the hundredths place, which is 0. This means the answer is $12.50.

Answer:

e is 63 degrees

d is 31 degrees

Answer:

below

Step-by-step explanation:

$ 5.25 /hr * 32.5 hr   *  .77 =  131.38 dollars

The time taken for the car and truck to meet is 36 minutes.

The time for the car and the truck must be the same.

distance:

Now,

Then trucks distance:

Time is:

Hence, the time taken for the car and truck to meet is 36 minutes.

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Barry's semester grade point average (GPA). Round to the nearest hundredth is 2.67

The GPA is calculated by following the procedures

the multiplication

credit hour * grade

= 4 * 3 = 12

= 2 * 4 = 8

= 3 * 2 = 6

= 3 * 2 = 6

sum of the products = 12 + 8 + 6 + 6 = 32

sum of credit hour =  4 + 2 + 3 + 3 = 12

The GPA

= sum of the products / sum of credit hour

= 32 / 12 =  2.67

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The values of x or y are as follows:

(a) y = 4

(b) x = -2

(c) y = 6

(d) x = 3

(a) Given, that a line passes through (-3 , y) and (-9 , -2) having slope m = 1

as, we know the formula of slope i.e. (y1 - y2)/(x1 - x2) = m

So, (y + 2)/(-3 + 9) = 1

= (y + 2)/6 = 1

= y + 2 = 6

So, y = 4

(b) Given, that a line passes through (x , -7) and (1 , 2) having slope m = 3

as, we know the formula of slope i.e. (y1 - y2)/(x1 - x2) = m

So, (-7 - 2)/(x - 1) = 3

= -9/(x - 1) = 3

= x - 1 = -3

So, x = -2

(c) Given, that a line passes through (9 , y) and (3 , 2) having slope m = 2/3

as, we know the formula of slope i.e. (y1 - y2)/(x1 - x2) = m

So, (y - 2)/(9 - 3) = 2/3

= (y - 2)/6 = 2/3

= y - 2 = 4

So, y = 6

(d) Given, that a line passes through (7 , 5) and (x , 2) having slope m = 3/4

as, we know the formula of slope i.e. (y1 - y2)/(x1 - x2) = m

So, (5 - 2)/(7 - x) = 3/4

= 3/(7 - x) = 3/4

=7 - x = 4

So, x = 3

Hence, the values of x or y are as follows:

y = 4 , x = -2 , y = 6 and x = 3.

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It  will be written as inequality

3 - (x / 2) ≤ 5

Inequality is a mathematical relation which is use to make non-equal comparisons between equations or numbers.

Now let us look at the question.

Half a number less than 3. Let us suppose the number to be 'x' so

3 minus half of x which can be written as 3 - (x / 2)

Next it says that it is at most 5 which means it will be 5 or less than that.

Therefore we can easily write it as inequality 3 - (x / 2) ≤ 5

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The equation of the line passing through (-6,0) and (0,-8) will be y = -4x/3-8.

According to the question,

We have the following information:

We have two points: (-6,0) and (0,-8) and we have to find the equation.

We know that following formula is used to find the slope of the line:

m = (y2-y1)/(x2-x1)

In this case, we have x1 = -6, y1 = 0, x2 = 0 and y2 = -8.

m = (-8-0)/{0-(-6)}

m = -8/(0+6)

m = -8/6

Dividing this fraction by 2:

m = -4/3

Now, the following formula is used to find the equation of the line:

(y-y1) = m(x-x1)

y-0 = -4/3{x-(-6)}

y = -4/3(x+6)

y = -4x/3-8

Hence, the equation of the line passing through (-6,0) and (0,-8) will be y = -4x/3-8.

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Using the triangle rule, the option B can form a triangle.

In the given question,

We have to choose the correct segment from the given segment,  which group of segments can form a triangle.

The given options are

A. 3, 10, 14

B. 8, 7, 13

C. 3, 2, 5

D. 20, 7, 13

To check which segment form a triangle we check that sum of two sides is always greater than the third side.

Now checking the first option.

The points is 3,10,14

When we add 3 and 10 we get 13 which is not greater than the 14. So the option A is not form a triangle.

Now checking the second option.

The points is 8,7,13

When we add 8 and 7 we get 15 which is greater than the 13. Similarly when we add 13 and 7 we get 20 which is also greater than the 8. Similarly when we add 8 and 13 we get 21 which is also greater than the 7. So the option B can form a triangle.

Since we get the right answer so we didn't check further option. The way of checking the remaining option is same.

Hence, the option B can form a triangle.

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Answer:

y = 5/2x - 8

Step-by-step explanation:

Answer: 6.16

minus all the values from 30

Answer:

$6.16

Step-by-step explanation:

30-6.97-11.37-5.5

=6.16

Answer:

Im pretty sure its 12,800 bacteria

Step-by-step explanation:

Answer: Troy

Step-by-step explanation:

Troy’s equation has a slope of 28, so next you need to calculate Lucy’s slope:   Go up 25, over to the right 1, so the slope is 25.

Troy has a greater slope, so his is steeper.

Answer:

[tex]\huge\boxed{\sf b = 28}[/tex]

Step-by-step explanation:

Point (x,y) = (2,20)

So, x = 2 and y = 20

Also,

Slope = m = -4

Where b is y-intercept.

Put the above given data in this equation.

20 = (-4)(2) + b

20 = -8 + b

Add 8 to both sides

20 + 8 = b

28 = b

[tex]\rule[225]{225}{2}[/tex]

y=mx+c. y=20

x=2

m=-4

20= -4(2)+c

20= -8+c

20+8=c

28=c

The linear regression equation that represents this set of data is given by:

y = 30x + 854.6.

The predicted calendar year in which the number of new cases would reach 1141 is:

2020.

The format of the linear regression equation is given as follows:

y = mx + b.

In which the coefficients are listed as follows:

The equation is built inserting the points given on the table into a linear regression calculator.

The points from the table given by the image at the end of the answer are given as follows:

(0, 856), (1, 871), (2, 924), (3, 961), (4,961).

Inserting these points into a calculator, the equation is given as follows:

y = 30x + 854.6.

The predicted calendar year in which the number of new cases would reach 1141 is 2011 + integer part of x, when y = 1141, hence:

1141 = 30x + 854.6

x = (1141 - 854.6)/30

x = 9.54.

Hence during the year of 2020.

The table is given by the image shown at the end of the answer.

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Equation of the line which is passing through the point (-2, -6) and has the gradient of -3 is equal to y = -3x -12.

As given in the question,

Gradient of the required equation of the line is given by :

Gradient is slope.

Let slope is represented by m = -3

Line passing through the point (-2, -6) is given by :

( x₁ , y₁) = ( -2 , -6)

Equation of the line which is passing through the point (-2, -6) and has the gradient of -3 is given by :

y - y₁ = m ( x - x₁)

⇒ y - (-6) = (-3)(x - (-2))

⇒ y + 6 = -3( x + 2)

⇒ y + 6 = -3x - 6

⇒ y = -3x -12

Therefore, equation of the line which is passing through the point (-2, -6) and has the gradient of -3 is equal to y = -3x -12.

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If we use both belts, it takes 4.5 minutes to carry the can to the storage area.

Let's assume, t = time required to move 300 pounds using both belts.

For this first calculate the speed or mass flow rate of each conveyor belt.

The big one can do 300 pounds in 6 minutes, so its speed is 300 pounds/6 minutes = 50 pounds/minute.

The smaller one takes 18 minutes, so the speed is 300 pounds/18 min = 50/3 pounds/minute.

We can see that the combined speed of both machines when working together is 50 + 50/3 = 50 (1 + 1/3) = 50 x 4/3 = 200/3 pounds/minute.

Then we find that the two machines together can transfer 300 pounds in t = 300/200/3 = 300/200 x 3 =  4.5 minutes.

Alternate Method:

We can do that too

Let t = the time required to move 300 pounds on both belts.

Job completed = 1 (300 pounds moved)

t/6 + t/18 = 1

Taking L.C.M

=> (3t + t)/18 = 1

=> 4t/18 = 1

=> t = 4.5 minutes

Hence, it takes 4.5 minutes to carry the can to the storage area.

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20 ounces of chocolate chips would be required to make 5 dozen cookies.

According to the question,

We have the following information:

Shondra used four ounces of chocolate chips to make 1 dozen cookies.

We know that when we find the cost or required amount of any product which is more than 1 then we use multiplication to find the result.

So, we will multiply 5 dozen of cookies by the number of ounces of chocolate chips required for 1 dozen cookies.

Chocolate chips for 5 dozen cookies = 5*4

Chocolate chips for 5 dozen cookies = 20 ounces

Hence, 20 ounces of chocolate chips would be required to make 5 dozen cookies.

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The range from the given table is 9, the population variance is 18.56, and the population standard deviation is 4.30.

Given the value:

xi         10     20      11        17       15     8     7     16       19    15     Total = 138

xi^2    100   400    121   289    225   64   49   256   361   225  Total = 2090

From the above, we get

n =10, ∑xi = 138, ∑xi^2 = 2090

(a) For the range:

Here, the smallest value = 10, and largest value = 19

Therefore, Range = Largest value - Smallest value

Range = 19 - 10 = 9

(b) For population variance:

For mean:

Mean of x = ∑xi/n = 138/10 = 13.8

V (X) = ∑(xi^2)/n - Mean of x^2

= 2090/10 - 13.8^2

= 209 - 190.44

V (X) = 18.56

(c) For population standard deviation:

[tex]SD (X) = \sqrt{VAR(X)}[/tex]

SD(X) = [tex]\sqrt{18.56}[/tex]

SD(X) = 4.30

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Step-by-step explanation:

The range from the given table is 9, the population variance is 18.56, and the population standard deviation is 4.30.

Given the value:

xi 10 20 11 17 15 8 7 16 19 15 Total = 138

xi^2 100 400 121 289 225 64 49 256 361 225 Total = 2090

From the above, we get

n =10, ∑xi = 138, ∑xi^2 = 2090

(a) For the range:

Here, the smallest value = 10, and largest value = 19

Therefore, Range = Largest value - Smallest value

Range = 19 - 10 = 9

(b) For population variance:

For mean:

Mean of x = ∑xi/n = 138/10 = 13.8

V (X) = ∑(xi^2)/n - Mean of x^2

= 2090/10 - 13.8^2

= 209 - 190.44

V (X) = 18.56

(c) For population standard deviation:

SD (X) = \sqrt{VAR(X)}SD(X)=

VAR(X)

SD(X) = \sqrt{18.56}

18.56

SD(X) = 4.30

The time taken for the rocket to reach its maximum height is; 2.25 seconds.

The maximum height reached by the toy rocket whose initial velocity is; 72 feet per second is; 88 feet.

It follows from the task content that the maximum height reached by the rocket is to be determined.

The given function is; h (t) = -16 t² + 72t + 7.

Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.

Therefore; at maximum height;

h'(t) = 0

h'(t) = -32t + 72 = 0

-32t = -72

t = -72/-32

t = 2.25 seconds.

Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.

Also, the maximum height reached by the rocket is at; h (2.25);

h(2.25) = -16(2.25)² + 72 (2.25) + 7

= -81 + 162 + 7

= 88.

The maximum height reached is; 88 feet.

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Answer:

x=9

Step-by-step explanation:

these 2 angles are equivalent so we set them equal to each other

124-x=8x+43

81-x=8x

81=9x

9=x

Hopes this helps please mark brainliest

Identify your Financial Situation,  

Determine Financial Goals,

Identify Alternatives for Investment,  

Evaluate Alternatives,

Put Together a Financial Plan and Implement,

Review, Re-evaluate and Monitor The Plan

The following tasks are part of the financial planning activity:

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Answer:

29+8x

Step-by-step explanation:

5+8(3+x)

5+24+8x - Open parentheses

29+8x - Add like terms

An equation that represents the depth of snow on Audrey's lawn, in inches, t hours after the snow stopped falling is S = 10 - 2t

In this question, there was a depth of 10 inches of snow on the lawn when the storm ended and then it started a melting at a rate of 2 inches per hour.

We need to write an equation for S in terms of t, snow representing the depth of snow on Audrey's lawn, in inches, t hours after the snow stopped falling.

So, the equation would be,

S = 10 - 2t

Therefore,  an equation that represents the depth of snow on Audrey's lawn, in inches, t hours after the snow stopped falling is S = 10 - 2t

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The Least percentage point = 41

The Greatest percentage point = 47

What is percent?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

Given:

Percentage of voters who plan to re-elect mayor = 44%

Margin of Error in measurement = ±3 % points

The absolute value inequality to find the lowest and greatest percent of points :

X = mid value

44% = estimated percentage

≤3 = error margin

Therefore,

|mid value - estimate| ≤ error margin

|x − 44| ≤ 3

⇒  -3 ≤ x - 44 ≤ +3

Add 44 on both sides,

   -3 + 44 ≤ x ≤ 3 + 44

Simplifying,

       41 ≤ x ≤ 47

Hence,

The Least percentage point = 41

The Greatest percentage point = 47

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