Open Response 2
A glass containing water is in the shape of a right circular cylinder with a radius
of 3 centimeters. The height of the water in the glass is 10 centimeters.
a) What is the volume of the water in the glass? Be sure to include units of
measure in your answer. Show or explain how you obtained your answer.
b) Five spherical marbles of equal size are dropped into the glass. The water in
the glass rises to a height of 11 centimeters. What is the increase in the
volume of the contents of the glass? Be sure to include units of measure in
your answer. Show or explain how you obtained your answer.
c) What is the volume of one of the marbles? Be sure to include units of
measure in your answer. Show or explain how you obtained your answer.
d) What is the radius of one of the marbles? Be sure to include units of
measure in your answer. Show or explain how you obtained your answer. ​

Answer:

The graph that passes through (-3,-3), (-3,0), and (-3,3) does not represents a linear function.

Step-by-step explanation:

The graph that passes through (-3,-3), (-3,0), and (-3,3) does not represents a linear function. Because if we tried to find the slope for either two pairs of these coordinates. The slope would equal infinity

Lets say we find the slope of (-3,-3) and (-3,0)

[tex]\frac{-3-0}{(-3)-(-3)} =\frac{-3}{0}[/tex]  Slope = [tex]\infty}[/tex]

Now lets say we find the slope of (-3,0) and (-3,3)

[tex]\frac{0-3}{(-3)-(-3)} =\frac{-3}{0}[/tex] Slope = [tex]\infty[/tex]

So now we can see that both lines of each slope is parallel to the y-axis which means that the lines a Undefined Slope (also known as Infinite Slope).

Answer: ( 11, -2 )

Step-by-step explanation:

The mid point of a line is calculated using the formula:

M = ([tex]\frac{x_{1}+x_{2}}{2}[/tex] , [tex]\frac{y_{1}+y_{2}}{2}[/tex] )

From the question , the mid point is already given , substituting , we have :

(5 , - 7.5 ) = ([tex]\frac{x-1}{2}[/tex] , [tex]\frac{y-13}{2}[/tex] )

Equating the x component to x and the y component to y , we have

5 = [tex]\frac{x-1}{2}[/tex]

x - 1 = 10

x = 11

Also

- 7.5 = [tex]\frac{y-13}{2}[/tex]

-15 = y - 13

-15 + 13 = y

Therefore : y = -2

Therefore : the location of point P is ( 11, -2 )

The sale price of the coats is 160% of the purchase price of the coats.

Step-by-step explanation:

The owner buys the coats at a purchase price= $60

He sells the coats for a selling price= $96

Now, the question is:

The selling price $96 is what percentage of the purchase price $60

step 1: 96= x% of 60

step 2: 96= (x/100)*60

step 3: 96= 6x/10

step 4: 960/6 = x

step 5: x = 160%

Answer:

Step-by-step explanation:

each box is 375 grams...and there are 28 boxes

total mass(m) = 28 * 375 = 10,500 grams

The weight of all the boxes of cereals can be found by the equation (C) "28 x 375 = m" and the weight is 10,500 grams.

So, the total mass of all the boxes:

Then, calculate as follows:

So, option (C) is correct.

Therefore, the weight of all the boxes of cereals can be found by the equation (C) "28 x 375 = m" and the weight is 10,500 grams.

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Answer:

The answer is [tex]10\frac{1}{2}\ per\ hour.[/tex]

Step-by-step explanation:

Given:

Darcy harvest 8 3/4 acres of corn every 5/6 of an hour.

Now, to find the acres per hour it takes to harvest.

Darcy harvest = [tex]8\frac{3}{4}=\frac{35}{4}\ acres.[/tex]

The time he took to harvest = [tex]\frac{5}{6}\ hour.[/tex]

So, to get the acres per hour we put formula:

[tex]Distance = \frac{35}{4}\ acres.[/tex]

[tex]Time=\frac{5}{6}\ hour.[/tex]

[tex]Speed=\frac{distance}{time}[/tex]

[tex]Speed=\frac{\frac{35}{4}}{\frac{5}{6}}[/tex]

[tex]Speed=\frac{35}{4}\times \frac{6}{5}[/tex]

[tex]Speed=\frac{210}{20}[/tex]

[tex]Speed=\frac{21}{2}[/tex]

[tex]Speed=10\frac{1}{2}\ per\ hour.[/tex]

Therefore, the answer is [tex]10\frac{1}{2}\ per\ hour.[/tex]

Answer: c. 22X

Step-by-step explanation:

Answer:

22x

Step-by-step explanation:

7 + 1 5

or

7+15

22

=================================================

Explanation:

In general if

u = < a, b > and v = < c, d >

then,

u+v = < a+c, b+d >

Basically we add the x coordinates separately and the y coordinates are added separately.

----------

So,

u = < -3, 4 >

v = < 8, 2 >

u + v = < -3+8, 4+2 >

u + v = < 5, 6 >

Answer:

Jared offer $6,000.

Step-by-step explanation:

Given:

A used car is for sale for $24,000. Jared took a chance and offered the owner 1/4 of the selling price.

Now, to find the price Jared offer.

Selling price = $24,000.

Jared offer = [tex]\frac{1}{4}[/tex]  of selling price.

So, to get the price Jared offer:

[tex]\frac{1}{4}\ of\ \$24000[/tex]

[tex]=\frac{1}{4} \times 24000[/tex]

[tex]=\frac{24000}{4}[/tex]

[tex]=\$6000.[/tex]

Therefore, Jared offer $6,000.

Answer:

s = 20   F = 100    T = 60

Step-by-step explanation:

F = 5s                F + s + T = 180

T = 5s - 40

I picked numbers until I found the one that worked. For me, 20 worked for the second angle.

The measure of first angle, second angle, and the third angle is 100, 20 and 60.

Given that,

Based on the above information, the calculation is as follows:

F = 5s                

F + s + T = 180

T = 5s - 40

Now

5s + s + 5s - 40 = 180

11s = 220

s = 20

F = 100

T = 100 - 40

= 60

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Answer:

2x^3 + 3x - 10

Step-by-step explanation:

The complete question is:

Trapezoid JKLM is shown below.

What is the length, in centimeters, of KL ?

A. 12 cm

B. 10 cm

C. 9 cm

D.  6 cm

The mentioned figure is attached.

Answer:

[tex]\large\boxed{option\text{ B. }(\overline{KL})=10cm}[/tex]

Explanation:

1. KL is the hypotenuse of a right triangle; hence, you can use Pythagora's theorem to find its length.

2. The height 8 cm is one leg of the right triangle.

3. The other leg may be found by difference:

     [tex]\overline{ML} -\overline{JK}=15cm-9cm=6cm[/tex]

4. Now you can use Pythagora's theorem:

[tex]hypotenuse^2=(leg_1)^2+(leg_2)^2\\ \\ (\overline{KL})^2=(8cm)^2+(6cm)^2\\ \\ (\overline{KL})^2=64cm^2+36cm^2=100cm^2\\ \\ (\overline{KL})=10cm[/tex]

Answer:

3,600 from $26 tickets  and  1,400 from $40 tickets.  

Step-by-step explanation:

Let x = number of $26 tickets and y= number of $40 tickets

x + y = 5000  ⇒ x = 5000 - y

26x + 40y = 149,600

26(5000 - y) + 40y = 149600

130,000 - 26y + 40y = 149600

14y = 19600

y = 19600/14 = 1,400

x = 5000 - 1400 = 3,600

So, 3,600 from $26 tickets  and  1,400 from $40 tickets.

To determine the number of tickets sold at each price, set up a system of equations using the given information and solve for the variables.

To determine how many tickets should be sold at each price, we can set up a system of equations using the given information.

Let's assume the number of $26 tickets sold is x and the number of $40 tickets sold is y.

The total number of tickets sold is x + y, so we have the equation x + y = 5000.

The revenue generated from $26 tickets is 26x, and the revenue generated from $40 tickets is 40y. The total revenue

is given as $149,600, so we have the equation 26x + 40y = 149600.

Solving this system of equations will give us the values of x and y.

Answer Problem 1: 3*(y+4)

Show Work:

1) y = (1/3)*x-4 // - (1/3)*x-4

2)  y-((1/3)*x)+4 = 0

3) (-1/3)*x+y+4 = 0

4)  y-1/3*x+4 = 0 // - y+4

5)  -1/3*x = -(y+4) // : -1/3

6)  x = (-(y+4))/(-1/3)

7)  x = 3*(y+4)

8) x = 3*(y+4)

Answer Problem 2: Y=-7/12

Show Work:

Step 1: Flip the equation.

7/3 x+4=y

Step 2: Add -4 to both sides.

7/3x+4+−4=y+−4

7/3x=y−4

Step 3: Divide both sides by 7/3.

Answer:

2.40

Step-by-step explanation:

tangent of an angle= opposite side/ adjacent side

tan(T)= RS/ RT

tan(T)= 12/5

tan(T)= 2.40 (nearest hundredth)

Answer:

 = $ 49.5

Step-by-step explanation:

We are given;

Required to determine the amount paid

Taking the retail price as 100%

Then, amount paid will be (100 % - 10%) 90% of the retail price

Therefore;

Amount paid = 90% × $ 55

                     = 0.9 × $ 55

                     = $ 49.5

Thus, the employee paid $ 49.5 for the book.

Answer:

34/5

Step-by-step explanation:

6*5=30 + 4 = 34

34/5

The mixed number 6 4/5 can be converted into an improper fraction by multiplying the whole part by the denominator and adding the numerator to the result, giving us 34/5.

To convert the mixed number 6 4/5 into an improper fraction, you follow these steps:

So, (6*5)+ 4 = 34. Therefore, the mixed number 6 4/5 can be written as the improper fraction 34/5.

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Consider the two numbers as

x and y

. From the given data, we write:

x−y=3

x+y=13

From the first equation, we determine a value for x.

x−y=3

Add y to both sides.

x=y+3

In the second equation, substitute x with (y+3).

x+y=13

(y+3)+y=13

Open the brackets and simplify.

y+3+y=13

2y+3=13

Subtract 3 from each side.

2y=10

Divide both sides by 2.

y=5

In the first equation, substitute y with 5.

x−y=3

x−5=3

Add 5 to each side.

x=8

Answer:

B salary

Step-by-step explanation:

Your employment status, salary, and bank account balances are never disclosed on your report and have no bearing on your rating.

Although your income has no bearing on your credit score, it's still crucial to understand the five key components of a FICO credit score, the most widely used credit score by lenders.

History of payments (35%): Your credit score is mostly influenced by whether you have a history of making on-time payments on your credit accounts.

Your salary does not directly affect your credit score, but it does affect your ability to pay off credit card debt.

Therefore, Your race, gender, marital status, level of education, religion, political party, or source of income are all factors that are never taken into account when calculating your credit ratings.

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Answer:

2/4 of his money was spent on dinner

Step-by-step explanation:

Answer:

2/4 or 1/2 of his money of dinner

Step-by-step explanation:

When using your brain you come to the conclusion that the pizza and the salad is his dinner because it is food, so we add those two fractions together to get 2 out of 4 or 1 out of 2.

Answer:

The second choice

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.971

This is the correct answer.

The perimeter of the garden is 57.14 m and

the total area of the garden is 178.28 sq. m.

Solution:

Given length of the rectangle = 16 m

Width of the rectangle = 8 m

Radius of the semi-circle = half of the width of the rectangle

Radius = 4 cm

Perimeter of the garden is two lengths of the rectangle and 2 curve sides of the semi-circle.

Perimeter = [tex]2l+2(\frac{2\pi r}{2} )[/tex]

               = [tex]2l+2\pi r[/tex]

               = [tex]2(16)+2\times\frac{22}{7}\times4[/tex]

               = 32 + 25.14

               = 57.14 m

Total area of the garden is the area of the rectangle and area of the two semi-circles.

Area of the garden = [tex](l\times w)+ 2(\frac{\pi r^2}{2})[/tex]

                              = [tex](l\times w)+ \pi r^2[/tex]

                              = [tex]16\times8+\frac{22}{7} \times 4\times 4[/tex]

                              = 128 + 50.28

                              = 178.28 square meter

Hence, the perimeter of the garden is 57.14 m and

the total area of the garden is 178.28 sq. m.

Answer:

6, -4

Step-by-step explanation:

abs(-1+x)=5

-1+x=5 and -1+x=-5

-------------------------

-1+x=5

x=5-(-1)=5+1=6

-------------------

-1+x=-5

x=-5-(-1)=-5+1=-4

The value of numerators are 3 and 5

Solution:

Let the numerators of two fractions be x and y

Two fractions have denominators 4 and 6. Their sum is 19/12

Therefore,

[tex]\frac{x}{4} + \frac{y}{6} = \frac{19}{12}[/tex]

Cross multiply L.H.S to get simplified

[tex]\frac{6x+4y}{24} = \frac{19}{12}\\\\6x + 4y = 38 ------- eqn 1[/tex]

If the numerators are switched their sum is 7/4

Therefore,

[tex]\frac{y}{4} + \frac{x}{6} = \frac{7}{4}[/tex]

On simplification, we get

[tex]\frac{6y + 4x}{24} = \frac{7}{4}\\\\4x + 6y = 42 -------- eqn 2[/tex]

Solve eqn 1 and eqn 2

Multiply eqn 1 by 4

24x + 16y = 152 --------- eqn 3

Multiply eqn 2 by 6

24x + 36y = 252 ---------- eqn 4

Subtract eqn 3 from eqn 4

24x + 36y = 252

24x + 16y = 152

( - ) -------------------

20y = 100

Substitute y = 5 in eqn 1

6x + 4(5) = 38

6x = 38 - 20

6x = 18

Thus the value of numerators are 3 and 5

1/4=.25

3/12=.25

yes they are equal

If the caterpillar crawled 22cm farther than the ant, then we are adding 53 and 22 to get 75cm.

Answer:

75cm

Step-by-step explanation:

53 + 22 = 75

answer x = 8

because 3/4 times 2 equals 6/8 so the solution is 6/8