0.1574 is the probability that more than half of the sampled students live on the campus.
It is well known that 45% of students at a large university live on campus. A random sample of 100 students will be chosen by the head of student life. The fixed value that offers the potential of the number of successful outcomes is the sample proportion. The sample proportion is an estimate of the population proportion's actual value.
100 samples are taken.
45 percent of students reside on campus.
The normal probability distribution is used to assess the likelihood that more than half of the sampled students live on campus.
[tex]P(p^{O} > 0.5)=P(\frac{p^{o}-p }{\sqrt{\frac{p(1-p)}{n} } } > \frac{0.5-0.45 }{\sqrt{\frac{0.45(1-0.45)}{100} } })[/tex]
=P(Z>1.00)
=0.1574 (Z- score table)
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You and your best friend are picking apples at a local orchard. If there were already 12 bushels of apples on the tractor when you began at 8:00am and you picked apples until noon, what was your rate of change if there were 44 bushels filling the tractor when you stopped?
The rate of change picking the apples is 8 bushels of apples per hour.
What is rate of change?Rate of change is used to mathematically describe the percentage change in value over a defined period of time, the formula for rate of change is: R = (D2 - D1)/T. where: R = rate of change.
Given that, you and your best friend are picking apples at a local orchard. there were already 12 bushels of apples on the tractor when you began at 8:00 am and you picked apples until noon, we are asked to find, what was your rate of change if there were 44 bushels filling the tractor when you stopped,
So, the rate change = total apples picked in 8 am to noon / number of hours.
Therefore, the total apples picked in 8 am to noon =
Since, it was 44 bushels at the end and when they started there were already 12 bushels, so the number of bushels of apples filled between given hours = 44 - 12 = 32 bushels.
The number of hours in picking 32 bushels of apples = 12 noon - 8 am
= 4 hours
Therefore,
The rate of change = 32 / 4
= 8
Hence, the rate of change picking the apples is 8 bushels of apples per hour.
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Given ABCD is a parallelogram.From B draw a line meets CD at M ; from D draw a line meets BC at N such that BM = DN . Intersection of DN and BM is point I. Prove that IA is a bisector of ∠BID
Given a parallelogram ABCD with points B and D, we draw two lines such that line BM intersects CD at point M and line DN intersects BC at point N, and BM = DN. The intersection of these lines is point I. Our goal is to prove that IA is a bisector of angle BID.
To prove this, we first note that since ABCD is a parallelogram, AB is parallel to CD and AD is parallel to BC. This means that ∠BAD and ∠CDA are congruent, and ∠BAC and ∠DCB are congruent.
Next, we consider triangle ABM. Since BM is perpendicular to AB, we have ∠BAM = 90°. By the same reasoning, we have ∠BID = 90°. This means that IA is perpendicular to both AB and BD.
Since IA is perpendicular to AB and BD, it follows that IA bisects ∠BAD and ∠BDC. Additionally, we know that AB = BD and ∠BAD = ∠BDC, so it follows that IA bisects ∠BID.
This completes the proof that IA is a bisector of ∠BID. The key idea here is that a line perpendicular to two parallel lines bisects the angles formed by the intersection of the two parallel lines with a third line.
In conclusion, given a parallelogram ABCD with points B and D, the intersection of lines BM and DN, point I, is the bisector of angle BID. This result can be used to prove various geometric theorems and helps to understand the properties of parallelograms and their related figures.
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evaluate xy- x 2 - 5x - 4 if x = -1 and y = 6
The value of the expression xy - x² - 5x - 4 when x = -1 and y = 6 is -6.
What is the value of xy - x² - 5x - 4 when x = -1 and y = 6?Given the expression in the question;
xy - x² - 5x - 4
x = -1y = 6To find the value of the expression; substitute in x = -1 and y = 6 for all occurrence of x and y in the expression and simplify.
xy - x² - 5x - 4
Plug in x = -1
(-1)y - (-1)² - 5(-1) - 4
Plug in y = 6
(-1)(6) - (-1)² - 5(-1) - 4
Simplify
-6 - 1 + 5 - 4
Add -6 and -1
-7 + 5 - 4
Add -7 and 5
-2 - 4
Add -2 and -4
-6
Therefore, the value of the expression is -6.
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what is an equation of the line that is parallel to y+1=-3(x-5) and passes through the point (4,-6)?
Answer:y + 6 = 1/3 (x - 4)
Step-by-step explanation:Replace the second y (y1) and the 2nd x (x1) with the new points and then -3 become 1/3 due to perpendicular meaning opposite reciprocal (2/3 reciprocal is 3/2 and the opposite would be its negative, -3/2, for example
Dr. Powell is a veterinarian. He gave Ruby, one of the cats he is treating, 40 micrograms of
medication. Based on Ruby's size, Dr. Powell expects there will be about 32 micrograms of
medication remaining in her body after one hour. Dr. Powell knows that the amount of
medication remaining in Ruby's body will continue decreasing each hour.
Write an exponential equation in the form y = a(b)* that can model the amount of medication
in Ruby's body, y, x hours after it was administered.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y = 40(31)*
ola
To the nearest whole number, how many micrograms of medication can Dr. Powell expect to
be remaining in Ruby's body after 4 hours?
micrograms
Submit
Answer: 8 micrograms, y=40-(8)4
Step-by-step explanation: after four hours, 8 (4) micorgrams will stil be in her body
Answer:
the answer is y=40(0.8)^x
16 micrograms
what is 3422.4 divided by 544
6.29117647059
This is the answer
Answer: 6.29117647059
Step-by-step explanation:
divide the problem :)
Find a possible formula for the trigonometric function whose values are in the following table .
A possible formula for the trigonometric function whose values are in the given table is u(x) = 3cos(πx/2)
What is the possible formula for the trigonometric function whose values are in the following table? .From the table, it is clear that the function has a period of 4 and its maximum value is 6 and minimum value is 0. These observations suggest that the function is a cosine function.The period of cosine function is 2π, so we need to find a constant that will make the period of the function 4, which is half of the period of cosine function. This constant is π/2.The amplitude of the function is 3, which is the difference between its maximum and minimum values. The amplitude of cosine function is 1, so we need to multiply the cosine function by 3 to get the correct amplitude.Putting these together, we get the formula:u(x) = 3cos(πx/2)To learn more about trigonometric function refer:
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You are building a ramp that must cover a horizontal distance of
exactly 14 feet. The angle of the ramp from the ground is 9º.
Determine the length of the ramp, in feet. Round to two decimal
places as needed.
The length of the ramp, which is the hypotenuse of a right triangle, can be found using the formula:
length = horizontal distance / sin(angle)
Plugging in the given values, we get:
length = 14 feet / sin(9º)
Using a calculator, we find:
length ≈ 85.67 feet (rounded to two decimal places)
Therefore, the length of the ramp is approximately 85.67 feet.
Find the value of the expression
s+2/5
for s = 8 .
Write your answer as a fraction or as a whole or mixed number.
If Julian starts a bank account with $10,000 and his bank compounds the interest quarterly at an annual interest rate of 8%, how much money does he have at the year's end?
After 5 years?
Julian has $10,824.32 at the end of the year and $14,859.47 after 5 years.
What is compound interest?Compound interest is the interest paid by the bank for both of principle amount and the interest the account has already earned.
Julian starts bank with principle amount $10,000.
Bank compounds the interest quarterly at an annual interest rate 8%.
Then, total amount in the end of the year.
[tex]A = p(1+\frac{r}{n} )^{nt}[/tex]
= [tex]10,000(1+\frac{0.08}{4} )^{4}[/tex]
= $10,824.32.(at the end of the year)
After 5 years,
[tex]A=10000(1+\frac{0.08}{4} )^{(4)(5)}[/tex]
= $14,859.47(after 5 years)
Hence, Julian has $10,824.32 at the end of the year and $14,859.47 after 5 years.
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2 A recipe uses 150 g butter, 500 g flour, 50 g su make 18 cakes. How much of each ingredient will be needed to make 72 cakes?
Answer:
600g Butter, 2000g Flour, 200g Sugar
Step-by-step explanation:
First we divide the final number of cakes by the initial
[tex]72 \div 18 = 4[/tex]
Then we multiply each of the ingredients by 4
[tex]150 \times 4 = 600[/tex]
[tex]500 \times 4 = 2000[/tex]
[tex]50 \times 4 = 200[/tex]
A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
The ratio for this problem is:
(Ingredients: number of cakes)
150, 500, 50: 18Therefore, we need to know how many times 18 can fit into 72.
72 ÷ 18 = 4Now, if we know that 18 can be multiplied by 4 to get 72, we need to multiply all of the ingredients by 4.
150 × 4 = 600 (butter)500 × 4 = 2000 (flour)50 × 4 = 200 (sugar)Therefore, if the recipe stays proportional, we will need 600g butter, 200g flour and 200g sugar to make 72 cakes.
What is the x-value of the solution to the system of equations shown
below?
-3
-1
1
3
Answer:
-3
Step-by-step explanation:
you can use elimination to remove y from this equation
your first equation will be
4x+10y=-2; and you can multiply the other one by -10
30x-10y=-100
if you add the two equations, 10y and -10y will cancel out and you'll get
34x = -102
divide both sides by 34
x=-3
10. MGSE8.F.2, MGSE8.EE.5, MGSE8.F.3: A reporter collected data on y, the depreciation of a certain
car for various years, x, after it had been purchased new. The equation below was fit to the data.
y = 16,500 -1,500x
Part D Generate a table to show the depreciation over time show all your work
The table to show the depreciation over time for the first three years is:
Year (x) Depreciation (y)
1 $15,000
2 $13,500
3 $12,000
How to calculate the valueIt should be noted that in order to generate a table to show the depreciation over time for the first three years, we can use the given equation:
y = 16,500 - 1,500x
where y is the depreciation and x is the number of years since the car was purchased new.
Substituting x = 1, 2, and 3 into the equation, we get:
When x = 1, y = 16,500 - 1,500(1) = 15,000
When x = 2, y = 16,500 - 1,500(2) = 13,500
When x = 3, y = 16,500 - 1,500(3) = 12,000
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how many different ways are there to create a four-digit even number?
A. 2,000
B. 3,645
C. 4,500
D. 10,000
I need a little help
Answer:
y=-2x+1
Explanation:
you can see that the x goes up by 1 every time. Y goes down by 2 every time, because 1-2=-1, -1-2=-3, etc. So the -2 goes in your m part of y=mx+b. Then you need to figure out what y is when x is 0, for your y-intercept, or your b part of y=mx+b. The picture makes it simpler, showing that when x is 0, y is 1. Therefore, 1 is your b part of y=mx+b. If you put it all together, it looks like this:
Y=-2x+1
Step-by-step explanation:
It looks Iike the equation is in slope intercept form
[tex]y = mx + b[/tex]
m is the slope
b is the y intercept
Finding B is easy, it's just where X = 0. On this table, Y is 1 when X is 0.
Finding the slope. We'll take two different (X,Y) coordinates. Let's do the first two rows (0,1) and (1,-1)
Next we apply the slope formula. That being
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
So plugging that in
[tex] = \frac{ - 1 - 1}{1 - 0} [/tex]
That gives you -2/1, also known as -2
Now that we have everything, we can put the forumla together
[tex]y = - 2x + 1[/tex]
Where -2 is the answer that belongs in the [?]
Angela has a collection of nickels and quarters worth 8.80 if she has 68 total buckles and quarters how many quarters does she have
Answer:
Step-by-step explanation:
We got two equations.
First modeling the total money using x for nickels and y for quarters.
0.05x + 0.25y = $8.80
Our second equation is modeling the total coins.
x + y = 68
Which we can change to substitute for x.
x = 68 - y
Substitute for x to find the answer.
0.05(68 - y) + 0.25y = 8.80
3.4 - 0.05y + 0.25y = 8.80
3.4 + 0.20y = 8.80
0.20y = 5.4
y = 27.
So, there is 27 quarters and 41 nickels.
hich of these sequences is the order of the steps below in the iterative problem-solving process? a) formulate and test hypothesis b) collect information c) analyze results d) consider alternative explanations
The order of the steps in the iterative problem-solving process is: a) collect information, b) formulate and test hypothesis, c) analyze results, and d) consider alternative explanations. (option c)
The iterative problem-solving process is a cycle that involves gathering information, forming hypotheses, testing hypotheses, analyzing the results, and then considering alternative explanations.
The second step is to formulate and test hypotheses. Hypotheses are educated guesses about what might be causing the problem or why the problem is occurring.
The third step is to analyze the results. This involves interpreting the data and determining if the hypothesis was correct or incorrect.
The final step is to consider alternative explanations. This involves looking at the data and considering other potential causes for the problem.
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Complete Question:
Which of these sequences is the order of the steps below in the iterative problem-solving process? a) formulate and test hypothesis b) collect information c) analyze results d) consider alternative explanations.
Option:
a,b,c,da,c,d,bb, a,c,dd,b, a,ca bicycle is traveling at 14 miles per hour. how many feet will it cover in 30 seconds? round your answer to the nearest tenth of a foot.
The feet the bicycle will it cover in 30 seconds is 306 feet
When we talk about speed, it is often expressed in miles per hour (mph). However, in this problem, we must determine the distance covered in feet per second. To convert mph to feet per second, we can use the following formula:
1 mph = 5280 feet/hour = 5280/3600 feet/second
Therefore, to convert 14 mph to feet per second, we multiply 14 by the conversion factor of 5280/3600:
14 mph * (5280/3600 feet/second/mph) = 14 * 5280/3600 feet/second = 10.2 feet/second
So, the bicycle is traveling at a speed of 10.2 feet per second. To find the distance covered in 30 seconds, we multiply the speed by the time:
10.2 feet/second * 30 seconds = 306 feet
Finally, rounding to the nearest tenth of a foot, we have:
306 feet ≈ 306.0 feet to the nearest tenth.
Therefore, the bicycle covers 306.0 feet in 30 seconds, rounded to the nearest tenth of a foot.
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3x-2 - 5x-1.
Please help ASAP
Someone help me please
The required solution to the system of equations using elimination, as follows:
18. The solution is (x, y) = (40/11, -17/11).
19. The solution is (x, y) = (6, 1).
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
To solve the system of equations using elimination, we can multiply one equation by a scalar so that one of the variables has the same coefficient in both equations.
18.
-6x + 4y = -28
6x + 7y = 11
Add the two equations to eliminate x:
11y = -28+11
11y = -17
y = -17/11
Now that y is known, we can substitute back into either equation to find x:
-6x + 4(-17/11) = -28
-6x - 68/11 = -28
x = 40/11
So the solution is (x, y) = (40/11, -17/11).
19.
2x + 3y = 15
x - 3y = 3
Add the two equations to eliminate y:
3x = 18
x = 18/3
x = 6
Now that x is known, we can substitute back into either equation to find x:
2(6) + 3y = 15
12 + 3y = 15
3y = 3
x = 1
So the solution is (x, y) = (6, 1).
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Input (x): a number
Output (y): 5 less than 2 times
Which equation represents the rule?
y = 2x - 5
y = -5x - 2
y = -5x + 2
y = -2x + 5
Which one is a linear function
The equation represents the rule is y = 2x-5
About FunctionThe best fits the terms x and y is y=2x-5
In function rules, the output of the function depends on the input of the function. This makes the output of the function the dependent variable and the input the independent variable. This means that the output depends on the values of the inputs, and we can create a function with inputs that give a given output.
The definition of a function in mathematics can also be interpreted as a relation that connects each member of x in a set called the domain (domain) with a single value f(x) from a second set called the codomain (codomain).
The set of values obtained from these relations is called the range. A function is a rule that connects each element in a set, so that a function can be said to be a special part of a relation.
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suppose we roll two fair dices. what is the probability of the event that the second dice is not smaller than the first dice?
The probability of the event that the second dice is not smaller than the first dice is 15/36.
It's simple to rule out every option:
First die is a 1, and the second die wins 5/6.
First die is a 2, and the second die wins 4/6.
First die is a 3, and the second die wins 3/6.
First die is a 4, and the second die wins 2/6.
First die is a 5, and the second die wins 1/6.
First die is a 6, winning with a score of 0/6.
In total, 15 out of the 36 results favor the second die. All of these might be tabulated.
So the probability of the event that the second dice is not smaller than the first dice = 15/36
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If 9x^2 – 6x + 5 is rewritten as p2 – 2p + 5, what is p in terms of x?
By applying the algebra concept, it can be concluded that p = 3x or p = 2 - 3x.
Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems.
We want to express p in terms of x of this equation:
9x² – 6x + 5 = p² – 2p + 5
First, we have to eliminate 5, so we have:
9x² – 6x = p² – 2p
Then we add 1 on each side, so we have:
9x² – 6x + 1 = p² – 2p + 1
(3x - 1)² = (p - 1)²
p - 1 = √(3x - 1)²
Thus the solutions are:
p - 1 = 3x - 1 ⇔ p = 3x
or
p - 1 = -(3x - 1) ⇔ p = 2 - 3x
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A paperweight, the shape of a hemisphere, fits snugly inside a cylinder-shaped box with a radius of 9 cm. A cone fits snugly inside the paperweight hemisphere.
What is the volume of the cylinder in terms of
? Show all work.
What is the volume of the cone in terms of
? Show all work.
Estimate the volume of the hemisphere in terms of
by calculating the average of the volumes of the cylinder and cone. Show all work.
(a).The volume of the cylinder is 216π [tex]cm^{3}[/tex]
(b). The volume of the cone is 72π [tex]cm^{3}[/tex]
(c). The volume of the hemisphere is 144π [tex]cm^{3}[/tex]
(a). Volume of the cylinder:
The volume of the cylinder is 216π [tex]cm^{3}[/tex]
Since the hemisphere fits snugly inside the cylinder, and the radius of the cylinder is 6 cm, the radius of the hemisphere equals the radius of the cylinder. Also, the height of the cylinder equals the radius of the hemisphere.
So, the volume of the cylinder V = [tex]\pi r^{2} h[/tex] where
r = radius of cylinder = 6 cm and
h = height of cylinder = radius of hemisphere = 6 cm
So, V = [tex]\pi r^{2} h[/tex]
=[tex]\pi r^{2}[/tex]× r
=[tex]\pi r^{3}[/tex]
= π(6 cm)³
= 216π [tex]cm^{3}[/tex]
So, the volume of the cylinder is 216π [tex]cm^{3}[/tex]
(b). Volume of the cone
The volume of the cone is 72π [tex]cm^{3}[/tex]
Since the cone fits snugly inside the same hemisphere, the radius and height of the cone equals the radius of the hemisphere.
So, the volume of the cone V' = [tex]\frac{\pi r^{2} h}{3}[/tex] where
r = radius of cone = 6 cm and
h = height of cone = radius of hemisphere = 6 cm
So, V' = [tex]\frac{\pi r^{2} h}{3}[/tex]
= [tex]\frac{\pi r^{2} *r}{3}[/tex]
= [tex]\frac{\pi r^{3} }{3}[/tex]
=[tex]\frac{ \pi(6 cm)^{3} }{3}[/tex]
[tex]= \frac{216 \pi}{3}cm^{3} = 72 \pi cm^{3}[/tex]
So, the volume of the cone is 72π [tex]cm^{3}[/tex]
(C). Volume of hemisphere
The volume of the hemisphere is 144π cm³
Since the volume of hemisphere, V" equals the averages of the volume of the cylinder, V and volume of the cone, V'
So, V" =[tex]\frac{ (V + V')}{2}[/tex]
V" =[tex]\frac{ (216\pi cm^{3} + 72\pi cm^{3})}{2}[/tex]
V" = [tex]\frac{288\pi cm^{3} }{2}[/tex]
V" = 144π [tex]cm^{3}[/tex]
So, the volume of the hemisphere is 144π [tex]cm^{3}[/tex].
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What's the code and how do i solve this?
The code of the puzzle is 75.5 which is the sum of all the sides of the missing triangles.
What are Pythagorean Triples?Pythagorean triples are a collection of three positive numbers that fit into the Pythagorean theorem formula, which is written as, a² + b² = c², where a, b, and c are positive integers.
1.
Substitute the known values in the Pythagorean theorem formula, and solve for a:
a² + 8² = 12²
a² + 64 = 144
a² = 144 - 64
a² = 80
a = √80
a = 8.9
Similarly, solve the length of the missing side of the other triangles.
2. The missing side b = 14.5
3. The missing side c = 10.3
4. The missing side a = 18.8
5. The missing side b = 8
6. The missing side c = 15
Now, the sum of all the sides of the missing triangles as:
8.9 + 14.5 + 10.3 + 18.8 + 8 + 15 = 75.5
Thus, the code of the puzzle is 75.5.
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If equilateral polygon PENTA is inscribed in a circle of radius 15 inches so that Al of its vertices are on the circle what is the length of the shorter arc from vertex P to vertex N
The length of the shorter arc from vertex P to vertex N is 37.68 inches.
What are Polygons?In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words poly (which means numerous) and gon (which means sides).
To create a closed figure, at least three line segments must be connected end to end.
Given an equilateral polygon, PENTA is inscribed in a circle of radius 15 inches,
The central angle of the polygon leaning to the shortest chord is
α = 2π/5
α = 2*360/5 = 72°
The central angle of the polygon leaning to the shorter arc from vertex P to vertex N is
β = 2(2π/5)
β = 144°
The length of the corresponding arc is
= r*β
here r = 15 inches, and π = 3.14
length = r*2*2π/5
length = 15*2*2(3.14/5)
length = 37.68 inches.
Hence length is 37.68 inches.
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How many terms are there in the expression?
-11 - 7c + 5 - 2x - 13b - 7
The number of terms in the expression -11 - 7c + 5 - 2x - 13b - 7 is 6
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed with coefficients, terms, factors, constants and variables.
They are also known to consist of mathematical operations, such as;
SubtractionMultiplicationDivisionAdditionBracketParenthesesfloor divisionFrom the information given, we have the algebraic expression as;
-11 - 7c + 5 - 2x - 13b - 7
The terms are either single number or variables in the expression. They are six
Hence, the number is 6
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What is the factored form of 25b²-60b + 36?
O A. (6b-5)²
O B. (5b-6)²
O C. (5b-4)(5b - 9)
OD. (5b-12)(5b - 3)
Answer: B. (5b-6)2
Step-by-step explanation:
Graph the following system of equations and find the y-coordinate of the solution. y = -2 y = 3 y = 1 y = 0
Therefore, we can see that equation the only y-value that is part of all four lines is y = 1. Therefore, the y-coordinate of the solution is 1.
Which equation is this?In arithmetic equations, the exact symbol (=) is used to denote the equivalence of two assertions. It is demonstrated that mathematical methods, which have acted as manifestations of reality, can be used to assess a variety of numerical factors. The equal sign actually splits the number 12 into two separate pieces, despite the fact that the result is y + 6 = 12.
Here,
The given system of equations is:
y = -2
y = 3
y = 1
y = 0
To graph this system, we plot the horizontal lines y=-2, y=3, y=1, and y=0 on the same coordinate plane:
lua
Copy code
| * <-- y=3
4 +
| <-- y=1
3 + * <-- y=0
|
2 +
| * <-- y=-2
1 +
|
+----------------
1 2 3 4
From the graph, we can see that the only y-value that is part of all four lines is y = 1. Therefore, the y-coordinate of the solution is 1.
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PLS HELP DUE TODAY
i need this done asap
Answer:
1. 4
2. $52
3. $20
4. 58
5. 30
6. 2
7. 132
8. 24
Step-by-step explanation:
1. If he needs 10 feet all together, and only has 6, you can put it in an equation as “6+x=10” because 10 would be the final amount, and he already had 6 feet, so he needs x feet. Then you need to get the x alone in the equation, so you would subtract 6 from both sides. 10-6 is 4, which means x=4. So Phil needs 4 more feet of lumber.
2. Emmet paid $64 in total. Within that total, $12 is for the case. You can set up an equation as either 12+x=64 or 64-12=x, both get the same answer, as shown in the first problem. 64-12 is 52, so that would be your answer.
3. So if he paid $x, 6+14=x. 6 from how much money was spent, 14 from how much was returned. 6+14=20. In total, brandy gave the cashier $20.
4. If the temprature dropped 15 degrees, and it is now 43, all you need to do is undo the dropping. If it didnt drop, it rose. To you need to add 15 to 43, giving you 58. The starting temperature was 58.
5. Her rate per hour is $12. That means if she worked x hours, you would set it up as 12x=m, m being the amount of money she earns. If she earns $360, you plug that in, making it look like 12x=360. Then you do the opposite of multiplication, on both sides, so you decide both sides by 12. On the left it cancels out, on the right 360/12 is 30. That means that Cindy worked for 30 hours.
6. If she used 32 cups and there is 16 cups in a gallon, all you need to do is divide 32 by 16. 32/16 is 2. So Mary used 2 gallons of juice.
7. You can write an equation for this one that looks like x/12=11. X is the total number. From there, you multiply 12 on both sides, giving you 132. That means there are 132 students in the gym class.
8. If there are 4 ping-pong balls in each package and there are 6 packages, all you need to do it multiply 6 by 4. 6 times 4 is 24. So Matthew has 24 ping-pong balls.