All the given options are valid and correct.
If Karen boards the bus first, the possible outcomes for the event are those where the other three band members board the bus in various orders after Karen. Let's consider the options:
1. KHIJ: This represents Karen boarding first, and the remaining band members (Harry, Isabel, and Jose) boarding in the order H, I, J. This is a valid outcome.
2. KHIJ, KHJI: These arrangements represent Karen boarding first, and the remaining band members boarding in different orders (H, I, J and H, J, I). Both are valid outcomes.
3. KHIJ, KHJI, KJHI, KJIH: These arrangements include all possible orders of the remaining band members after Karen. All of them are valid outcomes.
4. KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH: These arrangements cover all possible orders of the band members after Karen, including swapping the positions of Harry and Isabel. All are valid outcomes.
Therefore, the possible outcomes for this event are all of the given options.
The given question seems incomplete, but the complete question could be:
Four band members, Harry, Isabel, Jose, and Karen, are all boarding a bus to attend a concert. In each arrangement below, the first initial of each person's name represents that person's position as he or she boards the bus: first, second, third, and fourth. If we know that Karen boards the bus first, which shows the possible outcomes for this event?
A. KHIJ
B. KHIJ, KHJI
C. KHIJ, KHJI, KJHI, KJIH
D. KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH
Michael walks his black lab 1 2/3 miles on Mondays, Wednesday's, Friday's, and Sunday's. He walks his poodle 1/6 of a mile on Tuesdays, Thursdays, and Saturdays. How many total miles does Michael walk his dogs each week?
Answer:
Total for the week T;
T = 20/3 + 3/6 = 40/6 + 3/6 = 43/6 miles
T = 7.17 miles
Step-by-step explanation:
Given;
Michael walks his black lab 1 2/3 miles on Mondays, Wednesday's, Friday's, and Sunday's.
On four days = 1 2/3 = 5/3 miles per day
Total for the 4 days = 4 × 5/3 = 20/3 miles
He walks his poodle 1/6 of a mile on Tuesdays, Thursdays, and Saturdays
On 3 days = 1/6 miles per day
Total for the 3 days = 3 × 1/6 = 3/6 miles
Total for the week T;
T = 20/3 + 3/6 = 40/6 + 3/6 = 43/6 miles
T = 7.17 miles
Chester has a coupon for 1/10 off the price of a shirt. If the shirt originally costs $28.70, what discount would chester recieve from using his coupon
Answer:
Chester would receive a discount of $2.87 on using the coupon.
Step-by-step explanation:
We are given the following in the question:
Original cost of shirt = $28.70
Discount =
[tex]\dfrac{1}{10}\text{ of the original price}[/tex]
We have to find the discount Chester would receive from using this coupon.
Discount amount =
[tex]=\dfrac{1}{10}\times \text{Original Price}\\\\=\dfrac{1}{10}\times 28.70\\\\=2.87[/tex]
Thus, Chester would receive a discount of $2.87 on using the coupon.
Let the random variable X represent the winnings at one play of game A. The mean, H. Of X is known to be -$0.42 and its standard deviation, o, is $0.26. Let the random variable Y represent the winnings at one play of game B. The mean, , of Y is known to be -$0.42 and its standard deviation, o, is $0.21. You have decided to play one of these two games just once. At which game are you more likely to make a profit (i.E., to not lose money)? Explain your thinking.
Answer:
345
Step-by-step explanation:
i know it not
Answer:
565$
Step-by-step explanation:
Y because he got more money
Ava's aquarium is 95% filled with water. The tank holds 1,120 gallons of water. Select the remaining number of gallons of water needed to fill the aquarium to the top.
Answer:
The answer to your question is 56 gal
Step-by-step explanation:
Data
Percent filled = 95%
Total water can hold = 1120 gal
remaining water = ?
Process
1.- Calculate the 95% of 1120 gal
1120 gal ------------------ 100%
x ------------------ 95%
x = (95 x 1120) / 100
x = 106400 / 100
x = 1064 gal
2.- Calculate the remaining water by subtracting the previuos value to the total capacity.
Remaining water = 1120 - 1064
= 56 gal
Answer:
sgdggggggggggggsdfgfgfg
Step-by-step explanation:
The doctor recommended that Mike increase the number of calories he burns working out from 1,500 to 1,800. By what percent did the number of calories increase?
Answer: The number of calories increased by 20%.
Step-by-step explanation:
Given : The doctor recommended that Mike increase the number of calories he burns working out from 1,500 to 1,800.
Previous number of calories he used to burn = 1,500
Increase in calories = 1800-1500=300
Now , the percent increase in calories = [tex]\dfrac{\text{Increase in calories}}{\text{previous calories}}\times100[/tex]
[tex]=\dfrac{300}{1500}\times100=20\%[/tex]
Hence , the number of calories increased by 20%.
Answer:
20%
Step-by-step explanation:
Which measures are $1 greater for Group B than for Group A?
the median and the mode
the mean and the range
the mean and the median
the mode and the range
Answer: C
the mean and the median
Step-by-step explanation:
From the attached table,
The range of group A = 5 - 0 = 5
The range of group B = 4 - 1 = 3
Difference in range is not equal to $1
The mode of A = 1
The mode of B = 3
Difference in mode is not equal to $1
The median of A = (1 + 2)/2 = 1.5
The median of B = 3
Difference = 3 - 1.5 = $1.5
The mean of A = 16/15 = 1.07
The mean of B = 40/15 = 2.67
The difference = $1.6
From the above analysis, we can therefore conclude that non of the measures are $1 greater for Group B than for Group A
The best option among the options is
the mean and the median
Answer:
the right answer is c. mean and the median
Step-by-step explanation:
because i took the test and got the answer right
If n(U) = 360, n(A) = 240, n(B) = 160, find the maximum value of
n(AUB) and the minimum value of n(A n B). When will the value of
n(An B) be maximum and find its value.
Answer:
here is answer
Step-by-step explanation:
n(AUB) = n(A) + n(B) - n(AnB )
= 240 + 160 - n(A n B)
= 400 - n(AnB )
Since n(AnB) 20, so n(AUB) S 400
But n(U) = 360, so n(A U B)* 360
.. the maximum value of n(AUB) = 360.
When n(A U B) is maximum, n(AnB) will be minimum.
.. min. value of n(An B)
= n(A) + n(B) - Max, value of n(AUB)
= 240 - 160 - 360 = 40
Again, n(
A B) will be maximum when B C A.
..the max. value of n(
A B) = n(B) = 160
What is the volume of this rectangular prism?
A rectangular prism with a length of 6 and one-fourth foot, a width of 14 feet, and a height of 3 feet.
87 and one-half feet cubed a
131 and one-fourth feet cubed b
252 feet cubed c
262 and one-half feet cubed d
Mark this and return
Answer:
262 1/2 cubic feet
Step-by-step explanation:
The volume of a prism is (length)(width)(height).
Here we have
V = (6 1/4 ft)(14 ft)(3 ft)
Converting 6 1/4 ft to an improper fraction, we get 25/4.
Then the above product is V = (25 ft/4)(14 ft)(3 ft) = 262 1/2 cubic feet
The volume of the rectangular prism is 262.5 cubic feet. Thus, the correct option is D.
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as,
V = L x W x H
A rectangular prism with a length of 6 and one-fourth feet, a width of 14 feet, and a height of 3 feet. Then the volume of the rectangular prism is calculated as,
V = (6 + 1/4) x (14) x (3)
V = 25/4 x 42
V = 1050/4
V = 262 + 1/2 cubic feet
V = 262.5 cubic feet
Thus, the correct option is D.
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Alvin has a prism-like water tank whose base area is 0.9 square meters and height is 0.6 meters. He wants to buy guppy fish, and the pet store owner tells him to make sure their density in the tank isn't more than 5 fish per cubic meter. How many fish can Alvin get, at most?
Answer:
Alvin can't have more than 2 fishes on his tank.
Step-by-step explanation:
In order to calculate how many fish Alvin can have in his tank we first need to calculate the volume of the tank. A prism's volume is given by the following formula:
v = Abase*h
Therefore for Alvin's, we have:
v = 0.9*0.6 = 0.54 m³
Since he can't have more than 5 fish per cubic meter we can use a rule of three in a way that:
5 fish -> 1 m³
x fish -> 0.54 m³
5/x = 1/0.54
x = 0.54*5 = 2.7
Since he can't have a 0.7 fish and in order to mantain the density to the recommended level, he can't have more than 2 fishes.
At the beginning of the year, Omar has $120 in his bank account. He deposits $24 each week.
How many weeks will it take for Omar to have $480 in his account?
A) 4
B) 5
C) 15
D) 20
E) 25
Answer:
15 weeks
Step-by-step explanation:
He deposits 24 each week, so 480-120 is 360. Then if you divide 360 by 24 to see how many weeks, it is 15.
Answer:
that will be 15
Step-by-step explanation:
A rectangle is 2 inches wide, and more than 2 inches long. It so happens that this rectangle can be divided, by a single cut, into a 2-inch square and a small rectangle that has exactly the same shape as the large rectangle. What is the length of the large rectangle
Answer:
6 in.
Step-by-step explanation:
The Length of the large rectangle is 2 units.
It is required to find the length of the large rectangle.
What is rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
Given:
A rectangle is 2 inches wide, and more than 2 inches long.
According to given question we have,
Ratio of width to length of known rectangle is 2:4 this simplifies to 1:2
The smaller similar rectangle will have the same ratio. .i.e. 1:2
Since the width is 1 then the length will be 2.
.This can also be looked at another way. the second value in the ratio is
2:1 of the first value in the ratio and the first value is 1:2 of the second value.
So, Length of the large rectangle is 2 units.
Width of the large rectangle is 1 units.
Therefore, the Length of the large rectangle is 2 units.
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Let x denote the sum of two distinct numbers selected randomly from the set of numbers StartSet 1 comma 2 comma 3 comma 4 comma 5 EndSet . {1, 2, 3, 4, 5}. Construct the probability distribution for the random variable x.
Answer:
Step-by-step explanation:
Given:
The set of numbers {1, 2, 3, 4, 5}
Affter that, we find the sum um of two distinct numbers selected randomly from the set above;
1+2 =31+3=41+4=51+5=62+3=52+4=62+5=73+4=73+5=84+5 = 9Therefore, we have the following number: 3,4,5,6,5,6,7,7,8,9
so we have x = {3,4,5,6,5,6,7,7,8,9 }
now we find P(x) of each number, we have n(S) = 10
x 3 4 5 6 7 8 9
P(x) 1/10 1/10 1/10 2/10 2/10 2/10 1/10
Hope it will find you well.
The probability distribution of a set gives the probabilities of possible outcomes of the set
The set of numbers is given as:
[tex]\mathbf{Set = \{1, 2, 3, 4, 5\}}[/tex]
Add two distinct numbers of the set.
The sum is as follows
[tex]\mathbf{1+2 =3}[/tex]
[tex]\mathbf{1+3=4}[/tex]
[tex]\mathbf{1+4=5}[/tex]
[tex]\mathbf{1+5=6}[/tex]
[tex]\mathbf{2+3=5}[/tex]
[tex]\mathbf{2+4=6}[/tex]
[tex]\mathbf{2+5=7}[/tex]
[tex]\mathbf{3+4=7}[/tex]
[tex]\mathbf{3+5=8}[/tex]
[tex]\mathbf{4+5 = 9}[/tex]
The sum of the distinct numbers are:
[tex]\mathbf{Sum = \{3,4,5,6,5,6,7,7,8,9\}}[/tex]
Calculate the probability of each number in the sum set i.e. 3, 4, 5, 6, 7, 8 and 9
[tex]\mathbf{P(3) = P(4) = P(5)= P(9)= \frac{1}{10} = 0.10}[/tex]
[tex]\mathbf{P(6) = P(7) = P(8)= \frac{2}{10} = 0.20}[/tex]
So, the probability distribution for the random variable is:
x - - P(x)
3 -- 0.10
4 -- 0.10
5 -- 0.10
6 -- 0.20
7 -- 0.20
8 -- 0.20
9 -- 0.10
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Identify the volume and surface area in terms of π of a sphere with a great circle area of 225π ft2
V = 900π ft3; S = 4500π ft2
V = 4500π ft3; S = 900π ft2
V = 300π ft3; S = 900π ft2
V = 900π ft3; S = 300π ft2
Answer:
B (V = 4500π ft3; S = 900π ft2)
Step-by-step explanation:
If the great circle's area is 225pi, that makes the radius sqrt225 = 15
The volume of a sphere is (4/3) pi r^3, so the volume would be 3375 * 4/3 pi= 4500pi
The surface area of a sphere is 4 pi r^2, so the Surface area would be 4 * 225 pi = 900pi
That makes the answer B (V = 4500π ft3; S = 900π ft2)
hi what is the four time pi?
Answer:
12.5663706144 or just 12.57.Step-by-step explanation:
4 x pi = 12.57
EstimatePi is approx. equal to 3.14
4 x 3 = 12
The graph of f(x) = x6 – 2x4 – 5x2 + 6 is shown below.
How many roots of f(x) are rational numbers?
Answer:
B. 2
Step-by-step explanation:
egd. 2021
Answer:
B
Step-by-step explanation:
The roots of rational numbers is when you find the square root making it B
Which expression correctly represents "twice the sum of four and a number"?
Answer:
2(4+x)
Step-by-step explanation:
"Twice the sum of" tells us it will be the equation times two
"the sum of four and a number" is easy, thats 4 + x
The second number is x because the number is not specified so we need a place holder, x in this case, to tell us that the number is not given.
All this put together = twice the sum of four and a number, or 2(4+x)
The expression for "twice the sum of four and a number" is represented by 2(x + 4) or 2 * (x + 4), signifying that you first sum the number with four and then double the result.
Explanation:The expression that correctly represents "twice the sum of four and a number" is 2(x + 4) or 2 * (x + 4), where x is the variable representing the unknown number. To arrive at this expression, you first find the sum of four and the number (x + 4) and then multiply the result by two to get twice this sum.
In this context, the word 'twice' is similar to triple as in triple the amount of money being three times as much. This operation is an example of simple addition, much like when two numbers are added in any order, such as 2 + 3 or 3 + 2, which illustrates the commutative property of addition.
A wheel with a diameter of 25 in. is in a puddle of water 8.1 in. deep. What is the width of the wheel, AB, at the surface of the water?
Answer:
AB = 23.4 inches
Step-by-step explanation:
If the diameter of the wheel is 25 inches, we have that its radius is 25/2 = 12.5 inches.
If we draw a radius to the bottom of the wheel and a radius to point A, we have a triangle where we can use Pythagoras' formula:
(see image attached for better understanding)
r^2 = (r-8.1)^2 + (AB/2)^2
12.5^2 = 4.4^2 + AB^2/4
156.25 = 19.36 + AB^2/4
AB^2/4 = 136.89
AB^2 = 547.56
AB = 23.4 inches
Help please I really need it
Answer:
402.705 cm^2
Step-by-step explanation:
pi * r^2 * h /3 ---> (Volume of a cone)
3.14* 4.5^2 * 19 /3 =
3.14 * 20.25*19/3 = 402.705
Answer:
it would be around 318.09 cubic centimetres in volume for the cone
I don’t understand 1 2 and 3 please help
Answer:
1. 336 in3
2. 384 cm3
3. 336 m3
Step-by-step explanation:
im not positive but i think you just multiply the numbers and put the label as cubed
a 20 ounce bottle of lotion costs $3.95. how much does each ounce costs ?
Answer:
3.95 divided by 20 equals 0.1975
Each ounce costs $0.1975.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units. Hence this method aims at determining values in relation to a single unit.
Given here, a 20 ounce bottle and it costs $3.95
1 ounce of lotion would cost $3.95 / 20= $0.1975.
Hence, Each ounce costs $0.1975.
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Check all that apply
Answer:
The first and last option.
Step-by-step explanation:
This is true because in the first chart, different y values correspond to different x values. In the other chart and option, the same y value corresponded to multiple x values - when this happens, it is not a function. This is why the first option is a function. In the last option, you gave an equation to a parabola. When graphed, the parabola opens downwards. Only parabolas that open upwards or downwards are considered functions. Parabolas that open left or right are not considered parabolas. You can test whether or not a parabola is considered a function by conducting the "Vertical Line Test."
Answer:
To determine if they are functions or not, each y value needs to have only one x value. There should never be 2 values with the same x.
The first one is a function.
The second one is not a function because there are two coordinates that have -1.
The third on is not a function because there are two of them that have 0.
The fourth one is a function because when listing the inputs and outputs, there are different x values for each y value.
Hope this helps ;)
I need help with summation notation. Look at picture
Answer:
[tex]=18[/tex]
Step-by-step explanation:
[tex]\sum _{j=1}^33j[/tex]
Apply the constant multiplication rule:
[tex]=3\cdot \sum _{j=1}^3j[/tex]
[tex]\sum _{j=1}^3j[/tex]
Apply sum formula:
[tex]=\frac{1}{2}\cdot \:3\left(3+1\right)[/tex]
[tex]\frac{1}{2}\cdot \:3\left(3+1\right)[/tex]
[tex]=3\cdot \:4\cdot \frac{1}{2}\\[/tex]
[tex]=\frac{1\cdot \:3\cdot \:4}{2}[/tex]
[tex]=\frac{12}{2}[/tex]
[tex]=6[/tex]
[tex]=3\cdot \:6[/tex]
[tex]=18[/tex]
Simplify the expression 0.8y-1.5-0.2y+3.6
Answer:
0.6y+2.1
Step-by-step explanation:
In this question, it is required to simplify the given expression i.e. 0.8y-1.5-0.2y+3.6. It can be done by combining like terms together.
Here y is a variable. We can combine y terms together such that we get :
[tex]=(0.8y-0.2y)-1.5+3.6\\\\=0.6y+2.1[/tex]
Hence, the simplified expression is 0.6y+2.1
Kermit's favorite iced tea is made with 151515 tea bags in every 222 liters of water. Peggy made a 121212-liter batch of iced tea with 909090 tea bags.
Answer:
The answer is (Choice C) It is just right.
Step-by-step explanation:
The question is incomplete, so the complete question is below:
Kermit's favorite iced tea is made with 15 tea bags in every 2 liters of water. Peggy made a 12-liter batch of iced tea with 90 tea bags. What will Kermit think of Peggy's iced tea? Choose 1 answer: (Choice A) It is too strong. (Choice B) It is too weak. (Choice C) It is just right.
Now, to find which of the choice is correct.
So, we find first the unit rate of Peggy's iced tea bags per liter:
If, Peggy made a 12-liter batch of iced tea with 90 tea bags.
Then, Peggy would made a 1-liter batch of iced tea with = [tex]\frac{90}{12} =7.5\ tea\ bags.[/tex]
Now, to get the unit rate of Kermit's iced tea bags per liter:
If, Kermit made a 2 liter of iced tea with 15 tea bags.
Then, Kermit would made a 2 liter of iced tea with = [tex]\frac{15}{2} =7.5\ tea\ bags.[/tex]
Thus, the quantity of tea bags per liter is same of both Kermit and Peggy.
Hence, Kermit will think of Peggy's iced tea that it is just right.
Therefore, the answer is (Choice C) It is just right.
Answer:
C
Step-by-step explanation:
The following data points represent the yearly salaries of high school cheerleading coaches in Dakota County (in thousands of dollars).
qquad 41,38, 36 , 57, 4341,38,36,57,4341, , 38, , 36, , 57, 43
Find the mean absolute deviation (MAD) of the data set.
_____ thousand dollars
Answer:
Step-by-step explanation:
I think the data is repeated
The given data should be
41, 38, 36, 57, and 43
So, we want to find the absolute mean deviation, absolute here means we will discard the negative sign and make it possible
So, let find the mean of data
X~ = Σx / N
x is the given data
And N is the number of data given
X~ = (41 + 38 + 36 + 57 + 43) / 5
X~ = 215 / 5
X~ = 43
The mean is 43, so we and to find now the data given deviate from the mean.
X....... X-X~.......….|X-X~|
36..... —7............... 7
38..... —5.............. 5
41...... —2............... 2
43....... 0.........., ...0
57...... 14............. 14
So, the sum of the mean deviation is expected to be 0
ΣX-X~ = -7 -5 - 2 + 0 + 14 = 0
As expected
But the sum of the absolute mean is
Σ|X-X~| = 7 + 5 + 2 + 0 + 14 = 28
The mean deviation is given as
M•D = Σ|X-X~| / N
M•D = 28 / 5
The mean absolute deviation is 5.6 thousand dollars
This question is not correct
Correct Question:
The following data points represent the yearly salaries of high school cheer leading coaches in Dakota County (in thousands of dollars). 43, 41, 38, 36 , 57. Find the mean absolute deviation (MAD) of the data set.
Answer:
5.6 thousand dollars
Step-by-step explanation:
Mean Absolute Deviation is mean of or the average of absolute deviation of a set of data from it's central point.
We were given the following sets of data in thousands( the yearly salaries of high school cheer leading coaches)
43, 41, 38, 36, and 57
We would determine the Mean Absolute Deviation in the following steps:
Step 1
The first step is calculate the mean of the salaries
= (43+ 41 + 38+ 36+ 57) ÷ 5
= 215 ÷ 5
= 43
The mean of the salaries is 43 in thousand dollars.
Step 2
The second step would be to find the absolute difference of the values by subtracting the mean of the salaries from each of the salaries of the high school teachers , find the absolute values, after which we would sum up this absolute values together and divide by the number of the observed values
The number of observed values = 5
[|43 - 43| + |41 - 43| + |38- 43| + |36 - 43| + |57- 43| ]÷ 5
= 0 + |- 2|+ |- 5 |+|-7| + |-14| ÷ 5
= (0 + 2+ 5 +7 + 14) ÷ 5
= (28 ÷ 5) in thousand dollars
= 5.6 in thousand dollars
Therefore, the mean absolute deviation (MAD) of the data set in thousand dollars is 5.6.
Use 3.14 for π. Round answer to the nearest tenth if necessary. A can of chili has a radius of 5.25 cm and a height of 13 cm. Find the volume. (Enter a numerical answer only)
Answer:
V=1,125.1
Step-by-step explanation:
The equation for the volume of a cylinder is (V= πr^2h)
V= π(5.25)^2(13)
V= π(27.5625)(13)
V= π(358.3125)
V=1,125.10125
Locate the y-intercept for the graph of the linear function, and for the equation of the linear function. Which has a larger y-intercept
y=-3/2x- 1/2
A. The graph has a larger y-intercept
B. the equation has a larger y-intercept
C. The y-intercepts are equal
Slope-intercept form: y = mx + b
(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)
y = -3/2x - 1/2
b = -1/2
To locate the y-intercept on the graph, find the point where the line crosses through the y-axis or the y-value when x = 0
I can't see the graph but hopefully this information helps you find the answer
Answer:
It’s A. The graph has a larger y/intercept.
Step-by-step explanation:
f y = x2 − 2x, which ordered pair gives the location for one of the points on the graph?
Answer: C) (-3,15)
Step-by-step explanation:
Just did USATestPrep and that is the order pair that gives u one of the points on the graph if y= x^2 - 2x
Amanda is 3 years older than Brantley and Carlos is twice as old as Amanda. The sum of their ages is 57. How old is Amanda?
Answer:
15 years old
Step-by-step explanation:
Let's say Amanda's age is a, Brantley's age is b, and Carlos's age is c.
"Amanda is 3 years older than Brantley" means that a = 3 + b
"Carlos is twice as old as Amanda" means that c = 2 * a = 2a
"The sum of their ages is 57" means a + b + c = 57
We know that a = 3 + b, which can be written as b = a - 3. Substitute a - 3 in for b and 2a in for c in the equation a + b + c = 57 so that we have one variable to solve for:
a + b + c = 57
a + (a - 3) + 2a = 57
4a - 3 = 57
4a = 60
a = 15
Amanda is 15 years old.
Answer:
15
Step-by-step explanation:
A = B + 3
B = A - 3
C = 2A
A + B + C = 57
A + A - 3 + 2A = 57
4A - 3 = 57
4A = 60
A = 15
2c+2=10
A.-4
B.3
C.5
D.4
Answer: 4
Step-by-step explanation: Subtract 2 on both sides, you get 2c=8 ... divide 2 on both sides. C = 4
Answer:
D 4
Step-by-step explanation:
2c+2=10
Subtract 2 from each side
2c+2-2=10-2
2c = 8
Divide each side by 2
2c/2 = 8/2
c =4