20% of a = 11
[tex]\frac{20}{100}[/tex] a = 11
[tex]\frac{1}{5}[/tex] a = 11
a = 55
I hope this helps! If you have any questions, feel free to ask.
Answer.
2.2
Why:
in percents you always put the percent above 100% ( so it'll look like this---- 20/100) and your number that is left out would be 11 so you put it by your percent like this----20 a
100 11
so now you do divide and multiply: you divide 20 by 100 and multiply by 11 to get a which is 2.2
Work out the area of this semicircle take pie to be 3.142 and write down all the digits given by your calculator 18cm
Final answer:
The area of the semicircle is 0.051 square meters.
Explanation:
The area of a semicircle can be found using the formula A = πr²/2, where r is the radius of the semicircle. In this case, the radius is given as 18 cm. So, substituting this value into the formula, we get A = 3.142 x (18 cm)²/2. Now, let's calculate the area step by step:
Convert the radius to meters: 18 cm = 0.18 m
Square the radius: (0.18 m)² = 0.0324 m²
Multiply by π and divide by 2: 0.0324 m² x 3.142 / 2 = 0.051 m²
Therefore, the area of the semicircle is 0.051 square meters.
The area of the triangle is 35 square feet. Use a quadratic equation to find the length of the base. Round your answer to the nearest tenth.
Answer:
10.6 ft
Step-by-step explanation:
The complete question is:
The area of the triangle is 35 square feet. Use a quadratic equation to find the length of the base. Round your answer to the nearest tenth.Base=x+4 Height=x
SOLUTION:
As you know, Area of triangle 'A' = 1/2 x b x h
Where,
Base 'b' = x+4
Area 'A' = 35 ft²
Height 'h'= x
35 = (1/2)(x+4)x
35 =(x² + 4x)/2
2 * 35 =x² + 4x
70 = x² + 4x
x² + 4x - 70=0
Formula for the quadratic equation is
x = [- b ± √(b² - 4ac)]/2a
Where,
a=1, b= 4, c=-70
Plugging in the values.
x = [- 4 ± √4² - (4 × 1 × - 70)] / (2 × 1 )
x = [- 4 ± √(16 + 280)]/2
x = [- 4 ± √296]/2
x = (- 4 + 17.2)/2 or x = (- 4 - 17.2)/2
x = 13.2/2 or x = - 21.2/2
As, we choose to ignore negative value of 'x'
Therefore, x = 13.2/2 = 6.6
And, Length of the base will be:
x + 4 = 6.6 + 4 => 10.6 ft
The base is approximately 10.6 feet when rounded to the nearest tenth.
We know the area of the triangle is 35 square feet, the base is x + 4, and the height is x.
The formula for the area of a triangle is:
Area = 1/2 × base × height
1. Substitute the given values into the formula:
35 = 1/2 × (x + 4) × x
2. To simplify, multiply both sides by 2 to eliminate the fraction:
70 = (x + 4) × x
3. Expand the equation:
70 = [tex]x^{2}[/tex] + 4x
4. Rearrange into a standard quadratic form:
[tex]x^{2}[/tex] + 4x - 70 = 0
5. To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √([tex]b^{2}[/tex] - 4ac)) / 2a
6. Here, a = 1, b = 4, and c = -70. Plug these values into the formula:
x = (-4 ± √([tex]4^{2}[/tex] - 4(1)(-70))) / 2(1)
x = (-4 ± √(16 + 280)) / 2
x = (-4 ± √296) / 2
x = (-4 ± 17.2) / 2
7. This gives us two potential solutions:
x = (-4 + 17.2) / 2 ≈ 6.6
x = (-4 - 17.2) / 2 ≈ -10.6 (This solution is not valid since the height cannot be negative)
8. So, the height (x) is 6.6 feet. Therefore, the length of the base is:
Base = x + 4 ≈ 6.6 + 4 = 10.6 feet.
Question- The area of the triangle is 35 square ft. Use a quadratic equation to find the length of the base. Round your answer to the nearest tenth. Base = x + 4, Height = x.
A survey of 47 people was conducted to compare their self-reported height to their actual height. the difference between reported height and actual height was calculated. you're testing the claim that the mean difference is greater than 1. from the sample, the mean difference was 1.2, with a standard deviation of 0.78. calculate the test statistic, rounded to two decimal places
Answer: The test statistic is 1.75.
Step-by-step explanation:
Since we have given that
n = 47
First mean difference = 1
and second mean difference = 1.2
Standard deviation = 0.78
So, the value of test statistic would be
[tex]t=\dfrac{\bar{x_1}-\bar{x_2}}{\dfrac{\sigma}{\sqrt{n}}}\\\\t=\dfrac{1.2-1}{\dfrac{0.78}{\sqrt{47}}}\\\\t=\dfrac{0.2}{0.114}\\\\t=1.754[/tex]
Hence, the test statistic is 1.75.
The test statistic for the sample showing the difference between reported and actual height, with a mean difference of 1.2 inches, standard deviation of 0.78, and sample size of 47, is 1.96 when rounded to two decimal places.
Explanation:The test statistic for a sample where the population standard deviation is unknown and the sample size is small can be calculated using a t-test. The formula for the test statistic in a one-sample t-test is t = (\bar{X} - \mu) / (s/\sqrt{n}), where \bar{X} is the sample mean, \mu is the population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.
In this case, we are testing the claim that the mean difference in reported and actual height is greater than 1 inch. The null hypothesis (H0) is that the mean difference is less than or equal to 1 inch, and the alternative hypothesis (H1) is that the mean difference is greater than 1 inch. Given a sample mean difference of 1.2, a sample standard deviation of 0.78, and a sample size of 47, the test statistic is calculated as follows:
t = (1.2 - 1) / (0.78/\sqrt{47})
After calculating and rounding to two decimal places, the test statistic is approximately 1.96
a 50 gram sample of a substance thats used to treat thyroid disorders has a k value of 0.1133
Answer:
6.1
Step-by-step explanation:
(PLEASE HELP) Evaluate the expression 2(8 − 4)^2 − 10 ÷ 2.
A. 11
B. 27
C. 56
D. 59
Answer:
27
Step-by-step explanation:
please tell me if i am wrong
Sally has 2 cats and each cat eats 1/4 of a tin of cat food each day.
Sally buys 9 tins of cat food.
For how many days will the cat food feed her 2 cats?
Please show your working.
Answer:
18 days
Step-by-step explanation:
Each cat eats 1/4 of the thin in a day, so between the two cats they eat:
of the tin in one day.
if the two cats eat 1/2 of the tin in one day, this means that in 2 days they eat a whole tin of cat food.
we can represent this as follows
days tins of cat food
2 1
and because she has 9 tins of cat food, and x represents the quantity of days:
days tins of cat food
2 1
x 9
thus, we must multiply cross quantities from the table and divide by the remaining amount:
x = 2*9/1 = 18
the 9 tins of cat food will last 18 days
pls mark me brainliest
What is the measure of Arc NM?
a: 55
b: 60
c: 120
d: 125
please help ive been stuck on this question for so long i dont understand how to do this
Answer:
a: 55°
Step-by-step explanation:
The measure of arc NM is the same as the measure of the central angle that intercepts it: Q. The sum of the central angles of a circle is 360°, so ...
Q = 360° -120° -60° -65° -60° = 55°
The measure of arc NM is 55°.
Rosa picked some peaches from one tree, and then she picked 8 peaches from a different tree. She gave 10 peaches to Sten. She has 12 peaches left. How many peaches did Rosa pick from the first tree?
Answer:
14
Step-by-step explanation:
she had 22 in all take away 8 then you get 14.
take away 8 because they came from another tree
Answer:
14 peaches
Step-by-step explanation:
10-8=2+12=14
Juan drove his car on a vacation trip. His odometer Read 1460.3 when he began and 1830.2 at the end. If he used 20 gallons of gas how many miles per gallon did he get
Answer:
Juan got 18.50 miles per gallon.
Step-by-step explanation:
We are given the following in the question:
Odometer in the beginning of trip = 1460.3 miles
Odometer at the end of trip = 1830.2
Gallons of gas used for trip = 20 gallons
Distance of trip =
= Odometer at the end of trip - Odometer in the beginning of trip
[tex]=1830.2-1460.3\\=369.9\text{ miles}[/tex]
Thus, the trip was of 369.9 miles.
Miles per gallon =
[tex]=\dfrac{\text{Distance cover in trip}}{\text{Gallons of gas used}}\\\\=\dfrac{369.9}{20}\\\\=18.495\approx 18.50\text{ miles per gallon}[/tex]
Thus, Juan got 18.50 miles per gallon.
You interview all of your family members at a picnic and record their age and shoe sizes. The data is shown in the table. Which number summarizes all of the data points in the age column with a single number? A.1.1 B.4 C.9.2 D.11
Answer:
no
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
There are 27 chocolates in a box, all identically shaped. There 4 are filled with nuts, 8 with caramel, and 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting a solid chocolate candy followed by a nut candy.
Answer:
Therefore the required probability is [tex]\frac{30}{351}[/tex].
Step-by-step explanation:
Two events are dependents event if the occurrence of one of them has effect on the probability of the other.
If A and B are dependents,
then,
P(AB)=P(A)P(B).
Given that,
There are 27 chocolates in a box.
Number of nuts chocolates = 4
Number of caramel chocolates = 8
Number of solid chocolates= 15.
The probability of that a solid candy is drawn is
[tex]=\frac{\textrm{Number of solid chocolate}}{\textrm{Total number of chocolate}}[/tex]
[tex]=\frac{15}{27}[/tex].
After selecting a solid chocolate, the number of chocolate is= (27-1)=26.
The probability that a nut candy is drawn is
[tex]=\frac{\textrm{Number of nut chocolate}}{\textrm{Total number of chocolate}}[/tex]
[tex]=\frac{4}{26}[/tex]
[tex]=\frac{2}{13}[/tex]
Therefore the required probability is
[tex]=\frac{15}{27}\times\frac{2}{13}[/tex]
[tex]=\frac{30}{351}[/tex]
1 2 3 4 5 6 7 8 9 10 TIME REMAINING 54:32 Because the lid of a marker is wider than the marker itself, a set of markers can be packaged in a container that is in the shape of a trapezoid instead of a rectangle. A trapezoid has a base of 12 inches, height of 10 inches, and top side length of 10 inches. A rectangle has a base of 12 inches and height of 10 inches. What is the difference in area between the two packages
Answer:
10 Square Inches
Step-by-step explanation:
Trapezoid
Base =12 inches
Height =10 inches
Top side= 10 inches.
Area of a Trapezoid[tex]=\frac{1}{2}(a+b)h, $where a and b are the lengths of the base and top respectively$[/tex]
[tex]=\frac{1}{2}(10+12)*10\\=5*22=110 \:Square\:Inches[/tex]
Area of the Trapezoid=110 Square Inches
Rectangle
Base = 12 inches
Height =10 inches.
Area of a Rectangle=Base X Height
=12 X 10
=120 Square Inches
Difference in Area between the two packages
Difference=Area of Rectangle-Area of Trapezoid
=120-110
=10 Square Inches
Answer:
10 Square Inches
Step-by-step explanation:
+30 POINTS FOR THIS QUESTION
1. I just bought a kite at the departmnet store for $5.95. The owner of the store bought it from a wholesaler for $3.10. Which price is retail price?
The $5.95 is retail price because the owner got it for wholesale.
2. What precentage of the retail price is the whole sale price in #1?
3. If the sandals cost $58.00 wholesale and $105.00 retail, what is the markup in dollars?
4.The markup in #3 is what percent of the retail?
5.What precent of the wholesale in #3 is the markup?
6. A dozen eggs are purchased from the farmer at $1.05 per dozen. They are then sold to the consumer for $1.45. What percent of the retail is the markup.
1. I just bought a kite at the department store for $5.95. The owner of the store bought it from a wholesaler for $3.10. Which price is retail price?
Answer: The $5.95 is retail price because that's what I paid for it at the store
2. What percentage of the retail price is the wholesale price in #1?
3.10 / 5.95 = 0.52100 = 52.1%
3. If the sandals cost $58.00 wholesale and $105.00 retail, what is the markup in dollars?
markup = 105 - 58 = $47
4.The markup in #3 is what percent of the retail?
47/105 = 0.44761904761904764 = 44.8%
5.What percent of the wholesale in #3 is the markup?
47/58 = 0.8103 = 81.0%
6. A dozen eggs are purchased from the farmer at $1.05 per dozen. They are then sold to the consumer for $1.45. What percent of the retail is the markup.
(145-105)/145 = 0.2758620 = 27.6%
Answer:
uh what he said (:
Step-by-step explanation:
The sum of two numbers is 39. The sum of twice the larger number and three times the smaller number is 93. Find the smaller number.
Answer:3 * (n + 4) = 93
3n + 12 = 93
Subtract 12 to both sides:
3n = 81
Divide 3 to both sides:
n = 27
Step-by-step explanation:
Final answer:
The smaller number is 15.
Explanation:
To find the smaller number, let's assign variables to the two numbers. Let's call the larger number 'x' and the smaller number 'y'. According to the given information, we have two equations:
x + y = 39
2x + 3y = 93
To solve this system of equations, we can use the method of substitution.
Rearrange the first equation to get x = 39 - y.
Substitute this expression for x into the second equation:
2(39 - y) + 3y = 93
Now, simplify and solve for y:
78 - 2y + 3y = 93
y = 15
Therefore, the smaller number is 15.
What is the correct factorization of
x² + 5x – 6?
0 (x - 1) (x + 6)
o (x + 1) (x – 6)
o (x - 2) (x – 3)
O (x - 2) (x + 3)
Answer:
(x-1)(x+6)
Step-by-step explanation:
Answer:
What is the correct factorization of x2 + 5x – 6?
A.) (x – 1) (x + 6)
Complete the factorization shown: 3 then 2 are the blank numbers
Step-by-step explanation:
name the highlighted angle
Answer:
not able to see the angel
Step-by-step explanation:
What is 0.090 % of the US population?
Answer:
9/100
Step-by-step explanation:
It would be 9/100 as a fraction if thats what your asking!
PreCalc help with sums. I will mark brainliest. (also can you explain WHY you got what answer you got? Thanks)
Answer:
8
Step-by-step explanation:
a = -4
r = 16/-4 = -4
Sn = a(r^n - 1)/(r - 1)
52428 = -4[(-4)^n - 1]/(-4-1)
(-4)^n - 1 = 65535
(-4)^n = 65536
Means n is even
(4)^n = 65536
nln(4) = ln(65536)
n = 8
8. Mr. Jimerson earns $24 per hour working. He qualifies for a 15% raise in salary. What is his salary
after his raise?
Answer:
75/2=32.5
Step-by-Step explanation
15/24 x 100
3/8 x 100
3/4 x 50
3/2 x 25
What is the slope of the line that passes through the points (3, 6)(3,6) and (1, 2) ?(1,2)
Answer:
-2
Step-by-step explanation:
Using the slope theorem:
[tex]m=\frac{y_{1}-y_{0}}{x_{1}-x_{0}}[/tex]
[tex]\frac{6-2}{1-3} = \frac{4}{-2} =-2[/tex]
The slope of a line passing through two points can be calculated using a formula. In this case, the slope of a line passing through (1, 0.1) and (7, 26.8) is found to be 4.45.
The slope of a line passing through two points (x₁, y₁) and the (x₂, y₂) can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Plugging in the values of the points (1, 0.1) and (7, 26.8) into the formula, we get:
m = (26.8 - 0.1) / (7 - 1) = 26.7 / 6 = 4.45
Therefore, the slope of the line passing through the points (1, 0.1) and (7, 26.8) is 4.45.
Benjamin is riding a unicycle. The tire of his unicycle has a circumference of 2.8 \text{ m}2.8 m2, point, 8, start text, space, m, end text, and the tire revolves 1.51.51, point, 5 times per second. What is the distance Benjamin travels in 100100100 seconds
Answer:
420 meters
Step-by-step explanation:
Q. Benjamin is riding a unicycle. The tire of his unicycle has a circumference of 2.8 m, and the tire revolves 1.5 times per second. What is the distance Benjamin travels in 100 seconds?
Given:
Circumference of circular tire = 2.8 meters
Tire revolves per second = 1.5 times
Question asked:
What is the distance Benjamin travels in 100 seconds?
Solution:
Circumference of circular tire means distance covered by the unicycle's tire when it revolves 1 time that is 2.8 meters.
Now, by unitary method:
In 1 second, tire revolves = 1.5 times
In 100 seconds, tire revolves = 1.5 [tex]\times[/tex] 100
= 150 times
Distance covered by the tire when it revolves 1 time = 2.8 m
Distance covered by the tire when it revolves 150 times = 2.8 [tex]\times[/tex] 150
= 420 meters
Therefore, Benjamin travels 420 meters in 100 seconds.
Answer:
420 meters
Step-by-step explanation:
Q. Benjamin is riding a unicycle. The tire of his unicycle has a circumference of 2.8 m, and the tire revolves 1.5 times per second. What is the distance Benjamin travels in 100 seconds?
Given:
Circumference of circular tire = 2.8 meters
Tire revolves per second = 1.5 times
Question asked:
What is the distance Benjamin travels in 100 seconds?
Solution:
Circumference of circular tire means distance covered by the unicycle's tire when it revolves 1 time that is 2.8 meters.
Now, by unitary method:
In 1 second, tire revolves = 1.5 times
In 100 seconds, tire revolves = 1.5 100
= 150 times
Distance covered by the tire when it revolves 1 time = 2.8 m
Distance covered by the tire when it revolves 150 times = 2.8 150
= 420 meters
Therefore, Benjamin travels 420 meters in 100 seconds.
Suppose that in solving an equation over the interval [0 comma 360 degrees )[0,360°), you reach the step sine theta equals negative one halfsinθ=− 1 2. Why is minus−30degrees° not a correct answer?
The angle -30 degrees is not a correct answer because it falls outside of the given interval [0, 360 degrees). The correct answer is theta = 210 degrees, which satisfies the equation sine theta = -1/2 over the interval. In the fourth quadrant, the angle whose sine is -1/2 should be in the third quadrant to satisfy the inequality sine theta <= 0.
Explanation:In solving the equation Σ theta = -1/2, the student is looking for the values of theta that satisfy the equation over the interval [0, 360 degrees). The value -30 degrees is not a correct answer because it falls outside of the given interval. To find the correct answer, we need to determine the values of theta that make sine of theta equal to -1/2.
To find an angle whose sine is -1/2, we can look at the unit circle. In the first and second quadrants, the sine function is positive, so we need to look in the third and fourth quadrants.In the third quadrant (180 to 270 degrees), the sine function is negative. The angle whose sine is -1/2 in this quadrant is theta = 210 degrees.In the fourth quadrant (270 to 360 degrees), the sine function is positive again. However, the angle whose sine is -1/2 should be in the third quadrant to satisfy the inequality sine theta <= 0. Therefore, -1/2 is not a valid value for sine theta in the fourth quadrant.Learn more about Solving Equations here:https://brainly.com/question/29050831
#SPJ3
ten years ago, a printing company charged $15 to produce 100 ten-page brochures. every year, the cost increased by 2%
Answer:
C[10] = $18.28
Step-by-step explanation:
This is the initial tableau of a linear programming problem. Solve by the simplex method.
Answer:
Step-by-step explanation:
We start by selecting our pivot column as the most negative value on the bottom row.
This means our pivot column is [tex]x_{1}[/tex]. We now generate a new column by diving our pivot value by our value on the right-most column. This gives us (on a new row)
P/V
12/1 = 12
4/2 = 2
4/1 = 4
We pick our smallest positive value to be our pivot row.
This means our pivot row is our second row, and our pivot column is our first column. We now divide our entire row by our pivot point (our intersection of these two pivots)
This gives us our new second row as
1 3 0 1/2 0 0 2
now we need to eliminate our [tex]x_1[/tex] values from our other rows.
old row 1 - new row 2 gives us new row 1
row two stays the same
old row 3 - new row 2 gives us new now 3.
old row P + 2 new row 2 gives us new row P
After the first iteration of this algorithm this gives our tableau as: (see attached screenshot)
The time is 1:25 A.M. What time will it be in 6 hours and 55 minutes?
Answer:
8:20 am
Step-by-step explanation:
Dimitri determined that the ordered pair (2, –2) is a solution to the system of linear equations 7x + 9y = –4 and 5x – 2y = 6 as shown.
He mixed up the coordinates of the ordered pair when substituting it into the equations 7x + 9y = –4 and 5x – 2y = 6.
He checked the equation 7x + 9y = –4 first when he should have checked first.
He made a mistake in his calculations when substituting the ordered pair into the equation 7x + 9y = –4 and simplifying.
He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.
Answer: D. He made a mistake in his calculations when substituting the ordered pair into the equation 5x -2y =6 and simplifying.
Step-by-step explanation: I got the answer correct on a test. Hope this helps!
48 divided by 4,756
im really behind-
Answer:
0.0100925147183
Step-by-step explanation:
Answer:
48/4,756= 0.010
Step-by-step explanation:
Alma is estimating the proportion of students in her school district who, in the past month, read at least 1 book. From a random sample of 50 students, she found that 32 students read at least 1 book last month. Assuming all conditions for inference are met, which of the following defines a 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month?
a. [tex]32 \pm 1.645\sqrt{\frac{(32)(18)}{50}}[/tex]b. [tex]32 \pm 1.96\sqrt{\frac{(32)(18)}{50}}[/tex]c. [tex]0.64 \pm 1.282\sqrt{\frac{(0.64)(0.36)}{50}}[/tex]d. [tex]0.64 \pm 1.645\sqrt{\frac{(0.64)(0.36)}{50}}[/tex]e. [tex]0.64 \pm 1.96\sqrt{\frac{(0.64)(0.36)}{50}}[/tex]
Answer: D
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 50
x = 32
p = 32/50 = 0.64
q = 1 - 0.64 = 0.36
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.9 = 0.1
α/2 = 0.01/2 = 0.05
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.95
The z score corresponding to the area on the z table is 2.05. Thus, confidence level of 90% is 1.645
Therefore, the 90% confidence interval is
0.64 ± 1.645√(0.64)(0.36)/50
construct a 95% prediction interval for y given x=-3.5, ^y= 2.097x - .552 and se= .976
Answer:
95% Confidence interval for y
= (-9.804, -5.979)
Lower limit = -9.804
Upper limit = -5.979
Step-by-step explanation:
^y= 2.097x - 0.552
x = -3.5
Standard error = 0.976
Mathematically,
Confidence Interval = (Mean) ± (Margin of error)
Mean = 2.097x - 0.552 = (2.097×-3.5) - 0.552 = - 7.8915
(note that x=-3.5)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value for 95% confidence interval = 1.960
Standard Error of the mean = 0.976
95% Confidence Interval = (Mean) ± [(Critical value) × (standard Error of the mean)]
CI = -7.8915 ± (1.960 × 0.976)
CI = -7.8915 ± 1.91296
95% CI = (-9.80446, -5.97854)
95% Confidence interval for y
= (-9.804, -5.979)
Hope this Helps!!!
find the area of the shape shown below.
Answer:
Ok so lets start with finding the equations or the steps:
so for a trapazoid the formula is A= A+B/2 SO the area is 6
Step-by-step explanation: For more info on how i did this just contact me or reply to this also inform it if its wrong Thanks! have a good day
Answer:
10
Step-by-step explanation:
The area of a triangle is given by the formula [tex]\frac{(base)(height)}{2}[/tex].
The first triangle has 4 units in base and 2 in height, in the formula is
[tex]\frac{(4)(2)}{2}[/tex] = 4
The second triangle has 2 units in base and 2 in height, in the formula is
[tex]\frac{(2)(2)}{2}[/tex] = 2
The area of a square is given by the formula base x height = 2 x 2 = 4.
The sum of the areas is 10.