Given:
A circle of radius r inscribed in a square.
To find:
The expression for the area of the shaded region.
Solution:
Area of a circle is:
[tex]A_1=\pi r^2[/tex]
Where, r is the radius of the circle.
Area of a square is:
[tex]Area=a^2[/tex]
Where, a is the side of the square.
A circle of radius r inscribed in a square. So, diameter of the circle is equal to the side of the square.
[tex]a=2a[/tex]
So, the area of the square is:
[tex]A_2=(2r)^2[/tex]
[tex]A_2=4r^2[/tex]
Now, the area of the shaded region is the difference between the area of the square and the area of the circle.
[tex]A=A_2-A_1[/tex]
[tex]A=4r^2-\pi r^2[/tex]
[tex]A=4r^2-\pi r^2[/tex]
[tex]A=r^2(4-\pi )[/tex]
Therefore, the correct option is (a).
There were two times as many pepperoni pizzas as cheese pizzas, plus one pizza they ordered 13 pizzas altogether how many pepperoni pizzas were there? How many cheese pizzas were there
Answer:
pepperoni pizzas = 8
cheese pizzas = 4
Step-by-step explanation:
let x = cheese pizza
2x + x + 1 = 13
3x = 13 -1
3x = 12
x = 4
pepperoni = 2x4 = 8
i light is faster then anything how did dark get there first
hello there enjoy 30 points on da house
Answer:
this just confused me so much
Step-by-step explanation:
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Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!
Answer: n=4
Step-by-step explanation:
Given
3n-(2+n)=6
Expand Parenthesis (REMEMBER TO CHANGE SIGNS)
3n-2-n=6
Combine like terms
2n-2=6
Add 2 on both sides
2n-2+2=6+2
2n=8
Divide both sides by 2
2n/2=8/2
n=4
Hope this helps!! :)
Please let me know if you have any questions
Answer:
4
Step-by-step explanation:
4 Is the Answer because you have to multiply 4 to all the N's. Which means you have to multiply 4 by 3 which equals 12. Then 2+4=6. Then you would do 12-6=6. There's your answer. Here is the equation if it were like the problem: 12 - (2+4). I'm sure you can figure out the rest. Thanks. If you find any fault in my answer let me know! Have a good day!
Two angles are supplementary. The first angle is 3x degrees. The second angle is (2x + 25) degrees. Determine the measure of each angle.
Answer: a = 3x
b = 2x+25
180 = a + b
180 = 3x + 2x + 25
180 = 5x + 25
155 = 5x
x = 31
a = 3*31 = 93
b = 2*31 + 25 = 87
Step-by-step explanation: pls mark as branlyest
Which system of inequalities has this graph as its solution?
y 10
-10
- म
5
10
-10
OA. y < 21 - 3
y
OB.y > 2 - 3
y> : +4
Ocy > 21 - 3
y < = + 4
Welp what is 103883+293883=? please helppp mah mum in city :')
[tex]\huge{\mathbb{\tt { PROBLEM:}}}[/tex]
Help What is 103883+293883=?
[tex]\huge{\mathbb{\tt { ANSWER:}}}[/tex]
397766[tex]{\boxed{\boxed{\tt { SOLUTION:}}}}[/tex]
[tex] \: \: \: 103883 \\ \frac{+293883}{ \: \: \: \: 397766} [/tex]
----------------------------------------------------------------------------------------------------[tex]\huge{\mathbb{\tt { WHAT \: IS \: ADDITION \: ?}}}[/tex]
Addition is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of those values combined#CarryOnLearning
#JustEnjoyTheSummer
XxKim02xXCan someone please help me with math
Answer:
A
Step-by-step explanation:
Hello There!
This is the formula for volume of a cylinder
[tex]V=\pi r^2h[/tex]
where r = radius and h = height
we are given the height and diameter height - 10 ft diameter - 22 ft
we are not give the radius directly but we can easily convert the diameter to the radius by dividing by 2
22/2=11 so the radius is 11
now having found the radius and height we plug in the values into the formula (note: it says leave answer in terms of pi so we will not apply pi to the final answer.)
[tex]V=\pi 11^210\\11^2=121\\121*10=1210\\V=1210\pi[/tex]
so we can conclude that the answer is A
Question in pic plz help! ~
Im gonna label the long side of a rectangle a and the smaller side b.
For the perimeter, 2a + 2b = 34
For the area, a x b = 66
if a is 11 and b is 6, the equation for perimeter would be 22 + 12 = 34.
So a = 11 and b = 6
Answer:
Longer side = 11
Shorter side = 6
Step-by-step explanation:
L x W = 66, then W = 66/L
2L + 2W = 34
substitute for W:
2L + 2(66/L) = 34
2L + 132/L = 34
multiply both sides of the equation by L:
2L² + 132 = 34L
divide both sides by 2:
L² + 66 = 17L
L² - 17L + 66 = 0
factor:
(L - 11)(L - 6) = 0
L = 11 or L = 6
if L = 11, then W = 6
if L = 6 then W = 11
Question is in picture
Answer:
27.5ft
Step-by-step explanation:
a² + b² = c²
Plug in what you have:
a² + 12² = 30²
Get a by itself:
a² = 30² - 12²
Simplify:
a² = 900 - 144
Simplify:
a² = 756
Simplify:
√a = √756
Then you get 27.49 and when you round you get 27.5
Write an equation in slope intercept form that represents the line shown?
Answer:
I think the answer would be Y=-2X+5
Hope it helps you *^*
What’s the opposite of -5/8
How many solutions does the system of linear equations have? Use the drop-down menus to explain your answer.
y = 3/4x + 12
y = 4/3x
The system of linear equations will have
Choose...
no solution
exactly one solution
infanite many solutions
because the slopes of the equations are
Choose...
the same
different
, so the lines will
Choose...
not intersect at all
intercect at one point
both be the same line
Answer:
There is one equation, the slopes are different so they will intersect at one point
Step-by-step explanation:
At 5 am, the temperature was -10°F. By noon the temperature was 7°F, What Integer
represents the change in temperature from 5 am, to noon?
Answer:
The integer that represents the change in temperature is 17.
Step-by-step explanation:
HELP PLEASE
Marcus works at the grocery store. He earns 8.75 per hour. Last week he worked 6.5 hours. How much did Marcus make last week?
It cost Erica $9.75 for the ingredients to make 30 cupcakes. She sold them for $1.00 each. What was Erica’s total profit?
Can i please get some help, I NEED A STEP BY STEP TO FULLY UNDERSTAND THE QUESTION AND YOUR ANSWER
Answer: $20.25
Step-by-step explanation:
If each cupcake is sold for $1, then all the cupcakes are sold together for $30. Now subtract 9.75 from 30 and you get 20.25.
Hope this helps :)
Can somebody help me
Answer:
25
Step-by-step explanation:
If it has 25 miles across from the 1 hour it means that it goes 25 miles per hour.
PLEASE HELP ME PUT THEM IN ORDER
Answer
picture below of order. Not entirely
Step-by-step explanation:
Peterkin park has a square fountain with a walkway aroind it. The fountain measures 12 feet on each side. The walkway is 3 1/2 feet wide.Find the area of the walkway
Answer: 829.44 ft²
Step-by-step explanation:
Correction - The walkway is 31.2 feet wide.
To solve this, first find the area of the fountain:
Area of a square = Length * Width
= 12 * 12
= 144 ft²
The find the area of the walkway including the fountain:
= 31.2 * 31.2
= 973.44 ft²
To find the area of the walkway alone, subtract the area of the square from the area of the rectangle:
= 973.44 - 144
= 829.44 ft²
can somebody help me please
Answer:
B
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² = 4² + ([tex]\sqrt{5}[/tex] )² = 16 + 5 = 21 ( take the square root of both sides )
x = [tex]\sqrt{21}[/tex] → B
Alicia would like to know if there is a difference in the average price between two brands of shoes. She selected and analyzed a random sample of 40 different types of Brand A shoes and 33 different types of Brand B shoes. Alicia observes that the boxplot of the sample of Brand A shoe prices shows two outliers. Alicia wants to construct a confidence interval to estimate the difference in population means.
This question is incomplete, the complete question is;
Alicia would like to know if there is a difference in the average price between two brands of shoes. She selected and analyzed a random sample of 40 different types of Brand A shoes and 33 different types of Brand B shoes. Alicia observes that the boxplot of the sample of Brand A shoe prices shows two outliers. Alicia wants to construct a confidence interval to estimate the difference in population means.
Is the sampling distribution of the difference in sample means approximately normal?
a) Yes, because Alicia selected a random sample
b) Yes, because for each brand it is reasonable to assume that the population size is greater than ten times its sample size.
c) Yes, because the size of each sample is at least 30
d) No, because the distribution of Brand A shoes has outliers
e) No, because the shape of the population distribution is unknown.
Answer:
the sampling distribution of the difference in sample means is approximately normal because the size of each sample is al least 30
Option (c) Yes, because the size of each sample is at least 30 ) is the correct answer.
Step-by-step explanation:
Given the data in the question;
sample size of brand A shoes [tex]n_A[/tex] = 40
sample size of brand B shoes [tex]n_B[/tex] = 33
As we can notice,
[tex]n_A[/tex] = 40 > 30
[tex]n_B[/tex] = 33 > 30
Hence, we consider both samples to be large.
Therefore, the sampling distribution of the difference in sample means is approximately normal because the size of each sample is al least 30.
Option (c) Yes, because the size of each sample is at least 30 ) is the correct answer.
what is the distance between (3,-5), (-3,0)
Answer: 11 units
Step-by-step explanation:
-3 and 3 are 6 units apart, so that would be 6 units, and when you add the -5 into the problem, the 6 units become 11 units. Hope this helped :)
Answer:
Exact Form:
√ 61
Decimal Form:
7.81024967 …
4. Which ordered pair best represents a point
on Tia's route to the store?
F .(-5, 6)
G. (-2.5, 0)
H. (-2,5)
J. (-3.5, -3)
Answer:
G. (-2.5, 0)
Step-by-step explanation:
Starting from the origin, (0, 0), go 2.5 units to the left (because it's negative) on the x-axis, and then 0 units on the y-axis. You end up on (-2.5,0).
hope this helped :)
Help please :) (asap)
x^2 - x - 6= 0
(x - 3) ( x + 2) = 0
Equating
x - 3 = 0
x = 3
x+ 2= 0
x = -2
Answer: x - 6
Step-by-step explanation:
Please help me finish this i will give brainlest :) to the first person.
Answer: 8
Step-by-step explanation:
64 ÷[4* 27 (-5^2
-5 times -5 =25
27-25=2
4*2=8
64 divided by 8= 8
8 is your answer
Jamar to the local snack shop near his school He bought 3 hotdogs and 2 bags of chips for $Kenny went to the same snack shop and bought 5 hotdogs and 6 bags of chips for $9.55 ordered 2 hotdogs and 3 bags of chips, then how much did she pay her order?
Answer:
Marcy paid $4.15
Step-by-step explanation:
Given
Represent hotdogs with x and chips with y.
So, we have:
Jamal
[tex]3x + 2y = 4.85[/tex]
Kenny
[tex]5x + 6y = 9.55[/tex]
See attachment for complete question
Required
Determine the amount for 2x and 3y
From Jamal's and Kenny's orders we have:
[tex]3x + 2y = 4.85[/tex] --- (1)
[tex]5x + 6y = 9.55[/tex] --- (2)
Multiply (1) by 3
[tex]3 * [3x + 2y = 4.85][/tex]
[tex]9x + 6y = 14.55[/tex] --- (3)
Subtract (2) and (3)
[tex]9x - 5x + 6y - 6y = 14.55 - 9.55[/tex]
[tex]9x - 5x = 5[/tex]
[tex]4x = 5[/tex]
Solve for x
[tex]x = \frac{5}{4}[/tex]
[tex]x = 1.25[/tex]
Substitute [tex]x = 1.25[/tex] in [tex]3x + 2y = 4.85[/tex]
[tex]3 * 1.25 + 2y = 4.85[/tex]
[tex]3.75 + 2y = 4.85[/tex]
Solve for y
[tex]y = \frac{4.85 - 3.75}{2}[/tex]
[tex]y = \frac{1.10}{2}[/tex]
[tex]y = 0.55[/tex]
So, the cost of 2x and 3y is:
[tex]Cost = 2x + 3y[/tex]
[tex]Cost = 2*1.25 + 3*0.55[/tex]
[tex]Cost = \$4.15[/tex]
Help me please!!!!!!!!!!!
Answer:
A reflection over the y-axis.
If an item is on sale for 60% off, that means you actually PAY _____% of the price.
Answer:
40%
Step-by-step explanation:
100-60=40
Find the value of x in the picture below. (round to nearest tenth if needed) THANK YOU FOR HELPING ME:)
Answer:
x ≈ 9.6
Step-by-step explanation:
Using Pythagoras' identity in the right triangle, that is
x² + 14² = 17²
x² + 196 = 289 ( subtract 196 from both sides )
x² = 93 ( take the square root of both sides )
x = [tex]\sqrt{93}[/tex] ≈ 9.6 (to the nearest tenth )
The simple interest on birr 400 invested for 4 months was birr 12, what is the annual (yearly) rate of interest?
Answer:
9%
Step-by-step explanation:
Given :
Principal, P = 400
Time, t = 4 months = 4/12 = 0.33333
Simple interest = 12
Simple interest = (principal * rate * time)
Rate = r
12 = (400 * r * 0.33333)
12 = 133.3333r
r = 12 / 133.3333
r = 0.090000
r = 0.09
rate = 0.09 * 100% = 9%
can someone tell me the answer to this
Answer: W=12m
Step-by-step explanation: