Answers
The diameter of the large circle = 3 diameters of the small circle.
The radius of the large circle = 3 radii of the small circles.
Step one
Find the radius of the large circle.
r_small = 5 cm Given
r_large = 5 * 3 cm Construction
r_large = 15 cm
Step Two
Find the Area of the large circle
Area = pi * r^2
Area = 3.14 * 15^2
Area = 3.14 * 225
Area = 706.5.
Step Three
Find the area of the 7 small circles.
r = 5 cm given
pi = 3.14
Area = 3.14 * 5^2
Area = 3.14 * 25
Area = 78.5 cm^2
Area of 1 circle = 78.5 cm^2
Area of 7 circles = x Cross multiply
x * 1 = 78.5 cm^2 * 7
x = 549.5 cm^2
Step four
Find the area of the 6 congruent shapes (one of which is shaded).
Area of the six congruent shapes = area of the large circle - area 7 small circles.
Area of seven large circle = 706.5 cm^2
Area of 7 small circles = 549.5 cm^2 Subtract
Area of 6 congruent shapes 157 cm^2
Step 5
Find the area of the shaded area
6 congruent shapes = 157 cm^2 Cross multiply
1 shaded = x
6x = 1 * 157 Divide by 6
x = 157 / 6
x = 26.166667 cm^2 <<<<<<<<<<< answer
If your answer is in terms of pi then the answer us
X = 50 pi / 6 or 25 pi / 3 Alternate possibilities.
Related Questions
Need help with finding the volume of this cone for #35
Answers
Volume of cone = π·r²·h /3
π = 3.14
r = 8
8 × 8 = 64
h = 12
Multiply:
3.14 × 64 × 12 = 2,411.52
Answer = 2,411.52
Hope this helped☺☺
Kevin had 6 nickles and 4 dimes in his pocket. If he took out one count and then a second coin without replacing the first coin-
what is the probability that both coins were nickels?
what is the probability that both coins were dimes?
what is the probability that the first coin was a nickel and the second a dime?
Answers
P(2 Nickels): 6/10 x 5/9 = 30/90 (1/3 chance)
P(2 Dimes): 4/10 x 3/9 = 12/90 (4/30 chance)
P(1 nickel and 1 dime): 6/10 x 4/9 = 24/90 (8/30 chance)
In this detailed answer, the probabilities of drawing two coins from Kevin's pocket - with 6 nickels and 4 dimes - are explained. The probabilities of both coins being nickels and dimes are 0 due to the lack of replacement, while the probability of one nickel and one dime is 4/15.
To calculate the probabilities of drawing coins from Kevin's pocket, where he has 6 nickels and 4 dimes:
Probability both coins are nickels: Since each draw affects the remaining number of nickels and dimes, the probability is 0.
Probability both coins are dimes: Similarly, as the draws are not independent, the probability here is also 0.
Probability of one nickel and one dime: Since Kevin has 6 nickels and 4 dimes, the probability of drawing a nickel first is 6/10 (6 nickels out of 10 coins) and drawing a dime second is 4/9 (4 dimes remaining out of 9 coins), which equals 24/90 or 4/15.
Alfonso went to famous Sam’s appliance store
Answers
If Mrs garcia maintains a constant speed, consistent with the results above, how many words can she type in 49 minutes
Answers
To find the amount of words she types in a minute, multiply 49 minutes by the average wpm Mrs. Garcia types.
[tex]70 * 49 = 3430[/tex]
Mrs. Garcia can type 3430 words in 49 minutes.
What is 0.(24) ̅ (the 24 is repeating) expressed as a fraction in simplest form?
What is 0.24 ̅ (the 4 is repeating) expressed as a fraction in simplest form?
What is 0.24 expressed as a fraction in simplest form?
PLEASE SHOW YOUR WORK
Answers
a)let 0.24 be x.
100x(two zeros because two decimals are repeating)=24.24 ̅(24 is repeating)
Now subtract 100x-x on both sides. This forms an equation.
100x-x=24.24(.24 is repeating) -0.24(.24 is repeating)
99x=24
x=24/99
simplest form=8/33
b)Follow the same rule.
let 0.24(4 is repeating) be x
Since there is two decimals in total , 100x=24.44(4 is repeating)
But since there is one decimal that is repeating, there will be one zero. Hence it will become 100x-10x= 24.4(4 is repeating)-2.4(4 is repeating and get the decimal point closest to the repeating decimal)
90x=22
x=22/90
Simplest form=11/45
c) 0.24 is expressed as 8/25
0.24/1
24/100(make it a whole number and add no. of zeros based on how many decimals places you move.)
Simplest form=6/25
Hope this helps you.
which equation models the population (in millions), p, of austinberg t years after january 1, 2000
Answers
A!!!!!!!!!!!!
if a ship sailed due south from iceland to antarctica, it would sail through an angle of rotation of about 140 degrees around Earth's center. Find this measure in radians. Then, using 3960 miles for Earth's radius, find how far the ship would travel
Answers
the ship would travel approximately 9685.82 miles from Iceland to Antarctica.
To convert the angle from degrees to radians, we use the conversion factor[tex]\( \pi \)[/tex]radians = 180 degrees.
[tex]\[ \text{Angle in radians} = \frac{\text{Angle in degrees} \times \pi}{180} \][/tex]
In this case, the angle in degrees is 140 degrees:
[tex]\[ \text{Angle in radians} = \frac{140 \times \pi}{180} \]\[ \text{Angle in radians} = \frac{140}{180} \times \pi \]\[ \text{Angle in radians} = \frac{7}{9} \pi \][/tex]
Next, we'll find how far the ship would travel using Earth's radius. The distance traveled on a circle is given by the formula:
[tex]\[ \text{Distance} = \text{radius} \times \text{angle in radians} \][/tex]
Given Earth's radius as 3960 miles and the angle in radians as [tex]\( \frac{7}{9} \pi \)[/tex], we can calculate the distance:
[tex]\[ \text{Distance} = 3960 \times \frac{7}{9} \pi \]\[ \text{Distance} = 3080 \pi \]\[ \text{Distance} \approx 9685.82 \text{ miles} \][/tex]
So, the ship would travel approximately 9685.82 miles from Iceland to Antarctica.
Which of the following sets of numbers could be the lengths of the sides of a triangle? A. 81 mm, 7 mm, 6 mm B. 81 mm, 7 mm, 72 mm C. 81 mm, 7 mm, 88 mm D. 81 mm, 7 mm, 77 mm
Answers
The triangle inequality states that for any triangle, the sum of the lengths of any two sides of a triangle is greater than the length of the third side
so
case A. 81 mm, 7 mm, 6 mm
6+7 is not > 81
case B. 81 mm, 7 mm, 72 mm
72+7 is not > 81
case C. 81 mm, 7 mm, 88 mm
81+7 is not > 88
case D. 81 mm, 7 mm, 77 mm
81+7 is > 77------> ok
77+7 is > 81-----> ok
81+77 is > 7-----> is ok
the answer is the option
D. 81 mm, 7 mm, 77 mm
The correct option is B. 81 mm, 7 mm, 72 mm could be the lengths of the sides of a triangle.
To determine if a set of numbers could be the lengths of the sides of a triangle, the Triangle Inequality Theorem must be satisfied. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's apply this theorem to each set of numbers:
A. 81 mm, 7 mm, 6 mm
- The sum of the two smallest sides is 81 + 6 = 87 mm, which is greater than the third side, 7 mm. However, the sum of the two smallest sides, 7 + 6 = 13 mm, is not greater than the largest side, 81 mm. Therefore, these lengths cannot form a triangle.
B. 81 mm, 7 mm, 72 mm
- The sum of the two smallest sides is 7 + 72 = 79 mm, which is greater than the third side, 81 mm. This set satisfies the Triangle Inequality Theorem.
C. 81 mm, 7 mm, 88 mm
- The sum of the two smallest sides is 81 + 7 = 88 mm, which is equal to the third side, 88 mm. According to the Triangle Inequality Theorem, the sum must be strictly greater than the third side, so these lengths cannot form a triangle.
D. 81 mm, 7 mm, 77 mm
- The sum of the two smallest sides is 7 + 77 = 84 mm, which is greater than the third side, 81 mm. However, the sum of the two smallest sides, 81 + 7 = 88 mm, is not greater than the third side, 77 mm. Therefore, these lengths cannot form a triangle.
Based on the Triangle Inequality Theorem, the only set of lengths that can form a triangle is option B: 81 mm, 7 mm, 72 mm.
Latoya drives 8 miles to work in 13 minutes what is her average rate
Answers
If a PENNY has a circumference of 59.69 millimeters, what is the radius?
Answers
59.69 = 2[tex] \pi [/tex]r
Divide both sides by [tex]2 \pi [/tex] to isolate the variable r.
r = 59.69 / [tex]2 \pi [/tex]
Put that into the calculator
r ≈ 93.7608 mm
The radius of the penny is 9.54 millimeters.
What is circumference?The circumference means the length of the literal line that surrounds and forms a circle.
What is the formula for the circumference of circle?The formula for the circumference of the circle is given by
[tex]circumference = 2\pi r[/tex]
Where,
r is the radius
and π = 3.14
What is radius?A radius is a straight line from the center of a circle to the circumference of a circle.
According to the given question.
We have a penny whose circumference is 59.69 millimeters.
Let r be the radius of the penny and 2πr be the circumference of the penny.
Since we know that, the shape of the penny is circular.
Therefore,
The radius, r of the penny is given by
[tex]2\pi r= 59.69[/tex]
[tex]\implies r = \frac{59.69}{2\pi }[/tex]
[tex]\implies r = \frac{59.69}{2(3.14)}[/tex]
[tex]\implies r = \frac{59.69}{6.28}[/tex]
[tex]\implies r = 9.54\ millimeters[/tex]
Hence, the radius of the penny is 9.54 millimeters.
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Factor completely 2x3 + 10x2 + 4x + 20.
2(x3 + 5x2 + 2x + 10)
2[(x + 5)(x2 + 2)]
(2x + 10)(x2 + 2)
(x + 5)(2x2 + 4)
Answers
= 2(x^3 + 5x^2 + 2x + 10)
= 2[x^2(x + 5) + 2(x + 5)]
= 2[(x+5)(x^2 + 2)]
answer
2[(x + 5)(x^2 + 2)]
Answer:
Step-by-step explanation:
Alright, lets get started.
The given expression is :
[tex]2x^3+10x^2+4x+20[/tex]
taking 2 common factor
[tex]2(x^3+5x^2+2x+10)[/tex]
[tex]2(x^3+2x+5x^2+10)[/tex]
[tex]2[(x+5)(x^2+2)][/tex]
So, the correct answer is option B : answer
Hope it will help :)
help me pls with the answers pls, identify each pair of angles as complementary,supplementary, or neither
Answers
2. Supplementary
3. Supplementary
4. Complementary
40 + 2x = 90
2x = 50
x = 25
5. Supplementary
6x + 60 = 180
6x = 120
x = 20
2. Supplementary
3. Complementary
sorry i am not sure about 4 and 5.
A child’s piggy bank contains quarters and dollar coins. There are 6 times as many quarters as dollar coins. If there are 140 coins the piggy bank, what is the total amount of money it contains?
Answers
Variables well use:
Quarters = Q
Dollar Coins = D
What we know:
Q + D = 140
Q = 6(D)
First well substitute Q into the first equation to find the amount of dollar coins (D).
6D+D = 140
7D = 140
D = 20
Since we know how many dollar coins are in the piggy bank and also how many coins total, we can substract the total amount of coins minus the amount of dollar coins to find the amount of quarters.
140 - 20 = 120 Q
To find the total money amount we take the variables we solved for and multiply is by the money amount:
(120(.25)) + (20(1)) = $50
The function f(x) = 68(1.3)x represents the possible squirrel population in a park x years from now. Each year, the expected number of squirrels is ____ the number the year before. A. 3 times B. 1.3 times C. 3 more than D. 0.3 times
Answers
It is 1.3 times more than the year before. (APEX)
A scientist conducted an experiment to determine whether an organic cleaner is as effective as a non-organic cleaner in killing germs that cause colds and the flu. To conduct the experiment, the scientist randomly selected 50 doorknobs in a hospital. He cleaned 25 of the door knobs with the organic cleaner, and he cleaned the remaining 25 door knobs with the non-organic cleaner. After cleaning and testing all of the doorknobs, the scientist reported that the organic cleaner killed 90% of germs that cause colds and the flu on the doorknobs, while the non-organic cleaner killed 95% of germs that cause colds and the flu on the doorknobs. What can be concluded from the scientist's report?
Answers
1. A non-oraganic cleaner is 95% effective
2. An organic cleaner is 90% effective
3. Therefore, an organic cleaner is not as effective as a non-organic cleaner in killing germs that cause colds and the flu.
Therefore, an organic cleaner is not as effective as a non-organic cleaner in killing germs that cause colds and the flu.
For one week, Consuela kept a log of the number of pages she read each night. She read 8 pages on Monday, 11 pages on Tuesday, 10 pages on Wednesday, 7 pages on Thursday, 8 pages on Friday, 8 pages on Saturday, and 10 pages on Sunday. Create a line plot of this information. Are there any outliers in the data? Explain.
Answers
A line plot has been created based on the number of pages Consuela read each night over a week, showing the data without any outliers. Values range from 7 to 11 pages, with no significant deviations that would classify as outliers.
To create a line plot of the number of pages Consuela read each night, you would place a horizontal axis labeled with numbers representing the number of pages read, e.g., 7, 8, 10, and 11. Above each number, you would put a dot for each night that she read that number of pages. For example, she read 8 pages 3 times across the week, so above the number 8 on the line plot, you would place three dots.
Line Plot Creation and Outliers
The line plot for Consuela's reading log:
7 pages: 1 dot (Thursday)
8 pages: 3 dots (Monday, Friday, Saturday)
10 pages: 2 dots (Wednesday, Sunday)
11 pages: 1 dot (Tuesday)
To determine if there are any outliers in the data, we have to look for any dots that are not close to the other dots. An outlier is typically a data point that is significantly higher or lower than the rest of the data. In the case of Consuela’s reading log, the values are all quite close to each other, with the range being from 7 to 11 pages. There doesn't appear to be a value significantly different from the others; therefore, there are no outliers.
A rectangular bathtub is 5 1/2 feet Long, 1 1/2 feet wide, and 3 feet high. Daniel fills the tub to a depth of 2 feet. What is the volume of the water in the tub?
Answers
[volume of a rectangular prism]=L*W*H
for
L=5 1/2 ft-----> (5*2+1)/2----> 11/2 ft
W=1 1/2 ft----> (1*2+1)/2----> 3/2 ft
H=2 ft
so
volume of the water in the tub=(11/2)*(3/2)*2---> 16.5 ft³
the answer is
the volume of the water in the tub is 16.5 ft³
toothbrushes are $4.00 each. there is a 10% discount but also 6% sales tax. What is the new price?
Answers
10% ⇒ 0.1
4 × 0.1 = 0.4
Subtract 0.4 from 4.
4 - 0.4 = 3.6 (price with discount)
Multiply 3.6 by 6%.
6% ⇒ 0.06
3.6 × 0.06 = 0.216
Add 0.216 to 3.6.
0.216 + 3.6 = 3.816
Round 3.816 to the hundredths.
3.816 ⇒ 3.82 (price with tax)
The new price of toothbrushes is $3.82.
Khalil is wrapping a cylindrical candle for a gift. The candle is 10 inches tall and has a diameter of 1.5 inches. How many square inches of wrapping paper will Khalil need to cover the candle? Use 3.14 for pi.
Answers
[tex]A = 2 \pi rh + 2 \pi r^2[/tex]
r (radius)= 0.75 since radius is half of the diameter
h (height) = 10
So:
[tex]A = 2 \pi rh + 2 \pi r^2 A = 2 (3.14)(0.75)(10) + 2 (3.14)(0.75)^2 A = 47.1 + 3.5325 A = 50.6325 = 50.63in^2 [/tex]
Final answer:
To cover a cylindrical candle with a height of 10 inches and diameter of 1.5 inches, Khalil would need at least 50.635 square inches of wrapping paper, calculated by adding the lateral surface area and the areas of the top and bottom circles.
Explanation:
Khalil needs to calculate the amount of wrapping paper to cover a cylindrical candle. To find the surface area needed to wrap around the sides of the candle, we'll use the formula for the lateral surface area of a cylinder, which is Area (A) = 2πrL, where 'r' is the radius and 'L' is the height of the cylinder. Given that the candle is 10 inches tall and has a diameter of 1.5 inches, we calculate as follows:
The radius (r) is half of the diameter, so r = ½ × 1.5 inches = 0.75 inches.The height (L) of the candle is 10 inches.Using π as 3.14, the area A is A = 2×π× r× L = 2× 3.14 × 0.75 inches × 10 inches = 47.1 square inches.To calculate the area needed to cover the top and bottom of the candle, we use the formula for the area of a circle, which is Area (A) = πr². The candle has two circular ends.
The area for one end A = π × 0.75² inches = 3.14 × (0.5625) inches² = 1.7675 square inches.Since there are two ends, the total area for both is 2 × 1.7675 square inches = 3.535 square inches.Adding the side area and the areas of the ends, the total wrapping paper needed is 47.1 square inches + 3.535 square inches = 50.635 square inches. Khalil should therefore use at least 50.635 square inches of wrapping paper to fully cover the cylindrical candle.
Use the Babylonian method to estimate √80 to the nearest hundredth.
Answers
Most people guess that a square root is half, so we will make that our first guess; 80/2 = 40, so 40 is our guess.
80/40 = 2
Average 40 & 2: (40+2)/2 = 21; this is our new guess.
80/21 = 3.80952381
Average 21 & 3.80952381: 12.40476191 is our new guess
80/12.40476191 = 6.449136274
Average 12.40476191 & 6.449136274: 9.426949092 is our new guess
80/9.426949092 = 8.48630869
Average 9.426949092 & 8.48630869 = 8.956628891 is our new guess
80/8.956628891 = 8.931931977
Average 8.956628891 & 8.931931977: 8.944280434 is our new guess
80/8.944280434 = 8.944280434
Average 8.944280434 & 8.944280434 = 8.944263386
By this point, we have the same number to the hundredths place, so we stop. Our estimate is 8.94.
Step 1. We are going to make a guess. Our guess is 9 because [tex]9^2=81[/tex].
Step 2. We are going to dive the original radicand (80) by our guest:
[tex] \frac{80}{9} =8.88[/tex]
Step 3. We are going to find the average between our initial guest and the result of our previous calculation:
[tex]\frac{8.88+9}{2} = \frac{17.88}{2} =8.94[/tex]
We can conclude that [tex] \sqrt{80} [/tex] to the nearest hundredth using the Babylonian method is: 8.94
What’s $54.00 for 3 tickets in unit rate
Answers
What is the surface area of the ramp in square feet and if each square foot of wood on the ramp is sold for three dollars how much would the ramp sell for
Answers
[surface area of the ramp]=10*16+8*16+6*16+2*[6*8/2]
[surface area of the ramp]=160+128+96+48-----> 432 ft²
the answer Part a) is
the surface area of the ramp is 432 ft²
if 1 ft² is sold for--------------------> $3
432 ft²-------------------> x
x=432*3-----> x=$1296
the answer Part b) is
$1296
Find the unknown. = (764 × 2) + 12
Answers
Short answer: 1540
Why?
To find the answer to this, you must do what is in the parenthesis. The equation inside of the parenthesis is 764 * 2. Evaluate. (764 * 2 ==> 1528) Now, add by 12. 1528 + 12 == 1540.
Hope this helped you! ♥
Hope this helps!
A recipe for dessert calls for 2/4 cup of powdered sugar and 1/6 cup of brown sugar . What is the total amount of sugar needed for the recipe
Answers
write and solve an inequality for this situation. To honor 50 years of business, All Strikes Bowling is having an anniversary special. Shoes rent for $1.25 and each game is $0.75. If Charlie has $20 and needs shoes, how many games can he bowl?
Answers
20 - 1.25 = 18.75
18.75/.75 = 25 games
To honor 50 years of business, All Strikes Bowling is having an anniversary special. The game he can bowl is 25.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
To honor 50 years of business, All Strikes Bowling is having an anniversary special.
Shoes rent for $1.25 and each game is $0.75. If Charlie has $20 and needs shoes.
Charlie can bowl 25 games.
= 20 - 1.25
= 18.75
So, he can bowl game
= 18.75/ 0.75
= 25 games
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Kristin’s three-year old sister is trying to arrange pink and red Starbursts in rows. She has 360 pink Starbursts and 150 red Starbursts. She wants to arrange them in rows so that there are either only pink or only red Starbursts in each row, and so that each row has the same number of Starburts. What is the least number of rows she can make?
Answers
You can use prime factorizations of each number to find the gcf.
150 - 2 x 3 x 5 x 5
360 - 2 x 2 x 2 x 3 x 3 x 5
The common prime numbers are 2 x 3 x 5
You can make 12 (360/30) rows of pink and 5 (150/30) rows of red.
The least number of rows she can make is when she puts N marbles in each row, such that N is the greatest common factor between 150 and 360.
To find the greatest common factor between 150 and 360 we can write them as the product of prime numbers.
150 = 15*10 = (3*5)*(2*5)
360 = 36*10 = (6*6)*(2*5) = (2*3*2*3)*(2*5)
greatest common factor between 150 and 360 is the product of these 3 factors:
GCF = 2*3*5 = 30
this means that we need to make rows with 30 marbles each.
150/30 = 5 rows of red marbles
360/30 = 12 rows of pink marbles.
A total of 5 + 12 = 17 rows.
Seed corn was $5 per bag, whereas dog food cost only $3 per bag. Wewoka bought 50 bags and spent $190. How many bags of dog food did she buy?
Answers
You can make two equations based on what you know
x + y = 50
5x + 3y = 190
Subtract y from both sides of the first equation
x = 50 - y
Put x into the second equation
5(50 - y) + 3y = 190
Distribute the 5
250 - 5y + 3y = 190
Combine like terms
250 - 2y = 190
Subtract 250 from both sides
-2y = -60
Divide both sides by -2
y = 30
Put y into the first equation
x + 30 = 50
Subtract 30 from both sides
x = 20
She bought 20 seed corn bags and 30 bags of dog food
Hope this helps!
Answer:
30 bags
Step-by-step explanation:
Nc + Nd = 50
5Nc + 3Nd = 190
Multiply by -5 becomes:
-5Nc - 5Nd = -250
5Nc + 3Nd = 190
Equals:
-2Nd= -60
simplify:
-2Nd/-2 and -60/-2 = Nd= 30 bags
write an equation that represents each mixed number as a sum of whole numbers and unit fractions 4 1/4
Answers
The equation that represents each mixed number as a sum of whole numbers and unit fractions of [tex]4\frac{1}{4}[/tex] is [tex]4\frac{1}{4}[/tex] = 4 + 1/4.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
We have the mixed fraction,
[tex]4\frac{1}{4}[/tex].
Converting the mixed fraction to an improper fraction,
[tex]4\frac{1}{4}[/tex] = 17/4
We need to write it as a sum of whole numbers and unit fractions:
So, it becomes,
[tex]4\frac{1}{4}[/tex] = 4 + 1/4
[tex]4\frac{1}{4}[/tex] = (16 + 1)/4
[tex]4\frac{1}{4}[/tex] = 17/4
Therefore, [tex]4\frac{1}{4}[/tex] = 4 + 1/4 is the required equation.
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At what position does the ball have its maximum potential energy
A) a
B) d
C) f
D) g
Answers
So it is D the highest point of the trajectory.
A bag contains 5 red marbles, 7 white marbles, and 6 blue marbles. Find P(red or blue).
Answers
Answer:
P(red or blue) = 5/18 + 6/18 = 11/18