To find the perimeter of the quarter circle, the radius is first calculated using the area, and then the perimeter formula for a circle is applied, adjusting the final calculation to include the straight edges of the quarter circle.
The student has provided the area of a quarter circle and is seeking to find its perimeter. The area of the full circle can be found by multiplying the quarter circle area by 4, yielding an area of 3.14 square kilometers (since the area of a quarter circle is 0.785 square kilometers). Using the formula for the area of a circle, A = πr², we can solve for the radius (r).
Let's calculate the radius of the circle:
A = πr² = 3.14 km²r² = A/πr² = (3.14)/(3.1415927)r = 1 km (Here we're considering π to be approximately 3.1415927)Now, the perimeter (or circumference) of the full circle is given by the formula P = 2πr. For a quarter circle, the perimeter includes the arc of the quarter circle and the two radii.
The perimeter of the quarter circle is thus:
P = (1/4) × 2πr + 2rP = (1/4) × 2 × 3.1415927 × 1 km + 2 × 1 kmP = 1.57079635 km + 2 kmP = 3.57079635 kmBut since we know the measurements are to a certain precision, we must adjust our answer accordingly:
The final perimeter of the quarter circle, rounded to an appropriate number of significant figures based on the original measurement given, is approximately 3.57 km.
there are226 pets enter in the pet show what is 226 rounded to the nearest hundreds
A spherical tank has a radius of 6 yards. It is filled with a liquid that costs $7.15 per cubic yard.
What is the total value of the liquid in the tank?
Use 3.14 for π .
Enter your answer in the box to the nearest cent.
Four cups of hummingbird food that is 20% corn syrup is mixed with six cups of humming bird food that is 15% corn syrup. What percent of corn syrup is in the mixture??
Can someone help me with this math ploblem.
Fossils are remains of organisms found in sedimentary rock. These remains are found in thousands of rock layers around the world and provide evidence for Earth's long history of changing lifeforms. Rock layers that formed more recently A. contain fossils of animals only. B. contain fossils of plants only. C. contain fossils that resemble existing species less closely than do fossils found in older rock layers. D. contain fossils that resemble existing species more closely than do fossils found in older rock layers.
Rock layers that formed more recently contain fossils that resemble existing species more closely than do fossils found in older rock layers.
Explanation:Fossils found in rock layers provide evidence for Earth's long history of changing lifeforms. Rock layers that formed more recently contain fossils that resemble existing species more closely than do fossils found in older rock layers. This is because the more recent layers contain organisms that are more similar to the species that exist today.
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mark all the statements that are true :)
You are right Its A and C
The statements that are true for the function given in the image is, the domain of the function is set of all real numbers, the range of the function is set (-5 }, the correct option is A and C.
What is a Function?A function is a law that relates a dependent and an independent variable.
The function in the image is y = -5,
The range of the function is [-5 ].
The domain of the function is set of all real numbers.
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A smoothie recipe calls for 2 1/4 cups of frozen mango. If the recipe serves two, how many cups of frozen mango is needed to serve one
Peach juice and mango juice were mixed in a ratio of 6 to 4 to make tropical punch. A tape diagram representing the ratio of peach juice to mango juice is shown
The total quantity of the tropical punch in terms of cups is 60 units.
How to get the total quantityLet P represent the volume of peach juice and M represent the volume of mango juice in the tropical punch.
Given the ratio of Peach : Mango is 6:4, which simplifies to 3:2:
This can be mathematically represented as:
[tex]\( \frac{P}{M} = \frac{3}{2} \) or \( P = \frac{3}{2}M \)[/tex]
In this ratio:
- The volume of peach juice contributes 3 units out of a total of 5 units (3 units peach : 2 units mango) of the tropical punch.
- The volume of mango juice contributes 2 units out of a total of 5 units (3 units peach : 2 units mango) of the tropical punch.
1 unit of the mixture = 12 cups
Therefore, 5 units of the mixture = 5 * 12 = 60 cups
Hence, the total quantity of the tropical punch in terms of cups is 60 units.
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Question
Peach juice and mango juice were mixed in a ratio of 6 to 4 to make tropical punch.
Fill in the blank with the correct number below to complete the statement.
(statement)… After 12 cups of mango juice were added, the amount of mango juice and peach juice were the same. There were ____ cups of tropical punch to start with
Number choices to fill in the blank: 18, 69, 36, 72, 60, or 24
Because they are both closed under the operations of addition, subtraction, and multiplication, polynomials form an analogous set to which of the following?
Select one:
A. The imaginary numbers
B. The natural numbers
C. The irrational numbers
D. The integers
Answer:
The integers
Step-by-step explanation:
Can somebody please help me, I’m stumped. Please explain easily too
Your home state uses a linear model y= 24(x - 70) + 1274 to predict the number of vacationers (y) as compared to the average temperature for that week (x). Find the number of vacationers predicted for a week with an average temperature of 85 degrees.
Today, the great Pyramid of Giza bear Cario, Eygpt, stands 137 meters tall, coming to a point . A base is a square with each side measuring 230 meters wide. What is the slope of the pyramid
The correct answer is [tex]1.191[/tex]
To find the slope of the pyramid, we need to calculate the ratio of the vertical change (height) to the horizontal change (half of the base length).
Given information:
- Height of the pyramid (vertical change) = 137 meters
- Base length of the pyramid = 230 meters
- The base of the pyramid is a square, so each side is 230 meters wide
Step 1: Calculate the horizontal change, which is half of the base length.
Horizontal change = [tex]\frac{1}{2} \times Base length[/tex]
Horizontal change = [tex]\frac{1}{2} \times 230 meters[/tex]
Horizontal change = 115 meters
Step 2: Calculate the slope by dividing the vertical change (height) by the horizontal change.
Slope =[tex]\frac{\text{Vertical change}}{\text{Horizontal change}}[/tex]
Slope = [tex]\frac{137}{115}[/tex]
Slope = [tex]{1.191}[/tex]
Therefore, the slope of the pyramid is 1.191.
Brooke has 24 pencils and 36 erasers. If she makes identical goodie bags for her friends with no pencils or erasers left over, what is the greatest number of snack bags Brooke can make?
Jeff had $20. He spent 1/8 of his money on lunch and 2/5 of his money at the movies. How much money does Jeff have left?
:) anyone know this please
how do i add 1 1/6+ 3/5
The data below show the number of games won by a football team in each of the last 15 seasons. What is a histogram that represents the data? 3 4 8 12 7 2 1 15 16 6 10 13 4 1 5
The histogram that represents the data will be given below.
0-4, with a frequency of 6
5-9, with a frequency of 4
10-14, with a frequency of 3
15-19, with a frequency of 2
What is a histogram representation of data?One of its most used graphs for displaying frequency tables is the histogram. The ordinal scale, as we all know, describes how frequently each individual value appears in the data collection.
The data below show the number of games won by a football team in each of the last 15 seasons.
3, 4, 8, 12, 7, 2, 1, 15, 16, 6, 10, 13, 4, 1, 5.
Arrange in ascending order. we have
1, 1, 2, 3, 4, 4, 5, 6, 7, 8, 10, 12, 13, 15, 16.
Then we have
Using intervals of width 5, we have
0-4, with a frequency of 6
5-9, with a frequency of 4
10-14, with a frequency of 3
15-19, with a frequency of 2
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A set of cards contains cards numbered 1 – 8. Mrs. Jacob’s class is conducting an experiment in which a card is drawn from the pile, the number is recorded, and then the card is returned to the set. The class will conduct 1,000 trials. Based on the theoretical probability, which is the best prediction for the number of times a 4 will be drawn from the pile?
111
125
143
250
Answer:
2nd Option is correct.
Step-by-step explanation:
We are given a set of cards containing numbers from 1 to 8 on each cards.
Randomly a card is drawn and noted.
This is repeated 1000 times.
To find: Number of time 4 will be drawn from the pack using theoretical probability.
We know that,
Theoretical Probability: Probability which is based on reasoning and written as a ratio of the number of favorable outcomes to the total number of outcomes.
Probability of getting 4 from the pack = [tex]\frac{1}{8}[/tex]
Now, Number of the times 4 will be drawn from pack out of 1000 times
= [tex]\frac{1}{4}\times1000[/tex]
= 125
Therefore, 2nd Option is correct.
What is the LCD of 3 8/9 and 1 5/12?
What is the effect on the graph of the parent function f(x) = x when f(x) is replaced with f(x - 7)?
Adiya said that the first step to solving the quadratic equation x2 + 6 = 20x by completing the square was to divide 6 by 2, square that value, and add the result to both sides. Is Adiya’s solution method correct? Explain.
Thus, Adiya's approach is incorrect. The constant needs to be isolated solely on a single side of the equation in order to construct a perfect square trinomial.
Explain about the method of completing square:Mathematicians employ the "completing the square" technique to change a quadratic expression of the type ax² + bx + c into the vertex form a(x + m)² + n. The quadratic equation can be solved using this method most frequently by rearranging that expression acquired after the square has been completed.Given condition-
Adiya explained that the first step to completing the square and finding the solution to the quadratic equation x² + 6 = 20x was to divide 6 by 2, square that number, and then add the answer to both sides.
Adiya's approach is incorrect.
The constant needs to be isolated solely on a single side of the equation in order to construct a perfect square trinomial. The constant in the perfect square trinomial is also found using the coefficient of the term with an exponent of 1. The 20x term needs to be placed on the exact same side of the formula as x², according to Adiya. Then multiply 20 by 2 to get a square, add 100 to each sides.Correct method:
x² + 6 = 20x
x² - 20x - 6 = 0
x² - 2*10x - 6 = 0
x² - 2*10x - 6 + 100 - 100 = 0
x² - 2*10x + 100 - 6 - 100 = 0
(x - 10)² - 94 = 0
(x - 10)² = 94
Thus, Adiya's approach is incorrect. The constant needs to be isolated solely on a single side of the equation in order to construct a perfect square trinomial.
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Aphrodite traveled 144 leagues in 12 days. Then she doubled her rate. How long would it take her to travel 168 leagues at this new speed?
The first step in solving this problem is to compute for the original rate of Aphrodite.
144 leagues / 12 days = 12 leagues/day (original rate)
It was stated in the problem that she doubled her rate which she means she has a new rate of 24 leagues/day (12 x 2).
168 leagues / 24 leagues/day = 7
Therefore, it would take her 7 days to travel 168 leagues at her new speed.
Mason’s friends want him to contribute $300 toward a weekend trip, but he doesn’t have that much money in his budget. He does have $150 to spend. What is a financially responsible decision for Mason?
A.
Mason should ask his friends to plan a less expensive trip.
B.
Mason should spend the $300 because his friends asked him.
C.
Mason should get an easy-access loan to pay for the trip.
D.
Mason should go into debt and spend $450 on the trip.
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The boys' soccer team is having a celebration at the end of the season.There are 8 boys on the team and they have ordered 7 pizzas to share.What fraction of a pizza will each boy get?
Which is greater 80 oz or 5 lb
Help pleaseeeeeeeeeeeeeeeeeeeeeeeee will give brainliest
A box of colored game pieces contains 60 pink, 55 silver, and 40 white pieces. One piece is randomly selected. To the nearest percent, what is the probability of the event? Drag and drop the correct value into the box. P(silver)=
26%35%37%39%
how do you find the least common multiple of 16 and 42?
Is rolling doubles a simple event or compound event? Explain.