Answer:
25π yd²
Step-by-step explanation:
You want the exact area of a 40° sector of a circle of radius 15 yards.
AreaThe area of a sector is given by ...
A = 1/2r²θ
where θ is the central angle in radians.
RadiansThere are π radians in 180°, so there are (40/180)π = 2π/9 radians in 40°.
SectorThen the area of the sector is ...
A = 1/2(15 yd)²(2π/9) = 25π yd²
The area of sector GPH is 25π square yards.
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there are 64 teams in a tournament. in the first round, each team will play against another team. how many ways are there to divide the teams into 32 pairs?
Therefore, there are 2,436,686,400 ways of combination to divide the teams into 32 pairs.
To calculate the number of ways to do this, you can use the concept of combinations.
In this case, you can use the formula:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of teams (64) and k is the number of teams in each pair (2).
First, we need to divide the teams into pairs, so there will be 32 pairs in total. To find the number of ways to do this, we can use the combinations formula:
C(64, 2) = 64! / (2!(64-2)!)
C(64, 2) = 64! / (2! * 62!)
Next, we need to multiply this by the number of ways to create the remaining 31 pairs:
=C(62, 2) * C(60, 2) * ... * C(4, 2)
So, the total number of ways to divide the 64 teams into 32 pairs is:
=C(64, 2) * C(62, 2) * ... * C(4, 2) / (32!)
This will give you the number of ways to divide the teams into 32 pairs for the tournament's first round.
(64 x 63 x 62 x ... x 2 x 1) / (2 x 2 x 2 x ... x 2 x 2) = 64! / (2³²)
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Please help hurry
Which of the following inferences can be made based on the data? (1 point)
O a
Most members prefer a beach vacation.
O b
Most members prefer an adventure vacation.
• с
O d
More members prefer a cruise vacation and a ski vacation than an adventure vacation.
More members prefer an adventure vacation and a cruise vacation than a beach vacation.
The answer is A: Most members prefer a beach vacation.
Select all that are undefined.
The expressions csc(π), cot(π/2), cot(π), csc(0°), and sec(90°) are undefined.
Since the sin(π) is 0, the calculation csc(π) results in division by zero, which is undefinable.
Due to the infinite tangent of π/2, cot(π/2) results in division by zero, making it undefinable.
Due to the infinite tangent of π, cot(π) divides by zero and is hence undefinable.
Since the sine of 0° is zero, csc(0°) is undefined since it divides by zero.
Since the cosine of 90° is zero, sec(90°) results in division by zero, which is an undervalue.
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For banquets, Flourishing Flowers charges $60 for each standard floral arrangement plus a one-time $125 fee for delivery and set up. Write an equation in slope-intercept form that shows the cost y for flowers for x number of arrangements.
If the flourishing-flowers charges $60 for each standard "flower-arrangement", then the equation to represent the cost is "y = 60x + 125".
The number-of-arrangements be = "x",
The cost of flowers for x number of standard floral arrangements can be calculated as "sum" of "cost of each arrangement" and the "one-time delivery and set up fee".
The cost of each standard floral arrangement is given to be = $60, and The delivery and set-up fee is = $125,
The total cost of flowers for "x" arrangements can be expressed in equation as :
y = $60x + $125.
Therefore, the required equation is "y = 60x + 125".
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Choose a number for each blank that is not 1. Then solve each equation using guess and check.
Change your number if you need to so that the solution is a whole number.
Show your thinking.
a)_n + 15 = 125
b)4x +_ = 317
c)_s + 103 = 705
Which rational number can be represented by the decimal value 0. 33
Answer:
1/3
Step-by-step explanation:
let x = 0.333.....(1)
10x = 3.333......(2)
Subtract (1) from (2)
[tex]10x = 3.333 \\ x = 0.333[/tex]
9x = 3
X = 3/9
[tex]x = \frac{1}{3} [/tex]
A lifeguard spots a swimmer in the lake at an angle of depression of 32°
and spots a sailboat, further out, at an angle of depression of 13°. If the
lifeguard is 36.5 dm away from the swimmer and 84.7 dm away from the
sailboat, how far is the swimmer from the sailboat? Round your answer to
the nearest tenth of a dm. Include a diagram
how much larger is the hypotenuse of triangle B then the hypotenuse of triangle A?
A. 2.46
B. 8.64
C. 6.36
D. They are the same size.
Answer:
D. They are the same size.
Step-by-step explanation:
Triangle A:
sin 37 = 6 / H where H = the hy[otenuse
H = 6 / sin 37
H = 9.8698
Triangle B:
cos 53 = 6/H
H = 6 / cos 53
H = 9.9698
What is the step after calculate your test statistic chi-squared, when statistically testing a hypothesis. group of answer choices draw conclusions calculate degrees of freedom (df) and critical value state your null hypothesis collect data
The degrees of freedom is determined by the number of categories in your data minus 1.
The step after calculating your test statistic chi-squared is to calculate the degrees of freedom (df) and the critical value. The degrees of freedom is determined by the number of categories in your data minus 1. The critical value is found using a chi-squared distribution table and is based on your chosen significance level and degrees of freedom. Once these values are calculated, you can compare your test statistic to the critical value to determine if your results are statistically significant. This step is necessary to ensure that your hypothesis testing is valid and reliable.
This will help you determine whether to reject or accept the null hypothesis based on your data.
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A rectangular pool has a length of 15 meters and a width of 10 meters.
How many 25 cm x 25 cm tiles will you need to cover the entire surface of the pool?
2400 tiles of 25 cm* 25 cm needed to cover the surface of a rectangular pool with length of 15 meters and width of 10 meters.
The area of a rectangle with length 'L' and Breadth 'B' is given by,
A = L*B
We know that 1 meter = 100 centimeter.
The length of the rectangular pool is = 15 meters = 15*100 = 1500 cm.
The width of the rectangular pool is = 10 meters = 10*100 = 1000 cm.
So the area of the rectangular pool is = 1500*1000 square cm.
Now, the dimensions of a tile is = 25 cm* 25 cm
So the area of each tiles = 25*25 = 625 square cm.
So the number of tiles needed to cover the surface of the pool is given by
= (1500*1000)/625 = 2400.
Hence 2400 tiles are needed to cover the surface of the pool.
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Please help me with the question
Answer: Get smarter lol
Kyle is wrapping a large container of tennis balls for a gift. The radius of each end of the cylindrical container is 3 inches. The height is 8.4 inches. In terms of π, how much wrapping paper does he need to completely cover the container? Responses A 48.2π in2 48.2π in 2 B 68.4π in2 68.4π in 2 C 50.4π in2 50.4π in 2 D 59.4π in2
Answer:
B. 68.4π in2 68.4π in 2
Kyle needs approximately 68.4π square inches of wrapping paper to completely cover the cylindrical container.
Now,
For calculate the amount of wrapping paper needed to cover the cylindrical container, we need to find the surface area of the container.
Hence, We need to find the area of both the top and the bottom of the cylinder, as well as the lateral area (the curved part of the cylinder).
The formula for the area of a circle is,
A = πr²,
where r is the radius of the circle.
Since we have two circles (the top and bottom of the cylinder), we can calculate their combined area as:
A = 2π(3 inches)²
= 2π(9 square inches)
= 18π square inches
And, For the lateral area, we need to find the circumference of one of the circles and multiply it by the height of the cylinder.
Since, The formula for the circumference of a circle is,
C = 2πr.
C = 2π(3 inches)
C = 6π inches
So, the lateral area of the cylinder is:
6π inches x 8.4 inches
= 50.4π square inches
Adding these two areas together, we get the total surface area of the cylinder:
= 18π square inches + 50.4π square inches
= 68.4π square inches
Therefore, Kyle needs approximately 68.4π square inches of wrapping paper to completely cover the cylindrical container.
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Mr. Early has a rectangular garden in his back yard with an area of 3x2 square meters. He decided to make it larger and the new area will be (3x2 + 4x + 5) square meters. What is the difference between the new garden and the original garden?
The difference between new garden and the original garden is 4x + 5.
We have,
Area of yard = 3x² m²
New Area = 3x² + 4x + 5
So, the difference in
= (3x² + 4x + 5) - 3x²
= 3x² + 4x + 5 -3x²
= 3x² -3x² + 4x + 5
= 4x + 5
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Point f has coordinates (6,4) and lies on line FD, which has a slope 1/7. Determine the equation of line FD in slope-intercept form
The equation of line FD in slope-intercept form is y = (1/7)x + 22/7
Firstly, let's recall the slope-intercept form of the equation of a line:
y = mx + b
where m is the slope of the line and b is the y-intercept. To find the equation of line FD, we need to determine the value of b. We can do this by substituting the coordinates of the given point (6,4) and the slope (1/7) into the slope-intercept form and solving for b.
Using the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of the given point, we can substitute x1 = 6, y1 = 4, and m = 1/7 to get:
y - 4 = (1/7)(x - 6)
Simplifying, we can distribute 1/7 to x - 6 to get:
y - 4 = (1/7)x - 6/7
Adding 4 to both sides, we get:
y = (1/7)x + 22/7
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Maddy get 14. 98 dollers from her mom. Her brother got 12. 87dollers from his dad. Whats the differents
Answer: 2.11
Step-by-step explanation:n Difference in a equation is telling us to subtract the two numbers in the world problem
so 14.98-12.87 =2.11
Each side of a square office is 9 feet long. What is the office's area?
Answer:
81 square feet
Step-by-step explanation:
Area for square = side * side
= 9*9 = 81
In a popular online role playing game, players can create detailed designs for
their character's "costumes," or appearance. Tallulah sets up a website where
players can buy and sell these costumes online. Information about the
number of people who visited the website and the number of costumes
purchased in a single day is listed below.
138 visitors purchased no costume.
185 visitors purchased exactly one costume.
25 visitors purchased more than one costume.
If next week, she is expecting 1900 visitors, about how many would you
expect to buy no costume? Round your answer to the nearest whole number.
Answer:
The total number of visitors who purchased costumes is 185 + 25 = 210. Therefore, the number of visitors who did not purchase a costume is 138 + (1900 - 210) = 1828. Rounding this number to the nearest whole number gives us 1828 visitors who are expected to buy no costume
Step-by-step explanation:
Marco and two of his friends are going to share of a pizza. How much will each person get?
A. 1/6 of the pizza
B. 2/3 of the pizza
C. 1/12 of the pizza
D. 1/9* of the pizza
What is the sum of the x-intercepts of the function below?
f(x) = 3x² - 11x - 4
O 3 2/3
O -1 1/3
O 1 1/3
O-3 2/3
A forest has 5040 trees.
The trees are beech or maple.
number of beech : number of maple = 3.2 : 1
What fraction of the trees are beech?
Give your answer as a fraction in its simplest form.
Answer:
3/5
Step-by-step explanation:
Let the number of beech trees be 3x and the number of maple trees be 2x (since the ratio of beech to maple is 3.2 : 1, we can choose any common factor for the numbers of beech and maple trees).
So, the total number of trees is 3x + 2x = 5x.
We are given that the total number of trees is 5040, so:
5x = 5040
x = 1008
Therefore, the number of beech trees is 3x = 3(1008) = 3024, and the number of maple trees is 2x = 2(1008) = 2016.
The fraction of trees that are beech is:
3024 / (3024 + 2016) = 3024 / 5040
To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 1008:
3024 / 5040 = (3024 ÷ 1008) / (5040 ÷ 1008) = 3 / 5
Therefore, the fraction of trees that are beech is 3/5.
Asher has saved 78. 20. This is 3/8 of what he needs to save to buy a new playstation. What is the total amount that asher neds to save
The total amount that Asher needs to save to buy a new playstation is 208.53.
The keyword "total" is crucial in this problem because we are trying to find the total amount of money that Asher needs to save to buy a new playstation. It's essential to understand that 78.20 is only a fraction of the total amount, and we need to determine what that fraction is.
To start, we can set up a proportion that represents the relationship between the fraction of the total amount saved (3/8) and the actual amount saved (78.20). We can use x to represent the total amount Asher needs to save:
3/8 = 78.20/x
To solve for x, we can cross-multiply the equation:
3x = 8 * 78.20
3x = 625.6
x = 625.6/3
x = 208.53
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The radius of a cone is increasing at a constant rate of 3 inches per minute,
and the volume is increasing at a rate of 43 cubic inches per minute. At the
instant when the radius of the cone is 1 inches and the volume is 13 cubic
inches, what is the rate of change of the height? The volume of a cone can be
found with the equation V = r²h. Round your answer to three decimal
places.
Answer: ____in/min
The height is changing at a rate of 15 inches every minute.
To solve this problemWe can use the derivative of the volume formula to derive an equation that links the rates of change of the cone's volume, radius, and height:
Cone volume formula: V = (1/3)r2h
Using derivative on both sides with regard to time, we arrive at:
dV/dt equals (1/3) * 2r * dr/dt * h plus (1/3) r2 * dh/dt.
where
The rates of change for the volume Radius Height are denoted by dV/dt, dr/dt, and dh/dtWe can enter the values supplied here as substitutes in this equation:
dV/dt = 43 in3 minutes.
Dr/Dt = 3 In/Minute
r = 1 in
V = 13 in³
For dh/dt, we can solve for:
43 = (1/3)π * 2(1) * 3 * h + (1/3)π(1)² * dh/dt
43 = 2πh + (1/3)π * dh/dt
129 = 6πh + π * dh/dt
dh/dt = (129 - 6πh) / π
We may now change h = (3V) / (r2) to obtain:
dh/dt is equal to (129 - 6 (3V)/(r2)) /
(129 - 18V/r2) / dh/dt
By substituting the V and r values that are supplied, we obtain:
dh/dt = (129 - 18(13)/(1²)) / π
dh/dt = about 15 in/min
As a result, the height is changing at a rate of 15 inches every minute.
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It takes 4. 12 gallons of paint to paint a fence. How much paint is needed for 1/5 of the fence?
Answer: 103/125
Step-by-step explanation:
As the question says that It takes 4.12 gallons of paint to paint a fence. How much paint is needed for 1/5 of the fence?
so we have to multiply to get the amount of gallons of paint it is used to paint 1/5 of the wall.
First we can't multiply decimal number with fraction so we will convert the decimal number into a fraction so 4.12 in fraction = 103/25.
Thus we will multiply 103/25 x 1/5 to get our answer. So when we multiply we get 103/125.
So our answer will be 103/125.
again, julie took statistics with professor fisher, whose final exam scores follow a normal distribution with mean 75 and standard deviation of 6. her score on the final was 84. which of the two scores, ron's or julie's, is more impressive?
Option A: Due to its greater deviation from the mean and rarity, Ron's Z-score is more impressive.
The two scores must be transformed into a standard score (sometimes referred to as a z-score), which calculates how many standard deviations above or below the mean each score is, in order to be compared.
In a class where the mean was 72 and the standard deviation was 5, the standard score for Ron's score of 87 is:
z = (87 - 72) / 5 = 3
For Julie's score of 84 in a class where the mean was 75 and the standard deviation was 6, the standard score is:
z = (84 - 75) / 6 = 1.5
We can see that Ron's score of 87 is 3 standard deviations above the mean whereas Julie's score of 84 is just 1.5 standard deviations above the mean, the number of standard deviations above or below the mean is displayed by z-scores.
As a result, Ron's score is more outstanding because it deviates from the average more and highlights a more exceptional accomplishment.
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Complete question is:
In a statistics test, Ron's score in final examination follows a normal distribution with mean 72 and standard deviation of 5. His score on the final was 87.
Again, julie took statistics with professor fisher, whose final exam scores follow a normal distribution with mean 75 and standard deviation of 6. her score on the final was 84. which of the two scores, ron's or julie's, is more impressive?
A. Ron's score is more impressive.
B. Julie's score is more impressive.
C. Both scores are equally impressive.
assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $5,062 per hour and a standard deviation of $392. what is the operating cost for the lowest 5% of the airplanes? (round your z-value to 2 decimal places and final answer to the nearest whole dollar.
The operating cost for the lowest 5% of the airplanes is approximately $4,381 (rounded to the nearest whole dollar).
Using a standard normal distribution table or calculator, we can find that the z-score corresponding to the lowest 5% of the distribution is approximately -1.64.
[tex]z = (x - \mu) / \sigma[/tex]
where:
x = operating cost we want to find
μ = mean hourly operating cost = $5,062
σ = standard deviation = $392
z = -1.64
Plugging in the values, we get:
-1.64 = (x - 5062) / 392
Solving for x, we get:
x = -1.64 * 392 + 5062
x ≈ $4,381.28
Operating cost refers to the expenses incurred by a business or organization in the course of its regular operations. It includes all the expenses required to maintain and sustain the production of goods or services, but excludes one-time capital expenditures like the purchase of property or equipment. Some common examples of operating costs include rent, salaries and wages, utilities, supplies, maintenance and repair, insurance, taxes, and marketing expenses. These costs are ongoing and necessary to keep the business running on a day-to-day basis.
Operating costs are important because they impact the profitability of a business. In order to remain competitive and profitable, businesses need to minimize their operating costs while maximizing their revenue. By carefully managing operating costs, businesses can improve their bottom line and invest in growth opportunities.
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A pair of sunglasses is on sale for $144. This is 10%
less than the original price. Work out the original price of the sunglasses
Answer: $160
Step-by-step explanation: As a pair of sunglasses, or "x", is 144 when reduced by 10% (90% in total), you can assume 90% of x = 144. To get rid of the 90, or 9/10, multiply both sides by its reciprocal, or 10/9. 90% x 10/9 = 1 (left with only x), and 144 x 9 / 10 = 160.
Three softball players discussed their batting averages after a game.
Probability
Player 1 four sevenths
Player 2 five eighths
Player 3 three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)
Player 3 is more likely to hit the ball than Player 1 because P(Player 3) > P(Player 1)
Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)
It is true to say that "Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)" for the given probabilities. The correct option is B.
Convert the fractions into decimals or percentages to compare the probabilities and interpret the likelihood as:
Player 1's batting average: 4/7 = 0.571 ≈ 57.1%
Player 2's batting average: 5/8 = 0.625 ≈ 62.5%
Player 3's batting average: 3/6 = 0.5 ≈ 50%
By comparing the probabilities, we can see that Player 2 has the highest batting average (62.5%), followed by Player 1 (57.1%) and then Player 3 (50%).
Therefore, it is true to say that Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1).
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(√11 -√7) (√11 +√7) how do you find the answer for this
Answer:
(√11 -√7) × (√11 +√7) equals 4
Select the correct answer. Four lines of X axis from Negative 3 to plus 3. A. A point marked at Negative 2.5, B. A point marked at plus 1.5, C. A point marked at Negative 0.5, and D. A point marked at plus 2.5. Which image shows the correct position of − 2 1 2 on the number line? A. A B. B C. C D. D
A point marked at Negative 2.5, is the correct image that shows the position of -2.5 on the number line.
The correct answer is A, a point marked at Negative 2.5.
To locate -2.5 on the X-axis, we need to find the position that corresponds to a point 2.5 units to the left of the origin (0,0) on the X-axis.
Since each line segment on the X-axis represents one unit, we can count 2.5 units to the left of the origin to find the position of -2.5.
Therefore, A, which shows a point marked at Negative 2.5, is the correct image that shows the position of -2.5 on the number line.
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In a traffic survey of 495 vehicles, 390 are cars.
Work out the fraction of the vehicles that are not cars.
Give your answer as a fraction in its simplest form.
The requried fraction of vehicles that are not cars is 7/33.
The fraction of the vehicles that are not cars can be found by deducting the number of cars from the total number of vehicles and then dividing by the total number of vehicles:
Number of vehicles that are not cars = 495 - 390 = 105
Fraction of vehicles that are not cars = (Number of vehicles that are not cars) / (Total number of vehicles) = 105/495
To simplify this fraction, we can divide both the numerator and denominator by the greatest common factor, which is 15:
105/495 = (105 ÷ 15) / (495 ÷ 15) = 7/33
Thus, the fraction of vehicles that are not cars is 7/33.
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