The straight sections each have a length of 100. So, the total distance around the inner lane of the track is 200 + 40pi units
The area of one of the blue half circles can be found using the formula:
Area = pi x radius squared.
The diameter of the circle is given as 40, so the radius is half of that, which is 20.
Therefore, the area of one blue half circle is:
Area = pi x [tex]\frac{20^{2} }{2}[/tex]
Area = 200pi square units
To cover the entire circle, we need both blue half circles. So the total area needed to be covered with grass is:
Total area = 2 x 200pi = 400pi square units
The distance around one of the semicircles at either end of the soccer field can be found using the formula: Circumference = pi x diameter.
Since the diameter is given as 40.
The circumference is:
Circumference = pi x [tex]\frac{40}{2}[/tex]
Circumference = 20pi units
To find the distance around the inner lane of the track, we need to add the lengths of the straight distances (which are 100 each) to the circumference of the two blue half circles.
The circumference of one blue half circle is 20pi, so the total distance around the inner lane of the track is:
Distance = 2 x 100 + 2 x 20pi
Distance = 200 + 40pi units
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Saanvi recorded the number of math problems she did for homework each night for 10 days.
`0`, `5`, `5`, `4`, `5`, `10`, `5`, `6`, `50`, `0`
Calculate the mean and MAD of this data.
Answer:
Saanvi recorded the number of math problems she did for homework each night for 10 days.
Step-by-step explanation:
A store Sales a certain digital camera model for $108. During A special promotion, the camera is discounted by 30%. What is the discounted price?
Listed below are the amounts of net worth (in millions of dollars) of the ten wealthiest celebrities in a country. Construct a 99% confidence interval. What does the result tell us about the population of all celebrities? Do the data appear to be from a normally distributed population as required?
259
196
190
166
163
162
148
148
148
143
Using the appropriate statistical relation, the confidence interval estimate for the net worth of the wealthiest celebrities is (150.35; 204.77).
Given the samples :
X = 256,196,190,166,163,162,148,148,143.
Using a calculator, we could obtain the sample mean and sample standard deviation is-
Mean, μ = [tex]\sum\frac{x}{n}[/tex] = 174.55
Standard deviation, σ = 38.8
The confidence interval can be defined thus :
Mean ± standard error
Standard Error = Tcritical × σ/√n
Tcrit ; 95% ; df = n - 1 = 9 - 1 = 8; T-critical = 2.26
Standard Error = (2.26 × 38.06/√10) = 27.20
Lower confidence boundary = 177.55 - 27.20 = 150.35
Upper confidence boundary = 177.55 + 27.20 = 204.77
Therefore, the confidence interval is (150.35; 204.77)
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A bank account earns 1% interest each month has a balance of 1500 any interest is deposited into the account and no further deposits or withdrawals are made which expression represents the balance after two months
Therefore, the expression that represents the balance after two months is: 1500 * (1 + 0.01) * (1 + 0.01) = 1530.15.
What is percent?Percent, denoted by the symbol "%", is a way of expressing a number as a fraction of 100. For example, 50% is equivalent to the fraction 50/100, which can be simplified to 1/2. Percentages are commonly used to express ratios, proportions, or rates in various contexts such as finance, statistics, and everyday life. For instance, an interest rate of 3% means that for every $100 borrowed, the borrower will be charged $3 per year. Similarly, a score of 80% on an exam means that the student has answered 80 out of 100 questions correctly.
by the question.
To calculate the balance after two months, we first need to calculate the balance after the first month, including the interest earned:
Balance after 1 month = 1500 + (1% of 1500) = 1500 + 15 = 1515
Then, we can calculate the balance after two months, including the interest earned in the second month:
Balance after 2 months = 1515 + (1% of 1515) = 1515 + 15.15 = 1530.15
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What is the measure of each angle?
Answer:
a) 76
b) 26
I could only do the first two.
what is Bethany's score on the test if she answered 23 out of 30 right?
part:
whole:
percent:
Answer: 76.67%
Step-by-step explanation:
Determine whether the relation represents y as a function of x: X^2+y^2=4
The relation is not a function, but rather a circle with center at the origin and radius 2.
Does the given relation represents y as a function of x?Given the relation in the question;
x² + y² = 4.
First, lets solve for y.
x² + y² = 4
Subtract x² from both sides
x² - x² + y² = 4 - x²
y² = 4 - x²
Take the squre root of both sides
y = ±√( 4 - x² )
This shows that for a given value of x, there are two possible values of y. One positive and one negative, that satisfy the equation.
Therefore, the relation is not a function.
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PLSSSS HELPPPPPPPOO
Write an expression in standard form that
represents the AREA of the square. A = s²
5y+3
Answer:
Step-by-step explanation:
The expression in standard form that represents the area of the square with side length s is given by:
A = s^2
However, if you want to substitute the value of s with the expression 5y+3, then the area expression becomes:
A = (5y+3)^2
Expanding the expression, we get:
A = 25y^2 + 30y + 9
Therefore, the expression in standard form that represents the area of the square with side length 5y+3 is 25y^2 + 30y + 9.
Euclid Thales Hippocrates Pythagoras X regarded as the father of geometry a Greek geometer who has a theorem named after him a mathematician who compiled basic geometric facts, or elements, into a textbook X X a Greek philosopher who →contributed to five theorems of elementary geometry **got answer off here...showing the ones i got wrong ughh
Pythagoras - Has a theorem named after him
Thales - Contributed to the five basic theorems of geometry
What did Pythagoras do?Pythagoras was a Greek philosopher, mathematician, and founder of the Pythagorean school of philosophy. He lived in the 6th century BCE on the Greek island of Samos and is known for his contributions to mathematics, geometry, music, and philosophy.
Pythagoras is most famous for the theorem that bears his name, the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem is fundamental to the study of geometry and has applications in many fields, from architecture to physics.
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The equation P=20sin(2πt)+90 models the blood pressure, P , where t represents time in seconds. a. Find the blood pressure after 30 seconds. Enter the exact answer. The blood pressure is Number . b. What are the maximum and minimum blood pressures? Enter the exact answers. The maximum blood pressure is Number , and the minimum blood pressure is Number .
Suppose you have $50 in a savings account and deposit an additional $10 each week.
a) Write a recursive formula to represent the sequence.
b) Write an explicit formula to represent the sequence.
c) How much money do you have in savings after 26 weeks? Show all work.
According to the solving $310 money you have in savings after 26 weeks, we can use either the recursive or explicit formula:
Which equations are explicit?The explicit equations for L-functions are Riemann's relations between sums over an L-function's complex number zeroes and sums over prime powers for the Riemann zeta function.
According to the given information:a) Recursive formula:
Let S(n) be the amount of money in savings after n weeks. Then:
S(0) = 50 (initial amount)
S(n) = S(n-1) + 10 (deposit of $10 per week)
b) Explicit formula:
The explicit formula for this sequence is:
S(n) = 50 + 10n, where n is the number of weeks.
c) To find how much money you have in savings after 26 weeks, we can use either the recursive or explicit formula:
Using the recursive formula:
S(0) = 50 (initial amount)
S(1) = S(0) + 10 = 50 + 10 = 60
S(2) = S(1) + 10 = 60 + 10 = 70
S(3) = S(2) + 10 = 70 + 10 = 80
and so on, until:
S(26) = S(25) + 10 = 310
Therefore, after 26 weeks, you have $310 in savings.
Using the explicit formula:
S(26) = 50 + 10(26) = 50 + 260 = 310
after 26 weeks, you have $310 in savings.
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-3 minus the absolute vale of .5 =
Answer: -2.5
Step-by-step explanation: The absolute value of 0.5 is "0.5".
Therefore; if you subtract the value "3" from "0.5", you will end up with -2.5 as an answer.
Crystal Nelson would love to retire to Florida in 5 years. What amount should Crystal invest today so she can withdraw $46,500 at the end of each year for 20 years after she retires? Assume Crystal can invest money at 5% compounded annually.
The amount (Present Value) that Crystal Nelson can invest today so that she can withdraw $46,500 at the end of each year for 20 years when she retires in 5 years' time is $454,047.76.
How is the present value determined?Firstly, the present value of the periodic withdrawals for 20 years is determined and used as the future value for determining the present value in 5 years.
The present value is the future value discounted to the current period, removing the effect of compound interest.
Present Value in 5 Years' Time:N (# of periods) = 20 years
I/Y (Interest per year) = 5%
PMT (Periodic Withdrawals) = $-46500
FV (Future Value) = $0
Results:
Present Value (PV) = $579,492.78
Sum of all periodic payments = $-930,000.00
Total Interest = $350,507.22
Present Value Today:N (# of periods) = 5 years
I/Y (Interest per year) = 5%
PMT (Periodic Payment) = $0
FV (Future Value) = $579,492.78
Results:
Present Value (PV) = $454,047.76
Total Interest = $ 125,445.02
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A cylindrical chemical drum with a radius of 13 inches and a height of 20 1/2 inches needs painting. net of a cylinder What is the approximate surface area of this drum? Use 22,7 for pi.
1062 2/7 in²
1675 1/7 in²
1756 6/7 in²
2737 3/7 in²
Option D. The approximate surface area of the drum is 2744 1/7 in². The surface area of a cylinder can be calculated using the formula:
A = 2πr² + 2πrh
where r is the radius of the base, h is the height of the cylinder, and π is the mathematical constant pi, which we can approximate as 3.14.
Plugging in the given values, we get:
A = 2 x 3.14 x 13² + 2 x 3.14 x 13 x 20.5
= 1060.04 + 1684.06
≈ 2744.1
Rounding this to the nearest 1/7, we get:
2744 1/7 in²
Therefore, the approximate surface area of the drum is 2744 1/7 in². However, none of the given answer choices match this result exactly.
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A cylindrical chemical drum with a radius of 13 inches and a height of 20 1/2 inches needs painting. net of a cylinder What is the approximate surface area of this drum? Use 22,7 for pi.
A. 1062 2/7 in²
B. 1675 1/7 in²
C. 2737 3/7 in²
D. None of the above
A number written without a sign is a _______ number.
Answer:
Positive
Step-by-step explanation:
It's a positive number
If it doesn't have a (-) it's a positive number
Please help!! Correct answer gets brainliest!!
Answer : B. 36 Square Centimetres
Explanation : 9 × 8 = 72 72 ÷ 2 = 36
Answer:36 b
Step-by-step explanation:
Let f(x) = 1/x . Find the number b such that the average rate of change of f on the interval [2, b] is - 1/18.
The solution will be b=4, the number b such that the average rate of change of f on the interval [2, b] is - 1/18 if the provided assertion is correct.
What does interval look like in math?For instance, a range between 0 and 10 would include all of the integers between them, not just 1, 2, 3, 4, 5, 6, 7, 8, and 9. These would additionally incorporate fractional numbers like 1.3 and components like 1/10. We therefore have the job. We must determine b to the extent that the interval [2, b]'s average percentage of change or slope is -1/8. Discover f first(2).
f(2) = 1/(2) = 1/2
So, we have the point (2, 1/2)
At point b, f(b) = 1/b.
Let's plug this into the slope formula
We simply have to figure out b now. Let's start by multiplying the divisor and fraction by b.
Now, cross multiply.
Solve for b. Use the factors -4 and -2 to multiply.
Thus, b=4 or b=2.
However, b=2 cannot be the answer because the range [2,2] has no significance. Thus, b=4.
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A fair coin is tossed 29 times. In how many outcomes do at least 3 tails occur?
a) 536,866,822
b) 1
c) 536,870,477
d) 536,870,476
e) 3,654
Answer:
The answer to your problem is, A. 536,866,822
Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
The formula for calculating probability is expressed as:Probability = Expected outcome/Total outcomeIf a fair coin is tossed 29 times, the total number of outcomes will be expressed as: [tex]2^{29} = 536,870,476[/tex]
If at least 2 tails occur, the expected outcome will be 29 times
Pr(at least 2 tails occur) = [tex]2^{29} - 29 - 1[/tex]
Pr(at least 2 tails occur) = [tex]536,870,912 - 30 = 536,866,822[/tex]
Thus the answer to your problem is, A. 536,866,822
The length and breadth of a rectangular wire are 32 cm and 12 cm. It is bent into the shape of a circle. Find the radius of the circle. (Take p = 3.14)
The perimeter of the circle formed by bending the rectangular wire will be equal to the length of the wire.
Perimeter of the circle = Length of the wire
2πr = 2(l+b) where r is the radius of the circle, l is the length of the wire, and b is the breadth of the wire.
Substituting the given values, we get:
2 x 3.14 x r = 2(32 + 12)
6.28r = 88
r = 14 cm
Therefore, the radius of the circle is 14 cm.
Answer:
14.01 cm
Step-by-step explanation:
The length of the wire is equal to the perimeter of the rectangle. So, the length of the wire is:
2 × (32 + 12) = 88 cmWhen this wire is bent into a circle, its length becomes equal to the circumference of the circle. The formula for the circumference of a circle is:
(let r = radius)
2 × π × rSo, we can write:
2 × π × r = 88Solving for r, we get:
r = 88 ÷ (2 × π) = 14.01 cmSo, the exact value of the radius of the circle formed by bending this rectangular wire is 14.01 cm.
AP STATS HELP ANSWER RIGHT NOW PLS THANK YOU
Answer:c
Step-by-step explanation:
State the open intervals where the function is increasing, decreasing, or constant. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
f(x) = 81 − x2
The function f(x) = 81 − x2 is increasing on the interval (−∞, 9) and decreasing on the interval (9, ∞).
What is parabola?Parabola is a type of curve which is defined by the quadratic equation. It has a distinct "U" shape, with the vertex of the curve being the highest or lowest point.
The point x = 9 is the vertex of the parabola, which marks the point at which the function changes from increasing to decreasing.
Since the function is a parabola, it is also a polynomial of degree 2, and it is always decreasing for points greater than the vertex, and increasing for points less than the vertex.
This means that the function is increasing on the interval (−∞, 9) and decreasing on the interval (9, ∞).
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Ryan is installing new flooring in his house. Ryan can install 144 square feet of flooring in 3 hours. How much new flooring can Ryan install in 18 hours?
Here's what you need to do:
We know that Ryan can install 144 square feet of flooring in 3 hours.
So, if we take 144 square feet, and divide by 3 hours, 144 / 3, we end up with 48, meaning Ryan can install 48 square feet of flooring every hour.
Then, simply multiply 48 by 18, 48 x 18, and you end up with 864.
Meaning, in 18 hours, Ryan can install 864 square feet of flooring.
Answer: 864 square feet.
7) Use a proportion to solve this problem: Three ounces of a certain perfume cost $22.97. How much would six ounces of perfume cost?
The graph of f passes through (-4,7) and is perpendicular to the line that has
an x-intercept of 2 and a y-intercept of - 4.
The equation of the function is ?
Answer:
f(x) = - [tex]\frac{1}{2}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 0 ) , x- intercept and (x₂. y₂ ) = (0, - 4) , y- intercept
m = [tex]\frac{-4-0}{0-2}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute (- 4, 7 ) into the partial equation
7 = - [tex]\frac{1}{2}[/tex] (- 4) + c = 2 + c ( subtract 2 from both sides )
5 = c
y = f(x) = - [tex]\frac{1}{2}[/tex] x + 5 ← equation of function
aflati doua numere naturale stiind ca suma lor este 102 iar impartind numarul mare la cel mic obtinem catul 2 si restul 12
Starting at a particular time, each car entering an intersection is observed to see whether it turns left (L) or right (R) or goes straight ahead (S). The experiment terminates as soon as a car is observed to go straight. Suppose that the random variable y denotes the number of cars observed.
(b)List five different outcomes and their associated y-values.
Outcome Value of y
RRRS LLRLLS RRS LRRRLS S
Suppose that there is a random variable y, denotes the number of cars observed at car entering an intersection time.
a) Possible values of y are present in above table figure.
b) Five different outcomes and their associated y-values are also present in above figure 2.
Starting at a particular time, each car entering an intersection is observed to see whether it turns left (L) or right (R) or goes straight ahead (S). The experiment terminates as soon as a car is observed to go straight. Suppose that the random variable y denotes the number of cars observed. List five different outcomes and their associated y-values. In this experiment, each car entering an intersection is observed to see whether it turns left or right or goes straight. Let y denote the number of cars observed.
a) The experiment will terminate as soon as a car is observed to go straight. For this experiment, the possible outcomes are as shown above figure.
b) Also, from the above outcome, the five different outcomes are given below:
Outcome Value of y
RRRS 4
LLRLLS 6
RRS 3
LRRRLS 6
S 1
Hence,
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Complete question :
Starting at a particular time, each car entering an intersection is observed to see whether it turns left (L) or right (R) or goes straight ahead
(S). The experiment terminates as soon as a car is observed to go straight. Suppose that the random variable y denotes the number of cars observed.
a) what is the possible value of y?
(b)List five different outcomes and their associated y-values.
Outcome Value of y
RRRS
LLRLLS
RRS
LRRRLS
S
Help I’ll give points thanks
Answer:
(f•g)(x)=16x²+1
(g•f)(x)=4x²+4
Step-by-step explanation:
f(x)=x²+1, g(x)=4x
(f•g)(x)=f(g(x))
=f(4x)
=(4x)²+1
=16x²+1
(g•f)(x)=g(f(x))
=g(x²+1)
=4(x²+1)
= 4x²+4
How many pieces of rope measuring 5/8 of a foot can be cut from a rope of 4 3/8 feet?
We can cut 6 pieces of rope measuring 5/8 of a foot from a rope of 4 3/8 feet, with some rope left over.
What is area?Area is a measurement of the size of a surface or a region in a two-dimensional space. It is expressed in square units, such as square inches (in²), square meters (m²), or square feet (ft²). To find the area of a shape, you need to multiply its length by its width, or use an appropriate formula depending on the shape. For example, the formula for the area of a rectangle is A = l × w, where A is the area, l is the length, and w is the width.
To find the number of pieces of rope measuring 5/8 of a foot that can be cut from a rope of 4 3/8 feet, we need to divide the length of the rope by the length of each piece of rope:
4 3/8 feet = 4 + 3/8 feet = 4 feet + (3/8) x 12 inches = 4 feet + 3 inches = 51 inches
Each piece of rope measures 5/8 of a foot, which is equivalent to 5/8 x 12 inches = 7.5 inches.
Now we can divide the length of the rope (in inches) by the length of each piece of rope (in inches) to find the number of pieces:
51 inches ÷ 7.5 inches ≈ 6.8
Therefore, we can cut 6 pieces of rope measuring 5/8 of a foot from a rope of 4 3/8 feet, with some rope left over.
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Which is the sum of 8 3/4 + 2 and 1/2 ?
A. 11 1/6
B. 11 1/4
C. 10 1/2
D. 10 1/4
50 points giving brainlist to the one with explanation
The sum of 8 3/4 + 2 and 1/2 is 11 1/4 ( optionB)
What is sum ?A sum is the result of an addition. For example the sum of 10,15,4,6,12 is obtained by adding all the numbers together.
= 10+15+4+6+12 = 47
Similarly, the sum of 8 3/4 + 2 and 1/2 is obtained by,
35/4 +2 +1/2
The LCM of 4,2 and 1 is 4 and 8 can also be used.
= (70+16+4)/8
= 90/8
= 11 2/8
simplifying the fraction
= 11 1/4.
therefore the the sum of 8 3/4 + 2 and 1/2 is 11 1/4
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Ariel has the following data:
8 18 8 v 10 8 8 18 18
If the median is 10, which number could v be?
Answer:
Any number greater than 10; 11, 12, 15, 20, 100...etc
Step-by-step explanation:
Order the data from least to greatest and strikethrough numbers on each side until you reach the middle 1 or 2 numbers. In this case there are 9 numbers, so the middle number is our median.
8, 8, 8, 8, 10, v, 18, 18, 18
the variable v can be many numbers, but in order for the median to be 10, v must be a number greater than 10. If v = 11, the median is 10. Likewise, if v = 100000, the median is still 10 because it is the middle of the set.