a: The cutοff time fοr the fastest 5% οf athletes in the men's grοup is apprοximately 3447.68 secοnds.
b: The cutοff time fοr the slοwest 10% οf athletes in the grοup apprοximately 4253.68 secοnds.
What is the nοrmal distributiοn?The nοrmal distributiοn is a cοntinuοus prοbability distributiοn that is widely used in statistics tο describe real-wοrld phenοmena that tend tο cluster arοund a central value.
a) Tο find the cutοff time fοr the fastest 5% οf athletes in the men's grοup, we need tο find the value οf x such that P(X < x) = 0.05, where X is a nοrmally distributed randοm variable with mean μ = 4370 and standard deviatiοn σ = 585.
Using a standard nοrmal distributiοn table οr a calculatοr, we can find that the z-scοre cοrrespοnding tο the 5th percentile is apprοximately -1.645. Therefοre, we can write:
(x - μ) / σ = -1.645
Substituting the given values, we get:
(x - 4370) / 585 = -1.645
Sοlving fοr x, we get:
x = 4370 + (-1.645) * 585
x ≈ 3447.68 secοnds
Hence, the cutοff time fοr the fastest 5% οf athletes in the men's grοup is apprοximately 3447.68 secοnds.
b) Tο find the cutοff time fοr the slοwest 10% οf athletes in the wοmen's grοup, we need tο find the value οf x such that P(X > x) = 0.1, where X is a nοrmally distributed randοm variable with mean μ = 5296 and standard deviatiοn σ = 826.
Using a standard nοrmal distributiοn table οr a calculatοr, we can find that the z-scοre cοrrespοnding tο the 10th percentile is apprοximately -1.28. Therefοre, we can write:
(x - μ) / σ = -1.28
Substituting the given values, we get:
(x - 5296) / 826 = -1.28
Sοlving fοr x, we get:
x = 5296 + (-1.28) * 826
x ≈ 4253.68 secοnds
Hence, the cutοff time fοr the slοwest 10% οf athletes in the grοup apprοximately 4253.68 secοnds.
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THERMOMETER An outdoor thermometer claims to be accurate within
2 degrees Fahrenheit. One day, the thermometer reads 72°F.
a. Write an absolute value inequality that represents the possible actual
temperature t.
b. What is the range of possible actual temperatures?
Answer:
a. An absolute value inequality that represents the possible actual temperature t is:
|t - 72| < 2
b. To find the range of possible actual temperatures, we can solve the inequality:
|t - 72| < 2
We can split this into two separate inequalities, one for when t is greater than 72 and one for when t is less than 72:
t - 72 < 2 and -(t - 72) < 2
Simplifying these inequalities, we get:
t < 74 and t > 70
Therefore, the range of possible actual temperatures is 70°F < t < 74°F.
Step-by-step explanation:
Find the volume of a right circular cone that has a height of 3. 5 ft and a base with a diameter of 11. 9 ft. Round your answer to the nearest tenth of a cubic foot
By dividing the diameter by 2, one may get the radius of the cone's base:[tex]r = d/2 = 11.9/2 = 5.95 ft[/tex] The volume of a cone is calculated as follows: V = (1/3)πr^2h Inputting the values provided yields.
[tex]V = (1/3)π(5.95^2)(35) (3.5) V equals 138.2 cubic feet[/tex]. Using tenths of a cubic foot increments, we obtain: V ≈ 138.2 ft^3 Hence, the right circular cone has a volume of around 138.2 cubic feet. some further data on the volume of the cone. The formula: can also be used to express a cone's volume in terms of its height and slant height. V is equal to (1/3)r2h plus (1/3)r2(h2 + r2). where the square root symbol is represented by. Since we already know the height and radius, we can use the Pythagorean theorem to get the slant height.
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You are flipping two coins. The probability of flipping two heads is 1/4. What is one way this can be calculated?
A. 1/2 subtracted from 1/2
B. 1/2 multiplied by 1/2
C. 1/2 divided by 1/2
D. 1/2 added to 1/2
Answer:
B. 1/2 multiplied by 1/2
Step-by-step explanation:
To find the probability, you would multiply. If you did not know this, you could solve each answer choice to find which one equals 1/4 since the problem already said the probability of flipping two heads is 1/4.
A. 1/2 - 1/2 = 0
B. 1/2 x 1/2 = 1/4
C. 1/2 / 1/2 = 1
D. 1/2 +1/2 = 1
(Please answer quickly!!!)Simplify negative 4 and 1 over 4 minus 6 and 2 over 5.
negative 213 over 20
negative 43 over 20
negative 10 and one third
10 and 13 over 20
Since 4 and 5 have a least common denominator of 20, we can convert both fractions to have a denominator of 20:
-17/4 * 5/5 = -85/20, 32/5 * 4/4 = 128/20, -85/20 - 128/20 = -213/20
what are fractions?A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers. The depiction of fractions appears easier than when decimal values are used.
A fraction is used to denote a portion or component of a whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
To simplify:
-4 and 1/4 - 6 and 2/5
For the two mixed integers, we must identify a common denominator. The least frequent multiple of 4 and 5 is 20 since their prime components are 2 and 5. Both mixed numbers can be transformed into improper fractions with a denominator of 20 as follows:
-4 and 1/4 = -17/4
6 and 2/5 = 32/5
Now we can subtract these fractions:
-17/4 - 32/5
We must locate a common denominator in order to subtract fractions. Since 4 and 5 have a least common denominator of 20, we can convert both fractions to have a denominator of 20:
-17/4 * 5/5 = -85/20
32/5 * 4/4 = 128/20
We can now take the two fractions apart:
-85/20 - 128/20 = -213/20
Therefore, -4 and 1/4 - 6 and 2/5 simplify to -213/20.
So, the answer is negative 213 over 20.
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need help asap pleasee
Answer:
a
Step-by-step explanation:
What is 0.06 written as a percent?
Answer:
6%
Step-by-step explanation:
0.06 is 6% as a decimal
Score: 1/6 1/6 answered
Question 1
Given the triangle
H=
* <>
15
/33°
answer to 4 decimal places.
Question Help: Video
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X find the length of side 2 using the Law of Cosines. Round your final
3
27 a
The length of side 2 of the given triangle is 16.22.
What is Law of Cosines?The Law of Cosines is a mathematical formula that is used to calculate the length of sides and angles in a triangle. It is based on the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides
The Law of Cosines helps to solve for the side length in triangles when we are given two sides and the angle between them. In this triangle we are given side 1 (15) and the angle between the two sides (33°). To find side 2, we will use the formula:
c² = a² + b²- 2ab*cosC
Where c is the length of the unknown side, a is the length of the given side, b is the length of the other given side, and C is the angle between the two given sides.
In this case, c is side 2, a is 15, b is unknown, and C is 33°. We will plug in the known values and solve for b:
b² = 15² + c² - 2*15*c*cos(33°)
b² = 225 + c² - 30c*cos(33°)
We can solve this equation for c:
c = (225 + b² - 30b*cos(33°))/2
Now, we can solve for b using the values for c and a given in the problem:
b²= 225 + 27² - 30*27*cos(33°)
b² = 225 + 729 - 690.8
b²= 264.2
b = 16.22
Therefore, the length of side 2 is 16.22.
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Brian wants to exchange south African Rand for British pound. If R1 is worth 0. 075199 pound, how many pounds will he get for R2100 if he must pay an agent commission of 1. 5%
After deducting a commission of 1.5%, Brian will receive 155.71 pounds in exchange for R2100.
To find out how many pounds Brian will get, we first need to calculate the amount of commission he will pay. The commission is 1.5% of R2100, which is equal to 0.015 x R2100 = R31.50.
The amount of money he will actually receive in pounds is the remaining R2100 minus the commission, which is R2068.50. To convert this to pounds, we multiply by the exchange rate of R1 = 0.075199 pound:
2068.50 x 0.075199 = 155.706675 pounds
Therefore, Brian will get 155.71 pounds for R2100 after paying the agent commission.
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Evaluate 2^x for (a) x= -2 and (b) x=3. Write your answers in simplest form.
a. The expression is__
when x= -2
b. The expression is__
when x= 3
(a) When [tex]x=-2, 2^x = 2^(-2) = 1/2^2 = 1/4[/tex]. So, the expression 2^x when x=-2 is 1/4.
(b) When [tex]x=3, 2^x = 2^3 = 8[/tex]. So, the expression 2^x when x=3 is 8.
The expression 2^x represents exponential growth, where the base 2 is multiplied by itself x number of times. When x is a negative number, the expression becomes a fraction because we are dividing 1 by the base raised to the absolute value of x. In this case, 2^(-2) is equivalent to 1/2^2, which is equal to 1/4. On the other hand, when x is a positive number, the expression grows exponentially. When x=3, the expression becomes 2^3, which is equal to 2x2x2 = 8.
In summary, the evaluation of 2^x when x is a negative number produces a fraction, whereas when x is a positive number, it produces a positive integer.
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Assessment Practice 18. Data were collected from a random sample of 50 eighth-grade students. It was found that 15 eighth-grade students spent 2 hours each night on homework. If there are 280 eighth graders in the school, how many can you estimate spend 2 hours each night on homework?
We can estimate that 84 eighth graders in the school spend 2 hours each night on homework.We can use the proportion of students in the sample who spend 2 hours each night on homework to estimate the number of students in the school who spend the same amount of time on homework.
We are given that a random sample of 50 eighth-grade students was taken, and 15 of them spent 2 hours each night on homework. Therefore, the proportion of students in the sample who spend 2 hours each night on homework is:
15/50 = 0.3
We can use this proportion to estimate the number of eighth graders in the school who spend 2 hours each night on homework. If we assume that the sample is representative of the larger population, we can multiply the proportion by the total number of eighth graders in the school:
0.3 x 280 = 84
Therefore, we can estimate that 84 eighth graders in the school spend 2 hours each night on homework. It's important to note that this is just an estimate and the actual number may differ due to sampling variability.
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Calculate 15% of 12000 for two (2) years
Answer:
look below
13,800
three potential employees took an aptitude test. each person took a different version of the test. the scores are reported below. demetria got a score of 85.1 ; this version has a mean of 61.1 and a standard deviation of 12 . vincent got a score of 299.2 ; this version has a mean of 264 and a standard deviation of 22 . tobias got a score of 7.26 ; this version has a mean of 7.1 and a standard deviation of 0.4 . if the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
The best applicant to fill the only position available based on the test score is Vincent as he scored highest. The method for determining which applicant performed the best on the aptitude test is to use z-scores, which are measurements of how far from the mean a test score falls in standard deviation units.
Since the test is not on the same scale, it is impossible to compare raw test scores. What are Z-scores?A z-score, also known as a standard score, is a score that indicates the number of standard deviations from the mean a raw score is. In other words, a z-score tells you how far from the mean the score is in terms of standard deviations.
In other words, we can use the following formula to calculate the z-score for each person's test result.$$Z = \frac {x - \mu}{\sigma}$$where x is the test score, μ is the test mean, and σ is the standard deviation.The Z-scores for each of the candidates based on their test results are as follows: Demetria:$$Z = \frac {85.1 - 61.1}{12} = 2.00$$,Vincent:$$Z = \frac {299.2 - 264}{22} = 1.6$$,Tobias:$$Z = \frac {7.26 - 7.1}{0.4} = 0.4$$. From the calculations, Vincent has the highest z-score, indicating that he outperformed the other candidates. The candidate with the highest z-score is the best performer, thus Vincent is the best candidate for the job.
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Solve for vertex algebraically 3x^2+6x+7
Mrs. Williams and her husband went to dinner in NYC last night. The total bill was $265 for the two of them. There was a 7% sales tax added to the bill. They decided to tip the waiter 15% on the bill after tax. How much tip did she leave?
The value of the tip she left is $42.53.
How much tip did she leave?Sales tax is a compulsory amount levied by the government on the sales price of a good or service. Sales price increase the cost of a good or service.
The first step is to determine the total bill after the sales tax has been included.
Total bill after sales tax = (1 + percent sales tax/100) x total bill
(1 + 7/100) x $265
(1 + 0.07) x $265
1.07 x $265
= $283.55
Now, multiply the total bill after sales tax by the percentage value of the tip.
Value of the tip = 15% x $283.55
0.15 x $283.55 = $42.53
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a shopkeeper bought 300 lanterns. he sold 2/3 of them on Saturday and 1/6 of them on Sunday how many lanterns did he have left?
Answer:
150 Lanterns
Step-by-step explanation:
Total lanterns : 300
[tex]\frac{2}{6} * 300 = 100[/tex]
[tex]\frac{1}{6} * 300 = 50[/tex]
so He sold 150 lanterns in total , leaving 300-150 = 150 Lanterns left.
Solve for x. Please show all steps needed.
x+8/(x+3)(x+4) = 3/x+3
Answer:
[tex]x = -2[/tex]
Step-by-step explanation:
[tex] \frac{(x + 8)}{[(x + 3) (x + 4)]} = \frac{3}{(x + 3)}[/tex]
Multiplying both sides by (x + 3) (x + 4), we get:
[tex](x + 8) = 3 (x + 4)[/tex]
Expanding the right-hand side, we get:
[tex]x + 8 = 3x + 12[/tex]
Subtracting x and 8 from both sides, we get:
[tex]2x = -4[/tex]
Dividing both sides by 2, we get:
[tex]x = -2[/tex]
Therefore, the solution to the given equation is x = -2. We can check this solution by substituting x = -2 into the original equation and verifying that both sides are equal.
Please help super confused
Answer:
1. 4, 28, 80
2. P(x)=4x
3. P(9.1)=36.4
The perimeter is 36.4 and the side length is 9.1
Step-by-step explanation:
To find perimeter you multiple a squares side length by 4.
if 3 Sin A + 4 cos A= 5 prove that tan A = 3/4
match the equation with its graph
[tex]y=-\frac{2}{3} x+1[/tex]
identify the slope and the y-intercept
( i already did the first part i just need help finding the slope also the y intercept )
Answer:
slope is -2/3, and the y intercept is 1.
Step-by-step explanation:
Using y=Mx+b (slope intercept form), where M=slope, and B = Y intercept , you can find which valurs are which.
Which equation could represent a line that is parallel to y = -2x
+ 4?
a. 1/2+y=1
b.-2x+y=8
c.-2x-y=3
d.-1/2+y=5
The calculated equation that represents a line parallel to y = -2x + 4 is (c) -2x - y = 3.
How to determine the parallel equationThe equation of a line that is parallel to y = -2x + 4 will have the same slope as -2 since parallel lines have the same slope.
Therefore, we need to look for an equation that has a slope of -2.
(a) 1/2x + y = 1 has a slope of -1/2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.
(b) -2x + y = 8 has a slope of 2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.
(c) -2x - y = 3 can be rearranged to y = -2x - 3, which has a slope of -2, so it is parallel to y = -2x + 4.
(d) -1/2x + y = 5 has a slope of 1/2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.
Therefore, the equation that represents a line parallel to y = -2x + 4 is (c) -2x - y = 3.
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Find the area of the shaded parts.
[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{outer}{radius}\\ r=\stackrel{inner}{radius}\\[-0.5em] \hrulefill\\ R=4\\ r=2 \end{cases}\implies A=\pi (4^2 - 2^2) \\\\\\ A=12\pi \implies A\approx 37.70~in^2[/tex]
Answer:
12πin² = 37.7in² (3sf)
Step-by-step explanation:
area of whole circle = π(4)² = 16π
area of small circle = π(2)² = 4π
area of shaded = 16π - 4π = 12π
12π = 37.6991... ≈ 37.7in² (3sf)
Someone please explain the answer to this problem
Select the correct answer. Which equation represents a circle with center T(5,-1) and a radius of 16 units? A. (x − 5)2 + (y + 1)2 = 16 B. (x − 5)2 + (y + 1)2 = 256 C. (x + 5)2 + (y − 1)2 = 16 D. (x + 5)2 + (y − 1)2 = 256
The equation of the given circle is: (x - 5)² + (y+ 1)² = 256
How to find the equation of the circle?The center-radius form (most formally called the standard form) of a circle is usually expressed as;
(x - h)² + (y - k)² = r²
where (h, k) is the center and r is the radius.
We are given a circle with center T(5,-1) and a radius of 16 units
The equation then becomes:
(x - 5)² + (y - (-1))² = 16²
(x - 5)² + (y+ 1)² = 256
Thus, we can conclude that is the equation of the circle.
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Which describes a financial product offered by insurance companies that, in
return for an investment, provides fixed payments each month for the
remainder of a person's life?
The financial product described is an annuity.
An annuity is a contract offered by insurance companies, where the buyer makes a lump-sum payment or a series of payments in exchange for regular payments made over time, usually until the end of the buyer's life. An annuity can be either fixed or variable, depending on the type of investment chosen by the buyer.
In a fixed annuity, the payments are predetermined and do not change over time, while in a variable annuity, the payments are based on the performance of the underlying investments. An annuity is often used as a retirement income stream.
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36 is 15% of what number?
54
240
360
540
Answer:
240
Step-by-step explanation:
15% of 54=8.1
15% of 240=36
15% of 360=54
15% of 540=81
so the answer is 240
36 is 15 percent of 240.
We have,
To find out what number 36 is 15% of, we can set up the equation:
36 = 0.15x
Here, x represents the unknown number we are trying to find.
To solve for x, we divide both sides of the equation by 0.15:
36 / 0.15 = x
Simplifying the right side gives:
240 = x
Therefore,
36 is 15 percent of 240.
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
the vertex of∠5 is point M
Step-by-step explanation:
Answer: M
Step-by-step explanation: M represents the vertex. Think of the vertex almost like the starting point of an angle.
Which of the following tables represents a linear function? x −4 −2 0 2 4 y 5 1 −3 −7 −11 x −3 −2 0 2 3 y 5 2 0 2 4 x 3 3 0 3 3 y −3 −2 0 2 −3 x 0 2 3 4 5 y −3 2 0 2 −3
A table that represents a linear function include the following: A.
x −4 −2 0 2 4
y 5 1 −3 −7 −11
What is a linear function?In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
This ultimately implies that, a linear function has the same (constant) slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.
Next, we would determine the slope by using the points contained in the table as follows;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (1 - 5)/(-2 + 4) = (-3 - 1)/(0 + 2) = (-7 + 3)/(2 - 0)
Slope (m) = -2.
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express in the form n:1
Answer:3/2
Step-by-step explanation:
[tex]\frac{9}{6} = \frac{\frac{9}{3} }{\frac{6}{3} }=\frac{3}{2}[/tex]
Please help me solve this! Please and thank you! :D PLEASE HELP I WILL GIVE BRAINLIEST
The equation that shows a proportional relationship is y = 12x; where the constant of proportionality is 12
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
A proportion relationship is in the form:
y = kx; where x is the constant of proportionality
Let y represent the number of paper towel rolls and x represent the number of cases. Hence:
y = kx
From the table, using the point (1, 12):
12 = k(1)
k = 12
The equation is y = 12x
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A coin is flipped and a card is randomly selected from a deck of 52. What is the probability the coin will land on heads and the card will be a club? There are 13 clubs in a deck of cards.
A. 1/8
B. 1/24
C. 4/9
D. 1/2
My answer:
There are 4 cards of number eight in a deck of 52 cards, namely: 8 Spades, 8 Diamond, 8 Clubs, and 8 Hearts. So the probable outcomes are 4 and the total cards are 52. So, x 100 = 1/13. So there is a 1/13 chance for getting an eight, i.e, for every 13 cards, one card will be an eight.
hope it helps :)
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