Using the normal distribution, it is found that:
a) The cutoff time for the fastest 5% of athletes in the men's group is of 3448.58.
b) The cutoff time for the slowest 10% of athletes in the women's group is of 6298.72.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.Item a:
For men, we have that [tex]\mu = 4378, \sigma = 565[/tex].
The cutoff for the fastest 5% of the athletes is the 5th percentile, which is X when Z has a p-value of 0.05, that is, X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 4378}{565}[/tex]
[tex]X - 4378 = -1.645(565)[/tex]
[tex]X = 3448.58[/tex]
The cutoff time for the fastest 5% of athletes in the men's group is of 3448.58.
Item b:
For women, we have that [tex]\mu = 5212, \sigma = 849[/tex].
The cutoff is the 90th percentile, which is X when Z = 1.28, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 5212}{849}[/tex]
[tex]X - 5212 = 1.28(849)[/tex]
[tex]X = 6298.72[/tex]
The cutoff time for the slowest 10% of athletes in the women's group is of 6298.72.
More can be learned about the normal distribution at https://brainly.com/question/24663213
What is the value of the expression below? 64^2/8
Answer:
512
Step-by-step explanation:
64^2=4096
4096/8=512
A crate is 3/4 yard long and 2/3 yard wide. The crate is also 2 feet tall. What is the area of the top of the crate?
Answer:
1/2 or 6/12
Step-by-step explanation:
To get the area of the crate's top, multiply the length and width together. Should not multiply the height by anything because it simply measures the height of the box and not the length or breadth of any of its bases (the top and bottom of the box). When you multiply the length by 3/4 and the breadth by 2/3, you should obtain 6/12, or 1/2 yard squared, as your answer for the area of the crate's top.
What is the answer and how did you get it
Answer:
You didn't include a picture!
Step-by-step explanation:
Fun fact ; More twins are born now then they ever were before!
Susan makes 12 cups of curd in 1 week. after 10 weeks how many cups are made
Answer:
120
Step-by-step explanation:
12 x 10 = 120
What’s the answer??????
Answer:
-186,624
Step-by-step explanation:
Because you multiply each time by -6
-4 x -6 = 24
24 x -6 = -144
-144 x -6 = 864
864 x -6 = -5,184
-5,184 x -6 = 31,104
31,104 x -6 = -186,624
Mr. Garza has a picture that measures 4 by 12 inches. It must be reduced so that the longest side measures 4 inches to fit in the school newspaper. Find the length of the shorter side of the picture once it has been reduced.
A. 2in
B. 1 1/2in
C. 1 1/3in
D. 1in
Answer:
The answer is C
Step-by-step explanation:
Divide 4 by 3
4 ÷ 3 = 1.33
1 1/3 as a fraction
Answer:
cCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
Step-by-step explanation:
Answer for ( f^-1 )
Answer:
Step-by-step explanation:
A bank offers an investment account with an annual interest rate of 1.14% compounded monthly. Lashonda invests $3400 into the account for 2 years. Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas х 5 ? (a) Assuming no withdrawals are made, how much money is in Lashonda's account after 2 years?
Answer:
≈$3478.4
Step-by-step explanation:
Using the compound interest formula:
[tex]A = P(1+\frac{r}{n})^{nt}[/tex]
A = Total
P = Principle
r = Interest Rate
n = No. of times applied in each time period
t = No. of periods
In this case,
P = 3400
r = 1.14% = 0.0114
n = 12 (months)
t = 2 (years)
Hence,
[tex]A = 3400(1+\frac{0.0115}{12})^{12*2}[/tex]
[tex]A = 3478.372836......[/tex]
A ≈ 3478.4 (nearest cent)
If a number is raised to a power of 2, It Is
Answer: a square i think
Step-by-step explanation:
because you multiply the number by itself, you're squaring it.
Ruth has a piece of wood that measures 2 2/9 feet. She cut off 1 1/3 feet of wood for a project. How much wood does she have remaining?
please answer please
Answer:
ill say the answer is 76849302
Step-by-stepStep-by-step explanation:
because 18 over 1/3 ad 3 over 1/3 is 76849302 . Hopefully this helped
a pet supply company makes a small bag that holds 2 pounds of dog food.they want to make a bag for large dogs that holds 40 pounds of dog food. by approximately what scale factor will the surface area of the bag increase? round your answer to the nearest tenth
Help me answer this question please Its not hard IM JUST REALLY TIRED I about 5 hours worth of khan lol
I will consider marking Brainliest
Answer:
A= -13 - b/4
Step-by-step explanation:
Hoped this helped!
From: Aug1e
[tex]4a+b=-52\\4a=-52-b\\a=-(52+b)/4=-52/4-b/4=-13-b/4[/tex]
OK done. Thank to me :>
Given the equation in standard form, put it in slope-intercept form. Show all work.
25x + 5y = 50
Please please look at the picture and answer it. Thank you!
Please answer quickly
Answer:
Step-by-step explanation:
1. the diameter of the circle is like in the diagram: d = 18 in ;
2. the radius of a circle measures the half of its diameter so: r = d/2 = 18 / 2 = 9 in ;
Jack Thomas has an ice cream cone with 280 calories. How long would it take him to burn off the calories by:
running (5mph) - minutes
walking (3mph) - minutes
taking a nap -minutes
Answer:
28
70
280
Step-by-step explanation:
A rancher uses a bucket that holds 15,000 milliliters of water to fill a water trough for her horse. The trough holds 2.7 x 10^5 milliliters of water. How many buckets of water will the rancher need to fill the trough?
Step-by-step explanation:
the volume of the bucket is
15,000 = 1.5 × 10⁴ ml
the trough holds
2.7 × 10⁵ ml
by calculating how often the volume of the bucket fits into the volume of the trough, we will know how many buckets of water are needed :
2.7 × 10⁵ / (1.5 × 10⁴) = 2.7/1.5 × 10⁵/10⁴ = 2.7/1.5 × 10¹ =
= 27/1.5 = 18
the rancher needs 18 buckets of water to fill the trough.
Prove that!
[tex]\tiny\displaystyle\rm \sum_{q=1}^{\infty}\left(a^{q}\left(1+\sum_{r=1}^{\infty} \frac{\prod \limits_{i=0}^{r+1}(q-i)}{\Gamma(r+1)}\left(\frac{b x^{m}}{a}\right)^{r}\right)\right)=\frac{a+b x^{m}}{1-\left(a+b x^{m}\right)}[/tex]
if all variables belong to natural number.
Recall that if |x| < 1, then
[tex]\displaystyle \frac1{1-x} = \sum_{k=0}^\infty x^k[/tex]
So if |a + bxᵐ| < 1, then
[tex]\displaystyle \frac{a+bx^m}{1 - (a+bx^m)} = \sum_{q=1}^\infty (a+bx^m)^q = \sum_{q=1}^\infty a^q \left(1 + \frac{bx^m}a\right)^q[/tex]
By the binomial theorem,
[tex]\displaystyle \left(1 + \frac{bx^m}a\right)^q = \sum_{r=0}^q \binom qr \left(\frac{bx^m}a\right)^r[/tex]
The binomial coefficient is defined as
[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]
if 0 ≤ k ≤ n, and 0 otherwise. Then we can rewrite the sum as
[tex]\displaystyle \left(1 + \frac{bx^m}a\right)^q = \sum_{r=0}^\infty \binom qr \left(\frac{bx^m}a\right)^r[/tex]
and pulling out the first term,
[tex]\displaystyle \left(1 + \frac{bx^m}a\right)^q = 1 + \sum_{r=1}^\infty \binom qr \left(\frac{bx^m}a\right)^r[/tex]
Finally,
[tex]\dbinom qr = \dfrac{q!}{r! (q-r)!} \\\\\\ = \dfrac{q(q-1)(q-2)\cdots(q-(r-1))(q-r)(q-(r+1))\cdots3\cdot2\cdot1}{r! (q-r) (q-(r+1)) (q-(r+2))\cdots3\cdot2\cdot1} \\\\\\ = \dfrac{q(q-1)(q-2)\cdots(q-(r-1))}{r!} \\\\ = \dfrac{\prod\limits_{i=0}^{r-1}(q-i)}{\Gamma(r+1)}[/tex]
since n! = Γ(n + 1). (I think the given upper limit in the product may be a mistake.)
Kennedy is working two summer jobs, making $11 per hour babysitting and making $8 per hour clearing tables. In a given week, she can work at most 17 total hours and must earn no less than $160. If x represents the number of hours babysitting and y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
| x+y(less than or equal to)17
| 11x+8y(greater than or equal to)160
Step-by-step explanation:
Hope this helped! ·∪·
An electronics manufacturing process has a scheduled mean completion time of 70 minutes. It is claimed that, under new management, the mean completion time,u , is less than 70 minutes. To test this claim, a random sample of 18 completion times under new management was taken.
The sample had a mean completion time of 64 minutes and a standard deviation of 11 minutes. Assume that the population of completion times under new management is normally distributed. At the 0.05 level of significance, can it be concluded that the mean completion time ,u, under new management is less than the scheduled mean?
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
Answer:
one or three I'm not sure
MATH PEOPPE PLEASE HELP
After sitting out of a refrigerator for a while, a turkey at room temperature (72°F) is
placed into an oven. The oven temperature is 305°F. Newton's Law of Heating
explains that the temperature of the turkey will increase proportionally to the
difference between the temperature of the turkey and the temperature of the oven, as
given by the formula below:
T = T. + (T. – T.)e-kt
To = the temperature surrounding the object
To = the initial temperature of the object
t the time in hours
T = the temperature of the object after t hours
k = decay constant
The turkey reaches the temperature of 123°F after 2 hours. Using this information,
find the value of k, to the nearest thousandth. Use the resulting equation to
determine the Fahrenheit temperature of the turkey, to the nearest degree, after 4.5
hours.
Enter only the final temperature into the input box.
Answer:
156 °F
Step-by-step explanation:
Newton's Law of Heating results in the exponential function you show in your problem statement. We can use the given starting and "in-progress" temperatures and times to solve for the value of the factor "k" in the exponential function.
[tex]T(t)=T_\infty+(T_0-T_\infty)e^{-kt}\\\\T(2.5)=123=305+(72-305)e^{-k\cdot2.5}\qquad\text{substitute given temps and times}\\\\\dfrac{123-305}{72-305}=e^{-2.5k}=\dfrac{182}{233}\qquad\text{subtract 305, divide by $(72-305)$}\\\\k=\dfrac{-1}{2.5}\ln\dfrac{182}{233}\approx0.0988127\approx0.099\qquad\text{rounded to 3 places}[/tex]
Then the temperature after 4.5 hours is ...
T(4.5) = 305 -233e^(-0.099·4.5) ≈ 156 . . . . °F
_____
Additional comment
It will take about 6.3 hours for the turkey temperature to reach 180 °F.
21/56 and 3/8 divisor
The result of this operation is 1
Data;
21/563/8Division of FractionsTo solve this problem, we are asked to divide the fraction. Whenever two fractions are given and the operation required is division, it is best to take the inverse of one of the fraction and then multiply it by the other fraction.
[tex]\frac{21}{58} / \frac{3}{8}[/tex]
This can become
[tex]\frac{21}{56} * \frac{8}{3} = \frac{7}{7} = 1[/tex]
This shows that dividing the two fractions will give us 1.
Learn more on division of fractions here;
https://brainly.com/question/1622425
https://brainly.com/question/18925320
Help me on this pls
I will give brainliest
Also 20 points
(all of it)
Answer:
12/32?
Step-by-step explanation:
Answer:6/16 & 9/24
Step-by-step explanation: Look at the grey highlighted parts. Match up the numbers to each row. 3 is on the same row as 8, 6 is on the same row as 16, and it continues up until 15/40.
it took the Phillips family 6 hours
to drive to their vacation
destination. Due to traffic, it took
them 8 hours and 42 minutes to
drive home.
Percentage for Increase or Decrease!!
Answer:
Percentage increase.
Step-by-step explanation:
It took the Phillips family 6 hours to drive to their vacation destination. 2 hours and 42 minutes extra because of traffic.
8 hours 42 minutes
-
6 hours 0 minutes
=
2 hours and 42 minutes
Percentage increase.
what is the solution to 8(2^x+3)= 48
This is how to solve it.
Hope this helps
These models represent 0.71 and 0.6.
How does 0.71 compare to 0.6?
Drag and drop a symbol into the box to make the comparison statement true.
0.71 Response area 0.6
Answer:
0.71 > 0.6
Step-by-step explanation:
Here, 0.71 has 7 tenths while 0.6 has 6 tenths, so 0.71 must be greater than 0.6
The net of a triangular prism is shown in the diagram. Use the ruler provided to measure the dimensions of the net to the nearest half centimeter.
Which measurement is closest to the volume of the triangular prism in cubic centimeters?
A.12 cm3
B. 30 CM3
C. 24 CM3
D. 15 CM3
Answer:24 cm
Step-by-step explanation:
i took the test
The two triangles
are similar.
What is the value of x?
Enter your answer in the box.
X =
Solution:
Note that:
(3x)/20 = (4x + 2)/28Using cross multiplication:
(3x)/20 = (4x + 2)/28=> (3x) × 28 = (4x + 2) × 20Simplifying both sides:
=> 84x = 80x + 40Subtracting 80x both sides:
84x = 80x + 40=> 84x - 80x = 80x + 40 - 80xSimplify the LHS:
=> 84x - 80x = 40=> 4x = 40=> x = 10Ratio remains same
[tex]\\ \rm\bull\rightarrowtail \dfrac{20}{3x}=\dfrac{28}{4x+2}[/tex]
[tex]\\ \rm\bull\rightarrowtail 84x=20(4x+2)[/tex]
[tex]\\ \rm\bull\rightarrowtail 84x=80x+40[/tex]
[tex]\\ \rm\bull\rightarrowtail 4x=40[/tex]
[tex]\\ \rm\bull\rightarrowtail x=10[/tex]
There is a pair of parallel sides in the following shape.
what is the area of the shape? units^2
Answer:
A = 15 units²
Step-by-step explanation:
The figure has 1 pair of parallel sides and is therefore a trapezium.
The area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between bases and b₁, b₂ are bases
here h = 3, b₁ = 3 , b₂ = 7 , then
A = [tex]\frac{1}{2}[/tex] × 3 × (3 + 7) = 1.5 × 10 = 15 units²
The area of the square is the square of one of its sides. The area of the plate is 15 units².
What is the area of a square?The area of the square is the square of one of its sides.
[tex]\text{Area of square} = a^2[/tex]
What is the area of a triangle?The area of a triangle is half the product of its base and height.
[tex]\rm\text{Area of Triangle} = \dfrac{1}{2} \times Base \times Height[/tex]
The shape of the plate can be divided into two parts a square of side 3 cm and a triangle with of base 4 cm and a height of 3 cm, therefore, the area of the plate is,
[tex]\text{The area of the shape} = \text{Area of the triangle} + \text{Area of the square}[/tex]
[tex]= (\dfrac{1}{2} \times 4 \times 3) + (3 \times 3)\\\\= 6 + 9\\\\=15\rm\ units^2[/tex]
Hence, the area of the plate is 15 units².
Learn more about Area of Square:
https://brainly.com/question/1658516
