Answer:
Approximately 68% of people have IQs between 84 and 116.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 100, standard deviation of 16.
Percentage of people with IQs between 84 and 116.
84 = 100 - 16
116 = 100 + 16
So within 1 standard deviation of the mean, which, by the Empirical Rule, is approximately 68%.
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis.
Using the shell method, the volume integral would be
[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx[/tex]
That is, each shell has a radius of x (the distance from a given x in the interval [0, 2] to the axis of revolution, x = 0) and a height equal to the difference between the boundary curves y = x ⁸ and y = 256. Each shell contributes an infinitesimal volume of 2π (radius) (height) (thickness), so the total volume of the overall solid would be obtained by integrating over [0, 2].
The volume itself would be
[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx = 2\pi \left(128x^2-\frac1{10}x^{10}\right)\bigg|_{x=0}^{x=2} = \boxed{\frac{4096\pi}5}[/tex]
Using the disk method, the integral for volume would be
[tex]\displaystyle \pi \int_0^{256} \left(\sqrt[8]{y}\right)^2\,\mathrm dy = \pi \int_0^{256} \sqrt[4]{y}\,\mathrm dy[/tex]
where each disk would have a radius of x = ⁸√y (which comes from solving y = x ⁸ for x) and an infinitesimal height, such that each disk contributes an infinitesimal volume of π (radius)² (height). You would end up with the same volume, 4096π/5.
The volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have a function:
[tex]\rm y = x^8[/tex] or
[tex]x = \sqrt[8]{y}[/tex]
And y = 256
By using the vertical axis of rotation method to evaluate the volume of the solid formed by revolving the region bounded by the curves.
[tex]\rm V = \pi \int\limits^a_b {x^2} \, dy[/tex]
Here a = 256, b = 0, and [tex]x = \sqrt[8]{y}[/tex]
[tex]\rm V = \pi \int\limits^{256}_0 {(\sqrt[8]{y}^2) } \, dy[/tex]
After solving definite integration, we will get:
[tex]\rm V = \pi(\frac{4096}{5} )[/tex] or
[tex]\rm V =\frac{4096}{5}\pi[/tex] cubic unit
Thus, the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.
Learn more about integration here:
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Dylan has a coworker who is always showing up late and then not finishing his work on time. It's frustrating the other members of the team. What can he do that might help the situation? a) Complain about the coworker to other team members O b) Ask his coworker if he understands his job responsibilities c) Tell his boss that the coworker is slacking off O d) Complete his coworker's work for him
The lengths of the parallel sides of
a trapezium are 12cm and 26cm
If Its area is 228cm square Find the
perpendicular distance between the
Parallel sides
Answer:
12 cm
Step-by-step explanation:
12+26/2 ×x =228
19x =228
X=12cm
Frances bought a new dress that was discounted by 24%. she used the following expressions to find the price of the dress after the discount was applied
Answer:
[tex]0.76d[/tex]
Step-by-step explanation:
Given
[tex]Formula = d - (0.24)d[/tex]
Required
Equivalent expression
We have:
[tex]Formula = d - (0.24)d[/tex]
Open bracket
[tex]Formula = d - 0.24d[/tex]
[tex]Formula = 0.76d[/tex]
A student determines the density of a chunk of metal to be 5.1 g/cm3. She then repeats the measurement four more times on the same chunk of metal and obtains values of 5.0, 4.9, 5.4, and 5.2 g/cm3 for the density. What is the standard deviation of the five measurements?
A. 0.148
B. 0.19
C. 0.037
D. 0.22
E. 0.17
Answer:
E. 0.17
Step-by-step explanation:
Mean:
Sum of all values divided by the number of values, so:
[tex]\overline{x} = \frac{5.1 + 5 + 4.9 + 5.4 + 5.2}{5} = 5.12[/tex]
Standard deviation:
Square root of the sum of the difference squared between each value and the mean, divided by the sample size, so:
[tex]s = \sqrt{\frac{(5.1-5.12)^2 + (5-5.12)^2 + (4.9-5.12)^2 + (5.4-5.12)^2 + (5.2-5.12)^2}{5}} = 0.172[/tex]
Thus the correct answer is given by option E.
1. A helicopter is at a position from two VORS (VHF Omnidirectional
Radio Range, an aircraft navigation system operating in the VHF band -
not covered in chapter) as in the diagram shown below. Given the angles
shown, find the third angle.
Helicopter
74.0°
66.0°
VOR
VOR
The position of the helicopter and the two VORs forms a triangle and the third angle formed by these three entities is 40 degrees
The diagram is not shown; however, the question can still be answered.
The given angles are:
[tex]\theta_1 = 74.0^o[/tex]
[tex]\theta_2 = 66.0^o[/tex]
Represent the third angle as [tex]\theta_3[/tex]
The helicopter and the 2 VORs form a triangle.
So, we make use of the following theorem to calculate the third angle
[tex]\theta_1 + \theta_2 + \theta_3= 180^o[/tex] ---- sum of angles in a triangle
Substitute known values
[tex]74.0^o + 66.0^o + \theta_3= 180^o[/tex]
[tex]140.0^o + \theta_3= 180^o[/tex]
Collect like terms
[tex]\theta_3= 180 -140.0^o[/tex]
[tex]\theta_3= 40^o[/tex]
Hence, the third angle is 40 degrees.
Learn more about angles in a triangle at:
https://brainly.com/question/14780489
What's the slope and y-intercept of the equation 4x + 2y = 8?
Question 13 options:
m = –2; b = –4
m = 2; b = 4
m = –2; b = 4
m = 2; b = –4
Answer:
m= - 2, b = 4
Step-by-step explanation:
structure of a linear equation
y = mx + c
m = gradient / slope
c = intercept
convert the given equation according to this structure of linear equations
4x+2y = 8
2y = -4x + 8
y = -2x +4
according to this intercept is 4 and slope is -2
Valerie set out to bicycle from TBLS to the beach, a distance of 10 miles. After going a short while at 15 miles per hour, the bike developed a flat tire, and the trip had to be given up. The walk back to TBLS was made at a dejected 3 miles per hour. The whole episode took 48 minutes. How many miles from TBLS did the flat occur
Answer:
I think it is 3 miles becos the bicycle broke at 15miles per hour and the walk from the current place to the TBLS is 3 miles per hour
ANSWER NOW IM TIMED Louie uses 10 feet of wood, 16 wheels and one can of paint for every 4 skateboards he builds.
A 4-column table with 3 rows. Column 1 is labeled Skateboards with entries 1, 4, 10. Column 2 is labeled Wood with entries blank, 10 feet, blank. Column 3 is labeled Wheels with entries blank, 16, blank. Column 4 is labeled paint with entries blank, 1 can, blank.
Use the table to find how much of each item Louie needs to build 10 skateboards.
Louie needs
feet of wood,
wheels, and
cans of paint.
Answer: 25 feet of wood
40 wheels and 2.5 cans of paints
Step-by-step explanation:
Answer:
25 feet of wood
40 wheels and
2.5 cans of paints
Step-by-step explanation: I did this before Also can i get brainlyist please
Find the numerical value of the area under the normal curve given the following information:
to the right of z = 2.28
enter your answer as a decimal (NOT percentage) and lead with a zero...for example: 0.1234
Answer:
1 - 0.9887 = 0.0113
Step-by-step explanation:
write your answer as an integer or as a decimal rounded to the nearest tenth.
Answer:
6.43
Step-by-step explanation:
Cosine: cos(θ) = Adjacent / Hypotenuse
cosine of 39 degrees = 5/x
.77714596145 = 5/x
x = 5/.77714596145
x= 6.43379782952
Convert the improper fraction to a whole or mixed number. (Enter your answer as a simplified mixed number.)
25
7
∫dx/(x+√(x^{2} +x+1)
Answer:
es1433
Step-by-step explanation:
What type of function is represented by the following table?
Number of weeks
1 2 3 4 5
Cost of rental car 79,
158,
237,
316,
395
Answer:
Linear
Step-by-step explanation:
cost = 79 * weeks
79*1=79
79*2=158
etc.
State and prove the Cantor Intersection Theorem.
Answer:
Cantor's intersection theorem refers to two closely related theorems in general topology and real analysis, named after Georg Cantor, about intersections of decreasing nested sequences of non-empty compact sets.
Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 2323 Pennies 55 Dimes 2020 Nickels 1919 Quarters Copy Data What is the probability that you reach into the jar and randomly grab a dime and then, without replacement, a nickel
Answer:
The answer is "0.081"
Step-by-step explanation:
Dimes [tex]= 55[/tex]
Calculating total coins [tex]= (23+55+20+19) = 117[/tex]
P(for a dime) [tex]= \frac{55}{117}[/tex]
Calculating remaining coins [tex]= 116[/tex]
Nickels [tex]= 20[/tex]
P(for nickel draw in second) [tex]= \frac{20}{116}[/tex]
P(for a dime after that a nickel, without replacement)
[tex]= \frac{55}{117} \times \frac{20}{116} \\\\= \frac{1100}{13572} \\\\=0.081[/tex]
Suppose A is the sum of the first 50 consecutive multiples of 3, and B is the sum of the first 50 consecutive multiples of 6. What percent of A is B ?
E. 50%
F. 75%
G. 100%
H. 200%
The correct answer is H. B is the 200% of A.
Since A is the sum of the first 50 multiples of 3, while B is the sum of the first 50 multiples of 6, to determine what percentage of A is B, the base numbers of both calculations must be considered, that is, 3 and 6. Thus, since 6 is 200% of 3 (6/3 = 2), B is 200% of A.
Learn more about percentages in https://brainly.com/question/18925632.
You need a 75% alcohol solution. On hand, you have a 60 mL of a 55% alcohol mixture. You also have 85% alcohol mixture. How much of the 85% mixture will you need to add to obtain the desired solution?
You will need_____ mL of the 85% solution
60 mL=55% alcohol
?mL=85% alcohol
85×60÷55
=92.727 mL
I think do like this....I'm not sure
Hope this help you
9514 1404 393
Answer:
120 mL
Step-by-step explanation:
Let x represent the amount of 85% solution needed. Then the total amount of alcohol in the mix is ...
0.55(60) +0.85(x) = 0.75(60 +x)
33 + 0.85x = 45 +0.75x . . . . . . . eliminate parentheses
0.85x = 12 +0.75x . . . . . . . . . .subtract 33
0.10x = 12 . . . . . . . . . . . . . . subtract 0.75x
x = 120 . . . . . . . . . . . . . . multiply by 10
You will need 120 mL of the 85% solution.
There are 36 tables and 7 booths in the family restaurant. Each table seats 4 people. If the restaurant can seat up to 179 people, what is the capacity of each booth?
4 people
5 people
6 people
7 people
Answer:
5 people.
Step-by-step explanation:
First we need to find how many people 36 tables seats. In order to do this, we need to multiply 36 (tables) by 4 (people sitting) to get 144. Now just subtract 144 from 179 to see how many people are left, here we get 35. Since there are 7 booths, we divide 35 by 7 to get 5. Each booth holds 5 people.
(179-36x4)/7=5
The doubling time for an investment is 7.5 yeas. Find an exponential model for the growth of your money. Then find how long will take your investment to grow by factor of 5(Assume that you make an investment P)
Answer:
The correct answer is "17.414 years".
Step-by-step explanation:
Given:
Doubling time,
= 7.5 years
As we know,
[tex]P(t) = P_oe^{rt}[/tex]
now,
⇒ [tex]2P_o=P_o e^{r\times 7.5}[/tex]
[tex]2 = e^{r\times 7.5}[/tex]
[tex]r = \frac{ln2}{7.5}[/tex]
[tex]=0.092[/tex]
[tex]=9.2[/tex]%
then,
⇒ [tex]P(t) = P_o e^{0.092 t}[/tex]
here,
[tex]P(t) = 5P_o[/tex]
hence,
⇒ [tex]5P_o = P_o e^{0.092 t}[/tex]
[tex]e^{0.092t}=5[/tex]
[tex]t = \frac{ln5}{0.092}[/tex]
[tex]=17.414 \ years[/tex]
Answer:
The correct answer is "17.414 years".
Step-by-step explanation:
A duck has 1,100 feathers. It went for a swim in a pond and lost 2/100 of its feathers. How many feathers did it lose?
Answer:
It lost 22 feathers.
Step-by-step explanation:
To complete this problem, this expression will be used: 2x/100.
2(1100)/100 {Multiply 2 by 1100}
2200/100 {Simplify by cancelling out 100}
22/1 {Divide}
22 feathers were lost.
The graph below displays a fire department’s response time, which measures the time from when the alarm is sounded at the firehouse to the time the first fire engine leaves the station.
A histogram titled Fire Department Response Times has response time (seconds) on the x-axis and relative frequency on the y-axis. 20 to 30, 0.07; 30 to 40, 0.08; 40 to 50, 0.2; 50 to 60, 0.32; 60 to 70, 0.18; 70 to 80, 0.13; 80 to 90, 0.04.
Which interval accounts for the lowest percentage of response times?
20–30 seconds
30–40 seconds
70–80 seconds
80–90 seconds
I think its (D), 80-90 seconds. Someone check me.
Answer:
I also think this is D.
Step-by-step explanation:
This question isn't asking for a lot of math so.
According to the graph, the 80-90 seconds response times are the shortest, meaning it is the least frequent or common.
Plus, it would be a bad thing if it was average anyways, and is outlined by the histogram.
Need help please ^-^
Factored form: (x + 1/5)(x + 1/4)
Foil: x^2 + 1/4x + 1/5x + 1/20
Simplify: x^2 + 9/20x + 1/20
Hope this helps!
Which phrase describes an unknown or changeable quality?
3 feet and 7 inches
4 quarts in a gallon
2 o'clock in the afternoon
The height of the building times 1/2
Answer:
it should be the height of the building time 1/2
Step-by-step explanation:
let me know if its correct or incorrect we'll I hope this help you
a store sells pencils pens and markers that sells two times as many markers as pencils and three times as many pens as pencils is the store sells a total of 1950 pencils and pens and markers in a week how many of each were sold
Answer:
325 pencils, 650 markers, 975 pens
Step-by-step explanation:
in picture.
Add .003, 265.8, 83.04
and 1972
2^17+2^14 chia hết cho 9
Step-by-step explanation:
không khó lắm đâu ._.._.._.
HELP ASAP! Can someone please help me with this problem. I tried inputting the numbers to find the mean but I did not get the right answer. Can someone please help me with the last box? Thank you for your time!
Answer:
try 17.6
Step-by-step explanation:
for the mean you have to add all the numbers then divide the sum by the total number of numbers you added
Assume the sample is a random sample from a distribution that is reasonably normally distributed and we are doing inference for a sample mean
(a) Find endpoints of a t-distribution with 5 % beyond them in each tail if the sample has size n = 12.
(b) Find endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20.
Answer:
a) Hence the endpoints of a t-distribution with 5% beyond them in each tail if the sample has size n=12 is ± 1.796.
b) Hence the endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20 is ± 2.539.
Step-by-step explanation:
Here the answer is given as follows,
A simple random sample of 41 men from a normally distributed population results in a standard deviation of 10.7 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts(a) through (d) below.
a. Identify the null and alternative hypotheses.
b. Compute the test statistic; χ2 = ___ (Round to three decimal places as needed.)
c. Find the P-value; P-value = ____ (Round to four decimal places as needed.)
d. State the conclusion. (choose one from each ( x, y) set)
(Do not reject, Reject) Upper H0, because the P-value is (greater than, less than, or equal to) the level of significance. There is
(sufficient, insufficient) evidence to warrant rejection of the claim that the standard deviation of men's pulse rates is equal to
10 beats per minute.
Answer:
H0 : σ²=10²
H1 : σ²>10²
χ² = 45.796
Pvalue = 0.2442
Do not reject H0 because Pvalue is greater Than significance level
There is insufficient evidence to warrant rejection of the claim that the standard deviation of men's pulse rates is equal to 10 beats per minute.
Step-by-step explanation:
Given that :
Sample size, n = 41
Sample standard deviation, s = 10.7
Population standard deviation, σ = 10
Significance level, α = 0.10
The Hypothesis :
H0 : σ²=10²
H1 : σ²>10²
Using the χ² test for population variance :
The test statistic, χ² = (n-1)*s²/σ²
χ² = (41 - 1) * 10.7²/ 10²
χ² = (40 * 114.49) / 100
χ² = 4579.6 / 100
χ² = 45.796
The Pvalue ;
df = n - 1 ; 41 - 1 = 40
Pvalue(45.796, 40) = 0.2442
Since Pvalue > α ; WE fail to reject H0
Do not reject H0 because Pvalue is greater Than significance level
There is insufficient evidence to warrant rejection of the claim that the standard deviation of men's pulse rates is equal to 10 beats per minute.
