The expected value of a normal distribution is the mean of the distribution, while the variance measures the squared deviation of a value from the expected value. The expected value and the variance are: [tex]13.6190 \times 10^{-5}[/tex] and [tex]580.8000 \times 10^{-9}[/tex]
Given that, the diameters are:
[tex]d_1 = 0.02[/tex]
[tex]d_2 = 0.08[/tex]
The radius is:
[tex]r = \frac{d}{2}[/tex]
So, we have:
[tex]r_1 = \frac{0.02}{2} = 0.01[/tex]
[tex]r_2 = \frac{0.08}{2} = 0.04[/tex]
The volume of the sphere is:
[tex]V = \frac{4}{3} \times \pi \times r^3[/tex]
For [tex]r_1 = 0.01[/tex], the volume is:
[tex]V_1 = \frac{4}{3} \times \frac{22}{7} \times 0.01^3 = 0.419047 \times 10^{-5}[/tex]
For [tex]r_2 = 0.04[/tex], the volume is
[tex]V_2 = \frac{4}{3} \times \frac{22}{7} \times 0.04^3 = 26.819047 \times 10^{-5}[/tex]
The mean of a uniform distribution is:
[tex]E(y) = \frac{a + b}{2}[/tex]
In this case, the mean is:
[tex]E(y) = \frac{V_1 + V_2}{2}[/tex]
So, we have:
[tex]E(y) = \frac{0.419047 \times 10^{-5} + 26.819047 \times 10^{-5}}{2}[/tex]
[tex]E(y) = \frac{27.238094\times 10^{-5} }{2}[/tex]
[tex]E(y) = 13.619047 \times 10^{-5}[/tex]
Approximate
[tex]E(y) = 13.6190 \times 10^{-5}[/tex]
The variance of a uniform distribution is:
[tex]V(y) = \frac{(b-a)^2}{12}[/tex]
In this case, the volume is:
[tex]V(y) = \frac{(V_2-V_1)^2}{12}[/tex]
So, we have:
[tex]V(y) = \frac{(26.819047 \times 10^{-5}- 0.419047 \times 10^{-5})^2}{12}[/tex]
[tex]V(y) = \frac{(26.4 \times 10^{-5})^2}{12}[/tex]
[tex]V(y) = \frac{(696.96 \times 10^{-10})}{12}[/tex]
[tex]V(y) = 58.08000 \times 10^{-10}[/tex]
Rewrite as:
[tex]V(y) = 580.8000 \times 10^{-9}[/tex]
Hence, the expected value and the variance of the sphere are:[tex]13.6190 \times 10^{-5}[/tex] and [tex]580.8000 \times 10^{-9}[/tex]
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Which is a graph of g(c) = (0.5)x+3^ -4
Answer:
I've attached a graph with this, that's your answer
Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a 95% confidence interval for the mean height of male Swedes. Forty-eight mile Swedes are surveyed. The sample mean is 71 inches. The sample standard deviation is 2.8 inches.
Required:
a. Calculate the error bound.
b. What will happen to the level of confidence obtained if 1,000 male Swedes are surveyed instead of 48? Why?
Answer:
a) The error bound of the confidence interval is of 0.66.
b) The confidence interval will be narrower.
Step-by-step explanation:
Question a:
We have to find the margin of error. Considering that we have the standard deviation for the sample, the t-distribution is used.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 71 - 1 = 70
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 70 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.9944
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
For this problem, [tex]s = 2.8, n = 71[/tex]. So
[tex]M = T\frac{s}{\sqrt{n}} = 1.9944\frac{2.8}{\sqrt{71}} = 0.66[/tex]
The error bound of the confidence interval is of 0.66.
b. What will happen to the level of confidence obtained if 1,000 male Swedes are surveyed instead of 48? Why?
The margin of error is inversely proportional to the square root of the sample size, so increasing the sample size leads to a smaller margin of error and a narrower confidence interval.
A simple random sample of 400 individuals provides 112 Yes responses. (a) What is the point estimate of the proportion of the population that would provide Yes responses
Answer:
The point estimate of the proportion of the population that would provide Yes responses is 0.28.
Step-by-step explanation:
Point estimate of the proportion of the population that would provide Yes
The sample proportion of yes responses.
In the sample:
112 yes responses in the sample of 400, so:
[tex]p = \frac{112}{400} = 0.28[/tex]
The point estimate of the proportion of the population that would provide Yes responses is 0.28.
Please help will give brainliest
Complete the equation describing how
x and y are related.
ws
х
-2
-1
0
1
2
3
y
-4
-4.5
-5
-5.5
-6
-6.5
y = [? ]x + [ ]
Enter the answer that belongs in [?].
the answer is 6.5
Step-by-step explanation:
3) Consider the sequence -11 ; 2sin3x ; 15; ...
3.1.1) Determine the values of x in the interval [0 ; 90] for whichthe sequence will be arithmetic.
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Answer:
x = 30
Step-by-step explanation:
In an arithmetic sequence, any given term is the average of the two terms that come before and after. The middle term of this sequence must be ...
2sin(3x) = (-11 +15)/2
sin(3x) = 1 . . . . . . . . . . simplify and divide by 2
Then the value of 3x must be 90°, so ...
x = 90/3 = 30
There is one value of x in the interval [0, 90] that makes this sequence arithmetic: x = 30.
Solve the system.
x-y =-1
x+z=-5
y-z=2
Answer:
x= -2
y= -1
z= -3
Step-by-step explanation:
x-y= -1 (1)
x+z= -5 (2)
y-z= 2 (3)
(1)+(3)==> x-z= 1 (4)
(4)+(2)==> 2x= -4 ==> x= -2
we replace x by its value in equation (2):
-2+z= -5 ==> z= -3
we replace z by its value in equation (3):
y-(-3)= 2 ==> y+3=2 ==> y= -1
A population is equally divided into three class of drivers. The number of accidents per individual driver is Poisson for all drivers. For a driver of Class I, the expected number of accidents is uniformly distributed over [0.2, 1.0]. For a driver of Class II, the expected number of accidents is uniformly distributed over [0.4, 2.0]. For a driver of Class III, the expected number of accidents is uniformly distributed over [0.6, 3.0]. For driver randomly selected from this population, determine the probability of zero accidents.
Answer:
Following are the solution to the given points:
Step-by-step explanation:
As a result, Poisson for each driver seems to be the number of accidents.
Let X be the random vector indicating accident frequency.
Let, [tex]\lambda=[/tex]Expected accident frequency
[tex]P(X=0) = e^{-\lambda}[/tex]
For class 1:
[tex]P(X=0) = \frac{1}{(1-0.2)} \int_{0.2}^{1} e^{-\lambda} d\lambda \\\\P(X=0) = \frac{1}{0.8} \times [-e^{-1}-(-e^{-0.2})] = 0.56356[/tex]
For class 2:
[tex]P(X=0) = \frac{1}{(2-0.4)} \int_{0.4}^{2} e^{-\lambda} d\lambda\\\\P(X=0) = \frac{1}{1.6} \times [-e^{-2}-(-e^{-0.4})] = 0.33437[/tex]
For class 3:
[tex]P(X=0) = \frac{1}{(3-0.6)} \int_{0.6}^{3} e^{-\lambda} d\lambda\\\\P(X=0) = \frac{1}{2.4} \times [-e^{-3}-(-e^{-0.6})] = 0.20793[/tex]
The population is equally divided into three classes of drivers.
Hence, the Probability
[tex]\to P(X=0) = \frac{1}{3} \times 0.56356+\frac{1}{3} \times 0.33437+\frac{1}{3} \times 0.20793=0.36862[/tex]
Which of the following is a solution to 6x - 5y=4?
(2,7)
(-1, -2)
(-2, -1)
(2, -7)
Answer:
2,7
Step-by-step explanation:
Answer:
(-1,-2)
Step-by-step explanation:
(6 x -1) -(-2 x 5) = 4
-6 + 10 = 4
Find the measure of angle FGE
35 degrees
40 degrees
100 degrees
30 degrees
60 degrees
The measure of angle FGE is 52.5°.
What is the Angles of Intersecting Secants Theorem?Angles of Intersecting Secants Theorem states that, If two lines intersect outside a circle, then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs.
Thus, applying the angles of intersecting secants theorem
m∠FGE = 1/2[(100 + 35) - 30]
m∠FGE = 1/2[(105]
m∠FGE = 52.5°
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The scatterplot shows the selling prices of homes and the square feet of living space.
A graph titled home value has square feet (thousands) on the x-axis, and price (hundred thousand dollars) on the y-axis. Points are at (1.2, 1), (1.5, 1.1), (2, 1.5), (2.5, 2). An orange point is at (3.8, 3.9).
Complete the statements based on the information provided.
The scatterplot including only the blue data points shows
✔ a strong positive
correlation. Including the orange data point at (3.8, 3.9) in the correlation would
✔ strengthen
and
✔ increase
the value of
Answer:
✔ a strong positive
✔ strengthen
✔ increase
ED2021
Answer:
- a strong positive
- strengthen
- increase
PLS HELP
If f(x) = x2 -1, what is the equation for f–1(x)?
We have a function,
[tex]f(x)=x^2-1[/tex]
and we are asked to find its inverse function.
An inverse function essentially gets you the original value that was dropped into a function.
For example,
If I put 5 into [tex]f(x)[/tex] I will get 24. Now If I take 24 and put it into the inverse function I have to get number 5 back.
The way to determine the inverse function swap the x and the [tex]f(x)[/tex], then solve for [tex]f(x)[/tex],
[tex]x=f(x)^2-1[/tex]
[tex]f(x)^2=x+1[/tex]
[tex]f(x)=\pm\sqrt{x+1}[/tex]
Of course the notation demands that the obtained function be called,
[tex]f^{-1}(x)=\pm\sqrt{x+1}[/tex]
Hope this helps :)
A local cinema reduced its ticket prices by 15% which means a ticket now costs £10.88. how much was a ticket before the reduction?
The whole number 23 is an example of a ____ number.
prime or composite?
The answer is prime! I hope this helps you out!
Answer:
23 is a prime number. Reason: Prime number are those numbers which are divisible by 1 and itself. Example: 5 is divisible by 1 and 5 only.
A 90% confidence interval is (35 45). What is the margin of error?
A.5
B.4.5
C.9
D.10
Answer:
option a 5......
...
I hope it's correct
Given the function h(t) = 2t to the power of 2 + 9 evaluate h(5)
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Answer:
59
Step-by-step explanation:
Put 5 where t is and do the arithmetic.
[tex]h(t)=2t^2+9\\\\h(5)=2\cdot5^2+9=2\cdot25+9\\\\\boxed{h(5)=59}[/tex]
Using the order of operations, what is the last calculation that should be done to evaluate 4(8 - 6952 - 6+(-3)
4(8 - 6352 – 6 + (-3)
4(2)52 - 6+(-3)
4(2)(25) - 6+(-3)
200 - 6+(-3)
200 - (-2)
Answer:
200 + 2
Step-by-step explanation:
you know that two (2) negatives multiplying each other is = +
=200 +2
=202
PLEASEEEE PLEASEEEE HELPPPP
i need an equation for a vertical line going through f(x) = 2x^2 + 6x + 2
Answer:
dont understand clearly
Step-by-step explanation:
dont understand clearly
Given h(x) = -x + 1, find h(0).
Answer:
Answer:
1
Step-by-step explanation:
Given,
h ( x ) = - x + 1
To find : h ( 0 ) = ?
h ( 0 )
= - ( 0 ) + 1
= 1
Answer: 1
Step-by-step explanation:
h(x) = -x + 1
To Find = h(0)
= -(0) + 1
= 1
Answered by GauthMath if you like pls heart it and comment thanks
Can someone help please
Answer: it should be A
Step-by-step explanation:
Rabi Sahu fixed the marked price of his radio to make a profit of 30 %. Allowing 15 % discount on the marked price, the radio was sold. What percent profit did he make?
The percent profit that Rabi made will be 10.5%
Let's assume that the price of the house is $100.
Since he fixed the marked price of the good to make a profit of 30%, then the price will be:
= $100 + (30% × $100)
= $100 + $30
= $130
Now, there is a discount of 15%, then the selling price of the good will be:
= $130 - (15% × $130)
= $130 - (0.15 × $130)
= $130 - $19.50
= $110.50
Then, the percentage of profit made will be:
= [($110.50 - $100) / $100] × 100%
= $10.50/$100 × 100%
= 10.5%
In conclusion, the percent profit that he makes is 10.5%.
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helpppp asap pleaseee
Answer:
29/3 is your answer
Step-by-step explanation:
pls mark as brainliest
A cricket bat is bought for $330. Later, it is sold with a loss of 15%.
How much is the oricket bat sold for?
After selling the cricket bat, how much money has been last?
Give your answer to two decimal places because it is a currency.
Answers:
Discount price = 280.50 dollarsAmount lost = 49.50 dollars================================================
Explanation:
If it's sold at a loss of 15%, then the store owner loses 0.15*330 = 49.50 dollars
So it was sold for 330- 49.50 = 280.50 dollars
----------------------------
An alternative method:
If the store owner loses 15%, then they keep the remaining 85% since 15%+85% = 100%.
85% of 330 = 280.50 dollars is the discount price
This means 330-280.50 = 49.50 dollars is the amount lost.
Find the value of x
A. 15
B. 6
C. 60
D. 10
Answer:
hmm observe the diagram carefully there are 2 arcs drawn which means angle BEC and angle KEC are equal so
6x + 24 = 10x
4x = 24
x = 6
BRAINLIEST PLS
The value of x in the given figure is 6.
Used the concept of an angle of the figure,
An angle is a combination of two rays (half-lines) with a common endpoint.
Given that,
A figure with two congruent triangles is shown in the figure.
Now by definition of congruency of triangles,
∠ BEC = ∠ CEK
Substitute given values,
[tex]6x + 24 = 10x[/tex]
Solve for x,
[tex]24 = 10x - 6x[/tex]
[tex]24 = 4x[/tex]
Divide both sides by 4;
[tex]x = 6[/tex]
Therefore, the value of x is 6.
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Lament has a jar containing 6 red chips, 10 blue chips, and 4 yellow chips. If he removes one chip at random, what is the probability that it will not be red?
The probability of not getting red is 7/10
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given
Your bowl has 20 chips. (4+10+6).
6 of them are red. 6/20 = 3/10
so the odds of getting a red chip are 3/10 ,
meaning the odds against getting red are 1-(3/10) = 7/10
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Determine a scalar c so that the angle between a = i + cj and b = i + j is 45°.
Answer:
c=0
Step-by-step explanation:
ATQ a.b=|a||b|sin(45)
1+c=sqrt(1+c^2)*sqrt(2)*1/sqrt(2)
1+c=sqrt(1+c^2)
(1+c)^2=(1+c^2)
2c=0, c=0
The required simplified value of c is zero for which the angle between a and b is 45°.
What is a vector?Vector is defined as the quantities that have both magnitude and direction are called a vector quantity and the nature of the quantity is called a vector.
Here,
scaler product is given as,
a . b = |a|.|b|cos45
(i + cj). (i + j) = √[1² + c²] . √[1²+1²] × 1/√2
1 + c = √1 + c²
Squaring both sides
(1 + c)² = 1 + c²
1 + c² + 2c =1 + c²
2c = 0
c = 0
Thus, the required simplified value of c is zero for which the angle between a and b is 45°.
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Ivan drove 335 miles in 5 hours.
At the same rate, how long would it take him to drive 737 miles?
hours
Х
?
Answer: x= 11
Step-by-step explanation:
To answer the question, we first need to know how many miles he/she/it can drive in one hour (to make it simpler. Doing a bunch of calculations involving decimals and other stuff can be very confusing)
335 divided by 5 is 67
Therefore in one hour Ivan can drive 67 miles. We want to know the TIME it takes for Ivan to drive 737 miles and the formula for time is Distance / Speed.
The distance is 737 miles
The speed is 67 miles/hour
737 divided by 67 is 11
Therefore Ivan takes 11 hours to drive 737 hours
Bearings And Vectors • The bearing of X from Y is 045 and the bearing of Z from Yis 145, where X, Y and Z are three points in the plane. If Y is equidistant from X and Z, find the bearing of Z from X.
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Answer:
185°
Step-by-step explanation:
The triangle internal angle at Y is 145° -45° = 100°. Since the triangle is isosceles, the internal angles at X and Z are both (180° -100°)/2 = 40°. Then the bearing of Z from X is the bearing of Y from X less the internal angle at X:
(45° +180°) -40° = 185°.
Z from X is 185°.
Help me please with this question
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Answer:
21
Step-by-step explanation:
Let c represent the number of child tickets sold. Then 2c is the number of adult tickets sold. The total revenue is ...
5.80c +9.50(2c) = 520.80
24.80c = 520.80 . . . . . . . . . simplify
c = 21 . . . . . . . . . . . . . . divide by 24.80
21 child tickets were sold that day.
56 x 10^-4)
Group of answer choices
2.37 x 10^-16
4.21 x 10^15
2.4 x 10^-16
4.2 x 10^15
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Answer:
(d) 4.2×10^15
Step-by-step explanation:
Your calculator will tell you the quotient is about ...
4.21348...×10^15
The least precise number in the division is 1.5, which has 2 significant digits. Therefore, the result should be rounded to 2 significant digits:
4.2×10^15
In the figure, find the measure of TU⎯⎯⎯⎯⎯⎯⎯⎯
Answer:
TU = 27
Step-by-step explanation:
We are given two secant segments that are drawn from a circle to meet at an exterior point of the circle. Thus, according to the secant secant theorem, the product of the measure of one secant segment and its external secant segment equals that of the product of the other and its external secant segment.
Thus:
VU*TU = VW*BW
Substitute
7(x + 4) = 9(-2 + x)
7x + 28 = -18 + 9x
Collect like terms
7x - 9x = -18 - 28
-2x = -46
Divide both sides by -2
x = -46/-2
x = 23
✔️TU = x + 4
Plug in the value of x
TU = 23 + 4
TU = 27
