The volume of the sphere is 3,052.08 cubic millimeters. The correct answer is A.
What is the volume of sphere?If the given sphere is of radius r units, then its volume is given as:
[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3[/tex]
A glass marble has a diameter of 18 millimeters.
The radius is 9
[tex]V= \dfrac{4}{3} (3.14) (9)^3 \: \rm unit^3\\\\V = 3,052.08 cubic millimeters[/tex]
The volume of the sphere is 3,052.08 cubic millimeters. The correct answer is A.
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Sofia's audio player has 15,000 songs. the play time for the songs is skewed to the right, with a mean of 255 seconds and a standard deviation of 30 seconds. part a: can you accurately calculate the probability that the mean play time is more than 260 seconds for an srs of 15 songs? explain. (4 points) part b: if you take a random sample of 40 songs instead of 15, explain how the central limit theorem allows you to find the probability that the mean play time is more than 260 seconds. calculate this probability and show your work. (6 points)
Using the normal distribution and the central limit theorem, it is found that:
a) Since the distribution is skewed and the sample size is less than 30, the probability cannot be calculated.
b) There is a 0.1469 = 14.69% probability that the mean play time is more than 260 seconds.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], as long as the underlying distribution is normal and the sample size is at least 30.The mean and the standard deviation are given by, respectively:
[tex]\mu = 255, \sigma = 30[/tex]
In item a, according to the Central Limit Theorem, since the distribution is skewed and the sample size is less than 30, the probability cannot be calculated.
For item b, we have that n = 40 > 15, hence the standard error is given by:
[tex]s = \frac{30}{\sqrt{40}} = 4.74[/tex]
The probability is one subtracted by the p-value of Z when X = 260, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{260 - 255}{4.74}[/tex]
Z = 1.05
Z = 1.05 has a p-value of 0.8531.
1 - 0.8531 = 0.1469.
There is a 0.1469 = 14.69% probability that the mean play time is more than 260 seconds.
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Two lines, A and B, are represented by the equations given below: Line A: y = x − 6 Line B: y = 3x + 4 Which of the following shows the solution to the system of equations and explains why? (1 point) a (−5, −11), because the point satisfies both equations b (−5, −11), because the point does not lie on any axis c (−3, −5), because the point satisfies one of the equations d (−3, −5), because the point lies between the two axes
The solution to the system of linear equations is: (−5, −11).
What is the Solution to the System of Linear Equations?The solution to a system is the x and y -coordinates that satisfies the two linear equations.
Given the linear equations:
Line A: y = x − 6
Line B: y = 3x + 4
Now, equating these two equations
x - 6 = 3x + 4
2x = -10
x = -5
y = -11
Hence, the solution is: (−5, −11), because the point satisfies both equations.
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What critical value of t* should be used for a 95% confidence interval for the population mean based upon a random sample of 20 observations
Using a calculator, the critical value of the t-distribution that should be used for a 95% confidence interval with 20 observations is of t* = 2.0930.
How to find the critical value of the t-distribution?A calculator is used, with two inputs:
The confidence level.The number of degrees of freedom, which is one less than the sample size.In this problem, we have a 95% confidence interval, with 20 - 1 = 19 df, hence the critical value is of t* = 2.0930.
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#24. you and your friends go to the county fair the cost to get in is $8 and the tickets per game to my cost $0.25 each. Write an equation to create a table of reasonable values and identify the domain and range for the scenario.
The equation of the scenario is y = 8 + 0.25x and the domain is x ≥ 0 and the range is y ≥ 8
How to determine the equation?The given parameters are:
Entrance fee = $8Rate = $0.25 per personLet the total cost be y, and the number of people be x.
The equation would be:
y = Entrance + Rate * x
This gives
y = 8 + 0.25x
Hence, the equation of the scenario is y = 8 + 0.25x
The table of valuesSet x = 0 to 5, and calculate the function values
y = 8 + 0.25 * 0 = 8
y = 8 + 0.25 * 1 = 8.25
y = 8 + 0.25 * 2 = 8.50
y = 8 + 0.25 * 3 = 8.75
y = 8 + 0.25 * 4 = 9.00
y = 8 + 0.25 * 5 = 9.25
So, the table of values is:
x y
0 8
1 8.25
2 8.50
3 8.75
4 9.00
5 9.25
The domain and the rangeThe domain is the set of people that can get in (i.e. at least 0), while the range is the total amount (i.e. at least the entrance fee)
Hence, the domain is x ≥ 0 and the range is y ≥ 8
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geometry please help!
Answer:
x = 3
Step-by-step explanation:
Angle S and Angle T are consecutive interior angles. Therefore, we know that T + S = 180°.
First, we need to solve for T, and since angles S and T are consecutive interior angles, we know that T + S = 180°. If we reorganize the equation to include the things we know (S = 105°), then we get 180° - 105° = 75°. So T is 75°.
Now, we use T = 75° and the information given to us in the picture to set up an equation. 75 = 24x + 3. Now, we can find x by isolating it. Do this by:
1) Subtracting 3 from both sides to give you 72 = 24x. We do this to get rid of the 3 from the "x side", but we must also do it to the other to keep the equation true. This moves the 3 from the "x side" to the other since we're trying to isolate x.
2) Divide 24 by both sides to get 3 = x. We use the same logic as we did for 3, except this time we divide since that's the opposite of multiplying.
In conclusion, x = 3.
PLEASE HELP!!! 50 POINTS!!!
Answer:
Part A:
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
Part B:Simply put, coterminal angles start at 0° and end at the same place, though in different directions and multiple times around (you're probably going to want to make that sound a little more formal). Since each time around is 360°, boom
Part C: 75° is in Quadrant II, right? If I go one more time around, 75 + 360 = 435°. I can also go "backward. Starting at 0 and going clockwise, I'm going 75 fewer degrees than all the way around, so 360-75 = 285° but since I'm going "backward" 75 - 360 = -285°. One more is on you.
Step-by-step explanation:
The graph of the function f (x) = StartFraction 3 Over x + 5 EndFraction is shown below.
On a coordinate plane, a hyperbola is shown. Both curves approach x = negative 5.
What is the vertical asymptote of the function?
Using it's concept, it is found that the vertical asymptote of the function [tex]f(x) = \frac{3}{x+5}[/tex] is of x = -5.
What are the vertical asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
In this problem, the function is fraction given by:
[tex]f(x) = \frac{3}{x + 5}[/tex]
At the denominator, we have that:
x + 5 = 0 -> x = -5
Hence the vertical asymptote of the function [tex]f(x) = \frac{3}{x+5}[/tex] is of x = -5.
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Answer: A) x= -5
Took the test and got 100% :)
so i have 56 8 year old kids in my basement and i auction off 25 of them how many kids do i have left?
Answer:
none because i boiled them all
Step-by-step explanation:
Answer:
31 kids
Step-by-step explanation:
56-25=31
The sum of the lengths of any two sides of a triangle is greater than the length of the third side. What can you conclude about AC in ABC?
BC + AC = 22; AB + BC = 12
Answer:
ab<6 units
Step-by-step explanation:
One of the basic property of any triangle is that the sum of the length of any two sides of a triangle is always greater than the length of the third side. Here we are given a triangle abc, in whicn bc=4ac= 8-abIf have to make some conclusion about ab.As per the property discussed above ab<ac+bcab<8-ab+42ab<12ab<6Hence the length of ab must be less than 6 units
Martin wants to use coordinate geometry to prove that the opposite sides of
a rectangle are congruent. He places parallelogram ABCD in the coordinate
plane so that A is (0, 0), B is (a,0), C is (a, b), and D is (0, b).
What formula can he use to determine the distance from point D to point A?
A. 0-0)2+(b-0)² = √√b² = b
B. (a-a)2+(b-0)² = 6²
C. (0-0)² + (b-0)² = 6²
OD. √(-a)2+(b-0)²-√√b² = b
The correct answer is option A which is the distance between A and D will be AD = [tex]\sqrt{(0-0)^2-(b-0)^2}=\sqrt{b^2}=b[/tex].
What is coordinate geometry?A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
The formula utilised to find the distance between two points is;-
X = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
We have the coordinates of the point A = (0, 0) and D is (0, b).By applying the formula to find the distance between A and D.
AD = [tex]\sqrt{(0-0)^2-(b-0)^2}=\sqrt{b^2}=b[/tex].
Therefore the correct answer is option A which is the distance between A and D will be AD = [tex]\sqrt{(0-0)^2-(b-0)^2}=\sqrt{b^2}=b[/tex].
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The probability that Janet will win the marathon is 44%. What is the probability that Janet will not win the marathon? Write the probability as a percent and include the percent symbol.
Answer:
56%
Step-by-step explanation:
If the percentage that she wont win is 44% she still has a 64 percent chance of winning
Find a fraction equivalent to 5/7 whose squared terms add up to 1184.
The system of equations of two unknowns is formulated and solved.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ \ \ \dfrac{x}{y} = \dfrac{5}{7} \\ x^2+y^2 = 1184 \end{matrix}\right. \ \Longrightarrow \ x=\dfrac{5}{7}y } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left (\dfrac{5}{7}y \right )^2+y^2=1184\ \Longrightarrow\ 25y^2+49y^2=58016 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{74y^{2}=58016} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ \ y^{2}=784 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ y=\pm\sqrt{784}=\pm28 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x=\dfrac{5}{7}(\pm 28)=\pm 20 } \end{gathered}$}[/tex]
The fraction that satisfies the request is [tex]\bf{\dfrac{20}{28}}[/tex] , since in [tex]\bf{\dfrac{-20}{-28}}[/tex] the negative signs are canceled and the first fraction is obtained.
A biologist hypothesizes that the mean life expectancy of a mosquito is 14 days. Researchers believe the true mean is less than 14 days and they plan a hypothesis test at the 5% significance level on a random sample of 60 of these mosquitos. If the alternative hypothesis is correct, for which of the following values of μ is the power of the test greatest?
μ = 9
μ = 7
μ = 10
μ = 14
μ = 18
Based on the alternative hypothesis, the value of μ that will have the greatest test power is μ = 7.
Which value of μ will have the greatest power of test?The alternative hypothesis is that Hₐ : μ < 14.
For the alternative hypothesis to be right, μ will have to be less than 1.4.
μ will also give a greater test power the lower it is below 14. From the options therefore, μ with the greatest test power would be 7.
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Answer:
μ = 7
Step-by-step explanation:
Got this right on the segment exam. Good luck, my FLVS fellows!
If 0.15% of budget is spent on office supplies, what decimal should you multiply budget
Answer:
0.015
Step-by-step explanation:
0.15% = 0.0015
{transfer}
the average wieght of three children a b and c is 60 lbs if another child D is included in the grouo in the place of C the average weight of the group becomes 54 lb what is
The weight of the last child is 36 lbs.
How to calculate the mean?The average weight of the three children is 60 lbs. The total weight will be:
= 60 × 3
= 180 lbs.
When another child is added, the weight is 54lb. The total weight will be:
= 54 × 4
= 216 lbs
The weight of the last child will be:
= 216 - 180
= 36 lbs.
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A car used of a gallon of gas to drive of a mile. At this rate, how many miles
can the car travel using 1 gallon of gas?
The equation in Question 4 shows a relationship between the length of arc EF in circle AB and the radius of circle AB. So, for a given central angle, what does the length of the arc it intersects depend on?
For a given central angle, the length of the arc it intersects depends on the radius of the circle and the central angle.
What is the Length of an Arc?Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,
Length of an Arc = 2π×R×(θ°/360°)
where
θ is the angle, that which arc creates at the center of the circle in degree.
The measurement of the length of an arc formed by a central angle that intersects the circle at two points is given as,
[tex]\rm {Length\ of\ the\ arc} = 2\pi \times \text{Radius of the circle}\times \dfrac{\text{(Measurement of central angle)}}{360^o}[/tex]
Now, the length of the arc EF will be,
Arc EF = 2π × (AB) × (θ/360°)
Where θ is the measurement of the central angle.
Hence, For a given central angle, the length of the arc it intersects depends on the radius of the circle and the central angle.
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Answer: Plato/edmentum sample answer
Step-by-step explanation:
For a given central angle, the length of the arc it intersects depends only on the radius of the associated circle.
The NUK Energy Company is designing a new logo, as shown in the accompanying
diagram, with mNK-130 and mNK-m.NU.
N
K
What is the measure of ZKNU?
1) 80°
2) 65°
3) 50°
4) 100°
U
The measure of the angle KNU (∠KNU) of the cyclic quadrilateral is; Option 3: 50°
How to find the angle in a quadrilateral?
From the attached cyclic quadrilateral of NUK Energy Company's new logo, we can say that equal angles intercept equal arcs and as such, the measure of angle KNU will be;
∠KNU 1/2 * 100 = 50°
This is because If two inscribed angles of a circle intercept the same arc or arcs of equal measure, then the inscribed angles have equal measure.
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7x+8y=-18
-5+y=-14
system by substitution ^
Answer:
y=5+14=19
Step-by-step explanation:
Y=5+14=19 this is the right answers
plss help, ill give brainiest
Answer:
A
Step-by-step explanation:
Cylinder volume= V = π r ^2 h
So you times Pie by the radius (diametre divided by two- 3.5) you then square this. After that, times it by the height (10)
So the volume is 384.85.
You then find 30% of this, so times 384.85 by 30%.
You then get an answer of 115.455, and this is equal to A.
I hope this helps, have a lovely day.
If ab = 10 ft, ac = 14 ft, and bc = 20 ft, what is rs? 10 ft 14 ft 20 ft 24 ft
The side |rs| is congruent to side |ac| which is 14 ft.
What are congruent triangles?Congruent triangles are two similar triangles that have corresponding sides and angles and they are of equal measure.
The figures from the textbook illustrate that following rotation, the two triangles are congruent.
This signifies that the angles and sides of the first triangle are equal to the angles and sides of the other triangle.
Therefore:
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A craftsperson must attach a lead strip around all four sides of a stained glass window that is
6 4/5 in. by
15 14/25 in. before it is installed. find the length of lead stripping needed.
Answer: 37.9 inch the length of lead stripping .
Step-by-step explanation:
Given ,
Sides of windows are [tex]6\frac{4}{5}[/tex] and [tex]15\frac{14}{25}[/tex]
[tex]= (6\frac{4}{5} + 15 \frac{14}{25} ) * 2\\ \\=\frac{34}{5} + \frac{389}{25} * 2\\\\ \frac{170}{25} + \frac{389}{25}* 2 \\\\= \frac{559}{25} * 2\\\\= \frac{948}{25} \\\\= 37.9 inch[/tex]
So , the answer is 37.9 inch
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If ten rolls of tape cost $30, how much will 12 rolls cost?
Answer:
Step-by-step explanation:
10 rolls = $30
12 rolls = ...
Because $3 for each roll of tape, so 3 x 10 = 30. All we have to do is multiply 3 by 12 to get how much for 12 rolls.
36.
Given that p(x) = 2(x - 12)2 + 5, what is the value p(3)
Answer:
p(3) = 25
Step-by-step explanation:
p(3) = 2(3 - 12)2+5
p(3) = 6 - 24 + 2 + 5
p(3) = 25
what is pi times squared
Answe
Step-by-step explanation:
cuanto es 3,072 en fraccion ?
Can I get help with this pls
Answer:
2 [tex]\leq[/tex] x [tex]\leq[/tex] 7
Step-by-step explanation:
See attachment.
GRADE 11 MATH
PLEASE HELP!
Nelson received $10,000 on his 17th birthday. This is the accumulated amount of an
investment his parents made on the day he was born. The investment earned 9.5%/a,
compounded semi-annually.
a) Determine the amount that Danny’s parents invested 17 years ago. [3 marks]
b) How much interest did the investment earn? [1 mark]
The amount that was invested 17 years ago is $2064.25.
The interest earned is $7935.75.
What is the amount invested 17 years ago?The formula that would used to determine the amount that was invested 17 years ago is:
P = FV / (1 + r)^nm
Where:
FV = Future value = 10,000P = Present value R = interest rate = 9.5 / 2 = 4.75%m = number of compounding = 2 N = number of years = 1710,000 / (1.0475)^(17 x 2) = $2064.25
Interest earned = 10,000 - 2064.25 = $7935.75
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Later on in this module, you will learn how to model events by writing trigonometric functions. for now, do some research on events that are cyclical or periodic. write a discussion post about one of those events. be sure to describe the event and the period.
The events that are cyclical are:
The change of seasons each yearEarth Rotation.Moon Phases.Tides.The events that are periodic are:
Pendulum OscillationSimple harmonic motionstuning fork,, etc.What are Cyclical events?Cyclical events are known to be event that occurs in a specific order e.g. Changes in the economy.
The Events that take place only after a regular interval of time are known to be periodic event.
Therefore, the events that are cyclical are:
The change of seasons each yearEarth Rotation.Moon Phases.Tides.The events that are periodic are:
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When written in factored form, 4w² -11w-3 is equivalent to
When written in factored form, 4w² -11w-3 is equivalent to (4w+1)(w−3).
What is the factored form of an expression?When an expression is written as a result of the multiplication of some terms, then that multiplication form is called the factored form of that expression.
Example: 6 = 3 x 2 is a factored way of writing 6.
Given expression as
4w² -11w-3
4w²- 12 w− 1w − 3
(4w+1)(w−3)
Thus, the factored form of 4w² -11w-3 is (4w+1)(w−3).
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As the sample size increases, the margin of error _____.
The margin of error is inversely proportional to the sample size. As the sample size increases, the margin of error decreases.
What is the margin of error?The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.
The margin of error is given as
[tex]\rm ME = z\times \sqrt{\dfrac{p(1-p)}{n}}[/tex]
We know that margin of error is inversely proportional to the sample size.
As the sample size increases, the margin of error decreases.
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