The volume is given by the integral,
[tex]\displaystyle\int_0^{2\pi}\int_0^{\cos^{-1}((\sqrt{65}-1)/8)}\int_0^4\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta[/tex]
That is, [tex]\rho[/tex] ranges from the origin to the sphere of radius 4. The range for [tex]\varphi[/tex] starts at the intersection of the cone [tex]z=x^2+y^2[/tex] with the sphere [tex]x^2+y^2+z^2=16[/tex], which gives
[tex]z+z^2=16\implies z^2+z-16=0\implies z=\dfrac{\sqrt{65}-1}2[/tex]
and
[tex]z=4\cos\varphi\implies\varphi=\cos^{-1}\left(\dfrac{\sqrt{65}-1}8\right)[/tex]
and extends to the x-y plane where [tex]\varphi=\frac\pi2[/tex]. The range for [tex]\theta[/tex] is self-evident.
The volume is then
[tex]V=\displaystyle\int_0^{2\pi}\int_0^{\cos^{-1}((\sqrt{65}-1)/8)}\int_0^4\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta[/tex]
[tex]V=\displaystyle\left(\int_0^{2\pi}\mathrm d\theta\right)\left(\int_0^{\cos^{-1}((\sqrt{65}-1)/8)}\sin\varphi\,\mathrm d\varphi\right)\left(\int_0^4\rho^2\,\mathrm d\rho\right)[/tex]
[tex]V=2\pi\left(\dfrac{\sqrt{65}-1}8\right)\left(\dfrac{64}3\right)=\boxed{\dfrac{16\pi(9-\sqrt{65})}3}[/tex]
A sphere is a three-dimensional object with a round form. The volume of the sphere is [16π(9-√65)]/3 unit³.
What is a sphere?A sphere is a three-dimensional object with a round form. A sphere, unlike other three-dimensional shapes, has no vertices or edges. Its centre is equidistant from all places on its surface. In other words, the distance between the sphere's centre and any point on its surface is the same.
We know that the volume of the given sphere can be given by the integral,
[tex]{\rm Volume} = \int^{2\pi}_0\int^{cos^{-1}(\frac{\sqrt{65}-1}{8})} \int_0^4\rho^2sin\varphi\ d\rho\ d\varphi\ d\theta[/tex]
where ρ ranges from the origin of the plot to the sphere of radius 4 while the range of φ starts at the intersection of the cone z=x²+y² with the sphere x²+y²+z²=16.
Now, the value of z and φ can be written as,
[tex]x^2+y^2+z^2 = 16\\\\(x^2+y^2)+z^2 = 16\\\\z+z^2 = 16\\\\z^2+z-16=0 \implies z=\dfrac{\sqrt{65}-1}{2}[/tex]
And
[tex]z =4\ cos\ \varphi \implies \varphi =cos^{-1}(\dfrac{\sqrt{65}-1}{8})[/tex]
Further, the volume of the sphere can be written as,
[tex]{\rm Volume} = \int^{2\pi}_0\int^{cos^{-1}(\frac{\sqrt{65}-1}{8})} \int_0^4\rho^2sin\varphi\ d\rho\ d\varphi\ d\theta\\\\\\{\rm Volume} = (\int^{2\pi}_0\ d\theta)(\int^{cos^{-1}(\frac{\sqrt{65}-1}{8})} sin\varphi\ d\varphi)(\int_0^4\rho^2 d\rho)\\\\\\V = 2\pi(\dfrac{\sqrt{65}-1}{8})(\dfrac{64}{3}) = \dfrac{16\pi(9-\sqrt{65})}{3}[/tex]
Hence, the volume of the sphere is [tex]\dfrac{16\pi(9-\sqrt{65})}{3}[/tex].
Learn more about Sphere:
https://brainly.com/question/11374994
1. The following are the number of hours that 10 police officers have spent being trained in how to handle encounters with people who are mentally ill:
4 17 12 9 6 10 1 5 9 3
Calculate the (a) range, (b) inter-quartile range, (c) variance, and (d) standard deviation.
(Use N)
Answer:
[tex]Range = 16[/tex]
[tex]Inter\ Quartile\ Range = 6.75[/tex]
[tex]Variance = 20.44[/tex]
[tex]Standard\ Deviation = 4.52[/tex]
Step-by-step explanation:
Given
4, 17, 12, 9, 6, 10, 1, 5, 9, 3
Calculating the range;
[tex]Range = Highest - Lowest[/tex]
From the given data;
Highest = 17 and Lowest = 1
Hence;
[tex]Range = 17 - 1[/tex]
[tex]Range = 16[/tex]
Calculating the Inter-quartile Range
Inter quartile range (IQR) is calculates as thus
[tex]IQR = Q_3 - Q_1[/tex]
Where
Q3 = Upper Quartile and Q1 = Lower Quartile
Start by arranging the data in ascending order
1, 3, 4, 5, 6, 9, 9, 10, 12, 17
N = Number of data; N = 10
---------------------------------------------------------------------------------
Calculating Q3
[tex]Q_3 = \frac{3}{4}(N+1) th\ item[/tex]
Substitute 10 for N
[tex]Q_3 = \frac{3}{4}(10+1) th\ item[/tex]
[tex]Q_3 = \frac{3}{4}(11) th\ item[/tex]
[tex]Q_3 = \frac{33}{4} th\ item[/tex]
[tex]Q_3 = 8.25 th\ item[/tex]
Express 8.25 as 8 + 0.25
[tex]Q_3 = (8 + 0.25) th\ item[/tex]
[tex]Q_3 = 8th\ item + 0.25 th\ item[/tex]
Express 0.25 as fraction
[tex]Q_3 = 8th\ item +\frac{1}{4} th\ item[/tex]
[tex]Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)[/tex]
From the arranged data;
[tex]8th\ item = 10[/tex] and [tex]9th\ item = 12[/tex]
[tex]Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)[/tex]
[tex]Q_3 = 10 +\frac{1}{4} (12 - 10)[/tex]
[tex]Q_3 = 10 +\frac{1}{4} (2)[/tex]
[tex]Q_3 = 10 +0.5[/tex]
[tex]Q_3 = 10.5[/tex]
Calculating Q1
[tex]Q_1 = \frac{1}{4}(N+1) th\ item[/tex]
Substitute 10 for N
[tex]Q_1 = \frac{1}{4}(10+1) th\ item[/tex]
[tex]Q_1 = \frac{1}{4}(11) th\ item[/tex]
[tex]Q_1 = \frac{11}{4} th\ item[/tex]
[tex]Q_1 = 2.75 th\ item[/tex]
Express 2.75 as 2 + 0.75
[tex]Q_1 = (2 + 0.75) th\ item[/tex]
[tex]Q_1 = 2nd\ item + 0.75 th\ item[/tex]
Express 0.75 as fraction
[tex]Q_1 = 2nd\ item +\frac{3}{4} th\ item[/tex]
[tex]Q_1 = 2nd\ item +\frac{3}{4} (3rd\ item - 2nd\ item)[/tex]
From the arranged data;
[tex]2nd\ item = 3[/tex] and [tex]3rd\ item = 4[/tex]
[tex]Q_1 = 3 +\frac{3}{4} (4 - 3)[/tex]
[tex]Q_1 = 3 +\frac{3}{4} (1)[/tex]
[tex]Q_1 = 3 +0.75[/tex]
[tex]Q_1 = 3 .75[/tex]
---------------------------------------------------------------------------------
Recall that
[tex]IQR = Q_3 - Q_1[/tex]
[tex]IQR = 10.5 - 3.75[/tex]
[tex]IQR = 6.75[/tex]
Calculating Variance
Start by calculating the mean
[tex]Mean = \frac{1+3+4+5+6+9+9+10+12+17}{10}[/tex]
[tex]Mean = \frac{76}{10}[/tex]
[tex]Mean = 7.6[/tex]
Subtract the mean from each data, then square the result
[tex](1 - 7.6)^2 = (-6.6)^2 = 43.56[/tex]
[tex](3 - 7.6)^2 = (-4.6)^2 = 21.16[/tex]
[tex](4 - 7.6)^2 = (-3.6)^2 = 12.96[/tex]
[tex](5 - 7.6)^2 = (-2.6)^2 = 6.76[/tex]
[tex](6 - 7.6)^2 = (-1.6)^2 = 2.56[/tex]
[tex](9 - 7.6)^2 = (1.4)^2 = 1.96[/tex]
[tex](9 - 7.6)^2 = (1.4)^2 = 1.96[/tex]
[tex](10 - 7.6)^2 = (2.4)^2 = 5.76[/tex]
[tex](12 - 7.6)^2 = (4.4)^2 = 19.36[/tex]
[tex](17 - 7.6)^2 = (9.4)^2 = 88.36[/tex]
Sum the result
[tex]43.56 + 21.16 + 12.96 + 6.76 + 2.56 + 1.96 + 1.96 + 5.76 + 19.36 + 88.36 = 204.4[/tex]
Divide by number of observation;
[tex]Variance = \frac{204.4}{10}[/tex]
[tex]Variance = 20.44[/tex]
Calculating Standard Deviation (SD)
[tex]SD = \sqrt{Variance}[/tex]
[tex]SD = \sqrt{20.44}[/tex]
[tex]SD = 4.52[/tex] (Approximated)
The area of a triangle is 14 square inches. The base is 28 inches. What is the height in inches? Do not include units in your answer.
Answer:
Hey there!
A=1/2bh
14=1/2(28)h
14=14h
h=1
Hope this helps :)
Answer:
the height is 1 inchStep-by-step explanation:
Area of a triangle is
[tex] \frac{1}{2} \times b \times h[/tex]
where b is the base
h is the height
From the question
Area = 14in²
b = 14 inches
So we have
[tex]14 = \frac{1}{2} \times 28 \times h[/tex]
which is
[tex]14 = 14h[/tex]
Divide both sides by 14
That's
[tex] \frac{14}{14} = \frac{14h}{14} [/tex]
We have the final answer as
h = 1
Therefore the height is 1 inch
Hope this helps you
Which could be the area of one lateral face of the triangular prism?
6.5 ft
6 ft
8 ft
2.5 ft
[Not drawn to scale]
7.5 ft2
15 ft?
20 ft
39 ft
Answer:
[tex](A)7.5 ft^2\\(C)20 ft^2[/tex]
Step-by-step explanation:
The diagram is attached below.
Area of the Rectangular Faces
[tex]8 X 6.5 =52$ ft^2\\8 X 2.5 =20$ ft^2\\8 X 6= 48$ ft^2[/tex]
Area of the Triangular face
[tex]=\dfrac12 X 2.5 X 6 =7.5$ ft^2[/tex]
Therefore, Options A and C could be the area of one lateral face of the triangular prism.
Answer:
C
Step-by-step explanation:
Which input value produces the same output value for the two functions on the graph?
Answer:
x=3
Step-by-step explanation:
To solve this problem, we should check the x coordinate of the point where both graphs intersect. Based on both graphs, they intersect at the point (3,-1). So, the input value for which both graphs have the same value is x=3.
Answer:
its x=-2
Step-by-step explanation:
cause i got it wrong and it said the answer was x=-2
letry. 14 Chapter 9: Chapter 9 rest Chapter Test
A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. Find the height of the roof.
Round your answer to the nearest tenth.
15 ft
h
8 ft
17 ft
Answer:
h = 7.1 cm
Step-by-step explanation:
To find the height of the triangle, we can first find the area of the triangle using the Heron's formula:
[tex]S = \sqrt{p(p-a)(p-b)(p-c)}[/tex]
Where a, b and c are the sides of the triangle and p is the semi perimeter of the triangle:
[tex]p = \frac{a+b+c}{2} = \frac{15 + 8 + 17 }{2} = 20\ cm[/tex]
So the area of the triangle is:
[tex]S = \sqrt{20(20-15)(20-8)(20-17)}[/tex]
[tex]S = 60\ cm^2[/tex]
Now, to find the height, we can use the following equation for the area of the triangle:
[tex]S = base * height/2[/tex]
The height draw in the figure is relative to the side of 17 cm, so this side is the value of base used in the formula. So we have that:
[tex]60 = 17 * h/2[/tex]
[tex]h = 120/17[/tex]
[tex]h = 7.06\ cm[/tex]
Rounding to the nearest tenth, we have h = 7.1 cm
Answer:
7.1 cm
Step-by-step explanation:
:D
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
The complete question is;
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
(a) less than 10 minutes
(b) longer than 5 minutes
(c) between 8 and 15 minutes
Answer:
A) P (x < 10) = 0.6700
B) P (x > 5 ) = 0.9406
C) P (8.0000 < x < 15.0000) = 0.6332
Step-by-step explanation:
A) we are given;
Mean;μ = 8.9 minutes
Standard deviation;σ = 2.5 minutes
Normal random variable;x = 10
So to find;P(x < 10) we will use the Z-score formula;
z = (x - μ)/σ
z = (10 - 8.9)/2.5 = 0.44
From z-distribution table and Z-score calculator as attached, we have;
P (x < 10) = P (z < 0.44) = 0.6700
B) similarly;
z = (x - μ)/σ =
z = (5 - 8.9)/2.5
z = -1.56
From z-distribution table and Z-score calculator as attached, we have;
P (x > 5 ) = P (z > -1.56) = 0.9406
C)between 8 and 15 minutes
For 8 minutes;
z = (8 - 8.9)/2.5 = -0.36
For 15 minutes;
z = (15 - 8.9)/2.5 = 2.44
From z-distribution table and Z-score calculator as attached, we have;
P (8.0000 < x < 15.0000) = P (-0.36 < z < 2.44) = 0.6332
A man is standing 20 feet away from the base of a tree and looking at the top of a tree wondering it’s height. If the man’s eyes are located 6 feet off the ground and the angle of elevation is 67°, how tall is the tree? Round to the nearest tenth of a foot.
Answer: 53.1ft
Step-by-step explanation:
We can draw a triangle rectangle.
Where the distance between the man and the tree is one cathetus, (the vertex is on the man's eyes)
The tree itself is the other cathetus, and the line that connects the man's eyes and the tip of the tree is the hypotenuse.
We know that:
The angle at the vertex of the man's eyes is 67°
And the adjacent cathetus, the distance between the man and the tree, is 20ft.
Then using the relation:
Tan(A) = (opposite cathetus)/(adjacent cathetus)
We can find the height of the treee:
Tan(67°) = X/20ft
Tan(67°)*20ft = X = 47.1ft
But remember that this is measured from the mans eye's, and the man's eyes are 6ft away from the ground.
Then the height of the tree is 47.1ft + 6ft = 53.1ft
for f(x)=1/x-5 and g(x)=x^2+2 find the expression for g(x) and substitute the value of g(x) into the function in place of x to find the value of f(g(x))
Answer:
f(x) = (1/x) - 5
g(x) = x^2 + 2
=> f[g(x)] = [1/(x^2 +2)] - 5
someone please do this like literally please
Answers:
sin a=12/15=4/5
step by step explanation:
AB=9, and BC=12
find c: hyp.=√12²+9²=c²
c=15
sin a=opp/hyp.=12/15=4/5 ( convert to degrees)
a=41.10
Find the coordinate vector [Bold x ]Subscript Upper B of x relative to the given basis BequalsStartSet Bold b 1 comma Bold b 2 comma Bold b 3 EndSet.
Answer:
3
Step-by-step explanation:
3
Please answer this correctly without making mistakes
Answer:
1/2
Step-by-step explanation:
There are eight equal pieces. Oliver used four pieces to make toast. Since the total is eight pieces, the fraction he used to make toast is 4/8, which simplifies to 1/2
Answer:
4/8
Step-by-step explanation:
He cut the bread into 8 equal pieces, so the denominator is 8.
He used 4 pieces for making toast.
He saved 4 pieces for later.
Hope this helps ;) ❤❤❤
On August 21, 2009, the World Health Organization announced its prediction that the number of new cases of H1N1 (swine flu) virus would double every 4 days for several months. As of July 27, 2009, the number of new cases was 15,784. Determine the instantaneous growth rate for the virus (rounded to the nearest ten-thousandths).
Answer:
growth rate = 0.1733 per day, or 17.33% per day
Step-by-step explanation:
Since the doubling time is 4 days, the growth factor over a period of t days is ...
2^(t/4)
Then the growth factor for 1 day is
2^(1/4) ≈ 1.189207
The instantaneous growth rate is the natural log of this:
ln(1.189207) ≈ 0.1733 . . . per day
Digital music distribution provides an opportunity for everyone to get their music heard. In order to get on a service like iTunes, one needs to pay for distribution through a service like Tunecore or CD Baby. These services make sure that your music is heard in the different platforms. Suppose the distributor charges the artist a $50.00 cost for distribution, and the streaming services pays $4.00 per one thousand streams. Model the profit for the total number of streams by answering the questions below: Use the cost for distribution to build your y-intercept. What is the y-intercept? Hint: the y-intercept is a point on the y axis, so your answer should be an ordered pair. Hint: you have to keep in mind that any time you pay for something, you are SPENDING money, if your y-intercept is incorrect, all your numbers will be off Use the payment per thousand streams to build your slope. What is the slope? Use the slope-intercept format (y = mx + b) to give the equation of the line. What is the equation of this line? Graph the line by adjusting the sliders below. Show your line by attaching an image below. After how many streams will you pay for the distributor charges? (hint: this is where the line crosses the x-axis, round to the nearest thousand) How many streams would it take to profit $300,000? Challenge Question: In 2019, Old Town Road became one of the most streamed songs of all time passing the previous record holders, Despacito and One Sweet Day. The second week the song was #1, it set an all time streaming record. It was streamed 143 million times (143,000,000) in the US, nearly 30 million higher than the previous record holder Drake, In My Feelings. Calculate the profit earned using these numbers. (Hint: use the slope intercept format to build this equation).
Answer:
the answer is 1.00
Step-by-step explanation:
pls mark me as the brainliest and tell me thanks
You pick two students at random, one at a time. What is the probability that the second student is a sophomore, given that the first is a freshman
Answer:
0.40
Step-by-step explanation:
The computation of the probability for the second student be sophomore and the first is a freshman is shown below:
Let us assume
Sophomore = S
Freshman = F
Based on this assumption, the probability is as follows
So,
[tex]= \frac{P(S\cap F)}{P(F)} \\\\ = \frac{P(S) \times P(F)}{P(F)} \\\\ = \frac{16}{40}[/tex]
= 0.40
Hence, the probability for the second student be sophomore and the first student be freshman is 0.40
C(t) = 2t^4 – 8t^3 +6t^2 Find the t-intercept?
Answer:
0
Step-by-step explanation:
The t-intercept here is what's khown as the x-intercept wich is given by C(t)=0
● C(t) = 2t^4-8t^3+6t^2
● 0 = 2t^4-8t^3+6t^2
Factor using t
● t(2t^3-8t^2+6t^1) = 0
Wich means that t=0
Let x and y be real numbers satisfying 2/x=y/3=x/y Determine the value of x^3
Answer:
64/27Step-by-step explanation:
If x and y be real numbers satisfying 2/x=y/3=x/y, then any two of the equation are equated as shown;
2/x = y/3 ... 1 and;
y/3 = x/y... 2
From equation 1, 2y = 3x ... 3
and from equation 2; y² = 3x ... 4
Equating the left hand side of equation 3 and 4 since their right hand sides are equal, we will have;
2y = y²
2 = y
y = 2
Substituting y = 2 into equation 3 to get the value of x;
2y = 3x
2(2) = 3x
4 = 3x
x = 4/3
The value of x³ will be expressed as (4/3)³ = 4*4*4/3*3*3 = 64/27
A cubical container measures 9 ft on each edge. What does it cost to fill the container at $2.58 per cubic ft?
Answer:
1,880.82
Step-by-step explanation:
Evaluate f(x) when x= 9
f(x) = {6x² +2 if 6
112 if 9
No solution
O 110
O 12
56
Answer:
[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]
[tex] f(x) = 12 , 9 \leq x <13[/tex]
And we want to evaluate f(x=9)
And for this case the answer would be:
[tex] f(9)= 12[/tex]
Best answer:
O 12
Step-by-step explanation:
For this problem we have the following function given:
[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]
[tex] f(x) = 12 , 9 \leq x <13[/tex]
And we want to evaluate f(x=9)
And for this case the answer would be:
[tex] f(9)= 12[/tex]
Best answer:
O 12
What is the size of the matrix resulting from...
Answer:
1 x 3
Step-by-step explanation:
The order of the first matrix is 1 × 3
The order of the second matrix is 3 × 3
that is (1 × 3 ) × (3 × 3 )
The bold values at the ends of the orders give the order of the product, that is
1 × 3
PLZ HURRY WILL MARK BRAINLIEST The stem and leaf plot shows the number of points a basketball team scored each game during its 15-game season. In how many games did the team score at least 70 points? 4 5 8 10
Answer:
5 games
Step-by-step explanation:
To find how many games the team scored at least 70 points, we need to look at the 7 on the stem side. The 7 means 70, and we add the digits on the leaf side. For example, 7 | 2 is 72. The numbers on the leaf side are: 1, 1, 2, and 3.
There are no points for the 8 on the stem side, but on 90, there is one digit on the leaf side: 1. So, the points they scored over 70 are 71, 71, 72, 73, and 91, which equals to five games.
Answer:
[tex]\boxed{\mathrm{5 \ games}}[/tex]
Step-by-step explanation:
At least 70 points makes it 70 and more. It should be at least 70 and at most anything above then 70.
So, In 5 games, the team scored at least 70. (71,71,72,73 and 91)
How much of a radioactive kind of sodium will be left after 9 years if you start with 96 grams and the half-life is 3 years?
Answer:
9 years = 12 grams
Step-by-step explanation:
0 years = 96 grams
After 3 years , the amount left is 1/2 of what you started with
3 years = 1/2 *96 = 48 grams
After 3 years , the amount left is 1/2
6 years = 1/2 (48) = 24 grams
After 3 years , the amount left is 1/2
9 years = 1/2 ( 24) = 12 grams
What is the converse of r->(~q v p)
Answer:
[tex]r => (\neg q \ \lor p) \ \equiv \ q \ \land \ \neg p => \neg r[/tex]
Step-by-step explanation:
In general, remember that the converse of [tex]a => b[/tex] is [tex]\neg b => \neg a[/tex] , therefore in this case [tex]a = r \ \ , b = \neg q \ \lor p[/tex]
so [tex]r => (\neg q \ \lor p) \ \equiv \ q \ \land \ \neg p => \neg r[/tex]
Diners frequently add a 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is $
Question:
Diners frequently add a 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is $20.70? How much was the tip?
Answer:
Price of meal = $18
Tip price = $2.70
Step-by-step explanation:
Let the price of the meal be y;
Let the tip be t
From the question;
15% of y is the tip charge (t). i.e
t = 15%y
=> t = 0.15y --------(i)
The total amount charged is $20.70 (This means that the sum of the price of the meal and the tip is $20.70)
=> y + t = 20.70 [substitute the value of t=0.15y from equation (i)]
=> y + 0.15y = 20.70
=> 1.15y = 20.70
=> y = [tex]\frac{20.70}{1.15}[/tex]
=> y = $18
Therefore the price of the meal, y, is $18.
From equation (i),
t = 0.15y [substitute the value of y = $18]
t = 0.15(18)
t = $2.70
Therefore the tip was $2.70
x-5y=-15x−5 Complete the missing value in the solution to the equation. (-5, )
Answer:
y = -15
Step-by-step explanation:
x-5y=-15x−5
Let x = -5
-5 -5y = -15 * -5 -5
Combine like terms
-5 -5y = 75-5
-5 -5y = 70
Add 5 to each side
-5y = 75
Divide by -5
y = -15
A statistical program is recommended.
The following observations are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions.
32.1 30.9 31.6 30.4 31.0 31.9
The report states that under these conditions, the maximum allowable stopping distance is 30. A normal probability plot validates the assumption that stopping distance is normally distributed.
Required:
a. Does the data suggest that true average stopping distance exceeds this maximum value? Test the appropriate hypotheses using α= 0.01.
b. Calculate the test statistic and determine the P-value.
c. What can you conclude?
Answer:
We conclude that the true average stopping distance exceeds this maximum value.
Step-by-step explanation:
We are given the following observations that are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions.;
X = 32.1, 30.9, 31.6, 30.4, 31.0, 31.9.
Let [tex]\mu[/tex] = true average stopping distance
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 30 {means that the true average stopping distance exceeds this maximum value}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 30 {means that the true average stopping distance exceeds this maximum value}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean stopping distance = [tex]\frac{\sum X}{n}[/tex] = 31.32 ft
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 0.66 ft
n = sample size = 6
So, the test statistics = [tex]\frac{31.32-30}{\frac{0.66}{\sqrt{6} } }[/tex] ~ [tex]t_5[/tex]
= 4.898
The value of t-test statistics is 4.898.
Now, at 0.01 level of significance, the t table gives a critical value of 3.365 at 5 degrees of freedom for the right-tailed test.
Since the value of our test statistics is more than the critical value of t as 4.898 > 3.365, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the true average stopping distance exceeds this maximum value.
Solve the right triangle.
A = 48.31º. c = 49.9
Assuming angle A is opposite to side a, B is the opposite to side b, and angle C is the opposite to side c.
Answer:
The right triangle has the following angles:
A = 48.31º, B = 41.69º and C = 90º.
The sides are:
[tex] \\ a = 37.26[/tex], [tex] \\ b = 33.12[/tex] and c = 49.9.
Step-by-step explanation:
The inner sum of a triangle = 180º.
A=48.31º,
C=90º
A + B + C = 180º
48.31º+ B + 90º = 180º
B = 180º - 90º - 48.31º
B = 41.69º
We can apply the Law of Sines to solve for unknown sides:
[tex] \\ \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]
We know that sin(90º) = 1.
[tex] \\ \frac{a}{sin(48.31)} = \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]
Then, a is:
[tex] \\ \frac{a}{sin(48.31)} = \frac{49.9}{1}[/tex]
[tex] \\ a = 49.9*sin(48.31)[/tex]
[tex] \\ a = 49.9*0.7467[/tex]
[tex] \\ a = 37.26[/tex]
Thus, b is:
[tex] \\ \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]
[tex] \\ b = 49.9*sin(41.69)[/tex]
[tex] \\ b = 33.12[/tex]
In a study of the gasoline mileage of model year 2017 automobiles, the mean miles per gallon was 27.5 and the median was 26.8. The smallest value in the study was 12.70 miles per gallon, and the largest was 50.20. The first and third quartiles were 17.95 and 35.45 miles per gallon, respectively. Determine the type of skewness.
Answer:
This is skewed torwards the right. Or in other words positively skewed distribution.
Step-by-step explanation:
All of the values are fairly close together torwards the lower range. While 50.20 is more of an outlier, so this graph would gradualy skew to the right.
Y + 1 1/6 = 7 5/6 what is Y
Answer:
6[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
y + 1[tex]\frac{1}{6}[/tex] = 7[tex]\frac{5}{6}[/tex]
y + [tex]\frac{7}{6}[/tex] = [tex]\frac{47}{6}[/tex]
y = 40/6 = 20/3 = 6[tex]\frac{2}{3}[/tex]
Angle bisectors AX and of triangle ABC meet at point I. Find angle C in degrees, if AIB = 109.
Answer:
angle C = 38 degrees
Step-by-step explanation:
Refer to attached figure (sorry, forgot to attach earlier)
Given
AIB = 109
Let
CAX = XAB = x
CBY = YBA = y
XIB = YIA = x+y ........exterior angles
XIB = YIA = 180-109 = 71 ............ sum of angles on a line
=>
x+y = 71
ACB = 180 - 2x -2y ................. sum of angles of a triangle
= 180 - 2(x+y)
= 180 - 2(71)
= 180 - 142
= 38
4. A bank vault has 3 locks with a key for each lock. Key A is owned by the bank manager. Key B is owned by the senior bank teller. Key C is owned by the trainee bank teller. In order to open the vault door at least two people must insert their keys into the assigned locks at the same time. The trainee bank teller) can only open the vault when the bank manager is present in the opening. X= Bank Manager Y= Senior Bank teller Z= Trainee bank teller. (25 marks) LO 01 a) Construct a truth table for this system
1 means that he is present, 0 means that he is not.
True means that they can open.
[tex]\begin{array}{cccccccccccc} \text{X} &&& \text{Y} &&& \text{Z} &&& \text{True} \\1 &&& 1 &&& 1&&& 1 \\ 1 &&& 1 &&& 0&&&1 \\ 0 &&& 1 &&& 1&&&0 \\ 1 &&& 0 &&& 1&&&1 \\ 0&&& 1 &&& 0&&&0 \\ 0 &&& 0 &&& 1&&&0 \\ 1 &&& 0 &&& 0&&&0 \\ 0 &&& 0 &&& 0&&&0 \\ \end{array}[/tex]
Answer:
police
Step-by-step explanation: