Answer:
500
Step-by-step explanation:
I assume each number is from 0 to 9. Also there are 5 letters.
10 * 5 * 10 = 500
Determine the area (in units2) of the region between the two curves by integrating over the x-axis. y = x2 − 24 and y = 1
The area bounded by region between the curve [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] is
[tex]0[/tex] square units.
To find the Area,
Integrate the difference between the two curves over the interval of intersection.
Find the points of intersection between the curves [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] .
The point of Intersection is the common point between the two curve.
Value of [tex]x[/tex] and [tex]y[/tex] coordinate will be equal for both curve at point of intersection
In the equation [tex]y = x^2- 24[/tex], Put the value of [tex]y = 1[/tex].
[tex]1 = x^2-24[/tex]
Rearrange, like and unlike terms:
[tex]25 = x^2[/tex]
[tex]x =[/tex] ±5
The point of intersection for two curves are:
[tex]x = +5[/tex] and [tex]x = -5[/tex]
Integrate the difference between the two curve over the interval [-5,5] to calculate the area.
Area = [tex]\int\limits^5_{-5} {x^2-24-1} \, dx[/tex]
Simplify,
[tex]= \int\limits^5_{-5} {x^2-25} \, dx[/tex]
Integrate,
[tex]= [\dfrac{1}{3}x^3 - 25x]^{5} _{-5}[/tex]
Put value of limits in [tex]x[/tex] and subtract upper limit from lower limit.
[tex]= [\dfrac{1}{3}(5)^3 - 25(5)] - [\dfrac{1}{3}(-5)^3 - 25(-5)][/tex]
= [tex]= [\dfrac{125}{3} - 125] - [\dfrac{-125}{3} + 125][/tex]
[tex]= [\dfrac{-250}{3}] - [\dfrac{-250}{3}]\\\\\\= \dfrac{-250}{3} + \dfrac{250}{3}\\\\\\[/tex]
[tex]= 0[/tex]
The Area between the two curves is [tex]0[/tex] square units.
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On average, the printer uses 500 sheets of paper each day with a standard deviation of 10 sheets. What is the probability that the printer uses more than 508 sheets?
Answer:
P [ x > 508 ] = 0,2
Step-by-step explanation:
P [ x > 508 ] = 1 - P [ x ≤ 508]
P [ x ≤ 508 ] = ( 508 - 500 ) / 10
P [ x ≤ 508 ] = 8/10
P [ x ≤ 508 ] = 0,8
Then
P [ x > 508 ] = 1 - P [ x ≤ 508]
P [ x > 508 ] = 1 - 0,8
P [ x > 508 ] = 0,2
help with this I don't know how to solve please and thanks
Answer:
6.5 ft
Step-by-step explanation:
When we draw out our picture of our triangle and label our givens, we should see that we need to use cos∅:
cos57° = x/12
12cos57° = x
x = 6.53567 ft
The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.2 minutes, and the standard deviation is 3.4 minutes.
Requried:
a. What is the probabilty that a random sample of n = 40 oil changes results in a sample mean time less than 15 minutes?
b. Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, there
would be a 10% chance of the mean oil-change time being at or below what value? This will be the goal established by the manager.
Answer:
(a) Probability that a random sample of n = 45 oil changes results in a sample mean time < 10 minutes i=0.0001.
(b) The mean oil-change time is 15.55 minutes.
Step-by-step explanation:
Let us denote the sample mean time as x
From the Then x = mean time = 16.2 minutes
The given standard deviation = 3.4 minutes
The value of n sample size = 45
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.)
Answer:
85.932 cm³
Step-by-step explanation:
The volume of rectangular prism is obtained as the product of its length (l) by its width (w) and by its height (h):
[tex]V=l*w*h[/tex]
The volume of a prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm is:
[tex]V=4.4*3.1*6.3\\V=85.932\ cm^3[/tex]
The volume of this prism is 85.932 cm³.
In a large city, the city supervisor wants to find the average number of aluminum cans that each family recycles per month. So, she surveys 18 families and finds that these 18 families recycle an average of 140 cans per month with a standard deviation of 26 cans per month. Find the 90 % confidence interval for the mean number of cans that all of the families in the city recycle per month.
Answer:
The 90% onfidence interval for the mean number of cans that all of the families in the city recycle per month is between 129.34 and 150.66 cans per month
Step-by-step explanation:
We have the standard deviation of the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 18 - 1 = 17
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.74
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.74\frac{26}{\sqrt{18}} = 10.66[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 140 - 10.66 = 129.34 cans per month
The upper end of the interval is the sample mean added to M. So it is 140 + 10.66 = 150.66 cans per month.
The 90% onfidence interval for the mean number of cans that all of the families in the city recycle per month is between 129.34 and 150.66 cans per month
Find the slope of the line passing through (6,8) and (-10,3)
Answer:
5/16
Step-by-step explanation:
Use the formula to find slope when 2 points are given.
m = rise/run
m = y2 - y1 / x2 - x1
m = 3 - 8 / -10 - 6
m = -5 / -16
m = 5/16
The slope of the line is 5/16.
Answer: m=5/16
Step-by-step explanation:
Who'd be better at speed answering? Datguy323 or some Helping Hand? (Not a serious question) Solve for the variables: [tex]x^3+y^7=28\\x^3=27[/tex]
Answer:
x = 3
y = 1
Step-by-step explanation:
The equations are:
[tex]x^3+y^7 = 28[/tex]
and
[tex]x^3 = 27[/tex]
Putting second equation in the first one:
=> [tex]27+y^7 = 28[/tex]
Subtracting 27 to both sides
=> [tex]y^7 = 28-27[/tex]
=> [tex]y^7 = 1[/tex]
Taking power 7 to both sides
=> y = 1
Now,
[tex]x^3 = 27[/tex]
Taking cube root on the both sides
x = 3
Answer: (3,1)
Step-by-step explanation:
First, to find x, simply take the cube root of 27, or 3. Thus, x = 3.
Then, simply plug it in:
[tex]27+y^7=28\\Subtract(27)\\y^7=1\\y=1[/tex]
Thus, y = 1
Hope it helps <3
p.s. for some reason, in a graphing calculator, it shows no solutions
Hope it helps <3
2 in a row!
Besides the 90° angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13? Round to the nearest degree.
Answer:
45
Step-by-step explanation:
I really don't but it seems right
Answer:
b
Step-by-step explanation:
just did it on edge
I NEED HELP PLEASE, THANKS! :)
Answer:
68
Step-by-step explanation:
The number of chips tested is the integral of the rate over the specified time interval: t = 2 to 6.
[tex]\displaysyle n=\int_2^6{-3t^2+16t+5}\,dt=\left.-3\dfrac{t^3}{3}+16\dfrac{t^2}{2}+5t\right|_2^6\\\\=-(6^3-2^3) +8(6^2-2^2)+5(6-2)=-(216-8)+8(32) +5(4)\\\\=-208+256+20=\boxed{68}[/tex]
The technician can test 68 chips in that time period.
At the farm, corn costs $2.50 per pound. How much would 3 1/2 pounds of corn cost? Write your answer in dollars and cents.
Multiply price per pound by total pounds:
2.50 x 3.5 = 8.75
Total cost = $8.75
Answer:
The cost is $8.75 for 3.5 lbs
Step-by-step explanation:
The rate is 2.50 per pound
Multiply the number of pounds by the rate
3.5 * 2.50 =8.75
The cost is $8.75 for 3.5 lbs
F(x)+6x+11 inverse function
Answer:
y = x/6 − 11/6
Step-by-step explanation:
y = 6x + 11
To find the inverse, switch x and y, then solve for y.
x = 6y + 11
x − 11 = 6y
y = x/6 − 11/6
Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000, with probabilities 0.80, 0.08, 0.10, and 0.02, respectively. A particular company offers three different policies: a $200 deductible with a $780 premium, a $500 deductible with a $700 premium, and a $1000 deductible with a $590 premium. (A $Y deductible means the insurance company pays X - Y for X Y and 0 for X Y.) Compute the expected profit for each policy.
Answer:
Expected profit policy 1 = $40
Expected profit policy 2 = $20
Expected profit policy 3 = $10
Step-by-step explanation:
X values | Probability P(x)
0 | 0.80
1,000 | 0.08
5,000 | 0.10
10,000 | 0.02
A particular company offers three different policies:
Policy 1: $200 deductible with a $780 premium
Policy 2: $500 deductible with a $700 premium
Policy 3: $1000 deductible with a $590 premium
The company pays X - Y in damages if X > Y and 0 otherwise.
So the expected profit is given by
Expected profit = Premium amount - Expected payout
Expected profit = Premium amount - [ (X - deductible) × P(x) ]
Expected profit Policy 1:
E(x) = $780 - [ 0×0.80 + (1,000 - 200)×0.08 + (5,000 - 200)×0.10 + (10,000 - 200)×0.02 ]
E(x) = $780 - [ 0 + 64 + 480 + 196 ]
E(x) = $780 - $740
E(x) = $40
Expected profit Policy 2:
E(x) = $700 - [ 0×0.80 + (1,000 - 500)×0.08 + (5,000 - 500)×0.10 + (10,000 - 500)×0.02 ]
E(x) = $700 - [ 0 + 40 + 450 + 190 ]
E(x) = $700 - $680
E(x) = $20
Expected profit Policy 3:
E(x) = $590 - [ 0×0.80 + (1,000 - 1,000)×0.08 + (5,000 - 1,000)×0.10 + (10,000 - 1,000)×0.02 ]
E(x) = $590 - [ 0 + 0 + 400 + 180 ]
E(x) = $590 - $580
E(x) = $10
Therefore, the expected profits for the three policies are:
Expected profit policy 1 = $40
Expected profit policy 2 = $20
Expected profit policy 3 = $10
What is the solution to this sysiem of inear equacions?
3x-2= 14
5x+y=32
• (3,5)
• (6,2)
• (8,-1)
• (14,-18)
Answer:
the answer i got was (16/3,16/3)
Step-by-step explanation:
An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers.
Answer:
3, 12
Step-by-step explanation:
Et x and y be the required integers.
Case 1: x = 5y - 3...(1)
Case 2: xy = 36
Hence, (5y - 3)*y = 36
[tex]5 {y}^{2} - 3y = 36 \\ 5 {y}^{2} - 3y - 36 = 0 \\ 5 {y}^{2} - 15y + 12y - 36 = 0 \\ 5y(y - 3) + 12(y - 3) = 0 \\ (y - 3)(5y + 12) = 0 \\ y - 3 = 0 \: or \: 5y + 12 = 0 \\ y = 3 \: \: or \: \: y = - \frac{12}{5} \\ \because \: y \in \: I \implies \: y \neq - \frac{12}{5} \\ \huge \purple{ \boxed{ \therefore \: y = 3}} \\ \because \: x = 5y - 3..(equation \: 1) \\ \therefore \: x = 5 \times 3 - 3 = 15 - 3 = 12 \\ \huge \red{ \boxed{ x = 12}}[/tex]
Hence, the required integers are 3 and 12.
let
x = one integer
y = another integer
x = 5y - 3
If the product of the two integers is 36, then find the integers.
x * y = 36
(5y - 3) * y = 36
5y² - 3y = 36
5y² - 3y - 36 = 0
Solve the quadratic equation using factorization method
That is, find two numbers whose product will give -180 and sum will give -3
Note: coefficient of y² multiplied by -36 = -180
5y² - 3y - 36 = 0
The numbers are -15 and +12
5y² - 15y + 12y - 36 = 0
5y(y - 3) + 12 (y - 3) = 0
(5y + 12) (y - 3) = 0
5y + 12 = 0 y - 3 = 0
5y = - 12 y = 3
y = -12/5
The value of y can not be negative
Therefore,
y = 3
Substitute y = 3 into x = 5y - 3
x = 5y - 3
x = 5(3) - 3
= 15 - 3
= 12
x = 12
Therefore,
(x, y) = (12, 3)
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The ratio of the areas of two circles is 121/100. What is the ratio of the radii of the two circles
Answer:
11/10
Step-by-step explanation:
The area ratio is the square of the radius ratio (k):
(121/100) = k²
k = √(121/100) = 11/10
The ratio of radii is 11/10.
whats the answer ?? ill mark brainliest
Answer:
[tex]\boxed{Option A ,D}[/tex]
Step-by-step explanation:
The remote (non-adjacent) interior angles of the exterior angle 1 are <4 and <6
consider a politician discussion group consisting of eight Democrats three Republicans and seven Independents suppose that two group members are randomly selected in succession to attend political convention find the probability of selecting an independent and then a Democrat
Answer:
(38.8%...7/10), than (47%...8/17) I didnt know if u needrd it in fraction or percent.
Step-by-step explanation:
You want to first add up everyone. So in total there are 18 people.
There is than a 38.8% chance that a independent will be picked first. 7/18.
But since one person was picked already you have to subtract 1 person from the total, so now its out of 17.
There is now a 47% chance that a democrat will be picked next. 8/17.
Pls help me help me
Answer:
C. -4/3
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes.
We know that line m is perpendicular to line l.
Line l has a slope of 3/4. To find the slope of line m, find the negative reciprocal of 3/4. Negate the fraction and find the reciprocal.
Negative: switch the sign
3/4 --> -3/4
Reciprocal: switch the numerator (top number) and denominator (bottom number)
-3/4 --> -4/3
Line m has a slope of -4/3 and C is correct.
Find the work (in ft-lb) required to pump all the water out of a cylinder that has a circular base of radius 7 ft and height 200 ft. Use the fact that the weight-density of water is 62.4 lb/ft3
Answer:
work done is equal to 384279168 lb-ft
Step-by-step explanation:
The cylinder has a circular base of 7 ft.
The height of the cylinder is 200 ft
The weight density of water in the cylinder is 62.4 lb/ft^3
First, we find the volume of the water in the cylinder by finding the volume of this cylinder occupied by the water.
The volume of a cylinder is given as [tex]\pi r^{2} h[/tex]
where, r is the radius,
and h is the height of the cylinder.
the volume of the cylinder = [tex]3.142* 7^{2}*200[/tex] = 30791.6 ft^3
Since the weight density of water is 62.4 lb/ft^3, then, the weight of the water within the cylinder will be...
weight of water = 62.4 x 30791.6 = 1921395.84 lb
We know that the whole weight of the water will have to be pumped out over the height of cylindrical container. Also, we know that the work that will be done in moving this weight of water over this height will be the product of the weight of water, and the height over which it is pumped. Therefore...
The work done in pumping the water out of the container will be
==> (weight of water) x (height of cylinder) = 1921395.84 x 200
==> work done is equal to 384279168 lb-ft
The required work done will be "384279168 lb-ft".
Work done:Whenever a force pushes anything across distances, work is performed. This same energy transmitted, as well as work done, maybe determined by calculating the force through the kilometers moved throughout the direction of the applied force.
According to the question,
Circular base of cylinder = 7 ft
Height of cylinder = 200 ft
Weight density of water = 62.4 lb/ft³
The Volume of cylinder be:
= πr²h
By substituting the values,
= [tex]3.142\times (7)^2\times 200[/tex]
= [tex]3.142\times 49\times 200[/tex]
= [tex]30791.6[/tex] ft³
Now,
The weight of water be:
= [tex]62.4\times 30791.6[/tex]
= [tex]1921395.84[/tex] lb
hence,
The work done be:
= Water's weight × Cylinder's height
= [tex]1921395.84\times 200[/tex]
= [tex]384279168[/tex] lb-ft
Thus the above answer is right.
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Use matrix operations to solve the following systems of linear equations. Use comments to explain which value is x1, x2, etc
3x1-10 x2- 5x3+30x4 = -1
4x1+7x2+ 5x3- 3x4=0
x2+ x3-3x4 =1
x1-2x2-10x3+6x4 = -1
Answer:
x⁴ = -0.955939
x³ = 0.206897
x² = -2.07471
x = 2.65517
Step-by-step explanation:
Step 1: Rewrite equations in standard form
30x⁴ - 5x³ - 10x² + 3x = -1
-3x⁴ + 5x³ + 7x² + 4x = 0
-3x⁴ + x³ + x² = 1
6x⁴ - 10x³ - 2x² + x = -1
Step 2: Write in matrix form
Top Row: [30 -5 -10 3 | -1]
2nd Row: [-3 5 7 4 | 0]
3rd Row: [-3 1 1 0 0 | 1]
Bottom Row: [6 -10 -2 1 | -1]
Step 3: Plug in calc with RREF function
Top Row: [1 0 0 0 | -499/522]
2nd Row: [0 1 0 0 | 6/29]
3rd Row: [0 0 1 0 | -361/174]
4th Row: [0 0 0 1 | 77/29]
[10 points] A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimensions will produce a box with maximum volume?
Answer:
6 inches square by 3 inches high
Step-by-step explanation:
For a given surface area, the volume of an open-top box is maximized when it has the shape of half a cube. If the area were than of the whole cube, it would be 216 in² = 6×36 in².
That is, the bottom is 6 inches square, and the sides are 3 inches high.
_____
Let x and h represent the base edge length and box height, respectively. Then we have ...
x² +4xh = 108 . . . . box surface area
Solving for height, we get ...
h = (108 -x²)/(4x) = 27/x -x/4
The volume is the product of base area and height, so is ...
V = x²h = x²(27/x -x/4) = 27x -x³/4
We want to maximize the volume, so we want to set its derivative to zero.
dV/dx = 0 = 27 -(3/4)x²
x² = (4/3)(27) = 36
x = 6
h = 108/x² = 3
The box is 6 inches square and 3 inches high.
_____
Comment on maximum volume, minimum area
In the general case of an open-top box, the volume is maximized when the cost of the bottom and the cost of each pair of opposite sides is the same. Here, the "cost" is simply the area, so the area of the bottom is 1/3 the total area, 36 in².
If the box has a closed top, then each pair of opposite sides will have the same cost for a maximum-volume box. If costs are uniform, the box is a cube.
Find the general formula for the following sequence.
300000, 480000, 768000, 1228800, 1966080, ....
Answer:
3,145,728
Step-by-step explanation:
x1.6
300000 x 1.6 = 4800000
480000 x 1.6 = 7680000
768000 x 1.6 = 1228800
122800 x 1.6 = 1966080
1966080 x 1.6 = 3145728
32 percent of the customers of a fast food chain order the Whopper, French fries and a drink. A random sample of 10 cash register receipts is selected. What is the probability that eight receipts will show that the above three food items were ordered?
Answer: 0.0023
Step-by-step explanation:
Let X be the binomial variable that represents the number of receipts will show that the above three food items were ordered.
probability of success p = 32% = 0.32
Sample size : n= 10
Binomial probability function :
[tex]P(X=x)= \ ^nC_xp^x(1-p)^{n-x}[/tex]
Now, the probability that eight receipts will show that the above three food items were ordered :
[tex]P(X=8)=\ ^{10}C_8(0.32)^8(1-0.32)^2\\\\=\dfrac{10!}{8!2!}(0.32)^8(0.68)^2\\\\=5\times9(0.0000508414176684)\\\\=0.00228786379508\approx0.0023[/tex]
hence, the required probability = 0.0023
The equation of a parabola in the xy-plane is given as
y= n(x + 5)(x - 3) where n is a non-zero constant. What
is the y-coordinate of the vertex of this parabola in
terms of n?
A. -18n
B. -16n
C. -15n
D. -12n
Answer:
B
Step-by-step explanation:
y=n(x+5)(x-3)
or y=n(x²-3x+5x-15)
or y=n(x²+2x-15)
=n(x²+2x+1-1-15)
=n(x+1)²-16n
y -coordinate of vertex=-16n
!!HELP WILL GIVE BRAIN LIST!! Examine the diagram and information to answer the question. A circle in the coordinate plane has a radius of 6 and a center at the point (3,2). Point (x,y) lies on the circle. The triangle formed by points (3,2), (x,2) and (x,y) is a right triangle. What is the equation of the circle? Match the expression or equation to the steps used to find the equation of the circle. answers TO fill IN the match |x−3| (x−2)2+(y−3)2=62 |x−2| |y−3| (x−3)2+(y−2)2=62 |y−2|
Answer:
|y-2||x-3|(x-3)²+(y-2)² = 36Step-by-step explanation:
1. The length of the vertical leg of the triangle is the magnitude of the difference between the y-coordinate of the point on the circle and the y-coordinate of the center:
|y -2|
2. The length of the horizontal leg of the triangle is the magnitude of the difference between the x-coordinate of the point on the circle and the x-coordinate of the center:
|x -3|
3. The Pythagorean theorem tells you the sum of the squares of the leg length is equal to the square of the hypotenuse length. The hypotenuse is given as 6, so the equation is ...
[tex]|y-2|^2 +|x-3|^2=6^2[/tex]
Since the square of a number is the same as the square of its magnitude, we can write this as ...
[tex](x-3)^2+(y-2)^2=36[/tex]
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145 a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Answer:
a. Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. P(at least B) = 0.330
c. P(pass) = 0.855
Step-by-step explanation:
Professor Sanchez has been teaching Principles of Economics for over 25 years.
He uses the following scale for grading.
Grade Numerical Score Probability
A 4 0.090
B 3 0.240
C 2 0.360
D 1 0.165
F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
The cumulative probability distribution is given by
Grade = F
P(X ≤ x) = 0.145
Grade = D
P(X ≤ x) = 0.145 + 0.165 = 0.310
Grade = C
P(X ≤ x) = 0.145 + 0.165 + 0.360 = 0.670
Grade = B
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 = 0.910
Grade = A
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 + 0.090 = 1
Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
At least B means equal to B or greater than B grade.
P(at least B) = P(B) + P(A)
P(at least B) = 0.240 + 0.090
P(at least B) = 0.330
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Passing the course means getting a grade of A, B, C or D
P(pass) = P(A) + P(B) + P(C) + P(D)
P(pass) = 0.090 + 0.240 + 0.360 + 0.165
P(pass) = 0.855
Alternatively,
P(pass) = 1 - P(F)
P(pass) = 1 - 0.145
P(pass) = 0.855
Would this be correct even though I didn’t use the chain rule to solve?
Answer:
Dy/Dx=1/√ (2x+3)
Yeah it's correct
Step-by-step explanation:
Applying differential by chain differentiation method.
The differential of y = √(2x+3) with respect to x
y = √(2x+3)
Let y = √u
Y = u^½
U = 2x +3
The formula for chain differentiation is
Dy/Dx = Dy/Du *Du/Dx
So
Dy/Dx = Dy/Du *Du/Dx
Dy/Du= 1/2u^-½
Du/Dx = 2
Dy/Dx =( 1/2u^-½)2
Dy/Dx= u^-½
Dy/Dx=1/√ u
But u = 2x+3
Dy/Dx=1/√ (2x+3)
Consider rolling dice and getting a total of 8. Find the probability if two dice are rolled. (Enter the value of probability in decimals. Round the answer to three decimal places.)
Answer:
13.89%
Step-by-step explanation:
The probability when two dices are rolled and their sum is 8 is shown below:
But before that we need to see the probabilities of the sum i.e 8
2 + 6 = 8
3 + 5 = 8
4 + 4 = 8
5 + 3 = 8
6 + 2 = 8
There are 5 outcomes
And, the two dice is 36 i.e square of 6
So, the probability of two dices are rolled and their sum is 8 is
= [tex]\frac{5}{36}[/tex]
= 13.89%
Among 20 golden hamster litters recorded, there was a sample mean of =7.72 baby hamsters, with a sample standard deviation of s=2.5 hamsters per liter. Create a 98% confidence interval for the mean number of baby hamsters per liter.
Answer:
[tex] 7.72 -2.539 \frac{2.5}{\sqrt{20}} =6.30[/tex]
[tex] 7.72 +2.539 \frac{2.5}{\sqrt{20}} =9.14[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex]\bar X= 7.72[/tex] represent the sample mean
[tex]s= 2.5[/tex] represent the sample deviation
[tex] n=20[/tex] represent the sample size
The confidence interval is given by:
[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
The confidence interval is 98% and the significance level is [tex]\alpha=0.02[/tex] the degrees of freedom are given by:
[tex] df= n-1 = 20-1=19[/tex]
And the critical value would be:
[tex] t_{\alpha/2}= 2.539[/tex]
And replacing we got:
[tex] 7.72 -2.539 \frac{2.5}{\sqrt{20}} =6.30[/tex]
[tex] 7.72 +2.539 \frac{2.5}{\sqrt{20}} =9.14[/tex]
The 98% confidence interval is between 6.42 hamsters per liter to 9.02 hamsters per liter
Mean (μ) = 7.72, standard deviation (σ) = 2.5, sample size (n) = 20, Confidence (C) = 98% = 0.98
α = 1 - C = 0.02
α/2 = 0.01
The z score of α/2 is the same as the z score of 0.49 (0.5 - 0.01) which is equal to 2.326.
The margin of error E is:
[tex]E = Z_\frac{\alpha }{2} *\frac{\sigma}{\sqrt{n} } \\\\E=2.326*\frac{2.5}{\sqrt{20} } =1.3[/tex]
The confidence interval = (μ ± E) = (7.72 ± 1.3) = (6.42, 9.02)
Hence the 98% confidence interval is between 6.42 hamsters per liter to 9.02 hamsters per liter
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