A plane flies 1.4 hours at 150 mph on a bearing of 10. It then turns and flies hours at the same speed on a bearing of . How far is the plane from its starting point?
Answers
Answer:
The answer is "1035.76 miles"
Explanation:
The aircraft flies at 120 mph for 1.5 hours at a [tex]10^{\circ}[/tex] bearing, then flies at the very same speed at [tex]100^{\circ}[/tex] bearings for 8.5 hours.
However an angle of [tex]100-10 = 90^{\circ}[/tex] between displacements
First shifts[tex]= 1.5 \times 120 = 180\ miles.[/tex]
Second shift [tex]= 8.5\times 120 = 1020\ miles.[/tex]
These two shifts are at [tex]90^{\circ}[/tex] and therefore the final shift is:
[tex]\to \sqrt{180^2+1020^2}=1035.76 \ miles[/tex]
Related Questions
In a test of a heat-seeking rocket, a first rocket is launched at 2000 fts and the heat-seeking rocket is launched along the same flight path 20 s later at a speed of 3000 fts. Find
the timest, and t, of flight of the rockets until the heat-seeking rocket destroys the first rocket
What are the times of the flight?
Answers
Answer:
Time of flight of first rocket = 60 seconds
Time of flight of second rocket = 40 seconds
Step-by-step explanation:
Let the time of flight of first rocket be t1.
Since the second rocket is launched 20 seconds later, then it means that;
t1 = t2 + 20
Where t2 is the time of flight of the second rocket.
When destruction has occurred, it means that both of the rockets would have covered the same distance.
We know that;
Distance = speed × time
Thus;
2000t1 = 3000t2
We know that t1 = t2 + 20
Thus;
2000(t2 + 20) = 3000t2
2000t2 + 40000 = 3000t2
3000t2 - 2000t2 = 40000
1000t2 = 40000
t2 = 40000/1000
t2 = 40 seconds
Thus;
t1 = 40 + 20
t1 = 60 seconds
in the number 36,802 if the 8 was replaced with a 2 would the value increase or decrease
Answers
Answer:
decrease
Step-by-step explanation:
If Mr. David does a job in x hours and Mr. Ludwig in y hours. What part of the job they could do together if they worked for k hrs?
Answers
Answer:
(1/x + 1/y)k is the answer :)
8th Grade Which expression is equivalent to 1/27
Answers
Answer:
[tex]( \frac{1}{3})^{3} [/tex]
Step-by-step explanation:
There are many expressions that can be equivalent to 1/27.
For example, 2/54, 3/81 etc
But I think the expression you are looking for is
[tex] \frac{1}{27} = \frac{1 \times 1 \times 1}{3 \times 3 \times 3} = \frac{ {1}^{3} }{ {3}^{3} } = ( \frac{1}{3} )^{3} [/tex]
Hope this is helpful
g Assuming the probability of a single sample testing positive is 0.15, find the probability of a positive result for two samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely necessary?
Answers
Solution :
The objective is to obtain the [tex]\text{probability of a positive result}[/tex] for 2 samples combined into a [tex]\text{mixture}[/tex].
Given that the [tex]\text{probability of a single sample testing positive is 0.15}[/tex]
The probability of the positive test result is calculated as follows :
P ( positive mixture ) = P(1 or more samples positive)
= 1 - P (none +ve)
= 1 - P ((-ve) x (-ve))
[tex]$= 1-P(-ve )^2$[/tex]
[tex]$=1-[1-P(+ve)]^2$[/tex]
[tex]$=1-(1-0.15)^2$[/tex]
[tex]$=1-(0.85)^2$[/tex]
= 1 - 0.7225
= 0.2775
No, the probability is not low enough.
answer it correctly:)
can anyone help me?:)
Answers
Answer:
JAR WITH MARBLES.
There's
5 Blue Marbles
3 Red Marbles
2 Yellow Marbles
Pr = No of desired outcome/No of Possible Outcomes
No of Possible Outcomes = 10.
1. Pr(yellow) = 2/10 = 1/5.
2. Pr(Red) = 3/10
3. Pr(Blue) = 5/10 = 1/2
4. Pr(Yellow and Red) = 2/10 x 3/10 = 6/100 = 3/50.
5.Pr(Blue and Red)= 5/10 x 3/10 = 15/100 = 3/20.
6.Pr( Yellow and Blue) = 2/10 x 5/10 = 10/100 = 1/10.
THE CHIPS ARE PLACED IN A JAR AND MIXED.
No of Possible Outcomes = 8.
The Numbers are 1,2,3,4,5,6,7,8.
There's
4 Even Numbers
4 Odd Numbers
1. Pr(Even) = 4/8 = 1/2
2. Pr(Odd) = 4/8 = 1/2
3. Pr(Chip with Biggest No) = 1/8.
Reason. There can only be one Number which Is the biggest amongst all. So the Probability of picking it is 1.
4.Pr(Smallest Number) = 1/8 (Same concept).
5.Pr(Prime Number)
The prime Numbers above are 2,3,5,7
Pr(Prime) = 4/8 = 1/2.
Hope this helps!.
one story with author and summary please
Answers
Answer:
The story tells of a plain-looking little bird (the Ugly Duckling) born in a barnyard. His brothers and sisters as well as the other birds and animals on the farm tease him for being plain and ugly, so he runs off to live with a flock of wild ducks and geese until hunters shoot down the flock. Alone again, the Ugly Duckling finds a home with an old woman, but her cat and hen also tease him, so he doesn't stay there long.
In his wanderings, the Ugly Duckling comes across a flock of migrating swans, and he wishes to join them but can't because he's too young and can't fly well enough. When winter sets in, a farmer rescues the Ugly Duckling, but the farmer's children and other animals frighten him with their noise and teasing, so again, he flees. He spends a cold and lonely winter hiding in a cave until springtime, when the flock of swans comes to the lake near his hiding place.
When the Ugly Duckling approaches the swans, he's delighted to find that they accept him and treat him like one of them. When he looks at his reflection in the lake, he realizes, to his astonishment, that he's matured into a beautiful swan himself. When the swans fly off from the lake, he spreads his wings and joins them, finally having found a family who accepts him.
You get GPS units from two manufacturers, A and B. You get 43% of your units from A and 57% of your units from B. In the past, 2% of the units from A have been defective, and 1.5% of the units from B have been defective. Assuming this holds true, if a GPS unit is found to be defective what is the probability that it came from manufacturer A (think Bayes Theorem AND round to two decimal places)
Answers
Answer:
0.5015 = 50.15% probability that it came from manufacturer A.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Defective
Event B: From manufacturer A.
Probability a unit is defective:
2% of 43%(from manufacturer A)
1.5% of 57%(from manufacturer B). So
[tex]P(A) = 0.02*0.43 + 0.015*0.57 = 0.01715[/tex]
Probability a unit is defective and from manufacturer A:
2% of 43%. So
[tex]P(A \cap B) = 0.02*0.43 = 0.0086[/tex]
What is the probability that it came from manufacturer A?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0086}{0.01715} = 0.5015[/tex]
0.5015 = 50.15% probability that it came from manufacturer A.
find the sum and difference between the place value and face value of 5 in the number 3508 6941
Answers
Answer:
Sum= 5000005
Difference= 4999995
Step-by-step explanation:
The place value of 5 in the number 35086941 is 5000000
The face value is 5
The sum between the face value and place value can be calculated as follows
°= 5000000+5
= 5000005
The difference can be calculated as follows
= 5000000-5
= 4999995
Find the volume of the box. The box shows the length is 6 feet, the width is 5 feet, and the height is 3 feet. The volume of the box is blank cubic feet. The solution is
Answers
Answer:
[tex]90[/tex] [tex]ft^3[/tex]
Step-by-step explanation:
----------------------------------------
The formula to find the volume of a rectangular prism is [tex]V=lwh[/tex]
Let's substitute the number for the length, width, and height now.
[tex]V=(6)(5)(3)[/tex]
[tex]V=(30)(3)[/tex]
[tex]V=90[/tex]
--------------------
Hope this is helpful.
PLEASE may I get help, I'm so lost. It would mean a lot to me, please.
A grade school is putting on its Spring show. The theater seats 120 people. Because of the demand for tickets, the school has made the following specifications:
•The number of tickets for children will be twice as many as the number for adults.
•Full-price adult tickets will be $24; children's tickets will be $12
•At least 10 of the adult tickets will be made available to seniors aged 60 and over at 25% discount
•Total ticket sales must be at least $1,800
1)How many children's tickets will be sold? 2)How many adult tickets (full-priced and senior) will be sold?
3)How many of the adult tickets can be sold with the senior discount?
Answers
9514 1404 393
Answer:
804010 to 20, inclusiveStep-by-step explanation:
1. The various goals can be met without filling the theater. This fact means there is a range of possibilities for each of the answers. However, we take the wording, "because of the demand for tickets ..." to mean demand is high and the theater will be sold out.
Since two children's tickets will be sold for each adult ticket sold, the number of children's tickets is 2/3 of the total.
children's tickets = 2/3 × 120 = 80
__
2. The remaining 40 tickets will be adult tickets.
40 adult tickets will be sold.
__
3. The total revenue must be at least $1800. If we allow 'd' tickets to be sold at a discount, then we can find the limits on d using the inequality ...
24(40-d) +24(0.75)d +12(80) ≥ 1800 . . . . revenue from ticket sales
-6d ≥ -120 . . . . . . . . . . . . . . . . . . . collect terms, subtract 1920
d ≤ 20 . . . . . . . . . . divide by -6
At least 10 and at most 20 adult tickets can be sold with a discount.
("At least 10" comes from the problem requirements.)
Identify the sampling method that was used. Cattle tag numbers at a livestock auction are selected using a random number generator. The cattle are then tested for mad cow disease.
a. Stratified
b. Systematic
c. Random
d. Cluster
Answers
Answer:
c. Random
Step-by-step explanation:
In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.
There are various types of sampling used by researchers and these are;
1. Systematic sampling.
2. Convenience sampling.
3. Stratified sampling.
4. Cluster sampling.
5. Random sampling.
Random sampling can be defined as a type of sampling in which the researcher select a sample of the population in order to determine an outcome.
Thus, the type of sampling used is random sampling.
Anne plans to increase the prices of all the items in her store but 5%. To the nearest cent how much will an artist saved if the artist buys a canvas and a frame that each measures 24 by 36 in before the price increase goes into effect. 24/36 canvas price 22.80 and the frame price is 89.98
Answers
9514 404 393
Answer:
5.64
Step-by-step explanation:
The increase in price for the given items will be ...
5% × (22.80 + 89.98) ≈ 5.64
The artist will save 5.64 by making a purchase before the price increase.
If you multiply 0.47 × 3.2, then what is the answer?
Answers
Answer:
1.504
Step-by-step explanation:
0.47×100 = 47
3.2×100 = 320
47×320 = 15040
15040÷10000 = 1.504
6. Calculate the area of the octagon in the
figure below.
Answers
Answer:
[tex]41\text{ [units squared]}[/tex]
Step-by-step explanation:
The octagon is irregular, meaning not all sides have equal length. However, we can break it up into other shapes to find the area.
The octagon shown in the figure is a composite figure as it's composed of other shapes. In the octagon, let's break it up into:
4 triangles (corners)3 rectangles (one in the middle, two on top after you remove triangles)Formulas:
Area of rectangle with length [tex]l[/tex] and width [tex]w[/tex]: [tex]A=lw[/tex] Area of triangle with base [tex]b[/tex] and height [tex]h[/tex]: [tex]A=\frac{1}{2}bh[/tex]Area of triangles:
All four triangles we broke the octagon into are congruent. Each has a base of 2 and a height of 2.
Thus, the total area of one is [tex]A=\frac{1}{2}\cdot 2\cdot 2=2\text{ square units}[/tex]
The area of all four is then [tex]2\cdot 4=8[/tex] units squared.
Area of rectangles:
The two smaller rectangles are also congruent. Each has a length of 3 and a width of 2. Therefore, each of them have an area of [tex]3\cdot 2=6[/tex] units squared, and the both of them have a total area of [tex]6\cdot 2=12[/tex] units squared.
The last rectangle has a width of 7 and a height of 3 for a total area of [tex]7\cdot 3=21[/tex] units squared.
Therefore, the area of the entire octagon is [tex]8+12+21=\boxed{41\text{ [units squared]}}[/tex]
Please help NO LINKS
Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by
y
=
x
2
,
y
=
0
, and
x
=
5
,
about the
y
-axis.
V
=
Answers
Answer:
[tex]\displaystyle V = \frac{625 \pi}{2}[/tex]
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationGraphingCalculus
Integrals
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Shell Method: [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]
[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is volumeStep-by-step explanation:
Step 1: Define
y = x²
y = 0
x = 5
Step 2: Identify
Find other information from graph.
See Attachment.
Bounds of Integration: [0, 5]
Step 3: Find Volume
Substitute in variables [Shell Method]: [tex]\displaystyle V = 2\pi \int\limits^5_0 {x(x^2)} \, dx[/tex][Integrand] Multiply: [tex]\displaystyle V = 2\pi \int\limits^5_0 {x^3} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle V = 2\pi \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^5_0[/tex]Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle V = 2\pi \bigg( \frac{625}{4} \bigg)[/tex]Multiply: [tex]\displaystyle V = \frac{625 \pi}{2}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e
The lebgth of a rrctangle is 3 inches more than its width.The perimeter of the rectangle is 34 inches.
Answers
Step-by-step explanation:
there is the answer. good luck
Jason wants to fill a cylindrical water tank to its full capacity. He knows that the volume of the tank is equal to the product of , the square of the radius of the tank, and the height of the tank. Jason measured the height of the tank and found it to be 15 feet. He also measured the radius of the cylindrical tank and found it to be 10 feet. If Vrepresents the volume of the cylindrical tank, then which of the following equations can be used to calculate the volume of the tank?
Answers
Answer:
B) [tex]\sqrt{\frac{v}{15\pi } } = 10[/tex]
Step-by-step explanation:
Find the perimeter of WXYZ. Round to the nearest tenth if necessary.
Answers
Answer:
C. 15.6
Step-by-step explanation:
Perimeter of WXYZ = WX + XY + YZ + ZW
Use the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex] to calculate the length of each segment.
✔️Distance between W(-1, 1) and X(1, 2):
Let,
[tex] W(-1, 1) = (x_1, y_1) [/tex]
[tex] X(1, 2) = (x_2, y_2) [/tex]
Plug in the values
[tex] WX = \sqrt{(1 - (-1))^2 + (2 - 1)^2} [/tex]
[tex] WX = \sqrt{(2)^2 + (1)^2} [/tex]
[tex] WX = \sqrt{4 + 1} [/tex]
[tex] WX = \sqrt{5} [/tex]
[tex] WX = 2.24 [/tex]
✔️Distance between X(1, 2) and Y(2, -4)
Let,
[tex] X(1, 2) = (x_1, y_1) [/tex]
[tex] Y(2, -4) = (x_2, y_2) [/tex]
Plug in the values
[tex] XY = \sqrt{(2 - 1)^2 + (-4 - 2)^2} [/tex]
[tex] XY = \sqrt{(1)^2 + (-6)^2} [/tex]
[tex] XY = \sqrt{1 + 36} [/tex]
[tex] XY = \sqrt{37} [/tex]
[tex] XY = 6.08 [/tex]
✔️Distance between Y(2, -4) and Z(-2, -1)
Let,
[tex] Y(2, -4) = (x_1, y_1) [/tex]
[tex] Z(-2, -1) = (x_2, y_2) [/tex]
Plug in the values
[tex] YZ = \sqrt{(-2 - 2)^2 + (-1 -(-4))^2} [/tex]
[tex] YZ = \sqrt{(-4)^2 + (3)^2} [/tex]
[tex] YZ = \sqrt{16 + 9} [/tex]
[tex] YZ = \sqrt{25} [/tex]
[tex] YZ = 5 [/tex]
✔️Distance between Z(-2, -1) and W(-1, 1)
Let,
[tex] Z(-2, -1) = (x_1, y_1) [/tex]
[tex] W(-1, 1) = (x_2, y_2) [/tex]
Plug in the values
[tex] ZW = \sqrt{(-1 -(-2))^2 + (1 - (-1))^2} [/tex]
[tex] ZW = \sqrt{(1)^2 + (2)^2} [/tex]
[tex] ZW = \sqrt{1 + 4} [/tex]
[tex] ZW = \sqrt{5} [/tex]
[tex] ZW = 2.24 [/tex]
✅Perimeter = 2.24 + 6.08 + 5 + 2.24 = 15.56
≈ 15.6
Answer:CCCCCCCCCCCCCCCCC
Step-by-step explanation:
In isosceles △HAM, m∡A =32°, . What is m∠H?
32°32 degrees
58°58 degrees
74°74 degrees
148°
Answers
Answer:
32°
Step-by-step explanation:
in 32° is right answer
In isosceles triangle, △HAM, m∠H is 74 degree.
What is isosceles triangle?A triangle in which any two sides are equal in length and angles opposite to equal side are also equal. And sum of all angles in a triangle is 180.
Given, m∠A = 32°
sum of all angles = 180°
In △HAM
∠H = ∠M
∠H+ ∠A+ ∠M = 180°
2∠H = 180 - 32
2∠H = 148
∠H = 74°
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(2x4−7x3−6x2+23x−12)÷(x−4)
Answers
Answer:
[tex]\frac{23x-37}{x-4}[/tex]
Step-by-step explanation:
Assume one individual from the group is randomly selected. Find the probability of getting someone who tests negative, given that he or she had the disease. the probability is approximately?
Answers
Answer:
[tex]P(Negative | Yes) = 0.0486[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccc}{} & {Yes} & {No} & {Positive} & {137} & {24} & {Negative} & {7} & {132} \ \end{array}[/tex]
Required
[tex]P(Negative | Yes)[/tex]
This is calculated as:
[tex]P(Negative | Yes) = \frac{n(Negative\ n\ Yes)}{n(Yes)}[/tex]
So, we have:
[tex]P(Negative | Yes) = \frac{7}{137+7}[/tex]
[tex]P(Negative | Yes) = \frac{7}{144}[/tex]
[tex]P(Negative | Yes) = 0.0486[/tex]
What is the scale factor from ALMN to AOPQ?
M
P
3
3
3
3
2
4
N
0
4
A. 4
(
B. 0
c
C. 3
D. 1
Answers
Answer:
D
Step-by-step explanation:
There 2 ways to interpret this problem.
From the info given:
These two triangles are congruent by SSS and congruent triangles have congruent or equal side lengths so the answer have to be 1.
If the triangles are similar, the side lengths form a proportion of that
[tex] \frac{3}{3} = \frac{3}{3} [/tex]
So the ratio or scale factor is 1.
The scale factor in the figure is 1.
What is a scale factor?A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.
Given that two triangles, LMN and OPQ, we need to find the scale factor,
We can see triangles are congruent, and we know that
Two triangles are congruent, by the SSS congruence criterion, if they are similar and the scale factor happens to be 1,
Hence, the scale factor in the figure is 1.
Learn more about scale factors, click;
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WILL GIVE BRAINLIEST!!! I WILL BE VERY GRATEFUL IF YOU HELP ME ASAP
Answers
Answer:
According to me its 90 degree
Step-by-step explanation:
If one table and two lamps cost $88, and two
tables and three lamps cost $153, how much
does a lamp cost?
Answers
Answer:
One lamp is equal to 23 dollars
One table is equal to 42 dollars.
Step-by-step explanation:
We can solve this by first organizing what we have.
1 table (t) + 2 lamps (l) = 88.
2 tables (t) + 3 lamps (l) = 153.
_____________
===============
1t + 2l = 88
2t + 3l = 153
===============
-------------------------
If we multiply both sides by 2 on the first equation of
1t + 2l = 88
we could get
2t + 4l = 176.
If that is true, we can subtract the second equation of
2t + 3l = 153 from the new equation to get the price of a lamp.
2t + 4l = 176
- 2t + 3l = 153
____________
= 0t + l = 23
One lamp is equal to 23.
We can check this by plugging it into an equation.
1 + 2(23) = 88
1t + 46 = 88
1t + 46 - 46 = 88 - 46
1t = 42
If one table equals 42, we can put this back into the second equation to check.
2 (42) + 3 (23) = 153
84 + 69 = 153
That is correct.
Another way to solve is to put this like a system of equations in a graph, by replacing "t" by "x" for example, and "l" by y.
Then you could put it into a graphing calculator and solve by looking for the place where the two lines converge or meet.
Since we put "x" for "t", that means that whatever the x-value is on the solution point, that is the cost of a table, and the y-value is the cost of the lamps.
Another way to solve, is to find the unit rate first by subtracting the first equation from the second equation.
2t + 3l = 153
- 1t + 2l = 88
____________
= t + l = 65
If t + l = 65, we can rearrange that equation to be something like t = 65 - l.
That means "t" is equal to 65 bucks minus a lamp.
We put this back into the first equation of
1t + 2l = 88
and replace "t" with the previous expression.
1(65 - l) + 2l = 88
Simplify/distributive property
65 - l + 2l = 88
65 - 65 - l + 2l = 88 - 65
-l + 2l = 23
l = 23
One lamp is equal to 23 bucks.
Confirmed :)
A lamp cost $23
Let the cost of a table be represented by x
Let the cost of a lamp be represented by y.
Since one table and two lamps cost $88, this can be represented as:
x + 2y = 88 ........ equation i
Since two tables and three lamps cost $153, this can be represented as:
2x + 3y = 153 ........ equation ii
Therefore, the equations are:
x + 2y = 88 ....... i
2x + 3y = 153 ....... ii
From equation i,
x + 2y = 88
x = 88 - 2y ...... iii
Put the value of x into equation ii
2x + 3y = 153
2(88 - 2y) + 3y = 153
176 - 4y + 3y = 153
Collect like terms
-4y + 3y = 153 - 176
-y = -23
y = 23
Therefore, a lamp cost $23
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48. What is the volume of the cuboid below? 3cm 2cm 2cm
Answers
Answer:
Cuboid = width*height*length
Cuboid = 24 cm^2
According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.0746 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 318 independent returns from this year, what is the probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS
Answers
Answer:
0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS
Step-by-step explanation:
We use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Approximately 0.0746 of the tax returns filed are fraudulent or will contain errors.
This means that [tex]p = 0.0746[/tex]
Random sample of 318 independent returns
This means that [tex]n = 318[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 318*0.0746 = 23.7228[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{318*0.0746*0.9254} = 4.6854[/tex]
What is the probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS?
Using continuity correction, this is [tex]P(X \geq 23 - 0.5) = P(X \geq 22.5)[/tex], which is 1 subtracted by the p-value of Z when X = 22.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22.5 - 23.7228}{4.6854}[/tex]
[tex]Z = -0.26[/tex]
[tex]Z = -0.26[/tex] has a p-value of 0.3974.
1 - 0.3974 = 0.6026
0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS
work out the value of 5x8 x 5-2/5x4
Answers
Answer:
=6
Step-by-step explanation:
(5×8)×(5-2)/(5×4)
Numerator =40×3
=120
Denominator = 5×4
=20
simplifying 120/20
=6
Answer:
6
follow the BDMAS rule
bracket ,division ,multiplication, addition and last subtraction
you won't get any maths problem wrong
Ross Times, the student newspaper of Ross College, printed a "What do you think?" column feature asking: "Do you think that the college is doing enough to provide student parking?" Anyone could mail in a response or use the paper's Web site to respond. In all, 126 answers were received. This is an example of what type of sample? A convenience sample A simple random sample A multistage sample A voluntary response sample
Answers
Answer: A simple random sample
Step-by-step explanation:
Simple random sampling refers to the probability sampling whereby the researcher chooses selects a subset of participants from the population.
In this case, every member has an equal chance of being chosen. Since anyone could mail in a response or use the paper's Web site to respond, then it's a simple random sampling.
In 2005, there were 14,100 students at college A, with a projected enrollment increase of 1000 students per year. In the same year, there were 34,350 students at college B, with a projected enrollment decline of 1250 students per year. According to these projections, when will the colleges have the same enrollment? What will be the enrollment in each college at that time?
Answers
Let A be college A and let B be College B
A= 14,100
Rule: 1 Year = +1,000 students
B= 34,350
Rule: -1250 per year
1st Answer: 2017
Notice: I didn't show the formula because I'm not %100 sure I'm kind of off so if this is incorrect I'm deeply sorry. I truly am. On the bright side, I think its correct.
