Answer:
The pipe C alone can fill the tank in 14 hours .
Step-by-step explanation:
Given as :
The three pipes a , b , c can fill the pipes in 6 hours
They work for 2 hours
After that c pipe is close and a , b finish remaining work
Now, According to question
In 1 hour pipes ( a + b + c ) fill [tex]\frac{1}{6}[/tex] of the tank
∴ In 2 hour pipes ( a + b + c ) fill [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex] of the tank
Remaining ( 1 - [tex]\frac{1}{3}[/tex] ) = [tex]\frac{2}{3}[/tex] part is filled by pipes a and b in 7 hours
∴ The whole tank is filled by a and b in 7 × [tex]\frac{3}{2}[/tex] = [tex]\frac{21}{2}[/tex] hours
∴ In 1 hour pipes A and b fill the tank in [tex]\frac{2}{21}[/tex] hours
∴ In 1 hour pipes C alone can fill the tank in[tex]\frac{1}{6}[/tex] - [tex]\frac{2}{21}[/tex] hours
Or, In 1 hour pipes C alone can fill the tank in [tex]\frac{9}{126}[/tex] = [tex]\frac{1}{14}[/tex]
Or, In 1 hour pipes C alone can fill the tank in 14 hours
Hence The pipe C alone can fill the tank in 14 hours . Answer
The moving averages method refers to a forecasting method that
a. relates a time series to other variables that are believed to explain or cause its behavior.
b. uses regression relationship based on past time series values to predict the future time series values.
c. uses the average of the most recent data values in the time series as the forecast for the next period.
d. is used when considerable trend, cyclical, or seasonal effects are present
Answer:
c. uses the average of the most recent data values in the time series as the forecast for the next period.
Step-by-step explanation:
We assume you want to complete the description of moving averages method.
The moving in moving averages refers to the fact that the data points used to compute the average are some number of most recent data points. As data is accumulated, the data used to compute the average "moves" to include the newest data and exclude the oldest data.
A large explosion causes wood and metal debris to rise vertically into the air with an initial velocity of 160 feet per second. The function h(t) = 160 t − 16 t 2 160t-16t2 gives the height of the falling debris above the ground, in feet, t t seconds after the explosion.
a. Use the given polynomial to find the height of the debris 2 second(s) after the explosion.
b. Factor the given polynomial completely.
Answer:
a) The debris was 256 feet into the air after 2 seconds of the explosion.
b)
[tex]h(t) = -16t(t-10)[/tex]
Step-by-step explanation:
We are given the following in the question:
Initial Velocity = 160 feet per second
[tex]h(t) = 160t-16t^2[/tex]
The above function gives the height in feet and t is seconds after the explosion.
a) Height of the debris 2 second(s) after the explosion.
We put t = 2 in the above function
[tex]h(2) = 160(2)-16(2)^2 = 256[/tex]
Thus, the debris was 256 feet into the air after 2 seconds of the explosion.
b) Factor the polynomial
[tex]h(t) = 160t-16t^2\\= 16t(10-t)\\=-16t(t-10)[/tex]
Final answer:
The height of the debris 2 seconds after the explosion is 256 feet. The given polynomial can be factored completely as -16t(t - 10)
Explanation:
To find the height of the debris 2 seconds after the explosion, we can substitute t = 2 into the equation h(t) = 160t - 16t^2.
So, h(2) = 160(2) - 16(2)^2 = 320 - 16(4) = 320 - 64 = 256 feet.
Therefore, the height of the debris 2 seconds after the explosion is 256 feet.
To factor the given polynomial completely, we can rewrite it as:
h(t) = -16t^2 + 160t.
Now, we can factor out a common factor of -16t:
h(t) = -16t(t - 10).
This gives us the completely factored form of the polynomial.
a. Find PR in the diagram
b. Find the perimeter of quadrilateral PQRS
Answer:
Step-by-step explanation:
The quadrilateral has 4 sides and only two of them are equal.
A) to find PR, we will consider the triangle, PRQ.
Using cosine rule
a^2 = b^2 + c^2 - 2abcos A
We are looking for PR
PR^2 = 8^2 + 7^2 - 2 ×8 × 7Cos70
PR^2 = 64 + 49 - 112 × 0.3420
PR^2 = 113 - 38.304 = 74.696
PR = √74.696 = 8.64
B) to find the perimeter of PQRS, we will consider the triangle, RSP. It is an isosceles triangle. Therefore, two sides and two base angles are equal. To determine the length of SP,
We will use the sine rule because only one side,PR is known
For sine rule,
a/sinA = b/sinB
SP/ sin 35 = 8.64/sin110
Cross multiplying
SPsin110 = 8.64sin35
SP = 8.64sin35/sin110
SP = (8.64 × 0.5736)/0.9397
SP = 5.27
SR = SP = 5.27
The perimeter of the quadrilateral PQRS is the sum of the sides. The perimeter = 8 + 7 + 5.27 + 5.27 = 25.54 cm
A boat's crew rowed 7.5 miles downstream, with the current, in 1.5 hours. The return trip upstream, against the current, covered the same distance, but took 2.5 hours. Find the crew's average rowing velocity in still water and the average velocity of the current.
Answer:
Average rowing velocity of boat in still water is 4 miles per hour and average velocity of the current is 1 mile per hour.
Step-by-step explanation:
We are given the following in the question:
Let x be the average rowing velocity of boat in still water and y be the the average velocity of the current.
[tex]\text{Speed} = \displaystyle\frac{\text{Distance}}{\texr{Time}}[/tex]
The boat rowed 7.5 miles downstream, with the current, in 1.5 hours.
Velocity with the current =
[tex]=\text{average rowing velocity of boat in still water} + \text{ average velocity of the current} = x + y[/tex]
Thus, we can write the equation:
[tex]7.5 = (x+y)1.5\\x+y = 5[/tex]
The return trip upstream, against the current, covered the same distance, but took 2.5 hours.
Velocity against the current =
[tex]=\text{average rowing velocity of boat in still water} - \text{ average velocity of the current} = x - y[/tex]
Thus, we can write the equation:
[tex]7.5 = (x-y)2.5\\x-y = 3[/tex]
Solving, the two equations:
[tex]2x = 8\\x = 4, y = 1[/tex]
Thus, average rowing velocity of boat in still water is 4 miles per hour and average velocity of the current is 1 mile per hour.
Han spent 75 minutes practicing the piano over the weekend. Priya practiced the violin for 152% as much as Han practiced the piano. How long did she practice
Priya practiced the violin for 114 minutes
Solution:Given that
Han spent 75 minutes practicing the piano over the weekend
Priya practiced the violin for 152% as much as Han practiced the piano
Need to determine how long did priya practice
Duration of Han practicing the piano over weekend = 75 minutes
As given that Priya practiced the violin for 152% as much as Han practiced the piano
=> Duration of Priya practicing the piano = 152% of Han practicing the piano
=> Duration of Priya practicing the piano = 152% of 75 minutes
We know that a % of b is written in fraction as [tex]\frac{a}{100} \times b[/tex]
[tex]\Rightarrow \text { Duration of Priya practicing the piano }=\frac{152}{100} \times 75=114 \text { minutes }[/tex]
Hence Priya practiced the violin for 114 minutes
4x+9+3x=30
solve for x
Answer:
the answer is 3
7x + 9= 30
7x = 21
x = 3
Answer:
x = 3
Step-by-step explanation:
Collect like terms;
7x + 9 = 30
Subtract 9 from both sides;
7x = 21
Divide both sides by 7;
x = 3
The monthly utility bills in a city are normally distributed with a mean of $121 and a standard deviation of $23. Find the probability that a randomly selected utility bill is between $110 and $130.
To find the probability that a randomly selected utility bill is between $110 and $130, we can use the formula for z-score. By calculating the z-scores for both values, we can find the areas under the curve and subtract them to get the probability.
To find the probability that a randomly selected utility bill is between $110 and $130, we can use the formula for the z-score:
z = (x - μ) / σ
where x is the value we are looking for, μ is the mean, and σ is the standard deviation.
In this case, x = $110, μ = $121, and σ = $23.
Substituting these values into the formula, we get:
z = (110 - 121) / 23 = -0.4783
Using a z-table or a calculator, we can find that the area to the left of -0.4783 is approximately 0.3186.
Next, we repeat the process for $130:
z = (130 - 121) / 23 = 0.3913
Using a z-table or a calculator, we can find that the area to the left of 0.3913 is approximately 0.6480.
To find the probability that the utility bill is between $110 and $130, we subtract the area to the left of $110 from the area to the left of $130:
P(110 ≤ X ≤ 130) = 0.6480 - 0.3186 = 0.3294
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please help me!!!!!!!!!!!!!!!!
Answer:
0.91
Step-by-step explanation:
The total of all numbers in the diagram is 35 +5 +10 +5 = 55.
The total of the numbers inside one or both circles is 35 +5 +10 = 50.
The probability of choosing a random student from inside one or both circles (plays some instrument) is 50 out of 55, or ...
50/55 ≈ 0.9090909... ≈ 0.91
P(A∪B) ≈ 0.91
Mia recently bought a car worth $20,000 on loan with an interest rate of 6.6%. She made a down payment of $1,000 and has to repay the loan within two years (24 months). Calculate her total cost.
Answer:
$22,508
Step-by-step explanation:
Edmentum
The total cost that she pays for car will be $22,508.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
A = P + (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
Mia as of late purchased a vehicle worth $20,000 borrowed with a financing cost of 6.6%. She made an initial investment of $1,000 and needs to reimburse the credit in the span of two years (two years).
Then the total cost that she pays will be calculated as,
A = $20,000 + ($19,000 x 6.6 x 2) / 100
A = $20,000 + $2,508
A = $22,508
The total cost that she pays will be $22,508.
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The 8 leaders of the G8 nations convene in Rome and stand in a row as they get ready to have some pictures of them taken by the press. What is the probability that the picture that the New York Times' editors will randomly select for publishing the next day is one in which Berlusconi is not standing next to Obama? (assuming that there are pictures of all possible standing arrangements).
Answer:
The required probability is [tex]\frac{3}{4}[/tex].
Step-by-step explanation:
Consider the provided information.
There are 8 leaders.
Thus, the total number of ways to arrange 8 leaders are 8!.
Assume that Obama and Berlusconi is one person.
Therefore the total number of leaders are 7 (As Obama and Berlusconi is one person).
The number of ways in which 7 leader can be arranged: 7!
Although Obama and Berlusconi is one unit but they can interchange their place in 2 ways. Like Obama and Berlusconi or Berlusconi and Obama
That means the total number of ways : 7!×2
The number of ways in which they are not next to each other = Total number of ways - The number of ways in which they are next to each other
Number of ways they are not next to each other = 8!-7!×2
The probability that they are not next to each other = [tex]\frac{8!-7!\times2}{8!}=\frac{3}{4}[/tex]
Hence, the required probability is [tex]\frac{3}{4}[/tex].
In a box of 15 tablets, 4 of the tablets are defective. Three tablets are selected at random. what is the probability that a store buys three tablets and receives: a) no defective tablets, b) one defective tablet, and c) at least one non-defective tablet.
Answer:
a) 0.394
b) 0.430
c) 0.981
Step-by-step explanation:
Use binomial probability:
P = nCr pʳ (1−p)ⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
and p is the probability of success.
Here, n = 3 and p = 4/15.
r is the number of defective tablets.
a) If r = 0:
P = ₃C₀ (4/15)⁰ (1−4/15)³⁻⁰
P = 1 (1) (11/15)³
P = 0.394
b) If r = 1:
P = ₃C₁ (4/15)¹ (1−4/15)³⁻¹
P = 3 (4/15) (11/15)²
P = 0.430
c) If r ≠ 3:
P = 1 − ₃C₃ (4/15)³ (1−4/15)³⁻³
P = 1 − 1 (4/15)³ (1)
P = 0.981
To find the probability of selecting no defective tablets, multiply the probabilities of selecting non-defective tablets.
Explanation:a) To find the probability of selecting no defective tablets, we need to find the probability of selecting 3 non-defective tablets. There are 11 non-defective tablets out of the total of 15 tablets. So, the probability is:
Multiplying these probabilities together:
(11/15) * (10/14) * (9/13) = 990/2730 ≈ 0.362 = 36.2%
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What is the value of x?
Answer:
Step-by-step explanation:
Set this up according to the Triangle Proportionality Theorem:
[tex]\frac{3x}{4x}=\frac{3x+7}{5x-8}[/tex]
Cross multiply to get
[tex]3x(5x-8)=4x(3x+7)[/tex]
and simplify to get
[tex]15x^2-24x=12x^2+28x[/tex]
Get everything on one side of the equals sign and solve for x:
[tex]3x^2-52x=0[/tex] and
[tex]x(3x-52)=0[/tex]
By the Zero Product Property,
x = 0 or 3x - 52 = 0 so x = 17 1/3
An employment agency requires applicants average at least 70% on a battery of four job skills tests. If an applicant scored 70%, 77%, and 81% on the first three exams, what must he score on the fourth test to maintain a 70% or better average.
Answer:
atleast 52
Step-by-step explanation:
Given that an employment agency requires applicants average at least 70% on a battery of four job skills tests.
An applicant scored 70%, 77%, and 81% on the first three exams,
Since weightages are not given we can assume all exams have equal weights
Let x be the score on the 4th test
Then total of all 4 exams = [tex]70+77+81+x\\= 228+x[/tex]
Average should exceed 70%
i.e.[tex]\bar X \geq 70\\Total\geq 70(4) =280[/tex]
Comparing the two totals we have
[tex]228+x\geq 280\\x\geq 280-228 = 52[/tex]
Hemust score on the fourth test a score atleast 52 to maintain a 70% or better average.
Simplify the rational expressions. state any excluded values.
1. 2x-8/x-4
2. 4x-8/4x+20
3. x+7/x^2+4x-21
4. x^2-3x-10/x+2
5. x^2-4/2-x
I need help pleeeese
See the answers in explanation
Explanation:Let's solve this problem as follows:
First.[tex]\bullet \ \frac{2x-8}{x-4} \\ \\ Common \ factor \ 2 \ from \ the \ numerator: \\ \\ \frac{2x-8}{x-4}=\frac{2(x-4)}{x-4} =2[/tex]
Second.[tex]\bullet \ \frac{4x-8}{4x+20} \\ \\ Common \ factor \ 4 \ from \ the \ numerator \ and \ denominator: \\ \\ \frac{4x-8}{4x+20}=\frac{4(x-2)}{4(x+5)}=\frac{(x-2)}{(x+5)}[/tex]
Third[tex]\bullet \ \frac{x+7}{x^2+4x-21} \\ \\ Rearranging \ denominator: \\ \\ \frac{x+7}{x^2-3x+7x-21}=\frac{x+7}{x(x-3)+7(x-3)}=\frac{x+7}{x(x-3)+7(x-3)} \\ \\ Common \ factor \ x-3 \ from \ denominator: \\ \\ \frac{x+7}{(x-3)(x+7)}=\frac{1}{x-3}[/tex]
Fourth.[tex]\bullet \ \frac{x^2-3x-10}{x+2} \\ \\ Rearranging \ numerator: \\ \\ \frac{x^2-3x-10}{x+2}=\frac{x^2-5x+2-10}{x+2}=\frac{x(x-5)+2(x-5)}{x+2} \\ \\ Common \ factor \ x-5 \\ \\ \frac{(x-5)(x+2)}{x+2}=x-5[/tex]
Fifth.[tex]\bullet \ \frac{x^2-4}{2-x} \\ \\ Difference \ of \ squares \ from \ numerator: \\ \\ \frac{(x-2)(x+2)}{2-x} \\ \\ Common \ factor \ -1 \ from \ denominator: \\ \\ \frac{(x-2)(x+2)}{-(x-2)}=-(x+2)[/tex]
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If all men had identical body types, their weight would vary directly as the cube of their height. The tallest person reached a record height of 8 feet 11 inches (107 inches) before his death at age 22. If a man who is 5 feet 10 inches tall (70 inches) with the same body type as the tallest person weighs 170 pounds, what was the tallest person's weight shortly before his death?
Answer: The weight of tallest person would be 607.16 pounds.
Step-by-step explanation:
Since we have given that
height of the tallest person = 8 feet 11 inches = 107 inches
If all men had identical body types, their weight would vary directly as the cube of their height.
If a man who is 5 feet 10 inches tall (70 inches) with the same body type as the tallest person weighs 170 pounds,
So, it becomes,
[tex]W=xh^3[/tex]
[tex]170=x(70)^3\\\\\dfrac{170}{70^3}=x\\\\x=\dfrac{170}{343000}[/tex]
So, weight of tallest person would be
[tex]W=\dfrac{170}{343000}\times 107^3\\\\W=607.16\ pounds[/tex]
Hence, the weight of tallest person would be 607.16 pounds.
First, let's consider the information we're given and set up an equation. We know that, given identical body types, a person's weight would vary directly as the cube of their height. What this means is that the ratio between the weight of two people and the cube of their respective heights will be the same regardless of their individual heights or weights. We can represent this as:
W_tall / W_normal = (Height_tall ^ 3) / (Height_normal ^ 3)
Where:
W_tall is the weight of the tallest person.
W_normal is the weight of the normal person (which we know is 170 pounds).
Height_tall is the height of the tallest person (which we know is 107 inches).
Height_normal is the height of the standard person (which we know is 70 inches).
We are looking to find the weight of the tallest person, so, to isolate W_tall in the equation above, we will multiply both sides of the equation by W_normal:
W_tall = W_normal * (Height_tall ^ 3) / (Height_normal ^ 3)
Substituting the known values into the equation, we get:
W_tall = 170 * (107 ^ 3) / (70 ^ 3)
Computing the values on the right-hand side of the equation, we find that the tallest person weighed approximately 607.16 pounds just before his death.
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What is the remainder when 6x+12 is divided by 2x-8.
Answer:
4(3x-2)
Step-by-step explanation
6x+12/2x-8
6x+6x-8
12x-8
4(3x-2)
Answer:
Step-by-step explanation:
2x-8 ) 6x+12 ( 3
6x-24
- +
-----------
36
quotient=3
remainder=36
You have been saving money in a piggy bank. Your piggy bank contains 75 coins that are all nickels and dimes. You take the money out of the bank to count, and find out that you have $5.95 saved up. How many dimes and how many nickels do you have?
You have 31 nickels and 44 dimes.
Step-by-step explanation:
Total coins = 75
Worth of coins = $5.95 = 5.95*100 = 595 cents
1 nickel = 5 cents
1 dime = 10 cents
Let,
Number of nickels = x
Number of dimes = y
According to given statement;
x+y=75 Eqn 1
5x+10y=595 Eqn 2
Multiplying Eqn 1 by 5
[tex]5(x+y=75)\\5x+5y=375\ \ \ Eqn\ 3\\[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](5x+10y)-(5x+5y)=595-375\\5x+10y-5x-5y=220\\5y=220[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{220}{5}\\y=44[/tex]
Putting y=44 in Eqn 1
[tex]x+44=75\\x=75-44\\x=31[/tex]
You have 31 nickels and 44 dimes.
Keywords: linear equations, subtraction
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The hypotenuse of a right triangle has one end at the origin and one end on the curve y = x 2 e −3x , with x ≥ 0. One of the other two sides is on the x-axis, the other side is parallel to the y-axis. Find the maximum area of such a triangle. At what x-value does it occur?
Answer:
At x = 1 and maximum area = 0.0499
Step-by-step explanation:
The hypotenuse of a right triangle has one end at the origin and other end on the curve, [tex]y=x^2e^{-3x}[/tex] with x ≥ 0.
One leg of right triangle is x-axis and another leg parallel to y-axis.
Length of base of right triangle = x
Height of right triangle = y
Area of right triangle, [tex]A=\dfrac{1}{2}xy[/tex]
[tex]A=\dfrac{1}{2}x^3e^{-3x}[/tex]
For maximum/minimum value of area.
[tex]\dfrac{dA}{dx}=\dfrac{3}{2}x^2e^{-3x}-\dfrac{3}{2}x^3e^{-3x}[/tex]
Now, find critical point, [tex]\dfrac{dA}{dx}=0[/tex]
[tex]\dfrac{3}{2}x^2e^{-3x}-\dfrac{3}{2}x^3e^{-3x}=0[/tex]
[tex]\dfrac{3}{2}x^2e^{-3x}(1-x)=0[/tex]
x =0,1
For x = 0, y = 0
For x = 1, [tex]y=e^{-3}[/tex]
using double derivative test:-
[tex]\dfrac{d^2A}{dx^2}=\dfrac{6}{2}xe^{-3x}-\dfrac{9}{2}x^2e^{-3x}-\dfrac{9}{2}x^2e^{-3x}-\dfrac{9}{2}x^3e^{-3x}[/tex]
At x= 0 , [tex]\dfrac{d^2A}{dx^2}=0[/tex]
Neither maximum nor minimum
At x = 1, [tex]\dfrac{d^2A}{dx^2}=-0.14<0[/tex]
Maximum area at x = 1
The maximum area of right triangle at x = 1
Maximum area, [tex]A=\dfrac{1}{e^3}\approx 0.0499[/tex]
The point of maxima will be x=3 and the maximum area will be 0.002 square units.
According to the diagram attached
The area of the given triangle will be = 0.5*base*height
As one end of the hypotenuse is on the curve [tex]y = x^2e^(-3x)[/tex], Coordinates of one end of the hypotenuse will be [tex](x, x^2e^(-3x)[/tex].
Area A(x) of the given triangle = 0.5*base* height
Base = x
Height = [tex]x^2e^(-3x)[/tex]
So A(x) = [tex]0.5*x*x^{2} *e^(-3x)[/tex]
[tex]A(x) = 0.5*x*x^{2} *e^(-3x)\\\\A(x) = 0.5 x^3e^(-3x)[/tex]
For the maximum area,
[tex]A'(x) = 0\\\\x^2e^(-3x) (x-3) = 0\\x = 0 and x=3[/tex]will be the points of extremum.
What are the points of the extremum?
Points of extremum are the values of x for which a function f(x) attains a maximum or minimum value.
A(0) = 0
A(3) = 0.002
Therefore, The point of maxima will be x=3, and the maximum area will be 0.002 square units.
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What is the volume of the cylinder?
Answer:
B. 2010.62 ft³
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h . . . . . where r is the radius and h is the height
Filling in the numbers and doing the arithmetic, we get ...
V = π(8 ft)²(10 ft) = 640π ft³ ≈ 2010.6193 ft³ ≈ 2010.62 ft³
The volume of the cylinder is about 2010.62 ft³.
Solve for x (log equation) (don’t mind the work)
Answer:
Step-by-step explanation:
In a recent Super Bowl, a TV network predicted that 50 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 106 people who saw the commercials and found that 48 of them said they would watch one of the television shows.Suppose you are have the following null and alternative hypotheses for a test you are running:H0:p=0.5Ha:p≠0.5Calculate the test statistic, rounded to 3 decimal placesz=
Answer:
z= -0.968
We can conclude that we fail to reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they would watch one of the television shows not differs from 0.5 or 50% .
Step-by-step explanation:
1) Data given and notation n
n=106 represent the random sample taken
X=48 represent the people who says that they would watch one of the television shows.
[tex]\hat p=\frac{48}{106}=0.453[/tex] estimated proportion of people who says that they would watch one of the television shows.
[tex]p_o=0.5[/tex] is the value that we want to test
[tex]\alpha[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that 50% of people who says that they would watch one of the television shows.:
Null hypothesis:[tex]p=0.5[/tex]
Alternative hypothesis:[tex]p \neq 0.5[/tex]
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.453 -0.5}{\sqrt{\frac{0.5(1-0.5)}{106}}}=-0.968[/tex]
4) Statistical decision
P value method or p value approach . "This method consists on determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level is not provided, but we can assume [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z<-0.968)=0.333[/tex]
So based on the p value obtained and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we fail to reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they would watch one of the television shows not differs from 0.5 or 50% .
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Two wires help support a pole. The wire at point A forms an angle of 54° with the ground and the wire at point B forms an angle of 72° with the ground. The distance between the wires on the ground is 23 m. Find the height of the pole to the nearest tenth of a meter.
Height of the pole (DC) is 57.2709m
Step-by-step explanation:
Here, Wire DA and Wire DB supports a pole.
Given that Angle, A=54 , B= 72.
Also, AB = 23m
Now, Taking triangle BCD and Using basic trigonometry
Height of pole H = DC
[tex]TanB = \frac{DC}{BC}[/tex]
[tex]BC= \frac{DC}{TanB}[/tex]
Now, Taking triangle ACD and Using basic trigonometry
[tex]TanA = \frac{DC}{AC}[/tex]
[tex]AC= \frac{DC}{TanA}[/tex]
From figure, we know that
AC = AB + BC
AC - BC = AB = 23
Replacing values of AC and BC
[tex]\frac{DC}{TanA} - \frac{DC}{TanB}=23\\
DC(\frac{1}{TanA}-\frac{1}{TanB})=23[/tex]
Now, TanB= Tan72 =3.0776 and TanA = Tan54=1.3763
[tex]DC (\frac{1}{1.3763} - \frac{1}{3.0776})_= 23[/tex]
[tex]DC ( 0.7265-0.3249)= 23[/tex]
[tex]DC ( 0.4016 )= 23[/tex]
[tex]DC = 57.2709 [/tex]
Thus, Height of thepole is 57.2709m
Each person in a simple random sample of 1,800 received a survey, and 267 people returned their survey. How could nonresponse cause the results of the survey to be biased?
-Those who did not respond reduced the sample size, and small samples have more bias than large samples.
- Those who did not respond caused a violation of the assumption of independence.
-Those who did not respond are indistinguishable from those who did not receive the survey.
-Those who did not respond may differ in some important way from those who did respond.
-Those who did not respond represent a stratum, changing the random sample into a stratified random sample.
Nonresponse can cause bias in survey results due to differences in characteristics, the representation of strata, and the smaller sample size.
Explanation:Nonresponse can cause the results of a survey to be biased in several ways:
Those who did not respond may differ in some important way from those who did respond. This means that the characteristics of the nonresponders may be different from the characteristics of the responders, leading to biased results.Those who did not respond may represent a stratum, changing the random sample into a stratified random sample. This can introduce bias if the nonresponders differ from the rest of the population in a systematic way.Those who did not respond may reduce the sample size, and small samples have more bias than large samples. When the sample size is small, the results may not accurately reflect the population.Overall, nonresponse can introduce bias into a survey by excluding certain individuals or groups from the sample, leading to potentially inaccurate and biased results.
Machine A working alone can complete a job in 3 1/2 hours. Machine B working alone can do the same job in 4 2/3 hours. How long will it take both machines working together at their respective constant rates to complete the job?A. 1 hr 10 minB. 2hrC. 4hr 5 minD. 7hrE. 8 hr 10 min
Answer:
B) 2 hours
Step-by-step explanation:
If machine A complete a job in 3 1/2 hours or 7/2 of an hour
means that in one hour finished 1÷ 7/2 or 2/7
If machine B complete a job in 4 2/3 hours or 14/3 of an hour
means that in one hour finished 1÷ 14/3 or 3/14 of an hour
Then the two machines working together in one hour will make
2/7 + 3/14 = (4 + 3)/ 14
or 7/14 = 1/2
half of the job. Therefore these two machines working together will take two hours
Jacob distributed a survey to his fellow students asking them how many hours they'd spent playing sports in the past day. He also asked them to rate their mood on a scale from 000 to 101010, with 101010 being the happiest. A line was fit to the data to model the relationship.
Jacob's survey is a study in statistics, specifically looking at the correlation between the amount of time spent on sports and student's mood ratings. A line is fit to the data to determine the relationship, with the direction of the line offering insights into how these two variables correlate, but this does not imply causation.
Explanation:From your question, Jacob performed a survey asking about the number of hours students spent playing sports in the past day and asked them to rate their mood. It's a study of basic statistics, specifically focusing on correlation between two variables, here those are the number of hours spent on sports and mood ratings. To determine a relationship between these variables, a line is often fit to the data, using methods like linear regression.
For example, if the line on the graph is rising, it indicates a positive correlation between the amount of sports played and a student's mood, meaning that as sports playtime goes up, so does mood ratings. A falling line means there's a negative correlation. If there's no clear direction, it's likely that there's no significant correlation between the two variables. But remember that correlation doesn't mean causation: just because two things correlate doesn't mean that one causes the other.
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The regression equation for predicting number of speeding tickets (Y) from information about driver age (X) is Y = -.065(X) + 5.57. How many tickets would you predict for a twenty-year-old? a. 4 b. 5.57 c. 4.27 d. 6 e. 1
Answer:
c. 4.27
Step-by-step explanation:
We have been given the regression equation of for predicting number of speeding tickets (Y) from information about driver age (X) as [tex]Y=-0.065(X)+5.57[/tex].
To find the predicted number of tickets for a twenty-year-old, we will substitute [tex]X=20[/tex] in our given equation.
[tex]Y=-0.065(20)+5.57[/tex]
[tex]Y=-1.3+5.57[/tex]
[tex]Y=4.27[/tex]
Therefore, the predicted number of tickets for a twenty-year-old would be 4.27 tickets.
Which function is graphed on the right?
y = 2x+3 – 2
y = 2x–3 + 2
y = 2x–2 + 3
y = 2x–2 – 3
Answer:
y = 2^(x–2) + 3
Step-by-step explanation:
The equation above is the one that is graphed. You can pick it from the offered choices by recognizing that the horizontal asymptote on the graph is y=3. That is 3 units above the horizontal asymptote of the parent exponential function. Hence, you must have ...
y = (some exponential) +3
_____
Please note that the exponent indicator (^) and the grouping parentheses on the exponent are essential. Without those, the equation is that of the line y=2x+1, which is not what is graphed.
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. (5 points)
f(x) = x2 - 3 and g(x) = square root of quantity three plus x
Answer:
f(g(x)) = g(f(x)) = x and f and g are the inverses of each other.
Step-by-step explanation:
Here, the given functions are:
[tex]f(x) = x^2 - 3, g(x) = \sqrt{({3+x)} }[/tex]
To Show: f (g(x)) = g (f (x))
(1) f (g(x))
Here, by the composite function:
[tex]f (g(x)) = f (\sqrt{3+x} ) = \sqrt{(3+x)} ^2 - 3 = (3 + x) - 3 = x[/tex]
⇒ f (g(x)) = x
(2) g (f(x))
Here, by the composite function:
[tex]g(f(x)) = g(x^2 -3) = \sqrt{3 +(x^2 -3) } = \sqrt{x^2} = x[/tex]
⇒ g (f(x)) = x
Hence, f(g(x)) = g(f(x)) = x
⇒ f and g are the inverses of each other.
A fish tank contains tetras,guppies,and minnows. The ratio of tetras of guppies.Is 4:2.The ratio is minnows of guppies is 1:3. There are 60 fish on the fish tank. How many more tetras are there then minnows .
To find the difference between the number of tetras and minnows, set up a system of equations using the given ratios. Solve the system to find the number of tetras, guppies, and minnows. Finally, subtract the number of minnows from the number of tetras to find the difference.
Explanation:To determine the difference between the number of tetras and minnows in the fish tank, we need to first find the number of each type of fish. We can do this by setting up a system of equations using the given ratios. Let T represent the number of tetras, G represent the number of guppies, and M represent the number of minnows.
From the first ratio, we have T/G = 4/2. Simplifying this equation, we get T = 2G.
From the second ratio, we have M/G = 1/3. Simplifying this equation, we get M = (1/3)G.
Since we know there are a total of 60 fish in the tank, we can create the equation T + G + M = 60. Substituting the previous equations into this equation, we get 2G + G + (1/3)G = 60. Solving for G, we find G = 9. Plugging this value into the equations for T and M, we get T = 2(9) = 18 and M = (1/3)(9) = 3.
Therefore, there are 18 tetras and 3 minnows in the fish tank. The difference between the number of tetras and minnows is 18 - 3 = 15.
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Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. [5,0] sin(x^2) dx, n = 5 M5 =
PLZZZZZZ HELP ME ASAP
deltax = (56-0)/4 = 14
number of intervals 4
The intervals are:
(0,14),(14,28),(28,42),(42,56)
The Midpoint Rule =
f(7)+f(21)+f(35)+f(49)
[0.47577]+[-0.99159]+[-0.35892]+[0.65699]
deltax =14
sum = -0.21774
Multiplying by deltax = -3.0484
To approximate the integral of sin(x^2) dx from 0 to 5 using the Midpoint Rule with n=5, first calculate Δx = 1. Next, perform calculations with x values 0.5, 1.5, 2.5, 3.5, and 4.5. Finally, use the Midpoint Rule formula to calculate the approximated integral.
Explanation:To solve this problem, you'll need to use the Midpoint Rule, which is a numerical method used to approximate definite integrals. In this case, we want to approximate ∫ from 0 to 5 of sin(x^2) dx with an n value of 5.
The Midpoint Rule can be represented as: Mn = Δx[f(x1) + f(x2) + ... + f(xn)], where Δx = (b-a)/n and each xi = a + (Δx/2) + (i-1)Δx.
Here, we'll first find our Δx = (5-0)/5 = 1, then calculate each xi and plug those into our function. Our xi values will be 0.5, 1.5, 2.5, 3.5, and 4.5. Finally, we plug into our formula and solve to find our approximated integral value.
A detailed and step-by-step solution would involve calculating each f(xi) with the xi values given above, and then adding these up
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