We must find p′, q′ in order to calculate the confidence interval; the sample proportion is p′ = 0.842; This is the population proportion's point estimate. Since CL = 0.95 is the requested confidence level, = 1 – CL = 1 – 0.95 = 0.05 (2) (2) = 0.025.
For P, what is the confidence interval at 95 percent?
Since 95% of the area under the curve falls within this interval, the interval (-1.96, 1.96) serves as a 95% confidence interval for the standard normal distribution.
What is the 95 percent confidence interval for the population's proportion of smokers?
Standard Error for Proportion Calculating a 95% Confidence Interval for each group separately is another way to consider whether smokers and nonsmokers have significantly different proportions with wrinkles. For the smokers, we have a certainty time period ± 2(0.0394) or 0.63 ± 0.0788.
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Which expression is equivalent to 9^3/3^3
Answer:
3^3
Step-by-step explanation:
Exponents
9^3 can be rewritten as
3^2 ^3
Using exponent rules a^b^c = a^ (b*c)
3^2^3 = 3^6
3^6 / 3^3
We know that a^b / a^c = a^(b-c)
3^6 / 3^3 = 3^(6-3) = 3^3
Answer:
2nd answer is correct
Step-by-step explanation:
We know that,
[tex] \rightarrow \sf {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \rightarrow \sf \frac{{x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ \rightarrow \sf( {x}^{a} )^{b} = {x}^{ab} [/tex]
Accordingly, let us solve it now.
[tex] \sf \frac{ {9}^{3} }{ {3}^{3} } \\ \\ \sf \frac{ {3}^{2 \times 3} }{ {3}^{3} } \\ \\ \sf\frac{ {3}^{6} }{ {3}^{3} } \\ \\ \sf {3}^{6 - 3} \\ \sf {3}^{3} [/tex]
A furniture maker uses the specification 17.9≤w≤18.1 for the width w in inches of a desk drawer. Write the specification as an absolute value inequality.
The specifications of the furniture as an absolute value inequality is |x - 18| ≤ 0.1 .
In the question ,
it is given that ,
the specification of the furniture , is 17.9 ≤ w ≤ 18.1 ,
where w is the width of the desk drawer in inches .
we need to write the given inequality in absolute inequality form ,
we know that the a-b < x < a+b , then the absolute inequality is |x-a|<b ,
On comparing the given inequality with a-b < x < a+b ,
we get
a - b = 17.9 and
a + b = 18.1
adding both the equations , we get
2a = 36
a = 36/2
a = 18
Substituting a = 18 in a + b = 18.1 , we get
18 + b = 18.1
b = 18.1 - 18
b = 0.1
The required inequality is |x-a| ≤ b .
|x - 18| ≤ 0.1
Therefore , The specifications of the furniture as an absolute value inequality is |x - 18| ≤ 0.1 .
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Solve for z.
Assume the equation has a solution for z.
a⋅(t+z)=45z+67
[tex]a(t+z)=45z+67\implies at+az=45z+67\implies az=45z+67-at \\\\\\ az-45z=67-at\implies \stackrel{common~factoring}{z(a-45)}=67-at\implies z=\cfrac{67-at}{a-45}[/tex]
A watusi, a Ubangi, and a Pigmy compare the speeds at which ech can run.
The sum of the speeds of the natives is 30 miles per hour (mph). The Pigmy's
speed plus one-third of the Watusi's speed is 22 miles per hour more that the
Ubangi's sped. Four times the Watusi's speed plus three times the Ublani's
speed minus twice the Pigmys' speed is 12 miles per hour. Find out how fast
each can run. Then, tell what is unfortunate about the Ubangi.
*write system of equations
There is Watusi's speed is 6miles per hour (mph), Ubangi's speed is 3 mph, and Pigmy's speed is 21 mph.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let x represent Watusi's speed,
y represent Ubangi's speed,
And z represents Pigmy's speed.
According to the given information, we can write the system of equations as
x + y + z = 30 .....(i)
z + 2x/3 = 22 - y .....(ii)
4x + 3y - z = 12 .....(iii)
The above system of equations gives the values of x, y, and z when solving
x = 6, y = 3, z = 21
This means Watusi's speed is 6miles per hour (mph), Ubangi's speed is 3 mph, and Pigmy's speed is 21 mph.
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Given that line t is the perpendicular bisector of Jk, JG=x+12, and KG=3x-17, find KG
A delivery truck is coming from San Antonio with avocados. The avocados are boxed in 2 different boxes small and large. The weight of both small and large boxes is 75lb. If the truck has 70 large boxes and 55 small boxes with a total weight of 4800 lb. How much does each type of box weigh?
#8 i
Write an equation of the line passing through the point A(3,-4) that is parallel to the line y = -x +8.
y =
1/x+1242
Answer:
y = -x -1
Step-by-step explanation:
You want an equation of the line parallel to y=-x+8 through point (3, -4).
Parallel lineThe parallel line will have the same slope as the given line. That slope is the coefficient of x: -1.
Point-slope formThe point-slope form of the equation of a line with slope m through point (h, k) is ...
y -k = m(x -h)
You have m=-1, (h, k) = (3, -4), so the desired line has equation ...
y -(-4) = -1(x -3)
y +4 = -x +3 . . . . . . point-slope form
Slope-intercept formAdd -4 to get this to slope-intercept form.
y = -x -1 . . . . . . . . . slope-intercept form
Please I need help please
The value of x in the given triangle is x = 2 .
In the question ,
it is given that ,
a triangle is given ,
let us name the triangle as triangle ABC ,
So , By Basic Proportionality Theorem , which states that ,
The line drawn parallel to one side of triangle and cuts the other two sides divides the other two sides in equal proportion.
So , By Basic Proportionality Theorem
AD/AB = AE/AC
substituting the value from the triangles , we get
4/12 = 6/(6+6x)
1/3 = 1/(1+x)
1 + x = 3
x = 3 - 1
x = 2
Therefore , The value of x in the given triangle is x = 2 .
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Mohammed is trying to find angle h. He finds angle g first and then he finds angle h from angle g.
a) Which angle fact does he use to find angle g
b) which angle fact does he then use to find angle h
a. The angle fact that Mohammed can use to find angle g is alternate angles
b) The angle fact that he then use to find angle h is alternate interior angles.
What is an alternate angle?When two parallel lines are cut by a transversal, the resulting alternate interior angles or alternate exterior angles are congruent, according to the alternate angle theorem. To demonstrate: If a transversal cuts two parallel lines, the alternate interior angles are equal.
When two parallel lines are intersected by a transversal, the angles formed inside them are equal to their alternate pairs. These are known as alternate interior angles.
In this case, it should be noted that the angles will be 137° based on the illustration.
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the population is decreasing at a rate of 2%2% per year. if the population is 28,80028,800 today, what will the population be in 99 years? round your answer to the nearest whole number, if necessary.
By using the concept of depreciation, it is obtained that
New population after 9 years = 24012
What is Depreciation?
Depreciation is the decrease in the value of a population or any asset over a period of time at a certain rate.
The concept of depreciation has been used here
Original population = 28800
Rate of decrease of population = 2%
Time = 9 years
New population after 9 years = [tex]28800(1 - \frac{2}{100})^9[/tex]
= [tex]28800({1 - \frac{1}{50})^9\\[/tex]
= [tex]28800(\frac{49}{50})^9[/tex]
= 24011.94
= 24012
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1. In the following figure, തതതത is the bisector of ∠BAC. GE is perpendicular to AB, GF is perpendicular to AC.
Andrea says that ∆ ≅ ∆ by the AAS congruence postulate. Do you agree or disagree? Explain
Based on the information given in the figure, you will agree with Andrew because ∆AEG ≅ ∆AFG by the AAS congruence postulate.
What is the AAS Congruence Postulate?Two triangles that have a pair of congruent included sides that is non-included and two pairs of corresponding angles are proven to be congruent to each other by the AAS congruence postulate.
In the figure shown above, the following information are ascertained:
Side AG is congruent to side AG by the reflexive property Angle AEG and angle AFG are congruent to each other because they are both right angles.Angle GAF and angle GAE are congruent to each other because they are angles formed when angle BAC is bisected line AD.Thus, the above information shows that triangle AEG has two angles and one non-included side that are congruent to two corresponding angles and one non-included side in triangle AFG.
Therefore, you will agree with Andrea for stating that ∆AEG ≅ ∆AFG by the AAS congruence postulate.
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Multiply. (-5 5/8) • (-2 1/3) What is the product?
Answer:
105/8 = 13 1/8 = 13.125
Step-by-step explanation:
The first step is to turn the (-5 5/8) into a mixed number. The mixed number you should be getting is - 45/8. The second step is to convert the (-2 1/3) into a mixed number as well, your second mixed number should be -7/3. Next multiply the two fractions, - 45/8 x (-7/3) = 315/24.
We can simplify 315/24 by dividing by 3, so you'll divide 315 divided by 3 and 24 divided by 3 and you should get ... 105/8. So 105/ 8 is equal to
13 1/8. If you need this fraction in decimal form it is 13.125.
A CFL Factory uses 24,325.208 litre of water in 4 hours. How much water does the factory use in 3 hours
Answer:
18243.906
Step-by-step explanation:
Find how much water is used in 1 hour and then multiply that by 3
24325.208/4
6081.302
6081.302x3
18243.906
1. The quality control manager at a light bulb factory needs to estimate the mean life of a new type of light-bulb. The population standard deviation is assumed to be 50 hours. A random sample of 30 light-bulbs shows a sample mean life of 475 hours. Construct and explain a 90% confidence interval estimate of the population mean life of the new light-bulb. 2. A survey of first-time home buyers found that the sample mean annual income was $46,000. Assume that the survey used a sample of 20 first-time home buyers and that the sample standard deviation was $1,200. Compute and explain a 95% confidence interval estimate of the population mean. 3. A telephone poll of 750 American adults asked "where would you rather go in your spare time?" One response, by 275 aduits, was "the Mall. Compute and explain a 99% confidence interval estimate of the proportion of all American adults who would respond "the Mall". 4. For problem #1 above, what size sample would be needed to achieve a margin of error of 15 hours or less? 2. A survey of first-time home buyers found that the sample mean annual income was $46,000. Assume that the survey used a sample of 20 first-time home buyers and that the sample standard deviation was $1,200. Compute and explain a 95% confidence interval estimate of the population mean cer
At 95% of confidence interval estimate of the population is
(478.332, 471.668)
Given that,
Population standard deviation is assumed to be 50 hours.
Random sample of 30 light bulb
and, sample mean of 475 hours.
Sample size n =30,
x = 475 and σ = 50
At 95% confidence interval for μ is,
x ± zₙ₎₂ σ /n -------------------- (1)
We already know that the table value of z = 1.96
At 95% confidence interval,
putting the values in equation (1),
x ± zₙ₎₂ σ /n
= 475 ± 1.96 × 50/30
Taking the positive sign, we get,
= 475 + 1.96 × 1.7
= 475 + 3.332
= 478.332
Now,
Taking the negative value, we get,
= 475 - 1.96 × 1.7
= 475 - 3.332
= 471.668
Therefore, At 95% of confidence interval estimate of the population is
(478.332, 471.668)
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How many angles are formed by the intersection of the diagonals?
The number of angles that are formed by the intersection of the diagonals is 4.
What is a square?A square is a four-equal-sided figure with diagonals cut perpendicular to each other, with a total of four angles formed by diagonals.
It is a geometrical figure with four sides, each of which must be equal, and an angle of 90 degrees between two adjacent sides.
Square area = Side²
The square's perimeter = 4 sides
Every square contains two diagonals. The intersection angle of both diagonals is 90 degrees. The number of diagonal angles equals four.
Therefore, the correct option is 4.
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Complete question
How many angles are formed by the intersection of the diagonals in a square?
How many laps around the lake does Latrell jog? Write your answer as a whole number of laps plus a fraction of a lap.
The number of laps around the lake that Latrell jogs is 5 1/4 laps.
What is a fraction?A fraction simply means a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
From the information he jogs 7 miles and each lap is 4/3 miles. The number of laps will be:
= Total laps / Number of miles
= 7 ÷ 4/3
= 7 × 3/4
= 21 / 4.
= 5 1/4 laps.
He jogs 5 1/4 laps.
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PLEASE HELP FAST! 2. Find the volume of the following figure. Use 3.14 for pi. Show work please
Answer:
Step-by-step explanation:
the equation of the cone is given already
r=6 inches
h=7 inches
Substitute in the equation =84pi=263.89
for the sphere substitute the radius r= 6 inches in the equation, and then divide by 2. This is because the spherical shale in top of the cone is half a sphere, as it can be clearly seen.
So It’s 288pi= 904.78 /2 =452.39
add the volume of cone and volume of sphere
The final answer is 716.28 inches^3
The missing quantity in the double number line
Answer: 1840 pounds
Step-by-step explanation:4x4=16
460 x 4 = 1840
Which is the smallest number. 0.5 0.17 0.07 1.7 0.071
The smallest number among the given options is 0.07.
To determine the smallest number, we compare the given options. Among the numbers 0.5, 0.17, 0.07, 1.7, and 0.071, the smallest number is 0.07. This can be determined by examining the decimal places. The number 0.07 has the fewest decimal places and is the smallest value.
When comparing decimal numbers, the digits after the decimal point are crucial.
In this case, we observe that 0.07 has the smallest digit in the hundredths place, while the other numbers have larger digits in that place. Therefore, 0.07 is the smallest number among the given options.
It is important to note that the order of magnitude (the number before the decimal point) does not affect the comparison when determining the smallest number among decimal values.
In summary, by comparing the decimal places, we find that 0.07 is the smallest number among the given options.
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If A ⊂ B, then A ∩ B = ∅. true or false
The statement if A ⊂ B, then A ∩ B = ∅ is false.
First, let us understand the set:
A set is a mathematical model for a collection of different things; a set contains elements or members that can be any mathematical object: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
We are given;
A ⊂ B
We need to find A ∩ B.
Let us understand the given set;
A ⊂ B means A is a proper subset of B.
All the elements of set A are in set B.
So, A ∩ B = A
But, A ∩ B = ∅ is given.
So, the statement is false.
Thus, the statement if A ⊂ B, then A ∩ B = ∅ is false.
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Which of the following is a polynomial with roots:-√3,√3, and 3?
x3-2x²-3x+6
x3-3x2-3x+9
x3+2x²-3x-6
x3+3x²-3x-9
Answer:
[tex]x^{3}[/tex]-3[tex]x^{2}[/tex]-3x+9
Step-by-step explanation:
(x-3)([tex]x^{2}[/tex]-3) = 0
x = -[tex]\sqrt{3}[/tex], [tex]\sqrt{3}[/tex], 3
Kiara and Lee are collecting violas in a ratio of 2:5 . If they collected 266 violas altogether , how many violas did Kiara collect?
The quantity of violas Kiara collected is 76
Calculating quantity of violas collectedFrom the question, we are to determine the quantity of violas Kiara collected.
From the given information,
"Kiara and Lee are collecting violas in a ratio of 2:5"
First, we will determine the sum of ratios
Sum of ratios = 2 + 5 = 7
Also, from the given information
The total number of violas they collected is 266
Thus,
The quantity of violas Kiara collected will be
2/7 × 266
= 2 × 38
= 76
Hence, the quantity she collected is 76
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Use the spinner shown. It is equally probable that the pointer will land on
any one of the six regions. If the pointer lands on a borderline, spin again. If
the pointer is spun twice, find the probability that it will land on
grey and then purple
Find the probability that the spinner will land on grey and then purple.
The probability that the spinner will land on grey and then purple is 1/18.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Number of grey regions = 1
Number of purple regions = 2
Total number of regions = 6
Now,
The probability that the spinner will land on grey.
= Number of grey regions / Total number of regions
= 1 / 6
The probability that the spinner will land on purple.
= Number of purple regions / Total number of regions
= 2 / 6
The probability that the spinner will land on grey and then purple.
= 1/6 x 2/6
= 1/6 x 1/3
= 1/18
Thus,
The probability that the spinner will land on grey and then purple is 1/18.
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Reese is installing an in-ground rectangular pool in her backyard. Her pool will be 30 feet long, 14 feet wide, and have an average depth of 8 feet. She is installing two pipes to bring water to fill the pool; these pipes will also be used to drain the pool at the end of each season. One pipe can fill and drain the pool at a rate that is 1 more than 2 times faster than the other pipe. If both pipes are open and working properly, it will take 3.5 hours to fill the pool.
Use this information and what you know about solving rational equations to answer the questions below.
1. When Reese opens the pipes to fill the pool, she finds that only the slower pipe is working. Write a rational equation that you can use to find out how long it will take to fill the pool under these circumstances. Explain how you came up with your equation.
2. Solve the equation that you wrote in question 1. You can round your final answer(s) to the nearest hundredth. Show all your work.
3. Interpret your answer(s) to question 2 in context of the problem. What do the number(s)
The 30 feet by 14 feet by 8 feet, filled in 3.5 hours by two pipes in which one pipe is 1 more than twice the other, indicates;
1. The rational equation from which the time the smaller pipe takes to fill the pool is; [tex]t = \dfrac{3360}{x} =\dfrac{3360}{959-2\cdot x }[/tex]
2. The solution of the equation is t ≈ 10.51 hours
3. The time it takes to fill the pool using only the small pipe is about 10.51 hours
What is a rational equation?Rational equation are equations that have rational polynomial expressions.
The dimensions of the pool are;
Length = 30 feet
Width = 14 feet
Depth = 8 feet
1. Let x represent the flow rate of the slower pipe
The flow rate of the faster pipe = 2·x + 1
Time it will take both pies to fill the pool = 3.5 hours
The volume of the pool, V = 30 × 14 × 8 = 3360
The volume of the pool is 3360 cubic feet
The rate equation is therefore;
[tex]\dfrac{x}{3360} +\dfrac{2\cdot x+1}{3360} =\dfrac{1}{3.5}[/tex]
[tex]\dfrac{x}{3360} =\dfrac{1}{3.5} - \dfrac{2\cdot x+1}{3360}[/tex]
From the rate equation above, the time it takes the smaller pipe to fill the pool is; t = 3360/x therefore;
[tex]t = \dfrac{3360}{x} =\dfrac{3360}{959-2\cdot x }[/tex]
2. Solving for x from the volume of water in the pool, V, therefore;
The volume of water that fills the pool, V, is found from the equation;
V = 3.5 × (2·x + 1 + x) = 10.5·x + 3.5
V = 10.5·x + 3.5
Therefore;
3360 = 10.5·x + 3.5
[tex]x = \dfrac{3360-3.5}{10.5} =319.\overline 6[/tex]
t = 3360/319.[tex]\overline 6[/tex] ≈ 10.51
The time it takes to fill the pool using only the smaller pipe is approximately 10.51 hours
Aliter;
[tex]\dfrac{3\cdot x}{3360} =\dfrac{1}{3.5}-\dfrac{1}{3360}[/tex]
[tex]t = \dfrac{3360}{x} =\dfrac{3}{\left(\dfrac{1}{3.5}-\dfrac{1}{3360}\right)} \approx 10.51[/tex]
3. The interpretation of the solution is that it takes about 10.51 hours for the smaller pipe working alone to fill the pool
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A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 miles.
What is the actual length of the park in miles?
What is the actual width of the park in miles?
miles
What is the actual area of the park in square miles?
miles squared
The actual area of the park in square miles is 21600 miles².
A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 miles.
* Lets explain how to solve the problem
- A drawing that shows a real object with accurate sizes reduced or
enlarged by a certain amount called the scale
- Drawing scale is a ratio between the drawing length and the
actual length
- To find the actual dimensions from the drawing dimensions use the
scale drawing
* Lets solve the problem
- A map of a rectangular park has a length of 4 inches and a width
of 6 inches
∴ The drawing dimensions are:
# length = 4 inches
# width = 6 inches
- The scale of the map is 1 inch for every 30 miles
∴ The scale drawing is 1 : 30
- To find the actual area find the actual dimensions
∵ The scale drawing is 1 : 30
∵ The length = 4 inches and the width = 6 inches
- By using cross multiplication
∴ 1 : 30
4 : actual length
6 : actual width
∴ Actual length = (4 × 30)/1 = 120
∴ Actual length = 120 miles
∴ Actual width = (6 × 30)/1 = 180
∴ Actual Width = 180 miles
∴ The actual dimensions are 120 miles and 180 miles
∵ The area of any rectangle = length × width
∴ The actual area = 120 × 180 = 21600
∴ The actual area 21600 miles²
Hence the answer is the actual area of the park in square miles is 21600 miles².
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Find the LCM of 1 and 5 using lists of multiples.
Answer:
5
Step-by-step explanation:
Multiples of 1: 1, 2, 3, 4, 5, 6, 7, ...
Multiples of 5: 5, 10, 15, 20, 25, ...
The smallest number that appears in both lists is 5, and that is the least common multiple.
NEED ANSWER SOON PLEASE
The graph shows how many cnetimeters a bamboo plant can grow and the number that the plant has been growing. Determine the constant of proportionatlity and explain what it means.
The numbers below are what the dots are plotted-
10,50
20,100
30,150
40,200
50,250
The constant of proportionality of the graph shows how many centimeters a bamboo plant can grow and the number that the plant has been growing is 5.
We know that the constant of proportionality is nothing but the slope of the line.
The slope of the line is given by;
Slope = Change in y-coordinate / change in x-coordinate
We are given:
The numbers below are what the dots are plotted-
10, 50
20, 100
30, 150
40, 200
50, 250
Take any two points.
Let us choose (20, 100) and (30, 150).
Put the values in the slope formula;
Slope = (150 - 100) / (30 - 20) = 50 / 10 = 5
So, the slope of the line is 5.
Thus, the constant of proportionality of the graph shows how many centimeters a bamboo plant can grow and the number that the plant has been growing is 5.
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Translate this sentence into an equation. 53 is the sum of 22 and Han's height. Use the variable h to represent Han's height.
Answer:
22 + h = 53
Step-by-step explanation:
I don't know if I am correct
Answer:
The answer is 31, H=31
Step-by-step explanation:
53-22=31 :)
according to city reports, it was found that the mean age of the prison population in the city was 26 years. marc wants to test the claim that the mean age of the prison population in his city is less than 26 years. he obtains a random sample of 25 prisoners and finds a mean age of 24.4 years and a standard deviation of 9.2 years. at a significance level of 0.05, what should his conclusion be? note: the p-value
The value of P0.05 < 0.19658. We do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 26 years.
According to the question we will set up Hypothesis
Null, H0: U=26
Alternate, H1: U<26
Test Statistic
Population Mean(U)=26
Sample X(Mean)=24.4
Standard Deviation(S.D)=9.2
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/√(n))
to =24.4-26/(9.2/√(25))
to =-0.87
| to | =0.87
Critical Value
The Value of |t α| with n-1 = 24 d.f is 1.711
We got |to| =0.87 & | t α | =1.711
According to this, we have to make a decision
Hence Value of |to | < | t α |
P-Value: Left Tail -Ha : ( P < -0.8696 ) = 0.19658
Hence Value of P0.05 < 0.19658
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please help me solve this.
Answer:
a) gradient
b) Line A and Line C
Step-by-step explanation:
Parallel lines are lines that have the same slope - they never intersect! Another name for slope is gradient.
Of all the lines in the image, only Line A and Line C will never intersect! They are parallel!