In order to construct a right triangle with a given hypotenuse and acute angle, draw a straight line segment that represents the given hypotenuse.
How to construct the triangleMark one endpoint of the hypotenuse as point A.
From point A, construct a perpendicular line to the hypotenuse. This perpendicular line will represent one of the legs of the right triangle.
Use a protractor to measure the given acute angle from the perpendicular line you just drew.
From the point where the acute angle intersects the perpendicular line, draw another line segment that extends away from the hypotenuse. This line segment will represent the other leg of the right triangle.
The intersection point of the two legs will be the third vertex of the right triangle.
Make sure to measure and construct accurately to ensure the triangle is a right triangle with the desired properties.
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The following table shows Kamal’s bank account balance after 7 months.
*TABLE IN THE FILE ATACHED BELOW*
a) What is the rate of change? Show your work.
b) What does the rate of change mean in Kamal’s scenario?
c) What is the initial value?
d) What does the initial value represent in Kamal’s scenario?
e) Determine the equation of the linear relation which represents his bank account balance.
PLEASE HELP I DON'T HAVE ANY TIME
a. The rate of change = -25/month
b. Kamal's account balance reduces by 25$ per month.
c. To find the $725.
d. Kamal's opening balance or initial deposit.
e. The linear equation is: A = -25n + 725.
How to Find the Rate of Change and Initial Value of a Linear Relation?The rate of change (m) = change in y/change in x.
a. The rate of change (m) = change in A / change in n = (700 - 650)/(1 - 3) = -25/month.
b. -25 dollar per month means every month, Kamal's account balance reduces by 25$
c. To find the initial value (b), substitute m = -25 and (7, 550) = (n, A) into A = nm + b:
550 = 7(-25) + b
550 = -175 + b
550 + 175 = b
b = 725.
Initial value is: 725.
d. The initial value, $725, is Kamal's opening balance or initial deposit.
e. To write the linear equation, Substitute m = -25 and b = 725 into A = nm + b:
A = -25n + 725
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Part A:
What is the solution to the inequality below?
|x + 6| ≥ 5
Part B:
In 3-4 sentences, write a description of solution as it would look on a number line. Be sure to include the words:
-Shaded or Not Shaded
-Open or closed
-Solution
The solution of the inequality, |x + 6| ≥ 5 is given as follows,
(A) x > -1
(B) It follows that x either belongs to the interval (-∞, -11) or to the interval (-1,∞) for the given absolute inequality.
(A) Solving the Given Inequality:
|x + 6| ≥ 5
x+6 ≥ 5 or x+6 ≤ (-5)
x+6-6 ≥ 5-6 or x+6-6 ≤ (-5)-6
x ≥ -1 or x ≤ -11
Hence the solution of the given inequality is given as,
x ∈ (-∞, -11] or x ∈ [-1, ∞)
(B) Description of the Solution
From the given absolute inequality, it can be concluded that x either belongs to the interval (-∞, -11] or to the interval [-1, ∞). Hence, on the number line, the solution of the inequality will be shown as a shaded region from -∞ to -11 and from -1 to ∞. The area between -1 and -11 will remain unshaded.
In the deduced solution, the interval is either open or closed on both sides. Open interval means the extreme value is not includes. On the other hand, closed interval indicates inclusion of the extreme point in the solution of the inequality.
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what is the volume of the truck bed which is
10 feet long, 4 feet wide, and has a height of 3
feet?
Answer:
120 ft cubed
Step-by-step explanation:
V=lwh
V=10(4)(3)
V=120 ft cubed
Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Answer: [tex]\triangle XYZ \sim \triangle GFH[/tex] by AA.
Step-by-step explanation:
Finding the third angle in triangle XYZ,
[tex]m\angle YXZ=180^{\circ}-77^{\circ}-48^{\circ}=55^{\circ}[/tex],
Thus, [tex]\triangle XYZ \sim \triangle GFH[/tex] by AA.
In what type of triangle is the orthocenter located outside of the triangle?
Answer:
obtuse angle triangle
Step-by-step explanation:
please make me Brilliant for this correct answer
Can you please solve for X please
Answer: 100
Step-by-step explanation:
The angles with measure 100° and x° are vertical angles, which are two opposite angles made from two intersecting lines. These vertical angles are always the same measure.
Hence, both x and 100 have the same measure.
Choose the correct simplification of the expression (C^4)^3
A. C^1
B. C^7
C. C^12
D. C^64
Use the rules of exponents to simplify the expression.
[tex]\large\displaystyle\text{$\begin{gathered}\sf (C^{4})^{3} \end{gathered}$}[/tex]
To raise a power to another power, multiply the exponents.
[tex]\large\displaystyle\text{$\begin{gathered}\sf C^{4\times3} \ \to \ Multiply \end{gathered}$}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf C^{12} \end{gathered}$}}[/tex]
Therefore, the correct option is "C".
A steel mill manufactures steel plates. The average number of flaws in the steel is 1.28 flaws per square foot. Find the probability that a randomly selected 1-foot-by-1-foot area of steel plate has 2 flaws or fewer. Use Excel to find the probability. Round your answer to three decimal places.
Using excel, we can determine that the likelihood that a randomly picked steel plate measuring 1 foot by 1 foot contains two or fewer faults is 0.862.
This is further explained below.
What is probability?Generally, the characteristic or condition of being probable; the degree to which something is likely to occur or be the case. the likelihood of anything happening or something is the case.
In conclusion, In this section, we will make the assumption that the number of defects found in a steel plate measuring 1 foot by 1 foot has a Poisson distribution with a mean of 1.28.
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Write the equation of the line that is parallel to the line y = -7/4x - 2 through the point (4,-2).
Answer:
y = - [tex]\frac{7}{4}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{7}{4}[/tex] x - 2 ← is in slope- intercept form
with slope m = - [tex]\frac{7}{4}[/tex]
• Parallel lines have equal slopes , then
y = - [tex]\frac{7}{4}[/tex] x + c ← is the partial equation
to find c substitute (4, - 2 ) into the partial equation
- 2 = - 7 + c ⇒ c = - 2 + 7 = 5
y = - [tex]\frac{7}{4}[/tex] x + 5 ← equation of line
As a construction estimator you estimate the cost of bathroom remodels for a general contractor one client asks for an estimate for two bathroom remodels. you estimate it will cost $20,000 for both remodels when the project is finished all the supplies came in at the estimated budget except for two vanities which were each $100 less than the budgeted amount what was the difference between the actual cost and estimated cost for the two bathroom remodels
For two bathroom remodel estimate budget is $[tex]20000[/tex] for both remodels. when the project is finished all the supplies came in at the estimated budget except for two vanities which were each $[tex]100[/tex] less than the budgeted .So the actual cost of two bathroom remodel is $ [tex]19800[/tex] and the different of actual and expected budgets is $[tex]200[/tex]
How can we find the actual costing of the bathroom remodel ?
Expected estimate budget of two bathroom's remodel is $[tex]20000[/tex]
So budget of one bathroom remodel is
[tex]20000/2\\=10000[/tex]
All supplies are come except for two vanities which were each $[tex]100[/tex]
So for two bathroom remodels
[tex]=2*100\\=200[/tex]
So the actual cost of remodel of both bathroom is
[tex]=20000-200\\=19800[/tex]
And difference between actual and estimated cost is
[tex]=20000-19800\\=200[/tex]
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The marks obtained by 10 student in a test are as follows: 3,7,6,2,8,5,9,1,4 and 10. find the mean mark
Answer:
[tex]5.5[/tex]
Step-by-step explanation:
Mean:
The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is
[tex]\mu = \frac{{\sum}x}{N}[/tex]
The formula for the mean of a sample is
[tex]\bar{x} = \frac{{\sum}x}{n}[/tex]
Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:
[tex]\frac{55}{10} = 5.5[/tex]
I don't understand any recursive sequences please help explain so
The graph of f(x) = |x| is reflected across the y-axis and translated to the left 5 units. Which statement about the domain and range of each function is correct?
A).Both the domain and range of the transformed function are the same as those of the parent function.
B).Neither the domain nor the range of the transformed function are the same as those of the parent function.
c).The range of the transformed function is the same as the parent function, but the domains of the functions are different.
D).The domain of the transformed function is the same as the parent function, but the ranges of the functions are different.
The statement that is true about the domain and range of each function is; A) Both the domain and range of the transformed function are the same as those of the parent function.
How to interpret reflection of a function?We are told that the graph of f(x) = |x| is reflected across the y-axis. Thus;
|-x| = x
Now, the function is translated to the left by 5 units and so the transformed function is; g(x) = |x + 5|
Thus, from the graph, we get;
Domain of both functions is the set of all real numbers.
Range of both functions is the set {y|y ≥ 0}
Thus, we conclude that Both the domain and range of the transformed function are the same as those of the parent function.
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Tristen is packing lunch boxes for the school trip. Each lunch box consists of 1 sandwich, 1 fruit, and 1 drink. Tristen can choose from 3 types of sandwiches, 4 types of fruit, and 2 types of drinks. How many different lunch boxes can Tristen pack
Answer:
24
Step-by-step explanation:
3x4x2=24
When finding the answer to this problem, you times all of the options by each other.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
A, B, F
- The radius of the circle is 3 units
- The center of the circle lies on the x-axis
- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9
Step-by-step explanation:
The first option is correct because the standard equation of the circle is:
[tex](x - 1)^{2} + {y}^{2} = 9[/tex]
making the radius equal to 3.
The center is at (-1,0), therefore it lies on the x-axis.
And lastly, the last option is correct because both options have the radius of 3.
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answer:
[tex]x^2+(y-3)^2=36\\[/tex] and [tex]x^2+(y+8)^2=36[/tex]
Step-by-step explanation:
So the general formula for a circle is usually represented as: [tex](x-h)^2+(y-k)^2=r^2[/tex] where (h, k) is the center of the circle and r is the radius of the circle.
Since the diameter is 12, the radius is going to be 6, because the radius is half the diameter. We now square that value (since it's squared in the equation), you get 36, which is going to be on the right side.
The last thing to know is since it's on the y-axis, that means h=0, since if h didn't equal 1, it would either be to the right or left of the y-axis. So the equation should look something like this: [tex]x^2+(y-k)^2=36[/tex] where k can be any real number.
So this gives you the two equations:
[tex]x^2+(y-3)^2=36\\[/tex] and [tex]x^2+(y+8)^2=36[/tex]
2. The prices of several different cereals are given below. Find the mean, median, mode, MAD, and IQR of these values. Which measure of center and which measure of variability best describe the data? $3.50, $4.25, $6, $4.75, $5.80, $4
I need this with explanation please:(
Mean = $ 4. 72
Median = $ 4. 5
Mode = No mode
MAD = $ 4. 8
IQR = $ 0. 5
Measure of center = $ 4. 5
Measure of variability = $ 2. 50
How to determine the valuesGiven the data;
$3.50, $4.25, $6, $4.75, $5.80, $4
Mean = sum of data/ number of data values
Mean = [tex]\frac{3. 50 + 4. 25 + 6 + 4. 75 + 5. 80 + 4}{6}[/tex]
Mean = $ 4. 72
Median is the number in the center when the data is arranged in an ascending order
$3. 50, $4, $4. 25, $4. 75, $5. 80, $6
Median = [tex]\frac{4. 25 + 4. 75}{2}[/tex]
Median = $ 4. 5
Mode is the number with the highest repeats.
From the given data, none of the numbers was repeated.
Thus, there is no mode.
MAD, mean absolute deviation = |data value - mean|
MAD = [tex]|(3. 50 - 4. 72) + (4. 25 - 4. 72) + (6 - 4. 72) + (4. 75 - 4. 72) + (5. 80 - 4.72) + (4- 4. 72) |[/tex]
MAD = [tex]1. 22 + 0. 47 + 1. 28 + 0. 03 + 1. 08 + 0. 72[/tex]
MAD = $ 4. 8
IQR, interquartile range = Quartile 3 - quartile 1
IQR = 4. 75 - 4. 25
IQR = $0. 5
Note that the mean and median are the most common measures of center.
A measure of variability is a single number that is used to describe the spread of a data set
The measure of the center best for the data is the median = $4. 5
Measure of variability = range = highest value - lowest value = $6 - $3. 50 = $2. 50
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44. The table below lists the tallest waterfalls in the world, in feet.
Name/Location Height (ft.)
Mutarazi - Zimbabwe 24.99 x 102
Gocta Cataracts - Peru 2.532 x 103
Utigord - Norway 2,625 x 100
Angel - Venezuela .3212 x 104
Espelands - Norway 2.307 x 103
Yosemite - California (USA) 2,425
Monge - Norway 25.4 x 102
Tugela - South Africa 3.11 x 103
**Heights are approximations**
[Part 1]
List the waterfalls from tallest to shortest.. Show all of your work and/or explain your reasoning.
[Part 2]
What is the difference between the tallest and shortest heights? Show your work.
The difference between the tallest and shortest heights is 0.787 × 10
StatisticsMutarazi - Zimbabwe 24.99 x 10²Gocta Cataracts - Peru 2.532 x 10³Utigord - Norway 2,625 x 10^0Angel - Venezuela .3212 x 10⁴Espelands - Norway 2.307 x 10⁴Yosemite - California (USA) 2,425Monge - Norway 25.4 x 10²ugela - South Africa 3.11 x 10³From tallest to shortest:
Angel - Venezuela 3.212 x 10⁴Espelands - Norway 2.307 x 10⁴ugela - South Africa 3.11 x 10³Utigord - Norway 2,625 x 10^0Monge - Norway 25.4 x 10²Gocta Cataracts - Peru 2.532 x 10³Mutarazi - Zimbabwe 24.99 x 10²Yosemite - California (USA) 2,425Difference between tallest and shortest heights =
3.212 x 10⁴ - 2,425
= 3.212 x 10⁴ - 2.425 × 10³
= (3.212 - 2.425) × 10^4 - 3
= 0.787 × 10
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A machine fills bags with sweets there are 4275 sweets there are 28 sweets in each full bag the machine fills as many bags as possible how many sweets are left must show your working
19 sweets are lefted.
Lets simplify the problem,
Maximum no. of bag filled by 4275 sweets
Through Simple Division we get,
4275/28 ~=152
Therefore , there is 4256 sweets in 152 bags
Therefore, 4275-4256=19 sweets are left
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please i seriously need step-by-step on this tyty
Answer: G=4
Step-by-step explanation:
A roller coaster’s height is given by the equation h = –.025t2 + 4t + 50, where t represents the time in seconds. How long will it take riders to pass over the hill and reach ground level? Hint: Set h = 0.
Answer Options:
A.11.65
B.50.00
C.171.65
D.210.00
The time it took the rider to reach the ground level is 171.651seconds
Quadratic functionsQuadratic functions are functions that has a leading degree of 2.
Given the equation that represents roller coaster’s height as shown
h = –0.025t^2 + 4t + 50
The coaster will reach the ground when h = 0
Substitute
0 = –0.025t^2 + 4t + 50
Factorize
On factorizing, the time it took the rider to reach the ground level is 171.651seconds
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Answer:
171.65 seconds
Step-by-step explanation:
did the test and got it right
The volume of a rectangular box is 1.0 ft3. what is the length if the width is 1.0 ft and the height is 1.5 ft?
The length of the rectangular box is 0.67 feet
How to determine the length of the box?The given parameters are:
Length = ??
Width = 1.0 ft
Height = 1.5 ft
Volume = 1.0 ft^3
The volume is calculated as:
Volume = Length * Width * Height
Substitute the known values in the above equation
1 = Length * 1 * 1.5
Evaluate the product
1 = Length * 1.5
Divide both sides by 1.5
Length = 0.67
Hence, the length of the rectangular box is 0.67 feet
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How does the figure help verify the triangle inequality theorem?
The line is drawn from a length of 15, two lines constructing a triangle and intersecting the arc from a length of the lines 7, 4
A.
by showing that only one triangle can be formed when the sum of the lengths of two sides equals the length of the third
B.
by showing that a triangle cannot be formed when the sum of the lengths of two sides equals the length of the third
C.
by showing that only one triangle can be formed when the sum of the lengths of two sides is less than the length of the third
D.
by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side
Option D. The triangle inequality theorem is verified by by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side.
How to make this proofFrom the given picture we can see the length of the sides. These are 7, 4 and 15.
The length of the two sides cannot join due to the fact that they are less than 15.
4 + 7 < 15
11< 15
Hence the answer is D.
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by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side
g(x) = (x ^ 3 - 9x)/(x ^ 2 - 6x + 9)
The expression is simplified to x
How to simplify the expressiong(x) = (x ^ 3 - 9x)/(x ^ 2 - 6x + 9)
First, we simplify the numerator
= [tex]\frac{x (x^2 - 3^2)}{x^2 - 6x + 9}[/tex]
Now, let's solve the quadratic equation in the denominator
= [tex]\frac{x(x^2 - 3^2)}{x^2 - 3x - 3x + 9}[/tex]
= [tex]\frac{x(x^2 - 3^2)}{x(x-3) - 3(x - 3)}[/tex]
= [tex]\frac{x(x - 3) (x -3)}{(x -3) ( x-3)}[/tex]
Divide the like factors
= x
The answer is x
Thus, the expression is simplified to x
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i need help quick!!
you can have brainliest this is algerbra btw
Answer:
Step-by-step explanation:
Day 1 = 2 birds
day 2 = 3 birds
day 3 = 9 birds
day 4 = 8 birds
day 5 = 1 bird
On day 1 the points are (1,2)
On day 5 the points are (5,1)
(I am picking these for the points because I don't know your options for the selecting area.)
we use this formula y2-y1/x2-x1
2-5/1-1
3/0
our answer is infinite which is the relation and this is an infinite function
Answer:
◘ (1, 2)
◘ (2, 3)
◘ 3
◘ is
◘ each value of Day corresponds to exactly one value of Number of birds
Explanation:
◘◘ In the graph, Days represents the x-axis, and Number of birds represents the y-axis. Therefore each marked point on the graph can be thought of as a Cartesian coordinate. This means that the answers for the first and second question could be any of (1, 2), (2, 3), (3, 9), (4, 8), or (5, 1).
◘ In the graph, we can see that the point above Day 2 corresponds to 3 on the Number of birds axis, which means on day 2, 3 birds visited the feeder.
◘ The relation shown is a function because each value of Day corresponds to exactly one value of Number of birds. A function is a relationship that provides one output for each input, and this graph follows that.
Factorize the expressions 8a⁶ + 5a³ + 1.
Use a³+b³ +c³ - 3abc
Here a = 2a²
b= -a
And c = 1
Answer:
Step-by-step explanation:
Twenty new members are elected to an agency every two years. The agency has 100 members on average overall. How long does a member hold his/her position at the agency
The time that a member hold his/her position at the agency is approximately 0.1 year.
Given that twenty members are elected to an agency every two years and there are 100 members on a average overall.
We have to find the time that a member hold his position at the agency.
To calculate the time we have to use multiplication which means product of two numbers.
In 2 years agency elected 20 members. It shows like under:
2 years=20 members
We require 100 members at one end so we will multiply by 5 both sides.
10 years=100 members
Now take 100 to left side of equal to sign.
10/100=1 member
1 member=1/10
=0.1
Hence a member holds 0.1 year at the agency.
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please answer all of them with a clear answer
See below for the solution to the questions
The parallel side of the trapezoidThe given parameters are:
Area = 138
a = 4x - 1
b = x - 4
Height = 12
The area is calculated as:
Area = 0.5 * (a + b) * height
So, we have:
0.5 *(4x - 1 + x - 4) * 12 = 138
This gives
5x - 5 = 23
Add 5 to both sides
5x = 28
Divide by 5
x = 5.6
Recall that:
a = 4x - 1 = 4 * 5.6 - 1 = 21.4
b = x - 4 = 5.6 - 4 = 1.6
Hence, the short base length is 1.6 meters and the long base length is 21.4 meters
The largest angle in the triangleThe sides are given as:
x = 22
y = 24
z = 25
The largest angle always opposite the largest side.
This means that the largest angle is Z
The CircumferenceThe radius is given as:
r = 29
The circumference is calculated as:
[tex]C = 2\pi r[/tex]
So, we have:
[tex]C = 2\pi *29[/tex]
Evaluate
C = 182.21
Hence, the circumference is 182.21 inches
Measure of angle from arcThe measure of the arc is given as:
[tex]\theta = 69^o[/tex]
The angle LIK is calculated as:
[tex]m\angle LIK = \frac{\theta}2[/tex]
So, we have:
[tex]m\angle LIK = \frac{69^o}2[/tex]
Evaluate the quotient
[tex]m\angle LIK = 34.5^o[/tex]
Hence, the measure of the angle is [tex]m\angle LIK = 34.5^o[/tex]
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#12Writethe converse, inverse, and contrapositive of the following statement. Find the truth value of each.“If Brielle drives at exactly 0 mi/h, then she travels 10 mi in 0 mins
See below for the converse, inverse, and contrapositive of the statement
How to write the conditional statements?The statement is given as:
If Brielle drives at exactly 30 mi/h, then she travels 10 mi in 20 mins
The speed is calculated as:
Speed = Distance/Time
So, we have:
Speed = 10 mi/20 mins
This gives
Speed = 10 mi/1/3 h
Speed = 30 mi/h
The converse
To do this, we simply switch the hypothesis and the conclusion
So, the converse is:
If Brielle travels 10 mi in 20 mins, then she drives at exactly 30 mi/h
The above statement is true
The inverse
To do this, we simply negate the hypothesis and the conclusion
So, the inverse is:
If Brielle did not drive at exactly 30 mi/h, then she did not travel 10 mi in 20 mins
The above statement is false
The contrapositive
To do this, we simply negate the hypothesis and the conclusion, and then switch them
So, the contrapositive is:
If Brielle did not travel 10 mi in 20 mins, then she did not drive at exactly 30 mi/h
The above statement is false
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true ir false .
A central angle is equal to half the measure of its intercepted arc.
Answer:
Step-by-step explanation:
Answer
False but close.
The intercept arc and the central angle are equal.
The average expenditure per student (based on average daily attendance) for a certain school year was $10,337 with a population standard deviation of $1560. A survey for the next school year of 150 randomly selected students resulted in a sample mean of $10, 798. Find the P-value
The true mean expenditure per student is different from $10,337.
What is hypothesis in math?
A hypothesis is a proposition that is consistent with known data, but has been neither verified nor shown to be false.There are basically two types, namely, null hypothesis and alternative hypothesis.Sample size is greater than 30 and the population standard deviation is given. Thus, in order to test
H0: µ =$10,337
H1: µ≠$10,337
The appropriate test is one sample z test.
The formula for one sample z test:
Z= x−μ / σ √ n
x−μ
x=10798
μ=10337
σ=1560
n=150
[tex]Z = \frac{10798 - 10337}{1560 / \sqrt{150} } = 3.62[/tex]
Computation of p-value:
The EXCEL formula to find the p-value for a two-tailed z-test is
“=2*(1-NORM.S.DIST(3.62, TRUE))”
Thus, the p-value obtained is 0.00029
Conclusion using α = 0.05:
Rejection rule using p-value:
If p-value ≤ α, then reject the null hypothesis.
Since, 0.00029 < 0.05, there is sufficient evidence to reject the null hypothesis.
Therefore, the true mean expenditure per student is different from $10,337.
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