analyze the solution to the system to determine whether there is a catapult arm length that aiden and natalie can both use to launch their tennis balls the same distance. explain your reasoning.
Answers
There is no catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance.
From the graph,
x axis represents the arm length of the catapult and the y axis represents the distance.
The point at which the catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance is the intersecting point of the both line
The coordinates of the intersecting point = (-30, 90)
Here arm length represents -30, but the arm length cannot be a negative value
Therefore, there is no arm length that gives equal distance
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Answer:
There is no catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance.
Step-by-step explanation:
Related Questions
if a 10 percent increase in the price of good x results in a 20 percent decrease in the quantity of good y demanded, which of the following is true?
Answers
Elastic demand for a good is defined as when the price of a good rises by 10% while the quantity required falls by 20%.
What is Elastic demand?When a product's price changes, consumer demand is said to be elastic. Consumers will purchase significantly more if the price drops just a little. They won't buy as much if prices increase somewhat instead opting to wait for them to level out.
If all other variables remain constant, the ratio of a product's percent change in demand to its percent change in price determines whether a product's demand is elastic or inelastic.
It is neither elastic nor inelastic for an item's price to alter in proportion to its change in demand. In other words, a product has elastic demand if demand fluctuates more than price does.
Hence, Elastic demand for a good is defined as when the price of a good rises by 10% while the quantity required falls by 20%.
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i need some help plsssssss
Answers
Answer:
Option 3 (Parentheses, division, multiplication, subtraction)
Step-by-step explanation:
Using PEMDAS, we can know that we need to solve the parentheses first. Next, we need to solve the multiplication and division, so we can eliminate the first option and last option. However, we need to solve the operations left to right, meaning we'd solve the division first. Therefore, the answer is option 3.
Answer:
The answer is Parentheses multiplication division subtraction
Step-by-step explanation:
Always remember
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Hassan knows how to sing 6 vocal pieces, thanks to his choir class. Now he's about to start private lessons. His teacher says he will learn 2 new pieces each month.
Write an equation that shows the relationship between the number of months Hassan takes voice lessons, x, and the number of pieces he knows, y.
y=
Answers
Answer:
2x + 6
Step-by-step explanation:
If the number of months Hassan takes voice lessons is x, and he learns two pieces every month, you would multiply the number of months, x, together with the number of pieces he will learn each month, 2, making 2x.
Hassan already knows how to sing 6 vocal pieces, which you would add to 2x.
That makes 2x + 6.
Trapezoid abcd has vertices a(2, 4), b(5, 4), c(7, 1), and d(0, 1). Is this trapezoid an isosceles trapezoid? select from the drop-down menu to correctly complete the statement.
Answers
Yes, if Trapezoid abcd has vertices a(2, 4), b(5, 4), c(7, 1), and d(0, 1) , ABCD is an isosceles trapezoid.
Since, If in a trapezoid two opposite nonparallel sides are equal then it is called isosceles trapezoid.
In trapezoid ABCD sides are AB, BC, CD and DA.
According to the question, A≡(2,4) B≡(5,4) C≡(7,1) and D≡(0,1)
After making the diagram of ABCD, we found that DA and BC are nonparallel sides.
And, by the distance formula BC = √((7 - 5)² + (1 - 4)²) =
⇒ BC =√(4 + 9)
⇒BC = √13 unit.
Similarly, DA = √((0 - 2)² + (1 - 4)²)
DA = √(4 + 9)
⇒ DA = √13 unit.
Thus, In trapezoid ABCD, two non parallel sides BC and DA are equal.
Therefore, trapezoid ABCD is a isosceles trapezoid.
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Which rule best red the following patterns 8,4,10,6,12,8,14
Answers
The rule with describes the expression 8,4,10,6,12,8,14 is the alternating numbers gets increased by 2
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the expression be represented as A
Now , the expression A is
A = 8,4,10,6,12,8,14
Taking out the alternate numbers from the expression A , we get
A₁ = 8 , 10 , 12 , 14
So ,the values of A₁ increases by 2
And ,Taking out the alternate numbers from the expression A , we get
A₂ = 4 , 6 , 8 , 10
So , the values of A₂ also increases by 2
Hence , the alternating numbers in the expression increases by 2
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a swimming pool open 12 3/4 hours each day. the life gurads work shifts that are 3/4 hour long . how many shifts are there each day?
Answers
Answer:
17
Step-by-step explanation:
I hope this helps!!!
3/4 3/4 3/4 3/4= 3 hours
3 hours equals 4 shifts
you do this 4 times and it equals 12 hours, and 16 . Then you have 3/4 left which equals a shift. So 16+1=17
A leaky faucet is losing water and is filling a 5-gallon bucket every 20 hours. At that rate, how many buckets will the leaky faucet fill after 3 days?
Answers
The number of gallons that can be filled is 18 gallons.
What is a rate?Rate demonstrates how many times one number can fit into another number. It contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this case, the number of hours in 3 days will be:
= 24 × 3
= 72 hours.
Since the leaky faucet is losing water and is filling a 5-gallon bucket every 20 hours. The gallon filled in 72 hours will be represented by x.
5/20 = x/72
Cross multiply
20x = 72 × 5
20x = 360
x = 360/20
x = 18
There'll be 18 gallons
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Ms.D bought 8 1/2 pounds of ham from Excellente Hambaked Shop. She gave 1 3/4 pounds of ham to Mr.Chavir. How many pounds of ham does she have left?
Answers
The amount of ham Ms.D has left is [tex]6\frac{3}{4}[/tex] pounds.
How to find the pounds of ham she has left?Ms.D bought [tex]8\frac{1}{2}[/tex] pounds of ham from Excellente Hambaked Shop. She gave [tex]1\frac{3}{4}[/tex] pounds of ham to Mr.Chavir. The number of pounds of ham she has left can be calculated as follows:
Hence, the amount of hams in pounds she has left is the difference between what she had and the amount of pounds of hams she gave to Mr Chavir.
Therefore,
Amount bought by Ms.D = [tex]8\frac{1}{2}[/tex] pounds
Amount given to Mr.Chavir. = [tex]1\frac{3}{4}[/tex] pounds
Therefore,
Amount of she has left = [tex]8\frac{1}{2}[/tex] - [tex]1\frac{3}{4}[/tex]
Amount of she has left = [tex]\frac{17}{2} - \frac{7}{4}[/tex]
Amount of she has left = [tex]\frac{34-7}{4}[/tex]
Amount of she has left = [tex]\frac{27}{4}[/tex]
Amount of she has left = [tex]6\frac{3}{4}[/tex] pounds
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Ameekah is working with consecutive integers. if she uses x to represent her first number, what should she use to represent her second number? x x 1 x 2 2x
Answers
The second number used by Ameekah to represent the consecutive integers is (x + 1).
Explain the term consecutive integers?Integers that follow one another in a predictable counting pattern are referred to as consecutive integers. There are no numbers missed while showing consecutive integers in either a sequence, so the range between them is absolutely fixed. The consecutive integers in increasing order are referred to as consecutive integers.Let 'x' be the first number written by Ameekah.
Then, the second number will be obtained by adding one to first number.
= x + 1
Thus, the second number used by Ameekah to represent the consecutive integers is (x + 1).
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Answer:
"B" is correct, "x + 1"
Step-by-step explanation:
Have a Jocular Day
13. Grace is an egg farmer who sells eggs in two different-sized containers: a
dozen eggs for $5 or a 30-egg flat for $10.80. She is going to start selling an
18-ege carton as well and is wondering what price to charge. She wants to
set the unit price of the 18-egg carton between the unit prices for the other
two sizes. What price range can she choose from for the new size?
Answers
Answer:
6.48 <= x <= 7.5
Step-by-step explanation:
(5/12)×18=7.5
(10.80/30)×18=6.48
6.48 <= x <= 7.5
please help me solve this asap
Answers
(6+1)/(2+4) it becomes adding as you are subtracting a negative. So then you get
7/6 as your slope.
Since it is a positive slope, the line is rising. That is the second answer.
Sketch the line by plotting the two given points. The slope should be rise 7 over run 6
Answer:
B. Falls
Step-by-step explanation:
What is the value of 16/2
Answers
Answer: 8
Step-by-step explanation: 16/2 is simply 16 ÷ 2 in fraction form,
16 ÷ 2 = 8
consider an arbitrary n × n matrix a. what is the relationship between the characteristic polynomials of a and at ? what does your answer tell you about the eigenvalues of a and at ?
Answers
When a linear transformation is done to a nonzero vector in linear algebra, the vector is said to have an eigenvector, or characteristic vector, which only changes by a scalar amount. The scaling factor for the eigenvector is the appropriate eigenvalue, frequently represented as lambda.
When a linear transformation is done to a nonzero vector in linear algebra, the vector is said to have an eigenvector, or characteristic vector, which only changes by a scalar amount. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by.
Hence, characteristic polynomial of A and A^T are the same, therefore their eigenvalues are also same.
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where do i start with this world problem
Answers
The measure of an angle ∠TQU is 26.6° if PQ=3 and QR=4
What is meant by an angle?In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
Angle can also refer to a rotation or the measurement of an angle. This measurement is the ratio of the length of a circular arc to its radius.
Given,
Rectangle PQRS has PQ=3 and QR=4
The points T and U are on side PS such that PT=US=1
As PQRS is rectangle so opposite sides of rectangle should be equal.
PS=QR and PQ=RS
QR=4, PS=4
But, PS=PT+TU+US
4=1+TU+1
TU=4-2
TU=2
And PU=PT+TU
1+2=3
PU=3
Consider, ΔQPU, Right angled at P.
We know that,
tan Q=PU/PQ
tan Q=3/3
tan Q=1
Q=tan⁻¹
Q=45°
∠PQU=45°
Now, let us consider ΔQPT is right angled at P
tan Q=PT/PQ
tan Q=1/3
Q= tan⁻¹(1/3)
Q=18.43°
∠PQT=18.43°
∠PQU=∠PQT+∠TQU
45°=18.43°+∠TQU
∠TQU=45°-18.43°
∠TQU=26.57°
∠TQU≈26.6°
Therefore, the measure of ∠TQU is 26.6°.
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**WILL MARK BRAINLIEST AND GIVE 30 POINTS**
Fill in the blanks to solve the system of equations. Enter only 1 term in each blank.
Answers
Answer:
1st blank = 6x
2nd blank = 12
3rd blank = 2
4th blank = 2
5th blank = 8
6th blank = 5
Find the sum of 3x^2 + 2x - 4 and 2x^2 -3x+1
Answers
Answer:
5x^2-1x-3
Step-by-step explanation:
First bring the like terms together:
= 3x^2+2x^2+2x-3x-4+1
then solve it
Ans =5x^2-1x-3
I hope its useful
you have 2,000 feet of fencing to enclose a rectangular pasture. one side of the pasture is up against a river. what is the maximum area you could enclose?
Answers
The maximum area to enclose a rectangular pasture with one side of the pasture up against a river is equal to 500,000 square feet.
As given in the question,
Let 'x' represents the length of the rectangular pasture
And 'y' represents the width of the rectangular pasture
Condition:
One side of the pasture is up against a river
Perimeter of the rectangular pasture with one side up against river
= x + 2y
⇒ 2000 = x + 2y
⇒x= 2000 - 2y
Area of the rectangular pasture
=( 2000 - 2y )( y )
= - 2 ( y² - 1000y)
= -2( y² - 1000y + 250000 - 250000 )
= -2 (y - 500 )² + 500, 000
Maximum area is at y = 500
Maximum area is 500,000
Therefore, the maximum area of the given rectangular pasture is 500,000 square pasture.
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can you help me solve this problem (x - 5)(x+2) = 0
Answers
Answer: -2
Step-by-step explanation:
(x - 5) (x + 2) = 0
(x - 5) = 0
(x - 2) = 0
Add 5 to both sides, then simplify. After that, you will subtract 2 from both sides. Simplify again, and the solution is -2.
An equation and some of the steps used to solve the equation are shown below. One step is missing: 2(x-3) + 10x = 5(3 + x) ? 2x-5x + 10x = 15 + 6 7x = 21 x=3 Which set of statements is most likely the missing step and the property that justifies the step?
Answers
The missing step was 2x-6+10x= 15+5x, the step where was applied the distributive property.
Applying the distributive property, the given radical expression can be represented by 15.
Properties of MultiplicationThe properties of multiplication are:
Distributive: a(b±c)= ab±acCommutative: a . b = b. aAssociative: a(b+c)= c(a+b)Identity: b.1=bFor answering the question, you should solve the given expression step by step. After that, you should identify the missing step from the information given for the question.
The question gives: 2(x-3) + 10x = 5(3 + x), from the distributive property. you have
2x-6+10x= 15+5x (step 1)
2x -5x +10x = 15+6 (step 2)
7x=21 (step 3)
x=3 (step 4)
See that step 1 (2x-6+10x= 15+5x ) is not shown in the question.
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4x+16=-12
What’s the answer?
Answers
Answer:
x = -7
Step-by-step explanation:
4x + 16 = -12 Subtract 16 from both sides
4x = -28 Divide both sides by 4
x = -7
Answer:
x = -7
Step-by-step explanation:
1. Subtract 16 from both sides
4x + 16 = -12
4x + 16 - 16 = -12 -16
2. Simplify
Subtract the numbers:
4x + 16 - 16 = -12 - 16
4x = -12 - 16
Subtract the numbers:
4x = -12 - 16
4x = -28
3. Divide both sides by the same factor
4x = -28
[tex]\frac{4x}{4}[/tex] = [tex]\frac{-28}{4}[/tex]
4. Simplify
Cancel terms that are in both the numerator and denominator:
[tex]\frac{4x}{4}[/tex] = [tex]\frac{-28}{4}[/tex]
x = [tex]\frac{-28}{4}[/tex]
Divide the numbers:
x = [tex]\frac{-28}{4}[/tex]
x = -7
Solution:
x = -7
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 5 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
What is the volume of the following triangular prism?
Answers
The required volume of the triangular prism will be 126 cubic meters.
What is the volume of a triangular prism?The triangular prism is the amount of space occupied by an object. It is determined by the number of unit cubes required to completely fill the solid.
V = 1/2 x H x W x L
The volume of the triangular prism will be
Volume of triangular prism = 1/2 x 9 x 6 x 13
Volume of triangular prism = 9 x 3 x 13
Volume of triangular prism = 27 x 13
Volume of triangular prism = 351 cubic yards
Thus, the volume of the triangular prism will be 126 cubic meters.
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location is known to affect the number, of a particular item, sold by walmart. two different locations, a and b, are selected on an experimental basis. location a was observed for 18 days and location b was observed for 18 days. the number of the particular items sold per day was recorded for each location. on average, location a sold 39 of these items with a sample standard deviation of 9 and location b sold 55 of these items with a sample standard deviation of 6. select a 99% confidence interval for the difference in the true means of items sold at location a and b.
Answers
The required confidence interval for the difference of means is (-18.52, -13.48).
Explain confidence of interval.Statisticians use confidence intervals to gauge vulnerability in an example variable. For instance, a scientist chooses various examples haphazardly from a similar populace and registers a certainty span so that each example might be able to perceive how it might address the genuine worth of the populace variable. The subsequent datasets are different where a few stretches incorporate the genuine populace boundary and others don't.
According to question:[tex]n_{a}[/tex] = 18 represent the sample of A
[tex]n_{b}[/tex] = 18 represent the sample of B
μₐ = 39 represent the mean sample for A
μᵇ = represent the mean sample for B
σ = 9 represent the sample deviation for A
σ = 6 represent the sample deviation for B
α = 0.01 represent the significance level
Confidence =99% or 0.99
confidence interval for the difference of means is given by the following formula,
μₐ - μᵇ± [tex]t_{\frac{α}{2}}[/tex][tex]\sqrt{\frac{S_{a}}{n_{a}} +\frac{S_{b}}{n_{b}} }[/tex]
39 - 55 ± 2.756[tex]\sqrt{\frac{9}{18} +\frac{6}{18} }[/tex]
-16 - 2.756(0.912) = -18.52
-16 + 2.756(0.912) = -13.48
Thus, required confidence interval is (-18.52, -13.48).
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Josh is 6 years older than 5 times Kim's age. The sum of their ages is less than 54.
What is the oldest Kim could be? Show all your work.
I
Answers
Answer:
8
Step-by-step explanation:
Josh is 6 years older than 5 times Kim's age. The sum of their ages is less than 54. What is the oldest Kim could be?
J + k < 54 when J = 5k + 6 so:
5k + 6 + k < 54
6k + 6 < 54
subtract 6 from both sides:
6k + 6 - 6 < 54 - 6
6k < 48
divide both sides by 6:
6k/6 < 48/6
k < 8
Kim could be 8 at maximum.
In a one-way ANOVA situation, if the overall F value is statistically significant, then you know that all of the means are significantly different from one another (T/F)?
Answers
It is true that in a one-way ANOVA situation, if the overall F value is statistically significant, then you know that all of the means are significantly different from one another.
ANOVA, which represents the analysis of variance, is a statistical test used to examine the distinction between the means of more than two groups.
One independent variable is used in a one-way ANOVA, while two independent variables are used in a two-way ANOVA.
In a one-way ANOVA scenario, the overall F value must be statistically significant for more than two of the means to be significantly different.
thus we can say that the given statement is true.
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45 POINTS
i really need help
--
Hikers walk 3 miles east and then 2 miles north and take a water break. They continue hiking 4 miles east and a final 2 miles south to their destination. What single
transformation took place from their starting position to their final destination? Use
mathematical language and create a graphic to explain your answer. Be sure to use a
straight edge and grid paper for your graphic to represent this problem.
(please add steps and notes)
Answers
Answer:
they could've walked 4 miles east to make the trip quicker. Would look alot nicer if i had grid paper
Step-by-step explanation:
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3(12-5)+8x4 what is this problem? How do I solve it?
Answers
PEMDAS
a piece of wire of length l cm is cut into two pieces. one piece, of length x cm, is made into a circle; the rest is made into a square. (a) find the value of x that makes the sum of the areas of the circle and square a minimum. find the value of x giving a maximum. (b) for the values of x found in part (a), show that the ratio of the length of wire in the square to the length of wire in the circle is equal to the ratio of the area of the square to the area of the circle.3 (c) arethevaluesofxfoundinpart(a)theonlyvalues of x for which the ratios in part (b) are equal?
Answers
As we can see, the equality is equal for only one value of xx, which was the same as the one we found in part (a).
(a) [tex]x = \frac{L\pi }{4+\pi }[/tex]
(b) True
(c) Yes
What is maximum and minimum?
The smallest value in the data set is the minimum. The largest value in the data set is the maximum.
(a) The circumference of the circle is xx, which means that
[tex]P_ 1= 2\pi r\\x = 2\pi r\\r = \frac{x}{2\pi }[/tex]
The area of the circle is,
[tex]A_c = \pi r^2\\A_c = \frac{x^2}{4\pi }[/tex]
The circumference of the square is L - x, which means
[tex]P_2 = 4a \\L-x=4a\\a = \frac{L-x}{4}[/tex]
The area of the square is,
[tex]A_s = a^2\\A_s=\frac{(L-x)^2}{16}[/tex]
The sum of the areas of the circle and the square is
[tex]A = A_c + A_s\\A = \frac{x^2}{4\pi } +\frac{(L-x)^2}{16} \\A = \frac{4x^2+(L-x)^2\pi \pi }{16\pi } \\A = \frac{4x^2+(L^2 -2Lx+x^2)\pi }{16\pi } \\A = \frac{(4+\pi )x^2-2Lx\pi +L^2\pi }{16\pi }[/tex]
The derivative of the function of the total area is
[tex]A = \frac{4+\pi }{8\pi }x-\frac{L}{8}[/tex]
We solve the equation A'(x) = 0
[tex]\frac{4+\pi }{8\pi }x-\frac{L}{8}=0\\ \frac{4+\pi }{\pi }x=L\\ x = \frac{L\pi }{4+\pi }[/tex]
So, [tex]x = \frac{L\pi }{4+\pi }[/tex] is a critical point A, and it is a global minimum of A since
[tex]A"(x) = \frac{4+\pi }{8\pi } > 0[/tex] for all x.
(b) The area of the circle for [tex]x = \frac{L\pi }{4+\pi }[/tex] is
[tex]A_c = \frac{(\frac{L\pi }{4+\pi } )^2}{4\pi } \\A_c = \frac{(\frac{L^2\pi ^2}{(4+\pi )^2} )}{4\pi } \\A_c= \frac{L^2\pi }{4(4+\pi )^2}[/tex]
The area of the square for [tex]x = \frac{L\pi }{4+\pi }[/tex] is
[tex]A_s = \frac{(L-\frac{L\pi }{4+\pi } )^2}{16}[/tex]
The ratio of the area is,
[tex]\frac{A_s}{A_c} = \frac{(\frac{(L-\frac{L\pi }{4+\pi })^2 }{16} )}{(\frac{L^2\pi }{4(4+\pi )^2} )}[/tex]
[tex]= \frac{(L - \frac{L\pi }{4+\pi })^2 }{16}*\frac{4(4+\pi )^2}{L^2\pi } \\ = \frac{L^2-\frac{2L^2\pi }{4+\pi }+(\frac{L\pi }{4+\pi } )^2 }{4} *\frac{(4+\pi )^2}{L^2\pi } \\= \frac{(4+\pi)^2 }{4\pi }-\frac{4+\pi }{2}+\frac{\pi }{4}\\ = \frac{4}{\pi }[/tex]
The ratio of the length of wire in the square to the length of wire in the circle for [tex]x = \frac{L\pi }{4+\pi }[/tex] is
[tex]\frac{L-x}{x} =\frac{L-\frac{L\pi }{4+\pi } }{\frac{L\pi }{4+\pi } } \\= \frac{\frac{4L}{4+\pi } }{\frac{L\pi }{4+\pi } } \\= \frac{4}{\pi }[/tex]
As we can see (1) = (2)
(c) To prove this, we solve the equation
[tex]\frac{A_s}{A_c} = \frac{L-x}{x} \\ \frac{\frac{(L-x)^2}{16} }{\frac{x^2}{4\pi } } = \frac{L-x}{x}\\ \frac{(L-x)^2}{4}*\frac{\pi }{x^2} = \frac{L-x}{x} \\ \frac{L-x}{4} *\frac{\pi }{x} =1\\L\pi -\pi x=4x\\L\pi = (4 + \pi )x\\x = \frac{L\pi }{4+x}[/tex]
As we can see, the equality is equal for only one value of xx, which was the same as the one we found in part (a).
Hence,
(a) [tex]x = \frac{L\pi }{4+\pi }[/tex]
(b) True
(c) Yes
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find a monic quadratic polynomial $f(x)$ such that the remainder when $f(x)$ is divided by $x-1$ is $2$ and the remainder when $f(x)$ is divided by $x-3$ is $4$.
Answers
f(x) = x + 1 is the monic quadratic polynomial used here
Given,
The monic quadratic polynomial f(x)
The remainder when f(x) divided by x - 1 is 2
The remainder when f(x) divided by x - 3 is 4
We have to find f(x).
Monic Quadratic Polynomial;-
A monic polynomial in algebra is a univariate polynomial with a single variable and a leading coefficient of 1. Its leading coefficient is the highest degree nonzero coefficient.
Here,
The remainder when f(x) divided by x - 1 is 2
Assume f(x) / x - 1 = 1
Then,
f(x) = (x - 1) × 1 + 2
f(x) = x - 1 + 2
f(x) = x + 1
Next,
The remainder when f(x) divided by x - 3 is 4
Assume f(x) / x - 3 = 1
Then,
f(x) = (x - 3) × 1 + 4
f(x) = x - 3 + 4
f(x) = x + 1
That is,
The monic quadratic polynomial used here is, f(x) = x + 1
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a survey of nonprofit organizations showed that online fundraising increased in the past year. based on a random sample of nonprofit organizations, the mean one-time gift donation in the past year was $, with a standard deviation of $. if you test the null hypothesis at the level of significance, is there evidence that the mean one-time gift donation is greater than $? interpret the meaning of the p-value in this problem.
Answers
A. There is enough data to conclude that the average one-time gift giving exceeds $75. with a 5% loss
B. The probability of receiving a sample mean one-time gift donation of $80 or more is the p-value.
What is a p-value?
The p-value, under the assumption that the null hypothesis is true, is the likelihood of receiving findings from a statistical hypothesis test that are at least as severe as the observed results. The p-value provides the minimal level of significance at which the null hypothesis would be rejected as an alternative to rejection points. The alternative hypothesis is more likely to be supported by greater evidence when the p-value is lower.
P-value is frequently utilized by government organizations to increase the credibility of their research or reports. The United States Census Bureau, for instance, mandates that any analysis with a p-value higher than 0.10 be accompanied by a statement stating that the difference is not statistically significant from zero.
A)
One wants to determine whether there is any proof that the average one-time gift giving exceeds $75.
The right response is thus E, i.e. E. H0:75 Vs H1:>75
Track down the test statistic.
n=54(sample size) (sample size)
Observed mean: 80
Observed standard deviation: 12
valid value=75
test statistic = (12[tex]\sqrt54[/tex])/(80-75)=3.06
Get the p-value by using the R-command shown below:
Lower. Tail=FALSE, p norm (3.06, 0, 1)
There is a 0.001 p-value.
What is the result of this experiment?
At a 5% threshold of significance, we reject H0 since the p-value is less than 0.05. (Los).
A. Dismiss the null theory. There is enough data to conclude that the average one-time gift giving exceeds $75. with a 5% loss
B)
In this situation, explain what the p-value means.
Take into account that the sample mean (Xbar) has a mean of 75 and a standard deviation of 12[tex]\sqrt54[/tex].
The chance that (Xbar) is larger than 80 is then equal to the p-value that was determined before.
The probability of receiving a sample mean one-time gift donation of $80 or more, given that the population mean one-time gift donation is $75, is represented by the p-value, which is B.
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A normal distribution is observed from the number of points per game for a certain basketball player. if the mean (μ) is 15 points and the standard deviation (σ) is 3 points, what is the probability that in a randomly selected game, the player scored greater than 24 points? use the empirical rule
Answers
The likelihood that a player will score more than 24 points in a randomly chosen game is 0.0013 or 0.13%.
Explain the term normal distribution?The majority of the observations are centered around the middle peak of the normal distribution, which is a cumulative distribution function which is symmetrical around its mean. The probabilities for values that are farther from the mean taper away equally in both directions.To compute the probability for the a data point, we must first get the value's z-score.
Mean = μ = 15 points
SD = σ = 3 points
When calculating the likelihood that a score will be higher than 24, the z-score for 24 is:
z-score = (x-μ)/σ
z = (24-15)/3
z = 9/3
z = 3
The chance of z3 must now be determined using the z-score table, and it will be deducted from 1 to determine the likelihood of z>3.
P(z < 3) = 0.9987
P(z > 3) = 1 - P(z < 3)
P(z > 3) = 1 - 0.9987
P(z > 3) = 0.0013 = 13%
Thus, the probability that a player will score more than 24 points in a randomly chosen game is 0.0013 or 0.13%.
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