Answer:
a
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis [tex]H_a : \mu_1 > \mu_2[/tex]
b
[tex]p-value = 0.232[/tex]
c
The decision rule is
Fail to reject the null hypothesis
Step-by-step explanation:
From the question we are told that
The value given is
S/N
1 7 5
2 4 3
3 8 7
4 8 8
5 7 9
6 7 5
7 6 5
Generally the sample mean for the first sample is mathematically represented as
[tex]\= x _1 = \frac{\sum x_i }{n}[/tex]
=> [tex]\= x _1 = \frac{7 +4 + \cdots + 6}{7}[/tex]
=> [tex]\= x _1 = 6.714[/tex]
Generally the sample mean for the second sample is mathematically represented as
[tex]\= x _2 = \frac{\sum x_i }{n}[/tex]
=> [tex]\= x _2 = \frac{5 + 3+ \cdots + 5}{7}[/tex]
=> [tex]\= x _2 = 6[/tex]
Generally the sample standard deviation for the first sample is mathematically represented as
[tex]s_1 = \sqrt{\frac{\sum (x_i - \= x_1)^2 }{n-1 } }[/tex]
=> [tex]s_1 = \sqrt{\frac{ (7 - 6.714 )^2 +(4 - 6.714 )^2 + \cdots + (6 - 6.714 )^2 }{7-1 } }[/tex]
=> [tex]s_1 = 1.905[/tex]
Generally the sample standard deviation for the second sample is mathematically represented as
[tex]s_2 = \sqrt{\frac{\sum (x_i - \= x_2)^2 }{n-1 } }[/tex]
=> [tex]s_2 = \sqrt{\frac{ (5 - 6.714 )^2 +(3 - 6.714 )^2 + \cdots + (5 - 6.714 )^2 }{7-1 } }[/tex]
=> [tex]s_1 = 4.33[/tex]
Generally the pooled standard deviation is
[tex]s = \sqrt{\frac{(n_1 - 1 )s_1^2 + (n_2 - 1 )s_2^2}{n_1 + n_2 -2 } }[/tex]
=> [tex]s = \sqrt{\frac{(7 - 1 )1.905^2 + (7 - 1 )4.333^2}{7 + 7 -2 } }[/tex]
=> [tex]s = 1.766[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis [tex]H_a : \mu_1 > \mu_2[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x _1 - \= x_2 }{s * \sqrt{\frac{1}{n_1} + \frac{1}{n_2}} }[/tex]
=> [tex]t = \frac{6.714 - 6 }{1.766 * \sqrt{\frac{1}{7} + \frac{1}{7}} }[/tex]
=> [tex]t = 0.757[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n_1 + n_2 - 2[/tex]
=> [tex]df = 7 + 7 - 2[/tex]
=> [tex]df = 12[/tex]
From the t distribution table the probability of [tex]t = 0.757[/tex] at a degree of freedom of [tex]df = 12[/tex] is
[tex]t_{ 0.757 , 12} = 0.232[/tex]
Generally the p-value is
[tex]p-value = t_{ 0.757 , 12} = 0.232[/tex]
From the values obtained we see that [tex]p-value > \alpha[/tex] hence
The decision rule is
Fail to reject the null hypothesis
a person is earning 600 per day to do a certain job. express the total salary S as a function of the number N of days that the person works.
Answer:
As im pretty sure the equation would be S=600N
Step-by-step explanation:
Determine the slope of the line represented by the table of values and the y-intercept
The slopes and the y - intercepts of the lines represented by the tables are calculated below.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
Given are the tables representing the coordinates [x] and [y].
Table [1]
m = (5 - 3)/(-1 + 2) = 2
[y] - intercept = 7
Table [2]
m = (2 - 5)/(-2 + 3) = -3
[y] - intercept = -4
Table [3]
m = (-13 + 17)/(2 - 1) = 4
-1 = 4 x 5 + c
c = - 1 - 20 = - 21
[y] - intercept = - 21
Table [4]
m = (-9 + 4)/(-5 + 6) = - 5
-6 = - 5 x - 4 + c
c = - 26
[y] - intercept = - 26
Table [5]
m = (6 - 3)/(1 - 0) = 3
[y] - intercept = 3
Table [6]
m = (2 - 5)/(-1 + 2) = - 3
[y] - intercept = - 3
Table [7]
m = (6/5 - 2/5)/(0 + 2) = 2/5
[y] - intercept = 6/5
Table [1]
m = (2 - 1)/(1 + 1) = 1/2
[y] - intercept = 1.5
Therefore, the slopes and the y - intercepts of the lines represented by the tables are calculated above.
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ILL GIVE YOU BRAiNLIEST I NEED HELP ON THIS ONE
There are 18 green, 11 white, 15 purple, and 7 blue gum balls in a gum ball machine. How many total possible outcomes are there?
a-51
b-7
c-18
d-4
Answer: A. 51
Step-by-step explanation:
Just count all the gum balls in the machine to get the TOTAL possible outcome! (18 green + 11 white + 15 purple + 7 blue gum balls= 51)
Alisha asked 120 students what kind of pet they liked the most. Exactly 45% of the students said they liked dogs best. What is the tottal number of students who said they liked dogs best?
Answer:
54 students
Step-by-step explanation:
45% of 120 is 54
Review: Key Concepts
.
Multiplication and division of rational__________ is similar to multiplication and division of rational numbers.
Answer:
Not helpful
Step-by-step explanation:
How many 25cm pieces of wires can
be cut out from a wire of length 4
metres?
Answer:
16
Step-by-step explanation:
4 meters is 400 centimeters and 400/25 is 16 so you can cut 16 pieces of 25cm wire from 4 meters of wire.
Answer: 16
Step-by-step explanation:
4 meters=400 cm
400 divided by 25=16
Victor read 2 1/3 books over 14 days last summer. Assume it took him the same amount of time to read each book. How many days did it take him to read a full book?
I answered 1/6. Is this correct? I need explanation and answer. Will give the branliest!
Answer:
It took 6 days for Victor to read a full book.
Step-by-step explanation:
Given that Victor read 2 1/3 books in 14 days, and that it took him the same time to read each book completely, to determine the number of days it took him to read a complete book it is necessary to perform the following calculation:
1/3 = 0.333
14 / (2 + 1/3) = X
14 / 2.333 = X
6 = X
So, it took Victor 6 days to read a full book.
You are given 3 to 1 odds against tossing three tails with three coins, meaning you win $3 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game. Would you expect to win or lose money in 1 game? In 100 games? Explain. Find the expected value (to you) for the game.
Step-by-step explanation:
To find the E(X) expected value, you come up with the different probabilities for each outcomeyour set of outcomes after 3 tosses would be = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} where H is heads and T is tailsEach element has a probability of 1/8 so let x represent number of tails[tex]Probability(x)=P(x)\\P(0)=\frac{1}{8} \\P(1)=\frac{3}{8} \\P(2)=\frac{3}{8} \\P(3)=\frac{1}{8}[/tex] The E(x)=Summation (x times P(x))[tex]E(X)=(0)(0.125)+(1)(0.375)+(2)(0.375)+(3)(0.125)=1.5[/tex] Now which probability is 1.5 tails? None, so it is either 2 tails or 1 tailsSo you can expect to lose money in 1 gameBut as you play more games the probability of getting 3 tails becomes more and more likely, so you can expect to win in a 100 gamesThe expected value is the value of winning made on a game when played overtime. Hence, the expected value of the game is -$0.5 ; with the player losing -$0.5 in the long run.
A coin toss :
{H, T}Sample space for 3 tosses :
{HHH, HHT, HHT, HTT, HHT, HTT, HTT, TTT}Toss required to win = 3 tails :
Amount won on success = $3 Amount lost otherwise = $1 = - $1Creating a discrete probability table :
X _____ 3 _______ - 1P(X) ___ 1/8 _____ 7/8The expected probability can be defined as :
E(X) = ΣX×P(X)E(X) = 3 × (1/8) + (-1) × 7/8
E(X) = 3/8 - 7/8 = - 4/8 = -1/2
Therefore, the expected value of the game = - 0.5 ; meaning that, I'll lose 0.5 in the long run.
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Roxanna has a collection of silver spoons from all over the world.
If the spoons are arranged in sets of 7, there are 5 left over.
If the spoons are arranged in sets of 8, there is 1 left over.
If the spoons are arranged in sets of 15, there are 14 left over.
If she has at least 50 spoons, what is the smallest possible number of spoons in her collection?
Answer: 89
Step-by-step explanation: 8 x 11 + 1 = 89, 7 x 12 + 5 = 89, 15 x 5 + 14 = 89
You build a model of Laurel Park using the scale 1.5 inches:10 feet. If the model 94.5
inches wide, what is the width of the school campus?
Answer:
The width of the school campus is:
[tex] \boxed{ \underline{ \rm{630 \: feet}}}[/tex]
Step-by-step explanation:
Scale = 1.5 inches : 10 feet
That means, 1.5 inches is equals to 10 feet in real.
Then for 1 inch:
⇛ 10 / 1.5 feet
⇛ 10/3 feet
We need to find for 94.5 inches,
⇛ 94.5 inches = 94.5 × 2/3 feet
⇛ 94.5 inches = 63 feet
Thus, the width of the school campus is 63 feet.
the area of a rectangular wall of a barn is 154 square feet. it's length is 8 feet longer than twice its width. find the length and the width of the wall of the barn.
Answer:
the length = 22 and width =7
Beach Hotel in Cancun is offering two weekend specials. One includes a 2-night stay with 3 meals and costs $195. The other includes a 3-night stay with 5 meals and cost $300. Which of the following shows the correct system to model this scenario?
Answer:
Step-by-step explanation:
-3 (2n+3m= 195)
2 (3n+5m= 300)
-6 - 9m= -585
6n + 10m= 600
m=5
Cory paid $9 for lunch and paid $11 to go to a movie. How much money did he spend?
Answer:
20
Step-by-step explanation:
Because if you add all the money up it would be 20=9+11
A lawn-mowing company is trying to grow its business. It had 26 clients when they started its business and wants to increase by 3 new clients each week. Use an arithmetic sequence to write a function to represent this real-world situation and determine the range of the function for the first four weeks of data.
A. f(x) = 3x + 26; 0 ≤ y ≤ 4
B. f(x) = 3x + 23; 26 ≤ y ≤ 35
C. f(x) = 3x + 26; 26 ≤ y ≤ 35
D. f(x) = 3x + 23; 0 ≤ y ≤ 4
Answer:
B
Step-by-step explanation:
I took had this question in my test and im pretty sure I got this correct
The range of the function for the first four weeks of data f(x) = 3x + 26; 26 ≤ y ≤ 35. The correct option is C.
What is the range of the function?The range of a function in mathematics can refer to one of two closely related ideas: The function's codomain a representation of the action A binary relation f between two sets X and Y is a function if there is exactly one y in Y such that f connects x to y for every x in X.
It is given that a lawn-mowing company is trying to grow its business. It had 26 clients when it started its business and wants to increase by 3 new clients each week.
The equation will be represented as follows:-
Let x be the number of the weeks then the expression will be written as:-
f(x) = 3x + 26
For the first four weeks, the range will be:-
26 ≤ y ≤ 35
Therefore, range of the function for the first four weeks of data f(x) = 3x + 26; 26 ≤ y ≤ 35. The correct option is C.
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Find the GCF from the two numbers, and rewrite the sum using the distributive property. 12+18= 42+14= 36+27= 16+72= 44+33= 6. 8 - 16 = 7. 54 + 24 = 8. 63 - 81 = 9. 25 - 60 = 10. 16 – 20 =
Answer:
65+7 too the test
Step-by-step explanation:
don't be putting random stuff and that's on period
Answer:
126 divided by 6 which is 27
Step-by-step explanation:
The answer is C
Answer is C!
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Solve two times five eighths.
Leave your answer as an improper fraction.
A) seven sixteenths
B) ten sixteenths
C) seven eighths
D) ten eighths
Answer:
c
Step-by-step explanation:
The improper fraction is ten eighths(10/8).
What is improper fraction?Improper fractions are ones that have been divided improperly for any number, object, or element, as indicated by the term. A fraction is a portion of a whole in mathematics. Denominator and numerator are the two components of fractions.
A fraction whose numerator exceeds the denominator is referred to as an improper fraction. Consider the case where x/y is an improper fraction and x exceeds y. The incorrect fraction is consequently always bigger than one.
Given two times five eighths.
we need to multiply 2 by 5/8
First, remember that 2 is equal to 2/1 since 2 divided by 1 equals 2. Therefore, frame the issue as follows to begin:
2/1 x 5/8
Combine the denominators (1 x 8) and the numerators (2 x 5 = 10) to create a single fraction, as seen below:
10/8
Hence two times five eighths is 10/8 in improper fraction.
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What is the exact angle measure in radians?
495°
Answer:
495° × π/180 = 8.639
Step-by-step explanation:
The exact angle measure in radians of 495 is; 8.64radians
From convention;We can say that 360° is equal to 2πrad.
On this note, we can evaluate the value of 495° in rads as; x.
Therefore;
x = (495 × 2 πrad)/360x = 8.64 radians.
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Factor using polynomial division
The polynomial p(x) = x3 + 7x2 – 36 has a known factor of (x + 3).
Rewrite p(x) as a product of linear factors.
p(2) =
Answer:
Rewriting p(x) as a product of linear factors: [tex]\mathbf{f(x)=(x+3)(x-2)(x+6)}[/tex]
Step-by-step explanation:
The polynomial [tex]p(x) = x^3 + 7x^2 - 36[/tex] has a known factor of [tex](x + 3)[/tex]
We need to find other factors.
First we find quotient of [tex]p(x) = x^3 + 7x^2 - 36[/tex] divided by [tex](x + 3)[/tex]
The division is shown in image attached.
The quotient is: [tex]x^2+4x-12[/tex]
Now, factoring the quotient [tex]x^2+4x-12[/tex]
[tex]x^2+4x-12\\=x^2+6x-2x-12\\=x(x+6)-2(x+6)\\=(x-2)(x+6)[/tex]
The other two factors are (x-2)(x+6)
So, Rewriting p(x) as a product of linear factors: [tex]f(x)=(x+3)(x-2)(x+6)[/tex]
What is the constant of proportionality in the equation y=5/9 x?
Answer:
In your question, the constant of proportionality already jump out at us which is to get y, we have to multiply x by 5/9. Therefore the constant of proportionality is y=5/9x.
Help me with this question pleaseee
Answer:
13
Step-by-step explanation:
In the figure provided,
∠(9y + 7) = ∠(2y + 98) [vertically opposite angles]
7y + 7 = 98 [subtracting 2y from both sides]
7y = 91 [subtracting 7 form both sides]
y = 13 [dividing both sides by 7]
Use the figure below to answer questions 3 and 4.
A gre pyramid is packaged indebo
5 inches
6 inches
Sinches
The space inside the box around the pyramid is then filled with protective foam. About how many cubic inches of foam is needed to fill the space around
the pyramid?
Your answer:
8 cubic inches
41 cubic inches
83 cubic inches
125 cubic inches
Volume is a three-dimensional scalar quantity. The volume of foam that is needed in cubic inches is 83.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of foam needed is the difference between the volume of the cube and the volume of the square pyramid. Therefore,
The volume of cube = a³ = 5³ = 125 in³
The volume of Pyramid = (1/3)×blh = (1/3)×5×5×5 = 41.667
The volume of foam needed = 125 in³-41.667 in³ = 83.3334 in³ ≈ 83 in³
Hence, the volume of foam that is needed in cubic inches is 83.
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3x – 2y = 17
–2x – 5y = 14
Solve using Elimination Please show work
Answer:
The solution is x=3 , y=-4 or (3,-4)
Step-by-step explanation:
Given equations (1 and 2) are:
[tex]3x- 2y = 17\\-2x -5y = 14[/tex]
To solve a system of equation with elimination method, the co-efficients of one of the variables has to be equated and then the equations are added or subtracted to get an equation in one variable.
Multiplying equation 1 by 2:
[tex]2(3x-2y) = 2*17\\6x-4y = 34\ \ \ \ \ Eqn\ 3[/tex]
Multiplying equation 2 by 3
[tex]3(-2x-5y) = 3*14\\-6x-15y = 42\ \ \ \ Eqn\ 4[/tex]
Adding equation 3 and 4
[tex](6x-4y) + (-6x-15y) = 34+42\\6x-4y-6x-15y = 76\\-19y = 76\\\frac{-19y}{-19} = \frac{76}{-19}\\y = -4\\[/tex]
Putting y = -4 in equation 1
[tex]3x-2(-4) = 17\\3x+8 = 17\\3x = 17-8\\3x = 9\\\frac{3x}{3} = \frac{9}{3}\\x = 3[/tex]
Hence,
The solution is x=3 , y=-4 or (3,-4)
which of these is positive values and which have negative values
7-(-4)
-3+(-2)
5-8
-10+12
Answer:
Positive: 7-(-4) and -10+12
Negative -3+(-2) and 5-8
Step-by-step explanation:
Addition and subtraction rules
5) (4 points each) Consider picking ONE card from a standard deck of cards.
a) What is the probability of picking a Jack or a
b) What is the probability of picking a Spade or
Queen?
a Face Card?
c) What is the probability of picking a Face Card d) What is the probability of picking a Face Card
and a Heart?
Can someone please help me with this question?
Which of the following represents a dilation that is a reduction with a scale factor larger than 1/2?
A: (x,y) ---> (0.4x,0.4y)
B: (x,y) ---> (0.5x,0.5y)
C: (x,y) ---> (1/4x, 1/4y)
D: (x,y) ---> (0.6x, 0.6y)
Thanks!
Answer:
D
Step-by-step explanation:
1/2 is less than .6 and still a reduction
There are 12 boys and 16 girls in a classroom. Which represents the simplified ratio of girls to students in the
classroom?
Answer: 2:3
Step-by-step explanation:
12/6=2
18/6=3
Answer:
Option A.
Step-by-step explanation:
Options:
A. 3 to 4
B. 4 to 3
C. 4 to 7
D. 7 to 4
In order to simplify a fraction the numerator and the denominator have to have common factors that they can be divided by.
[tex]\frac{12}{16}[/tex]
Divide
[tex]CF=4[/tex]
[tex]12\div4=3[/tex]
[tex]16\div4=4[/tex]
[tex]=\frac{3}{4}[/tex]
Hope this helps.
simpifly 54/27
..................
Answer:
2/1
Hope this helps.
Answer:
2/1
Step-by-step explanation:
continue dividing the denominator and numerator by 3
Need help plz I’m not rlly smart at math
Answer:
Step-by-step explanation:
ha ha
Answer:
9ft^2
Step by step explanation:
Area is L × W
so the L would be 3 3/4 ft x 2 2/5ft
with that equation in mind
how do we multiply whole number fractions? well, we make them into improper fractions
3 3/4 becomes (4x3) +3 / 4
2 2/5 becomes (2x5) + 2 / 5
Those answers become
15/4 x 12/5
^ Our improper fractions then we multiply across
15/4 x 12/5
^ 15 x 12 = 180
& 4 x 5 = 20
the final fraction becomes 180/20 and we can simplify that by 20
that becomes 9/1 = 9ft^2
For one Algebra test, John had to answer 23 questions. Of these questions, John
answered 47.8% of them correctly. How many questions did John correctly answer on his
test? Round your answer to the nearest whole number if necessary.
Answer:
11 questions
Step-by-step explanation:
Answer:
10 or 11
Step-by-step explanation:
cross multiply
47.8%/100%=x/23
=10.994