A laptop producing company also produces laptop batteries, and claims that the batteries
it produces power a laptop for about 4:00 hours. But, you doubted the claim and collected
data from 500 laptop users of the same brand and battery, and you found out the battery
powers the laptop for about 3:00 hours and 30 minutes. Considering an alpha of 0.05,
prove the claim of the company is true or false or show whether you accept the
company’s claim or reject it? Please also write H0 and Ha statements for testing your
hypothesis
Answers
Answer:
There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours. (P-value = 0).
The null and alternative hypothesis are:
\(H_0: \mu=4\\\\H_a:\mu< 4\)
Step-by-step explanation:
The question is incomplete: To test this claim a sample or population standard deviation is needed.
We will estimate that the sample standard deviation is 2 hours, and use a t-test to test that claim.
NOTE (after solving): The difference between the sample mean and the mean of the null hypothesis is big enough to reject the null hypothesis, even when we have a sample standard deviation of 3.5 hours, which can be considered bigger than the maximum standard deviation for the sample.
This is a hypothesis test for the population mean.
The claim is that the batteries power the laptops for significantly less than 4 hours.
Then, the null and alternative hypothesis are:
\(H_0: \mu=4\\\\H_a:\mu< 4\)
The significance level is 0.05.
The sample has a size n=500.
The sample mean is M=3.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.
The estimated standard error of the mean is computed using the formula:
\(s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{500}}=0.0894\)
Then, we can calculate the t-statistic as:
\(t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{3.5-4}{0.0894}=\dfrac{-0.5}{0.0894}=-5.5902\)
The degrees of freedom for this sample size are:
\(df=n-1=500-1=499\)
This test is a left-tailed test, with 499 degrees of freedom and t=-5.5902, so the P-value for this test is calculated as (using a t-table):
\(P-value=P(t<-5.5902)=0\)
As the P-value (0) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours.
Related Questions
For the polynomial below, -3 and -1 are zeros.
g(x)=x² +6x³
+9x²-2x-6
Express g (x) as a product of linear factors.
Answers
The complete factorization of the polynomial is:
h(x) = (x - 3)*(x - 1)*(x + 2)
Here we have the polynomial:
g(x)= x³ - 2x² - 5x + 6
And we know that x = 3 is a zero, then (x - 3) is a factor.
So if f(x) = a*x² + b*x + c
We can write:
h(x) = (x - 3)*f(x)
Let's find f(x).
Expanding that:
x³ - 2x² - 5x + 6 = (x - 3)*(a*x² + b*x + c)
x³ - 2x² - 5x + 6 = ax³ + bx² + cx - 3ax² - 3bx - 3c
x³ - 2x² - 5x + 6 = ax³ + (b - 3a)x² + (c - 3b)x - 3c
Comparing like terms, we can see that:
a = 1
b - 3 a = -2
c - 3b = -5
-3c = 6
With the first and last equation we can get:
a = 1
c = 6/-3 = -2
Now with one of these values and the second or third equation we can find the value of b.
b - 3 a = -2
b - 3*1 = -2
b - 3 = -2
b = -2 + 3 = 1
Then:
f(x) = x² + x - 2
The zeros of this quadratic function are given by:
x = -1±3 / 2
so, we get,
x = (-1 + 3)/2 = 1
x = (-1 - 3)/2 = -2
Then we can factorize this as:
f(x) = (x - 1)*(x + 2)
And then we can write h(x) as:
h(x) = (x - 3)*(x - 1)*(x + 2)
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complete question:
For the polynomial below, 3 is a zero.
g(x)= x³ - 2x² - 5x + 6
Express g (x) as a product of linear factors.
what operation do I use.
Answers
Answer:
Addition
Step-by-step explanation:
The first step to solving this equation would be to add 32 on both sides so the operation would be addition.
Hope this helps :)
A colony of insects triples every day. If the colony has 80 insects today, how many will be
present in 10 days?
Answers
There will be 4,723,920 insects present after 10 days.
Exponential functionGiven that a colony of insects triples every day, to determine, if the colony has 80 insects today, how many will be present in 10 days, the following calculation must be made:
80 x 3^10 = X80 x 59049 = X4,723,920 = XTherefore, there will be 4,723,920 insects present after 10 days.
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Solve the equation: 9-15x = 28 + 4x
Answers
Answer:
x = -1
Step-by-step explanation:
To solve this, we want to isolate x:
9 - 15x = 28 + 4x
Subtract 9 from both sides:
-15x = 19 + 4x
Subtract 4x from both sides:
-19x = 19
Divide both sides by -19:
x = -1
20 POINT!!
Can someone help me I don’t understand it at all
Answers
Answer:
second
Step-by-step explanation:
substitute y=6 and x=1 in the given relations and see if works
y=2x will be 6 = 2*1 false
y=x+5 will be 6 = 1+5 true
because this is true check all the other y and x and if all true is good
7=2+5 true, 8=3+5 true 9= 4+5 true, 10=5+5 true, so second is good
y=2x+1 will be 6=2*1+1 false
y=3x+1 will be 6=3*1+1 false
The data below represent commute times (in minutes) and scores on a well-being survey. Complete parts (a) through (d) below.
Commute Time (min),x Well-Being Index score,y
5 69.2
15 68.4
30 67.5
35 67.3
60 66.3
84 66.1
105 64.6
(a) Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable.
(b) Interpret the slope and y-intercept, if appropriate.
(c) Predict the well-being index of a person whose commute is 35 minutes.
(d) Suppose Barbara has a 15-minute commute and scores 68.5 on the survey. Is Barbara more "well-off" than the typical individual who has a 15-minute commute?
Answers
(a) The least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable is y = 70.22 - 0.075x
(b) The slope and y-intercept, if appropriate is the slope of the regression line, -0.075, indicates that for every additional minute of commute time, the well-being index score decreases by an average of 0.075.
(c) The well-being index of a person whose commute is 35 minutes is the slope of the regression line, -0.075, indicates that for every additional minute of commute time, the well-being index score decreases by an average of 0.075.
(d) Yes, she is. Barbara more "well-off" than the typical individual who has a 15-minute commute.
Regression of Commute Times(a) To find the least-squares regression line, we need to find the slope and y-intercept of the line that minimizes the sum of the squared vertical distances between the actual data points and the predicted values on the line. Using a calculator or software, we get:
Slope: b = -0.075
y-intercept: a = 70.22
Therefore, the least-squares regression line is:
y = 70.22 - 0.075x
(b) The slope of the regression line, -0.075, indicates that for every additional minute of commute time, the well-being index score decreases by an average of 0.075. The y-intercept, 70.22, represents the predicted well-being index score for someone with a commute time of 0 minutes (which is not a meaningful value in this context).
(c) To predict the well-being index of a person with a commute time of 35 minutes, we can substitute x = 35 into the regression equation and solve for y:
y = 70.22 - 0.075(35) = 67.97
Therefore, the predicted well-being index score for someone with a commute time of 35 minutes is 67.97.
(d) To determine whether Barbara is more "well-off" than the typical individual with a 15-minute commute, we can compare her actual well-being index score of 68.5 to the predicted score based on the regression equation:
y = 70.22 - 0.075(15) = 68.47
Barbara's score of 68.5 is slightly higher than the predicted score of 68.47, which suggests that she is somewhat better off than the typical individual with a 15-minute commute. However, we should note that this comparison is based on a single data point and may not be representative of the larger population.
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Azad sold some books at $42 each and used the money to buy some concert tickets at $54 each. He had no money left over after buying the tickets. What is the least amount of money he could have earned from selling the books? What is the least number of books he could have sold?
Answers
the least amount of money Azad could have earned from selling the books is $2268.
Let's assume that Azad sold x books.
From the given information, we know that he sold the books for $42 each. Therefore, the total amount of money he earned from selling the books is 42x dollars.
He used this money to buy concert tickets for $54 each, which means he bought a total of (42x/54) tickets.
Since he had no money left over after buying the tickets, the amount of money he earned from selling the books must be equal to the cost of the tickets. Therefore:
42x = 54(42x/54)
42x = 42x
x = 54
So, the least number of books Azad could have sold is 54.
To find the least amount of money he could have earned from selling the books, we simply substitute x = 54 into the expression for the amount of money earned from selling the books:
42x = 42(54) = $2268
Therefore, the least amount of money Azad could have earned from selling the books is $2268.
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if you disssolved 50 g of sugar in 30 g of water what would the sugar concentration be
Answers
Explanation:
There are 50+30 = 80 grams of sugar and water mixed together.
The percentage of sugar is 50/80 = 5/8 = 0.625 = 62.5%
Pls tell me I really need help
Answers
Answer:
The answer is C or 44/12
Step-by-step explanation:
1/2 is equivalent to 3/6
1 4/6 is equivalent to 1 4/6 or 10/6
1 2/4 is equivalent to 1 3/6 or 9/6
When you add all of these together you get 22/6
Then you multiply 22/6 by 2 to get 44/12
PLEASE HELP
‼️50 POINTS‼️
Answers
Answer:
Step-by-step explanation:
Answer: it is 4i78f4950
Step-by-step explanation:
blank minus 1/2 equls to 3/4
Answers
Answer:
5/4
Step-by-step explanation:
We can start but setting the blank as x.
x - 1/2 = 3/4
we can put a common denominator on both of the.
2, 4
4, 8
4 is a common denominator.
1/2 times 2/2 = 2/4
x - 2/4 = 3/4
add on both sides.
x = 5/4
Answer:
5/4
Step-by-step explanation:
____ - 1/2= 3/4
____= 3/4+1/2
= 3+2/4 ( LCM of 2,4 is 4)
5/4
Check
5/4-1/2=3/4
Please help meeeeeeeeee
Answers
The measures on the square are given as follows:
x = 3AM = 13.How to obtain the measures on the square?On a square, all the four sides of the square are congruent, as are the two diagonals.
The four sides for this problem are given as follows:
WA, AR, RM, MW.
The two diagonals are given as follows:
WR and AM.
Considering the congruence of the four sides, the value of x is given as follows:
WA = AR
6x + 14 = 9x + 5
3x = 9
x = 3.
Considering the congruence of the two diagonals, the length AM is given as follows:
AM = WR = 5x - 2
AM = 5 x 3 - 2
AM = 13.
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Jeremy solved the equation 3+x= 11 by drawing a model. Use numbers and words to explain how Jeremy's model can be used to find the solution.
Answers
The expression 3 + x = 11 is an equivalent equation of a model
The solution to the equation is x = 8
How to solve the equationThe equation is given as:
3 + x = 11
Subtract 3 from both sides of the equations
-3 + 3 + x = -3 + 11
Evaluate the expression on the right-hand side
-3 + 3 + x = 8
Evaluate the expression on the left-hand side
x = 8
Hence, the solution to the equation is x = 8
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factor equation. answer is second picture. I do not know to get there though. step by step. f=3-2(3a)^(2) is the equation.
Answers
Answer:
\(f=-18a^2+3\)
Step-by-step explanation:
Given equation:
\(f=3-2(3a)^2\)
\(\textsf{Apply exponent rule} \quad (ab)^n=a^n b^n:\)
\(\implies f=3-2(3^2a^2)\)
Rewrite 3² as 9:
\(\implies f=3-2(9a^2)\)
Remove the parentheses:
\(\implies f=3-2 \cdot 9a^2\)
Multiply the numbers 2 · 9 = 18 :
\(\implies f=3-18a^2\)
Rearrange to make the variable the first term:
\(\implies f=-18a^2+3\)
Two adjacent angles are inside a 90° angle. One angle is x+4 and the other angle is 3x+2. What is x?
Answers
When in a right angle triangle, the right angle has two angles inside it i.e. x+4° and 3x+2°, x is equal to 21.
what exactly is a triangle?
A triangle is a three-sided polygon, which is a two-dimensional shape with straight sides. It is one of the simplest and most common geometric shapes in mathematics. A triangle is defined by its three sides and three angles.
The total sum of the angles of a triangle is always equal to 180 °. The length of the sides and the size of the angles can vary, giving rise to different types of triangles, such as equilateral, isosceles, scalene, acute, obtuse, and right triangles.
Now,
The sum of two adjacent angles inside a 90° angle is 90°. So, we can set up an equation:
x + 4 + 3x + 2 = 90
Simplifying the left side by combining like terms:
4x + 6 = 90
Subtracting 6 from both sides:
4x = 84
Dividing by 4:
x = 21
Therefore, The value of x is 21.
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Chelsea bought a computer on Monday for $1,300. Its value is predicted to decrease by $250 per year. Her brother George also bought a computer on Monday. The function g(x) = 1,100 – 175x predicts how the value of his computer is expected to change after x years.
Whose computer is expected to have a greater value when it is 3 years old, and how much greater will it be?
A) Chelsea’s computer is expected to have a value of $25 greater.
B) George’s computer is expected to have a value of $25 greater.
C) Chelsea’s computer is expected to have a value of $125 greater.
D) George’s computer is expected to have a value of $125 greater.
Answers
Answer:
The correct answer is B. George’s computer is expected to have a value of $25 greater.
Step-by-step explanation:
Since Chelsea bought a computer on Monday for $ 1,300, and its value is predicted to decrease by $ 250 per year, while her brother George also bought a computer on Monday, and the function g (x) = 1,100 - 175x predicts how the value of his computer is expected to change after x years, to determine whose computer is expected to have a greater value when it is 3 years old, and how much greater will it be, the following calculation must be performed:
Chelsea:
1,300 - (250 x 3) = X
1,300 - 750 = X
550 = X
George:
1,100 - (175 x 3) = X
1,100 - 525 = X
575 = X
Therefore, George’s computer is expected to have a value of $ 25 greater.
Find the midpoint of the segment between (6,7) and (6,-5)
(0, -1)
(6,1)
(1,6)
(0, 1).
Helpppo pleasee
Answers
Answer:
(6,1)
Step-by-step explanation:
midpoint = ((x2+x1),(y2+y1)/2)
= (6+6)/2, (-5+7)/2
= 12/2, 2/2
= 6,1
Answer:
(6, 1)Step-by-step explanation:
GivenSegment (6, 7) and (6, -5)To findMidpoint Solutionx- coordinates same so the line is vertical and we'll only calculate the y-coordinate
x= 6y = (7 + (-5))/2 = 2/2 = 1So the point is
(6, 1)On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day.
x 25 50 75 100 Total
P(x) .27 .33 .29 .11 1.00
Answers
please help me
evaluate each funtion for the given value
the problem is f (x) = -4x + 7; f (1)
Answers
Answer:Therefore, f(−1)=6.
Step-by-step explanation:
So, if f(x)=x+7 then f(−1)=(−1)+7
Therefore, f(−1)=6.
Answer:
primeroaend:epr )
Step-by-step explanation:
Which expression is equivalent to 6 (a minus 3)?
Answers
Answer:
6a-18
Step-by-step explanation:
A wise man once said, "400 reduced by 3 times my age is 208" What is the mans age
Answers
Answer:
96
Step-by-step
explanation:
400−2x=208. 400−208=2x. 192=2x. x=96
Answer:
The wise man is 64 years old
Step-by-step explanation:
"400 reduced by 3 times my age is 208"
we don't know the man's age, so we can substitute it for x. This means 400-3x=208. Using this equation, we can now solve for x to find the man's age.
400-3x=208
400-208=3x
192=3x
64=x
Checking answer:
400-3•64=
400-192=208
log₂ (x) = 3 exponential form then solve
Answers
The required value of the x in the given expression log₂ (x) = 3 is x = 8.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.
Here,
The logarithmic equation log₂(x) = 3 can be rewritten in exponential form as 2³ = x, since the base 2 raised to the power of 3 is equal to x.
So, the solution to the equation is x = 8.
Therefore, log₂(8) = 3.
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brainlist asap!
___________
find the interest rate:
principal: $500
interest: $60
time: 3 years
Answers
Answer:
Describe Europe's Mediterranean Climate.
Describe Europe's Mediterranean Climate.
Describe Europe's Mediterranean Climate.
4). THE TEMPERATURE IN ANCHORAGE, ALASKA AT MIDNIGHT
WAS -12°F. BY NOON THE TEMPERATURE HAD RISEN 23°F. WHAT
WAS THE TEMPERATURE AT NOON?
Answers
Answer: 11 degrees F
If it was -12 and by noon it had risen 23 degrees just add the two numbers together and you get 11 degrees F
Can someone please help!!! I will mark Brainly if you get it right!!!!
Answers
Answer:
I think it is the last one
Can someone help !!
2. What is the probability that you select a Jack given that it is a Club?
P(Jack∣Club)=
3. What is the probability that you select a Club given that it is a Jack?
P(Club∣Jack)=
4. What is the probability that you select a card that is NOT a Jack given that it is NOT a Club?
P(NotJack∣NotClub)=
5. What is the probability that you select a card that is NOT a Club given that is it NOT a Jack?
Answers
The probability that you select a Jack given that it is a Club P(Jack∣Club) is 1/13.
The probability that you select a Club given that it is a Jack is P(Club∣Jack) is 1/4.
The probability that you select a card that is NOT a Jack given that it is NOT a Club,P(NotJack∣NotClub) is 47/38
The probability that you select a card that is NOT a Club given that is it NOT a Jack is 38/47
The probability that you select a Jack given that it is a Club P(Jack|Club):
There are 4 Jacks in a deck (one for each suit), and since we are given that the selected card is a Club, we only need to consider the 13 cards in the Club suit.
So, the number of favorable outcomes is 1 (the Jack of Clubs), and the total number of possible outcomes is 13 (the number of cards in the Club suit)
P(Jack|Club) = 1 / 13
The probability that you select a Club given that it is a Jack
P(Club|Jack):
P(Club|Jack) = Number of favorable outcomes / Total number of possible outcomes
P(Club|Jack) = 1 / 4
The probability that you select a card that is not a Jack given that it is not a Club
P(NotJack|NotClub):
The number of cards that are not Jacks is 52 - 4 = 48 (since there are 4 Jacks in the deck), and the number of cards that are not Clubs is 52 - 13 = 39 (since there are 13 cards in the Club suit).
P(NotJack|NotClub) = Number of favorable outcomes / Total number of possible outcomes
P(NotJack|NotClub) = (48 - 1) / (39 - 1)
=47/38
P(NotClub|NotJack) = (39 - 1) / (48 - 1)
=38/47
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Complete the table with the number of sit-ups you need to do on Sunday so that the mean number of sit-ups per day is 80.
Monday: 100
Tuesday: 80
Wednesday: 60
Thursday: 70
Friday: 90
Saturday: 100
Sunday: X
If correct you get brainliest!
Answers
Can someone please provide a step-by-step explanation for the answer?
If the universe of discourse is the real numbers, give the truth value of each of the
following propositions:
(a) ∀x∃y(x = y²)
(b) ∀x∃y(x² = y)
(c) ∃x∀y(xy = 0)
(d) ∀x∃y(x + y = 1)
Answers
The Propositions are resulting
(a) ∀x∃y(x = y²) is False
(b) ∀x∃y(x² = y) is True.
(c) ∃x∀y(xy = 0) is True.
(d) ∀x∃y(x + y = 1) is True.
(a) ∀x∃y(x = y²)
This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.
If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.
For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².
Therefore, the proposition (a) is false.
(b) ∀x∃y(x² = y)
For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.
For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.
Therefore, the proposition (b) is true.
(c) ∃x∀y(xy = 0)
The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.
Therefore, the proposition (c) is true.
(d) ∀x∃y(x + y = 1)
To determine the truth value, we need to check if this statement holds true for every value of x.
If we take any value of x, we can find a corresponding value of y that satisfies the equation.
For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.
Therefore, the proposition (d) is true.
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Duncan and his family are season ticket holders for their favorite baseball team. Last year, the cost of season tickets was $2,730. This year, the cost is $3,333.80. What was the percent of increase in the cost of season tickets?
Round your answer to the nearest tenth of a percent.
Answers
Answer:
10%
Step-by-step explanation:
To find the answer we need to know what percentage of $1030 is $927 and to do this we can multiply 927 by 100 and divide by 1030.
(927(100))/1030
92700/1030
90
so now that we know $927 is 90% of $1030 we can subtract 90 from 100 and it'll give us the percentage decrease. Which is 10%.
Hope this helps!!!!!!!!!!!!
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If you draw a card from a standard deck of 52 playing cards, what is the probability that it is a heart or a diamond?
Answers
Answer:
1/2
Step-by-step explanation:
In a deck of cards, there are 13 hearts and 13 diamonds
13+13 = 26 hearts or diamonds
P( hearts or diamonds) = numbers of hearts or diamonds / total
=26/52
= 1/2