Answer:
As x goes negative infinity, f(x) goes negative infinity and as x goes to infinity, f(x) goes to infinity
Step-by-step explanation:
If you put the function on a graphing calculator you can see how they work
may I get brainliest thanks
can you guys tell me what 2+2 is I cant figure it out
Answer:
really it's 4
Step-by-step explanation:
Answer:4
Step-by-step explanation:
The square ABCD is reflected over
the y-axis then translated five units
down and one unit to the left to
make the square A'B'C'D'.
Question: If the original coordinate
pair for the point A is (-5, 3), what is
the coordinate pair of A'?
The coordinate pair for A' is as a result (4, -2) in coordinated square.
After reflecting the square ABCD over the y-axis and translating it five units down and one unit to the left, we may use the following transformations in order to get the coordinate pair of A':
Across the y-axis, reflect the square: This modifies the x-sign coordinate's while maintaining the y-original coordinate's value. Hence, A's new coordinates would be (5, 3).
Five units down and one unit to the left, translate the square as follows: The y-coordinate is moved five units down and the x-coordinate one unit to the right as a result. A's new system coordinates are calculated to be (4, -2).
the coordinate pair for A' is as a result (4, -2).
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At a baseball game, a vender sold a combined total of 132 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
Answer:
Let x be the number of hot dogs sold.
Then the number of sodas sold is 3x.
The total number of sodas and hot dogs sold is 132, so we can write:
x + 3x = 132
4x = 132
x = 33
Therefore, the number of hot dogs sold is 33, and the number of sodas sold is 3x = 3(33) = 99.
Step-by-step explanation:
Utilizando 4 veces el numero 4 y las operaciones que conoce, hallar los numeros desde 0 a 10
The process of counting from 0 to 10 using 4 fours and the four basic operations can be explained mathematically by the following equation: 4 + 4 - 4 x 4 / 4 + 4 + 4 - 4 = 12
The result when using 4 fours and the four basic operations (addition, subtraction, multiplication, division) to count from 0 to 10 is as follows:
0 = 4 ,1 = 4 + 4 = 8 ,2 = 8 - 4 = 4 ,3 = 4 x 4 = 16 ,4 = 16 / 4 = 4 ,5 = 4 + 4 + 4 = 12 ,6 = 12 - 4 = 8 ,7 = 8 x 4 = 32, 8 = 32 / 4 = 8 ,9 = 8 + 4 + 4 = 16 ,10 = 16 - 4 = 12 .The process of counting from 0 to 10 using 4 fours and the four basic operations can be explained mathematically by the following equation: 4 + 4 - 4 x 4 / 4 + 4 + 4 - 4 = 12. This equation is made up of four parts, each representing an operation in the correct order. The first part of the equation is 4 + 4 = 8, which adds the two fours together to get 8. The second part of the equation is 8 - 4 = 4, which subtracts the four from the 8 to get 4. The third part of the equation is 4 x 4 = 16, which multiplies the two fours together to get 16. The fourth part of the equation is 16 / 4 = 4, which divides the 16 by 4 to get 4. The fifth part of the equation is 4 + 4 + 4 = 12, which adds the three fours together to get 12. The sixth part of the equation is 12 - 4 = 8, which subtracts the four from the 12 to get 8. Finally, the last part of the equation is 8 + 4 + 4 = 16, which adds the three fours together to get 16.
By combining these six operations together, we can count from 0 to 10 using 4 fours and the four basic operations.
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What is the result when using 4 fours and the four basic operations (addition, subtraction, multiplication, division) to count from 0 to 10?
Install the "rpart" package from CRAN and load the "car 90 " dataset. Hold out the last 20 percent of the observations as the test set. Train a decision tree using all the predictors to model the "Price" variable on the training data where the maximum depth of the tree is 1,2 and 3 respectively. Calculate the mean squared error on the held out test set data. Next, generate a bootstrapped prediction with 1,000 samples for the test set data using a decision tree of depth size 3. Report the test set MSE.
The can be done by running the following command in R:
The solution to this problem requires you to load the “rpart” package from CRAN and load the “car90” dataset. The last 20% of the observations should be held out as the test set. A decision tree should be trained using all the predictors to model the “Price” variable on the training data where the maximum depth of the tree is 1, 2, and 3 respectively. The mean squared error on the held-out test set data should be calculated. A bootstrapped prediction should then be generated with 1,000 samples for the test set data using a decision tree of depth size 3, and the test set MSE should be reported.
Here are the steps to follow:
Step 1: Install the “rpart” package from CRAN
This can be done by running the following command in R: install.packages("rpart")
Step 2: Load the “car90” dataset
This can be done by running the following command in R: data(car90)
Step 3: Hold out the last 20 percent of the observations as the test set
This can be done by running the following command in R: test_set <- car90[round(nrow(car90) * 0.8) + 1:nrow(car90), ]
Step 4: Train a decision tree using all the predictors to model the “Price” variable on the training data where the maximum depth of the tree is 1, 2, and 3 respectively
This can be done by running the following commands in R:
train_set <- car90[1:round(nrow(car90) * 0.8), ]
library(rpart)
set.seed(123)
depths <- 1:3
models <- lapply(depths, function(depth) rpart(Price ~ ., data = train_set, method = "anova", maxdepth = depth))
Step 5: Calculate the mean squared error on the held-out test set data
This can be done by running the following commands in R:
library(Metrics)
set.seed(123)
mse <- lapply(models, function(model) mse(predict(model, newdata = test_set), test_set$Price))
Step 6: Generate a bootstrapped prediction with 1,000 samples for the test set data using a decision tree of depth size 3
This can be done by running the following commands in R:
set.seed(123)
boot_preds <- replicate(1000, {
sampled_test_set <- test_set[sample(nrow(test_set), replace = TRUE), ]
predict(models[[3]], newdata = sampled_test_set)
})
Step 7: Report the test set MSE
This can be done by running the following command in R:
mse(predict(models[[3]], newdata = test_set), test_set$Price)
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what rattional numbers are between -5.25 and -5.26
Answer:
-5.255
Step-by-step explanation:
In the figure, OAPB is a quadrant of a circle and OAP is a sector. If | AOP = 30° and the area of the shaded region is 462 cm2, then find the length of the arc PB. A P B
By answering the above question, we may state that As a result, the arc's expressions PB length is around 20.45 cm.
what is expression ?In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
Area of sector OAP = (1/12) x r2 x (30/360)
OAP's area is equal to (1/2) x OA, PA, and sin (AOP)
Knowing that OA = PA = r and that AOP = 30°, we can calculate the area of the triangle OAP as (1/2) x r x r x sin(30°) = (1/4) x r2.
As a result, the darkened region's area is:
Area of the darkened zone is equal to (1/12) x r2 - (1/4) x r2 (462 cm2).
When we simplify this equation, we obtain:
[tex](\pi/3 - 1) x r^2 = 1848[/tex]
The result of dividing both sides by (/3 - 1) is:
[tex]r^2 = 1848 / (π/3 - 1) = 378.9[/tex]
When we square the two sides, we obtain:
[tex]r ≈ 19.47\\PB = (1/6) x 2r = (1/3) x r = 20.45 cm[/tex], where
As a result, the arc's PB length is around 20.45 cm.
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help plss 1/3(3m+6)-2(2m+6)
Answer:
To simplify the expression, you can start by using the distributive property of multiplication over addition/subtraction and then combine like terms.
1/3(3m+6) - 2(2m+6)
= 1/33m + 1/36 - 22m - 26 (distribute the multiplication)
= m + 2 - 4m - 12 (simplify by multiplying and adding the terms)
= -3m - 10 (combine like terms)
Therefore, 1/3(3m+6)-2(2m+6) simplifies to -3m - 10.
What is the equation of the line?
Answer:
Use the slope formula and slope-intercept form
y=mx+b to find the equation.
the steps and answers are in the photos
{I hope this helps you :)
A and B are events. Suppose P(A) = 0.3 and P(B│A) = 0.4. What is
the joint probability of A and B occurring
The jοint prοbability οf A and B οccurring is 0.12.
What is prοbability?Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.
Here the given P(A)=0.3 and P(B│A) = 0.4
The οbjective is tο find the jοint prοbability οf A and B οccurring.
A and B are twο events.
The cοnditiοnal prοbability fοrmula is given by,
P(B│A) =[tex]\frac{P(A\cap B)}{P(A)}[/tex]
=> 0.4 = [tex]\frac{P(A\cap B)}{0.3}[/tex]
=> P(A∩B) = 0.12.
Hence the joint probability of A and B occurring is 0.12.
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Statistics grades: In a statistics class of 42 students, there were 11 men and 31 women. Six of the men and seven of the women received an A in the course. A student is chosen at random from the class. Give all answers as decimals rounded to 4 digits after the decimal point 2 points (a) Find the probability that the student is a woman. (b) Find the probability that the student received an A. 3 points (c) Find the probability that the student is a woman or received an A . (d) Find the probability that the student did not receive an A
(a) The probability that the student is a woman is 0.7381. (b) The probability that the student received an A is 0.3095. (c) The probability that the student is a woman or received an A is 0.9405. (d) The probability that the student did not receive an A is 0.6905.
(a) Probability that the student is a woman:
P(woman) = number of women / total number of students
P(woman) = 31 / 42
P(woman) = 0.7381
Answer: 0.7381
(b) Probability that the student received an A:
P(A) = number of students who received an A / total number of students
P(A) = (6 + 7) / 42
P(A) = 0.3095
Answer: 0.3095
(c) Probability that the student is a woman or received an A:
P(woman or A) = P(woman) + P(A) - P(woman and A)
To find P(woman and A), we note that there are 7 women who received an A, so:
P(woman and A) = 7 / 42
P(woman or A) = 0.7381 + 0.3095 - (7 / 42)
P(woman or A) = 0.9405
Answer: 0.9405
(d) Probability that the student did not receive an A:
P(not A) = 1 - P(A)
P(not A) = 1 - 0.3095
P(not A) = 0.6905
Answer: 0.6905
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Pleaseeeee helpppp!!!!
Answer:
49.7 mm
Step-by-step explanation:
the circumference (C) of a circle (2πr) is also the perimeter of a circle. The figure shown is a half-circle. To get the perimeter of the shape shown, find the C/2 (half the circumference) and add the diameter:
P = 2π(12/2) + 12 = 49.7 mm
Which angles are corresponding angles?
Check all that apply.
8 4
7 3
2
M
6
1
5
A. 7and2
B. 6and 3
C. 5 and 7
D. 1and 3
E. 6and8
F. 1 and 6
the corresponding angles are A. 7 and 2, C. 5 and 7, and E. 6 and 8. The correct answer is A, C, and E.
Corresponding angles are angles that are in the same position at each intersection where a straight line crosses two others. In the given list of angles, we can see that:
Angles 1 and 3 are corresponding angles, because they are on opposite sides of the line and are in the same position relative to the other lines.
Angles 5 and 7 are corresponding angles, for the same reason.
Angles 6 and 8 are corresponding angles, because they are alternate interior angles (they are on opposite sides of the transversal and inside the two lines).
Angles 7 and 2 are vertical angles, not corresponding angles.
Angles 6 and 3 are alternate interior angles, not corresponding angles.
Angles 1 and 6 are alternate interior angles, not corresponding angles.
Therefore, the corresponding angles are A. 7 and 2, C. 5 and 7, and E. 6 and 8. The correct answer is A, C, and E.
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I need help on this asap!
If Mr Corazon produces the model that would give the most profit only, this idea would be incorrect. The reason is that that poor people would not be able to buy the product.
What is profit maximization?
Profit maximization is the process by which a business or a firm determines the optimal level of output or production that leads to the highest possible profit. It is an important goal for most firms, as it helps to ensure their long-term sustainability and competitiveness in the market.
Based on the question, at the profit of $375 a piece, it would mean that the price has become too high. Less people would but the product. This makes his idea a bad one.
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
The values of x are x = 13 and x = 1. The other two options, x = -29 and x = 42, are not correct.
What is expression ?
To solve for x, we need to take the square root of both sides of the equation:
[tex](x - 7)^2 = 36[/tex]
Taking the square root of both sides, we get:
x - 7 = ±6
Adding 7 to both sides, we get:
x = 7 ± 6
So, the values of x are:
x = 7 + 6 = 13 or x = 7 - 6 = 1
Therefore, the values of x are x = 13 and x = 1. The other two options, x = -29 and x = 42, are not correct.
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Find the slope of the line that contains (10 -1) and (-8 6)
The Slope of the line whose coordinates are given that (10 -1) and (-8 6) is the change in y coordinate with respect to the change in x coordinate is (-7/18).
Here the coordinates are (10 -1) and (-8 6) that means :-
X1 = 10
X2 = -8
Y1 = -1
Y2 = 6
So slope of line = (Y2-Y1)/(X2-X1)
slope = 6-(-1)/-8-10
slope = 7/-18
Hence the slope of the line containing (10 -1) and (-8 6) would be 7/-18.
In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.
Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,
m = change in y/change in x = Δy/Δx
Where “m” is the slope of a line.
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If you flip an unfair coin x times, the odds of getting three heads is y. What is the probability of getting heads after flipping the coin once?
The probability of getting heads after flipping the coin once would depend on the specific probabilities of the coin landing on heads or tails, which are not given in the problem statement.
The probability of getting heads after flipping the coin once cannot be determined from the given information. The probability of getting three heads in x flips of an unfair coin is not necessarily related to the probability of getting heads in a single flip.
For example, it is possible that the unfair coin has a very low probability of landing on heads, such as 0.1. In this case, the probability of getting three heads in a row after flipping the coin x times would be very low, but the probability of getting heads on a single flip would still be 0.1.
Therefore, the probability of getting heads after flipping the coin once would depend on the specific probabilities of the coin landing on heads or tails, which are not given in the problem statement.
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The 20% on a $8 sandwhich?
Answer: 1.60
Step-by-step explanation:
ask siri
Answer:
1.6$Step-by-step explanation:
Greetings!!
[tex]step1[/tex]
20%=100%/5
[tex]step2[/tex]
8/5=1.6
[tex]step3[/tex]
5= 10/2
[tex]step4[/tex]
Divide the numbers by 10:
8/10=0.8
[tex]step5[/tex]
Multiply the numbers from step4 by 2.
0.8×2= 1.6
If you have any questions tag it on comments
Hope it helps!!!
What is 2+2x -6=2720=1819
The solution to the equation √(2 + 2x) - 6 = 2 when evaluated is x = 31
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
√(2 + 2x) - 6 = 2
So, we have
√(2 + 2x) = 8
Take the square of both sides
so, we have the following representation
2 + 2x = 64
Evalyate the like terms
2x = 62
Divide by 2
This means that
x = 31
Hence, the solution is x = 31
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Complete question
What is √(2 + 2x) - 6 = 2
PLEASE HELP I NEED HELP ASAP
Answer:
Sin= 35/37
cos= 13/37
tan= 35/13
Step-by-step explanation:
Joey has 10 coins one of his coins is a 50 cent piece. If he has a total of $.85 what are the other coins
Answer:
Step-by-step explanation:
First, take 1 coin away and subtract .5 from the total of 85 cents to get 9 coins for 35 cents. Then, you must figure out any amount of coins that will fit that value for 9 coins; A penny = 1 cent, nickel = 5 cents and dime = 10 cents
You can do 2 nickels 2 dimes and 5 pennies for 9 coins total.
You can also do an equation for more intricate problems:
.10x + .05y + .01z = .35
where you would solve for a variable and input the new equation in that variable to solve for your variables. I hope this helps :)
i NEED HELP THIS IS FOR 70 PERCENT OF MY GRADE, I DONT UNDERSTAND THIS. HELP
Part A:
For Column 1 : Line AB = Line BC: always true
For Column 2: Line AD = Line CD; sometimes true
For Column 3: Line BD is always vertical; never true
Part B: m< CBD is 20 degrees. Option A
How to determine the valueIt is important to note the properties of a circle, they are;
Equal chords of a circle are subtended in the same way at the center.The radius that is drawn perpendicular to the chord bisects the chord into equal halvesCircles that have different radius are similar.A circle can have other shapes circumscribed into it like a rectangle, trapezium, triangle, square, kite.From the information given, we have that;
m< BDA = 20 degrees
To determine the angle of m< CBD, we need to understand that alternating angles are angles that on a transversal and are equal to each other.
Then, if m<BDA = 20
m<CBD = 20 degrees
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Given sec A = − 65 7 secA=− 7 65 and that angle A A is in Quadrant III, find the exact value of sin A sinA in simplest radical form using a rational denominator.
We can say that after answering the offered question Therefore, the equation exact value of[tex]$\sin A$ i[/tex]n simplest radical form using a rational denominator is [tex]{-\frac{4\sqrt{261}}{65}}[/tex]
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
[tex]$\sec A = \frac{1}{\cos A}$ to find the cosine of angle $A$.[/tex]
[tex]$\sec A = -\frac{65}{7}$, we have $\frac{1}{\cos A} = -\frac{65}{7}$.\\$$\cos A \cdot \frac{1}{\cos A} = \cos A \cdot \left(-\frac{65}{7}\right)$$\\$$[/tex]
Since angle A is in Quadrant III, we know that [tex]$\cos A < 0$ and $\sin A < 0$.[/tex]
Using the Pythagorean identity[tex]$\sin^2 A + \cos^2 A = 1$, we can solve for $\sin A$:[/tex]
[tex]$$\sin^2 A + \left(-\frac{7}{65}\right)^2 = 1$$\\$$\sin^2 A + \frac{49}{4225} = 1$$\\$$\sin^2 A = \frac{4176}{4225}$$\\$$\sin A = -\frac{4\sqrt{261}}{65}$$[/tex]
Therefore, the exact value of[tex]$\sin A$ i[/tex]n simplest radical form using a rational denominator is [tex]${-\frac{4\sqrt{261}}{65}}$[/tex]
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According to The Yankee Group, 53% of all cable households rate cable companies as good or excellent in quality transmission cable companies as good or excellent in having professional personnel. Suppose 300 cable households are randomly contacted. Sixty percent of all cable houtensidiate (a) What is the probability that more than 175 cable households rate cable companies as good or excellent in quality trans mission? between 165 and 170 (inclusive) cable households rate cable companies as good or excellent in quality transi or excellent in quality transmission? households rate cable companies as good or excellent in having professional personnel? d) What is the probability that fewer than 200 cable households rate cable companies as good or excellent in having professional person (Round z values and ? values to 2 places. Round your final answers to 4 decimal places.) (a) Px > 175) (b) P(165 SxS 170) (e) P(155 s x S 170) (d) P(x < 200)
The probability that more than 175 cable homes will assess cable firms as providing outstanding or exceptional transmission quality is roughly 0.0287.
What makes probability so special?The word "probability" comes directly from the Latin word "probabilitas," which means "credibility, likelihood," in Old French probability (14th century) (see probable). The word first appeared in mathematics around 1718.
Let X be the proportion of the 300 randomly chosen cable homes that are satisfied or excellent with their provider's transmission quality.
Let p be the probability that a cable household will rate cable firms as providing good or exceptional quality transmission, which in this instance is 53% or 0.53.
Let q represent the likelihood that a cable household does not consider cable companies to be providing good or exceptional quality transmission, which in this instance is 47% or 0.47.
Let 300 * 0.53 = 159, or the mean of the binomial distribution, be denoted by = n * p.
The binomial distribution's standard deviation, = sqrt(n * p * q), is sqrt(300 * 0.53 * 0.47) = 8.38. (rounded to two decimal places).
The binomial distribution can be approximated by the normal distribution:
P(X > 175) = P(Z > (175 - μ) / σ)
where Z is a standard normal variable.
P(Z > (175 - 159) / 8.38) = P(Z > 1.91)
Using a standard normal table or calculator, we can find that P(Z > 1.91) is approximately 0.0287.
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What is the term to term rule in the sequence 1,2,4,7,11
The term to term rule in the sequence is specific formula which describes the each term of sequence. So, term by term formula for sequence 1,2,4,7,11.. is equals to the [tex] x_n = \frac{n(n-1)}{2} + 1[/tex].
A sequence, or a series, is a chain of numbers obtained by following a particular common factor. To complete a series or sequence, we need to determine the common factor that guides the series . We have a sequence of number defined as 1, 2,4,7, 11, ... We have to determine term rule for this sequence. Each number in the sequence is called a term. Now, check the known terms of sequence, first term = 1.
Difference between first two terms =1
difference between second and third=2
difference between third and fourth terms = 3
difference between fourth and fifth terms = 4
So, the difference between two successive terms increases by 1. Thus the term by term rule is written as [tex] x_n = \frac{ n(n-1)}{2} + 1[/tex], where n is nᵗʰ term.
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a small cup has a hight of 6 in, and a large cup has a hight of 8 in. The large coffe holds 18oz. How much coffe is in the small cup
Given:-
A small cup has height of 6in. and a large cup has a height of 8in.Volume of coffee in large cup is 18oz .To find:-
The volume of coffee small cup .Answer:-
Here we can assume the shape of the cup to be cylindrical . And the volume of a cylinder is given by;
[tex]\implies V = \pi r^2 h \\[/tex]
where ,
[tex]r[/tex] is the radius of the base of the cylinder.[tex]h[/tex] is the height of the cylinder.Assuimg that the cups differ only in height and not in width (diameter) , we can say that ;
[tex]\implies V \propto h \\[/tex]
So , we can write;
[tex]\implies \dfrac{V_s}{V_l}=\dfrac{h_s}{h_l}\\[/tex]
[tex]\implies \dfrac{V_s}{18\ oz}=\dfrac{6\ in.}{8 \ in.}\\[/tex]
[tex]\implies V_s = \dfrac{6(18)}{8} \\[/tex]
[tex]\implies \underline{\underline{ V_s =13.5 \ oz}} \\[/tex]
Hence the volume of the smaller cup is 13.5 oz .
and we are done!
A wedding ring costs £15000. Work out the price after a 6% price increase
The total price of the ring after increment is $15900
A percentage is a term used in mathematics to describe a value or ratio that may be expressed as a fraction of 100. If we need to calculate a percentage of a number, we should first divide it by 100 before multiplying it by the remainder. As a result, the proportion denotes a component per 100. Percent is what the word "percent" means. Its symbol is the letter "%".
The current price of the ring= $ 15,000
Increase in percentage=6
New price:
15000*(1+0.06)=15900
The total price of the ring after increment is $15900
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An inverse variation includes the points (8, 3) and (2, n). Find n
An inverse variatiοn includes the pοints (8, 3) and (2, n), the value οf n is 12.
What is Inverse variatiοn?Inverse variatiοn fοrmula refers tο the relatiοnship οf twο variables in which a variable increases in its value, the οther variable decreases and vice-versa. In οther wοrds, the inverse variatiοn is the mathematical expressiοn οf the relatiοnship between twο variables whοse prοduct is a cοnstant.
Using the given pοints, we can set up a prοpοrtiοn tο find k:
8 * 3 = k
2 * n = k
Setting the twο expressiοns fοr k equal tο each οther, we get:
8 * 3 = 2 * n
24 = 2n
Dividing bοth sides by 2, we get:
n = 12
Therefοre, the value οf n is 12.
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ABCD is a rhombus.
BCE is an isosceles triangle.
ABE is a straight line.
Work out the size of angle DCA.
The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later, School Buses Still Late," Boston Globe, October 5, 2011). Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route. Historically, the bus service on the route has been, on average, 12 minutes late. After the schedule adjustment, the first 36 runs were an average of 8 minutes late. As a result, the Boston public school district claimed that the schedule adjustment was an improvement-students were not as late. Assume a population standard deviation for bus arrival time of 12 minutes. Develop the null and alternative hypotheses to determine whether the schedule adjustment reduced the average lateness time of 12 minutes
Calculated t-value (-3) is less than the critical t-value (-1.69), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that The average lateness time was cut by 12 minutes as a result of the schedule modification.
The null hypothesis would be that the schedule adjustment did not reduce the average lateness time of 12 minutes.
[tex]H0:[/tex][tex]\mu = 12[/tex]
The alternative hypothesis would be that the schedule adjustment did reduce the average lateness time of 12 minutes.
[tex]Ha:[/tex] [tex]\mu < 12[/tex]
Here, we are testing whether the population mean arrival time is less than 12 minutes, based on a sample of 36 runs that had an average of 8 minutes late. We can use a one-sample t-test to test this hypothesis, with the following test statistic:
[tex]t = (\bar x - \mu) / (s / \sqrt{n} )[/tex]
where[tex]\bar x[/tex] is the sample mean (8 minutes),[tex]\mu[/tex] is the population mean (12 minutes), s is the population standard deviation (12 minutes), and n is the sample size (36 runs).
Using these values, we get:
[tex]t = (8 - 12) / (12 / \sqrt{(36)} ) = -3[/tex]
The degrees of freedom for this test are n - 1 = 35. Using a t-distribution table, we can find the critical t-value for a one-tailed test with a significance level of 0.05 and 35 degrees of freedom to be approximately -1.69.
Since our calculated t-value (-3) is less than the critical t-value (-1.69), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that The average lateness time was cut by 12 minutes as a result of the schedule modification.
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