The diameter of a spindle in a small motor is supposed to be 2.9 millimeters (mm) with a standard deviation of 0.14 mm. If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of 16 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 2.96 mm. What are the null and alternative hypotheses (H0 = null hypothesis and Ha = alternative hypothesis)?
Answers
The null hypothesis (\(H_0\)) is that the mean diameter of the spindles is equal to the required measurement of 2.9 mm, while the alternative hypothesis (\(H_a\)) is that the mean diameter has deviated from this required measurement.
In statistical hypothesis testing, the null hypothesis represents the assumption of no significant difference or effect, while the alternative hypothesis represents the claim or hypothesis we are trying to support with evidence.
In this case, if the average diameter of the sample of 16 spindles is 2.96 mm, we are testing whether this deviation from the required measurement of 2.9 mm is statistically significant. The null hypothesis (\(H_0\)) would state that the mean diameter is equal to 2.9 mm, while the alternative hypothesis (\(H_a\)) would suggest that the mean diameter is either greater than or less than 2.9 mm.
Therefore, the null hypothesis (\(H_0\)) is that the mean diameter of the spindles is equal to 2.9 mm, and the alternative hypothesis (\(H_a\)) is that the mean diameter of the spindles has deviated from the required measurement.
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Related Questions
its all in the picture
Answers
Answer:
6
Step-by-step explanation:
..............................
Answer:
f(- 3) = 6
Step-by-step explanation:
f(- 3) means what is the value of f(x) when x = - 3
Locate x = - 3 on the x- axis
Then go vertically up to meet the graph at (- 3, 6 )
The value of f(- 3) is therefore 6, that is
f(- 3) = 6
5\6 of 45kg plz can u tell me ans
Answers
You are very welcome
Please Help!! 100 points!!
What is the value of x?
Enter your answer in the box.
□ units
Answers
Answer:5o
Step-by-step explanation: you add all of the numbers length with and high the
A bridge connects to a tunnel as shown in the figure. The bridge is 180 feet above the ground, At a distance of 235 feet atong the bridge out of the tunnel, the angle to the base and summit of the cliff is a right angle.
a. What is the height of the cuff? Round to the nearest whole number
b. How high is the cliff from base to summit? Round to the nearest whole number.
c. What is the value of d? Round to the nearest whole number.
Answers
32400 + 55225 = 87625
so cliff base to point on bridge = sqrt of 87625.
Then notice 87625 + d^2 = (x+180)^2
since x^2 +235^2 = d^2,
substitute (x^2 + 235^2) for d^2, like this:
87625 + x^2 + 235^2 = (x+180)^2
87625 + x^2 + 55225 = x^2 + 360x + 32400
87625 + 55225 - 32400 = x^2 - x^2 +360x
360x = 110450
x = about 306.8 feet
h = x+180, so h = 486.8 feet
Remember d^2 = x^2 + 235^2, so
d^2 = 306.8^2 + 235^2
d^2 = 149354.6489
d = about 386.46 feet
HELP PLEASE!! I’ll give
Answers
The square root x^4= x^2
all you need is in the photo
please answer fast pleaseee
please do the step by step
Answers
Answer:
1.601×10^9
Step-by-step explanation:
800.5 × 2×10^6
1601×10^6
1.601×10^9
You are riding your bike. At 8:00am you have ridden your bike 23 miles. By 9:00pm you have ridden 179 miles. Find the rate of change in miles per hour. If needed, round your answer to the nearest whole number.
Answers
Answer:
12 miles/hour
Step-by-step explanation:
8am to 9pm = 13 hours
in that time we were driving 179-23 = 156 miles.
so, our speed was 156 miles / 13 hours.
now simplify it to our standard miles/hour format :
156/13 = 12
therefore, or standardized speed was
12 miles/hour
James washes cars to earn money. He charges $7.00 per compact car, $10.00 per mid -sized car, and $15.00 per SUV. On Saturday, he washed 3 compact cars, 4 mid-sized cars, and 2 SUVs. How much money did he earn?
Answers
Answer:
$91.00
Step-by-step explanation:
From the above question, we obtained the following information.
James charges:
1 compact car = $7.00
1 mid sized car = $10.00
1 SUV = $15.00
On Saturday, he washed:
a) 3 compact cars
1 compact car = $7.00
3 compact cars = ?
= $7.00 × 3
= $21.00
b) 4 mid-sized cars
1 mid- sized car = $10.00
4 mid-sized cars = ?
= $10.00 × 4
= $40.00
c) 2 SUVs.
1 SUV = $15.00
2 SUVs = ?
= $15.00 × 2
= $30.00
How much money did he earn?
$21.00 + $40.00 + $30.00
= $91.00
Therefore, James earned $91.00
29,30,32,35,39,\ Which is the next number in this pattern?
Answers
Answer:
44
Step-by-step explanation:
it's adding one each time
Answer:
44 Its definitely this answer
solve: |2x - 1| - 2 = 7
Answers
Answer:
x =5
Step-by-step explanation:
transfer -2 to the other side it turns to +2
|2x-1|=7 +2
2x-1 =9
transfer -1 to the other side it turns to +1
2x=10
Divide both sides by 2
2x /2 = 10/2
x= 5
|2x-1|=5
then youre doing 2 equations
2x-1= 5 2x-1=-5
2x=6. 2x=-4
x=3. x=-2
Think About the Process Karen purchased a DVD player on sale. The orginal selling price was $179.30. The sale price was $154. 15. What is the first step in finding the percent markdown? Find the percent mandowen.
Answers
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
The percent markdown is 14%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Original price = $179.30
The selling price = $154.15
The percent markdown.
= (179.30 - 154.15) / 179.30 x 100
= 25.15 / 179.30 x 100
= 14%
Thus,
The percent markdown is 14%.
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The lengths of time (in minutes) several underwriters took to review applications for similar insurance coverages are: 50, 230, 52, and 57.What is the median length of time required to review an application
Answers
According to the question the median length of time required to review an application is the average of 52 and 57, which is \(\( \frac{52+57}{2} = 54.5 \)\) minutes.
To find the median length of time required to review an application, we need to arrange the given lengths of time in ascending order: 50, 52, 57, 230.
The median is the middle value in a sorted list. In this case, we have an even number of values, so we take the average of the two middle values.
Thus, the median length of time required to review an application is the average of 52 and 57, which is \(\( \frac{52+57}{2} = 54.5 \)\) minutes.
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a restaurant offers salads with 2 types of lettuce, 3 different toppings, and 3 different dressings. how many different salads could be ordered?
Answers
Answer:
36 different salads can be ordered
Step-by-step explanation:
Any has 10 pieces of fruit. 7 are apples and the rest are oranges.
She chooses a piece of fruit at random eats it then chooses a second piece of fruit at random
Please draw this
Answers
The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.
What fraction should go into the boxes?Total number of fruits Amy has = 10
Number of Apples = 7
Number of Oranges = 3
First random pieces of fruits chosen:
Probability of choosing Apples = 6/9
Probability of choosing Oranges = 3/9
Second random pieces of fruits chosen:
Probability of choosing Apples = 6/8
= 3/4
Probability of choosing Oranges = 2/8
= 1/4
Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.
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42r^2 -36=0
i need helpppp
Answers
Answer:
can I ask you something before I attempt to answer didn't u mean
42x^ +2x-6=0 then we must solve for x
i really dont know this
Answers
Answer:
y=x+6
Step-by-step explanation:
The gradient of the line is change in y/ change in x
Thus meaning the gradient is 1. (defined as x)
The line crosses through the y-axis on the point (0,6)
So your euqation will be y = (1 - the gradient) x + (interception of y-axis) 6
Answer:
y = x + 6
Step-by-step explanation:
The general form of an equation of a line is
y= mx+b
y = slope ·x + y-intercept
Find the slope of the line, m:
-Pick any 2 points on the line, for example lets pick the points (0, 6) and (3, 10)
-Start at any of the points and go towards the other while note the path
start at (0, 6) and to go to (4, 10) we have to
go up (rise) 4 units from 6 to 10 and
go to the right (run) 4 from 0 to 4.
Slope = m = rise/run = 4/4 = 1
m = 1
Find the y-intercept, b:
The y-intercept is where the line intersects the y-axis. By looking at the given graph we can see y-intercept is 6.
b = 6
The equation of our line is
y = x + 6
Consider the equations y = 3x and y = -12- x.
Complete the table of values for the equation y = 3x.
Х
-7
-5
-3
Answers
Answer:
x | -7 -5 -3
y | -21 -15 -9
Step-by-step explanation:
y = 3x
If x = -7 then y = 3 × (-7) = -21
x = -5 then y = 3 × (-5) = -15
x = -3 then y = 3 × (-3) = -9
Mrs Morraine bought some chocolates. At first, she gave Neighbour A 60% of the
chocolates and another 40 more chocolates. Later, she gave Neighbour B 25% of the
remainder but took back 50 because Neighbour B has too many chocolates at home. She
had 410 chocolates left.
(a) What was the number of chocolates given to Neighbour B in the end?
(b) How many chocolates did Mrs Morraine have at first?
Note : Dont use algebra in this Question i need the answer without algebra
Answers
Mrs Morraine bought some chocolates. At first, she gave Neighbour A 60% of the The final remainder after giving to Neighbour B and taking back 50 chocolates is (x - (0.6x + 40)) - (0.25 * (x - (0.6x + 40)) + 50) = 410.
To solve this problem without using algebra, we can follow the given steps and keep track of the chocolates at each stage.
Step 1: Mrs Morraine initially had some chocolates (unknown number).
Step 2: She gave Neighbour A 60% of the chocolates and an additional 40 chocolates. This means Neighbour A received 60% of the chocolates, and the remaining chocolates were reduced by 40.
Step 3: Mrs Morraine then had a remainder of chocolates after giving to Neighbour A.
Step 4: She gave Neighbour B 25% of the remaining chocolates and took back 50 chocolates because Neighbour B had too many chocolates.
Step 5: Mrs Morraine was left with 410 chocolates.
Now, let's calculate the answers step by step:
Step 1: Mrs Morraine initially had some chocolates (unknown number).
Step 2: She gave Neighbour A 60% of the chocolates and an additional 40 chocolates.
Let's assume Mrs Morraine had x chocolates initially. Neighbour A received 60% of x, which is 0.6x. And the remaining chocolates reduced by 40, so we have x - (0.6x + 40) chocolates remaining.
Step 3: Mrs Morraine then had a remainder of chocolates after giving to Neighbour A.
The remainder after giving to Neighbour A is x - (0.6x + 40).
Step 4: She gave Neighbour B 25% of the remaining chocolates and took back 50 chocolates.
Neighbour B received 25% of the remainder, which is 0.25 * (x - (0.6x + 40)), and Mrs Morraine took back 50 chocolates. So, the new remainder is (x - (0.6x + 40)) - (0.25 * (x - (0.6x + 40)) + 50).
Step 5: Mrs Morraine was left with 410 chocolates.
The final remainder after giving to Neighbour B and taking back 50 chocolates is (x - (0.6x + 40)) - (0.25 * (x - (0.6x + 40)) + 50) = 410.
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Order the numbers from least to greatest
Max points for u and brainliest if u answer ty <3
Answers
Answer:
-5.5,-5 4/5,5.33,5 5/11
Step-by-step explanation:
What is the solution for 9 > x - 7?
A: x<16
Answers
the inequality will be x<16.
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
9 > x - 7
=x-7<9
=x<9+7
=x<16
Hence, the inequality will be x<16.
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Ben measures the length of the street he lives on to be 80 000 cm. What is the street length in kilometres?
(1km 100 000 cm)
Answers
Answer:
.8Km
Step-by-step explanation:
There is exactly 100,000 CM in every KM, if someone such as Ben was to measure out 80,000, to convert to KM you'd take the given value and divide by the appropriate values.
80,000cm / 100,000cm = .8 KM
Street length in kilometers = 80,000 cm / 100,000 cm = 0.8 km
Therefore, the street length is 0.8 kilometers.
what is the soluton to the equation e^3x=12
Answers
Answer:
\(x=\frac{ln(12)}{3}\)
Step-by-step explanation:
We can solve this equation by taking the natural log of both sides.
This gives us the equation: \(ln(e^{3x})=ln(12)\)
And the definition of natural log is basically, "what do I have to raise e to, to get this result"
The result is just e^3x, so I have to raise e to what? Well that's just 3x, you could also use log properties to bring the exponent in front and realize ln(e) = 1
So this gives us: \(3x=ln(12)\)
Now divide both sides by 3: \(x=\frac{ln(12)}{3}\)
Show y=2x-7 on a graph
Answers
Answer:
Step-by-step explanation:
you could do is buy 2x on the x-axis
Starting at 1pm, the temperature changes -4 degrees per hour. How long will it take to reach -1 degrees?
Answers
Answer:
8 hours
Step-by-step explanation:
wait what is starting temperature?
In 1945. an organization surveyed 1100 adults and asked. "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?" Of the 1100 adults surveyed. 363 indicated that they were total abstainers In a recent survey, the same question was asked of 1100 adults and 341 indicated that they were total abstainers Complete parts (a) and (b) below. (a) Determine the sample proportion for each sample The proportions of the adults who took the 1945 survey and the recent survey who were total abstainers are .33 and .31. respectively. (Round to three decimal places as needed) (b) Has the proportion of adults who totally abstain from alcohol changed? Use the <<= 0.10 level of significance First verify the model requirements Select all that apply. A. The sample size is less than 5% of the population size for each sample. B. The data come from a population that is normally distributed. C. The samples are independent D. The samples are dependent E. n_1p_1 (1 - p_1) ≧ 10 and n_2p_2(1 - P_2) ≧10 F. The sample size is more than 5% of the population size for each sample.
Answers
The sample proportions of total abstainers in the 1945 and recent surveys are 0.33 and 0.31, respectively. Model requirements for testing the change in proportion need to be verified.
In the given scenario, we are comparing the proportion of adults who are total abstainers from alcohol in two different surveys: one conducted in 1945 and another more recent survey.
(a) The sample proportion for the 1945 survey is 363/1100 ≈ 0.33 (rounded to three decimal places), indicating that approximately 33% of the adults surveyed were total abstainers. For the recent survey, the sample proportion is 341/1100 ≈ 0.31, indicating that approximately 31% of the adults surveyed were total abstainers.
(b) To determine if the proportion of adults who totally abstain from alcohol has changed, we need to conduct a hypothesis test. Before conducting the test, we need to verify the model requirements.
The correct requirements for this scenario are:
C. The samples are independent (each survey is conducted on a different set of adults).
E. n₁p₁(1 - p₁) ≥ 10 and n₂p₂(1 - p₂) ≥ 10 (where n₁ and n₂ are the sample sizes, and p₁ and p₂ are the respective sample proportions).
Once we have confirmed these requirements, we can proceed with the hypothesis test to determine if the change in proportion is statistically significant at a significance level of 0.10.
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Evaluate the given integral by changing to polar coordinates.
sqrt1a.gif 25 − x2 − y2dA
iintegral.gif
R
where R =
leftbrace1.gif
(x, y) | x2 + y2 ≤ 25, x ≥ 0
rightbrace1.gif
Answers
The value of the given integral is (125π/6) - (25/3)√(6).
To evaluate the integral:
∫∫R √(25 - x² - y²) dA
R is the region in the first quadrant enclosed by the circle x² + y² = 25.
To change to polar coordinates, we make the substitutions:
x = r cos(θ)
y = r sin(θ)
r is the radius and θ is the angle from the positive x-axis to the point (x, y).
The region R can be described in polar coordinates by:
0 ≤ r ≤ 5
0 ≤ θ ≤ π/2
The integral becomes:
∫∫R √(25 - x² - y²) dA
= ∫(0 to π/2) ∫(0 to 5) √(25 - r²) r dr dθ
We can evaluate the inner integral first:
∫(0 to 5) √(25 - r²) r dr = [- (1/3) (25 - r²)^{(3/2)}]|(0 to 5) = (125/3) - (25/3)√(6)
Substituting this into the original integral and evaluating the outer integral, we get:
∫(0 to π/2) (125/3 - (25/3)√(6)) dθ = (125π/6) - (25/3)√(6)
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7m – 3m – 6 < 6 Solve each inequality and graph the solution.
Answers
Answer:
3
Step-by-step explanation:
Step-by-step explanation:
7m - 3m - 6 < 6
4m - 6 - 6 < 0
4m - 12 < 0
4m < 12
m < 12 ÷ 4
m < 3
25 POINTS!!!!
x =
5
6
10
Answers
Step-by-step explanation:
\(2 \times x = 4 \times 3\)
\(2 \times x = 12\)
\(x = 6\)
Write an equation of a line that passes through the point (1, 2) and is perpendicular to the line y=-1/4x+2
Answers
Answer:
y = 4x - 2 would be the equation
The first four terms of an arithmetic sequence are 7, 14, 21, 28... Calculate the sum of the first 50 terms.
Answers
Step-by-step explanation:
a = 7
d = 14-7 = 7
s(50) = n/2*[a+(n-1)*d]
= 50/2*[7+(50-1)*7]
= 8750