The product engineer conducted an experiment to optimize the cutting of wood strips used in plywood production. The engineer measured the torque applied to the chucks before they spun out of the log under different conditions of log diameter, chuck penetration, and log temperature.
The variables studied were log diameter (with two levels: 4.5 and 7.5), chuck penetration (with four levels: 1.00, 1.50, 2.25, and 3.25), and log temperature (with three levels: 60, 120, and 150). The response variable measured was the torque that could be applied before the chuck spun out.
The engineer designed a factorial experiment with three factors: log diameter, chuck penetration, and log temperature. Each factor was varied at different levels to assess their impact on the torque applied to the chucks. The log diameter had two levels (4.5 and 7.5), the chuck penetration had four levels (1.00, 1.50, 2.25, and 3.25), and the log temperature had three levels (60, 120, and 150). The response variable, torque, was measured to determine the optimal conditions for cutting wood strips.
By analyzing the experimental data, the engineer can identify the significant factors and their effects on torque. This information can be used to optimize the cutting process by adjusting the log diameter, chuck penetration, and log temperature accordingly.
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3. Given a normal distribution of test scores from that same statistics class where the mean is 80 and the standard deviation is 7.5, determine BY HAND what percent of the scores were 78 or less. Also, what percent of scores were 85 or better?
The percent of the scores that were 85 or better is 25.14%.
The percent of the scores that were 78 or less is 39.25%.
The percent of the scores that were 85 or better is 25.14%.
Given a normal distribution of test scores from that same statistics class where the mean is 80 and the standard deviation is 7.5, we are to determine what percent of the scores were 78 or less and what percent of the scores were 85 or better.
Below are the steps to determine what percent of the scores were 78 or less.
Step 1: Determine the Z-score
To determine the Z-score, we use the formula
Z = (X - μ) / σ
Where X is the score, μ is the mean and σ is the standard deviation
Z = (78 - 80) / 7.5
Z = -0.27
Step 2: Use the Z-table to determine the percentage
Using the Z-table, we can find the percentage of scores that lie below Z = -0.27 which is 0.3925 or 39.25%
Therefore, the percent of the scores that were 78 or less is 39.25%.
Below are the steps to determine what percent of the scores were 85 or better.
Step 1: Determine the Z-score
To determine the Z-score, we use the formula Z = (X - μ) / σ
Where X is the score, μ is the mean and σ is the standard deviation
Z = (85 - 80) / 7.5
Z = 0.67
Step 2: Use the Z-table to determine the percentage
Using the Z-table, we can find the percentage of scores that lie above Z = 0.67
Which is 0.2514 or 25.14%
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A recent Gallup poll found large differences in the type of household chores done by wives and husbands.1 Wives still do most of the indoor household chores. Husbands still tend to do more work outside and with family cars. The simulated data in this problem are based on the results of this poll.
Suppose we wish to demonstrate that there is a difference between the proportions of wives and husbands who do laundry at home. From a random sample of 66 randomly selected wives, we observe 44 who do laundry at home. From a random sample of 46 husbands, we observe 18 who do laundry at home.
Test the claim that the proportion of wives, p1 , who do laundry at home is different from the proportion of husbands, p2 , who do laundry at home. Use a 1% significance level.
Answer : There is enough evidence to suggest that a higher proportion of wives do laundry at home compared to the proportion of husbands who do laundry at home.
Explanation:
The null hypothesis is that the proportion of wives and husbands who do laundry at home is the same. The alternative hypothesis is that the proportion of wives and husbands who do laundry at home is different.
Mathematically, null and alternative hypotheses are given below. H0: P1 - P2 = 0H1: P1 - P2 ≠ 0 where P1 is the proportion of wives who do laundry at home and P2 is the proportion of husbands who do laundry at home. Let α = 0.01 be the significance level. Therefore, α/2 = 0.005 and the Zα/2 value for the two-tailed test is ±2.58.
The point estimate of the difference in the proportions is:Point estimate, PE = P1 - P2 = (44/66) - (18/46) = 0.6667 - 0.3913 = 0.2754
The standard error of the difference in the proportions is: SE = sqrt{(P1(1 - P1)/n1) + (P2(1 - P2)/n2)} = sqrt{[(44/66)(22/66)/65] + [(18/46)(28/46)/45]} = 0.1033
The test statistic is given by:Z = (PE - 0) / SE = 0.2754 / 0.1033 = 2.6641
Since the absolute value of the test statistic is greater than the Zα/2 value, we reject the null hypothesis and conclude that the proportion of wives who do laundry at home is different from the proportion of husbands who do laundry at home at a 1% significance level. Therefore, there is enough evidence to suggest that a higher proportion of wives do laundry at home compared to the proportion of husbands who do laundry at home.
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If dy /dx is undefined for a given value of x, then the line tangent to the curve y f(x) at that value does not exist Select one:
a. true b. false
The statement "If dy/dx is undefined for a given value of x, then the line tangent to the curve y = f(x) at that value does not exist" is false.
If the derivative dy/dx is undefined at a given value of x, it means that the slope of the tangent line is undefined at that point.
However, the tangent line can still exist.
For example, consider the curve y = |x| at x = 0.
The derivative dy/dx is undefined at x = 0 since the slope changes abruptly at that point. However, we can still draw a tangent line at x = 0, which is the y-axis itself.
Therefore, even if the derivative is undefined, it does not necessarily mean that the tangent line does not exist.
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Let f(x) = 9+√2-3. Find f(x).
The value of the function f(x) = 9 + √2 - 3 is a constant and can be simplified as f(x) = 6 + √2.
The given function f(x) = 9 + √2 - 3 is an expression that does not depend on the variable x. Therefore, it represents a constant value.
To evaluate the function, we can simplify the expression by combining like terms:
f(x) = 9 + √2 - 3
Combining the constants 9 and -3, we have:
f(x) = 6 + √2
Thus, the value of the function f(x) is a constant, which is 6 + √2.
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A food truck sells tacos, burritos, and drinks.
Let event A = A customer buys a taco.
Let event B= A customer buys a drink.
What does P(A or B) = 0.45 mean in terms of this problem?
Answer:
b, the probability that a customer buys a taco, a drink, or both is 45%
P(A or B) = 0.45 means that there is a 45% probability that a customer will buy a taco or a drink from the food truck.
In terms of this problem, P(A or B) = 0.45 represents the probability that a customer buys either a taco (event A) or a drink (event B).
When we say "P(A or B)," it refers to the probability of either event A or event B occurring. In this case, it means the probability of a customer buying a taco or a drink from the food truck.
The value of 0.45 indicates the numerical probability associated with the event A or B. It represents the likelihood that a randomly selected customer from the food truck will purchase either a taco or a drink.
Therefore, P(A or B) = 0.45 means that there is a 45% probability that a customer will buy a taco or a drink from the food truck.
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whats 10x10+111-21x999/999+21-111/10?
Answer:
199.9
Step-by-step explanation:
Gardening Jessica is planting a garden. It has the shape of a right triangle. She wants 3
plants for each square meter of area. How many plants does she want in the garden?
Answer:
28
Step-by-step explanation:
plants in the garden = area of the garden / number of plants per square meter
the garden is in the shape of a triangle
A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees
Area of a triangle = 1/2 x base x height
(1/2) x 24 x 7 = 84 meters^2
plants in the garden = 84/3 = 28
At a constant speed, a car travels 75 miles in 60 minutes. How far does
the car travel in 18 minutes? If you get stuck, consider using the table.
Answer:
22.5 miles
Step-by-step explanation:
75/60 = x/18
60x = 1350
x = 22.5
Two sides of a triangle measure 5
units and 3 units. The perimeter
of the triangle is 12 units. What is
the measure of the third side?
Answer:
4 units
Step-by-step explanation:
5+3=8
12-8=4
Which of the following properties is represented by the calculations in the photo?
A) multiplication property of equality
B) zero sum property
C) addition property of equality
D) zero product property
Answer:
D. zero product property
Step-by-step explanation:
Base on the Zero Product Property, if the product of factors gives us 0, either of the factors or both would equal 0.
Thus,
xy = 0, therefore,
x = 0 or y = 0
Therefore, the property that is represented by the calculation given in the photo is Zero Product Property.
please help thank u alot going to put pictures!
Priya has planted a garden shaped like a right triangle. One leg of the triangle is 5 meters long, and the angle formed by it and the hypotenuse is 50°. If Priya wants to build a fence around her garden, how many meters of fence will she need? Round your answer to the nearest meter.
Answer:
19
Step-by-step explanation:
:)
The amount of fence that Priya would need (in meters) is 19 meters approximately.
What are the six trigonometric ratios?Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slant side is called hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle (suppose its measure is θ),
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]
For this case, we've to find the length of the fencing she needs to cover her garden.
Length of fencing needed = Perimeter of the considered right triangle = sum of its sides' lengths
Using the image attached below, from the perspective of angle A which is of 50 degrees from inside, we get:
|AB| = base length = 5 meters (given)|BC| = perpendicular length = p meters (say)|AC| = hypotenuse length = h meters (say)Using tangent ratio,[tex]\tan(m\angle A) = \tan(50^\circ) = \dfrac{p}{5}\\\\p = 5 \tan(50^\circ) \approx 5.96 \: \rm m[/tex]
Using sin ratio,[tex]\sin(m\angle A) = \sin(50^\circ) = \dfrac{p}{h}\\\\h = \dfrac{p}{\sin(50^\circ)} \approx \dfrac{5.96}{\sin(50^\circ)} \approx 7.78 \: \rm m[/tex]
Thus, perimeter of the triangle = 5 + p + h ≈ 18.74 m ≈ 19 m
Thus, the amount of fence that Priya would need (in meters) is 19 meters approximately.
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Convert each of the following implicitly quantified statements
to their formally quantified statement equivalent.
Implicitly quantified statements can be converted into formally quantified statements by specifying the quantifiers and the domain of discourse.
To convert an implicitly quantified statement to its formally quantified statement equivalent, we need to determine the quantifiers and the domain of discourse.
1. For universally quantified statements, we use the universal quantifier (∀). It indicates that the statement holds for all elements in the domain of discourse. For example, if the statement is "All cats have tails," we can convert it to the formally quantified statement ∀x(Cat(x) → HasTail(x)), where Cat(x) represents "x is a cat" and HasTail(x) represents "x has a tail."
2. For existentially quantified statements, we use the existential quantifier (∃). It indicates that there exists at least one element in the domain of discourse for which the statement is true. For example, if the statement is "There is a red apple," we can convert it to the formally quantified statement ∃x(Red(x) ∧ Apple(x)), where Red(x) represents "x is red" and Apple(x) represents "x is an apple."
By explicitly stating the quantifiers and defining the predicates in the statement, we can convert implicitly quantified statements into their formally quantified statement equivalents, making the meaning and scope of the statement clear within a specific domain of discourse.
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Purple paint is made of a ratio of
16 white : 3 blue : 1 red
how much white paint is needed to make one gallon of purple paint?
plz help its important
there are 16/20 x 1 gallon = 4/5 gallons of white paint in one gallon of purple paint (got it from safari)
A cube. Point B is the top right point of the top face. Point A is the bottom left point of the bottom face and point C is the top right point of the bottom face. Diagonals are drawn from B to A and from A to C. Side B C is 10 inches long, and Side A B is StartRoot 300 EndRoot inches long. What is the length of Side A C? 14 in. StartRoot 200 EndRoot in. StartRoot 290 EndRoot in. 20 in.
Answer:
the answer is b
Step-by-step explanation:
i just did the assignment
Answer:
b
Step-by-step explanation:
which of the following fractions converts to a repeating decimal? a. 7/16 B.5/8 C. 2/3 D.4/10
Answer:
B
Step-by-step explanation:
What is the sum of 2 with exponent of 4 and 7 with an exponent of 2. please write in standard form.
Answer:
I think the answer would be 65 , because :
2^4 + 7^2 = 16 + 49 = 65 .
hope it helps u ^.^
Answer:
65
Step-by-step explanation:
First you would solve the exponent and then you would add them
2 to the power of 4 = 16
7 to the power of 2 = 49
16 + 49 = 65
2 to the power of 4 + 7 to the power of 2 = 65
Shana is doing a craft project
using yarn and sticks. She
has 3 green yam pieces and
7 blue yam pieces. She has 3
times as many sticks as yarn
pieces. Write an expression.
Plz help
Answer:
3(5 + 7)
Step-by-step explanation:
Shana is carrying our a craft project
She is making use of yarns and stuck
She has three green yarn pieces and seven blue yarn pieces
She has three times as many yarn pieces
Therefore the expression can be represented as follows
3(5 + 7)
12. Use Russian Peasant Multiplication to perform the following problem. Explicitly show your addition. 49 x 65
Using the Russian Peasant Multiplication, 49 x 65 is 3,185.
What is the Russian Peasant Multiplication?The Russian Peasant Multiplication method converts the problem into binary (base 2) multiplication from base 10 by halving the numbers on the first column repeatedly till the second number doesn't become 1 and doubling the numbers on the second column.
Then, add up the numbers in the second column that correspond to odd numbers in the first column to get the result.
49 65
÷ 2 24 130 x 2
12 260
6 520
3 1,040
1 2,080
Add:
65, because we ignored 1 when we divided 49 by 2
1,040, because we ignored 1 when we divided 3 by 2
2,080
= 3,185
Check:
49 x 65 = 3,185
Based on the Russian Peasant Multiplication method, the product of 49 x 65 is 3,185.
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Sasha had to run 1/3 of a mile. She decided to walk, jog, and run the 1/3 mile, in equal parts. What fraction of the mile will she run?
A.9
B.3/9
C.1/9
D.3/3
(Need help asap pls)
Answer:
C 1/9
Step-by-step explanation:
She needs to run 1/3 of a mile and is going to run/jog/walk that 1/3 mile
So she must do 1/9 of a mile running, 1/9 walking, and 1/9 jogging because 1/3 is equivalent to 3/9.
Since she is going to run/jog/walk the same amount of the 1/3 she is going to run 1/9 of the 1/3
Let me know if I'm wrong
Hope I helped :]
tomen puntos
toy aburridoooo
Answer:
aww thank you
pls mark brainliest
Step-by-step explanation:
A random sample of n_1 = 555 individuals results in x_1 = 451 successes. An independent sample of n_2 = 600 individuals results in x_2 = 510 successes. Does this represent sufficient evidence to conclude that p_1≠ p_2 at the α = 0.05 level of significance?
There is no sufficient evidence to conclude that p₁ ≠ p₂
How to determine if the conclusion is sufficientFrom the question, we have the following parameters that can be used in our computation:
n₁ = 555
x₁ = 451
n₂ = 600
x₂ = 510
Calculate the pooled sample proportion using
p = sum of x/sum of n
So, we have
p = (451 + 510)/(555 + 600)
p = 0.832
Calculate the test statistic using
[tex]z = (\frac{x_1}{n_1} - \frac{x_2}{n_2}) \div (\sqrt{(p * (1 - p) / n_1) + (p * (1 - p) / n_2)}}[/tex]
So, we have
[tex]z = (\frac{451}{555} - \frac{510}{600}) \div (\sqrt{(0.832 * (1 - 0.832) / 555) + (0.832 * (1 - 0.832) / 600)}})[/tex]
When solved, we have
z = -1.699
The critical value at α = 0.05 level of significance is 1.645
The z = -1.699 is less than this value
This means that we fail to reject the null hypothesis
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If You Have NO Explanation Than Don't Answer.
Answer: Option C
Step-by-step explanation:
C because 6+1=1+1+1+1+1+1+1
Answer:
C
Step-by-step explanation:
We want to find which model shows two equal expressions. We know that the value of x is 6. That being said, on the left side of each equation, plug in 6 for every "x" you see. Then, add the values on both sides. If they're equal, that's your answer.
For example:
In choice A, we see two x's, so we plug in 6 for them both and add them. That's 12 on the left side. On the other side of the equation, we have 7 "1" boxes, which simply just means add them, so that's 7 on the other side. 12 does not equal 7, therefore A is not the answer. However, for choice C, we are given x, which we know is 6, and a "1" box, which simply means 6 + 1, which is 7. On the other side of this equation, we have 7 "1" boxes, so that's 7. The equation becomes 7 = 7, which is true, so that is our answer.
multiple 2y(6y2+4y-3)
Answer:
Step-by-step explanation:
Y- intercepts (-3 = 2 3, 0) , (-3 - 2 3, 0)
En san pedro de atacama, un dia de septiembre a las 7a.M., la temperatura fue de 6°c, la que fue aumentando 2,3°c en promedio por hora hasta que alcanzo su maxima de 30,15 °c ¿ a que hora alcanzo su temperatura maxima
Answer:
5:30 p.m.
Step-by-step explanation:
30.15 - 6 = 24.15
24.15 / 2.3 = 10.5 hrs
7 + 10.5 = 17.5 = 5:30 p.m.
What is the slope of the line that
passes through these two points?
(1, 2)
(2, 8)
(x1.yı) Slope =
rise (y2-yı)
Remember, given two points,
(x2:y2) run (x2-x1)
Answer:
6
Step-by-step explanation:
8 - 2 / 2 - 1
6 / 1
6
20. An airport, a factory, and a shopping center are at the vertices of a right triangle formed by three highways. The airport and factory are 6.0 miles apart. Their distances from the shopping center are 3.6 miles and 4.8 miles, respectively. A service road will be constructed from the shopping center to the highway that connects the airport and factory. What is the shortest possible length for the service road? Round to the nearest hundredth
Answer:
2.88 mi
Step-by-step explanation:
Jackson has a table with a square top and he wants to buy a circular piece of lace
that will cover the entire top of the table. The top of the table has side lengths of 12
inches, as shown.
12 in
12 in
What is the area, in square inches, of the smallest circular piece of lace Jackson could
Answer:
144
Step-by-step explanation:
the area is 144 im prob wrong
Use the following picture to find the measure of angles 3 and 4. (picture)
Sarah donated $920 for a new park. Sarah's brother donated $850. How much more money did Sarah donate?