Answer:
a)CI 95 % = ( 6.7063 ; 6.7593) ( in hundredths of an inch)
b) CI 95 % = ( 0.05 < σ < 0.089 ) ( in hundredths of an inch)
Step-by-step explanation:
From the problem statement, we have a manufacturing process and we we assume a normal distribution, from sample data:
x = 6.7328 and s = 0.0644
a) CI 95 % = ( x ± t(c) * s/√n )
t(c) df = n -1 df = 25 - 1 df = 24
CI = 95 % α = 5 % α = 0.05 α /2 = 0.025
Then from t-student table t(c) = 2.060
s/√n = 0.0644/ √ 25 s/√n = 0.01288
CI 95 % = ( x ± t(c) * s/√n ) = ( 6.7328 ± 2.060*0.01288)
CI 95 % = ( 6.7328 ± 0.02653 )
CI 95 % = ( 6.7063 ; 6.7593) ( in hundredths of an inch)
b) CI 95 % of the variance is:
CI 95 % = ( ( n - 1 ) * s² / χ²₁ - α/₂ ≤ σ² ≤ ( n - 1 )*s² / χ²α/₂ )
( n - 1 ) * s² = ( 25 - 1 ) * (0.0644)² = 24* 0.00414
( n - 1 ) * s² = 0.09936
And from χ² table we look for values of
χ² α/₂ ,df df = 24 and α/2 = 0.025
χ² (0.025,24) = 12.40 and χ²₁ - α/₂ = χ² (0.975, 24)
χ² (0.975, 24) = 39.36
Then
CI 95 % = ( 0.09936 / 39.36 ≤ σ² ≤ 0.09936 / 12.40)
CI 95 % = ( 0.0025 ≤ σ² ≤ 0.0080)
Then for the standard deviation, we take the square root of that interval
CI 95 % = ( 0.05 < σ < 0.089 )
(08.07 MC)
A polynomial function is shown below:
f(x) = x3 − 3x2 − 4x + 12
Which graph best represents the function? (5 points)
Answer:
Graph A (first graph from top to bottom)
Step-by-step explanation:
Given [tex]f(x)=x^3-3x^2-4x+12[/tex], since the degree of the polynomial is 3, the function must be odd and will resemble the shown shape in the graphs. The degree of 3 indicates that there are 3 zeroes, whether distinct or non-distinct. Therefore, the graph must intersect the x-axis at these three points.
Factoring the polynomial:
[tex]f(x)=x^3-3x^2-4x+12,\\f(x)=(x+2)(x-2)(x-3),\\\begin{cases}x+2=0, x=-2\\x-2=0, x=2\\x-3=, x=3\end{cases}[/tex]
Thus, the three zeroes of this function are [tex]x=-2, x=2, x=3[/tex] and the graph must intersection the x-axis at these points. The y-intercept of any graph occurs when [tex]x=0[/tex]. Thus, the y-coordinate of the y-intercept is equal to [tex]y=0^3-3(0^2)-4(0)+12,\\y=12[/tex] and the y-intercept is (0, 12).
The graph that corresponds with this is graph A.
Find the measure of ∠BAC. Create another angle with the same measure. Measure the new angle to verify that it has the same angle measure. Take a screenshot of your work, and paste it below.
Answer:
The position and orientation of the new angle may vary, but it should have the same angle measure as ∠BAC
.Step-by-step explanation:
The measure of the angle is determined and the image is attached with the answer.
What is an Angle ?An angle is formed by two rays having a common end point.
The angle BAC is of certain measure.
To determine the value of the angle another angle is drawn in following steps
1. Draw a straight line XY
2. With an compass draw an arc of any length on BAC and on the new straight line XY keeping tip of the compass on the end points A and X.
3. Measure the point at which the arc cuts the angle BAC from the point at which it intersects AC and with the same measure , keeping the point of the compass on the point where the arc intersected XY ,cut an arc on the arc.
4. The intersecting point Z of the arc is joint to X
5.The angle ZXY is measured , and this is the value of the angle BAC.
The image is attached with the answer.
To know more about Angle
https://brainly.com/question/7116550
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Josh ate 7/8 pizza and Jerry ate 1/2 pizza. how much more did Josh eat then Jerry
Step-by-step explanation:
6/5 this is the answer hopes this help
Kyle was trying to decide which type of soda to restock based on popularity: regular cola or diet cola. After studying the data, he noticed that he sold less diet cola on weekdays and weekends. However, after combing through his entire sales records, he actually sold more diet cola than regular cola. Which paradox had Kyle encountered?
Answer:
Simpson's Paradox
Step-by-step explanation:
Answer:
Simpson's Paradox
Step-by-step explanation:
Got it right on the test.
Find the height of this triangle.
Answer:
[tex]\sqrt{3}[/tex]
Step-by-step explanation:
x^2 + 1 = 4
x^2 = 3
[tex]\sqrt{3}[/tex]
a basketball team playd 64 games they won 28 more than they lost
Owen is driving to a concert and needs to pay for parking. There is an automatic fee of $11 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $4 for every hour he had his car in the lot. How much total money would Owen have to pay for parking if he left his car in the lot for 5 hours? How much would Owen have to pay if he left his car in the lot for t hours?
Cost for 5 hours:
Cost for t hours:
Answer:
Cost = 11 + 4*t
Step-by-step explanation:
Cost = 11 + 4*t
Part A
t = 5 hours.
Cost = 11 + 4*5
Cost = 11 + 20
Cost = 31
Part B
time = t hours.
Cost = 11 + 4*t
for 5h he would need to pay $20 ( +$11 ) $31
i dont know what T is so ya :/
I need help please, i dont understand
9514 1404 393
Answer:
(a) none of the above
Step-by-step explanation:
The largest exponent in the function shown is 2. That makes it a 2nd-degree function, also called a quadratic function. The graph of such a function is a parabola -- a U-shaped curve.
The coefficient of the highest-degree term is the "leading coefficient." In this case, that is the coefficient of the x² term, which is 1. When the leading coefficient of an even-degree function is positive, the U curve has its open end at the top of the graph. We say it "opens upward." (When the leading coefficient is negative, the curve opens downward.)
This means the bottom of the U is the minimum value the function has. For a quadratic in the form ax²+bx+c, the horizontal location of the minimum on the graph is at x=-b/(2a). This extreme point on the curve is called the "vertex."
This function has a=1, b=1, and c=3. The minimum of the function is where ...
x = -b/(2·a) = -1/(2·1) = -1/2
This value is not listed among the answer choices, so the correct choice for this function is ...
none of the above
__
The attached graph of the function confirms that the minimum is located at x=-1/2
_____
Additional comment
When you're studying quadratic functions, there are few formulas that you might want to keep handy. The formula for the location of the vertex is one of them.
Multiply (5xy-4)(5xy+4)
[tex]{25x {}^{2} y}^{2} - 16[/tex]
There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is 3/8.
There are 72 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.
Answer:
27
Step-by-step explanation:
specific probability = number of specific possibilities divided by number of total possibilities.
the number of total possibilities is 72 (we can pull one out of 72).
the probability of pulling a red back is 3/8.
so, to find the actual number of specific possibilities (actual number of red balls in the overall sample size of 72) we need to bring this ratio of 3/8 to an expression of x/72.
what is the factor to turn 8 into 72 ? 9.
8×f = 72
f = 72/8 = 9
to keep the ratio unchanged in its dimension, we need to apply the same factor to 3 to get x.
3/8 × f/f = x/72
3/8 × 9/9 = x/72
3×9 / 72 = x/72
3×9 = x = 27
so, the probability ratio based on actual possibilities (number of balls available) is 27/72
=>
there are 27 red balls in the bag of total 72 balls.
Graph the following inequality. Then click to show the correct graph.
3x - 2y ≤ 6
Answer:
We want to graph the inequality:
3x - 2y ≤ 6
The first step is to write this as a linear equation, to do it, we can isolate y in one side of the inequality.
3x ≤ 6 + 2y
3x - 6 ≤ 2y
(3/2)x - 6/2 ≤ y
(3/2)x - 3 ≤ y
or:
y ≥ (3/2)x - 3
Because we have the symbol ≥
The points on the line are solutions, then the first part is to graph the line:
y = (3/2)*x - 3
Next, we have:
y equal to or larger than (3/2)*x - 3
Then we need to shade all the region above that line.
The graph can be seen below.
Find an expression which represents the difference when (102 + 8) is subtracted from (-8x - 10) in simplest terms.
Answer:
18x + 18
Step-by-step explanation:
(10x + 8) – (-8x – 10)
(10x – (-8x)) + (8 – (-10))
(10x + 8x) + (8 + 10)
18x + 18
Diana is going to roll a 6-sided die. What's the probability she will role a 4 or
a 5? *
The probability of rolling any one number on a 6 sided die is 1/6
The probability of rolling a 4 is 1/6
The probability of rolling a 5 is 1/6
The probability of rolling a 4 or a 5 is the probability of rolling a 4 plus the probability of rolling a 5:
1/6 + 1/6 = 2/6 = 1/3
The answer is 1/3
15 friends want to order pizza for dinner. If each friend can eat 1/3 of a pizza, how many pizzas should they order?
Answer:
5
Step-by-step explanation:
[tex]\frac{15}{3} =5\\3 friends=1 pizza\\15 friends=5 pizzas\\[/tex]
a trader borrowed 2500$ at a sumple interest at the end of 8 months he paid back $2500 find the rate
Answer:
8%
Step-by-step explanation:
Rate = 100×Interest ÷ Principal× Time
100× 2500/ 2500 × 8 = 800
800/100 = 8%
I hope this helps
step by step..............
Answer:
............Ans..............
The volume of a rectangular prism is given by 24x3+78x2+49x+10. The height of the prism is given by 2x+5. Find an expression for the area of the base of the prism
Answer:
?
Step-by-step explanation:
i cant not explian that
You survey 300 students at the highschool. Of the 300 students, 103 of them said that pizza is their
favorite food. If 751 students attend the high school, about how many students would choose pizza as
their favorite food?
Answer:
258
Step-by-step explanation:
The sum of two numbers is 19 and there differnce is 5
Answer:
x = 12 , y = 7
Step-by-step explanation:
Let the numbers be x and y
Sum of the numbers, x + y = 19 -------- ( 1 )
Difference of the number , x - y = 5 -------- ( 2)
( 1 ) + ( 2 ) => 2x = 24
x = 12
Substitute : x in ( 2 ) => 12 - y = 5
=> 12 - 5 = y
=> 7 = y
Paula, Adam, and Jessica are siblings. Adam is half the age of Paula, and Jessica is one quarter of Paula's age. In six years' time, Jessica will be 75% of Adam's age.
a How old is each sibling now?
b How old will each sibling be in six years' time?
c In how many years' time will Jessica be 75% of Paula's age?
Step-by-step explanation:
answer is in photo above
A veterinary assistant is working at a shelter that houses 53 animals. The shelter uses 1,484 pounds of food each month. How much on average does each animal consume per day in a 28-day month
Answer:
Each = 1 lb per animal
Step-by-step explanation:
Given
[tex]Animals = 53[/tex]
[tex]Food = 1484lb[/tex]
Required
Daily consumption of each animal in a 28-day month
First, we calculate the daily consumption of all animals
[tex]All = \frac{Food}{28}[/tex]
[tex]All = \frac{1484lb}{28}[/tex]
[tex]All = 53 lb[/tex]
The consumption of each animal is then calculated as:
[tex]Each = \frac{All}{Animals}[/tex]
[tex]Each = \frac{53lb}{53}[/tex]
Each = 1 lb per animal
Can someone please help me ?
Answer:
5x+3y=6
Step-by-step explanation:
Use the slope intercept form then rearrange
What is the difference between equation and function?
A. All of the options
B. An equation tells us in a clear term the nature of relationship between one variable and the other variable(s), but a function may not be explicit enough
C. An equation and a function is that, for an equation each of the values of independent variable should give a corresponding value of a dependent variable , that is not compulsory tor a function.
D. All equations are functions but not all functions are equations
Answer:
A is the answer........
Find the slope of the line containing the given pair of points. If the slope is undefined, state so.
(-1,-7) and (-6,1)
Answer:
m = [tex]-\frac{8}{5}[/tex]
Step-by-step explanation:
m = slope
m = [tex]\frac{y2-y1}{x2-x1}[/tex]
m = [tex]\frac{1--7}{-6--1}[/tex]
m = [tex]\frac{8}{-5}[/tex]
m = [tex]-\frac{8}{5}[/tex]
With the help of a diagram a boy starts at a and walks 3km east to b he then walk 4km north to c find the distance and bearing of c from a
Answer:
t=3
Step-by-step explanation:
sorry if its incorrect i got it right on edgy.
Can someone please help me?
Answer:
y=3^(x-2) + 1
Step-by-step explanation:
When dealing with graphs I always use a graphing calculator or Desmos to graph and double check my answers especially when doing translations!
Please help please guys how are you doing
Answer:
the answer of the the triangle is 6
Answer:
6
Step-by-step explanation:
First row:
8 ÷ 2 = 4. → Square: 4
Second row:
14 - 4 = 10.
[two circles] = 10. So, 10÷2 = 5.
Circle = 5
Third Row:
[triangle] + 5 = 11
11 - 5 = 6
Triangle = 6
In which of the following drawings is DE parallel to AC?
Answer:
its option D because the lines are not even close to crossing.
Step-by-step explanation:
hope this helps :)
HELP PLEASE! What is BD??
Answer:
[tex]BD=13[/tex]
Step-by-step explanation:
Note that Ray AC bisects ∠A. Therefore, we can use the Angle Bisector Theorem shown below.
Hence:
[tex]\displaystyle \frac{27}{x+5}=\frac{12}{x}[/tex]
Solve for x. Cross-multiply:
[tex]12(x+5)=27(x)[/tex]
Distribute:
[tex]12x+60=27x[/tex]
Subtract 12x from both sides:
[tex]15x=60[/tex]
Divide both sides by 15. Thus:
[tex]x=4[/tex]
BD is the sum of BC and CD:
[tex]BD=BC+CD[/tex]
Substitute:
[tex]BD=x+(x+5)[/tex]
Substitute and evaluate:
[tex]BD=(4)+(4+5)=13[/tex]
Therefore, BD is 13.
Find each. a. za_2 for the 99% confidence interval b. za_2 for the 98% confidence interval c. za_2 for the 95% confidence interval d. za_2 for the 90% confidence interval e. za_2 for the 94% confidence interval
Answer:
a) Z = 2.575.
b) Z = 2.327.
c) Z = 1.96.
d) Z = 1.645.
e) Z = 1.88.
Step-by-step explanation:
Question a:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Question b:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Question c:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Question d:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Question e:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.94}{2} = 0.03[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.03 = 0.97[/tex], so Z = 1.88.
