The requried, we cannot conclude that the mean cyclic time is greater than 3.5 hours for the new process of producing a type of novolac resin based on the given data.
To determine if we can conclude that the mean cyclic time is greater than 3.5 hours for the new process of producing a type of novolac resin, we need to perform a hypothesis test.
We can use a one-sample t-test to test the null hypothesis that the mean cyclic time is equal to 3.5 hours against the alternative hypothesis that the mean cyclic time is greater than 3.5 hours.
Using the given data, we can calculate the sample mean and sample standard deviation of the cyclic times for the six batches produced. The sample mean is:
x = (3.45 + 3.47 + 3.57 + 3.52 + 3.40 + 3.63) / 6
= 3.50 hours
The sample standard deviation is:
[tex]s = \sqrt ((3.45 - 3.50)^2 + (3.47 - 3.50)^2 + (3.57 - 3.50)^2 + (3.52 - 3.50)^2 + (3.40 - 3.50)^2 + (3.63 - 3.50)^2) / (6 - 1)) }[/tex]
= 0.086 hours
The test statistic for the one-sample t-test is:
[tex]t = ( \bar x-\mu) / (s / \sqrt(n))[/tex]
where μ is the hypothesized mean cyclic time, n is the sample size, and s is the sample standard deviation.
Substituting the given values, we get:
[tex]t = (3.50 - 3.5) / (0.086 / \sqrt(6))[/tex]
= 0
The degree of freedom for the t-test is n - 1 = 5.
Using a t-table or a calculator, we can find the critical value of t for a one-tailed test with α = 0.05 and 5 degrees of freedom to be 1.833.
Since the calculated t-value of 0 is less than the critical value of 1.833, we fail to reject the null hypothesis. Therefore, we cannot conclude that the mean cyclic time is greater than 3.5 hours based on the given data.
Therefore, we cannot conclude that the mean cyclic time is greater than 3.5 hours for the new process of producing a type of novolac resin based on the given data.
Learn more about the hypothesis here:
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the ratio of boys to girls in a group of 2:1. if there are 22 more boys than girls, work out how many people there are in a solo
Answer:
There is 11 girls but 33 people in solo
This shows the trapezoid cut into two triangles what are the areas of the two triangles?
2x + 5/4 = -5 -4x/12
Solve for x to make the proportion true.
What is the answer to this question?
Answer:
D
Step-by-step explanation:
so they ran the trial ten times so now you have to aks how many times did they get heads
which would be 2/10 times
you want the accuracy of which they got so divide 2/10
we know the probability of getting heads is 50%
so when you calulate it, it will give you 0.2 use the percent button and get 0.1
Please help me asap this is due in 10 min Ill also mark brainliest
As we know that formula of area of circle is πr²
So let's apply formula
π×8.6×8.6
=232.2
=200 is the nearest hundredth.
You have to do rest of all through this method.
I WiLL GiVe BrAnYeSt
Molly has 7,406 stickers in her collection. She wants to put them into a book. She can fit 14 stickers on each page. How many pages will she need? (1 point)
A.520
B.529
C.538
D.547
Answer:
the answer is 529
Step-by-step explanation:
divide 7,406 and 14 and the answer is 529
Evaluate x^2 + 2x -1 when x = -3
help
1. -2
2. 2
3. 16
4. -15
Answer:
2
Step-by-step explanation:
just put -3 to x
9-7=2
9x + 4
8x - 4
4x + 17
If the perimeter is 374 units, find the value of x and the area of the triangle.
The value of x is
The area is
square units.
Answer:
x = 17
Area = 10,362units²
Step-by-step explanation
Given the sides of the triangle
S1 = 9x+4
s2 = 8x-4
S3 = 4x+17
Perimeter of the triangle is the sum of all the sides
P = S1+S2+S3
374 = 9x+4+8x-4+4x+17
374 = 21x+17
21x = 374-17
21x = 357
x = 357/21
x = 17
Hence the value of x is 17
Area of the triangle is 1/2bh
A = 1/2bh
b is the base
h is the height
Let the base be 9x + 4 and height be 8x-4
b = 9x+4
b = 9(17)+4
b = 153+4
b = 157units
h = 8x-4
h =8(17)-4
h = 136-4
h = 132
Area = 1/2 * 157 * 132
Area = 157*66
Area = 10,362units²
If f(x) = 3x - 1 and g(x) = x + 2, find (f- g)(x).
I can’t find it
Answer:
[tex](f-g)(x)=2x-3[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]f(x)=3x-1\text{ and } g(x)=x+2[/tex]
And we want to find:
[tex](f-g)(x)[/tex]
This is equivalent to:
[tex]=f(x)-g(x)[/tex]
By substitution:
[tex]=(3x-1)-(x+2)[/tex]
Simplify. Distribute:
[tex]=(3x-1)+(-x-2)[/tex]
Rearrange:
[tex]=(3x-x)+(-1-2)[/tex]
Therefore:
[tex](f-g)(x)=2x-3[/tex]
(50pts)Solve for x:
a
7.125
b
6
c
8
d
4.125
Answer:
b. 6
Step-by-step explanation:
[tex](16x + 9) \degree = 105 \degree \\(corresponding \: \angle s) \\ \\16x + 9 = 105 \\ \\ 16x = 105 - 9 \\ \\ 16x = 96 \\ \\ x = \frac{96}{16} \\ \\ x = 6[/tex]
Using Properties to Simplify Expressions
Instruction Active
Matching Equivalent Expressions
Match each expression on the left with an equivalent expression on the right
PLS HELP
Answer:
1) 2x-3 = x -3 + x
2) 2x - 6 = -6 + 2x
3) [tex]\frac{3}{5}-\frac{13}{5}=-6.9+4.9[/tex]
4) 3x+0 = 3x
5) [tex]\frac{5}{3}-x+\frac{1}{3}=-\frac{3}{2}x+2+\frac{1}{2}x[/tex]
Step-by-step explanation:
We need to match each expression on the left with an equivalent expression on the right
The expressions are equivalent if the have the same results.
1) 2x - 3
Looking at the options the best match is:
x -3 + x
When solve we get:
2x-3
So, 2x-3 = x -3 + x
2) 2x - 6
Looking at the options the best match is:
-6 + 2x
Because according to commutative property: a+b = b+a
So, 2x - 6 = -6 + 2x
3) [tex]\frac{3}{5}-\frac{13}{5}[/tex]
First simplifying the given expression:
[tex]\frac{3}{5}-\frac{13}{5}\\=\frac{3-13}{5}\\=\frac{-10}{5}\\=-2[/tex]
Looking at the options, -6.9+4.9 = -2
So, [tex]\frac{3}{5}-\frac{13}{5}=-6.9+4.9[/tex]
4) 3x + 0
Looking at the options the best match is:
3x
Because, adding 0 in 3x will result in 3x
So, 3x+0 = 3x
5) [tex]\frac{5}{3}-x+\frac{1}{3}[/tex]
First simplifying:
[tex]\frac{5}{3}-x+\frac{1}{3}\\=\frac{5-3x+1}{3}\\=\frac{6-3x}{3}\\= \frac{3(2-x)}{3}\\=2-x[/tex]
Now, solving the option: [tex]-\frac{3}{2}x+2+\frac{1}{2}x[/tex]
[tex]=\frac{-3x+4+1x}{2}\\=\frac{-2x+4}{2}\\=\frac{2(-x+2)}{2}\\=-x+2\\or\\=2-x[/tex]
So, [tex]\frac{5}{3}-x+\frac{1}{3}=-\frac{3}{2}x+2+\frac{1}{2}x[/tex]
3. Which rule represents a linear function? Check all
that apply.
O A. y=-5x
C. Y= X-3
Q B. y=x4
PLEASE HELP!! ITS ALMOST DUE!! ILL MARK BRAINLIEST!!!
Answer:
25 units should be right
Step-by-step explanation:
prove me wrong
i need help with this!! i have to get my hw done quick!!
Step-by-step explanation:
221+w=274..................
.......
Answer:
53 + 221 = 274
Step-by-step explanation:
I'm pretty sure its saying
w + 221 = 274
and in this case, w = 53
because if you subtract 274 by 221 you get 53.
Best of luck to you!!!
Totally blanking on how medians work
===============================================
The three medians of this triangle are:
PFREQDThese segments go from one vertex to the midpoint of the opposite side.
The median we'll focus on is PF.
The point C is the centroid of the triangle. It's where the three medians intersect. It turns out that C divides PF such that CF is twice as long as PC
In other words,
CF = 2*PC
This means,
PF = PC+CF .... segment addition postulate
PF = PC+2*PC ... replace CF with 2*PC
PF = 3*PC .... combine like terms
So the median PF is three times the length of its portion PC
We're told that PF = 24
We can then find the following:
PF = 3*PC
24 = 3*PC
3*PC = 24
PC = 24/3
PC = 8
Then we double this to get the length of CF
CF = 2*PC
CF = 2*8
CF = 16
This is the same as FC because the order of the endpoints don't matter when it comes to naming a segment.
The final answer is 16.
Bo, Ryan and Zachary went for a walk. They walked 1/4 miles from school to Bocas House. Then they walked 4/6 miles From Paul’s house to the park. What is the total distance with the boys walked?
Answer:
Total distance walked by boys = [tex]\frac{11}{12}[/tex] miles
Step-by-step explanation:
Given that:
Distance walked from school to Bocas house = 1/4 miles
Distance walked from Paul's house to the park = 4/6 miles
Total distance walked = [tex]\frac{1}{4}+\frac{4}{6}[/tex]
Total distance walked = [tex]\frac{3+8}{12}[/tex]
Total distance walked = [tex]\frac{11}{12}[/tex] miles
Hence,
Total distance walked by boys = [tex]\frac{11}{12}[/tex] miles
[ 6 × ( 4 + 2 ) − 6 ] ÷ 3 can you plz give me the anwers plz and the right anwers
Answer: 10
Step-by-step explanation: I think
Answer:
Step-by-step explanation:
Solution:
=6×6-6÷3
=36-6÷3
=30÷3
=10
The average fuel efficiency of U.S. light vehicles (cars, SUVs, minivans, vans, and light trucks) for 2005 was 21 mpg. If the standard deviation of the population was 2.9 and the gas ratings were normally distributed, what is the probability that the mean mpg for a random sample of 25 light vehicles is Under 20
Answer:
0.042341
Step-by-step explanation:
We solve using z score formula
z = (x-μ)/σ/n, where
x is the raw score = 20 mpg
μ is the population mean = 21 mpg
σ is the population standard deviation = 2.9
n = random number of samples
Hence:
For x < 20
= z = 20 - 21/2.9/√25
= z = -1/2.9/5
= z = -1.72414
P-value from Z-Table:
P(x<20) = 0.042341
The probability that the mean mpg for a random sample of 25 light vehicles is Under 20 mpg is 0.042341
The probability that the mean mpg for a random sample of 25 light vehicles is 0.042341
Calculation:Here we used z score formula
z = (x-μ)/σ/n, wherex is the raw score = 20 mpgμ is the population mean = 21 mpgσ is the population standard deviation = 2.9n = random number of samplesSo,
For x < 20
= z = 20 - 21/2.9/√25
= z = -1/2.9/5
= z = -1.72414
Now
P-value from Z-Table:
P(x<20) = 0.042341
Learn more about the probability here: https://brainly.com/question/795909?referrer=searchResults
PLEASE ANSWER ASAP FOR BRANLEST!!!!!!!!!!!!!!!
Solve the equation
1/4t - 6 = -4
what is t?
Answer:
t = 8
Step-by-step explanation:
For a science experiment, students need to find 25% of 60 grams. How many grams is that?
List the next three terms in the following sequence:
1, 2, 4, 7, 11, 16,...
Also list the number that would be the twentieth number in the sequence.
a.
23, 31, 40; 200
b.
23, 31, 40; 191
c.
22, 28, 35; 185
d.
22, 29, 37; 191
Answer:
The answer is D
Step-by-step explanation:
Each time sum of previous number and position of that previous number in given series, with the formula being:
previous number + position of previous number = next number
For example, 7 is in the 4th spot so 7+4=11.
Answer:
d
Step-by-step explanation:
Graph the function.
f(x)= 3/5x}=-5
A piece of furniture has a retail price of $780 and it’s on sale at a 20% discount what will the sale price of the piece of furniture before taxes
Answer:
624$
Step-by-step explanation:
What is 3 p +2 ( 5p - 3 )
Answer:
15p + -6
Step-by-step explanation:
Each day a bobcat drinks about 7 times as much water as a mink drinks.
How much water can a bobcat drink in one day?
Water Consumption
Animal Average Amount
(Liters per day)
Canada Goose 0.24
Cat 0.15
Mink 0.10
Opossum 0.30
Bald Eagle 0.16
A bobcat drinks about liter(s) in one day.
Answer:
0.70
Step-by-step explanation:
It is 0.70 because you multiply 7 x 10 and that is 70 then you just put 0. in front of it
HELP! ASAP!! Will Mark brainliest!
Answer:
The Answer is D.
Step-by-step explanation:
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What is this equation in slope intercept form
There were 27 boxes of tea in the tea house. Each box weighed 18 kg. After selling 12 boxes, the shopkeeper packed the remaining tea into bags of 9 kg each. How many bags of tea can be packed?
Answer:
30 boxes of tea
Step-by-step explanation:
27 (overall tea boxes) - 12 (boxes sold) = 15
15 (leftover boxes) x 18 (kg of each box) = 270
270 (overall kg of the boxes) divided by 9 (kg of the bags) = 30, so all the tea boxes can be placed into the bags
Which math expression means "the product of an unknown number and 110"? O A. x+110 B. X. 110 C. X-110 D. x+ 110 please help me i give you 20 points and follow you
Answer:
x*110
Step-by-step explanation:
Answer:
It is B: x * 110
Step-by-step explanation:
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