Answer:
Step-by-step explanation:
From the given information:
Let assume:
[tex]\mu_1 =[/tex] population mean for catalyst 1
[tex]\mu_2 =[/tex] population mean for catalyst 2
Then:
Null hypothesis: [tex]\mu_1 \ge \mu_2[/tex]
Alternative hypothesis: [tex]\mu_1 <\mu_2[/tex]
[tex]\alpha= 0.01[/tex]
By using MINITAB software to compute the 2 sample t-test, we have:
Two-Sample T_Test and CI
Sample N Mean StDev SE Mean
1 12 94.00 3.00 0.87
2 15 90.00 2.00 0.52
Difference = [tex]\mu_1(1)-\mu_2(2)[/tex]
Estimate of difference: -6.00
99% upper bound for difference: -3.603
T-test of difference: 0 (vs <): T-value = -6.22
P.value = 0.000
DF = 25
Both use Pooled StDev = 2.4900
From above result
the test statistics = -6.00
p-value = 0.00
Decision Rule: To reject [tex]H_o\ \ if \ \ p \le \alpha[/tex]
Conclusion: Provided that p-value is < ∝, we reject [tex]H_o[/tex]. Hence, there is sufficient evidence to support the given claim.
b) From the MINITAB;
The 99% C.I on the difference in the mean yields that can be applied to test the claim in part (a) is:
[tex]\mathbf{\mu_1 -\mu_2 \le -3.60}[/tex]
What is the inverse relation of f(x)=1/5x−4/5?
y=1/5x−4
y=−1/5x+5/4
y=−5x−4
y=5x+4
Answer:
[tex]y' = 5x + 4[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{1}{5}x - \frac{4}{5}[/tex]
Required
The inverse relation
[tex]f(x) = \frac{1}{5}x - \frac{4}{5}[/tex]
Rewrite as:
[tex]y = \frac{1}{5}x - \frac{4}{5}[/tex]
Swap x and y
[tex]x = \frac{1}{5}y - \frac{4}{5}[/tex]
Multiply through by 5
[tex]5x = y - 4[/tex]
[tex]y = 5x +4[/tex]
Rewrite the new function as:
[tex]y' = 5x + 4[/tex]
The base of a solid is the region in the first quadrant between the graph of y=x2 and the x -axis for 0≤x≤1 . For the solid, each cross section perpendicular to the x -axis is a semicircle. What is the volume of the solid?
Answer:
The volume of the solid is π/40 cubic units.
Step-by-step explanation:
Please refer to the graph below.
Recall that the area of a semi-circle is given by:
[tex]\displaystyle A=\frac{1}{2}\pi r^2[/tex]
The volume of the solid will be the integral from x = 0 to x = 1 of area A. Since the diameter is given by y, then the radius is y/2. Hence, the volume of the solid is:
[tex]\displaystyle V=\int_0^1\frac{1}{2}\pi \left(\frac{y}{2}\right)^2\, dx[/tex]
Substitute:
[tex]\displaystyle V=\frac{1}{2}\pi\int_0^1\left(\frac{x^2}{2}\right)^2\, dx[/tex]
Simplify:
[tex]\displaystyle V=\frac{1}{2}\pi \int_0^1\frac{x^4}{4}\, dx[/tex]
Integrate:
[tex]\displaystyle V=\frac{1}{2}\pi \left[\frac{x^5}{20}\Big|_0^1\right][/tex]
Evaluate:
[tex]\displaystyle V=\frac{\pi}{40}\left((1)^5-\left(0\right)^5\right)=\frac{\pi}{40}\text{ units}^3[/tex]
The volume of the solid is π/40 cubic units.
Volume of a solid is the measure of the 3 dimensional space it occupies. The volume of the considered solid is obtained as [tex]\dfrac{\pi}{40} \: \rm unit^3[/tex]
How to find the volume of a three dimensional region bounded by curves?For that, we can try to find infinitesimally small 3-d region's volume, and then integrate that region over the dimensions available to get the total volume of the specified region.
We can also use the fact that continuous curves are almost linear and non-changing in infinitely zoomed region.
The given solid has base bounded by x-axis, [tex]y=x^2[/tex] and 0≤x≤1
Its three dimensional region is along the z axis, for each x, there is a semicircle perpendicular with radius being 'y'.
If we take [tex]dx[/tex]x-axis, then the curve [tex]y=x^2[/tex]cylinder(split from height because of semicircle)) with diameter y, and height [tex]dx[/tex]volume is : [tex]V_{dx} = \dfrac{1}{2} \times \pi (\dfrac{y}{2})^2 \times dx = \dfrac{\pi (x^2)^2}{8}dx = \dfrac{\pi x^4}{8} dx[/tex]
Integrating this for 0≤x≤1, we will get the volume of the three dimensional region needed as:
[tex]V = \int_0^4V_{dx} = \int_0^1 \dfrac{\pi x^4}{8} dx = \dfrac{\pi}{8} [\dfrac{x^5}{5}]^1_0 = \dfrac{\pi 1^4}{40} = \dfrac{\pi}{40}[/tex] (in cubic units).
Thus, the volume of the considered solid is obtained as [tex]\dfrac{\pi}{40} \: \rm unit^3[/tex]
Learn more about volume of three dimensional region here:
https://brainly.com/question/338504
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.
Answer:
Let x be the number of 3- point questions and y be the number of 5-points questions.
Step-by-step explanation:
Solve a" + 14a + 45 = 0 by factoring
Answer:
a = -3
Step-by-step explanation:
-3 + (14 * -3) + 45 = 0
-3 + -42 + 45 = 0
-3 + 3 = 0
So, the answer is -3
Hope this helps! :)
help me pls mathhh mhm
Answer:
f = -15
Step-by-step explanation:
3(f/3) equals f
3(-5) equals -15
The final equation becomes: f = -15
Help me please sjsjdjs it’s due in a few minutes
Answer:
The answer is the 3rd dot.
Step-by-step explanation:
hope this helps
Answer:
The one right below 8
Step-by-step explanation:
what is the value of A when we rewrite (32/5)^-2x as A^x
Answer:
[tex](\dfrac{25}{1024})^x[/tex]
Step-by-step explanation:
The given expression is :
[tex](\dfrac{32}{5})^{-2x}[/tex]
We need to rewrite it in the form of [tex]A^x[/tex].
We know that, [tex](\dfrac{1}{x})^{-a}=x^a[/tex]
So,
[tex](\dfrac{32}{5})^{-2x}=(\dfrac{5}{32})^{2x}\\\\=(\dfrac{5^2}{32^2})^x\\\\=(\dfrac{25}{1024})^x[/tex]
So, [tex]A=\dfrac{25}{1024}[/tex]. Hence, this is the required solution.
Answer: A = (32/5)^-2
Step-by-step explanation:
Write each product using an exponent.
9 × 9 × 9 × 9
Answer:
9^4 is what you’re looking for right?
Step-by-step explanation:
Answer:
9^4
Step-by-step explanation:
The number 9 is timed for 4 times (sorry for my broken english as my english is bad)
Solve
(Perimeter)
Rectangle
Side- 10
Side- 5
Please help will give brainliest
Answer:
One-third of the volume
Step-by-step explanation:
Volume of cylinder = πr²h
Volume of cone = (1/3)πr²h
At the book fair, Vald spends all of his money on new books. Pamela spends
2/3 as much as Vald. Eli spends 4/3 as much as Vald. Who spent the most?
The least?
Step-by-step explanation:
Lets take Vald spends $100 on the book fair which are all the money he had.
Pamela Spends 2/3 as much as Vald
Pamela Spends 2/3 x 100 = $66.67
Eli Spends 4/3 as much as Vald
Eli spends 4/3 x 100 = $133.33
From here, we can see Eli Spends the most and Pamela Spends the least.
HELP ME ASAP!!!! I’m very confused and I need help!! Thanks!
Answer:
Reason 2)The transitive property of congruenceStep-by-step explanation:
There are several sort of "obvious" properties of equality/congruence. Keeping them sorted out can be a bit of a trick.
A = A . . . . reflexive property
A = B ⇔ B = A . . . . symmetric property (erroneously cited in the proof)
A = B, B = C ⇒ A = C . . . . transitive property (the one needed in the proof)
__
Not to confuse the issue, but there is also the "substitution property of equality" that says if X = Y, then X can be substituted for Y or vice versa. In the end, the transitive property is an application of this, where we're substituting for B in the second equation, or for A in the first equation.
The A=B=C form of Statement 1) in the proof is what gives you the clue it is the transitive property that is wanted here.
PLEASEEEE I NEED IT ASAP 51 POINTS IS THE MAX I CAN GIVE PLEASEEEEE HELP ME
Answer:
A
Step-by-step explanation:
2(10+7)
2(17)
=34
Answer:
the answer is a
Step-by-step explanation:
10 times 2 plus 7 times 2=34
Which of the following describes an acute isosceles triangle?
A. At least one angle is 90° and two sides are equal in length.
B. All angles are less than 90° and two sides are congruent.
C. No two sides are equal in length and all angles are greater than 90°.
D All three sides are different lengths and all angles are less than 90°.
Please answer fast it’s for a test
For the following right triangle, find the side length x, Round your answer to the nearest hundredth.
12
x
6
Answer:
x=12
Step-by-step explanation:
simplify the expression
[tex] \sqrt[3]{686x {}^{4} } y {}^{7} [/tex]
The expression can be simplified as [tex]7x\sqrt[3]{ 2x} y^7[/tex].
What is an expression?An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)
A phrase in language may contain an action on its own, but it does not constitute a whole sentence.
Given:
The expression = [tex]\sqrt[3]{686x^4} y^7[/tex]
Factorize 686 we get 7³ × 2
= [tex]\sqrt[3]{7^3\times 2x^4} y^7[/tex]
= [tex]7x\sqrt[3]{ 2x} y^7[/tex]
Therefore, the expression can be simplified as [tex]7x\sqrt[3]{ 2x} y^7[/tex].
To know more about the expression:
https://brainly.com/question/13947055
#SPJ2
Find the distance between the points (4.5,-1.5), (4.5,7.25)
The distance is ____.
Answer:
8.75
Step-by-step explanation:
Hey y’all answers in the picture ABC or D. Plz help
Answer:
D
Step-by-step explanation:
Lets use the the chart. The (5,9) if the 5 was doubled that it would equal to 10. Now you subract 1 from it making it 9.
answer this please thanks
Answer:
4. c
6. e, a
Step-by-step explanation:
Hopefully, it correct
Three more than four times the difference of x and 2 is 36
Answer:
3+4 (x - 2) =36 x= 10.25
Step-by-step explanation:
Find the values of the variables and the lengths of the sides of the kite.
Answer: since you didnt answer mine.
Step-by-step explanation:
11. Saul's baseball bat has a mass of 1 kilogram His baseball has a mass
of 150 grams. What is the mass in grams of both items combined?
C. 1.150 grams
A. 1.15 grams
D. 115,000 grams
B. 115 grams
Approximately how many gallons are in
7 liters? (1 L -0.26 gal.)
A 1.8 gal
C 7.3 gal
B 6.7 gal
D 46 gal
Answer:
A po ang answer kahit icompute pa po.
Step-by-step explanation:
hope it helps you po!
Hey everyone it is math pleased help me it is due today
Answer:
93 in²Step-by-step explanation:
Given triangular prism with:
a = 1.5 in, b = 2 in, c = 2.5 in, l = 15 inTotal surface area is:
A = Pl + 2B, where P is the perimeter of base, B is area of baseConsidering all given values we have:
A = (1.5 + 2 + 2.5)*15 + 2*(1/2*1.5*2) = 93 in²Jerome wants to buy grass seed to cover his whole lawn, except for the pool. The pool is 7 1/2 m by 3 1/4 m. Find the area the grass seed needs to cover.
Answer:
24 [tex]\frac {3} {8}[/tex] m
Step-by-step explanation:
[tex]\frac{15}{2}[/tex]×[tex]\frac{13}{4}[/tex]
[tex]\frac{15x13}{2x4}[/tex]
Simplify
[tex]\frac{195}{8}[/tex]
Answer: 24 [tex]\frac{3}{8}[/tex] m
The area of the grass seed Jerome needs to cover is A = 34.375 m²
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the grass seed needs to cover be A
Now , the area of the lawn L = ( 11 3/4 ) x 5 m²
The area of the lawn L = 58.75 m²
where the length of the pool l= ( 7 1/2 ) m = 7.5 m
The width of the pool is w = ( 3 1/4 ) m = 3.25 m
Now , Area of Rectangle = Length x Width
On simplifying , we get
Area of the pool P = 7.5 x 3.25 = 24.375 m²
Now , the area of the grass seed needs to cover A = L - P
The area of the grass seed needs to cover A = 58.75 m² - 24.375 m²
The area of the grass seed needs to cover A = 34.375 m²
Therefore , the value of A is 34.375 m²
Hence , the area of the grass seed is 34.375 m²
To learn more about area of rectangle click :
https://brainly.com/question/15225905
#SPJ3
One half of a number , n is at most 24
Answer:
So if N is 24, then the number is 12.
Step-by-step explanation:
24 / 2 = 12
find the median of the list of data. 12, 18, 21, 25, 30, 43
PLEASE HELP ASAP!!! WILL MAKE YOU THE BRAINLYIST!!!!
Assume this dance floor is 20 feet long and 30 feet wide. How many people will fit on this dance floor if you assume each person will dance in a space that is 2 feet wide and 2 feet long?
A city has the population of 210,000 people. Suppose that each year the population grows by 7.5%. What will the population be after 13 years?
Answer:
6 5
Step-by-step explanation:
4 5 6 7
Using the order of operations, what are the steps for solving this expression? 40/8+3^2+(15-7)*2 Arrange the steps in the order in which they are performed.
9514 1404 393
Answer:
simplify parenthesesevaluate the exponential termdivide 40/8multiply 8*2add 5+9add 14+16Step-by-step explanation:
40/8+3^2+(15-7)*2 . . . . given
The order of operations tells you to start by evaluating expressions in parentheses. Here, that is the subtraction of 7 from 15.
40/8 +3^2 +8*2 . . . . (15-7) = 8
Then you evaluate exponential terms.
40/8 +9 +8*2 . . . . . 3^2 = 9
Then perform multiplication and division, left to right. Here, division is first, then multiplication.
5 +9 +8*2 . . . . . divide 40/8 = 5
5 +9 +16 . . . . . . multiply 8*2 = 16
Finally, perform addition and subtraction, left to right.
14 +16 . . . . add 5+9
30 . . . . . . . add 14+16
Answer:
it is 8
Step-by-step explanation: