Answer:
Null hypotheses = H₀ = σ₁² ≤ σ₂²
Alternative hypotheses = Ha = σ₁² > σ₂²
Test statistic = 1.9
p-value = 0.206
Since the p-value is greater than α therefore, we cannot reject the null hypothesis.
So we can conclude that the night shift workers don't show more variability in their output levels than day workers.
Step-by-step explanation:
Let σ₁² denotes the variance of night shift-workers
Let σ₂² denotes the variance of day shift-workers
State the null and alternative hypotheses:
The null hypothesis assumes that the variance of night shift-workers is equal to or less than day-shift workers.
Null hypotheses = H₀ = σ₁² ≤ σ₂²
The alternate hypothesis assumes that the variance of night shift-workers is more than day-shift workers.
Alternative hypotheses = Ha = σ₁² > σ₂²
Test statistic:
The test statistic or also called F-value is calculated using
Test statistic = Larger sample variance/Smaller sample variance
The larger sample variance is σ₁² = 38
The smaller sample variance is σ₂² = 20
Test statistic = σ₁²/σ₂²
Test statistic = 38/20
Test statistic = 1.9
p-value:
The degree of freedom corresponding to night shift workers is given by
df₁ = n - 1
df₁ = 9 - 1
df₁ = 8
The degree of freedom corresponding to day shift workers is given by
df₂ = n - 1
df₂ = 8 - 1
df₂ = 7
We can find out the p-value using F-table or by using Excel.
Using Excel to find out the p-value,
p-value = FDIST(F-value, df₁, df₂)
p-value = FDIST(1.9, 8, 7)
p-value = 0.206
Conclusion:
p-value > α
0.206 > 0.05 ( α = 1 - 0.95 = 0.05)
Since the p-value is greater than α therefore, we cannot reject the null hypothesis corresponding to a confidence level of 95%
So we can conclude that the night shift workers don't show more variability in their output levels than day workers.
What value of b will cause the system to have an infinite number of solutions?
A system of equations. y equals 6 x plus b. negative 3 x plus StartFraction one-half EndFraction y equals negative 3.
A coordinate grid with a line labeled negative 3 x plus StartFraction one-half EndFraction y equals negative 3 and passes through the points (1, 0) and (0, negative 6).
-6
-3
3
6
Answer:
-6 on edge
Step-by-step explanation:
The value of b that causes the system of equations to have infinite solutions will be: b = -6
System with infinite solutions:A system of linear equations will have infinite solutions only when both equations represent the same line.
In this case our equations are:
y = 6x + b
-3x + (1/2)*y = -3
So the value of b needs to be such that these two equations are equal
Let's isolate y in the second equation:
(1/2)*y = -3 + 3x
y = -3*2 + 3x*2 = -6 + 6x
Then we must have:
6x - 6 = 6x + b
-6 = b
Thus, the value of b that causes the system to have infinite solutions is b = -6.
If you want to learn more about systems of equations, you can read:
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ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. F(x) = 3(x - 2)² - 2
Step-by-step explanation:
→The function F(x) narrowed, meaning the absolute value being multiplied to the function is greater than 1.
→The function F(x) flipped over the x-axis, this means that the number being multiplied has to be a negative.
→The function F(x) shifted to the left 2 units, this means there needs to be a 2 being added.
→The function F(x) shifted downwards 2 units, meaning there needs to be a 2 being subtracted from the whole function.
This gives us the correct answer of "B. F(x) = 3(x - 2)² - 2."
Write an equation of the line containing the point (2,1) and perpendicular to the line 5x – 2y = 3.
So first, you want to isolate your Y. To do this, you must get it alone on ONE SIDE of the equation.
5x - 2y = 3
-5x -5x
[tex]\frac{-2y}{-2}[/tex] = [tex]\frac{3-5x}{-2}[/tex]
ANSWER: y = \frac{3-5x}{-2}
What’s the correct answer for this?
Answer:
270 inches³
Step-by-step explanation:
Volume of carton = wlh
Where w is width, h is height and length is l
V = (9)(5)(6)
V = 270 inches³
What is the difference? Negative 6 minus (11)
Answer:
-17
Step-by-step explanation:
-6-11=-17
Answer:
the answer is -17
Step-by-step explanation:
A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is this distance?
Answer:
150
Step-by-step explanation:
If you draw a diagram, this will be a rectangle and the line across cuts it into a right triangle, with a base of 120 and a height of 90. The need to know the length of the hypotenuse of the triangle, so we can use the pythagorean theorem.
90^2 + 120^2 = c^2
c=150
Question 14
For the following system of equations, determine how many solutions there are.
6x + y = -1 and -6x - 4y = 4
Answer:
The system of equations has a one unique solution
Step-by-step explanation:
To quickly determine the number of solutions of a linear system of equations, we need to express each of the equations in slope-intercept form, so we can compare their slopes, and decide:
1) if they intersect at a unique point (when the slopes are different) thus giving a one solution, or
2) if the slopes have the exact same value giving parallel lines (with no intersections, and the y-intercept is different so there is no solution), or
3) if there is an infinite number of solutions (both lines are exactly the same, that is same slope and same y-intercept)
So we write them in slope -intercept form:
First equation:
[tex]6x+y=-1\\y=-6x-1[/tex]
second equation:
[tex]-6x-4y=4\\-6x=4y+4\\-6x-4=4y\\y=-\frac{3}{2} x-1[/tex]
So we see that their slopes are different (for the first one slope = -6, and for the second one slope= -3/2) and then the lines must intercept in a one unique point. Therefore the system of equations has a one unique solution.
a newborn calf weighs 40 kilograms. Each week its weight increases by 5%. Let W be the weigh in kilograms of the calf after t weeks
Simplify the expression. Write the answer using scientific notation. (7 × 105)2 a. 4.9 × 1010 b. 4.9 × 1011 c. 4.9 × 109 d. 49 × 1010
Answer:
b. 4.9 × 1011
Step-by-step explanation:
Using scientific notation is similar to expressing in standard form. Given that (7 × 105)2
We open the parenthesis. This may first be expressed as
7² × 10⁽⁵⁾²
Then expand,
= 49 × 10¹⁰
To put in scientific notation, 49 = 4.9 × 10
Hence the expression becomes
= 4.9 × 10 × 10¹⁰
Using the laws of indices
= 4.9 × 10¹¹ in scientific notation
Answer:
4.9 × 1011
Step-by-step explanation:
I did it in grandpoint
of 5 points)
2. The two figures are similar. Write the similarity statement. Justify you
37.5
(Score for Question 2:
45
Y
40
30
Z
Answer:
Answer:
f\left(x\right)=x^3-x
Step-by-step explanation:
Solve:
5 thousands
ones
5 thousand ones is the same as 5,000. Each one takes up one place.
Answer:
5000
Step-by-step explanation:
What is the slope of line p?
ty
4
DONE
===========================================================
Explanation:
Start at the point (0,0) which is the origin. Move up 2 units then to the right 3 units to arrive at the next blue point (3,2). We see that
rise = 2
run = 3
slope = rise/run = 2/3
----------
If you want to use the slope formula, then you would say
m = (y2 - y1)/(x2 - x1)
m = (2 - 0)/(3 - 0)
m = 2/3
I used the two points (0,0) and (3,2). You could use any two points you like on this line.
Side note: The slope is positive because we are moving uphill as you move from left to right along this orange line.
The slope of the line p is given by 2/3.
What is Slope of a Straight line?The tangent value of the angle which the straight line makes with the positive X axis is called the slope of that particular straight line.
If s line passes through two points (a,b) and (c,d) then the slope of the line (m) is given by,
m = (d-b)/(c-a)
Here in the given figure we can see that the given line p passes through (3,2), (-3,-2) and the origin (0,0)
then taking any two points out of that three (3,2), (0,0) we get, the slope of p is given by,
m = (2-0)/(3-0) = 2/3
Hence slope of line p is given by 2/3.
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PLEEEASE HELLLLP!!!!!!! If x+7=2y and y=2x−1, what is the value of y?
Answer:
13
Step-by-step explanation:
We can add 1 to both sides of the second equation and divide by 2 to get
x = (y-1)/2
We can then substitute x in the first equation to get
(y-1)/2 + 7 = 2y
Multiply by 2
y-1 + 14 = 2y
Subtract y and combine like terms
y = 13
A prism is filled with 3 layers of cubes. Each layer has 25 cubes. The volume of each cube is 1 cubic inch. What is the volume of the prism?
Answer:
The volume of the prism is 75 cubic inches
Step-by-step explanation:
The volume of the prism is the amount of space contained on the interior of the prism.
Now we have that this entire space is filled with cubes of defined volumes. Therefore, to get the volume of the prism, we can simply get the total volume occupied by all the cubes. This should give us our answer.
From the information we are given, we know that the there are 3 layers of cubes each containing 25 cubes.
This gives the total number of cubes to be 3 X 25 = 75 cubes in total
We also know that the volume of 1 cube is 1 cubic inch.
Hence the volume of 75 cubes will be 75 X 1 cubic inch = 75 cubic inches.
write the equation of the line that is parallel to 2x-y=15 and passes through the point (3,7)
Answer:
work is shown and pictured
Simplify the answer pls
Answer:
Step-by-step explanation:
24/3 - 4
8 - 4 = 4
need help in b and c. show calculation pls.
√(16 - x^2) is defined only for -4 ≤ x ≤ 4, and is continuous over this domain, so
[tex]\displaystyle\lim_{x\to-4^+}\sqrt{16-x^2}=\sqrt{16-(-4)^2}=0[/tex]
From the other side, the limit does not exist, because all x < -4 do not belong to the domain.
Taken together, the two-sided limit also does not exist.
A manufacturing machine has a 40% defect rate. If 131 items are chosen at random, answer the following. a) Which is the correct wording for the random variable? rv X = the number of 131 randomly selected items that are defective Correct b) Pick the correct symbol: n Correct = 131 c) Pick the correct symbol: p Correct = 0.4
Answer:
A manufacturing machine has a 40% defect rate. If 131 items are chosen at random, then:
The random variable, X=Number of 131 randomly selected items that are defective.Number of Items, n=131The point estimate of defective items, p=40%=0.4Is –57 + 19 positive or negative?plz answerrrrrr ill mark 1st as brainliest
Answer: negative
Step-by-step explanation:
because –57 + 19= -38
and negative plus positive is negative
so the answer is negative
Hope this helps :)
Answer:
Negative
Compare the absolute values (how far the number is away from zero)
57 is bigger than 19
since 57 is negative and bigger than 19 when they add the sum will still be negative
Step-by-step explanation:
The m∠ABC = (10x-5)°and m∠CBD=35°. If the angles are supplementary, find the value of x.
Answer:
15
Step-by-step explanation:
Supplementary angles completes each other to 180°
if the teo angles are supplementary here the the sum of 10x - 5 + 35 should be 180°
10x - 5 + 35 = 180
10x + 30 = 180
10x = 150
x = 15
An icicle it's in the shape of an inverted cone with a diameter of 12 m m and a height of 100 mm. How much Frozen water is in the icicle? Round to the nearest hundredth.
Answer:
3768 mm ^ 3
Step-by-step explanation:
We have that the volume of a cone is given by:
V = 1/3 * Ac * h
Where Ac is the area of the circle, we know that the radius is half the diameter then:
r = d / 2
r = 12/2
r = 6
And Ac is equal to:
Ac = pi * r ^ 2
replacing:
Ac = 3.14 * 6 ^ 2
Ac = 113.04
113.04 mm ^ 2 is the area of the circle, replacing the volume form knowing that h = 100
V = 1/3 * 113.04 * 100
V = 3768
Therefore they fit a total of 3768 mm ^ 3
Which expression is equivalent to 4+2(1+3x)
Answer:
I'm glad you asked!
Step-by-step explanation:
OK,let's simplify the number for a equivalent expression.
[tex]4+2(1+3x)[/tex]
Distribute:
[tex]=4+(2)(1)+(2)(3x)[/tex]
[tex]= 4+2+6x[/tex]
Combine Like Terms:
[tex]=4+2+6x[/tex]
[tex]=(6x)+(4+2)[/tex]
[tex]=6x+6[/tex]
The Final Answer is : [tex]6x+6[/tex]
The expression that is equivalent to 4+2(1+3x) is 6x+6.
What is an Algebraic expression?Mathematical expressions that are made up of constants, variables, and coefficients that are combined using algebraic operations such as multiplication, addition, subtraction, and division are called Algebraic expressions.
How do simplify the algebraic expression?Given, 4+2(1+3x)
Firstly distribute 2(1+3x) to get 2+6x then,
4+2(1+3x)
=4+2+6x
=6x+6
Thus, 4+2(1+3x)=6x+6
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If P(A)=0.4, P(A and B)=0.2,and P(A or B)=0.5, What is P(B)
Answer:
[tex]\boxed{\ P(B)=0.3 \ }[/tex]
Step-by-step explanation:
Hi,
We know that
P(A or B)=P(A)+P(B)-P(A and B)
so P(B)= P(A or B) - P(A) + P(A and B)
so
P(B) = 0.5 - 0.4 + 0.2 = 0.3
thanks
Please answer this correctly
Answer:
A =12.56 m^2
Step-by-step explanation:
Find the area of a circle with radius 4
A = pi r^2
A = 3.14 * 4^2
A =50.24
Since this is 1/4 of the circle, multiply by 1/4
A = 1/4 * 50.24
A =12.56 m^2
Answer:
12.56
Step-by-step explanation:
the formula for the area of a circle is the following:
[tex]\pi r^{2}[/tex]
so divide that formula by 4 to get a quarter and plug in the radius for r.
[tex](\pi )(4^2)/4= 12.56[/tex]
Indicate in standard form equation of the line passing through the given 
Answer:
x - 3y= -14
Step-by-step explanation:
Slope is rise over run
m = (6-5)/(4-1) = 1/3
we write in slope-intercept form:
y = 1/3x + b
solve for b by plugging in either point
i'm going to plug in H
5 = 1/3 + b
b = 14/3
we get our equation
y = 1/3x + 14/3
now re-write it in standard form
-1/3x + y = 14/3
make it pretty
x - 3y = -14
An office building loses a third of its heat between sundown and midnight and an additional half of the original amount of heat between midnight and 4 AM. If five-eighths of the remaining heat is lost between 4 AM and 5 AM, what proportion of the total heat loss occurs between 5 AM and sunrise?
Answer:
[tex]\dfrac{1}{16}[/tex]
Step-by-step explanation:
Proportion of Heat Loss Between sundown and midnight[tex]=\dfrac{1}{3}[/tex]
Proportion of Heat Loss between midnight and 4 AM [tex]=\dfrac{1}{2}[/tex]
Proportion of Total Heat Already Lost [tex]=\dfrac{1}{3}+\dfrac{1}{2} =\dfrac{5}{6}[/tex]
Proportion of Remaining Heat [tex]=1-\dfrac{5}{6}=\dfrac{1}{6}[/tex]
Between 4 AM and 5 AM, five-eighths of the remaining heat is lost.
Proportion of Heat Loss between 4 AM and 5 AM= [tex]\dfrac{5}{8}$ X \dfrac{1}{6} = \dfrac{5}{48}[/tex]
Therefore, Proportion of Remaining Heat Left [tex]=\dfrac{1}{6}- \dfrac{5}{48}=\dfrac{1}{16}[/tex]
We therefore say that:
[tex]\dfrac{1}{16}$ of the total heat loss occurs between 5 AM and sunrise.[/tex]
Solve sin2x=-1/2 on the interval 0≤ angle≤360°
Answer:
x=135
Step-by-step explanation:
We know that sin(270) = -1/2
So 2x = 270
x = 135
What is the value of the expression 1/7 ÷8 A 1/12 B 1/35 C 5/7 D 6/7
Pss. Its multiple choice okay dont get confused
Answer:
Looks like it's none.
Step-by-step explanation:
[tex]\frac{1}{7}*\frac{1}{8}=\frac{1}{56}[/tex]
Answer:
Step-by-step explanation:B and D I belive.
what are the solutions
Answer:
2 and -8
Step-by-step explanation:
[tex]x^2+6x-6=10 \\\\x^2+6x-16=0 \\\\(x+8)(x-2)=0 \\\\x=2, -8[/tex]
Hope this helps!
6x +7y=-46 3x-2y=32 solve this system of linear equations
Hello
We have two equations and need to find x and y
(1) 6x+7y=-46
(2) 3x-2y=32
multiply (2) by 2 it gives
(2') 6x-4y=64
(1) - (2') gives
6x+7y-6x+4y=-46-64 = -110
so 11y = -110
y = -10
replace in (2) it gives
3x+20=32
3x=12
x = 12/3 = 4
the solution is (4,-10)
do not hesitate if you need further explanation
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