Company a samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company b samples 21 workers and their average time with the company is 4.6 years with a standard deviation 4.6 years
Company a samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company b samples 21 workers and their average time with the company is 4.6 years with a standard deviation 4.6 years
The populations are normally distributed. Determine the:
Hypothesis in symbolic form?
Determine the value of the test statistic?
Find the critical value or value?
determine if you should reject null hypothesis or fail to reject?
write a conclusion addressing the original claim?
Answer:
Step-by-step explanation:
GIven that :
Company A
Sample size n₁ = 16 workers
Mean [tex]\mu[/tex]₁ = 5.2
Standard deviation [tex]\sigma[/tex]₁ = 1.1
Company B
Sample size n₂ = 21 workers
Mean [tex]\mu[/tex]₂ = 4.6
Standard deviation [tex]\mu[/tex]₂ = 4.6
The null hypothesis and the alternative hypothesis can be computed as follows:
[tex]H_o : \mu _1 = \mu_2[/tex]
[tex]H_1 : \mu _1 > \mu_2[/tex]
The value of the test statistics can be determined by using the formula:
[tex]t = \dfrac{\overline {x_1}- \overline {x_2}}{\sqrt{\sigma p^2( \dfrac{1}{n_1}+\dfrac{1}{n_2})}}[/tex]
where;
[tex]\sigma p^2= \dfrac{(n_1 -1) \sigma_1^2+ (n_2-1)\sigma_2^2}{n_1+n_2-2}[/tex]
[tex]\sigma p^2= \dfrac{(16 -1) (1.1)^2+ (21-1)4.6^2}{16+21-2}[/tex]
[tex]\sigma p^2= \dfrac{(15) (1.21)+ (20)21.16}{35}[/tex]
[tex]\sigma p^2= \dfrac{18.15+ 423.2}{35}[/tex]
[tex]\sigma p^2= \dfrac{441.35}{35}[/tex]
[tex]\sigma p^2= 12.61[/tex]
Recall:
[tex]t = \dfrac{\overline {x_1}- \overline {x_2}}{\sqrt{\sigma p^2( \dfrac{1}{n_1}+\dfrac{1}{n_2})}}[/tex]
[tex]t = \dfrac{5.2- 4.6}{\sqrt{12.61( \dfrac{1}{16}+\dfrac{1}{21})}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{12.61( \dfrac{37}{336})}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{12.61(0.110119)}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{1.38860059}}[/tex]
[tex]t = \dfrac{0.6}{1.178388981}[/tex]
t = 0.50917
degree of freedom df = ( n₁ + n₂ - 2 )
degree of freedom df = (16 + 21 - 2)
degree of freedom df = 35
Using Level of significance ∝ = 0.05, From t-calculator , given that t = 0.50917 and degree of freedom df = 35
p - value = 0.3069
The critical value [tex]t_{\alpha ,d.f}[/tex] = [tex]t_{0.05 , 35}[/tex] = 1.6895
Decision Rule: Reject the null hypothesis if the test statistics is greater than the critical value.
Conclusion: We do not reject the null hypothesis because, the test statistics is lesser than the critical value, therefore we conclude that there is no sufficient information that the claim that company a retains it workers longer than more than company b.
PLEASE HELP TO BE MARKED THE BRAINLIEST
Answer:
4. m_LON + m_MON = m_LON; m_JKL + m_IKH = m_HKJ
Step-by-step explanation:
Both interior angles of each add up to m_LON:m_HKJ
To prove this we show the interior angles add + sign to each prove LON angle, and : colon separates from the proof of m_JKL+m_IKH= m_HKJ.
Solve for x: -2x - 4 > 8
x<-6
X > -6
x<-2
x>-2
Answer:
x < -6
Step-by-step explanation:
-2x - 4 > 8
-2x > 12
x < -6, you have to flip the inequality when you multiply or divide by a negative
Answer:
a
Step-by-step explanation:
One stool rocks slightly from side to side on your kitchen floor. Which of the two stools could this possibly be? Explain your answer Choices: 3 legged stool, 4 legged stool
Answer:
The four legged stool is the one that rocks slightly from side to side. The three legged stool does not.
Step-by-step explanation:
The four legged stool is the one that rocks slightly because the three legs determine a plane, and the three legs are stuck on that single plane.
Please answer this question now
Answer:
Surface Area = 85.75 ft²
Step-by-step explanation:
Surface area of pyramid = ½(Perimeter of triangular base * slant height of pyramid) + Area of triangular base
Perimeter of triangular base = sum of all sides of the triangular base = 5+5+5 = 15 ft
Slant height of pyramid = 10 ft
Area of triangular base = ½*base of triangle*height of triangle = ½*5*4.3 = 10.75 ft²
Plug in the above values:
Surface Area = ½(15*10) + 10.75
= (15*5) + 10.75
= 75 + 10.75
Surface Area = 85.75 ft²
Solve the equation
(If possible please show work)
Answer:
Step-by-step explanation:
-8 + 8a = -12 + 4a
4a - 8 = -12
4a = -4
a = -1
Answer:
a = -1
Step-by-step explanation:
[tex]4(-2+2a) = -12 +4a\\-8+8a=-12+4a\\8a = -4 +4a\\4a=-4\\\frac{4a}{4} =\frac{-4}{4} \\a=-1[/tex]
I hope that makes since... I tried to show my work the best I could.
Carly has averaged four goals per game for the first eight games of the indoor soccer season (which runs for 10 games)
She wants to finish the season with an average of 5 goals per game.
How many goals does she need to score in total in the last two games to achieve this?
Answer:
9
Step-by-step explanation:
i did 8x4 which is 32
and knowing how to do averages i knew the total of the numbers was going to be divided by the amount of numbers, so i knew that it had to add up to 50 because 50/10 is 5.
so i knew i needed 18 more points, 18/2 = 9 so
4(8) + 9(2) = 32 + 18 = 50
Complete the square to solve 4x2 + 24x = 4.
Answer:
x = - 3 ± [tex]\sqrt{10}[/tex]
Step-by-step explanation:
Given
4x² + 24x = 4 ( divide through by 4 )
x² + 6x = 1
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(3)x + 9 = 1 + 9
(x + 3)² = 10 ( take the square root of both sides )
x + 3 = ± [tex]\sqrt{10}[/tex] ( subtract 3 from both sides )
x = - 3 ± [tex]\sqrt{10}[/tex]
Answer:
X=1/8
Step-by-step explanation:
Calculate the product 4x×2 + 24x = 4
Collect like terms 8x + 24x = 4
Divide both sides of the equation by "32" 32x = 4
Solution x = 1/8
You want to borrow three rock CDs from your friend. She loves math puzzles and she always makes you solve one before you can borrow her stuff. Here's the puzzle: Before you borrow three CDs, she will have 39 CDs. She will have half as many country CDs as rock CDs, and one-fourth as many soundtracks as country CDs. How many of each type of CD does she have after you borrow three rock CDs?
Answer:
Rock CD's=21
Country CD's=12
Soundtrack CD's=3
Step-by-step explanation:
let
r= rock CD's
c = country CD's
s = soundtrack CD's
Total CD's=r + c + s =39
2c=r
c/4=s
2c+c+c/4=39
8c+4c+c=156
13c=156
c=12
Substitute c=12 into 2c=r
2c=r
3(12)=r
24=r
r=24
Substitute c=12 into c/4=s
c/4=s
12/4=s
3=s
s=3
Therefore, she has
c=12
s=3
r=24
before she borrowed you 3 rock CD's
Sha has
r=21
s=3
c=12
after you borrowed 3 rock CD's
NEED ANSWER ASAP!! PLEASE!!! The length of a rectangle is 1 foot more than twice the width. Write an expression that represents the length.
Answer:
The expressión that represents the length:
a = 2w + 1
a = length of the rectangle
w = width of the rectangle
plz help ASAP! last question thank u
Answer:
The correct Option is Option A
Step-by-step explanation:
how do i solve this ?(x+3)(x-5)=
[tex](x+3)(x-5)=x^2-5x+3x-15=x^2-2x-15[/tex]
Answer:
Step-by-step explanation:
Use FOIL method
(x + 3)(x - 5) = x*x + x *(-5) + 3*x + 3*(-5)
= x² - 5x +3x - 15 {add like terms}
= x² - 2x -15
please help me on this
Answer:
if an angle measures more than 90 degrees, then the angle is obtuse
Anna is planting in her garden the package says she needs to use 4 punds od fertilizer for 120 sqft the area of annas yard is 180 how much fertilizer is needed for the 180 sqft garden
Answer:
6 pounds
Step-by-step explanation:
The area of Anna's garden = 180 square feet
From the question, we know that:
120 square ft = 4 pounds of fertilizer
180 square ft = y
Cross Multiply
120 × y = 4 × 180
y = 4 × 180/120
y = 720/120
y = 6 pounds
Therefore, the amount of fertilizer that is needed for Anna's 180 square feet garden is 6 pounds.
29. A painter leans a ladder against the side of a
house that is 3 feet from the base. If the top
of the ladder reaches 16 feet, how long is the
ladder ?
HELP! answer if you can!
Answer:
16.2788 feet
Step-by-step explanation:
a²+b²=c²
3²+16²=c²
9+256=c²
265=c²
c=√265
c=16.2788 feet
If the ladder is 3 feet from the base of the house and the top is 16 feet from the base then the length of ladder is approximately 16.2788 feet long.
What is pythagoras theorem?Pythagoras theorem says that in a right angled triangle the square of hypotenuse of triangle is equal to the sum of squares of base and perpendicular of that respective triangle.
[tex]H^{2} =P^{2} +B^{2}[/tex] where H is hypotenuse, P is perpendicular, B is base of triangle.
How to find length of ladder?If a painter leans a ladder against a wall then it forms a right angled triangle so in this we will apply pythagoras theorem to find the length of ladder.
let the length of ladder be h so,
[tex]h^{2} =3^{2} +16^{2}[/tex]
[tex]h^{2} =9+256[/tex]
[tex]h^{2} =265[/tex]
h=[tex]\sqrt{265}[/tex]
h=16.2788 feet.
Hence the length of ladder is 16.2788 feet.
Learn more about pythagoras theorem at https://brainly.com/question/343682
#SPJ2
You are hiking and are trying to determine how far away the nearest cabin is, which happens to be due north from your current position. Your friend walks 245 yards due west from your position and takes a bearing on the cabin of N 22.6°
e. How far are you from the cabin?
Answer:
589 yards
Step-by-step explanation:
This is a question that requires the use of trigonometric functions.
The trigonometric function to be used here is the tangent function.
tan θ = Opposite side/ Adjacent side
In the question, we are told
Your friend walks 245 yards due west from your position = Opposite side
Your friend's takes a bearing on the cabin of N 22.6° = θ
Your distance from the cabin = Adjacent side
Hence,
tan 22.6 ° = 245/ Adjacent side
Cross Multiply
Adjacent side = 245/ tan 22.6°
Adjacent side = 588.57469726 yards.
Therefore, your distance from the cabin approximately to the nearest yard(whole number) = 589 yards
Identify the sample as biased or unbiased and describe its type. John wanted to know about the popularity of a particular movie. He surveyed 20% of the people in 5 different theaters.
Answer: unbiased; simple random sampling
Step-by-step explanation:
From the question, we are informed that John wanted to know about the popularity of a particular movie and that he surveyed 20% of the people in 5 different theaters.
This is an unbiased sample. This is because everybody at the theaters have an equal chance of being chosen by John.
Also, it's a simple random sampling. This is because a subset of the entire population is randomly selected.
[tex] \frac{15x - 8 }{3} + \frac{9x - 3}{2} [/tex]
Greetings from Brasil...
Here is the problem:
[(15X - 8)/3] + [(9X - 3)/2]
Let's multiply everything by 6
[6.(15X - 8)/3] + [6.(9X - 3)/2]
[2.(15X - 8)] + [3.(9X - 3)]
30X - 16 + 27X - 9
57X - 25There are 4 colas, 1 ginger, 7 root beers, and 6 cherry sodas in a cooler. What are the odds of choosing a ginger ale? Give your answer in a proportion in lower terms.
Answer:
Step-by-step explanation:
the odds of choosing a ginger ale is 1/21
What’s is the formula for the fill arithmetic sequence? -9,-2,5,12
Answer:
a +d = a2
Step-by-step explanation:
-2 - (-9) =
-2+9=7
a + d = a2
What is the greatest common factor of 30, 90 and 75?
i promise i will mark as brainiest
A triangle has sides of lengths 16, 63, and 65. Is it a right triangle? Explain.
Answer:
Yes
Step-by-step explanation:
If a triangle is a right triangle, the 3 side lengths will check out in the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
where a and b are the legs and c is the hypotenuse.
The legs are the 2 shorter lengths and the hypotenuse is the longest length. The 3 side lengths are: 16,63 and 65. Therefore, 16 and 63 are the legs and 65 is the hypotenuse.
a=16
b=63
c=65
[tex]16^2+63^2=65^2[/tex]
Evaluate each exponent.
16^2=16*16=256
[tex]256+63^3=65^2[/tex]
63^2=63*63=3969
[tex]256+3969=65^2[/tex]
65^2=65*65=4225
[tex]256+3969= 4225[/tex]
Add 256 and 3969
[tex]4225=4225[/tex]
The statement above is true; 4225 is equal to 4225. Therefore, this is a right triangle because the side lengths check out when plugged into the Pythagorean Theorem.
Find value of k
from below eqn
[tex] {2x}^{2} + 7xy + 3y {}^{2} - 5x - 5y + k = 0[/tex]
Answer:
k=10BY DPING PROCESS IT BECOME
Determine what type of model best fits the given situation: Farmer Joe has 1,000 bushels of corn to sell. Presently the market price for corn is $5.00 a bushel. He expects the market price to increase by $0.15 per week. For each week he waits to sell, he loses ten bushels due to spoilage.
Answer:
C. Quadratic model
Step-by-step explanation:
Determine what type of model best fits the given situation: Farmer Joe has 1,000 bushels of corn to sell. Presently the market price for corn is $5.00 a bushel. He expects the market price to increase by $0.15 per week. For each week he waits to sell, he loses ten bushels due to spoilage. A. none of these B. exponential C. quadratic D. linear
Given:
The quantity of corn Farmer Joe has to sell = 1,000 bushels
The present market price for corn = $5.00 a bushel
The amount by which he expects the market price to rise per week =$0.15
The number of bushels lost to spoilage per week = 10
The price of the corn per bushel with time = 5 + 0.15×t
The amount of corn left with time= 1000 - 10×t
Where;
t = Time in minutes
Value of the corn = Amount of corn left × Price of corn
Value of the corn = (1000 - 10×t) × (5 + 0.15×t)
=(1000-10t) × (5+0.15t)
=5,000 + 150t - 50t - 1.5t²
= -1.5t² +100t + 5000
Value of the corn= -1.5t² +100t + 5000.
It is a quadratic model
I don't think this is correct plz check me
Answer:
The answer is the first one
Step-by-step explanation:
The cost of an adult ticket is $15
The price of an adult ticket is 1/2 the price of a student ticket plus $8
x is the cost of a student ticket, so
1/2(x) + $8 = $15
The price of tiling a room varies directly as the size of the room. Sam is laying tile in his kitchen. If the tiling costs $4,224.00 for 264 square feet, what is the size of a kitchen that costs $3,824.00? A. 239 square feet B. 256 square feet C. 7,648 square feet D. 63,096 square feet
Answer:
The answer is option AStep-by-step explanation:
Let the price of the room be p
Let the size of the room be s
To find the size of a kitchen that costs $3,824.00 we must first find the relationship between them
The statement
The price of tiling a room varies directly as the size of the room is written as
p = kswhere k is the constant of proportionality
when
p = $4,224.00
s = 264 square feet
Substitute the values into the expression to find k
That's
4224 = 264k
Divide both sides by 264
k = 16
So the formula for the variation is
p = 16swhen
p = 3824
[tex]s = \frac{p}{16} [/tex]
[tex]s = \frac{3824}{16} [/tex]
s = 239
The final answer is
239 square feet
Hope this helps you
What is the prime factorization of 270?
Answer:
[tex]\boxed{3^3 * 2 * 5}[/tex]
Step-by-step explanation:
Look at the image below ↓
Answer:
16 factors of 270
Step-by-step explanation:
1*270
2*135
3*90
5*54
6*45
9*30
10*27
15*18
Please help solve this, I solved it on my own but I think my calculations are wrong. here is the problem,
b-(b+a×4c÷4); use; a=-6, b=1, and c=2?
Hi there! Hopefully this helps!
----------------------------------------------------------------------------------------------------------
Answer: 12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~First we need to substitute the value of the variable into the expression and simplify.
b-(b+a×4c÷4) = 1 - (1 + -6 × 4(2) ÷ 4).
Now we need to solve 1 - (1 + -6 × 4(2) ÷ 4).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1 - (1 + -6 × 4(2) ÷ 4)
|
| First, we cancel out 4 and 4.
\/
1 - (1 - 6 × 2)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Next, we multiply -6 and 2 to get -12.
1 - (1 - 12)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Then we subtract 12 from 1 to get -11.
1 - (-11)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The opposite of -11 is 11.
1 + 11.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Add 1 and 11 to get, you guessed it, 12!Answer:
Answer: 12
Hope this helps
Suppose the population of a country is 100 people: 40 work full-time, 20 work half-time but would prefer to work full-time, 10 are looking for a job, 10 would like to work but are so discouraged they have given up looking, 10 are not interested in working because they are full-time students, and 10 are retired. What is the number of unemployed
Answer:
10
Step-by-step explanation:
Those people who are actively seeking for a job are counted as unemployed. Underemployment is not considered as unemployment. Those who have given up looking for jobs are also not considered as unemployed as well. Hence there are 10 unemployed people.
