Answer:
The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.
Step-by-step explanation:
A machine, when working properly, produces 5% or less defective items.
This means that the null hypothesis is:
[tex]H_0: p \leq 0.05[/tex]
Test if the percentage of defective items produced by this machine is greater than 5%.
This means that the alternate hypothesis is:
[tex]H_a: p > 0.05[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.05 is tested at the null hypothesis:
This means that [tex]\mu = 0.05, \sigma = \sqrt{0.05*0.95}[/tex]
A random sample of 300 items taken from the production line contained 27 defective items.
This means that [tex]n = 300, X = \frac{27}{300} = 0.09[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.09 - 0.05}{\frac{\sqrt{0.05*0.95}}{\sqrt{300}}}[/tex]
[tex]z = 3.18[/tex]
Pvalue of the test:
Testing if the mean is greater than a value, which means that the pvalue of the test is 1 subtracted by the pvalue of Z = 3.18, which is the probability of a finding a sample proportion of 0.09 or higher.
Looking at the Z-table, Z = 3.18 has a pvalue of 0.9993
1 - 0.9993 = 0.0007
The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.
A company has 500 employees, and 60% of them have children. Suppose that we randomly select 4 of these
employees.
Which of the following would find the probability that exactly 3 of the 4 employees selected have children?
The probability that exactly 3 of the 4 employees selected will have children is given by binomial distribution formula ⁴C₃(0.60)³(0.40)
What is a Binomial Distribution?
The binomial distribution is a type of probability distribution that predicts the likelihood of obtaining one of two outcomes given a set of inputs. It summarizes the number of tries where each trial has the equal chance of producing the same result.
The formula for Binomial Distribution is given by
P ( x ) = ⁿCₓ pˣq⁽¹⁻ˣ⁾
where
n = number of trials
x = number of successes
p = probability of getting a success in one trial
q = probability of getting a failure in one trial
q = 1 - p
Given data ,
Let the total number of employees be = 500
Now , the probability of success of selecting employees having children is given by p = 0.60
So , the value of q = 1 - p
q = 1 - 0.60
q = 0.40
So , The probability that exactly 3 of the 4 employees selected will have children is given by binomial distribution formula
where,
P ( x ) = ⁿCₓ pˣq⁽¹⁻ˣ⁾
where
n = number of trials
x = number of successes
p = probability of getting a success in one trial
q = probability of getting a failure in one trial
q = 1 - p
Substituting the values in the equation , we get
P ( x ) = ⁴C₃(0.60)³(0.40)
On simplifying the equation , we get
P ( x ) = 4 x 0.246 x 0.4
P ( x ) = 0.3456
Therefore , the value of P ( x ) is 0.3456
Hence , The probability that exactly 3 of the 4 employees selected will have children is given by binomial distribution formula ⁴C₃(0.60)³(0.40)
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Fill in the number to find the sum . 2/10 + /100= 50/100 a. 30 b. 10 c. 28 d. 52
Answer:
2/10 + 30/100 = 50/100
Step-by-step explanation:
First, you want to multiply 2/10 by 10, to get the same common denominator in both numbers, you would get 20/100. Then, its pretty simple from there, you just add the number that gets you to 50, which is 30, 20 + 30 =50. I Hope This Helps :)
The required missing number is 30. So, the correct answer is (a) 30.
Arithmetic is a branch of mathematics that deals with the study of numbers, their properties, and their operations. It involves the basic operations of addition, subtraction, multiplication, and division.
Here,
To find the missing number, we can use the fact that 50/100 is equivalent to 1/2.
So, we need to find a number that, when added to 2/10, gives 1/2 as the sum.
We can write this as an equation:
2/10 + x/100 = 1/2
Multiplying both sides by 100 to eliminate the denominator, we get:
20 + x = 50
Subtracting 20 from both sides, we get:
x = 30
Therefore, the missing number is 30. So, the correct answer is (a) 30.
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I need help with this math problem.
Answer:
Answer and steps in picture.
0.2 of the money in my savings account is $1500. How much money do I have in my
savings account?
Answer:
$300
Step-by-step explanation:
what is 6,720 divided by 14??
480 because 6,720 divided by 14 is 480
Hunter took out a $3,500 loan with interest to pay for some business supplies. He will repay the loan in 3 years with monthly payments of $109.68.
Find the total amount of Hunter’s repayment as well as the amount he will pay in interest.
He will pay back ______ in total and ______ in interest.
(Can someone help me with this!! will mark brainiest)
Answer:
he will pay back $3829.04 in total and $329.04 in interest.
Step-by-step explanation:
HELP FAST
A house costing $500,000 with a 15-year mortgage and an APR of 4.5% would
have what monthly payment?
Answer:
3825
Step-by-step explanation:
PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
so formula for the volume of a cylinder is:
(πr^2)*h
so the diameter is given to us which is
2r=10 cm
then r=5 cm
h=6 cm and r=5 cm so we just plug it in
(5^2)*6π
25*6π
150π cm^3 or approximately 471.239 cm^3
Answer:
I will give 2 possible answers. One of them involves a pi key and one is jsut 3.14. I don’t know if your suppose to use the Pi key or 3.14.
Possible answer #1 (with Pi key)= The volume would be about 471.24
Possible answer #2 (using 3.14)= The volume would be 471
Explanation:
Well first yoi gotta find the area of the circle. Using a pi key or 3.14 you follow the formula πr^2
The diameter is 10.
To find the radius divide diameter by 2 or multiply by half.
You’d get 5 and then using pi key or 3.14 number.
You’d have your area. Now multiply that by 6 the height and you have your final answer.
The distance between itahari and Damak is
42 km. Mr. Dhamala travelled 18.325 km by a
bus / 15.675 km by a toxi and the re
remaining dis-
tance by a motorbike How many km did he
travelled ky motorbike?
Answer:
8 km by motorbike.
Step-by-step explanation:
The distance between itahari and Damak is 42 km.
Mr. Dhamala travelled 18.325 km by a bus / 15.675 km by a taxi and the remaining distance by a motorbike.
Let he covered x distance by motorbike. So,
Remaining distance = Total distance -(distance covered by bus + distance by taxi)
= 42 -(18.325 +15.675 )
= 42-34
= 8 km
So, he travelled 8 km by motorbike.
An aquarium 4 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3). Show how to approximate the required work by a Riemann sum.
Express the work as an integral.
Evaluate the integral.
Answer:
Workdone = 4900joules
Step-by-step explanation:
Work-done = force x distance
Force = mass x acceleration
If we suppose that the aquarium is at height 0 at the top and height 1 at the bottom (since it's 1m deep), then we need to lift the slide at height x by x metres.
Mass = Density x Volume, therefore force needed to lift the slice is given is
F = density*volume*∆x*acceleration
Since we the mass changes as we take out water then there will be a change in height, for this reason we have ∆x.
Acceleration is due to gravity, therefore g=9.8m/s²
Density = 1000kg/m³
Volume = 4*1*1 = 4m³
F = 1000*4*∆x*9.8 = 39200∆x
Since our distance from the top of the aquarium to the bottom is x metres, then
Work-done = 39200x∆x
To find the total workdone, we find the integral of 39200xdx and the limit will be from 0 to 0.5 since we are to pump halfway of the aquarium. Integrating that we have
19600*x² limit from 0 to 0.5
19600(0.5² – 0²) = 19600(0.25 – 0) = 19600(0.25) = 4900joules
what is the area of a square that is 2 feet length and 7 1/4 feet width
I WILL GIVE BRAINILYEST!!!This is a graded discussion:
Modules
Mathematical Modeling Discussion
Syllabus
Grades
99 Co
5.272 a
People
0.31 MeV B 99.80%
Office 365
1.48 Mev B-
1.1732 MeV Y
0365 Email
1.3325 MeV Y
The rate of decay of a radioactive substance depends upon the
amount present initially. The mass y (mg) of the radioactive substance
cobalt-60 present in a sample at time < (years) is represented by the
-0.13151
exponential equation y = 50 e
Answer the following questions in complete sentences.
1. How does the exponential equation above compare to the equation
for simple interest that is compounded continuously? Explain the
similarities. What is the initial amount of cobalt-60 in the sample?
2. How much cobalt-60 is left after 8.4 years? Show your work
3. What would be the y-intercept of the graph? What does it
represent?
4. After how many years will the amount of cobalt-60 left be 6.25
mg? Explain what happens to the cobalt-60 after 50 years?
5. Discuss some real-world" examples and uses of cobalt-60
Answer:1.40
2.20
3.100
4.39
5.7
7
Step-by-step explanation:
Help me please. I kinda need it right now.!
Step-by-step explanation:
Given
[tex]5y - 4 = 126(corresponding \: angles) \\ 5y = 126 + 4 \\ 5y = 130 \\ y = 130 \div 5 \\ = 26[/tex]
Also given
[tex]126 + (6z + 6) = 180(angles \: on \: a \: straight \: line) \\ 132 + 6z = 180 \\ 6z = 18 0 - 132 \\ 6z = 48 \\ z = 48 \div 6 \\ = 8[/tex]
Lastly,
[tex]x = 180 - 126 \\ = 54(angles \: on \: the \: same \: straight \: line \: and \: corresponding \: angles)[/tex]
Answer:
x = 126
y = 26
z = 8
Step-by-step explanation:
6z + 6 + 126 = 180
6z + 132 = 180
6z = 180 - 132
6z = 48
z = 8
6z + 6 + 5y - 4 = 180
6(8) + 6 + 5y - 4 = 180
48 + 2 + 5y = 180
50 + 5y = 180
5y = 180 - 50
5y = 130
y = 26
x = 126 (Because of alternate exterior angles thm)
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer:
117
Step-by-step explanation:
angle 2 = 117 so angle 1 has to =63 because they have to equal 180 (supplementary angles)
angle 1 =63 . angle 3 =117
angle 7 is the same measurement of angle 3
hope this makes sense
Answer:
117 degrees
Step-by-step explanation:
angle 1 and 2 are supplementary angles which are angles whose measurements add up to 180 degrees
this means angle 1 = 63 degrees
63 + 117 = 180
angle 1 and 3 are linear pair angles which means they also equal 180 degrees
angle 3 = 117 degrees
angle 3 and angle 7 are corresponding angles which means their degrees are equal to each other
angle 7 = 117 degrees
The relationship between angle 2 and 7 would be alternate exterior angles
The sum of three numbers is 30. The third number is twice the second, and is also 2 less than 3 times the first. What are the three numbers?
Answer:
First: 6 Second: 8 Third:16
Step-by-step explanation:
First number:x
Second number: 1.5x-1
Third number: 3x-2
x+1.5x-1+3x-2=30
5.5x-3=30
5.5x=33
x=33/5.5=6
So First =6
Second= 1.5(6)-1=8
Third " 3(6)-2=16
6x+2 = 5x+18 PLS QUICKKKK
Answer:
16
Step-by-step explanation:
Equation : 6x+2=5x+18
Like Terms : x + 2 = 18
Like Terms Again : x = 16
Answer:
6x+2=5x+18
6x-5x=18-2
X=16
Step-by-step explanation:
First you need to group numbers of like terms in one side. Then when you take the other number to the other side of equal sign changes it's form eg +6 change to - 6
Help with the calculus problem please
The area of the region is equal to the area under the curve y = cos(x) over the interval 0 ≤ x ≤ π/6, given by the integral
[tex]\displaystyle\int_0^{\frac\pi6}\cos(x)\,\mathrm dx = \sin(x)\bigg|_0^{\frac\pi6}=\sin\left(\frac\pi6\right)-\sin(0)=\boxed{\frac12}[/tex]
which follows from
• the fact that d/dx [sin(x)] = cos(x)
• the fundamental theorem of calculus
Determine the value of a.
?????????????????????????????????????????????????
it's not possible
I think -7 is the right answer but it's not possible actually
Answer:
c. -7
Step-by-step explanation:
(x+57) + (63+67) = 180
(x+57) + 130 = 180
x + 187 = 180
x = 180-187
x = -7
why did I make it equal to 180?
all the angles in a triangle always equal 180 :)
help pls
hannah is making a fleece tie blanket. it is 36 inches long. each tie will be 3/4 of an inch wide. how many times will she have
Proportionately, the number of times that Hannah will have to tie the blanket is 48 times.
What is proportion?Proportion is the relationship between two numerical values or variables. It shows the share or portion of a variable to the whole number.
Proportions are expressed as ratios, usually using fractions, decimals, or percentages.
Data and Calculations:The length of the fleece tie blanket = 36 inches
The width of each tie = 3/4 inches
The proportion of 3/4 inches to an inch = 0.75 (3/4)
The number of times to tie the blanket = 48 times (36/0.75)
Thus, the number of times that Hannah will tie the blanket is 48 times.
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I have a question for special product patterns.
It is in the attached image.
Which is the sum of 14t/10t^2 + 5t^2+40t/10t^2
Answer:
7t/5^3 + 5t^2 + 4t^3
Step-by-step explanation:
Repeated-measures and matched-subjects experiments
Repeated measures experiments measure the same set of research participants two or more times, while matched-subjects experiments study participants who are matched on one or more characteristics. Which of the following are true for both a repeated-measures experiment and a matched-subjects experiment when used to compare two treatment conditions?
A. If the researcher has n number of participants to use in the experiment, then the degrees of freedom will be the same in a repeated-measures experiment or in a matched-subjects experiment.
B. The researcher must compute a pooled variance to compute a t statistic.
C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistic.
D. Participants in both types of experiments are all measured the same number of times.
A matched-subjects experiment produced at statistic with a df of 13. How many subjects participated in this study?
a. 13.
b. 28.
c. 26.
d. 14.
For a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 17. How many subjects participated in this study?
a. 18.
b. 17.
c. 36.
d. 34.
If sin(38°) and cos(52°) does that add up to 90°?
Answer:
38 plus 52 is in fact 90, but Sin and Cos will be different.
Step-by-step explanation:
Honestly I haven't learned Sin or Cos
What is the 20th term of the linear sequence below?
1, 7, 13, 19, 25, ...
Answer:
115
Step-by-step explanation:
1, 7, 13, 19, 25...
1, 1+6, 1+6+6, 1+6+6+6, 1+6+6+6+6...
In 2nd number, 1 plus one 6
In 3rd number, 1 plus two 6s
:
In 20th, 1 plus nineteen 6s
1 + 6 × 19 = 115
The length of a rectangle is twice its width.
If the perimeter of the rectangle is 60 m, find its length and width.
WILL MARK THE BRAINLIEST!!!
Answer:
W = 10
L = 20
Step-by-step explanation:
2L + 2W = 60
L = 2W
Substitute for L in the first equation
2(2W) + 2W = 60
4W + 2W = 60
6W = 60
W = 10
Plug in W in the first equation
2L + 2(10) = 60
2L + 20 = 60
2L = 40
L = 20
Plug both answers in both equations to check
2(20) + 2(10) = 60
20 = 2 * 10
Hope that helps!
A rectangular picture is twice as long as it is wide. If the
area of the picture is 288 in^2, what are its dimensions?
The dimensions of the picture are_____ in long by_____ in wide.
Answer:
24 in long by 12 in wide.
Step-by-step explanation:
l=2w
288=(2w)×w
288=2w^2
144=w^2
12=w
width is 12 inches. Plug that in to find length...
l=2×12
l=24
Can someone help me with this please
One face of a prism is in the shape of an isosceles triangle with a base of 15 inches. The perimeter of the triangle is 47
inches. How long is each of the equal sides of the triangle?
Provide your answer below:
inches
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Answer:
16 Inches
Step-by-step explanation:
.........................
HELP PLEASE : For numbers 3 & 4, draw a triangle for each to find the missing side.
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: 1) b = 2
2) c = 20
Explanation:
I hope this helped!
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Answer:
3) b = 2.24
4) c = 15.62
Step-by-step explanation:
Pythagorean formula:
a² + b² = c²
3)
a² + b² = c²
2² + b² = 3²
4 + b² = 9
b² = 5
b = 2.24
4)
a² + b² = c²
10² + 12² = c²
100 + 144 = c²
244 = c²
c = 15.62