Answer:
Common factor
Factor by grouping
Factor by grouping
−
2
−
2
+
1
-x^{2}-2x+1
−x2−2x+1
−
1
(
2
+
2
−
1
)
{\color{#c92786}{-1(x^{2}+2x-1)}}
−1(x2+2x−1)
Solution−
-1(x²+ 2x-1 )
A binomial experiment is given. Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. A survey of U.S. adults found that 37% have been to court. You randomly select 30 U.S. adults and ask them whether they have been to court.
Answer:
Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], you can use a normal distribution to approximate the binomial distribution.
The mean is of 11.1 and the standard deviation is of 2.64.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Using the normal distribution to approximate the binomial distribution.
This is possible if:
[tex]np \geq 10, n(1-p) \geq 10[/tex]
A survey of U.S. adults found that 37% have been to court. You randomly select 30 U.S.
This means that [tex]p = 0.37, n = 30[/tex]
Test if it is possible:
[tex]np = 30*0.37 = 11.1[/tex]
[tex]n(1-p) = 30*0.63 = 18.9[/tex]
Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], you can use a normal distribution to approximate the binomial distribution.
Mean and standard deviation:
[tex]E(X) = np = 30*0.37 = 11.1[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{30*0.37*0.63} = 2.64[/tex]
The mean is of 11.1 and the standard deviation is of 2.64.
if the length is 9 cm,breadth is 10 cm and volume of cuboid is 1800cm cube ,,find the height and total surface area of cuboid,
Answer:
the height is 20 cm.
tsa is 940 cm square
Step-by-step explanation:
volume of cuboid = l*b*h
1800 = 9*10*h
h= 20 cm
TSA = 2(L*B+ B*H + L*H)
= 2(9*10 + 10*20 + 9*20)
=940 cm square
The height of the cuboid will be 20 cm
The total surface area of cuboid will be 940 cm²
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The length of cuboid = 9 cm
The breadth of cuboid = 10 cm
And, The volume of cuboid = 1800 cm³
Now,
We know that;
Volume of cuboid = Length × Breadth × Height
⇒ 1800 = 9 × 10 × h
⇒ 1800 / 90 = h
⇒ h = 20 cm
And, The total surface area of cuboid = 2lw + 2lh + 2hw
Substitute all the values, we get;
⇒ The total surface area of cuboid = 2 (9 × 10 + 9 × 20 + 20 × 10)
= 2 (90 + 180 + 200)
= 2 × 470
= 940 cm²
Learn more about the multiply visit:
brainly.com/question/14176303
#SPJ2
The quality-control manager at a compact flourescent light bulb factory wants to test the claim that the mean life of a large shipment of cfls is equal to 6500 hours. the population standard deviation is 500 hours. a random sample of 50 cfls indicates a sample mean life of 6,700 hours and sample standard deviation is 600 hours.
Critical values, where P(Z > Z) - a and P(t >) - a 2016-1282 20.06-1645 20.02 -1.960 10.10. - 1.299 10.06.45 - 1677 foto - 2010 1.115 pt.
a. At the 0.05 level of significance, is there evidence that the mean life is different from 6,500 hours?
b. Compute the p value and interpret its meaning.
c. Construct a 95% confidence interval estimate of the population mean life of the CFLs.
d. Compare the results of (a) and (c). What conclusions do you reach?
Answer:
a. At the 0.05 level of significance, there is evidence that the mean life is different from 6,500 hours.
b. The p value= ≈ 0.00480 for z- test which is less than 0.05 and H0 is rejected .
The p value= 0.006913 for t- test which is less than 0.05 and H0 is rejected for 49 degrees of freedom.
c. CI [6583.336 ,6816.336]
d. The range of CI [6583.336 ,6816.336] tells that the cfls having a different mean life lie in this range.
Step-by-step explanation:
Population mean = u= 6500 hours.
Population standard deviation = σ=500 hours.
Sample size =n= 50
Sample mean =x`= 6,700 hours
Sample standard deviation=s= 600 hours.
Critical values, where P(Z > Z) =∝ and P(t >) =∝
Z(0.10)=1.282
Z(0.05)=1.645
Z(0.025)=1.960
t(0.01)(49)= 1.299
t(0.05)= 1.677
t(0.025,49)=2.010
Let the null and alternate hypotheses be
H0: u = 6500 against the claim Ha: u ≠ 6500
Applying Z test
Z= x`- u/ s/√n
z= 6700-6500/500/√50
Z= 200/70.7113
z= 2.82=2.82
Applying t test
t= x`- u /s/√n
t= 6700-6500/600/√50
t= 2.82
a. At the 0.05 level of significance, there is evidence that the mean life is different from 6,500 hours.
Yes we reject H0 for z- test as it falls in the critical region,at the 0.05 level of significance, z=2.82 > z∝=1.645
For t test we reject H0 as it falls in the critical region,at the 0.05 level of significance, t=2.82 > t∝=1.677 with n-1 = 50-1 = 49 degrees of freedom.
b. The p value= ≈ 0.00480 for z- test which is less than 0.05 and H0 is rejected .
The p value= 0.006913 for t- test which is less than 0.05 and H0 is rejected for 49 degrees of freedom.
c. The 95 % confidence interval of the population mean life is estimated by
x` ± z∝/2 (σ/√n )
6700± 1.645 (500/√50)
6700±116.336
6583.336 ,6816.336
d. The range of CI [6583.336 ,6816.336] tells that the cfls having a different mean life lie in this range.
A stack of 14 cookies is 23.1 centimeters high. How thick is each cookie?
consider the following exam scores from a class of 8 students
55,65,77,79,84,89.91,99
What is the rank of the student that scored a 77 on the exam?
Answer:
rank 6
Step-by-step explanation:
A sphere has a volume of 1 cubic foot. What is the approximate diameter of the sphere?
Answer:
[tex]volume \ of \ sphere = \frac{4}{3} \pi r^3 \\\\1 =\frac{4}{3} \pi r^3\\\\r^ 3 = \frac{3}{4\pi} \\\\r = (\frac{3}{4\pi })^{\frac{1}{3} } \\\\r = 0.62ft\\\\diameter = 2 * 0.62 = 1.24ft[/tex]
Answer:
1.24 ft
Step-by-step explanation:
the volume of sphere = 4/3π.r³ = 1
=> r³ = 3/(4π)= 3/(12.56) = 0.239
r = ³√0.239
r = 0.62
d = 2×0.62 = 1.24 ft
What is the surface of the triangluar prism shown below
Answer: 36 ft^2
Step-by-step explanation: 4x3/2=6. 6x2=12. 3x2=6. 4x2=8. 5x2=10. 12+8+6+10=36
What is the surface area of the solid shown below?
Answer:
[tex]\text{C. }156\:\mathrm{cm^3}[/tex]
Step-by-step explanation:
The surface area of the triangular prism consists of three rectangles and two triangles.
Rectangle One - 5 x 12 = 60 cm^2
Rectangle Two - 4 x 12 = 48 cm^2
Rectangle Three - 3 x 12 = 36 cm^2
Triangles - 2 x 1/2 x 3 x 4 = 12 cm^2
Thus, the total surface area of the solid is [tex]60+48+36+12=\boxed{\text{C. }156\:\mathrm{cm^3}}[/tex]
Find the measure of the angle, round to the nearest tenth: Sin X = .7547
a food company can produce 732,291,285crackers per hour. A second food company can produce 732,341,285 crackers per hour.Which company can produce more crackers per hour. explain how you found your answer
Answer:
the second company
Step-by-step explanation:
the second company produces 50,000 more crackers an hour than the first company
PYTHAGOREAN THEOREM !! DONT NEED U TO EXPLAIN JUST GIVE ANSWER DONT HAVE TIME FOR THAT !
Answer:
√14 or 3.74
Step-by-step explanation:
_________________
Answer:
√14 or 3.74
Step-by-step explanation:
x = 3.74
Please help me
Find the circumference and the area of this shape
I'll give brainliest
A={the letters of the word ,HIPPOPOTAMUS}
•ω• Hewo fren!
☆☆●◉✿Answer:✿◉●☆☆
The letters of hippopotamus is H-I-P-P-O-P-O-T-A-M-U-S
☆☆●◉✿Step-by-step explanation:✿◉●☆☆
I’m sowy, I didn’t really understand your question... did you want to learn about a hippopotamus? If so, please tell me in the comments I would answer there too!
HOPE I HELPED! ∧∧
→⇒brainliest please? ∑(OΔO )♥♥︎
Is pop or country your favorite type of music?
Change This into a neutral question
You shot a space capsule into an orbit around the space station.
The total weight of the capsule was 1,330 kilograms. If the devices
on board to regulate speed weighed one fourth as much as the fuel
tank and the power unit weighed one half as much as the fuel tank,
how much did the power unit weigh?
In this word problem, what are you asked to find?
CD
The weight of the power unit
b
The weight of the devices to regulate speed
с
The weight of the capsule
d
The weight of the container
We often deal with weighted means, in which different data values carry different weights in the calculation of the mean. For example, if the final exam counts for 50% of your final grade and 2 midterms each count for 25%, then you must assign weights of 50% and 25% to the final and midterms, respectively, before computing the mean score for the term. Apply the idea of weighted mean in the following exercise.
A student is taking an advanced anatomy class in which the midterm and final exams are worth 30% each and homework is worth 40% Of his final grade. On a 100-point scale, his midterm exam score was 82.5, his homework average score was 91.6, and his final exam score was 88.6.
Required:
a. On a 100-point scale, what is the student's overall average for the class?
b. The student was hoping to get an A in the class, which requires an overall score of 93.5 or higher. Could he have scored high enough on the final exam to get an A in the class?
Answer:
a) The student's overall average for the class is 87.97.
b) He would need a score above 100 to get an A, which means that he could not have scored high enough on the final exam to get an A in the class.
Step-by-step explanation:
Weighed average:
To solve this question, we find the student's weighed average, multiplying each of his grade by his weights.
Grades and weights:
Scored 82.5 on the midterm, worth 30%.
Scored 88.6 on the final exam, worth 30%.
Scored 91.6 on the homework, worth 40%.
a. On a 100-point scale, what is the student's overall average for the class?
Multiplying each grade by it's weight:
[tex]A = 82.5*0.3 + 88.6*0.3 + 91.6*0.4 = 87.97[/tex]
The student's overall average for the class is 87.97.
b. The student was hoping to get an A in the class, which requires an overall score of 93.5 or higher. Could he have scored high enough on the final exam to get an A in the class?
Score of x on the final class, and verify that the average could be 93.5 or higher. So
[tex]A = 82.5*0.3 + 88.6*0.3 + 0.4x[/tex]
[tex]A \geq 93.5[/tex]
[tex]82.5*0.3 + 88.6*0.3 + 0.4x \geq 93.5[/tex]
[tex]0.4x \geq 93.5 - (82.5*0.3 + 88.6*0.3)[/tex]
[tex]x \geq \frac{93.5 - (82.5*0.3 + 88.6*0.3)}{0.4}[/tex]
[tex]x \geq 105.425[/tex]
He would need a score above 100 to get an A, which means that he could not have scored high enough on the final exam to get an A in the class.
move two choices to the blanks to correctly complete the sentences.
Answer:
(A) There should have been 5 outcomes of HT
(B) The experimental probability is greater than the theoretical probability of HT.
Step-by-step explanation:
Given
[tex]S = \{HH,HT,TH,TT\}[/tex] -- Sample Space
[tex]n(S) = 4[/tex] --- Sample Size
Solving (a); theoretical outcome of HT in 20 tosses
First, calculate the theoretical probability of HT
[tex]P(HT) = \frac{n(HT)}{n(S)}[/tex]
[tex]P(HT) = \frac{1}{4}[/tex]
Multiply this by the number of tosses
[tex]P(HT) * n= \frac{1}{4} * 20[/tex]
[tex]P(HT) * n= 5[/tex]
Solving (b); experimental probability of HT
Here, we make use of the table
[tex]P(HT) = \frac{n(HT)}{n(S)}[/tex]
[tex]P(HT) = \frac{6}{20}[/tex]
[tex]P(HT) = 0.30[/tex] ---- Experimental Probability
In (a), the theoretical probability is:
[tex]P(HT) = \frac{1}{4}[/tex]
[tex]P(HT) = 0.25[/tex] ---- Experimental Probability
By comparison;
[tex]0.30 > 0.25[/tex]
In the figure below, EC || AB. Find the length of EC.
Select the best choice from the answers provided.
A.) 12.5
B.) 18
C.) 25
D.) 39.6
Answer:
Letter a)
Step-by-step explanation:
quizlet
What are 3 combinations to equal the total
Answer:
1x 2x 3x
Step-by-step explanation:
Let x stand for the percentage of an individual student's math test score. 64 students were sampled at a time. The population mean is 78 percent and the population standard deviation is 14 percent. What is the standard deviation of the sampling distribution of sample means?
Answer:
[tex]\sigma_x= 1.75\%[/tex]
Step-by-step explanation:
Given
[tex]n = 64[/tex]
[tex]\mu = 78\%[/tex]
[tex]\sigma = 14\%[/tex]
Required
The sample standard deviation
This is calculated as:
[tex]\sigma_x= \frac{\sigma}{\sqrt n}[/tex]
This gives:
[tex]\sigma_x= \frac{14\%}{\sqrt {64}}[/tex]
[tex]\sigma_x= \frac{14\%}{8}[/tex]
[tex]\sigma_x= 1.75\%[/tex]
Elliot read a report from a previous year saying that 6%, percent of adults in his city biked to work. He wants to test whether this has changed, so he is going to take a random sample of adults in his city and see what percent of them bike to work. Let p represent the proportion of adults in Elliot's city that bike to work.
Required:
What is an appropriate set of hypotheses for his significance test?
Answer:
The appropriate set of hypothesis for his significance test is null hypothesis [tex]H_0: p = 0.06[/tex] and alternate hypothesis [tex]H_1: p \neq 0.06[/tex]
Step-by-step explanation:
Elliot read a report from a previous year saying that 6%, percent of adults in his city biked to work. He wants to test whether this proportion has changed.
At the null hypothesis we test if the proportion is still the same, that is, of 6%. So
[tex]H_0: p = 0.06[/tex]
At the alternate hypothesis, we test if the proportion has changed, that is, it is different of 6%. So
[tex]H_1: p \neq 0.06[/tex]
What is an appropriate set of hypotheses for his significance test?
The appropriate set of hypothesis for his significance test is null hypothesis [tex]H_0: p = 0.06[/tex] and alternate hypothesis [tex]H_1: p \neq 0.06[/tex]
CORRECT (SELECTED)
z=\dfrac{0.1-0.06}{\sqrt{\dfrac{0.06(0.94)}{240}}}z=
240
0.06(0.94)
0.1−0.06
In a psychology class, 60 students have a mean score of 96.9 on a test. Then 19 more students take the test and their mean score is 71.3.
What is the mean score of all of these students together? Round to one decimal place.
Help please, and thank you! C:
Answer:83.3
Step-by-step explanation:
You roll 2 dice and flip a coin. What's the probability of getting two 4's and a tails?
Answer:
2/4
Step-by-step explanation:
What is the volume of a regular triangular pyramid with an apothem of 2.3ft, a side length of 8ft and a height of 25 feet
230FT
Regular tetrahedron
Solve for volume
V≈1.15×107
Use the formula for the volume of a triangular pyramid: V=13Ah , where A = area of the triangular base, and H = height of the pyramid.
Construct an equation for the expression: 3 less than 2 times a number is 7. Show the solution to the equation and prove your solution to be true through your work.
Answer:
5 x 2 -3 = 7
Step-by-step explanation:
i mean.... thats all
Pls help ill give u brainlest!! 40 points
Hakeem owns seven less than 3/5 the number of DVDs that Manuel owns. Hakeem owns 20 DVDs. How many DVDs does Manuel own? Show your work.
Answer:
Manuel owns 5 DVDS
Step-by-step explanation:
3/5 = 12/20
12 - 7 = 5
you watch seven deadly sins?
hellpppppppppspspspspspspsp
I'd say 13, hope this helps
Step-by-step explanation:
HELPP IMA GIVE YOU 15 POINTS
For which data-generating process would a binomial distribution be an appropriate model?
A.flipping a coin to decide whether test subjects should use their left or right hand
B.randomly choosing a letter of the alphabet to pick the first names of test subjects
C.spinning a three-part spinner to decide whether each trial subject should be a child, an adult, or a senior
D.spinning a four-part spinner to decide whether survey customers should be from eastern, southern, midwestern, or western states
Answer:
A. flipping a coin to decide whether test subjects should use their left or right hand
Step-by-step explanation:
Since a coin has two outputs: heads or tails, it it has a binomial distribution
The diagram shows a cylindrical tank.
The radius is 30 cm and the height is 80 cm.
(a) Calculate the area of the base of the tank.
(b) Calculate the volume of the tank in litres.
Step-by-step explanation:
a) A=π302=900π CM2 =2,827 CM 2
b) V=Ah=900=72000 π cm 3 = 226,195 cm3
4) To estimate the height of your home, you measure its shadow. The shadow of your home is 5.5 feet.
The shadow of the 10 foot tree has a shadow of 2.5 feet. Find the height of your home. Show all work.
Answer:
1.375 ft
Step-by-step explanation:
10/2.5 = 4
5.5 / 4 = 1 1.5/4 = 1 3/8 = 1.375 ft
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K