Answers
Answer:
Option B
Step-by-step explanation:
Expression representing the series is,
[tex]\sum_{k=6}^{11}(2k+5)[/tex]
Here, k = Number of terms
By placing k = 6, 7, 8, 9, 10, 11 in the expression we can get the terms of the series.
For k = 6,
(2k + 5) = 2(6) + 5
= 17
For k = 7,
(2k + 5) = 2(7) + 5
= 19
For k = 8,
(2k + 5) = 2(8) + 5
= 21
For k = 9,
(2k + 5) = 2(9) + 5
= 23
For k = 10,
0(2k + 5) = 2(10) + 5
= 25
For k = 11,
(2k + 5) = 2(11) + 5
= 27
Therefore, expanded form will be,
17, 19, 21, 23, 25, 27
There, is a common difference in each successive to previous term,
d = 19 - 17
d = 2
Number of terms 'n' = 6
First term = 17
Sum of an arithmetic sequence is given by,
[tex]S=\frac{n}{2}[2a+(n-1)d][/tex]
Therefore, sum of the given sequence will be,
[tex]S=\frac{6}{2}[2(17)+(6-1)2][/tex]
= 3(34 + 10)
S = 132
Option B will be the correct option.
Related Questions
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.
Answers
Answer:
5 x 2 -3 = 7
Step-by-step explanation:
i mean.... thats all
4(x+2) help please.
Answers
Answer:
4x + 8
Step-by-step explanation:
4(x+2)
4*x + 4*2
4x + 8
[tex] \large\sf \leadsto 4(x + 2)[/tex]
[tex] \large\sf \leadsto 4 \times (x + 2)[/tex]
[tex] \huge\sf \leadsto \pmb {4x + 8}[/tex]
5 + {[2 X (14 - 9)] - 1}
Answers
Answer:
14
Step-by-step explanation:
[tex] 5 + (2 \times (14 - 9) - 1) \\ = 5 + (2 \times 5) - 1 \\ = 5 + (10 - 1) \\ = 5 + 9 \\ = 14[/tex]
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
Answers
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?
Answers
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 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
Answers
Answer:
the second company
Step-by-step explanation:
the second company produces 50,000 more crackers an hour than the first company
help me!!!!!!!!!plzzz
Answers
Answer:
B. 1/3
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation:
add all the values 10+14+6=30 since red is 10 divide 10 by 30 so 10/30 simplifying to 1/3.
PLEASE HELP WILL MARK BRAINLYIST HELP
Answers
Explanation
1/2 divided by 4 = 1/8
Just trust me, and mark me brainliest ty
Have a nice day!
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:
Answers
Answer:83.3
Step-by-step explanation:
What is the surface area of the solid shown below?
Answers
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]
Is pop or country your favorite type of music?
Change This into a neutral question
Answers
A sphere has a volume of 1 cubic foot. What is the approximate diameter of the sphere?
Answers
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
Please help me
Find the circumference and the area of this shape
I'll give brainliest
Answers
Area = 176.7
A vehicle owner interested in her vehicle’s fuel economy calculated the gas mileage in miles per gallon (mpg) each time she filled her tank, for several years. Here are the mpg values for a random sample of 20 of these records. Suppose that the standard deviation is known to be σ = 3.5 mpg.
Required:
Find the 95% confidence interval for the mean of gas mileage for this vehicle.
Answers
Answer:
The 95% confidence interval for the mean of gas mileage for this vehicle is (S - 1.53, S + 1.53), in which S is the mean of the sample of 20.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{3.5}{\sqrt{20}} = 1.53[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is S - 1.53.
The upper end of the interval is the sample mean added to M. So it is S + 1.53.
The 95% confidence interval for the mean of gas mileage for this vehicle is (S - 1.53, S + 1.53), in which S is the mean of the sample of 20.
At which value in the domain does f(x) = 0?
2
2
4
Answers
Answer:
4
Step-by-step explanation:
What is the surface of the triangluar prism shown below
Answers
Answer: 36 ft^2
Step-by-step explanation: 4x3/2=6. 6x2=12. 3x2=6. 4x2=8. 5x2=10. 12+8+6+10=36
!!!MAJOR HELP AND NO LINKS AND IF YOU DONT KNOW BUT YOU STILL ANSWER, I WILL REPORT IF YOU SAY SOMETHING THAT IS NOT AN ANSWER!!!
What is the solution to the equation 7.5 minus X =2.8?
Image above
Answers
Answer: A
Step-by-step explanation:
4.7+2.8 = 7.5
And
7.5 -4.7 = 2.8
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
Answers
Answer:
Letter a)
Step-by-step explanation:
quizlet
Find the measure of the angle, round to the nearest tenth: Sin X = .7547
Answers
X = INVERSE-SIN(.7547)
X = 49.0 degrees
Please answer it. I will give brainliest if its correct..
Answers
First find the circumference of the circle:
Circumference = 2 x radius x pi
Circumference = 2 x 4 x 3.14 = 25.12 cm
Now arc ML is 100 degrees.
Multiply the circumference by the arc degree/360 ( 360 is a full circle)
25.12 x 100/360 = 6.98 cm
The answer is 6.98 cm
A computer technician notes that 40% of computers fail because of the hard drive, 20% fail due to the processor, 15% of problems are with the keyboard, and 5% of problems are due to something else. What is the mean of the number of computers he will work on before seeing his first computer that has failed because of the hard drive?
Since there are four categories, the technician can expect 4 computers until one has failed due to the hard drive.
Since 40% is equivalent to Two-fifths, it is expected that Five-halves = 2.5 computers until one has failed due to the hard drive.
Since the highest percentage of failure is due to the hard drive, the technician can expect that the first computer will have failed due to the hard drive. So the expected value is 1.
Since it is more likely that a computer has failed due to some other issue, the technician can expect the first computer to fail due to some other issue, and the second to fail due to the hard drive. So the expected value is 2
Answers
Answer:
Answer is b
Step-by-step explanation:
hellpppppppppspspspspspspsp
Answers
I'd say 13, hope this helps
Step-by-step explanation:
if x varies inversely as y and x=2.5 when y = 40 , find y when x = 2
Answers
Answer:
2.5/40=2/y
2.5y=40x2
2.5y=80
y=80/2.5
y=32
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?
Answers
Answer:
rank 6
Step-by-step explanation:
PYTHAGOREAN THEOREM !! DONT NEED U TO EXPLAIN JUST GIVE ANSWER DONT HAVE TIME FOR THAT !
Answers
Answer:
√14 or 3.74
Step-by-step explanation:
_________________
Answer:
√14 or 3.74
Step-by-step explanation:
x = 3.74
y=x+5
please help me with this problem I'm really struggling to answer the question.
Answers
Answer:12
Step-by-step explanation:just know i did it and got it right
Determine the volume if the figures below round to the nearest hundredth
Answers
Answer:
48 m³
4,186.67 km³
Step-by-step explanation:
volume of pyramid =
⅓×6×6×4 = 48 m³
volume of ball =
4/3 × 3.14 × 10³ = 4,186.67 km³
A math teacher has a number cube with faces numbered 1 through 6. He will roll the number cube 400 times. Which of the following ranges contains the best prediction for the number of times the number cube will land with a 1 or a 4 on the top face?
A. 30-35
B. 65-70
C. 130-135
D. 265-270
Answers
Answer:
Step-by-step explanation:
B?
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.
Answers
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
You roll 2 dice and flip a coin. What's the probability of getting two 4's and a tails?
Answers
Answer:
2/4
Step-by-step explanation: