The series 14 + 6 + (–2) + (–10) + . . . + (–154) is arithmetic. How many terms are in the series?
Answer:
22
Step-by-step explanation:
In the series 14 + 6 + (–2) + (–10) + . . . + (–154)
The gap between entities is 8.
Therefore number of entities between -10 and -154 = (154 - 10)/8 =18
Total number of terms in the series = 18 + 4 = 22
There are 22 terms in the given arithmetic series.
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
T_n = a + (n-1)d
(for all positive integer values of n)
In the given arithmetic series 14 + 6 + (–2) + (–10) + . . . + (–154)
The common difference between entities is 8.
Therefore, the number of entities between -10 and -154
= (154 - 10)/8
=18
The Total number of terms in the series = 18 + 4 = 22
Hence, there are 22 terms in the given arithmetic series.
Learn more about arithmetic sequence here:
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the perimeter of a square is equal to the perimeter of an equilateral triangle the length of a side of the square is given by the x and lenghth of a side of equilaterel triangle is given x+1 which equation can be used to find the value of x?
Answer:
x = 3
Step-by-step explanation:
We are told that the length of a side of the square is x.
Now, perimeter of square = 4 × side length
Perimeter of square = 4x
Also,we are told that the triangle is equilateral and a side is (x + 1).
Thus, perimeter of triangle = 3(x + 1)
Since we are told that the perimeter of the square is equal to that of the equilateral triangle. Thus;
4x = 3(x + 1)
4x = 3x + 3
Subtract 3x from both sides to get;
4x - 3x = 3
x = 3
Answer:
pretty sure it's C
Step-by-step explanation:
Jen rode her bike 1/5 of a mile to her friend's house. It took her 5 minutes to get there. What was Jen's speed?
Answer:
1/25 miles per minute
Step-by-step explanation:
Speed is distance divided by time
1/5 miles ÷ 5 minutes
Copy dot flip
1/5 * 1/5
1/25 miles per minute
Answer:
speed(v)=1.07
Step-by-step explanation:
v=m/s (1/5 mile is 321 m and 5 min is 300 seconds)
=321/300=1.07
A sample of 50 impossible whoppersandwiches have a mean fat content of 37.6g and standard deviation of 4.9g . A sample of 58 regular whopper sandwiches have a mean fat content of 39.3g and standard deviation of 2.7g. Use a 0.05 significance level to test the claim that the mean fat content for the impossible whopper is less than the mean fat content for the regular whopper.
(Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal.)
USE A 0.05 SIGNIFICANCE LEVEL TO TEST THE CLAIM:
H0: μ1____ μ2For Q17(circle one: equal to, less than, greater than, not equal to )
H1 : μ1____ μ2For Q18(circle one: equal to, less than, greater than, not equal to )
Test Statistic t=__________ Q19(ROUND TO 2 DECIMAL PLACES)
P-value: p =_____________ Q20(ROUND TO 4 DECIMAL PLACES)
Decision/Conclusion: _________________________________Q21(CIRCLE ONE BELOW) Reject H0, There is sufficient evidence to warrant the rejection of the claim.
OR
Fail to Reject H0, There is not sufficient evidence to warrant the rejection of the claim.
Construct an appropriate confidence interval ( ______________ Q22, _______________ Q23) (ROUND TO 3 DECIMAL PLACES)
Answer:
Step-by-step explanation:
H0: μ1____ μ2For Q17(circle one: equal to, less than or equal to, greater than or equal to, not equal to )
H1 : μ1____ μ2For Q18(circle one: equal to, less than, greater than, not equal to )
Formula for calculating the the test:
t = [ (x₁ - x₂) - d ] / sqrt[(s₁²/n₁) + (s₂²/n₂)]
where x₁ = 37.6, x₂ = 39.3, d = 0 assuming equality = 37.6 - 39.3 = -1.7
s₁² = 4.92 = 24.01, s₂² = 2.72 = 7.29, n₁ = 50, n₂ = 58.
thus, t = [ (-1.7) - (0)] / √(24.01/50) + (7.29/58)
t = (-1.7) / (0.4802 + 0.1257)
t = -1.7 / 0.6059
t = -2.8057. = -2.81
P value:
Lets find the degree of freedom:
DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }
DF = (24.01/50 + 7.29/58)² / {[(24.01 / 50)² / 50-1)] + (7.29/58)² / 58-1)]}
DF = (0.4802 + 0.1257)² /{[ (0.4802)²/49] + (0.1257)²/57)]}
DF = (0.6059)²/ (0.00471 + 0.00028)
DF = 0.3671 / 0.00499 = 75.37
Thus, P value = 0.9968 using a t distribution calculator.
Decision/Conclusion: Since the P value 0.9968 is greater than α (.05), Fail to Reject H0, There is not sufficient evidence to warrant the rejection of the claim.
There are about 237 milliliter in 8 oz how many mililiters in 15 oz
Answer:
443
Step-by-step explanation:
Answer:426.196
Step-by-step explanation:
Suppose corn chips cost 21.5 cents per ounce . If a bag cost $2.91, how many ounces of chips
Answer:
13 ounces
Step-by-step explanation:
291/21.5=13.5348837209
PLEASE HELP ??
What is the length of x?
Answer:
[tex]1\dfrac{3}{5}[/tex]
Step-by-step explanation:
Because these two triangles are similar:
[tex]\dfrac{4}{5}=\dfrac{x}{2}\\x=\dfrac{8}{5}=1\dfrac{3}{5}[/tex]
Hope this helps!
graphic designworks employed three different sales people last year Person 1 earned 3500 in the first quarter person 2 earn 6500 in the first quarter and Person 3 earned 8000 in the first quarter what are the maximum FUTA deduction for the first quarter
A.1054.00
B. 620.00
C.1116.00
D.899.00
Answer:
B im not to sur tho tell me if you got it
Answer:
1054.00
Step-by-step explanation:
What type of number is the square root of 13
A decimal
3.60555127546
Have a great day
What is the range of values for the measurement 300 ± 2%?
To be honest, I really don’t understand this and need someone to help me out.
Answer:
A.
Explaintion:
n=13. 13+2 = 15
I hope this helps ( :
Answer: B
Step-by-step explanation:
because 4 is the number of (n) plus the 2
Is 656250 divisible by 10?
Answer:
Yes 656250 is divisible by 10. Answer is 656250.
A 2-kilogram bag of sugar costs $5.09. What is the unit price, rounded to the nearest cent?
Answer:their is something wrong in the question
Step-by-step explanation:
A mixture of 5 pounds of fertilizer A, 13 pounds of fertilizer B, and 4 pounds of fertilizer C provides the optimal nutrients for a plant. Commercial brand X contains equal parts of fertilizer B and fertilizer C. Commercial brand Y contains one part of fertilizer A and two parts of fertilizer B. Commercial brand Z contains two parts of fertilizer A, five parts of fertilizer B, and two parts of fertilizer C. How much of each fertilizer brand is needed to obtain the desired mixture? (If the system is dependent enter a for brand X and enter brand Y and brand Z in terms of a.)
Answer:
x = 2; y = 3; z = 1
Step-by-step explanation:
For the first fertilizer (A) we can form the equation:
y + 2z = 5
For the second fertilizer (B) we can form the equation:
x + 2y + 5z = 13
For the third fertilizer (C) we can form the equation:
x + 2z = 4
solving simulteneously:
y = 5 - 2z
x = 4 -2z
Substituting (i) and (ii) into (2)
4 - 2z + 10 -4z + 5z = 13
14-z =13, therefore z = 1
substituting z into (i) and (ii)
y = 3
x = 2
A population of 100 insects tripled in size every month. Write a function formula to represent the insect population after x months
Answer:
3x+100
Step-by-step explanation:
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.
Answer:
3/k = x
Step-by-step explanation:
5kx +6 = 7kx
Subtract 5kx from each side
5kx -5kx +6 = 7kx-5kx
6 =2kx
Divide each side by 2k
6 /2k = 2kx/2k
3/k = x
Translate the sentence into an inequality.
The quotient of b and 7 is greater than or equal to 26.
Answer: b/7>=26
Step-by-step explanation:
Answer:
[tex]\frac{b}{7} \geq 26[/tex]
Step-by-step explanation:
1) we are given "the quotient of b and 7", quotient means to divide and since b comes before 7 it must be [tex]\frac{b}{7}[/tex]
2) "greater than or equal to" means that the [tex]\frac{b}{7}[/tex] from earlier must be either greater than, or the same value as the following number so you use this sign: [tex]\geq[/tex]
3) 26 comes last in the problem meaning it must come after the [tex]\geq[/tex] sign
4) you then combine them together to get [tex]\frac{b}{7} \geq 26[/tex] !
Hope this helps!
HELP MEE ILL MARK BRAINLEIST
Answer:
3x-3 I think that's it.
Step-by-step explanation:
Answer:
The vertex is (1, -4)
Step-by-step explanation:
Calculate the perimeter
Answer:
Sqare = 6+6+6+6 = 6*4 = 24
Rectangle = 6+6+18+18 = 12+36 = 48
24+48 = 72
The perimeter is 72.
Please help ASAP
Find the sum of 2 x^2 + 3 x - 4, 8 - 3 x , and -5 x^2 + 2.
A. -3 x2 - 2
B. -7 x2 - 2
C. -3 x2 + 6
D. -7 x2 - 6 x - 2
answer:
B. -7x2-2
add the numbers and variables together and combine like terms
Wyatt analyzed the data from his science experiment and found that the MAD was greater than the IQR. What does this tell you about the variability of the data?
a
The average of the data is closer to the least value than it is to the greatest value.
b
The middle 50% of the data is spread out more than the average variation.
c
The average variation is spread out more than the middle 50% of the data.
d
The average of the data is closer to the greatest value than it is to the least value.
Answer:
The correct option is C
Step-by-step explanation:
The average variation is spread out more than the middle 50% of the data.
The city of Omaha decided to build a new parking garage in hopes of luring more people to the Old Market district.The city will pay for the parking garage through parking fees. For a random sample of 42 weekdays, daily fees collected averaged $126 with a standard deviation of $16. The consultant who advised the city on the project estimated the potential parking revenues to be $135 per day, though the city believes that estimate is too high. Perform a hypothesis test (by hand) using α=0.05 to check the advisor's claim that the revenue would be $135 per day. Include the following:
1. Write your hypotheses in both symbols and words.
2. Test an appropriate hypothesis "by hand" using an alpha level of 0.05. Assume conditions are met (so don't check them). Be sure to include the correct probability notation and use the editor for all work.
3. Support your test with the corresponding confidence interval, again "by hand". Use the editor to show all steps.
4. Write your 3-part final conclusion using the test results and interval results. Include a sentence that states whether the test and interval results agree.
Answer:
Given:
Mean, u = 135
Sample size, n = 42
Sample mean, x' = 126
Standard deviation = 16
Significance level = 0.05
1) The null and alternative hypotheses:
H0 : u = 135 (the revenue per day is $135)
H1 : u < 135 (the revenue per day is less than $135)
2) In this case, we have a left tailed test.
Let's use the formula:
[tex] = \frac{x' - u}{s/ \sqrt{n}} = \frac{126 - 135}{16 / \sqrt{42}} = -3.645 [/tex]
t = - 3.645
Critical value: at a significance level of 0.05, left tailed test,
tcritical = -1.683
We reject null hypothesis, H0, since t calculated, -3.645 is less than tcritical, -1.683.
3) Given, a = 0.05, df = 41, left tailed test,
t-value = 2.02
For the corresponding confidence interval, we have:
[tex] CI = (x' - \frac{t * \sigma}{\sqrt{n}}, x' + \frac{t * \sigma}{\sqrt{n}}) [/tex]
[tex] CI = (126 - \frac{2.02 * 16}{\sqrt{42}}, 126 + \frac{2.02 * 16}{\sqrt{42}}) [/tex]
CI = (121.014, 130.986)
4) Conclusion:
We reject the estimated potential revenue advised by the consultant, H0, as it is too high, because the t-calculated falls in rejection region(i.e, less than critical value), also the upper limit of the confidence interval is less than $135.
What is the area of a circle?
Answer:
area=πr2
Step-by-step explanation:
pie radius squared
Answer:pie r square
Step-by-step explanation:
What is the probability of flipping tails and rolling a three?
This includes a quarter and dice.
Answer:
1/12
Step-by-step explanation:
There is a 1/6 probability of getting a 3 on a dice roll because there are 6 sides, and there is a 1/2 probability of flipping a tails because there are only 2 possibilities in a coin, if you multiply these 2 values you get 1/12 which is the answer.
PLEASE HELP
Which of the following inequalities is true according to the number line?
Answer:
A ≥ D
Step-by-step explanation:
Evaluate √-75 where s = -3
PLS I NEED HELP ASAP!!!!
A local company is concerned about the number of days missed by its employees due to ill ness. A Random Sample of 10 employees is selected. The Number of days absent in one year is listed below. An Incentive program is offered in an attempt to decrease the number of days absent. The number of days ansent in one year after the incentive program is listed below. Test the claim that the incentive program cuts down on the number of days missed by employees. Use a=0.05. Assume that the distribution is normally distributied.Employee A B C D E F G H I JDays Absent Before incentive 3 8 7 2 9 4 2 0 7 5Days absent after incentive 1 7 7 0 8 2 0 1 5 5
Answer:
The incentive program does not cuts down on the number of days missed by employees.
Step-by-step explanation:
The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.
A paired t-test would be used to determine whether the incentive program cuts down on the number of days missed by employees.
The hypothesis for the test can be defined as follows:
H₀: The incentive program does not cuts down on the number of days missed by employees, i.e. d ≥ 0.
Hₐ: The incentive program cuts down on the number of days missed by employees, i.e. d < 0.
From the information provided the data computed is as follows:
[tex]n=10\\\bar d=-1.1\\SD_{d}=2.99[/tex]
Compute the test statistic value as follows:
[tex]t=\frac{\bar d}{SD_{d}/\sqrt{n}}[/tex]
[tex]=\frac{-1.1}{2.99/\sqrt{10}}\\\\=-1.16[/tex]
The test statistic value is -1.16.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
Compute the p-value of the test as follows:
[tex]p-value=P(t_{n-1}<-1.16)\\=P(t_{10-1}<-1.16)\\=P(t_{9}<-1.16)\\=0.1379[/tex]
*Use a t-table.
The p-value of the test is 0.1379.
The p-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.
Thus, there is not enough evidence to support the claim.
Conclusion:
The incentive program does not cuts down on the number of days missed by employees
please now is urgent
Answer:
[tex]15m^2+3[/tex]
Step-by-step explanation:
7 - 4 = 3
To add the m^2 you just add the first numbers together.
9m^2 + 6m^2 = 15m^2
The following 96% confidence interval based on a sample of 32 students was formed to estimate the population mean time that students will require to complete a particular examination: 62.4 ± 12.6 minutes. Which one of the following interpretations is correct for this confidence interval?A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutesB) We are 96% confident that the sample mean time (62.4 minutes) equals the true mean timeC) We are 96% confident that the population mean time required by students who take this test is 62.4 minutesD) We are 96% confident that the sample mean time (62.4 minutes) is correctE) We are 4% confident that an individual student taking this test will require less than 49.8 minutes or more than 75.0 minutes
Answer:
A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutes
Step-by-step explanation:
x% confidence interval is between a ± b.
a is the sample mean.
b is the margin of error.
Interpretation: We are x% sure that the population mean is between a-b and a+b.
In this question:
96% confidence interval for the mean time that students will require to complete a particular examination. Between 62.4 - 12.6 = 49.8 minutes and 62.4 + 12.6 = 75 minutes.
The correct interpretation is that we are 96% sure that the population mean is in this interval.
So the correct answer is:
A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutes
Answer:
The confidence interval for the true mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The confidence interval for this case i given by:
[tex] 62.4 -12.6 \leq \mu \leq 62.4+12.6[/tex]
[tex] 49.8 \leq \mu \leq 75.0[/tex]
For this case we can conclude that the true mean for the time that students will require to complete a particular examination is between 49.8 and 75.0 minutes. And the best option for this case by:
A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutes
Step-by-step explanation:
The confidence interval for the true mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The confidence interval for this case i given by:
[tex] 62.4 -12.6 \leq \mu \leq 62.4+12.6[/tex]
[tex] 49.8 \leq \mu \leq 75.0[/tex]
For this case we can conclude that the true mean for the time that students will require to complete a particular examination is between 49.8 and 75.0 minutes. And the best option for this case by:
A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutes
WILL GIVE BRAINLIEST ANSWER TO WHOEVER ANSWERS FIRST AND CORRECT PLEASE EXPLAIN WHY YOU ARE CORRECT