Answer:
The three geometric means are 3, 9/2 and 27/4Step-by-step explanation:
The nth term of a geometric sequence is expressed as Tn = [tex]ar^{n-1}[/tex] where;
a is the first term
r is the common ratio
n is the number of terms
Since we are to insert three geometric means between 2 and 81/8, the total number of terms in the sequence will be 5 terms as shown;
2, a, b, c, 81/8
a, b, and c are the 3 geometric mean to be inserted
T1 = [tex]ar^{1-1}[/tex] = 2
T1 = a = 2....(1)
T5= [tex]ar^{5-1}[/tex]
T5 = [tex]ar^{4}[/tex] = 81/8... (2)
Dividing equation 1 by 2 we have;
[tex]\frac{ar^{4} }{a}= \frac{\frac{81}{8} }{2}[/tex]
[tex]r^{4} = \frac{81}{16}\\\\r = \sqrt[4]{\frac{81}{16} } \\r = 3/2[/tex]
Given a =2 and r = 3/2;
[tex]T2=ar\\T2 = 2*3/2\\T2 = 3\\\\T3 = ar^{2} \\T3 = 2*\frac{3}{2} ^{2} \\T3 = 2*9/4\\T3 = 9/2\\\\T4 = ar^{3}\\T4 = 2*\frac{3}{2} ^{3} \\T4 = 2*27/8\\T4 = 27/4\\[/tex]
Therefore the three geometric means are 3, 9/2 and 27/4
In a geometric sequence where three terms lie between 2 and 81/8, the three geometric terms are:
[tex]\mathbf{T_2 =3 }[/tex]
[tex]\mathbf{T_3 =\frac{9}{2} }[/tex]
[tex]\mathbf{T_4 =\frac{27}{4} }[/tex]
Recall:
nth term of a geometric sequence is given as: [tex]\mathbf{T_n = ar^{n - 1}}[/tex]a = the first term; r = the common ratio; n = the number of termsGiven a geometric sequence, 2 . . . 81/8, with three other terms in the middle, first, find the value of r.
Thus:
First Term:
a = 2Fifth Term:
[tex]T_5 = ar^{n - 1}[/tex]
a = 2
n = 5
r = ?
T5 = 81/8
Plug in the value of a, n, and T5[tex]\frac{81}{8} = 2r^{5 - 1}\\\\\frac{81}{8} = 2r^4\\\\[/tex]
Multiply both sides by 8[tex]\frac{81}{8} \times 8 = 2r^4 \times 8\\\\81 = 16r^4\\\\[/tex]
Divide both sides by 16[tex]\frac{81}{16} = \frac{16r^4}{16} \\\\\frac{81}{16} = r^4\\\\[/tex]
Take the fourth root of both sides[tex]\sqrt[4]{\frac{81}{16}} = r\\\\\frac{3}{2} = r\\\\\mathbf{r = \frac{3}{2}}[/tex]
Find the three geometric means [tex]T_2, T_3, $ and $ T_4[/tex] between 2 and 81/8.
[tex]\mathbf{T_n = ar^{n - 1}}[/tex]
a = 2
r = 3/2
Thus:[tex]T_2 = 2 \times (\frac{3}{2}) ^{2 - 1}\\\\T_2 = 2 \times (\frac{3}{2}) ^{1}\\\\\mathbf{T_2 = 3}[/tex]
[tex]T_3 = 2 \times \frac{3}{2} ^{3 - 1}\\\\T_3 = 2 \times (\frac{3}{2}) ^{2}\\\\T_3 = 2 \times \frac{9}{4}\\\\\mathbf{T_3 =\frac{9}{2} }[/tex]
[tex]T_4 = 2 \times \frac{3}{2} ^{4 - 1}\\\\T_4 = 2 \times (\frac{3}{2}) ^{3}\\\\T_4 = 2 \times \frac{27}{8}\\\\\mathbf{T_4 =\frac{27}{4} }[/tex]
Therefore, in a geometric sequence where three terms lie between 2 and 81/8, the three geometric terms are:
[tex]\mathbf{T_2 =3 }[/tex]
[tex]\mathbf{T_3 =\frac{9}{2} }[/tex]
[tex]\mathbf{T_4 =\frac{27}{4} }[/tex]
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9+x-7 I need help bad
Step-by-step explanation:
9 + x - 7
Solving like terms
x + 2
If we find the value of x
X + 2 = 0
x = - 2
Last year, Jina had 30,000 to invest. She invested some of it in an account that paid 9%simple interest per year, and she invested the rest in an account that paid 5% simple interest per year. After one year, she received a total of $1540 in interest. How much did she invest in each account?
first account :
second:
Answer:
Amount invested in first account = $1,000
Amount invested in second account = $29,000
Step-by-step explanation:
Jina had total amount of $30,000 to invest last year.
Let x be the amount that Jina invested in the first account at interest rate of 9%
Mathematically,
0.09x
she invested the remaining amount in the second account at an interest rate of 5%
Mathematically,
0.05(30,000 - x)
Jina received $1540 in interest.
0.09x + 0.05(30,000 - x) = 1540
0.09x + 1500 - 0.05x = 1540
0.04x = 1540 - 1500
0.04x = 40
x = 40/0.04
x = $1,000
Therefore, Jina invested an amount of $1,000 in the first account at interest rate of 9%
The remaining amount that she invested in the second account is
Amount invested in second account = $30,000 - $1,000
Amount invested in second account = $29,000
Therefore, Jina invested an amount of $29,000 in the second account at interest rate of 5%
Verification:
0.09x + 0.05(30,000 - x) = 1540
0.09(1000) + 0.05(30,000 - 1000) = 1540
90 + 1450 = 1540
1540 = 1540 (satisfied)
During the chess championship, each player played with each other two games. Players who win in a game were awarded 1 point, while those who draws were given a half-point. Losing a game was worth zero points. The three best players scored together 24 points, which is twice less than the sum of points of all other players scored. How many players were participating in the championship?
Answer:
9
Step-by-step explanation:
If 24 points is half the number of points all other players scored, then the points scored by all other players total 24·2 = 48.
All points together total ...
24 + 48 = 72
A point is awarded for each game, so there were a total of 72 games.
N players will play a total of (N/2)(N-1) games if they play each opponent once. Here, each opponent is played twice, so the total number of games played by N players is ...
N(N-1) = 72
9·8 = 72 ⇒ N = 9
The number of players in the championship was 9.
Let’s look at another one of Homer’s rocket launches. It was launched from ground level with an initial velocity of 208 feet per second. Its distance in feet from the ground after t seconds is given by S(t) = -16t2 + 208t. What is the maximum altitude (height) the rocket will attain during its flight? (Think about where the maximum value of a parabola occurs.)
Answer:
Smax = 676 ft
the maximum altitude (height) the rocket will attain during its flight is 676 ft
Step-by-step explanation:
Given;
The height function S(t) of the rocket as;
S(t) = -16t2 + 208t
The maximum altitude Smax, will occur at dS/dt = 0
differentiating S(t);
dS/dt = -32t + 208 = 0
-32t +208 = 0
32t = 208
t = 208/32
t = 6.5 seconds.
The maximum altitude Smax is;
Substituting t = 6.5 s
Smax = -16(6.5)^2 + 208(6.5)
Smax = 676 ft
the maximum altitude (height) the rocket will attain during its flight is 676 ft
The business department at a university has 18 faculty members. Of them, 11 are in favor of the proposition that all MBA students should take a course in ethics and 7 are against this proposition. If 5 faculty members are randomly selected from the 18, what is the probability that the number of faculty members in this sample who are in favor of the proposition is exactly two
Answer:
0.225
Step-by-step explanation:
Total outcomes of choosing 5 out of 18 members = 18C5
Outcomes of choosing 2 out 11 favourers, 3 out of 7 members = 11C2 & 7C3
Probability = Favourable outcomes / Total outcomes
= ( 11C2 x 7C3 ) / 18C5
[ { 11 ! / 2! 9! } {7 ! / 3! 4! } ]
[ 18 ! / 5! 13! ]
( 55 x 35 ) / 8568
1925 / 8568
= 0.2246 ≈ 0.225
The lifetime of certain type of light bulb is normally distributed with a mean of 1000 hours and a standard deviation of 110 hours. A hardware store manager claims that the new light bulb model has a longer average lifetime. A sample of 10 from the new light bulb model is obtained for a test. Consider a rejection region After testing hypotheses, suppose that a further study establishes that, in fact, the average lifetime of the new lightbulb is 1130 hours. Find the probability of a type II error (round off to second decimal place).
Answer:
There is a probability of P=0.02 of making a Type II error if the true mean is μ=1130.
Step-by-step explanation:
This is an hypothesis test for the lifetime of a certain ype of light bulb.
The population distribution is normal, with mean of 1,000 hours and STD of 110 hours.
The sample size for this test is n=10.
The significance level is assumed to be 0.05.
In this case, when the claim is that the new light bulb model has a longer average lifetime, so this is a right-tailed test.
For a significance level, the critical value (zc) that is bound of the rejection region is:
[tex]P(z>z_c)=0.05[/tex]
This value of zc is zc=1.645.
This value, for a sample with size n=10 is:
[tex]z_c=\dfrac{X_c-\mu}{\sigma/\sqrt{n}}\\\\\\X_c=\mu+\dfrac{z_c\cdort\sigma}{\sqrt{n}}=1000+\dfrac{1.645*110}{\sqrt{10}}=1000+57.22=1057.22[/tex]
That means that if the sample mean (of a sample of size n=10) is bigger than 1057.22, the null hypothesis will be rejected.
The Type II error happens when a false null hypothesis failed to be rejected.
We now know that the true mean of the lifetime is 1130, the probability of not rejecting the null hypothesis (H0: μ=1100) is the probability of getting a sample mean smaller than 1057.22.
The probability of getting a sample smaller than 1057.22 when the true mean is 1130 is:
[tex]z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{1057.22-1130}{110/\sqrt{10}}=\dfrac{-72.78}{34.7851}=-2.0923 \\\\\\P(M<1057.22)=P(z<-2.0923)=0.01821[/tex]
Then, there is a probability of P=0.02 of making a Type II error if the true mean is μ=1130.
Using the normal distribution and the central limit theorem, it is found that there is a 0.0001 = 0.01% probability of a type II error.
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 1130 hours, hence [tex]\mu = 1130[/tex]Standard deviation of 110 hours, hence [tex]\sigma = 110[/tex]Sample of 10 bulbs, hence [tex]n = 10, s = \frac{110}{\sqrt{10}}[/tex].We test if the average lifetime is longer, and a Type II error is concluding that it is not longer when in fact it is longer, hence, it is the probability of finding a sample mean below 1000 hours, which is the p-value of Z when X = 1000.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1000 - 1130}{\frac{110}{\sqrt{10}}}[/tex]
[tex]Z = -3.74[/tex]
[tex]Z = -3.74[/tex] has a p-value of 0.0001.
0.0001 = 0.01% probability of a type II error.
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Lisa, a dentist, believes not enough teenagers floss daily. She would like to test the claim that the proportion of teenagers who floss twice a day is less than 40%. To test this claim, a group of 400 teenagers are randomly selected and its determined that 149 floss twice a day.
Answer:
[tex]z=\frac{0.3725 -0.4}{\sqrt{\frac{0.4(1-0.4)}{400}}}=-1.123[/tex]
The p value for a left tailed test would be:
[tex]p_v =P(z<-1.123)=0.131[/tex]
Since the p value is very higher we can conclude that the true proportion of teenagers who floss twice a day is NOT less than 40%.
Step-by-step explanation:
Information given
n=400 represent the random sample given
X=149 represent the floss twice a day
[tex]\hat p=\frac{149}{400}=0.3725[/tex] estimated proportion of floss twice a day
[tex]p_o=0.4[/tex] is the value the proportion that we want to check
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to check proportion of teenagers who floss twice a day is less than 40%, so then the system of hypothesis are.:
Null hypothesis:[tex]p \geq 0.4[/tex]
Alternative hypothesis:[tex]p < 0.4[/tex]
For the one sample proportion test the statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
If we replace the info given we got:
[tex]z=\frac{0.3725 -0.4}{\sqrt{\frac{0.4(1-0.4)}{400}}}=-1.123[/tex]
The p value for a left tailed test would be:
[tex]p_v =P(z<-1.123)=0.131[/tex]
Since the p value is very higher we can conclude that the true proportion of teenagers who floss twice a day is NOT less than 40%.
The first sail has one side of length 9 feet and another of length 6 feet. Determine the range of possible lengths of the third side of the sail.
first find the greatest possible length:
9 + 6 > x
15 > x
x < 15
Then find the lowest possible length:
x + 6 > 9
x > 9 - 6
x > 3
3 < x < 15
To determine the range of possible lengths of the third side of a sail, use the triangle inequality theorem. The range is 3 feet to 15 feet.
Explanation:To determine the range of possible lengths of the third side of the sail, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the two given sides are 9 feet and 6 feet. So, the third side must be less than the sum of these two sides and greater than the difference between these two sides.
Therefore, the range of possible lengths of the third side of the sail is 3 feet to 15 feet.
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What would be a correct expression for 0 ?
SELECT ALL THAT APPLY
Answer:
If its the sum then, 0+0 if its an quotient, 0 divided by 0 if its a multiply problem, 0 times 0.
Step-by-step explanation:
0 can only be the answer of a problem if its used on itself or if its multiplies by another.
Select the correct answer.
Determine the solutions to the following equation.
(1 – 4)2 = 81
O
x= -13 and 5
x= -5 and 13
x= -4 and 9
x = -9 and 4
Shouldn't the equation read " (x - 4)² = 81 ", instead of "(1 - 4)² = 81" ?
If so, then the solutions are x = -5 and x = 13 .
If it's really "(1 - 4)² = 81", then that's not even an equation, and there's no solution.
The solutions to the given equation are x = -5 and x = 13.
The correct solutions to the given equation are x = -5 and x = 13.
To solve the equation (1 - 4)2 = 81:
Calculate (1 - 4)2 = 81.Then simplify the equation: (-3)2 = 81, which gives 9 = 81.Finally, since 9 is not equal to 81, the solutions are x = -5 and x = 13.Simplify this expression
3.1 - 3.8n - 2n +6
Answer: 9.1 - 5.8n
Step-by-step explanation:
All you need to do here is combine like terms.
Lets identify the two sets of like terms:
-3.8n and -2n
AND
3.1 and 6
So, you will add or subtract them as needed.
I will start by combining 3.8n and -2n
= 3.1 -3.8 -2n + 6
= 3.1 + 6 -5.8n
Now combine the 3.1 and 6.
= 9.1 - 5.8n
This is your answer!
A teacher selects students from her class of 37 students to do 4 different jobs in the classroom: pick uphomework, hand out review forms, staple worksheets, and sort the submissions. Each job is performedby exactly one student in the class and no student can get more than one job. How many ways arethere for her to select students and assign them to the jobs?
Answer:
There are 1,585,080 ways for her to select students and assign them to the jobs
Step-by-step explanation:
The order in which the students are selected is important, since different orderings means different jobs for each student selected. So the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem:
4 students selected from a set of 37. So
[tex]P_{(37,4)} = \frac{37!}{(37-4)!} = 1585080[/tex]
There are 1,585,080 ways for her to select students and assign them to the jobs
How many decimal places are in 7,790,200
Final answer:
The number 7,790,200 has zero decimal places as it is a whole number with no fractional part and ends in the unit's place.
Explanation:
The student asked how many decimal places are in 7,790,200. This question is related to place value and decimals in mathematics. The number 7,790,200 has no decimal part since it is a whole number and ends in the unit's place. Therefore, it contains zero decimal places. To expand on place value, when expressing numbers in decimal form, the position of a digit represents its value in powers of ten. For instance, the number 1837 can be decomposed as (1 × 10³) + (8 × 10²) + (3 × 10¹) + (7 × 10⁰), which shows the ones, tens, hundreds, and thousands places respectively.
a show company makes blue shoes and black shoes with a ratio of 3:4 ratio. if the company makes 360 black shoes how many blue shoes will they make? plz halp and if u pway roblox my username is zaw1031 :3
In the given scenario, when the shoe company makes 360 black shoes, they will also make 270 blue shoes as the ratio was provided as 3:4.
Explanation:The problem involves the concept of ratio proportion. Given the ratio of blue shoes to black shoes is 3:4, this means for every 3 blue shoes, 4 black shoes are made. If the company makes 360 black shoes, this is like 90 sets of 4 black shoes (360/4). That means 90 sets of 3 blue shoes must also be made. Therefore, the company will make 270 (90*3) blue shoes when 360 black shoes are made.
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A city has a population of 360,000 people. Suppose that each year the population grows by 6.75%. What will the population be after 12 years.
Answer:
So, if it grows by 6.75%, each year the population is 106.75% of the year before.
After 1 year, 370,000(1.0675). After two years, 370,000(1.0675)(1.0675).
370,000(1.0675)12 = your answer
Step-by-step explanation:
Answer:
asdfgbhnjm
Step-by-step explanation:
zxcvb
A baseball player threw 82 strikes out of 103 pitches. what percentage of pitches were strikes?
We have been given that a baseball player threw 82 strikes out of 103 pitches. We are asked to find the percentage of pitches that were strikes.
To solve our given problem, we need to find strikes are what percent of pitches.
[tex]\text{Percentage of pitches that were strikes}=\frac{82}{103}\times 100\%[/tex]
[tex]\text{Percentage of pitches that were strikes}=0.7961165\times 100\%[/tex]
[tex]\text{Percentage of pitches that were strikes}=79.61165\%[/tex]
[tex]\text{Percentage of pitches that were strikes}\approx 79.6\%[/tex]
Therefore, approximately [tex]79.6\%[/tex] of pitches were strikes.
Many older homes have electrical systems that use fuses rather than circuit breakers. A manufacturer of 40-amp fuses wants to make sure that the mean amperage at which its fuses burn out is in fact 40. If the mean amperage is lower than 40, customers will complain because the fuses require replacement too often. If the mean amperage is higher than 40, the manufacturer might be liable for damage to an electrical system due to fuse malfunction. To verify the amperage of the fuses, a sample of fuses is to be selected and inspected. If a hypothesis test were to be performed on the resulting data, what null and alternative hypotheses would be of interest to the manufacturer? Describe type I and type II errors in the context.
Answer:
Type I error: Concluding μ ≠ 40, when in fact μ = 40.
Type II error: Concluding μ = 40, when in fact μ ≠ 40.
Step-by-step explanation:
In this case we need to determine whether the mean amperage at which the 40-amp fuses burn out is 40.
The hypothesis to test this can be defined as follows:
H₀: The mean amperage at which the 40-amp fuses burn out is 40, i.e. μ = 40.
Hₐ: The mean amperage at which the 40-amp fuses burn out is different from 40, i.e. μ ≠ 40.
A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).
In this context, a type I error will be committed if we conclude that the mean amperage at which the 40-amp fuses burn out is different from 40, when in fact it is 40.
And a type II error will be committed if we conclude that the mean amperage at which the 40-amp fuses burn out is 40, when in fact it is different from 40.
The null hypothesis for the manufacturer of 40-amp fuses is that the mean amperage at which fuses burn out is 40 amps, while the alternative hypothesis is that the mean is not 40 amps. A Type I error is incorrectly rejecting a true null hypothesis, and a Type II error is failing to reject a false null hypothesis, both of which have consequences for the manufacturer in terms of production and safety.
Explanation:A manufacturer of 40-amp fuses is interested in ensuring the mean amperage at which its fuses burn out is indeed 40 amps. To validate this, a sample of fuses must be tested, and a hypothesis test applied to the results. The null hypothesis (H0) of interest would state that the mean amperage at which the fuses burn out is 40 amps, formulated as H0: μ = 40, where μ is the population mean. The alternative hypothesis (H1) would indicate that the mean amperage is not 40 amps: H1: μ ≠ 40.
In this scenario, a Type I error would occur if the hypothesis test incorrectly rejects the null hypothesis when in fact the fuses do burn out at the mean of 40 amps. This could result in unnecessary production changes and costs for the manufacturer. Alternatively, a Type II error would occur if the test fails to reject the null hypothesis when the true mean amperage at which the fuses burn out is actually different from 40 amps. In such a case, the manufacturer might continue producing fuses that could either require frequent replacement or pose a risk of damage to electrical systems.
The determination of the true mean amperage is relevant because of the role of fuses and circuit breakers in protecting appliances and residents from harm due to large currents and because they are designed to tolerate high currents for brief periods, or in some cases like electric motors, for a longer duration. Thus, ensuring fuses operate correctly at their intended amperage is crucial for safety and functionality.
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You run a small trucking company that transports goods from Bristol, TN to Winslow, AZ. This trip should take 32 hours and 16 minutes (1936 minutes) if done in accordance with safety regulations. However, you believe that your employees have not been following these rules, because they are completing the trip too quickly. You decide to test your hypothesis. You record the time it takes for your employees to make the trip and record the following results
X =1736 minutes s = 635; n = 46
A) State your null and alternative hypotheses
B) Carry out the test with α=005, and state your conclusion
C) Carry out the test with α=0.01, and state your conclusion
D) Does your conclusion change with the change in a?
Answer:
a) Null hypothesis: [tex]\mu \geq 1936[/tex]
Alternative hypothesis: [tex]\mu <1936[/tex]
b) [tex] t = \frac{1736-1936}{\frac{635}{\sqrt{46}}}= -2.136[/tex]
The degrees of freedom are:
[tex] df = n-1= 46-1=45[/tex]
The p value for this case since is a left tailed test is given by:
[tex] p_v = P(t_{45} <-2.136) = 0.0191[/tex]
And since the p value is lower than the significance level 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 1736
c) [tex] p_v = P(t_{45} <-2.136) = 0.0191[/tex]
And since the p value is higher than the significance level 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is NOT significantly lower than 1736
d) For this case the answer is yes since when we change the significance level from 0.05 to 0.01 we see that the final decision changes.
Step-by-step explanation:
Part a
We are trying to proof the following system of hypothesis:
Null hypothesis: [tex]\mu \geq 1936[/tex]
Alternative hypothesis: [tex]\mu <1936[/tex]
Part b
We have the following data given:
[tex]\bar X =1736[/tex] minute s = 635; n = 46
And the statistic for this case is given by:
[tex] t = \frac{\bar X- \mu}{\frac{s}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] t = \frac{1736-1936}{\frac{635}{\sqrt{46}}}= -2.136[/tex]
The degrees of freedom are:
[tex] df = n-1= 46-1=45[/tex]
The p value for this case since is a left tailed test is given by:
[tex] p_v = P(t_{45} <-2.136) = 0.0191[/tex]
And since the p value is lower than the significance level 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 1736
Part c
We have the same statistic t = -2.136
[tex] p_v = P(t_{45} <-2.136) = 0.0191[/tex]
And since the p value is higher than the significance level 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is NOT significantly lower than 1736
Part d
For this case the answer is yes since when we change the significance level from 0.05 to 0.01 we see that the final decision changes.
Null and alternative hypotheses are created for a t-test regarding trip times. The t-test is conducted at two different significance levels (α = 0.05 and α = 0.01). The conclusion may change with adjustments to α.
Explanation:The hypotheses for this statistical test would be:
Null Hypothesis (H0): The drivers are adhering to the safety regulations, meaning the average trip time is equal to 1936 minutes (µ = 1936). Alternative Hypothesis (HA): The drivers are not adhering to safety regulations, meaning the average trip time is not equal to 1936 minutes (µ ≠ 1936).
To test these hypotheses, we can perform a two-sided t-test. We are given:
Mean trip time (X) = 1736 minutes Standard deviation (s) = 635 minutes Number of observations (n) = 46 trips
For α = 0.05, if the t-statistic's associated p-value is lesser than α, we reject the null hypothesis. Likewise, for α = 0.01, the same process is undertaken.
The conclusion reached will depend on the calculated p-value. If the p-value is less than the chosen α, we will reject the null hypothesis and conclude that the drivers are not following safety regulations. If the p-value is greater than α, we fail to reject the null hypothesis and cannot conclude that drivers are not following safety regulations.
The test conclusion may change with changes in α, as α establishes the threshold for rejecting the null hypothesis.
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Two cars started from the same point 5 am, traveling in opposite directions. The speed of one car is 40 mph and the speed of the other car is 50 mph. At what time will the cars be 450 miles apart?
Answer:
10:00 AM
Step-by-step explanation:
PLEASE HELP!!
A glass bead has the shape of a rectangular prism with a smaller rectangular prism removed. What is the volume of the glass that forms the bead?
The volume of the glass bead formed by a rectangular prism with a smaller prism removed can be found by subtracting the volume of the smaller prism from the larger prism. As an example, a larger prism of volume 60 cubic cm and smaller prism of volume 8 cubic cm gives a bead of volume 52 cubic cm.
Explanation:The volume of the glass bead formed by a rectangular prism with a smaller rectangular prism removed can be calculated using the formula for the volume of a rectangular prism, which is length × width × height. The volume of the glass bead would then be the volume of the larger prism minus the volume of the smaller prism.
As an example, if the larger prism has a length of 5cm, width of 4cm, and height of 3cm, its volume would be 5cm × 4cm × 3cm = 60 cubic cm. If the smaller prism removed has a length of 2 cm, width of 2 cm, and height of 2 cm, its volume would be 2cm × 2cm × 2cm = 8 cubic cm. Subtracting the volume of the smaller prism from the larger one gives a volume of 60 cubic cm - 8 cubic cm = 52 cubic cm which is the volume of the glass bead.
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The volume of the glass bead is then 200 cm³ - 6 cm³ = 194 cm³.
Calculating the Volume of a Glass Bead
To find the volume of a glass bead with the shape of a rectangular prism with a smaller rectangular prism removed, follow these steps:
Calculate the volume of the larger rectangular prism. Use the formula Volume = length × width × height.Next, calculate the volume of the smaller rectangular prism that is being removed using the same formula.Subtract the volume of the smaller prism from the volume of the larger prism. This will give you the volume of the glass bead.For example, if the dimensions of the larger rectangular prism are 10 cm (length), 5 cm (width), and 4 cm (height), its volume will be 200 cm³. If the smaller removed prism has dimensions of 3 cm (length), 2 cm (width), and 1 cm (height), its volume will be 6 cm³. The volume of the glass bead is then 200 cm³ - 6 cm³ = 194 cm³.
Write an equation to represent the following statement.
j divided by 9 is 5.
______
Solve for j.
j=______
Answer:
j / 9 = 5
j = 45
Step-by-step explanation:
j / 9 = 5
Multiply each side by 9
j/9 * 9 = 5*9
j = 45
A triangular prism has ( ) faces its the 2nd question in the edenuity assignment pls help u will get brainliest
Answer:
5 faces
Step-by-step explanation:
Giving brainliest for CORRECT awnser.
Answer:
D. x + 8
Step-by-step explanation:
factor. Find factors of x² and 48, in which, when combined, will equal 2x:
x² + 2x - 48
x 8
x -6
(x + 8)(x - 6)
D. x + 8 is your answer.
~
Solve the equation x^2+17x+12=-3x^2 to the nearest tenth.
Answer:
[tex]x=-\frac{17}{8}+\frac{\sqrt{97} }{8}[/tex] or [tex]x=-\frac{17}{8}-\frac{\sqrt{97} }{8}[/tex]
Step-by-step explanation:
[tex]x^2+17x+12=-3x^2[/tex]
Add [tex]3x^2[/tex] on both sides.
[tex]x^2+17x+12+3x^2=-3x^2+3x^2[/tex]
[tex]x^2+17x+12+3x^2=0[/tex]
Combine like terms;
[tex]4x^2+17x+12=0[/tex]
Use the quadratic formula;
a=4
b=17
c=12
[tex]x=\frac{-b\frac{+}{}\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-(17)\frac{+}{}\sqrt{(17)^2-4(4)(12)} }{2(4)}[/tex]
[tex]x=\frac{-17\frac{+}{}\sqrt{289-192} }{8}[/tex]
[tex]x=\frac{-17\frac{+}{}\sqrt{97} }{8}[/tex]
[tex]x=-\frac{17}{8}+\frac{\sqrt{97} }{8}[/tex] or [tex]x=-\frac{17}{8}-\frac{\sqrt{97} }{8}[/tex]
PLS HELP WILL GIVE BRAINILIST 20 POINTS!
If you have no more than $15 in your bank account, which of the following inequalities correctly represents the amount of money in your bank account?
m ≤ $15
m ≥ $15
m < $15
m > $15
Answer: M≤ $15
Step-by-step explanation:
The answer is [ m ≤ $15 ]
The question states, "If you have no more than $15." This means that you can only have up to $15 and no more.
So, the solutions to the set are all real numbers except the numbers after 15.
Let's say you had $9. If we were to substitute 9 with m in the inequality, we would get; 9 ≤ 15. This satisfies the inequality since the number is less than 15.
Best of Luck!
The length of a rectangle is 4 more than twice the width. The perimeter is 56 cm. Find the width and the area of the rectangle.
Answer:
W=12 area=192 12×16
Area192
Step-by-step explanation:
2(4+w)+2w=56
8+4w=56
-8
4w= 48
/4
W=12
To solve the problem, a system of equations is used based on the given conditions. Through algebraic process, we discover the width (W) to be 8 cm and the length (L) to be 20 cm. Consequently, the rectangle's area is calculated to be 160 cm².
Explanation:The given problem falls under algebra and can be solved through a system of equations. According to the problem, the length of a rectangle is 4 more than twice the width. So we can denote the length of the rectangle as L and the width as W, forming Equation 1: L = 2W + 4.
The perimeter of a rectangle is known to be 2L + 2W. Given that perimeter is equal to 56 cm, we can plug in L from Equation 1 to Equation 2: 2(2W + 4) + 2W = 56. Simplifying this, we get 6W + 8 = 56. By solving for W, we find W as 8 cm. Substituting W = 8 cm into Equation 1, L comes out as 20 cm.
Next, the area of a rectangle is calculated using the formula L * W, which yields the area as 160 cm².
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The line graph shows the number of video rental stores for the years 2005 through 2012.
There were________ stores in 2009.
Answer:
do you have a picture of the line graph ?
Answer is 4,000
Step-by-step explanation:
In ΔBCD, the measure of ∠D=90°, the measure of ∠C=42°, and CD = 7.5 feet. Find the length of DB to the nearest tenth of a foot.
We have been given that in ΔBCD, the measure of ∠D=90°, the measure of ∠C=42°, and CD = 7.5 feet. We are asked to find the length of DB to nearest tenth of foot.
First of all, we will draw a right triangle using our given information.
We can see from the attachment that DB is opposite side to angle C and CD is adjacent side to angle.
We know that tangent relates opposite side of right triangle to adjacent side of right triangle.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(\angle C)=\frac{DB}{CD}[/tex]
[tex]\text{tan}(42^{\circ})=\frac{DB}{7.5}[/tex]
[tex]7.5\cdot\text{tan}(42^{\circ})=\frac{DB}{7.5}\cdot 7.5[/tex]
[tex]7.5\cdot\text{tan}(42^{\circ})=DB[/tex]
[tex]7.5\cdot0.900404044298=DB[/tex]
[tex]DB=7.5\cdot0.900404044298[/tex]
[tex]DB=6.753030332235\approx 6.8[/tex]
Therefore, the length of DB is approximately 6.8 feet.
The weight of National Football League (NFL) players has increased steadily, gaining up to 1.5 lb. per year since 1942. According to ESPN, the average weight of a NFL player is now 252.8 lb. Assume the population standard deviation is 25 lb. If a random sample of 50 players is selected, what is the probability that the sample mean will be more than 262 lb.
Answer:
The probability that the sample mean weight will be more than 262 lb is 0.0047.
Step-by-step explanation:
The random variable X can be defined as the weight of National Football League (NFL) players now.
The mean weight is, μ = 252.8 lb.
The standard deviation of the weights is, σ = 25 lb.
A random sample of n = 50 NFL players are selected.
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The sample of players selected is quite large, i.e. n = 50 > 30, so the central limit theorem can be used to approximate the distribution of sample means.
[tex]\bar X\sim N(\mu_{\bar x}=252.8,\ \sigma_{\bar x}=3.536)[/tex]
Compute the probability that the sample mean weight will be more than 262 lb as follows:
[tex]P(\bar X>262)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{262-252.8}{3.536})\\\\=P(Z>2.60)\\\\=1-P(Z<2.60)\\\\=1-0.99534\\\\=0.00466\\\\\approx 0.0047[/tex]
*Use a z-table for the probability.
Thus, the probability that the sample mean weight will be more than 262 lb is 0.0047.
To find the probability that the sample mean will be more than 262 lb, calculate the z-score using the sample mean, population mean, standard deviation, and sample size. Then, find the corresponding probability using the standard normal distribution table. Subtract the probability from 1 to get the final result, which is approximately 0.2%.
Explanation:To solve this problem, we need to use the z-score formula and the standard normal distribution table. First, calculate the z-score using the formula: z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. In this case, x = 262 lb, μ = 252.8 lb, σ = 25 lb, and n = 50. Plug in these values and calculate the z-score. Next, find the corresponding probability using the standard normal distribution table. Look up the z-score and find the corresponding probability. The probability that the sample mean will be more than 262 lb can be found by subtracting the probability you found from 1.
Calculating the z-score:
z = (262 - 252.8) / (25 / sqrt(50)) = 2.901.
Using the standard normal distribution table, the probability corresponding to a z-score of 2.901 is approximately 0.998. Therefore, the probability that the sample mean will be more than 262 lb is approximately 1 - 0.998 = 0.002, or 0.2%.
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help help help help help
Answer:
Easy! The cool thing about correlations is you can easily determine them by reading your graph, no hard brain work involved!
It should be A.
Step-by-step explanation:
By looking at the graph, you can already determine that the correlation is negative, since it's going down, not up.
Now, you need to read what is happening on the graph. As the price (X-Axis) is increasing, less people are spending their money, presumably because it's not priced affordably. So as you can see according to your Y-Axis, the amount of people buying is lowered.
Hopefully this isn't confusing!