Answer:
A. The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative. Squared deviations can never be negative.
Step-by-step explanation:
As we know that
The standard deviation is the square root of the variance and on the other side the variance is the square of the standard deviation
In mathematically
[tex]\sigma = \sqrt{variance}[/tex]
And,
[tex]variance = \sigma^2[/tex]
Moreover, the standard deviation and the variance could never by negative neither the squared deviation is negative. All three are always positive
Hence, the correct option is a.
Answer:
B. The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.
Which two statements describe domestic stocks? They are directly affected by exchange rate fluctuations. They are always traded in local currency. They are likely to be unfamiliar to investors. They are based in the investor’s country of residence. They form an important part of foreign trade.
Answer:
They are based in the investor’s country of residence
They are always traded in local currency.
Step-by-step explanation:
Stocks, in general, indicate ownership shares of a company and domestic stocks as the name suggests are stocks that are based in the investor's home country.
These domestic stocks are almost always traded in local currency and they are a great help to local investors because it eliminates the currency risk because of exchange rates which can change at any time.
Answer
They are based in the investor’s country of residence
They are always traded in local currency.
Step-by-step explanation:
Stocks, in general, indicate ownership shares of a company and domestic stocks as the name suggests are stocks that are based in the investor's home country.
These domestic stocks are almost always traded in local currency and they are a great help to local investors because it eliminates the currency risk because of exchange rates which can change at any time.
6x-5<2x+11. plz helpppppp
Answer:
x < 4 or x = ( -∞, 4)
Step-by-step explanation:
6x - 5 < 2x + 116x - 2x < 11 + 54x < 16 x < 16/4x < 4or
x = ( -∞, 4)
[tex]\text{Solve the inequality for x:}\\\\6x-5<2x+11\\\\\text{Subtract 2x from both sides}\\\\4x-5<11\\\\\text{Add 5 to both sides}\\\\4x<16\\\\\text{Divide both sides by 4}\\\\\boxed{x<4}[/tex]
If I set my alarm to read 8:10 when it is really 8:00 (i.e., it is 10 minutes fast) and the alarm goes off each day when it reads 8:10, it will be ___________ but not ___________.
Answer:
If I set my alarm to read 8:10 when it is really 8:00 (i.e., it is 10 minutes fast) and the alarm goes off each day when it reads 8:10, it will be reliable but not valid.
Step-by-step explanation:
If I set my alarm to wake me earlier than I need to be woken, it might be in order to give me enough time to adjust to the alarm, and be awake enough to get out of bed before the normal time I need to be out of bed. This method is very reliable, as there is a very little probability of me waking up late, since I have a 10 minutes head start everyday to get out of bed. The problem is that this method is not valid, since I now actually wake earlier than I am supposed to. The extra 10 minutes can actually lead to a disorientation with time.
The cycle times for a truck hauling concrete to a highway construction site are uniformly distributed over the interval 50 to 70 minutes.
Required:
What is the probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 55 minutes?
Answer:
The probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 55 minutes, should be 1 / 3.
Step-by-step explanation:
It is known that the cycle times for a truck hauling concrete is uniformly distributed over a time interval of ( 50, 70 ). If c = cycle time, according to the question the probability that the cycle exceeds 65 minutes, respectively exceed 55 minutes should be the following - ' [tex]Probability( c > 65 | c > 55 )[/tex]. '
_____
[tex]f( c ) = \left \{ {{1 / 20,} \atop {0}} \right. \\50< c<70 - ( elsewhere )[/tex]
We know that the formula for Probability( A | B ) is P( A ∩ B ) / P( B ),
[tex]P( c > 65 | c > 55 ) =[/tex] [tex]P( c > 55[/tex] ∩ [tex]c > 65 )[/tex] / [tex]P( c > 55 )[/tex],
And now we come to the formula [tex]P( a < c < b )[/tex] = [tex]\int\limits^{70}_{65} {f(x)} \, dc[/tex]. Substitute known values to derive two solutions, forming a fraction that represents the probability we desire.
[tex]P( 65<c<70) = \int\limits^{70}_{65} {f(y)} \, dy\\ = \int\limits^{70}_{65} {(1/20)} \, dy\\ \\= 0.25[/tex]
-------------------------------------
[tex]P( 55<c<70) = \int\limits^{70}_{55} {f(y)} \, dy\\ = \int\limits^{70}_{65} {(1/20)} \, dy\\ \\= 0.75[/tex]
Take 0.25 over 0.75, 0.25 / 0.75, simplified to the fraction 1 / 3, which is our solution.
_____
Probability: 1 / 3
Give the null and alternative hypotheses in symbolic form that would be used in a hypothesis test of the following claim:
The mean time between "clicks" of the second hand on a particular clock is not 1 second.
a. H0: = 1 vs. H1: 1
b. H0: p = 1 vs. H1: p 1
c. H0: = 1 vs. H1:
d. none of these
Answer:
Step-by-step explanation:
The null hypothesis is usually the default statement. The alternative is the opposite of the null and usually tested against the null hypothesis
In this case study,
The null hypothesis in would be that the mean time between clicks of the second hand on a particular clock is 1 second. In symbolic form it would be u = 1
The alternative hypothesis would be that the mean time between clicks of the second hand on a particular clock is 1 not second. In symbolic form, it would be: u =/ 1
Simplify the expression:
– 10x + – 4 – 8 + 7x
Answer:
-3x-12
Step-by-step explanation:
-10x-4-8+7x
-3x-4-8
-3x-12
Answer:
-3x-12
Step-by-step explanation:
– 10x + – 4 – 8 + 7x
Combine like terms
-10x +7x -4-8
-3x -12
Sam weights 51kg. What is this weight to the nearest stone?. Use this conversion, 1kg= 2.2 pounds and 14 pounds= 1 stone
Sam's weight to the nearest stone is equal to 8.0 stone.
Given the following data:
Sam's weight = 51 kg.1 kg = 2.2 pounds.14 pounds = 1 stone.To determine Sam's weight to the nearest stone:
How to convert the units of measurement.In this exercise, you're required to determine Sam's weight to the nearest stone. Thus, we would convert his weight in kilograms to pounds and lastly to stone as follows:
Conversion:
1 kg = 2.2 pounds.
51 kg = [tex]51 \times 2.2[/tex] = 112.2 pounds.
Next, we would convert the value in pounds to stone:
14 pounds = 1 stone.
112.2 pounds = X stone.
Cross-multiplying, we have:
[tex]14X = 112.2\\\\X=\frac{112.2}{14}[/tex]
X = 8.01 ≈ 8.0 stone.
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Using the information regarding proportion of snoring events, choose the correct conclusion for this hypothesis test. H0:p=0.35 ; Ha:p>0.35 The p-value for this hypothesis test is 0.03. The level of significance is α=0.05
Select the correct answer below:
a. There is sufficient evidence to conclude that the proportion of snoring events compared to other events during a sleep study is more than 35%.
b. There is NOT sufficient evidence to conclude that the proportion of snoring events compared to other events during a sleep study is more than 35%.
c. There is sufficient evidence to conclude that the proportion of snoring events compared to other events during a sleep study is more than 5%.
d. There is NOT sufficient evidence to conclude that the proportion of snoring events compared to other events during a sleep study is more than 5%.
Answer:
Option A
Step-by-step explanation:
With the following data, H0:p=0.35 ; Ha:p>0.35 The p-value for this hypothesis test is 0.03. The level of significance is α=0.05.
Since the p value (0.03) is less than alpha (0.05), we will reject the null hypothesis and conclude that there is sufficient evidence to conclude that the proportion of snoring events compared to other events during a sleep study is more than 35%.
For the functions f(x)=8 x 2 +7x and g(x)= x 2 +2x , find (f+g)(x) and (f+g)(3)
Answer:
(f+g)(x)= 9x² + 9x
(f+g)(3) = 108
Step-by-step explanation:
f(x)=8x² +7x
g(x)= x² +2x
(f+g)(x) = f(x) + g(x) = 8x² +7x +x² +2x = 9x² + 9x
(f+g)(x)= 9x² + 9x
(f+g)(3)= 9*3² + 9*3 = 108
PLEASE PLEASE PLEASE HELP TIMEDCan you prove that DE F = HGF Justify your answer. A. Yes, the triangles are congruent by SAS. B. Yes, the triangles are congruent by SSS. C. Yes, the triangles are congruent by SSA. D. No, not enough information is given.
Answer:
A. Yes, the triangles are congruent by SAS.
Step-by-step explanation:
EF = FG and DF = FH-> Given
angle EFD = angle HFG -> Vertical angles are congruent
DE F = HGF -> SAS Triangle Congruence Theorem
We can prove ∠DE F = ∠HGF by SAS congruency.
Hence option A is correct.
In the given triangle,
DE = GE
DF = FH
We know that,
SAS congruency stands for "Side-Angle-Side" congruence,
Which is a rule used in geometry to prove that two triangles are congruent or equal in size and shape.
This rule states that if two sides and the angle between them of one triangle are congruent to the corresponding two sides and angle of another triangle, then the two triangles are congruent.
Since the triangles
DE,GE and DF, FH are the corresponding sides and
DE = GE
DF = FH
Since DEF and FHG are congruent.
Therefore,
∠DE F = ∠HGF
Hence proved.
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determining probability of events. please help!
Answer:
23/90
Step-by-step explanation:
55/90 + 12/90 = 67/9090 - 67 = 2323/9023/90 balls are green or white
i hope this helps!
Please help ASAP! Do not understand how to conduct problem!
Answer:
AB =-4 24 25
-5 15 15
BC= -5
4
10
2BC = -10
8
20
THE Operation AB -2BC cannot be performed because the unequality of the arrays
Step-by-step explanation:
AB=first row (3*2)+(1/2*0)+(5*-2), (3*-4)+(1/2*2)+(5*7), (3*0),(1/2*0),(5*5)
Second row ((1*1)+(-1*0)+(3*-2),(1*-4)+(-1*2)+(3*7), (1*0)+(-1*0)+(3*5)
AB =-4 24 25
-5 15 15
BC =FIRST ROW (1*1)+(-4*2)+(0*0)
SECOND ROW (0*1)+(2*2)+(0*0)
THIRSD ROW (-2*2)+(7*2)+(5*0)
BC= -5
4
10
2BC = -10
8
20
THE Operation AB -2BC cannot be performed because the unequality of the arrays
Two jokers are added to a $52$ card deck and the entire stack of $54$ cards is shuffled randomly. What is the expected number of cards that will be strictly between the two jokers?
Answer:
52/3.
Step-by-step explanation:
There are (54·53)/2 = 1431 ways the 2 jokers can be placed in the 54-card deck. We can consider those to see how the number of cards between them might work out.
Suppose we let J represent a joker, and - represent any other card. The numbers of interest can be found as follows:
For jokers: JJ---... there are 0 cards between. This will be the case also for ...
-JJ---...
--JJ---...
and so on, down to ...
...---JJ
The first of these adjacent jokers can be in any of 53 positions. So, the probability of 0 cards between is 53/1431.
__
For jokers: J-J---..., there is 1 card between. The first of these jokers can be in any of 52 positions, so the probability of 1 card between is 52/1431.
__
Continuing in like fashion, we find the probability of n cards between is (53-n)/1431. So, the expected number of cards between is ...
[tex]E(n)=\sum\limits_{n=0}^{53}{\dfrac{n(53-n)}{1431}}=\dfrac{53}{1431}\sum\limits_{n=0}^{53}{n}-\dfrac{1}{1431}\sum\limits_{n=0}^{53}{n^2}\\\\=\dfrac{53(53\cdot 54)}{1431(2)}-\dfrac{1(53)(54)(107)}{1431(6)}=53-\dfrac{107}{3}\\\\\boxed{E(n)=\dfrac{52}{3}}[/tex]
6 is what percentage of 10?l
Answer:
Hello! The answer will be below!
Step-by-step explanation:
The answer is 60, steps will be below....
Steps:
6 divided by 10
=0.6
And than we do (0.6 x 100)%
Which will give us 60%
Hope this helps! :)
⭐️Have a wonderful day!⭐️
A radio transmission tower is feet tall. How long should a guy wire be if it is to be attached feet from the top and is tomake an angle of with the ground
Answer:
Length of guy wire is 590.6 ft
Step-by-step explanation:
The complete question is
A radio transmission tower is 210 feet tall. How long should a guy wire be if it is to be attached 8 feet from the top and is to make an angle of 20° with the ground. Give your answer to the nearest tenth of a foot.
height of tower = 210 ft
8 ft fro the top leaves 210 - 8 = 202 ft to the ground
This is an angle of elevation problem
the opposite is 202 ft
hypotenuse = ?
angle is 20°
using sin ∅ = opp/hyp
sin 20° = 202/hyp
0.342 = 202/hyp
hyp = 202/0.342 = 590.6 ft this is the length of the guy wire
A lottery ticket has a grand prize of $31 million. The probability of winning the grand prize is .000000018. Determine the expected value of the lottery ticket.
Answer:
$0.558
Step-by-step explanation:
The expected value is the sum of the value of each outcome times the chance that it happens. In this case, there are two outcomes:
Win $31 millionWin $0Then our expected value can be calculated as:
[tex]EV=(31,000,000)(0.000000018)+(0)(1-0.000000018)=0.558[/tex]
Translate and solve: 3x less than two times the sum of 2X and one is equal to the sum of 2 and 5
Answer:
The answer is x = 5Step-by-step explanation:
The statement
3x less than two times the sum of 2X and one is written as
2( 2x + 1) - 3x
the sum of 2 and 5 is written as
2 + 5
Equate the two statements
We have
2( 2x + 1) - 3x = 2+5
Expand
4x + 2 - 3x = 7
Simplify
4x - 3x = 7 - 2
We have the final answer as
x = 5Hope this helps you
Pls help asap What is the number of degrees in the acute angle formed by the hands of a clock at 6:44?
Answer:
264 degree angle
Step-by-step explanation:
help huryyyyyyyyyyyyy
Answer: 4
Step-by-step explanation:
Because %s can be expressed as fractions over 100, because 90 is 70% of x, 70% is 70% of 100. Thus, 90/x = 70/100.
Hope it helps <3
Answer:
4
Step-by-step explanation:
90 is 70% of x.
90 = 70% × x
90 = 70/100x
Divide both sides by x.
90/x = 70/100
How many different lists containing the numbers 1, 4, 5, 8, 17, 21, and nothing else are there in which each odd integer appears before any even integer?
Answer:
4! * 2! = 48
Step-by-step explanation:
In general you have 6 elements so there are 6! = 6*5*4*3*2*1 lists in total, now, you have to think about the second condition, an odd integer has to appear before any even integer. Therefore odd integers go first, and since there are 4 odd integers, there are 4! possible lists, and since there are two even integers there are 2! lists, so in total you have 4! * 2! lists
can y’all help please
Answer: 0 ft, maximum, 11.6 ft, 6.8 ft, 13.6 ft
Step-by-step explanation:
y = -0.25x² + 3.4x
a= -0.25 b = 3.4 c = 0
"c" is the initial height = 0
"a" is negative ⇒ ∩-shaped parabola ⇒ vertex is a maximum
Axis of Symmetry (horizontal distance at maximum):
[tex]x=\dfrac{-b}{2a}=\dfrac{-(3.4)}{2(-0.25)}=\dfrac{-3.4}{-0.5}\quad = \large\boxed{6.8}[/tex]
Maximum: (heighth at maximum)
y = -0.25(6.8)² + 3.4(6.8)
= -11.56 + 23.12
= 11.56
Zeros (when the ball is on the ground):
0 = -0.25x² + 3.4x
0 = x(-0.25x + 3.4)
0 = x 0 = -0.25x + 3.4
-3.4 = -0.25x
[tex]\dfrac{-3.4}{-0.25}=x[/tex]
13.6 = x
x = 0 is where the ball started
x = 13.6 is where the ball landed
f(x)=2x+1 and g(x)=3x2+4, find (f∘g)(−2) and (g∘f)(−2).
Answer:
Step-by-step explanation:
Fog=2(g)+1
2(3x+2+4)+1
2{3x+6)+1
6x+12+1
=6x+13
Fog(-2)=6(-2)+13
-12+13
=1
Gof=3(f)+2+4
=3(2x+1)+6
6x+3+6
=6x+9
Gof(-2)=6(-2)+9
-12+9
=-3
There are five questions listed below. Each question includes the quantity 22. Match
the 22 in each question on the left to which part of the problem it represents on the right
-- the base, percent, or amount. Some answer options on the right will be used more
than once.
What percent of 22 is 3?
percent
22 is what percent of 164?
base
What is 4% of 22?
amount
8 is 22% of what number?
What is 5% of 22?
Using concepts of percentage,
3 is 16.63% of 22.
22 is 13.41% of 164.
0.88 is 4% of 22.
8 is 22% of 36.36.
1.1 is 5% of 22.
What is percentage?A percentage is a number or ratio expressed as a fraction of 100.
Let 3 be x% of 22.
[tex]=\frac{x}{100} *22 = 3\\\\=x = \frac{3*100}{22} = 13.63%[/tex]
3 is 13.63% of 22.
Let 22 be y % of 164.
[tex]=\frac{y}{100} *164 = 22\\\\=y = \frac{22*100}{164} = 13.41%[/tex]
13.41% of 164 is 22.
4% of 22 = 0.88
[tex]\frac{4}{100}*22 = 0.88[/tex]
Let 8 is 22% of z.
[tex]\frac{22}{100}*z = 8\\ \\z = \frac{8*100}{22} = 36.36[/tex]
5% of 22 = 1.1
[tex]\frac{5}{100}*22 = 1.1[/tex]
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The manager of a grocery store took a random sample of 100 customers. The avg. length of time it took the customers in the sample to check out was 3.1 minutes with a std. deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly > 3 min. At 95% confidence, it can be concluded that the mean of the population is
Answer:
Step-by-step explanation:
The data given are;
sample size n = 100
sample mean x = 3.1
standard deviation σ = 0.5
mean = 3
The value for Z can be determined by using the formula:
[tex]Z = \dfrac{x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \dfrac{3.1 - 3.00}{\dfrac{0.5}{\sqrt{100}}}[/tex]
[tex]Z = \dfrac{0.1}{\dfrac{0.5}{10}}}[/tex]
Z = 0.2
At 95% Confidence interval, level of significance ∝ = 0.05
From the z table ;P- value for the test statistics at ∝ = 0.05
P = 0.0228
We can see that the P-value is < ∝
Decision Rule:
Reject the null hypothesis [tex]H_o[/tex] if P-value is less than ∝
Conclusion:
At 0.05 level of significance; we conclude that the mean of the population is significantly > 3 min
Solve the quadratic equation by factoring 9x^2 -16 = 0
Answer: x= - 4/3 and x = 4/3
Step-by-step explanation:
(3x-4) times (3x+4) = 0
For each of the finite geometric series given below, indicate the number of terms in the sum and find the sum. For the value of the sum, enter an expression that gives the exact value, rather than entering an approximation.
3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}
(1) Number of terms
(2) Value of Sum
Answer:
Number of term N = 9
Value of Sum = 0.186
Step-by-step explanation:
From the given information:
Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}[/tex]
Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}[/tex]
Number of term N = 9
The Value of the sum can be determined by using the expression for geometric series:
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}[/tex]
here;
m = 5
n = 9
r = 0.5
Then:
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =0.186[/tex]
For the given the geometric series, 3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³,
the responses are;
(1) The number of terms are 9
(2) The value of the sum is approximately 0.374
How can the geometric series be evaluated?The given geometric series is presented as follows;
3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³
(1) The number of terms in the series = 13 - 4 = 9
Therefore;
The number of terms in the series = 9 terms(2) The value of the sum can be found as follows;
The common ratio, r = 0.5
The sum of the first n terms of a geometric progression is presented as follows;
[tex]S_n = \mathbf{\dfrac{a \cdot (r^n - 1)}{r - 1}}[/tex]
The sum of the first 4 terms are therefore;
[tex]S_4 = \dfrac{3 \times (0.5^4 - 1)}{0.5 - 1} = \mathbf{ 5.625}[/tex]
The sum of the first 13 terms is found as follows;
[tex]S_{13} = \dfrac{3 \times (0.5^{13} - 1)}{0.5 - 1} = \mathbf{ \dfrac{24573}{4096}}[/tex]
Which gives;
The sum of the 5th to the 13th term = S₁₃ - S₄
Therefore;
[tex]The \ sum \ of \ the \ 5th \ to \ the \ 13th \ term =\dfrac{24573}{4096} - \dfrac{45}{3} = \dfrac{1533}{4096} \approx \mathbf{0.374}[/tex]
The value of the sum of the terms of the series is approximately 0.374Learn more about geometric series here:
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Here is a sample distribution of hourly earnings in Paul's Cookie Factory:
Hourly Earning $6 up to $9 $9 up to $12 $12 up to $15
Frequency 16 42 10
The limits of the class with the smallest frequency are:_________
A) $6.00 and $9.00.
B) $12.00 and up to $14.00.
C) $11.75 and $14.25.
D) $12.00 and up to $15.00.
Answer:
The correct answer is:
$12.00 and up to $15.00 (D)
Step-by-step explanation:
Let us arrange the data properly in a tabular format.
Hourly Earnings($) 6 - 9 9 - 12 12 - 15
Frequency 16 42 10
The frequency of a distribution is the number of times that distribution occurs in a particular group of data or intervals.
From the frequency table above the following observations can be made:
Highest frequency = 42 (hourly earnings of $9 - $12)
smallest frequency = 10 ( hourly earnings of $12 - $15)
This means that among a total of 68 workers (16 + 42 + 10), the people earning $12 - $15 form the smallest group (only 10 people), while 42 workers earn $9 - $12, forming the largest majority
The regular octagon below has a perimeter of 80m What is the length of one side of the octagon?
Answer:
10 m
Step-by-step explanation:
Since all of the side lengths of a regular octagon are equal and there are 8 sides on an octagon, the answer would be 80 / 8 = 10 m.
Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Suppose slab avalanches studied in a region of Canada had an average thickness of μ = 66 cm. The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm). 59 51 76 38 65 54 49 62 68 55 64 67 63 74 65 79 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = 61.81 Correct: Your answer is correct. cm s = 10.64 Correct: Your answer is correct. cm (ii) Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in the region of Canada. (a) What is the level of significance? 0.100 Incorrect: Your answer is incorrect. State the null and alternate hypotheses. H0: μ = 66; H1: μ 66 H0: μ ≠ 66; H1: μ = 66 H0: μ < 66; H1: μ = 66 Incorrect: Your answer is incorrect.
Answer:
We conclude that the mean slab thickness in the Vail region is the same as that in the region of Canada.
Step-by-step explanation:
We are given that slab avalanches studied in a region of Canada had an average thickness of μ = 66 cm.
A random sample of avalanches in spring gave the following thicknesses (in cm);
X: 59, 51, 76, 38, 65, 54, 49, 62, 68, 55, 64, 67, 63, 74, 65, 79.
Let [tex]\mu[/tex] = true mean slab thickness in the Vail region
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 66 cm {means that the mean slab thickness in the Vail region is the same as that in the region of Canada}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 66 cm {means that the mean slab thickness in the Vail region is different from that in the region of Canada}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean thickness = [tex]\frac{\sum X}{n}[/tex] = 61.81 cm
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 10.64
n = sample of avalanches = 16
So, the test statistics = [tex]\frac{61.81-66}{\frac{10.64}{\sqrt{16} } }[/tex] ~ [tex]t_1_5[/tex]
= -1.575
The value of t-test statistics is -1.575.
Now, at a 1% level of significance, the t table gives a critical value of -2.947 and 2.947 at 15 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean slab thickness in the Vail region is the same as that in the region of Canada.
A runner can run 3 miles in 18 minutes. At this rate, how many miles can he run in 54
minutes?
6
9
12
I
18
Answer:
9 miles
Step-by-step explanation:
54 divided by 18
=
3.
3 x 3 (miles per 18 min)
=
9 miles
Answer:
9 miles in 54 minutes
Step-by-step explanation:
Create proportions
Do it miles:minutes
In this case it would be
3:18
Then divide both sides of the proportion by three to get
1 : 6
or the statement "It takes the runner 6 minutes to run a mile."
Now create another proportion
x: 54
If he can run a mile in 6 minutes,
he can run x miles in 54 minutes.
In this case divide 54 and 6 to get 9 miles in 54 minutes.
Hope this helps!