Hey there! :)
Answer:
x = 5/2 and 3.
Step-by-step explanation:
Factor the equation. Find numbers that will sum up to -11 involving the coefficient of 2, and that multiply into 15.
2x² - 11x + 15 = 0
(2x - 5)(x - 3) = 0
Use the Zero Product Property to solve for the roots of this equation:
2x - 5 = 0
2x = 5
x = 5/2
----------
x - 3 = 0
x = 3.
Therefore, the two values of x that are roots of this equation are:
x = 5/2 and 3.
━━━━━━━☆☆━━━━━━━
▹ Answer
x₁ = 5/2
x₂ = 3
▹ Step-by-Step Explanation
2x² - 11x + 15 = 0
2x² - 5x - 6x + 15 = 0
x(2x - 5) - 6x + 15 = 0
x(2x - 5) - 3(2x - 5) = 0
(2x - 5) * (x - 3) = 0
2x - 5 = 0
x - 3 = 0
x₁ = 5/2
x - 3 = 0 → x₂ = 3
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
The weight of people in a small town in Missouri is known to be normally distributed with a mean of 186 pounds and a standard deviation of 29 pounds. On a raft that takes people across the river, a sign states, "Maximum capacity 3,417 pounds or 17 persons." What is the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds?
Answer:
the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds is 0.0166
Step-by-step explanation:
The summary of the given statistical data set are:
Sample Mean = 186
Standard deviation = 29
Maximum capacity 3,417 pounds or 17 persons.
sample size = 17
population mean =3417
The objective is to determine the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds
In order to do that;
Let assume X to be the random variable that follows the normal distribution;
where;
Mean [tex]\mu[/tex] = 186 × 17 = 3162
Standard deviation = [tex]29* \sqrt{17}[/tex]
Standard deviation = 119.57
[tex]P(X>3417) = P(\dfrac{X - \mu}{\sigma}>\dfrac{X - \mu}{\sigma})[/tex]
[tex]P(X>3417) = P(\dfrac{3417 - \mu}{\sigma}>\dfrac{3417 - 3162}{119.57})[/tex]
[tex]P(X>3417) = P(Z>\dfrac{255}{119.57})[/tex]
[tex]P(X>3417) = P(Z>2.133)[/tex]
[tex]P(X>3417) =1- 0.9834[/tex]
[tex]P(X>3417) =0.0166[/tex]
Therefore; the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds is 0.0166
Find all the missing side lengths for the following triangles.
Answer:
Step-by-step explanation:
A) u = 4 v = 4/(sqrt)3
B) b = 5 c = 10
C) b = 2(sqrt)2 a = 4
D) m and n are both 7(sqrt)2/2
The missing side lengths for the three triangles are 10√3, 12, and 8. The first triangle is a 30-60-90 triangle, the second triangle is a 45-45-90 triangle, and the third triangle is a right triangle. The missing side lengths were found using the properties of special triangles and the Pythagorean Theorem.
Here are the missing side lengths for the following triangles:
Triangle 1:
The missing side length is 15.
The triangle is a 30-60-90 triangle, so the ratio of the side lengths is 1:√3:2. The hypotenuse of the triangle is 20, so the shorter leg is 10 and the longer leg is 10√3. The missing side length is the longer leg, so it is 10√3.
Triangle 2:
The missing side length is 12.
The triangle is a 45-45-90 triangle, so the ratio of the side lengths is 1:1:√2. The hypotenuse of the triangle is 12√2, so each of the legs is 12. The missing side length is one of the legs, so it is 12.
Triangle 3:
The missing side length is 8.
We can use the Pythagorean Theorem to find the missing side length. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is 10 and one of the other sides is 6. Let x be the missing side length.
[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]x^{2}[/tex]
100 = 36 +[tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 64
x = 8
Therefore, the missing side length is 8.
Learn more about side lengths here: brainly.com/question/18725640
#SPJ2
Write the equation of each line in slope-intercept form.
(If possible please show work)
Answer:
y= 3x+2
Step-by-step explanation:
i think im sorry if its wrong
What is the most accurate statement about correlations? a. Apparent correlations between two or more variables can stimulate investigation and present possible solutions to be explored. b. Correlations prove cause-and-effect relationships. c. Correlations are not useful as statistical analysis tools. d. All of these choices
Answer:
a. Apparent correlations between two or more variables can stimulate investigation and present possible solutions to be explored.
Step-by-step explanation:
Correlation is a scenario, where an action X causes another action Y to occur, but one of the actions does not really need to affect the other's occurrence. Correlation occurs because of the tendency of people to seek the relationship between events. The fact that two events are happening at the same time does not necessarily imply a cause and effect relationship, although there might be a possibility of such.
Correlation is used in scientific studies to draw the relationship between two events, but it does not stop at that. Through investigation has to be made to confirm that there is indeed a correlation.
8
Select the correct answer.
Which of these probability values fit the tree diagram?
O A.
PA) = 0.35, P(B) = 0.65, P{9 = 0.70, P(D) = 0.30, PC) = 0.30, PA) = 0.70
B.
P(A) = 0.35, PCB) = 0.65, PC = 0.70, PCD) = 0.30, PCE) = 0.70, RA= 0.30
O c.
PA) = 0.35, PCB) = 0.65, PC 9 = 0.30, PCD) = 0.70, PCE) = 0.70, PCA) = 0.30
OD. PCA) = 0.65, PCB) = 0.35, P = 0.70, PCD) = 0.30, PCE) = 0.30, PCA) = 0.70
Answer:
C. P(A) = 0.35, P(B) = 0.65, P(C) = 0.30, P(D) = 0.70, P(E) = 0.70, P(F) = 0.30
Step-by-step explanation: Plato / Edmentum
The probability values fit is:
P(A) = 0.35, P(B) = 0.65, P(C) = 0.70, P(D) = 0.30, P(E) = 0.70, P(F)= 0.30
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
The probability that an employee gets placed in a job that is suitable for the employee is 0.65.
The test has an accuracy rate of 70%.
So, P(A) = 0.35
Then, P(B) = 1 - P(A) = 1- 0.35 = 0.65
Now, P(C) = 70%= 0.70
P(D) = 1- 0.70 = 0.30
Now, P(E) = P( test for correct job) = 0.70
P(F) = 0.30
Learn more about Probability here:
https://brainly.com/question/11234923
#SPJ7
The life in hours of a battery is known to be normally distributed, with a standard deviation of 1.25 hours. A random sample of 10 batteries has a mean life x = 40.5 hours.
a) Is there evidence to support the claim that battery life exceeds 40 hours? Use
α = 0.05.
b) What is the P-value for this test?
Answer:
a) Test statistic
Z = 1.265 < 1.96 at 0.05 level of significance
The battery life is not exceeds 40 hours
b)
p- value = 0.8962
Step-by-step explanation:
Step(i):-
Given sample size 'n' =10
Mean of the sample x⁻ = 40.5 hours
Mean of of the Population μ = 40 hours
Standard deviation of the Population = 1.25 hours
Step(ii):-
Null Hypothesis:H₀: μ = 40 hours
Alternative Hypothesis :H₁ : μ < 40 hours
step(ii):-
Test statistic
[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{40.5 -40}{\frac{1.25}{\sqrt{10} } }[/tex]
Z = 1.265
Level of significance = 0.05
Z₀.₀₅ = 1.96
Z = 1.265 < 1.96 at 0.05 level of significance
The battery life is not exceeds 40 hours
Step(iii):-
P - value
P( Z < 1.265) = 0.5 + A( 1.265)
= 0.5 + 0.3962
= 0.8962
P( Z < 1.265) = 0.8962
i ) p- value = 0.8962 > 0.05
Accept H₀
There is no significant
The battery life is not exceeds 40 hours
What are the intercepts?
Answer:
A, C, E, and F.
Step-by-step explanation:
To find the y-intercept, simply plug in 0 for x since y-intercepts are (0,y):
[tex]f(0)=\frac{(0-3)(0+4)(0-1)}{(0+2)(0-12)} =\frac{(-3)(4)(-1)}{(2)(-12)} =\frac{12}{2(-12)}=-1/2[/tex]
[tex](0,-1/2)[/tex]
To find the x-intercepts, plug in 0 for y since x-intercepts have the format (x,0):
[tex]0=\frac{(x-3)(x+4)(x-1)}{(x+2)(x-12)}[/tex]
[tex]0=(x-3)(x+4)(x-1)[/tex]
[tex]x=3, -4, 1[/tex]
[tex](-4,0), (1,0), (3,0)[/tex]
The correct choices are:
A, C, E, and F.
The local news is conducting a poll of the residents’ opinions regarding a new traffic law that is being proposed. At the end of a news segment, viewers had the opportunity to dial in or use social media to choose whether they agree or disagree with the law. A large sample size was represented, and this poll was repeated again one week later with similar results. When working with this data, which of the following statements best applies?
a. The surveys are biased because people chose to respond or not.
b. Because of the large sample size, the results are most accurate of all members of the community.
c. The same sampling methods were used for both polls, demonstrating reliability.
Answer:
Option A is correct.
The surveys are biased because people chose to respond or not.
Step-by-step explanation:
When humans are given the choice whether to participate in a poll like in this question, most often than not, the poll is biased.
This is because only the people or set of people who feel strongly the most about the subject matter of the poll will participate in the poll. This favours the group that disagrees as this group, if given the choice to express their opinion, will most likely be the set of people that will readily express their discontent.
Discontent is more visibly and strongly expressed in humans.
In order to remove this bias, people should have been chosen at random and their responses recorded.
The two other options are not absolutely correct, these are the reasons.
b. Because of the large sample size, the results are most accurate of all members of the community.
Like I expressed above, the base of the sample is flawed and biased as it will most likely favour a group of the population that don't agree with the law. So, no matter how large the sample is, that type of bias makes the poll unreliable.
c. The same sampling methods were used for both polls, demonstrating reliability.
The sampling method is biased, so, it doesn't matter if it is repeated for both polls. it most likely will not represent the correct general consensus about the new traffic law.
Hope this Helps!!!
Each side of a square is increasing at a rate of 5 cm/s. At what rate is the area of the square increasing when the area of the square is 49 cm2
Answer:
70cm/sStep-by-step explanation:
Area of a square with side of length L is expressed as A = L². The rate at which the area is increasing will be expressed as dA/dt.
dA/dt = dA/dL * dL/dt where
dL/dt is the rate at which each side of the square is increasing.
Since dA/dL = 2L, dA/dt = 2L dL/dt
Given dL/dt = 5cm/s and the Area of the square = 49 cm²
49 = L²
L = √49
L = 7cm
dA/dt = 2(7) * 5
dA/dt = 14*5
dA/dt = 70cm/s
The rate at which the area of the square is increasing is 70cm/s
The perimeter of a rectangular city park is 1,428 feet. The length is 78 feet more than twice the width. Find the length and width of the park.
Answer:
Length = 502 ft
Width = 212 ft
Step-by-step explanation:
Recall the formula for the perimeter of a rectangle of length "L" and width "W":
Perimeter = 2 L + 2 W = 1428 ft
Now, since the length is 78 ft more than twice the width, then we can write this in mathematical form as:
L = 2 W +78
so, 2 W = L -7 8
and now replace "2 W" with it equivalent "L - 78" in the first perimeter equation and solve for "L":
2 L + L - 78 = 1428
3 L = 1428 + 78
3 L = 1506
L = 1506/3
L = 502 ft
Then the width W can be obtained via:
2 W = L - 78
2 w = 502 -78
2 W = 424
w = 212 ft
Please help me out. Answer quick
Answer: See below
Step-by-step explanation:
1. (fоg)(x) means f of g(x). You would plug in g(x) into f(x).
(fоg)(x)=3(4x²-5)-3
(fоg)(x)=12x²-15-3
(fоg)(x)=12x²-18
_____________________________________________________
2. (gоf)(x) means g of f(x). You would plug in f(x) into g(x).
(gоf)(x)=4(3x-3)²-5
(gоf)(x)=4(9x²-18x+9)-5
(gоf)(x)=36x²-72x+36-5
(gоf)(x)=36x²-72x+31
_____________________________________________________
3. (fоg)(0) means f of g(0). You would plug in g(0) into f(x).
(fоg)(0)=3(-5)-3
(fоg)(0)=-15-3
(fоg)(0)=-18
_____________________________________________________
4. (gоf)(0) means g of f(0). You would plug in f(0) into g(x).
(gоf)(0)=4(-3)²-5
(gоf)(0)=4(9)-5
(gоf)(0)=36-5
(gоf)(0)=31
Help! Match each linear equation with its graph
Answer:
y = -1/4 x+4 is blue
y = 1/2 x+4 is green
y = 3x is red
y = -1/2x is purple
y = 3 is black
y = -1/4 x+4 is blue, y = 1/2 x+4 is green, y = 3x is red, y = -1/2x is purple and y= 3 is black
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
y = -1/4 x+4 is blue
The slope is -1/4
y = 1/2 x+4 is green
Slope is 1/2
y = 3x is red
Slope is 3
y = -1/2x is purple
Slope is -1/2
y = 3 is black
Hence, y = -1/4 x+4 is blue, y = 1/2 x+4 is green, y = 3x is red, y = -1/2x is purple and y= 3 is black
To learn more on slope of line click:
https://brainly.com/question/14511992
#SPJ2
he weight of male babies less than months old in the United States is normally distributed with mean pounds and standard deviation pounds. (a) Find the nd percentile of the baby weights. (b) Find the th percentile of the baby weights. (c) Find the first quartile of the baby weights. Use the TI-84 Plus calculator and round the answers to at least two decimal places.
Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: Weight of a male baby (pounds)
X~N(μ;σ²)
μ= 11.5 pounds
σ= 2.7 pounds
a) Find the 81st percentile of the baby weights.
This percentile is the value that separates the bottom 81% of the distribution from the top 19%
P(X≤x₁)= 0.81
For this you have to use the standard normal distribution. First you have to look the 81st percentile under the Z distribution and then "translate" it to a value of the variable X using the formula Z= (X- μ)/σ
P(Z≤z₁)= 0.81
z₁= 0.878
z₁= (x₁- μ)/σ
z₁*σ= x₁- μ
(z₁*σ) + μ= x₁
x₁= (z₁*σ) + μ
x₁= (2.7*0.878)+11.5
x₁= 13.8706 pounds
b) Find the 10th percentile of the baby weights.
P(X≤x₂)= 0.10
P(Z≤z₂)= 0.10
z₂= -1.282
z₂= (x₂- μ)/σ
z₂*σ= x₂- μ
(z₂*σ) + μ= x₂
x₂= (z₂*σ) + μ
x₂= (2.7*-1.282)+11.5
x₂= 8.0386 pounds
c) Find the first quartile of the baby weights.
P(X≤x₃)= 0.25
P(Z≤z₃)= 0.25
z₃= -0.674
z₃= (x₃- μ)/σ
z₃*σ= x₃- μ
(z₃*σ) + μ= x₃
x₃= (z₃*σ) + μ
x₃= (2.7*-0.674)+11.5
x₃= 9.6802 pounds
I hope this helps!
You have a choice of receiving a wage of $39,000 per year,$2630 per month,$665 per week and 52 weeks of work per year
Answer:
$39,000
Step-by-step explanation:
This is the best answer because you recieve the most money. 2630*12 is 31560 dollars, and 665*52= $34580.
What is Pi* 457363225452-485092526+2671251971947691
(Please do not use calculator and pi=3.14)
Answer:
I don't think it's possible to have an exact answer with this without using a calculator.
Step-by-step explanation:
1. Get a calculator
2. input Pi* 457363225452-485092526+2671251971947691
3. Press =
You have different video games. How many different ways can you arrange the games side by side on a shelf? You can arrange the different video games in nothing different ways.
Answer:
See Explanation below
Step-by-step explanation:
This question has missing details because the number of video games is not stated;
However, you'll arrive at your answer if you follow the steps I'll highlight;
The question requests for the number of arrangement; That means we're dealing with permutation
Let's assume the number of video games is n;
To arrange n games, we make use of the following permutation formula;
[tex]^nP_n = \frac{n!}{(n-n)!}[/tex]
Simplify the denominator
[tex]^nP_n = \frac{n!}{0!}[/tex]
0! = 1; So, we have
[tex]^nP_n = \frac{n!}{1}[/tex]
[tex]^nP_n = n![/tex]
Now, let's assume there are 3 video games;
This means that n = 3
[tex]^3P_3 = 3![/tex]
[tex]^3P_3 = 3 * 2 * 1[/tex]
[tex]^3P_3 = 6\ ways[/tex]
So, whatever the number of video games is; all you have to do is; substitute this value for n;
Please answer this correctly
Answer:
7/8 chance
Step-by-step explanation:
There are 7 numbers that are either even or greater than 2: 2, 3, 4, 5, 6, 7, and 8. There is a 7/8 chance choosing either of those.
Answer:
7/8
Step-by-step explanation:
there are 6 numbers that are greater than 2: 3,4,5,6,7,8
there are 4 even numbers: 2,4,6,8
A jumper shrunk by 2/7 in the wash. The length of the jumper is now 70cm How long was the jumper originally
Answer:
Step-by-step explanation:
If it shrunk by 2/7 in the wash it is equal to the equation:
Original length x 2/7 = 70cm so we just have to work backwards so the answer is
Original length = 70/(5/7) = 98cm
OR
WE KNOW THAT 5/7 = 70 so 1/7 = 70/5 = 14 so we times 14 by 7 to get 98cm
You decide finance a $12,000 car at 3% compounded monthly for 4 years. What will your monthly payments be? How much interest will you pay over the life of the loan?
Answer:
Step-by-step explanation:
The cost of the car is $12,000
We would apply the periodic interest rate formula which is expressed as
P = a/[{(1+r)^n]-1}/{r(1+r)^n}]
Where
P represents the monthly payments.
a represents the cost of the car
r represents the interest rate
n represents number of monthly payments. Therefore
a = 12000
r = 3%/12 = 0.03/12 = 0.0025
n = 12 × 4 = 48
Therefore,
P = 12000/[{(1+0.0025)^48]-1}/{0.0025(1+0.0025)^48}]
12000/[{(1.0025)^48]-1}/{0.0025(1.0025)^48}]
P = 12000/{1.127 -1}/[0.0025(1.127)]
P = 12000/(0.127/0.0028175)
P = 12000/45.075
P = $266.22
The monthly payment is $266.22
The total amount that would be paid over the life of the loan is
266.22 × 48 = $12778.56
The amount of interest paid is
12778.56 - 12000 = $778.56
I need help on question 8.
Answer:
50.18°
Step-by-step explanation:
∠BAD = ∠BAC +∠CAD
102° = (8x+17)° +(9x+11)° . . . . . substitute given values
102 = 17x +28 . . . . . . . . . . simplify, divide by degrees
x = (102 -28)/17 = 74/17 . . . . . solve for x
Then the angle of interest is ...
∠CAD = (9x +11)° = (9(74/17) +11)° = 50 3/17°
∠CAD ≈ 50.18°
25 points Please help will mark brainleyest type the correct answer in each box use numerals instead of words if necessary use / for the fraction bars. the vertex of a parabola is (-2, -20) and its y-intercept is (0,-12) the equation of the parabola is y= ___ x^2+___x+___
Answer:
the three boxes should be filled with
2 8 -12
respectively
Step-by-step explanation:
The general equation of the parabola in this problem is
y = a(x-h)^2 + k
vertex is at (-2, -20), => k=-20, h = 2
so the equation is
y = a(x+2)^2 - 20
To have y-intercept = -12, we set x = 0
-12 = a(0+2)^2 - 20
a(2^2) = 8
a = 2
therefore the equation of the parabola is
y = 2 (x+2)^2 -20 = 2x^2 + 8x - 12
the three boxes should be filled with
2 8 -12
respectively
B.Imagine you are 1 of the people who left the luncheon with a contagious disease and interacted with an average of 9 different people each day. How many people could potentially be infected in 7 days
Answer:
5380839 infected
Step-by-step explanation:
Let's do the calculations day by day, we have:
Day 1
That person spread 9 people.
Day 2
Each of the nine people infect 9 others, plus that person infected 9 others, therefore it would be:
9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 = (9 x 9) + 9 = 9 ^ 2 + 9 (assume this number as first term + second term)
Day 3
By the end of day 2, there were a total of 9 ^ 2 persons (first term) will infect 9 each, which makes this figure:
9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 = 9x9 ^ 2 = 9 ^ 2. The second term will now become 9 ^ 2, plus another 9 infected by the person who started it all. Therefore it would remain:
9 ^ 3 + 9 ^ 2 + 9
Following the sequence would be:
Day 4
9 ^ 4 + 9 ^ 3 + 9 ^ 2 + 9
Day 5
9 ^ 5 + 9 ^ 4 + 9 ^ 3 + 9 ^ 2 + 9
Day 6
9 ^ 6 + 9 ^ 5 + 9 ^ 4 + 9 ^ 3 + 9 ^ 2 + 9
Day 7
9 ^ 7 + 9 ^ 6 + 9 ^ 5 + 9 ^ 4 + 9 ^ 3 + 9 ^ 2 + 9 = 5380839
Which means that in total there would be 5380839 infected
Use PQR below to answer the question that follows:
Answer:
Angle P is congruent to itself due to the reflexive property.
Explanation:
Angle P must be congruent to angle S through corresponding angle theory.
Otherwise, it wouldn't prove ΔPQR is similar to ΔSTR.
Answer:
Angle P is congruent to itself due to the reflexive property.
Step-by-step explanation:
The scheduled commuting time on the MTA Marc train from BWI to DC is 65 minutes. Suppose that the actual commuting time is uniformly distributed between 64 and 74 minutes. What is the probability that the commuting time will be less than 70 minutes
Answer:
60% probability that the commuting time will be less than 70 minutes
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X < x) = \frac{x - a}{b-a}[/tex]
Suppose that the actual commuting time is uniformly distributed between 64 and 74 minutes.
This means that [tex]a = 64, b = 74[/tex]
What is the probability that the commuting time will be less than 70 minutes
[tex]P(X < 70) = \frac{70 - 64}{74 - 64} = 0.6[/tex]
60% probability that the commuting time will be less than 70 minutes
The length of a rectangle is 9 feet less than twice the width. Express the length l (in feet) in terms of the width w (in feet) l = ______________
Answer:
[tex] L[/tex] represent the length
[tex] W[/tex] represent the width
And for this case we have the following info given:
The length of a rectangle is 9 feet less than twice the width
If we convert this statement to symbols we got:
[tex] L = 2W -9[/tex]
And that would be the solution for this case.
Step-by-step explanation:
For this problem let's define some notation first:
[tex] L[/tex] represent the length
[tex] W[/tex] represent the width
And for this case we have the following info given:
The length of a rectangle is 9 feet less than twice the width
If we convert this statement to symbols we got:
[tex] L = 2W -9[/tex]
And that would be the solution for this case.
A sample of 26 offshore oil workers took part in a simulated escape exercise, and their escape time (unit: second) were observed. The sample mean and sample standard deviation are 370.69 and 24.36, respectively. Suppose the investigators had believed a priori that true average escape time would be at most 6 minutes. Does the data contradict this prior belief? Assuming normality, test the appropriate hypotheses using the rejection region method at a significance level of 0.05.
Answer:
Yes, it contradict this prior belief as there is enough evidence to support the claim that the true average escape time is significantly higher than 6 minutes.
Test statistic t=2.238>tc=1.708.
The null hypothesis is rejected.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the true average escape time is significantly higher than 6 minutes (360 seconds).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=360\\\\H_a:\mu> 360[/tex]
The significance level is 0.05.
The sample has a size n=26.
The sample mean is M=370.69.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=24.36.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{24.36}{\sqrt{26}}=4.777[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{370.69-360}{4.777}=\dfrac{10.69}{4.777}=2.238[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=26-1=25[/tex]
The critical value for a right-tailed test with a significance level of 0.05 and 25 degrees of freedom is tc=1.708. If the test statistic is bigger than 1.708, it falls in the rejection region and the null hypothesis is rejected.
As the test statistic t=2.238 is bigger than the critical value t=1.708, the effect is significant. The null hypothesis is rejected.
There is enough evidence to support the claim that the true average escape time is significantly higher than 6 minutes (360 seconds).
Sam has stamps from Malaysia, Thailand and New Zealand. The ratio of the number of stamps from Malaysia to the number of stamps from Thailand is 3:2.The ratio of the number of stamps from New Zealand to the number of stamps from Thailand is 6:5. What fraction of Sam's stamps is from Malaysia?
Answer:
21
Step-by-step explanation:
9 plus 10= 21
The ratio shows how many times one value is contained in another value.
The ratio of stamps from Malaysia, Thailand, and New Zealand is
15M : 10T : 12N
The fraction of stamps from Malaysia is 15/37.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The ratio of the number of stamps from Malaysia to the number of stamps from Thailand is 3:2.
This can be written as,
Number of stamps from Malaysia = 3M
Number of stamps from Thailand = 2T
Multiply both by 5.
Number of stamps from Malaysia = 15M ____(1)
Number of stamps from Thailand = 10T _____(2)
The ratio of the number of stamps from New Zealand to the number of stamps from Thailand is 6:5.
Number of stamps from New Zealand = 6N
Number of stamps from Thailand = 5T
Multiply both by 2.
Number of stamps from New Zealand = 12N _____(3)
Number of stamps from Thailand = 10T _____(4)
From (1), (2), (3), (4) we get,
15M : 10T : 12N
The fraction of stamps from Malaysia.
= 15/37
Thus,
The fraction of stamps from Malaysia is 15/37.
Learn more about ratios here:
https://brainly.com/question/2462048
#SPJ2
Please help will definitely say thanks
Answer:
[tex]\mathrm{Image \: below.}[/tex]
Explanation:
Ruby talks about a 3D shape, so sphere.
Shriya talks about the points that are equal in distance from the opposite points, the diameter, she is right.
Abhishek's definition is not shown completely in the photo, so by process of elimination, he is incorrect.
What is organic chemistry
Organic chemistry is the study of molecules that contain carbon ("organic molecules").
Actividad 1.1
Investigue sobre el tema de diferenciabilidad en un punto para encontrar los valores de "a" y "b" tales que
la función
definida a continuación sea diferenciable en t = 2, luego construya su gráfica.
at +b, sit < 2
f(t) = {2t2 – 1, si 2 st
1
【>】【>】https://brainly.com/question/17076084【<】【<】
_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_
ENGLISH>> Click on the link above, answer the following question, then, I will answer your question. (IF YOU NEED HELP, REPLY TO THIS COMMENT.)
--------------------------------------------------------------------------------------------------------------
SPANISH>> Haga clic en el enlace de arriba, responda la siguiente pregunta, luego, responderé su pregunta. (SI NECESITA AYUDA, RESPONDA A ESTE COMENTARIO).
--------------------------------------------------------------------------------------------------------------
CHINESE>>
单击上面的链接，回答以下问题，然后，我将回答您的问题。 （如果需要帮助，请回复此评论。）
Dān jī shàngmiàn de liànjiē, huídá yǐxià wèntí, ránhòu, wǒ jiāng huídá nín de wèntí. (Rúguǒ xūyào bāngzhù, qǐng huífù cǐ pínglùn.)
--------------------------------------------------------------------------------------------------------------
HINDI>>
उपरोक्त लिंक पर क्लिक करें, निम्नलिखित प्रश्न का उत्तर दें, फिर, मैं आपके प्रश्न का उत्तर दूंगा। (यदि आप मदद की जरूरत है, यह टिप्पणी करने के लिए उत्तर दें।)
uparokt link par klik karen, nimnalikhit prashn ka uttar den, phir, main aapake prashn ka uttar doonga. (yadi aap madad kee jaroorat hai, yah tippanee karane ke lie uttar den.)