Answer:
0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean life of 82 months with a standard deviation of 7 months.
This means that [tex]\mu = 82, \sigma = 7[/tex]
Sample of 71
This means that [tex]n = 71, s = \frac{7}{\sqrt{71}}[/tex]
What is the probability that the mean monitor life would be greater than 83.8 months?
1 subtracted by the p-value of Z when X = 83.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{83.8 - 82}{\frac{7}{\sqrt{71}}}[/tex]
[tex]Z = 2.17[/tex]
[tex]Z = 2.17[/tex] has a p-value of 0.985.
1 - 0.985 = 0.015
0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
All I need is number one
Answer:
a. 7 ÷ 4 yes
b. 4 ÷ 7 no
c. [tex]\frac{7}{4}[/tex] yes
d. [tex]\frac{4}{7}[/tex] no
e. 7 × [tex]\frac{1}{4}[/tex] yes
f. [tex]1\frac{3}{4}[/tex] yes
Step-by-step explanation:
hope this helps ^^
Solve, then check algebraically and graphically. 9x-3=78
Answer:
[tex]9x - 3 = 78 \\ 9x - 3 + 3 = 78 + 3 \\ 9x = 81 \\ \frac{9x}{9} = \frac{81}{9} \\ x = 9[/tex]
Answer:
[tex]9x - 3 = 78 \\9 x = 78 + 3 \\ 9x = 81 \\ x = \frac{81}{9} \\ x = 9[/tex]
A fair dice is rolled. Work out the probability of getting a number less than 5. Give your answer in its simplest form.
Step-by-step explanation:
4/6
=2/3
That's what I could show you
The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees. If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample
Answer:
19 beers must be sampled.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees.
This means that [tex]\sigma = 0.26[/tex]
If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample?
This is n for which M = 0.1. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.1 = 1.645\frac{0.26}{\sqrt{n}}[/tex]
[tex]0.1\sqrt{n} = 1.645*0.26[/tex]
[tex]\sqrt{n} = \frac{1.645*0.26}{0.1}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645*0.26}{0.1})^2[/tex]
[tex]n = 18.3[/tex]
Rounding up:
19 beers must be sampled.
Johnny tripled his baseball card collection. Then he added 6 more cards to the collection. Now he has 24 cards. How many cards did he start with?
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Answer:
6
Step-by-step explanation:
Work backward.
If he has 24 after adding 6, he had 18 before that addition.
If he had 18 after tripling his collection, he had 18/3 = 6 cards to start with.
__
Note that this is the same process you would use if you started with an equation.
3c +6 = 24 . . . . where c is the number of cards Johnny started with
3c = 24 -6 = 18 . . . . . subtract 6 from the final number
c = 18/3 = 6 . . . . . . . . divide the tripled value by 3 to see the original value
Johnny started with 6 cards.
The half-life of a newly discovered radioactive element is 30 seconds. To the nearest tenth of a second, how long will it take for a sample of 9 grams to decay to 0.72 grams
Answer:
It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.
Step-by-step explanation:
We can write a half-life function to model our function.
A half-life function has the form:
[tex]\displaystyle A=A_0\left(\frac{1}{2}\right)^{t/d}[/tex]
Where A₀ is the initial amount, t is the time that has passes (in this case seconds), d is the half-life, and A is the amount after t seconds.
Since the half-life of the element is 30 seconds, d = 30. Our initial sample has nine grams, so A₀ is 9. Substitute:
[tex]\displaystyle A=9\left(\frac{1}{2}\right)^{t/30}[/tex]
We want to find the time it will take for the element to decay to 0.72 grams. So, we can let A = 0.72 and solve for t:
[tex]\displaystyle 0.72=9\left(\frac{1}{2}\right)^{t/30}[/tex]
Divide both sides by 9:
[tex]\displaystyle 0.08=\left(\frac{1}{2}\right)^{t/30}[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln(0.08)=\ln\left(\left(\frac{1}{2}\right)^{t/30}\right)[/tex]
By logarithm properties:
[tex]\displaystyle \ln(0.08)=\frac{t}{30}\ln(0.5)[/tex]
Solve for t:
[tex]\displaystyle t=\frac{30\ln(0.08)}{\ln(0.5)}\approx109.3\text{ seconds}[/tex]
So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.
* Insert a digit to make numbers that are divisible by 6 if it is possible:
234_6
Answer:
i put in 3 to make 23436 because 36 is divisible by 6
I really don’t understand graphs
In the diagram, point D is the center of the medium-sized circle that passes through C and E, and it is also the center of the largest circle that passes through A and G. Each of the diameters of the small circles with centers B and F equals the radius of the medium-sized circle with center D. The shaded area is what fraction of the largest circle?Single choice.
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Answer:
5/8
Step-by-step explanation:
The area of the smaller circles is proportional to the square of the ratio of their diameters. The two smallest circles have diameters equal to 1/4 the diameter of the largest circle. Hence their areas are (1/4)^2 = 1/16 of that of the largest circle.
Similarly, the medium circle has a diameter half that of the largest circle, so its area is (1/2)^2 = 1/4 of the are of the largest circle.
The smaller circles subtract 2×1/16 +1/4 = 3/8 of the area of the largest circle. Then the shading is 1-3/8 = 5/8 of the area of the largest circle.
Combine these radicals. 8 square root 5 + 2 square root 45
Answer
14√5
Step-by-step explanation:
8√5 + 2√45
= 8√5 + 6√5
= 14√5
Hope this helps
Answer:
[tex]\boxed {\boxed {\sf 14 \sqrt{5}}}[/tex]
Step-by-step explanation:
We are asked to combine the radicals. We have the following expression:
[tex]8 \sqrt{5} + 2 \sqrt{45}[/tex]
Currently, we cannot combine these radicals. The value under the square root is not the same for both terms.
However, we can simplify the radical 2 √45 because the value under the radical is divisible by a perfect square.
45 can be divided by 9 (the perfect square) for a quotient of 5. So, we can simplify the radical using this information.
Break the radical into 2 radicals: 9 and 5.
[tex]8 \sqrt{5}+ 2 \sqrt{9}\sqrt{5}[/tex]
Notice that a perfect square is under the radical. √9 can be simplifed to 3.
[tex]8 \sqrt{5}+ 2 *3 \sqrt{5}[/tex]
Multiply 2 and 3.
[tex]8 \sqrt{3} + 6 \sqrt{5}[/tex]
Now the value under the radical is the same for both terms, and we can add the numbers in front of the radicals.
[tex]14 \sqrt{5}[/tex]
The radicals combined is equal to 14√5
if 2 (3x - 4 ) =5, then x =
Answer:
2.167 (rounded to the nearest hundredths).
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, divide 2 from both sides of the equation:
(2(3x - 4))/2 = (5)/2
3x - 4 = 2.5
Next, isolate the variable, x. Add 4 to both sides of the equation:
3x - 4 (+4) = 2.5 (+4)
3x = 2.5 + 4
3x = 6.5
Then, divide 3 from both sides of the equation:
(3x)/3 = (6.5)/3
x = 6.5/3 = 2.167 (rounded).
~
Answer:
We have this equation
2*(3x-4) = 5
We can start solving the parentheses
2*(3x- 4) = 5
6x - 8 = 5
We can add 8 to both sides
6x - 8 + 8 = 5 + 8
6x = 13
And divide by 6
6x/6 = 13/6
x = 13/6
simplify 3x⁵y³ ÷2y² step by step
Answer:
3/2 x^5 y
Step-by-step explanation:
3x^5y^3
----------------
2y^2
Simplify the y terms
y^3 / y^2 = y^(3-2) = y
3/2 x^5 y
Answer:
[tex] \frac{3}{2} x {}^{5} y {}^{} [/tex]
Step-by-step explanation:
it's all in the image
Which of the following choices is the average speed of a tourist who traveled for 1 hour on a plane at 400 mph and 4 hours by car at 60 mph?
(average= total miles/total hours)
Answer:
128 mph
Step-by-step explanation:
1 hour = 400
4 hours = 240
240+400= 640
4+1 = 5
640/5=128
If f(1) =160 and f(n+1)=-2f(n),
What is f(4)?
Answer:
f(n+1=-2f(n)
f(x)=-2f(n)
f(4)
f(4)=-2f(4)
Answer:
f(4) = - 1280
Step-by-step explanation:
Using the recursive rule and f(1) = 60 , then
f(2) = - 2f(1) = - 2 × 160 = - 320
f(3) = - 2f(2) = - 2 × - 320 = 640
f(4) = - 2f(3) = - 2 × 640 = - 1280
Jack brought a new set of golf clubs of $186.75. The original price was $249. What percent of the original price did he pay?
133.3%
33.3%
25%
75%
Answer: 75%
Step-by-step explanation:
186.75/249 =.75
.75x100
75%
Please help !!!! will mark brainliest !!
Answer:
the first one
Step-by-step explanation:
x(x-y) - y( x- y) simplify
Step-by-step explanation:
x²-xy-xy+y²
x²+2xy+y²
hope it helps
which of the following is the median of 19, 31, 15, 50, 20
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\text{19, 31, 15, 50, \& 20}[/tex]
[tex]\large\text{When you see or hear the word \underline{median}, think of the question}\\\large\text{asking you \bf what is the MIDDLE NUMBER.}\large\text{To find the}\\\large\text{middle number you have to put the numbers from descending}\\\large\text{(least/decreasing) or ascending (greatest/increasing) order}[/tex]
[tex]\large\text{15, 19, 20, 31, \& 20}[/tex]
[tex]\large\text{Make sure it is even on BOTH SIDES of the DATA SET}[/tex]
[tex]\large\text{It seems to be even on both sides of the number \bf 20}\large\text{ so \underline{20}}\\\large\text{can be your median/middle number in this given set}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: the median is \bf 20}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]
SCALCET8 3.9.003. Each side of a square is increasing at a rate of 4 cm/s. At what rate is the area of the square increasing when the area of the square is 9 cm2
Answer: [tex]24\ cm^2/s[/tex]
Step-by-step explanation:
Given
Each side of square is increasing at a rate of 4 cm/s
Side of a square when area is [tex]9\ cm^2[/tex]
Suppose a is side of the square
[tex]\Rightarrow a=\sqrt{9}\\\Rightarrow a=3\ cm[/tex]
Area is given by
[tex]\Rightarrow A=a^2\\\text{Differentiate area w.r.t time}\\\\\Rightarrow \dfrac{dA}{dt}=2a\dfrac{da}{dt}\\\\\Rightarrow \dfrac{dA}{dt}=2\times 3\times 4\\\\\Rightarrow \dfrac{dA}{dt}=24\ cm^2/s[/tex]
Area is increasing at a rate of [tex]24\ cm^2/s[/tex]
Answer:
24cm^2/ s
Step-by-step explanation:
3. Of 1000 randomly selected cases of lung cancer, 450 resulted in death within 5 years. Calculate a 96% CI on the death rate from lung cancer.
Answer:
The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Of 1000 randomly selected cases of lung cancer, 450 resulted in death within 5 years.
This means that [tex]n = 1000, \pi = \frac{450}{1000} = 0.45[/tex]
96% confidence level
So [tex]\alpha = 0.04[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.04}{2} = 0.98[/tex], so [tex]Z = 2.054[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 - 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4177[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 + 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4823[/tex]
The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).
chang knows one side of a triangle is 13 cm which set of two sides is possible for the length of the other two sides
5 cm and 8 cm
6cm and 7 cm
7cm and 2 cm
8cm and 9 cm
Answer:
i dont knowwww dhehje ejhdjeke jsienje
Answer:
8cm and 9 cm
Step-by-step explanation:
Sum of sides rule:
The sum of the two smallest sides of a triangle has to be greater than the third side.
5 cm and 8 cm
One side is 5, other 8, 5 + 8 = 13. The sum has to be greater than 13, so this is not possible.
6cm and 7 cm
6 + 7 = 13, same as above, not possible.
7cm and 2 cm
7 + 2 = 9 < 13, so not possible.
8cm and 9 cm
8 + 9 = 17 > 13, so possible, and this is the answer.
7 is added to the product of 5 and 6
Answer:
37
Step-by-step explanation:
7 + (5×6)
= 7 + 30
= 37
.................
Answer:
37
Step-by-step explanation:
First Step: Multiply
5x6=30
Second Step: Add
30+7=37
Therefore your answer is 37
Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?
Write the range of the function using interval notation.
Answer:
[-3, -1]
Step-by-step explanation:
The minimum y value is -3.
The maximum y value is -1.
-3 and -1 are included, so we use square brackets.
Answer: [-3, -1]
insert a digit in a place of each "..." to make numbers that are divisible by 6 if it is possible: 4...6
Answer:
1 There is no number that make it divisible by 6 with no decimals
2 1,4,7
Step-by-step explanation:
2 23718/6= 3953
23748/6= 3958
23778/6= 3963
Please help
Find the value of x,
m∠5 = x-6, m∠4 = 2x+4, m∠2 = 2x-26
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Answer:
x = 30 2/3
Step-by-step explanation:
Angles 4 and 5 are complementary, so we have ...
m∠4 +m∠5 = 90°
(2x +4) +(x -6) = 90
3x -2 = 90 . . . . . . . . . collect terms
3x = 92 . . . . . . . . . . add 2; next, divide by 3
x = 92/3 = 30 2/3
Helppp and explain!!!
Test the claim that the mean GPA of night students is larger than the mean GPA of day students at the 0.10 significance level. The null and alternative hypothesis would be: H 0 : p N ≥ p D H 1 : p N < p D H 0 : p N ≤ p D H 1 : p N > p D H 0 : p N = p D H 1 : p N ≠ p D H 0 : μ N ≤ μ D H 1 : μ N > μ D H 0 : μ N ≥ μ D H 1 : μ N < μ D H 0 : μ N = μ D H 1 : μ N ≠ μ D The test is: two-tailed right-tailed left-tailed The sample consisted of 30 night students, with a sample mean GPA of 3.34 and a standard deviation of 0.02, and 30 day students, with a sample mean GPA of 3.32 and a standard deviation of 0.08. The test statistic is: (to 2 decimals) Use the conservative degree of freedoms. The p-value is: (to 2 decimals) Based on this we: Reject the null hypothesis Fail to reject the null hypothesis
Answer:
H0 : μN ≤ μD
H1 : μN > μD
Right tailed
Test statistic = 1.33
Pvalue = 0.097
Fail to reject the Null
Step-by-step explanation:
H0 : μN ≤ μD
H1 : μN > μD
The test is right tailed ; culled from the direction of the greater than sign ">"
Night students :
n1 =30 x1= 3.34 s1 = 0.02
Day students:
n2 = 30 x2 = 3.32 s2 = 0.08
The test statistic :
(x1 - x2) / √(s1²/n1) + (s2²/n2)
T= (3.34 - 3.32) / √(0.02²/30) + (0.08²/30)
T = 0.02 / 0.0150554
Test statistic = 1.328
Using the conservative approach ;
df = Smaller of n1 - 1 or n2 - 1
df = 30 - 1 = 29
Pvalue(1.328, 29) = 0.097
At α = 0.10
Pvalue < α ; Hence, we reject H0 ; and conclude that there is significant evidence that GPA of night student is greater than GPA of day student
PLEASE HELP!!! What is the equation of the line perpendicular to 2x – 3y = 13 that passes through the point (–6, 5)?
Answer:
2x + 3y -3=0
Step-by-step explanation:
The given equation of the line is ,
[tex]\implies 2x - 3y = 13 [/tex]
Now convert it into slope intercept form to get the slope , we get ,
[tex]\implies 3y = 2x - 13 \\\\\implies y =\dfrac{2}{3}x -\dfrac{13}{2}[/tex]
Therefore the slope is ,
[tex]\implies m = \dfrac{2}{3} [/tex]
We know that the product of slope of perpendicular lines is -1 . Therefore the slope of the perpendicular line will be ,
[tex]\implies m_{perpendicular}= -\dfrac{2}{3} [/tex]
Now one of the point is (-6,5) .On Using point slope form , we have ,
[tex]\implies y-y_1 = m( x - x_1) \\\\\implies y - 5 = -\dfrac{2}{3}( x + 6 ) \\\\\implies 3y - 15 = -2x -12
\\\\\implies 2x + 3y -15+12=0 \\\\\implies \underline{\underline{ 2x + 3y -3=0 }}[/tex]
Answer:
y = - [tex]\frac{3}{2}[/tex]x - 4
Step-by-step explanation:
2x – 3y = 13
3y = 2x + 13
y = [tex]\frac{2}{3}[/tex]x + [tex]\frac{13}{3}[/tex]
slope = 2/3
negative reciprocal = -3/2
y = -3/2x + b
(-6, 5)
5 = (-3/2)(-6) + b
5 = 9 + b
b = -4
y = -3/2x - 4
Study the table representing the price of different amounts of apples, in pounds, and then complete the sentences. The constant difference in the y-values is . The linear function is .
Answer: the first part is 1.25. The second part is y=1.25x
Step-by-step explanation: edge 2021
The figure below is a rhombus.
w = [? ]°
Answer:
Step-by-step explanation:
