Answer:
2.833 BTUs per cubic foot were produced.
Step-by-step explanation:
BTU's produced by one person = 800
No. of students = 34
Therefore no. of BTU's produced by 34 person = 800 * 34 = 27,200 BTU
Dimension of class 25 feet by 32 feet by 12 feet
Volume of class = length * width * height = 25 * 12 * 32 = 9,600 cubic feet
________________________________________________
BTUs per cubic foot produced = Total BTU's produced by 34 person/ Volume of class
Substituting the value of Total BTU produced and volume of class
BTUs per cubic foot produced = 27,200 BTU/ 9,600 cubic feet
= 2.833 BTUs per cubic foot
2.833 BTUs per cubic foot were produced.
What is the radian measure of the central angle of an arc that has an arc length of 5 units and radius of 2 units
Answer:
Central angle = θ = 2.5 radians
Step-by-step explanation:
The radian measure of central angle is given by
[tex]\theta = \frac{s}{r}[/tex]
Where s is the arc length, r is the radius of circle and θ is angle in radians
We are given an arc length of 5 units
[tex]s = 5[/tex]
We are given radius of 2 units
[tex]r = 2[/tex]
Therefore, the central angle in radians is
[tex]\theta = \frac{5}{2}\\\\\theta = 2.5 \: rad[/tex]
Bonus:
Radian is a unit which we use to measure angles.
1 Radian is the angle that results in an arc having a length equal to the radius.
Degree is another unit that we use to measure angles.
There are 360° in a circle.
There are 2π radians in a circle.
What formula is used to show lines are parallel
to one another?
Answer:
To figure out if 2 lines are parallel, compare their slopes. You can find the slope of a line by picking 2 points with XY coordinates, then put those coordinates into the formula Y2 minus Y1 divided by X2 minus X1. Calculate the slope of both lines. If they are the same, then the lines are parallel.
Step-by-step explanation:
To figure out if 2 lines are parallel, compare their slopes. You can find the slope of a line by picking 2 points with XY coordinates, then put those coordinates into the formula Y2 minus Y1 divided by X2 minus X1. Calculate the slope of both lines. If they are the same, then the lines are parallel.
The surface areas of two similar solids are 441 cm2 and 225 cm2. If the approximate volume of the smaller solid is 250 cm3, what is the volume of the larger solid?
Answer:
volume of the larger solid = 686 cm³
Step-by-step explanation:
The solids are similar . A solid is similar if all the corresponding sides are proportional . They are similar if they are the same type of solids and their corresponding sides like height, radius etc are proportional.
The ratio of the surface area of a similar solid is equal to the square of their scale factor.
(a/b)² = 441/225
square root both sides
a/b = √441/√225
a/b = 21/15
The ratio of the volume of a similar solid is equal to the cube of their scale factor.Therefore,
(21/15)³ = a/250
9261 /3375 = a/250
cross multiply
9261 × 250 = 3375a
2315250 = 3375a
divide both sides by 3375
a = 2315250/3375
a = 686 cm³
volume of the larger solid = 686 cm³
A stream traverses two lakes flowing downstream, and carrying fresh water as it enters the upper lake. The upper lake contains 4∗109 gallons of water, and the lower lake contains 2 ∗109 gallons of water. The flow rate of the stream is the same at all points and is 4 ∗ 106 gallons per day. A factory situated at the upper lake releases a pollutant at a rate of 200 lbs. per day. Let Q1(t) and Q2(t) be the amount, in pounds, of pollutant in the upper and lower lakes, respectively, where time t is measured in days. Assuming that each lake is well mixed, Q1 and Q2 obey the system(a) Q'1 = 4 ∗ 106 (200 − Q1), Q'2 = 4 ∗ 106 (Q1 − Q2).(b) Q'1 = 200 − Q1/1000, Q'2 = Q1/1000 − Q2/500.(c) Q'1 = 200 − 4 ∗ 106Q1, Q'2 = 4 ∗ 106 (Q1 − Q2).
(d) Q'1 = 200t − 4 ∗ 106Q1, Q'2 = 4 ∗ 106 (Q1 − Q2).
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached images for the step by step explanation to the question
» In a right triangle, a and b are the lengths of the legs and c is the length of the
hypotenuse. If b = 8.6 kilometers and c = 9.4 kilometers, what is a? If necessary, round to
the nearest tenth.
Answer:
3.8
Step-by-step explanation:
a=3.79 or 3.8km
√(9.4^2 - 8.6^2)
If necessaly, combine like terms.
(3x+8)2
Step-by-step explanation:
multiply 2 with the bracket numbers
6x+16=0
6x= - 16
x=-16/6
x= - 8/3
A Nissan Motor Corporation advertisement read, "The average man's I.Q. is 107. The average brown trout's I.Q. is 4. So why can't man catch brown trout?" Suppose you believe that the brown trout's mean I.Q. is greater than four. You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5; 4; 7; 3; 6; 4; 5; 3; 6; 3; 8; 5. Conduct a hypothesis test of your belief. (Use a significance level of 0.05.)
Answer:
We conclude that the brown trout's mean I.Q. is greater than four.
Step-by-step explanation:
We are given that the average brown trout's I.Q. is 4. Suppose you believe that the brown trout's mean I.Q. is greater than four.
You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5, 4, 7, 3, 6, 4, 5, 3, 6, 3, 8, 5.
Let [tex]\mu[/tex] = the brown trout's mean I.Q.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 4 {means that the brown trout's mean I.Q. is smaller than or equal to four}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 4 {means that the brown trout's mean I.Q. is greater than four}
The test statistics that would be used here One-sample t test statistics as we don't know about the 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 I.Q. of brown tout = [tex]\frac{\sum X}{n}[/tex] = 4.92
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X- \bar X)^{2} }{n-1} }[/tex] = 1.62
n = sample of brown trout = 12
So, the test statistics = [tex]\frac{4.92-4}{\frac{1.62}{\sqrt{12} } }[/tex] ~ [tex]t_1_1[/tex]
= 1.967
The value of t test statistics is 1.967.
Now, at 5% significance level the t table gives critical value of 1.796 at 11 degree of freedom for right-tailed test.
Since our test statistic is more than the critical value of t as 1.967 > 1.796, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the brown trout's mean I.Q. is greater than four.
To conduct a hypothesis test, compare the sample mean IQ of 12 brown trout to the hypothesized mean of 4 using a one-sample t-test at a 0.05 significance level.
Explanation:To conduct a hypothesis test of the belief that the brown trout's mean IQ is greater than four, we can use a one-sample t-test. The null hypothesis (H0) is that the mean IQ of brown trout is equal to four. The alternative hypothesis (Ha) is that the mean IQ is greater than four.
Using a proper significance level of 0.05, we can compare the sample mean IQ of the 12 brown trout to the hypothesized mean of four. If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is evidence to support the belief that the brown trout's mean IQ is greater than four.
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What is the value of the expression below? Negative 50 + 51 –101 –1 1 101
Answer:
the answer is 1
Step-by-step explanation:
bc if you add -50+51 you get 1
Answer:
uno
Step-by-step explanation
51- 50 =1
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 6262 minutes with a mean life of 606606 minutes. If the claim is true, in a sample of 9999 batteries, what is the probability that the mean battery life would be greater than 619619 minutes? Round your answer to four decimal places.
Answer:
0.0183 = 1.83% probability that the mean battery life would be greater than 619 minutes
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 normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
In this problem, we have that:
[tex]\mu = 606, \sigma = 62, n = 99, s = \frac{62}{\sqrt{99}} = 6.23[/tex]
What is the probability that the mean battery life would be greater than 619 minutes?
This is 1 subtracted by the pvalue of Z when X = 619. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{619 - 606}{6.23}[/tex]
[tex]Z = 2.09[/tex]
[tex]Z = 2.09[/tex] has a pvalue of 0.9817
1 - 0.9817 = 0.0183
0.0183 = 1.83% probability that the mean battery life would be greater than 619 minutes
) The National Highway Traffic Safety Administration collects data on seat-belt use and publishes results in the document Occupant Restraint Use. Of 1,000 drivers 16-24 years old, 79% said they buckle up, whereas 924 of 1,100 drivers 25-69 years old said they did. Does the data provide sufficient evidence to conclude that there is a difference in seat belt use? Go over all the steps in the process for comparing two sample percentages.
Answer:
We conclude that there is a difference in seat belt use.
Step-by-step explanation:
We are given that of 1,000 drivers 16-24 years old, 79% said they buckle up, whereas 924 of 1,100 drivers 25-69 years old said they did.
Let [tex]p_1[/tex] = population proportion of drivers 16-24 years old who buckle up .
[tex]p_2[/tex] = population proportion of drivers 25-69 years old who buckle up .
So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1-p_2[/tex] = 0 {means that there is no significant difference in seat belt use}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1-p_2\neq[/tex] 0 {means that there is a difference in seat belt use}
The test statistics that would be used here Two-sample z proportion statistics;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of drivers 16-24 years old who buckle up = 79%
[tex]\hat p_2[/tex] = sample proportion of drivers 25-69 years old who buckle up = [tex]\frac{924}{1100}[/tex] = 84%
[tex]n_1[/tex] = sample of 16-24 years old drivers = 1000
[tex]n_2[/tex] = sample of 25-69 years old drivers = 1100
So, test statistics = [tex]\frac{(0.79-0.84)-(0)}{\sqrt{\frac{0.79(1-0.79)}{1000}+\frac{0.84(1-0.84)}{1100} } }[/tex]
= -2.946
The value of z test statistics is -2.946.
Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.
Since our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that there is a difference in seat belt use.
A) 97°
C) 90°
B) 83°
D) 92°
Q Zoom
Answer:
B. 83
Step-by-step explanation:
Angle in a triangle sum to 180 degrees
-> 25 + 72 + ? = 180
? = 180 - 25 - 72 = 83
Answer:
the answer is B that's it
Which rules give a repeating pattern that has a 7 as the 15th number? Select all that apply.
a) 1, 7
b) 1, 7, 9
c) 1, 9, 7
d) 1, 7, 7
e) 7, 1, 9
Which polygon is a convex heptagon? A polygon has 7 sides. No angles go inside of the shape. A polygon has 8 sides. No angles go inside of the shape. A polygon has 8 sides. One angle goes inside of the shape. A polygon has 7 sides. One angle goes inside of the shape.
please it's for a unit test
The polygon which has 7 sides and all its angles inside of the shape is a convex heptagon.
Convex heptagon
A convex heptagon is a type of polygon that has 7 sides and 7 interior angles and 7 vertices.
How to find a convex heptagon?A polygon that has 7 sides and 7 interior angles and 7 vertices is considered as a convex heptagon.
This means a convex heptagon has 7 sides and all angles go inside of the shape.
So, the polygon which has 7 sides and all its angles go inside of the shape is a convex heptagon.
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Answer:
A
Step-by-step explanation:
on edge
A survey (random sample) of 700 office workers investigated telephone answering practices, including how often each office worker was able to answer incoming telephone calls and how often incoming telephone calls went directly to voice mail. A total of 280 office worker indicated that they never need voice mail and are able to take every telephone call. What is the 92% confidence interval for the actual proportion of all office workers who are able to take every telephone call
Answer:
The 92% confidence interval for the actual proportion of all office workers who are able to take every telephone call is (0.3676, 0.4324).
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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 700, \pi = \frac{280}{700} = 0.4[/tex]
92% confidence level
So [tex]\alpha = 0.08[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.08}{2} = 0.96[/tex], so [tex]Z = 1.75[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 1.75\sqrt{\frac{0.4*0.6}{700}} = 0.3676[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 1.75\sqrt{\frac{0.4*0.6}{700}} = 0.4324[/tex]
The 92% confidence interval for the actual proportion of all office workers who are able to take every telephone call is (0.3676, 0.4324).
How are the angle measurements of the opposite interior angles related ?
Answer:
opposite angles are congruent
Step-by-step explanation:
thats because if you think about two intersecting lines and draw a circle around the angles you can imagine it as a circle (360 degrees) so whatever value the angles are they have to equal 360
so you may ask the question what does that have to do with anything? well i'm getting to that...the vertical angles are congruent because well one there is a theorem for it (search it up) and two it makes sense if you think of cutting a pizza all the way across and another line intersecting it all the way across. You notice how no matter how you position the two intersecting lines the angle opposite each other look the same. Thats because they are the same exact angle just directly across from each other. I hope this made sense :)
Answer:
The opposite interior angles of the parallelogram have equal measurements.
Step-by-step explanation:
PLATO SAMPLE
helo asap !! will get branliest.
Answer:
1/25
Step-by-step explanation:
= 5^4/5^6
= 1/5^6-4
= 1/5^2
= 1/25
hope it helps!
Answer:
Here is the answer..
Step-by-step explanation:
It's simple.
look
=5^4/5^6
=1/25
Hope it helps ☺️
5 95 8,994 + 11 11 9,010 =
Answer:
5,95,9005,11,9010
Step-by-step explanation:
Find the volume of a right circular cone that has a height of 12.2 cm and a base with a circumference of 18.5 cm. Round your answer to the nearest tenth of a cubic centimeter.
We have been given that a right circular cone has a height of 12.2 cm and a base with a circumference of 18.5 cm. We are asked to find the volume of the cone to nearest tenth.
We know that circumference of circle is equal to [tex]2\pi r[/tex].
[tex]2\pi r=18.5[/tex]
[tex]r=\frac{18.5}{2\pi}[/tex]
[tex]r=2.944366[/tex]
Now we will use volume of the cone formula to solve our given problem.
[tex]V=\frac{1}{3}\pi r^2 h[/tex]
[tex]V=\frac{1}{3}\pi (2.944366)^2\cdot (12.2)[/tex]
[tex]V=\frac{1}{3}\pi (8.669291141956)\cdot (12.2)[/tex]
[tex]V=\frac{1}{3}\pi (105.7653519318632)[/tex]
[tex]V=\frac{1}{3}(332.2716526334804752)[/tex]
[tex]V=110.7572175[/tex]
Upon rounding to nearest tenth, we will get:
[tex]V\approx 110.8[/tex]
Therefore, the volume of the given cube would be approximately 110.8 cubic centimeter.
Final answer:
To find the volume of a right circular cone, the base radius is calculated from the circumference, and then the volume is determined using the cone volume formula V = (1/3)πr²h, with the final result being rounded to the nearest tenth. So, [tex]\( V \approx 110.415 \) cm^3[/tex].
Explanation:
To calculate the volume of a right circular cone, we first need to determine the radius of the base which can be found from the circumference. Since the formula for circumference is C = 2πr, where C is the circumference and r is the radius, we can solve for r. For a circumference of 18.5 cm, we have:
18.5 = 2πr => r = 18.5 / (2π)
Now that we have the radius, the volume of the cone can be found using the formula:
V = (1/3)πr²h
Plugging in the radius and height:
V = (1/3) * π * (18.5 / (2π))² * 12.2
After performing the calculation, we can round the result to the nearest tenth to find the volume in cubic centimeters.
Let's calculate it:
1. [tex]\( \frac{18.5}{2\pi} \) \approx \( \frac{18.5}{6.28319} \) \approx 2.942881[/tex]
2. Square the result: [tex]\( (2.942881)^2 \) \approx 8.66347[/tex]
3. Multiply by 12.2: [tex]\( 8.66347 \times 12.2 \)[/tex] ≈ 105.685554
4. Multiply by [tex]\( \frac{1}{3} \) and \( \pi \)[/tex]:
[tex]\( V = \frac{1}{3} \times \pi \times 105.685554 \)[/tex]
Now, let's calculate \( V \):
[tex]\[ V \approx \frac{1}{3} \times 3.14159 \times 105.685554 \]\[ V \approx \frac{1}{3} \times 3.14159 \times 105.685554 \]\[ V \approx 110.415 \][/tex]
So, [tex]\( V \approx 110.415 \) cm^3[/tex].
What is the hourly compensation per worker for a company with a unit labor cost of 0.9 and an hourly output per worker of $32.50? round your answer if necessary to the nearest whole number
Given Information:
Unit labor cost = 0.9
Hourly output per worker = $32.50
Required Information:
Hourly compensation per worker = ?
Answer:
Hourly compensation per worker = $36
Step-by-step explanation:
The unit labor cost is given by
[tex]U = \frac{O}{W}[/tex]
Where W is the hourly compensation per worker, O is the hourly output per worker and U is the unit labor cost.
Re-arranging for the hourly compensation yields,
[tex]U = \frac{O}{W}\\\\W =\frac{O}{U}\\ \\[/tex]
Now substitute the given values
[tex]W =\frac{32.50}{0.9}\\\\W = 36.11\\\\W = \$ 36[/tex]
Therefore, the hourly compensation per worker is $36.
Bonus:
Unit labor cost is the amount incurred with regard to labor expenses to produce one unit of a product. Calculating the unit labor cost helps in analyzing other aspects of the business such as product pricing, profit margin, sales etc.
Find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed. A 95% confidence interval for a difference in proportions p1-p2 if the samples have n1=70 with p^1=0.68 and n2=100 with p^2=0.56, and the standard error is SE=0.07. Round your answers to three decimal places. The 95% confidence interval is to .
Answer:
[tex] (0.68-0.56) -1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= -0.0263[/tex]
[tex] (0.68-0.56) +1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= 0.2663[/tex]
So then we are 95% confident that the true difference in the proportions is given by:
[tex] -0.0263 \leq p_1 -p_2 \leq 0.2663[/tex]
Step-by-step explanation:
The information given for this case is:
[tex]\hat p_1 = 0.68 , \hat p_2 = 0.56[/tex]
[tex] n_1 = 70, n_2 =100[/tex]
We want to construct a confidence interval for the difference of proportions [tex]p_1 -p_2[/tex] and for this case this confidence interval is given by:
[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1 (1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]
The confidence level is 0.95 so then the significance level would be [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex] if we find the critical values for this confidence level we got:
[tex]z_{\alpha/2}= \pm 1.96[/tex]
And replacing the info we got:
[tex] (0.68-0.56) -1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= -0.0263[/tex]
[tex] (0.68-0.56) +1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= 0.2663[/tex]
So then we are 95% confident that the true difference in the proportions is given by:
[tex] -0.0263 \leq p_1 -p_2 \leq 0.2663[/tex]
The 95% confidence interval is (0.257,-0.017).
To understand the calculations, check below.
Critical value:The critical value is a cut-off value that is used to mark the start of a region where the test statistic, obtained in hypothesis testing, is unlikely to fall in.
Given that,
[tex]n_1=70\\n_2=100\\\hat{p_1}=0.68\\\hat{p_1}=0.56\\SE=0.07\\\alpha=0.05[/tex]
The critical value is,
[tex]Z_{\frac{\alpha}{2} }=Z_{\frac{0.05}{2} }=1.96[/tex] (From standard normal probability table)
Therefore, the 95% confidence interval for the difference between population proportions [tex]p_1-p_2[/tex] is ,
[tex](\hat{p_1}-\hat{p_2})\pm Z_{\frac{\alpha}{2} }\times \sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1}+\frac{1}{n_2} ) }\\=(\hat{p_1}-\hat{p_2})\pm Z_{\frac{\alpha}{2} }\times SE\\=(0.68-0.56)\pm 1.96\times 0.07\\=0.12\pm 0.137\\=(0.257,-0.017)[/tex]
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The chance of winning a certain game at a carnival is 2 in 5. If Andy plays the game 12 times, what is the probability that he loses AT MOST 3 times?
Answer:
1.5267% probability that he loses AT MOST 3 times
Step-by-step explanation:
For each game that Andy plays, there are only two possible outcomes. Either he wins, or he loses. The probability of winning a game is independent of other games. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The chance of winning a certain game at a carnival is 2 in 5.
So the chance of losing is (5-2) in 5, that is 3 in 5.
So [tex]p = \frac{3}{5} = 0.6[/tex]
12 games:
This means that [tex]n = 12[/tex].
What is the probability that he loses AT MOST 3 times?
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex].
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.6)^{0}.(0.4)^{12} = 0.000017[/tex]
[tex]P(X = 1) = C_{12,1}.(0.6)^{1}.(0.4)^{11} = 0.000302[/tex]
[tex]P(X = 2) = C_{12,2}.(0.6)^{2}.(0.4)^{10} = 0.002491[/tex]
[tex]P(X = 3) = C_{12,3}.(0.6)^{3}.(0.4)^{9} = 0.012457[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.000017 + 0.000302 + 0.002491 + 0.012457 = 0.015267[/tex]
1.5267% probability that he loses AT MOST 3 times
Shameel has a flight to catch on Monday morning. His father will give him a ride to the airport. If it rains, the traffic will be bad and the probability that he will miss his flight is 0.06. If it doesn't rain, the probability that he will miss his flight is 0.01. The probability that it will rain on Monday is 0.19. Suppose that Shameel misses his flight. What is the probability that it was raining
Answer:
The probability that it was raining on Monday given that Shameel misses his flight is 0.5846.
Step-by-step explanation:
The Bayes' theorem states that the conditional probability of an event E[tex]_{i}[/tex], of the sample space S = {E₁, E₂, E₃,...Eₙ}, given that another event A has already occurred is given by the formula:
[tex]P(E_{i}|A)=\frac{P(A|E_{i})P(E_{i})}{\sum\limits^{n}_{i=1} {P(A|E_{i})P(E_{i})}}[/tex]
Denote the events as follows:
X = it will rain on Monday
Y = Shameel misses his flight.
The information provided is:
[tex]P(X) = 0.19\\P(Y|X)=0.06\\P(Y|X^{c})=0.01[/tex]
Compute the probability that it will not rain on Monday as follows:
[tex]P(X^{c})=1-P(X)\\\\=1-0.19\\\\=0.81[/tex]
Compute the probability that it was raining on Monday given that Shameel misses his flight as follows:
Use the Bayes' theorem:
[tex]P(X|Y)=\frac{P(Y|X)P(X)}{P(Y|X)P(X)+P(Y|X^{c})P(X^{c})}[/tex]
[tex]=\frac{(0.06\times 0.19)}{(0.06\times 0.19)+(0.01\times 0.81)}\\\\=\frac{0.0114}{0.0114+0.0081}\\\\=\frac{0.0114}{0.0195}\\\\=0.58462\\\\\approx 0.5846[/tex]
Thus, the probability that it was raining on Monday given that Shameel misses his flight is 0.5846.
Final answer:
The probability that it was raining given Shameel misses his flight is approximately 58.46%, calculated using Bayes' theorem with the given probabilities of rain and missing the flight under different weather conditions.
Explanation:
The student is asking about conditional probability related to Shameel missing his flight given that it is raining. We need to use Bayes' theorem to solve this problem. The equation for Bayes' theorem, in this case, is:
P(Rain|Miss) = (P(Miss|Rain) × P(Rain)) / (P(Miss|Rain) × P(Rain) + P(Miss|Not Rain) × P(Not Rain))
Let's plug in the values given:
P(Miss|Rain) = probability that Shameel misses his flight given it is raining = 0.06
P(Rain) = probability that it will rain = 0.19
P(Miss|Not Rain) = probability that Shameel misses his flight given it is not raining = 0.01
P(Not Rain) = probability that it does not rain = 1 - P(Rain) = 1 - 0.19 = 0.81
Substitute all the values into the equation:
P(Rain|Miss) = (0.06 × 0.19) / (0.06 × 0.19 + 0.01 × 0.81)
After calculating:
P(Rain|Miss) = 0.0114 / (0.0114 + 0.0081)
P(Rain|Miss) = 0.0114 / 0.0195 ≈ 0.5846 or 58.46%
So, if Shameel misses his flight, the probability that it was raining is approximately 58.46%.
What is the volume of a square pyramid if the length of an edge of the base is 7 and the altitude
of the pyramid is 12?
(1) 28
(2) 56
(3) 196
(4) 588
We have been given that the length of an edge of a square pyramid is 7 and altitude of the pyramid is 12. We are asked to find the volume of the pyramid.
We will use volume of pyramid formula to solve our given problem.
[tex]V=\frac{1}{3}\cdot b\cdot h[/tex], where,
b = Area of base of pyramid,
h = Height of pyramid.
We know that area of a square is square of its side length, so area of the base of pyramid would be [tex]7^2=49[/tex].
The height of the pyramid will be equal to altitude.
[tex]V=\frac{1}{3}\cdot 49\cdot 12[/tex]
[tex]V=49\cdot 4[/tex]
[tex]V=196[/tex]
Therefore, the volume of the given pyramid would be 196 cubic units and 3rd option is the correct choice.
what's the equivalent fraction of 3/8 tell me
Step-by-step explanation:
the equivalent of 3/8 is 6/16
Answer:
[tex]\frac{6}{16} = \frac{9}{24} =\frac{12}{32} =\frac{15}{40}[/tex]
Step-by-step explanation:
There are infinitely many equivalent fractions of [tex]\frac{3}{8}[/tex] but here are a few:
[tex]\frac{6}{16} = \frac{9}{24} =\frac{12}{32} =\frac{15}{40}[/tex]
A bank lent $200,500 for the development of two products. If the loan for product X was for $50,500 more than that for product Y, how much was lent for product Y?
Answer:
$75,000
Step-by-step explanation:
Given:
Total loaned amount = $200,500
Amount loaned for product Y = y
So, Amount loaned for product X = $50,500 + y
Computation:
Total loaned amount = Amount loaned for product Y + Amount loaned for product X
$200,500 = y + $50,500 + y
$200,500 = 2 y + $50,500
$200,500 - $50,500 = 2 y
$150,000 = 2 y
y = $75,000
Therefore, money loaned for product Y is $75,000
According to a 2014 research study of national student engagement in the U.S., the average college student spends 17 hours per week studying. A professor believes that students at her college study less than 17 hours per week. The professor distributes a survey to a random sample of 80 students enrolled at the college. From her survey data the professor calculates that the mean number of hours per week spent studying for her sample is 15.6 hours per week with a standard deviation of 4.5 hours per week. The professor chooses a 5% level of significance. What can she conclude from her data? Group of answer choices The data supports the professor’s claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week. The professor cannot conclude that the average number of hours per week spent studying for students at her college is less than 17 hours per week. The sample mean of 15.6 is not significantly less than 17. Nothing. The conditions for use of a T-model are not met. The professor cannot trust that the p-value is accurate for this reason.
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 17
For the alternative hypothesis,
µ < 17
This is a left tailed test.
Since the population standard deviation is not given, the distribution is a student's t.
Since n = 80,
Degrees of freedom, df = n - 1 = 80 - 1 = 79
t = (x - µ)/(s/√n)
Where
x = sample mean = 15.6
µ = population mean = 17
s = samples standard deviation = 4.5
t = (15.6 - 17)/(4.5/√80) = - 2.78
We would determine the p value using the t test calculator. It becomes
p = 0.0034
Since alpha, 0.05 > than the p value, 0.0043, then we would reject the null hypothesis.
The data supports the professor’s claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week.
A baker packages 12 cupcakes to a box. Sean orders 5 boxes for his sister’s graduation party and 3.5 boxes for the Variety Show Party. Write an expression that shows the calculations you could use to find the number of cupcakes Sean Orders
Answer:
The expression isTotal number of cupcakes Sean orders=5 boxes (12 cupcakes)+ 3.5 boxes (12 cupcakes)
Step-by-step explanation:
A box= 12 cupcakes
Sean's order
Sister's graduation=5 boxes
Variety show party=3.5 boxes
Total number of cupcakes Sean orders=5 boxes (12 cupcakes)+ 3.5 boxes (12 cupcakes)
Total number of cupcakes Sean orders=5(12)+3.5(12)
=60+42
=102 cupcakes
Which words or phrases describe some advantages of nonrenewable resources? Check all that apply.
easy to produce
habit-forming
finite
affordable
abundant
Answer:
a.)Easy to produce, d.)affordable, and e.)abundant
Step-by-step explanation:
i got it correct on the instructions
The correct options are easy to produce, affordable, and abundant.
What are nonrenewable resources?A nonrenewable resource is a natural substance that is not replenished with the speed at which it is consumed.
A non-renewable resource is defined as the natural resources which are not readily replaced through natural means and it takes thousands of years for their renewal.
Examples of non-renewable resources include Fossil fuels such as natural gas, oil, and coal.
There are many advantages of non-renewable resources such as:
Easy to produce: non-renewable resources are easy to produce because processing stations can be easily developed for refinement and distillation of non-renewable resources.Affordable and abundant: nonrenewable resources are affordable and abundant on the earth. for example, diesel and oil are good choices for powering vehicles.Hence, the correct options are easy to produce, affordable, and abundant.
Learn more about the nonrenewable resource here;
https://brainly.com/question/16183007
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Choose the function whose graph is given below.
-6
5
-3
4
5
-2.
-3
.4
O A. y= tan x
Determine whether the following series converges. Summation from k equals 2 to infinity (negative 1 )Superscript k Baseline StartFraction k squared minus 3 Over k squared plus 4 EndFraction Let a Subscript kgreater than or equals0 represent the magnitude of the terms of the given series. Identify and describe a Subscript k. Select the correct choice below and fill in any answer box in your choice. A. a Subscript kequals nothing is nondecreasing in magnitude for k greater than some index N. B. a Subscript kequals nothing and for any index N, there are some values of kgreater thanN for which a Subscript k plus 1greater than or equalsa Subscript k and some values of kgreater thanN for which a Subscript k plus 1less than or equalsa Subscript k. C. a Subscript kequals nothing is nonincreasing in magnitude for k greater than some index N. Evaluate ModifyingBelow lim With k right arrow infinitya Subscript k. ModifyingBelow lim With k right arrow infinitya Subscript kequals nothing Does the series converge?
Answer:
[tex]a_k=\left|\dfrac{k^2-3}{k^2+4}\right|;\text{ is nondecreasing for $k>2$}[/tex]
[tex]\lim\limits_{k \to \infty} a_k =1[/tex]
The series does not converge
Step-by-step explanation:
Given ...
[tex]S=\displaystyle\sum\limits_{k=2}^{\infty}{x_k}\\\\x_k=(-1)^k\cdot\dfrac{k^2-3}{k^2+4}\\\\a_k=|x_k|[/tex]
Find
whether S converges.
Solution
The (-1)^k factor has a magnitude of 1, so the magnitude of term k can be written as ...
[tex]\boxed{a_k=1-\dfrac{7}{k^2+4}}[/tex]
This is non-decreasing for k>1 (all k-values of interest)
As k gets large, the fraction tends toward zero, so we have ...
[tex]\boxed{\lim\limits_{k\to\infty}{a_k}=1}[/tex]
Terms of the sum alternate sign, approaching a difference of 1. The series does not converge.