Answer:
3 1/8 ft²
Step-by-step explanation:
The area of a parallelogram is equal to the product of its base and its height.
b × h
2.5 × 1.25
= 3.125
The area is 3.125 feet².
I need help please ASAPPP!
Answer:
16
Step-by-step explanation:
Please see attached photo for diagrammatic explanation.
Note: r is the radius
Using pythagoras theory, we can obtain the value of 'x' in the attached photo as shown:
|EB|= x
|FB| = 10
|EF| = 6
|EB|² = |FB|² – |EF|²
x² = 10² – 6²
x² = 100 – 36
x² = 64
Take the square root of both side.
x = √64
x = 8
Now, we can obtain line AB as follow:
|AB|= x + x
|AB|= 8 + 8
|AB|= 16
Therefore, line AB is 16
2
(08.06 MC)
The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function, and the other is an exponential function. Which function
is most likely increasing exponentially?
x F(x) G(x) 1 2 2 2 5 4 3 10 8 4 17 16 5 26 32 A.) f(x) because it grows slower than g(x). B.) f(x) because it eventually intersects g(x). C.) g(x) because it grows faster than f(x). D.) g(x) because it will not intersect f(x).
Answer:
Answer is 2
Step-by-step explanation:
It exceeds f(x)
C is the function is most likely increases exponentially. g(x), because it grows faster than f(x).
What is a function?A statement, rule, or legislation establishes a link between one variable in the function the dependent variable, and another the independent variable.
The difference between the first and second differences of f(x) is 2. This is a quadratic function's characteristic (second differences are constant).
The given function includes the both dependent and the independent function.
The first differences of g(x), as well as the terms of g, have a ratio of 2.
An exponential function has this property (terms and differences have a common ratio. We should also mention that g(x) increases faster than f. (x).
Any polynomial function will increase more slowly than an exponential function. The proper option is b.
Hence C is the function that most likely increases exponentially. g(x), because it grows faster than f(x).
To learn more about the function refer to the link
https://brainly.com/question/12431044
Use only the digits 0 - 9 and the decimal and the negative sign, if needed, to fill in the blank. If f(x) = 2x + 9, then f(-1) = _____.
Answer:
7
Step-by-step explanation:
f(x) = 2x + 9
Put x as -1.
f(-1) = 2(-1) + 9
Multiply both terms 2 and -1.
f(-1) = -2 + 9
Add the terms -2 and 9.
f(-1) = 7
Make the appropriate conclusion. Choose the correct answer below. A. RejectReject H0. There is insufficientinsufficient evidence at the alphaαequals=0.100.10 level of significance to conclude that the true mean heart rate during laughter exceeds 7171 beats per minute. B. Do not rejectDo not reject H0. There is insufficientinsufficient evidence at the alphaαequals=0.100.10 level of significance to conclude that the true mean heart rate during laughter exceeds 7171 beats per minute. C. RejectReject H0. There is sufficientsufficient evidence at the alphaαequals=0.100.10 level of significance to conclude that the true mean heart rate during laughter exceeds 7171 beats per minute. D. Do not rejectDo not reject H0. There is sufficientsufficient evidence at the alphaαequals=0.100.10 level of significance to conclude that the true mean heart rate during laughter exceeds 7171 beats per minute.
Answer:
a) Option D is correct.
H0: μ = 71
Ha: μ > 71
b) Option F is correct
z > 1.28
c) z = 2.85
d) Option C is correct.
Reject H0.There is sufficient evidence at the α = 0.10 level of significance to conclude that the true mean heart rate during laughter exceeds 71 beats per minute.
Step-by-step explanation:
a) For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
This question aims to test the the true mean heart rate during laughter exceeds 71 beats per minute.
Hence, the null hypothesis is that there isn't sufficient evidence to say that the true mean heart rate during laughter exceeds 71 beats per minute. That is, the true mean doesn't exceed 71 beats per minute.
And the alternative hypothesis is that there is sufficient evidence to say that the true mean heart rate during laughter exceeds 71 beats per minute.
Mathematically,
The null hypothesis is represented as
H₀: μ = 71
The alternative hypothesis is represented as
Hₐ: μ > 71
b) Using z-distribution, the rejection area is obtained from the confidence level at which the test is going to be performed. Since the hypothesis test tests only in one direction,
Significance level = (100% - confidence level)/2
0.10 = 10% = (100% - confidence level)/2
20% = 100% - (confidence level)
Confidence level = 100% - 20% = 80%
Critical value for 80% confidence level = 1.28
And since we are testing if the true mean heart rate during laughter exceeds 71 beats per minute, the rejection area would be
z > 1.28
c) The test statistic is given as
z = (x - μ)/σₓ
x = sample mean = 73.4
μ = 71
σₓ = standard error = (σ/√n)
σ = 8
n = Sample size = 90
σₓ = (8/√90) = 0.8433
z = (73.4 - 71) ÷ 0.8433
z = 2.846 = 2.85
d) Since the z-test statistic obtained, 2.85, is firmly in the rejection area, z > 1.28, we reject the null hypothesis, accept the alternative hypothesis and say that there is sufficient evidence at the α = 0.10 level of significance to conclude that the true mean heart rate during laughter exceeds 71 beats per minute.
Hope this Helps!!!
The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 17 minutes and a standard deviation of 4 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price? (b) If the automotive center does not want to give the discount to more than 2% of its customers, how long should it make the guaranteed time limit?
Answer:
a) 22.66% of customers receive the service for half-price.
b) The guaranteed time limit should be of 25.2 minutes.
Step-by-step explanation:
When the distribution is normal, we use 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.
In this question, we have that:
[tex]\mu = 17, \sigma = 4[/tex]
(a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price?
Longer than 20 minutes is 1 subtracted by the pvalue of Z when X = 20. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 17}{4}[/tex]
[tex]Z = 0.75[/tex]
[tex]Z = 0.75[/tex] has a pvalue of 0.7734
1 - 0.7734 = 0.2266
22.66% of customers receive the service for half-price.
(b) If the automotive center does not want to give the discount to more than 2% of its customers, how long should it make the guaranteed time limit?
The time limit should be the 100 - 2 = 98th percentile, which is X when Z has a pvalue of 0.98. So X when Z = 2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.054 = \frac{X - 17}{4}[/tex]
[tex]X - 17 = 4*2.054[/tex]
[tex]X = 25.2[/tex]
The guaranteed time limit should be of 25.2 minutes.
The driver of a car traveling at 42 ft/sec suddenly applies the brakes. The position of the car is s equals 42 t minus 3 t squared comma t seconds after the driver applies the brakes. How far does the car go before coming to a stop?
Answer:
after 7 seconds the driver applied the brakes to stop the car.
Step-by-step explanation:
Given:
The position of the car s(t)=[tex]42t-3t^2[/tex]
∴Speed of the car =[tex]\frac{ds}{dt}=\frac{d(42t-3t^2)}{dt}=42-6t[/tex]
When car stopped the speed of car=0
[tex]\Rightarrow42-6t=0\\\Rightarrow6t=42\\\Rightarrow\ t=7[/tex]
Therefore, after 7 seconds the driver applied the brakes to stop the car.
If AYWZ - AYXW, what is true about ZXWZ?
O ZXWZ is an obtuse angle.
ZXWZ is a right angle,
ZXWZ is congruent to ZWXY.
ZXWZ is congruent to ZXZW.
Answer:
<XWZ is a right angle
Step-by-step explanation:
Since <YWZ and <XWY both equal 45 degrees, So, <XWZ is a right angle.
Given that ΔYWZ and ΔYXW are similar triangles, the statement that is true about ΔYXW is: B. XWZ is a right angle,
Similar TrianglesTriangles that are similar possess equal corresponding angles.
We are given that:
ΔYWZ ~ ΔYXW
Therefore:∠YWZ = ∠XWY = 45 degrees
Thus:∠YWZ + ∠XWY = ∠XWZ
45 + 45 = ∠XWZ
∠XWZ = 90 degrees (right angle).
Therefore, given that ΔYWZ and ΔYXW are similar triangles, the statement that is true about ΔYXW is: B. XWZ is a right angle,
Learn more about similar triangles on:
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Which monomial is a perfect cube?
49pºq3,24
O 81012, 15,12
O 121pºq3,5
O 343pq21,69
Answer:
The last one is a perfect cube.
Step-by-step explanation:
I did the math
1. The Wall Street Journal reported that bachelor’s degree recipients with majors in business average starting salaries of $53,900 in 2012 (The Wall Street Journal, March 17, 2014). The results for a sample of 100 business majors receiving a bachelor’s degree in 2013 showed a mean starting salary of $55,144 with a sample standard deviation of $5,200. Conduct a hypothesis test to determine whether the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012. Use a = .01 as the level of significance
Answer:
The calculated value t = 4.976 > 2.6264 at 0.01 level of significance
Null hypothesis is rejected
Alternative hypothesis is accepted
The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Step-by-step explanation:
Given Mean of the population μ = $53,900
Given sample size 'n' = 100
Mean of the sample size x⁻ = 55,144
Sample standard deviation 'S' = 5200
Null hypothesis:H₀: There is no difference between the means
Alternative Hypothesis :H₁: The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{55144-53900}{\frac{5200}{\sqrt{100} } }[/tex]
t = 4.976
Degrees of freedom
ν = n-1 = 100-1 =99
t₀.₀₁ = 2.6264
The calculated value t = 4.976 > 2.6264 at 0.01 level of significance
Null hypothesis is rejected
Alternative hypothesis is accepted
Final answer:-
The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Answer:
We conclude that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012.
Step-by-step explanation:
We are given that the Wall Street Journal reported that bachelor’s degree recipients with majors in business average starting salaries of $53,900 in 2012.
A sample of 100 business majors receiving a bachelor’s degree in 2013 showed a mean starting salary of $55,144 with a sample standard deviation of $5,200.
Let [tex]\mu[/tex] = mean starting salary for business majors in 2013.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] $53,900 {means that the mean starting salary for business majors in 2013 is smaller than or equal to the mean starting salary in 2012}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $53,900 {means that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012}
The test statistics that would be used here 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 starting salary = $55,144
s = sample standard deviation = $5,200
n = sample of business majors = 100
So, the test statistics = [tex]\frac{55,144-53,900}{\frac{5,200}{\sqrt{100} } }[/tex] ~ [tex]t_9_9[/tex]
= 2.392
The value of t-test statistic is 2.392.
Now, at 0.01 significance level the t table gives a critical value of 2.369 at 99 degree of freedom for right-tailed test.
Since our test statistic is more than the critical value of t as 2.392 > 2.369, 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 mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012.
A parabola is defined by the equation x = 5y2 In which direction will the parabola open?
ОА.
up
OB.
down
O C. right
OD.
left
Answer:
C) To the right.
Step-by-step explanation:
A newspaper report says that a company made £700’000 profit last year. It’s says this was 12% more than the year before. How much profit did the company make the year before
Answer: £625,000
Step-by-step explanation:
Previous year's profit can be calculated as:
700000 / 1.12 = 625000
The profit that should make a year before should be £625,000.
Given that
The profit made last year should be £700,000.And, there is 12% more than the year before.So the profit that should make a year before should be
[tex]= \frac{700,000}{(1 + 0.12)} \\\\= \frac{700,000}{(1.12)}[/tex]
= £625,000
Therefore we can conclude that The profit that should make a year before should be £625,000.
Learn more about the profit here: brainly.com/question/9281343
Tickets for a raffle cost $19. There were 798 tickets sold. One ticket will be randomly selected as the winner, and that person wins $1300 and also the person is given back the cost of the ticket. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)
Answer:
-17.32
Step-by-step explanation:
(1319- 19*797)/798 = -17.3233
Edith earns an annual gross salary of $17,500. She has 28% of her gross salary withheld for taxes and other deductions. What is the net pay of each paycheck if she is paid weekly?
Answer:
$242.3
Step-by-step explanation:
She earns $17500 per year. Multiply that number by 0.28 to get how much she withholds for taxes and other deductions. Subtract that number from 17500. You get 12600. Since there are 52 weeks in a year, divide 12600 by 52 to get how much she earns each week minus the 28 percent.
The number you get from this is $242.3, which is the net pay of each paycheck.
Answer:
$242.31/wkly
Step-by-step explanation:
$17,500.00 × 28% = $4,900.00
$17,500.00-$4,900 = $12,600.00
$12,600.00 ÷ 52/(weeks in a year) = $242.31 a week
$12,600 ÷ 12/month = $1,050.00
$1,050 ÷ 4/weeks = $262.50
(d) A drinks machine dispenses coffee into cups. A sign on the machine indicates that each cup contains 100ml of coffee. The machine actually dispenses a mean amount of 105ml per cup and 10% of the cups contain less than the amount stated on the sign. Assuming that the amount of coffee dispenses into each cup is normally distributed, find the standard deviation of the amount of coffee dispensed per cup in ml.
Answer:
The standard deviation of the amount of coffee dispensed per cup in ml is 3.91.
Step-by-step explanation:
Let the random variable X denote the amount of coffee dispensed by the machine.
It is provided that the random variable, X is normally distributed with mean, μ = 105 ml/cup and standard deviation, σ.
It is also provided that a sign on the machine indicates that each cup contains 100 ml of coffee.
And 10% of the cups contain less than the amount stated on the sign.
To compute the probabilities of a normally distributed random variable, first convert the raw score to a z-score,
[tex]z=\frac{X-\mu}{\sigma}[/tex]
This implies that:
P (X < 100) = 0.10
⇒ P (Z < z) = 0.10
The value of z for the above probability is, z = -1.28.
*Use a z-table
Compute the value of standard deviation as follows:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]-1.28=\frac{100-105}{\sigma}[/tex]
[tex]\sigma=\frac{-5}{-1.28}[/tex]
[tex]=3.90625\\\\\approx 3.91[/tex]
Thus, the standard deviation of the amount of coffee dispensed per cup in ml is 3.91.
The commute time for people in a city has an exponential distribution with an average of 0.5 hours. What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours? Answer: (round to 3 decimal places)
Answer:
0.314 = 31.4% probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
In this question:
[tex]m = 0.5, \mu = \frac{1}{0.5} = 2[/tex]
What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours?
[tex]P(0.4 \leq X \leq 1) = P(X \leq 1) - P(X \leq 0.4)[/tex]
In which
[tex]P(X \leq 1) = 1 - e^{-2} = 0.8647[/tex]
[tex]P(X \leq 0.4) = 1 - e^{-2*0.4} = 0.5507[/tex]
So
[tex]P(0.4 \leq X \leq 1) = P(X \leq 1) - P(X \leq 0.4) = 0.8647 - 0.5507 = 0.314[/tex]
0.314 = 31.4% probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours
Expand and Simplify (x-2)^2
options
x^2+4x+4
x2 − 4
x^2 - 4x + 4
x^2+4
Answer:
[tex]\boxed{\ x^2-4x+4 \ }[/tex]
Step-by-step explanation:
[tex](x-2)^2 = (x-2)(x-2)=x(x-2)*-2(x-2)=x^2-2x-2x+4=x^2-4x+4[/tex]
In a survey of women in a certain country (ages 20 minus29), the mean height was 66.2 inches with a standard deviation of 2.86 inches. Answer the following questions about the specified normal distribution. (a) What height represents the 95th percentile? (round to two decimal places as needed)
(b) What height represents the first quartile? (round to two decimal places as needed.)
Answer:
(a) The height of 70.90 inches represents the 95th percentile.
(b) The height of 64.27 inches represents the first quartile.
Step-by-step explanation:
We are given that in a survey of women in a certain country (ages 20-29), the mean height was 66.2 inches with a standard deviation of 2.86 inches.
Let X = heights of women in a certain country.
So, X ~ Normal([tex]\mu=66.2,\sigma^{2} =2.86^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean height = 66.2 inches
[tex]\sigma[/tex] = standard deviation = 2.86 inches
(a) We have to find the height that represents 95th percentile, that means;
P(X < x) = 0.95 {wherex is the required height}
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-66.2}{2.86}[/tex] ) = 0.95
P(Z < [tex]\frac{x-66.2}{2.86}[/tex] ) = 0.95
Now, in the z table the critical value of x that represents the top 5% area is given by 1.645, that is;
[tex]\frac{x-66.2}{2.86}=1.645[/tex]
[tex]{x-66.2=1.645\times 2.86[/tex]
x = 66.2 + 4.70 = 70.90 inches
So, the height of 70.90 inches represents the 95th percentile.
(b) We have to find the height that represents the first quartile, that means;
P(X < x) = 0.25 {wherex is the required height}
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-66.2}{2.86}[/tex] ) = 0.25
P(Z < [tex]\frac{x-66.2}{2.86}[/tex] ) = 0.25
Now, in the z table the critical value of x that represents the below 25% area is given by -0.6745, that is;
[tex]\frac{x-66.2}{2.86}=-0.6745[/tex]
[tex]{x-66.2=-0.6745\times 2.86[/tex]
x = 66.2 - 1.93 = 64.27 inches
So, the height of 64.27 inches represents the first quartile.
Use the Central Limit Theorem to find a mean given a probability Question A video game company sells an average of 132 games a month, with a standard deviation of 9 games. The company is looking to reward stores that are selling in the top 7%. How many video games must a store sell in order to be eligible for a reward if the company is only looking at 36 of their stores. Use the 2-table below: z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 1.1 0.864 0.867 0.869 0.871 0.873 0.875 0.877 0.879 0.881 0.883 1.2 0.885 0.887 0.889 0.891 0.893 0.894 0.896 0.898 0.900 0.901 1.3 0.9030.905 0.9070.908 0.910 0.911 0.913 0.915 0.9160.918 1.4 0.919 0.921 0.922 0.924 0.925 0.926 0.928 0.929 0.931 0.932 1.5 0.933 0.934 0.936 0.937 0.938 0.939 0.941 0.942 0.943 0.944 1.6 0.945 0.946 0.947 0.948 0.949 0.951 0.952 0.953 0.954 0.954
Round the z.score and a to two decimal places. Round up to the nearest whole number.
Answer:
The number of games must a store sell in order to be eligible for a reward is 135.
Step-by-step explanation:
Let the random variable X represent the number of video games sold in a month by the sores.
The random variable X has a mean of, μ = 132 and a standard deviation of, σ = 9.
It is provided that the company is looking to reward stores that are selling in the top 7%.
That is, [tex]P (\bar X > \bar x) = 0.07[/tex].
The z-score related to this probability is, z = 1.48.
Compute the number of games must a store sell in order to be eligible for a reward as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]\bar x=\mu+z\cdot \sigma/\sqrt{n}[/tex]
[tex]=132+1.48\times (9/\sqrt{36})\\\\=132+2.22\\\\=134.22\\\\\approx 135[/tex]
Thus, the number of games must a store sell in order to be eligible for a reward is 135.
Answer:
1.48
1.5
135
Step-by-step explanation:
Multiply (9 − 4i)(2 + 5i).
Answer:
38 + 37i
Step-by-step explanation:
(9 − 4i)(2 + 5i)
FOIL
first: 9*2 = 18
Outer: 9*5i = 45i
inner: -4i * 2 = -8i
last : -4i * 5i = -20i^2 = -20(-1) = 20
Combine together
18+45i-8i +20
38 + 37i
Answer:
38+37i
Step-by-step explanation:
(9 − 4i)(2 + 5i)= 18+45i-8i-20i²= 18+20+37i= 38+37i
Suppose that the thickness of one typical page of a book printed by a certain publisher is a random variable with mean 0.1 mm and a standard deviation of 0.002 mm. A new book will be printed on 500 sheets of this paper. Approximate the probability that the
Answer:
The probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm is 0.97.
Step-by-step explanation:
The complete question is:
Suppose that the thickness of one typical page of a book printed by a certain publisher is a random variable with mean 0.1 mm and a standard deviation of 0.002 mm Anew book will be printed on 500 sheets of this paper. Approximate the probability that the thicknesses at the entire book (excluding the cover pages) will be between 49.9 mm and 50.1 mm. Note: total thickness of the book is the sum of the individual thicknesses of the pages Do not round your numbers until rounding up to two. Round your final answer to the nearest hundredth, or two digits after decimal point.
Solution:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e S, will be approximately normally distributed.
Then, the mean of the distribution of the sum of values of X is given by,
[tex]\mu_{S}=n\mu[/tex]
And the standard deviation of the distribution of the sum of values of X is given by,
[tex]\sigma_{S}=\sqrt{n}\sigma[/tex]
The information provided is:
[tex]n=500\\\mu=0.1\\\sigma=0.002[/tex]
As n = 500 > 30, the central limit theorem can be used to approximate the total thickness of the book.
So, the total thickness of the book (S) will follow N (50, 0.045²).
Compute the probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm as follows:
[tex]P(49.9<S<50.1)=P(\frac{49.9-50}{0.045}<\frac{S-E(S)}{SD(S)}<\frac{50.1-50}{0.045})[/tex]
[tex]=P(-2.22<Z<2.22)\\\\=P (Z<2.22)-P(Z<-2.22)\\\\=0.98679-0.01321\\\\=0.97358\\\\\approx 0.97[/tex]
Thus, the probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm is 0.97.
55 and 101 that is multiple of 2,3 and 9
Answer:
No, 55 and 101 are not multiples of 2, 3 and 9
Step-by-step explanation:
Circle O is represented by the equation (x + 7)2 + (y + 7)2 = 16. What is the length of the radius of circle O?
Answer:
4
Step-by-step explanation:
(x - h)² + (x - k)² = r²
r is the radius of the circle. We are given r as 16. So,
r² = 16
√r² = √16
r = 4
And we have our final answer!
Answer:
4
Step-by-step explanation:
(x - h)² + (x - k)² = r²
r is the radius of the circle. We are given r as 16. So,
r² = 16
√r² = √16
r = 4
This is the final answer!
What is AB? Geometry help please
Answer:
AB = 37 units.
Step-by-step explanation:
Solve for AB using the Pythagorean theorem:
c² = a² + b² (c being AB in this instance)
Plug in the values of the legs of the triangle:
c² = 12² + 35²
c² = 144 + 1225
c² = 1369
c = √1369
c = 37
Therefore, AB = 37.
Triangle J K L is shown. Angle J L K is 105 degrees. The length of J K is 4.7 and the length of J L is 2.7.
Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction
What is the approximate measure of angle K? Use the law of sines to find the answer.
20°
34°
41°
53°
Answer:
The approximate measure of angle K is 34°
Step-by-step explanation:
In ΔJKL
∠L = 105°
JK = 4.7
JL = 2.7
Sine Rule:
[tex]\frac{SinA}{a} = \frac{SinB}{b}= \frac{SinC}{c}[/tex]
So,[tex]\frac{SinL}{JK} = \frac{SinK}{JL}\\\frac{SinL}{4.7} = \frac{SinK}{2.7}\\\frac{Sin 105}{4.7} = \frac{SinK}{2.7}\\\frac{Sin 105 \times 2.7}{4.7} = SinK\\\frac{(0.9659 \times 2.7)}{4.7} = Sin K\\\frac{2.60793}{4.7} = Sin K\\0.5549 = Sin K\\Sin^{-1}(0.5549)= K\\K = 33.70[/tex]
K ≈ 34°
So, Option B is true
Hence The approximate measure of angle K is 34°
Answer:
B) 34
Step-by-step explanation:
Find the area of circle B in term of ( pie )
Answer:
C.
Step-by-step explanation:
[tex]1.5^2\pi =2.25\pi[/tex]
Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the line y equals one third x comma above left by yequalsxplus4, and above right by yequalsminusx squaredplus10.
Answer:
The bounded area is: [tex]\frac{73}{6}\approx 12.17[/tex]
Step-by-step explanation:
Let's start by plotting the functions that enclose the area, so we can find how to practically use integration. Please see attached image where the area in question has been highlighted in light green. The important points that define where the integrations should be performed are also identified with dots in darker green color. These two important points are: (2, 6) and (3, 1)
So we need to perform two separate integrals and add the appropriate areas at the end. The first integral is that of the difference of function y=x+4 minus function y=(1/3)x , and this integral should go from x = 0 to x = 2 (see the bottom left image with the area in red:
[tex]\int\limits^2_0 {x+4-\frac{x}{3} } \, dx =\int\limits^2_0 {\frac{2x}{3} +4} \, dx=\frac{4}{3} +8= \frac{28}{3}[/tex]
The next integral is that of the difference between [tex]y=-x^2+10[/tex] and the bottom line defined by: y = (1/3) x. This integration is in between x = 2 and x = 3 (see bottom right image with the area in red:
[tex]\int\limits^3_2 {-x^2+10-\frac{x}{3} } \, dx =-9+30-\frac{3}{2} -(-\frac{8}{3} +20-\frac{2}{3} )=\frac{39}{2} -\frac{50}{3} =\frac{17}{6}[/tex]
Now we need to add the two areas found in order to get the total area:
[tex]\frac{28}{3} +\frac{17}{6} =\frac{73}{6}\approx 12.17[/tex]
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X≤2), n=5, p=0.8
Answer:
0.0579
Step-by-step explanation:
P(X≤2) = P(X=0) + P(X=1) + P(X=2)
P(X≤2) = ₅C₀ (0.8)⁰ (0.2)⁵ + ₅C₁ (0.8)¹ (0.2)⁴ + ₅C₂ (0.8)² (0.2)³
P(X≤2) = 0.00032 + 0.0064 + 0.0512
P(X≤2) = 0.0579
Probability of obtaining a success is 0.0579 .
Here,
Binomial distribution formula:
P(x:n,p) = nCx px (1-p)n-x Or P(x:n,p) = nCx px (q)n-x
Substituting the values of n and p
n = 5
p = 0.8
So,
P(X≤2) = P(X=0) + P(X=1) + P(X=2)
P(X≤2) = ₅C₀ (0.8)⁰ (0.2)⁵ + ₅C₁ (0.8)¹ (0.2)⁴ + ₅C₂ (0.8)² (0.2)³
P(X≤2) = 0.00032 + 0.0064 + 0.0512
P(X≤2) = 0.0579
Know more about binomial distribution,
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An inlet pipe can fill an empty swimming pool in 5 hours, and another inlet pipe can fill the pool in 2 hours. How long will it take both pipes to fill the pool?
Answer:
1.42 hours
Step-by-step explanation:
In this case we must take into account that the speed would be to fill a pool for a time, that this case is in hours, therefore it would be like this:
1/5 for the first pipe
1/2 for the second pipe
Now, we will use both at the same time, therefore:
1/5 + 1/2 = 1 / x
0.7 = 1 / x
x = 1 / 0.7
x = 1.42
That is to say that if we use both we will take a total of 1.42 hours
simplify x
[tex] {x}^{2} + 6x - 12[/tex]
Answer: x=8
Step-by-step explanation:
Please help me with this problem
