Answer:
.05
Step-by-step explanation:
Khan
Using the normal distribution and the central limit theorem, it is found that the probability that the mean of these 100 sleep times is farther than 0.4 hours away from the population mean is:
a) 0.0455Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n, as long as n > 30, is approximately normal and has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 10 hours, hence [tex]\mu = 10[/tex].Standard deviation of 2 hours, hence [tex]\sigma = 2[/tex].Sample of 100, hence [tex]n = 100, s = \frac{2}{\sqrt{100}} = 0.2[/tex].We want the probability that the mean is farther than 0.4 hours away from the population mean, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{0.4}{s}[/tex]
[tex]Z = \frac{0.4}{0.2}[/tex]
[tex]Z = 2[/tex]
The probability is P(|Z| > 2), which is 2 multiplied by the p-value of Z = -2.
Z = -2 has a p-value of 0.0275.2 x 0.0275 = 0.0455Hence, option A is correct.
To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213
Find an exact value.
sine of negative eleven pi divided by twelve.
A. square root of six plus square root of two divided by four.
B. negative square root of six minus square root of two divided by four.
C. square root of two minus square root of six divided by four.
D. square root of six minus square root of two divided by four.
Answer:
(√2 - √6) / 4
C. square root of two minus square root of six divided by four.
Step-by-step explanation:
sine of negative eleven pi divided by twelve.
We have :
sin(-11π/12)
sin((4 - 15)π / 12) = sin(4π/12 - 15π/12)
sin(4π/12 - 15π/12) = sin(π/3 - 5π/4)
Recall:
Angle difference formula:
sin(A - B) = sinAcosB - sinBcosA
Hence,
sin(π/3 - 5π/4) = sin(π/3) cos(5π/4) − sin(5π/4) cos(π/3)
From trigonometry:
sinπ/3 = √3/2
cos5π/4 = -√2/2
sin5π/4 = -√2/2
cos π/3 = 1/2
(√3/2) (-√2/2) − (-√2/2) (1/2)
-√6/4 - -√2/4
-√6/4 + √2/4
√2/4 - √6/4
(√2 - √6) / 4
I need this ASAP HELP
Answer:
Srry I can't help
Step-by-step explanation:
i cant reallly see so yh
Step-by-step explanation:
Write the mixed number as an improper fraction.
23/4 =
Answer:
Improper fraction: 23/4
Mixed number: 5 3/4
Answer:
5 3/4
Step-by-step explanation:
how many times does 4 go into 23? well 4×5=20, which seems like too little, so we'll try 4×6=24,
but that's too much so were sticking with the 5. So 5 is the first number
then since 4 times 5 is 20. but you have 23, there are 3 extra numbers
So you make them into a fraction: 3/4
So the answer is 5 3/4
also 23/4 is the improper fraction, 5 3/4 is the mixed number
What is the slope of the line that passes through the points (-3, -3) and (-9,5)?
Write your answer in simplest form.
Answer:
our search - What is the slope of the line that passes through the points (-3, -3) and (-9,5)? Write your ... - did not match any documents.
Suggestions:
Make sure that all words are spelled correctly.
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Step-by-step explanation:
You are in charge of purchasing paper for the City of Fairfield. You want to show the mayor how much paper the city used in the past. Approximately how much more did the city budget for paper in 2015 than in 2011?
Answer:
0.2 million
Step-by-step explanation:
Find the IQR of the data in the box plot below
Answer:
3
Step-by-step explanation:
12 baseball cards cost $25 = How many dollars per baseball card?
Answer:
2.08333333333
Step-by-step explanation:
Answer: Each card costs $2.08
Step-by-step explanation: This is because you need to divide the cost for 12 cards by 12. 25/12 is 2.08333333... so you can round that to $2.08.
A carpenter is making a ramp for a ski jump.
The ramp is made from a 25 ft. board titled at
a 30° angle from the ground. Approximately
how far off the ground is the end of the ramp?
Answer:
12.5 ft
Step-by-step explanation:
To solve this, we would be applying Pythagoras theorem to it.
Assuming that our given angle is the hypotenuse. Since it says it's closer to the elevated angle. Then, we're looking for a side, A, which is on the opposite side of the angle in the question.
Using sine rule, we know that
Sin 30 = x/25
x = 25 sin 30
x = 25 * 0.5
x = 12.5 ft
Therefore the answer is 12.5 ft
Given the system of constraints name all vertices. Then find the maximum value of the given objective
x≥0
y≥0
y≤ 1/3x+1
5≥y+x
Objective function C = 7x-2y
Answer:
[tex]35[/tex]
Step-by-step explanation:
The constraints are
The red line represents the function
[tex]y\leq \dfrac{1}{3}x+1[/tex]
At [tex]y=0[/tex]
[tex]0=\dfrac{1}{3}x+1\\\Rightarrow -1=\dfrac{1}{3}x\\\Rightarrow x=-3[/tex]
At [tex]x=0[/tex]
[tex]y=0+1\\\Rightarrow y=1[/tex]
Two points are [tex](-3,0),(0,1)[/tex]
The blue line represents the function
[tex]5\geq y+x[/tex]
at [tex]y=0[/tex]
[tex]5=x[/tex]
at [tex]x=0[/tex]
[tex]y=5[/tex]
Two points are [tex](5,0),(0,5)[/tex]
The other two constraints are [tex]x\geq 0[/tex], [tex]y\geq 0[/tex]. So, the point has to be in the first quadrant
From the graph it can be seen there are two points where the function will be maximum let us check them.
[tex](3,2)[/tex]
[tex]7x-2y=7\times 3-2\times 2=17[/tex]
[tex](5,0)[/tex]
[tex]7x-2y=7\times 5-2\times 0=35[/tex]
So, the maximum value of the function is [tex]35[/tex].
Over what interval does this function remain constant? Do not use any spaces in your interval.
Answer:
We conclude that the function remains constant over the interval [0, 2].
Step-by-step explanation:
We know that if x increases from left to right and y remains constant, the function remains constant over a certain interval.
From the given graph below, it is clear that from x = 0 to x = 2 the value of y does not change.
In other words, the value of y remains constant from x = 0 to x = 2.
i.e.
at x = 0, y = 5
at x = 1, y = 5
at x = 2, y = 5
Therefore, we conclude that the function remains constant over the interval [0, 2].
A photographer is 6 feet tall and cast a shadow that is 2 feet long. He is photographing a palm tree with a shadow that is 7 feet long. What is the height of the tree
Answer: The height of the tree is 21 feet.
Step-by-step explanation:
Here we can assume that the angle at which the sun impacts the photographer and the tree to be the same angle.
Then we can think in both cases as triangles rectangles, where the height is a cathetus, and the shadow is the other cathetus.
Then we will have a relationship like:
Tg(angle) = shadow/height
height = shadow/Tg(angle)
Now, because for both triangles we have the same angle, then Tg(angle) will be the same number for both cases, and we can just think of it as constant K
Tg(angle) = K
Then we have the equation:
Height = Shadow/K
We know that the photographer is 6ft tall, and his shadow is 2 ft long, we can replace those two things in the above equation and find the value of k:
6ft = 2ft/K
K = 2ft/6ft = (1/3)
Now we know that the shadow of the tree is 7ft long, then the height will be:
height = 7ft/(1/3) = 7ft*3 = 21ft
The tree is 21 ft tall.
I WILL MAKE BRAINLIST OF CORRECT!
In the diagram, the measures of 21, 24, and 25 are 120°. The measure of 27 is 60°. Are lines cand d parallel?
Answer:
D
Step-by-step explanation:
1 and 5 are almost completely across from each other.
does anyone here know a guy named Connor this account on brainly starts with an r or w
Answer: are you ignoring me
Step-by-step explanation:
A family went on vacation and used 45.3 gallons of gasoline to travel 150 miles. How many total gallons of gasoline will they need to travel 200 more miles?
a.) 15.1 gallons
c.) 60.4 gallons
b.) 90.6 gallons
d.) 105.7gallons
Answer:
d) [tex]105.7\ \text{gallons}[/tex]
Step-by-step explanation:
[tex]150\ \text{miles}[/tex] requires [tex]45.3\ \text{gallons of fuel}[/tex]
[tex]1\ \text{mile}[/tex] requires [tex]\dfrac{45.3}{150}\ \text{gallons of fuel}[/tex]
[tex]200\ \text{miles}[/tex] requires [tex]200\times \dfrac{45.3}{150}=60.4\ \text{gallons of fuel}[/tex]
So, total amount of gasoline required for the trip is [tex]60.4+45.3=105.7\ \text{gallons}[/tex].
Whoever answers number 1 and 2 gets brainliest!! :)
Answer:
1: Yes they are both equivalent because 48/8 is 6 and 24/4 is 6.
2: They would score 750 points because you divide 150 by 3 and get 50, then you multiply 50 by 15 and get 750!
Step-by-step explanation:
IS (1, 2) of a solution set of x+ y = 3 and 2 x + 7 y = 16 ?
Answer:
yes
Step-by-step explanation:
x=3-y
2(3-y)+7y=16
6-2y+7y=16
5y=10
y=2
x=3-2=1
Add.
6.2 + 0.95 = ?
The sum is
.
Subtract.
2.53 – 0.8 = ?
The difference is
.
Answer:
The answer to the first question is 7.15
The answer to the second question is 1.73
Answer:
7.15; 1.73
Step-by-step explanation:
6.2 is the same as 6.20, so:
6.20
+ 0.95
= 7.15
0.8 is the same as 0.80, so:
2.53
- 0.80
= 1.73
A bake sale committee wants to raise $175 for a donation to a local charity. They set aside $14 of their profit at the end of each day. How many days will it take them to raise enough money for the whole donation?
Answer:
Number of days= 12.5
Step-by-step explanation:
Giving the following information:
A bake sale committee wants to raise $175 for a donation to a local charity. They set aside $14 of their profit at the end of each day.
To calculate the number of days required to raise $175, we need to use the following formula:
Number of days= total amount / profit per day
Number of days= 175/14
Number of days= 12.5
what is the HCF of -8xy and 20y ?
Answer:
Hcf of this will 4y I m sure because 4y divide that totally and it is greatest
Which expression is equal to 27 when x = -6?
A (-x)2 - 9
B (-2x)2 - 120
C 10(-x) +33
D 3(x-4) + 3
Answer:
C
Step-by-step explanation:
i got C & D to both be -27 but I think I made a mistake in C w the negatives so I believe it is C.
I hope this helps, have a great day/ night :)
One advantage to sexual reproduction versus asexual reproduction is that
Answer:
Time Efficient; no need to search for mate, requires less energy
Step-by-step explanation:
Hope This Helped if it did can i plz have brainliest
Answer:
I think it b
Step-by-step explanation:Because D it requires significant energy on the part of the organism to find a mate.C no they do not become extinct.A it takes a long time.
The face of a lamp shade is shaped like a trapezoid. The dimensions of the face are shown in the diagram.
six inches.....y inches....x inches....10 inches.....y inches...
Which equation can be used to find A , the area of the face of the lamp shade in square in
5.) A graph showing a proportional relationship will...
Answer:
C. A straight line that goes through the origin.
Step-by-step explanation:
A graph representing a proportional relationship between variable x and variable y will have a straight line. This straight line must also cut across or pass through the point of origin (0, 0).
Therefore, the answer is: "A straight line that goes through the origin."
Historically, only 35% of applicants for a statistical programming internship at a large pharmaceutical company have previous experience with the necessary software. Assume that applicants are selected at random and interviewed sequentially. What is the probability it takes exactly four interviews to find the first applicant with previous experience
The probability that takes exactly four interviews to find the first applicant with previous experience will be 0.3845.
What is binomial distribution?Frequency distribution of the percentage of successful outcomes that might occur in a certain number of trials with the same chance of success. If X~B(n, p), then the probability is given as
[tex]\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}[/tex]
At a big pharmaceutical company, historically, just 35% of applicants for an internship in statistical programming had prior computer software experience. Assume that candidates are chosen at random and questioned one at a time.
p = 0.35
Then the probability is given as,
P = ⁴C₁ x (0.35)¹ x (1 - 0.35)³
P = 0.3845
The probability that takes exactly four interviews to find the first applicant with previous experience will be 0.3845.
More about the binomial distribution link is given below.
https://brainly.com/question/14565246
#SPJ2
PLS HELP THIS IS DUE IN 10 MINUTES ASAP
Answer:
2) A.[tex]\frac{14+x}{5}[/tex]
3) B. [tex]4(\frac{11}{x} )[/tex]
Step-by-step explanation:
help! please look at the picture, the answer is needed quick the explanation doesn't matter. Thanks!
Step-by-step explanation:
49
only the positive 49
hope this helps bro!!
Alex conduct an experiment with a spinner he recorded the frequency of each spin landing on letters A through D in the table. based on the data in the table what is the experimental probability that the next spin will land on letter B? A. 4/15 B. 1/5 C. 1/4 D. 3/10
Answer
3/10
Step-by-step explanation:
Grayson is playing a game in which the object is to obtain a 0 by adding the points scored during each round.
Round 1 Round 2 Round 3 Round 4 Round 5
4
7
1
-12
Based on the points he scored during the first 4 rounds, what score does Grayson need on the 5th round?
-24
-11
12
Answer:
0. See explanation below.
Step-by-step explanation:
Grayson is playing a game in which the objective is to obtain a zero, by adding together the points scored in each round.
For rounds 1 to 4,
4 + 7 + 1 + -12 = 12 - 12 = 0
The summation of points in the first four rounds already results to a zero.
Let us see if the addition of any of the three options for round 5 will still result in a zero!
0 + -24 = -24
0 + -11 = -11
0 + 12 = 12
So all the options here are wrong. The only option that would have been correct is 0.
Since 4 + 7 + 1 + -12 + 0 = 0
Maybe the complete question has 0 as the fourth option. Use that.
wendy jogs every three days and xue jogs every four days. if today is a wednesday and wendy and sue both jog today, in how many days will they both jog again on the same day of the week which day of the week will it be
Answer:
Monday
Step-by-step explanation:
Given
[tex]Wendy = 3[/tex]
[tex]Xue = 4[/tex]
[tex]Today = Wednesday[/tex]
Required
Determine when next they will jog together
First, we calculate the L.C.M of the days they jog:
[tex]3 = 1 * 3[/tex] --- Wendy
[tex]4 = 1 * 2 * 2[/tex] ---- Xue
[tex]LCM = 1 * 3 * 2 * 2[/tex]
[tex]LCM = 12[/tex]
This means that they meet on the 12th day; The 12th day after a Wednesday is Monday.
Hence, they will meet on a Monday
Ben jogged 4 1/2 miles in 1 1/4 hours at a constant rate. How far did ben jog in 1 hour?
Answer:
3.6 miles
Step-by-step explanation:
do 4.5/1.25 because that is the unit rate. when you do that you get 3.6 miles in an hour
