What is the probability that a random sample of 17 pregnancies has a mean gestation period within 9 days of the mean?( length of pregnancies of a certain animal are approximately normally distributed with mean of 295 days and standard deviation of 15 days)
Answer:
0.9864
Step-by-step explanation:
The average sample mean is 295, and the standard deviation is:
σ = 15 / √17
σ = 3.64
The z-scores are:
z = (x − μ) / σ
z₁ = (-9) / 3.64
z₁ = -2.47
z₂ = (9) / 3.64
z₂ = 2.47
So the probability is:
P(-2.47 < Z < 2.47) = P(Z < 2.47) − P(Z < -2.47)
P(-2.47 < Z < 2.47) = 0.9932 − 0.0068
P(-2.47 < Z < 2.47) = 0.9864
Using the normal distribution and the central limit theorem, it is found that there is a 0.9864 = 98.64% probability that a random sample of 17 pregnancies has a mean gestation period within 9 days of the mean.
In a normal distribution with mean and standard deviation , 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.For a sample of size n, by the Central Limit Theorem, the standard deviation is given by [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]In this problem:
Mean of 295 days, thus [tex]\mu = 295[/tex].Standard deviation of 15 days, thus [tex]\sigma = 15[/tex].Sample of 17 pregnancies, thus [tex]n = 17, s = \frac{15}{\sqrt{17}}[/tex].Gestation period within 9 days of the mean is between 286 and 304 days, and the probability is the p-value of Z when X = 304 subtracted by the p-value of Z when X = 286.
X = 304:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{304 - 295}{\frac{15}{\sqrt{17}}}[/tex]
[tex]Z = 2.47[/tex]
[tex]Z = 2.47[/tex] has a p-value of 0.9932
X = 286:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{286 - 295}{\frac{15}{\sqrt{17}}}[/tex]
[tex]Z = -2.47[/tex]
[tex]Z = -2.47[/tex] has a p-value of 0.0068
0.9932 - 0.0068 = 0.9864.
0.9864 = 98.64% probability that a random sample of 17 pregnancies has a mean gestation period within 9 days of the mean.
A similar problem is given at https://brainly.com/question/24663213
Can someone please help me with this I will mark Brainly to whoever does
Answer:
Try A
Step-by-step explanation:
I did it myself, and the first one I did, which was A, all had the same slope, so I think it is A.
Let f(x) be defined for any positive integer x greater than 2 as the sum of all prime numbers less than x. For example, f(4)=2+3=5 and f(8)=2+3+5+7=17. What is the value of f(86)−f(82)?
(A) 3 (B) 4 (C) 47 (D) 59 (E) 83
The answer is not B pls remember this
Answer:
E
Step-by-step explanation:
RSM proves correct
The value of a given function is required.
So, the answer is (E)83.
The given function [tex]f(x)[/tex] is the sum of all prime numbers less than [tex]x[/tex].
The required function is [tex]f(86)-f(82)[/tex]
[tex]f(86)=2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79+83[/tex]
[tex]f(83)=2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79[/tex]
[tex]f(86)-f(83)=2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79+83-(2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79)=83[/tex]
All numbers become get subtracted except for 83.
So, the answer is (E)83.
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Mike and Krista rent a jet ski while on vacation. The rental cost is represented by the function c(h) = 50 + 20h, where h is the number of hours of use
and c(h) is the total cost for h hours of use. How much does the jet ski cost if they use it for 4 hours?
O $54
$80
. $130
$200
Answer:
130$
Step-by-step explanation:
put 4 instead of the h
50+4.20
50+80
130
QUICK HELP
What is the common ratio between successive terms in the sequence?
27, 9, 3, 1, 그 , ,
1
3
0
13
03
Answer:
the common ratio is
1/3
because
9*1/3=3
3*1/3=1
1*1/3=1/3
...
The common ratio is 1/3.
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
The given sequence is
27, 9, 3, 1, 1/3, 1/9 and so on....
Since we know that
Common ratio (r) = Second term/First term
Therefore,
r = 9/27 = 3/9 ....
So, The answer will be 1/3.
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dinners frequently add a 15% tip when charging a meal to a credit card. what is the price of the meal without the tip amount charged is $18.40? how much was the tip?
Answer:
Step-by-step explanation:
Let
'x' the price of the meal
15% of x or 0.15x is the tip
x + 0.15x = 20.70
1.15x = 20.70 divide both sides by 1.15
x = 20.70/1.15
x = $18
0.15*18 = $2.70
The price of the meal without the tip is $18.
The tip was $2.70.
Determine the circumference of a circle with a radius of 4 inches.
Answer:
c=2pi times r
c= 2 times pi times 4
c=25.1327
c= 25.13
A sofa regularly sells for $710. The sale price is $553.80. Find the percent decrease of the sale price from the regular price.
Given:
A sofa regularly sells for $710.
The sale price is $553.80.
To find:
The percent decrease of the sale price from the regular price.
Solution:
We have,
[tex]Decrease\%=\dfrac{\text{Regular price - Sale price}}{\text{Regular price}}\times 100[/tex]
[tex]Decrease\%=\dfrac{710-553.80}{710}\times 100[/tex]
[tex]Decrease\%=\dfrac{156.2}{710}\times 100[/tex]
[tex]Decrease\%=0.22 \times 100[/tex]
[tex]Decrease\%=22\%[/tex]
Therefore, the percent decrease of the sale price from the regular price is 22%.
Simplify the expression using the properties of operations.
The simplified form of the expression (5.23x + 3.76) − (3.67x − 6.39) is
Answer:
Step-by-step explanation:
5.23x+3.76-3.67x+6.39
x(5.23-3.67) +(3.76+6.39)
1.56x + 10.15
Answer:
1.56x + 10.15
Step-by-step explanation:
(5.23x + 3.76) – (3.67x – 6.39)
(a + b) – (c – d) = a + b – c + d
Remove the parentheses and change the signs as needed:
5.23x + 3.76 – 3.67x + 6.39.
Group the like terms and simplify:
5.23x – 3.67x + 3.76 + 6.39
1.56x +10.15.
Please for the love of god anwser my question lay correctly I really need your help :( I will give 25 points :)! This is geometry
Answer: x=8
for every 5 there is 2
so for x=8
there are four 5's in 20
I hope this is good enough:
Answer:
x = 8
Step-by-step explanation:
I can confirm this is right I took test
sally has to pay 1/3 of her paycheck in tax. After paying tax, she spends 2/5 of the remainig money on rent. What fraction of her paycheck remains after she pays rent? Express your answer as a fraction in simplest form
9514 1404 393
Answer:
2/5
Step-by-step explanation:
After paying 1/3 in tax, 2/3 of Sally's paycheck remains.
After paying 2/5 of that, 3/5 of that 2/3 remains. The remaining fraction is ...
(3/5)(2/3) = 2/5
After the indicated payments, 2/5 of Sally's paycheck remains.
Answer:
2/5
Step-by-step explanation:
3/5 * 2/3 = 2/5
ANSWER QUICK PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
case a) y=1/3x+8
case b) y=-3x+28
Step-by-step explanation:
case a)
parallel lines has the same slope, then, the searched line has the form:
[tex]y=\frac{1}{3} x +b[/tex]
Now, in order to find b, we must use the given point (6,10). By substituying this point into the last equation, one has
[tex]10=\frac{1}{3} 6+b\\10=\frac{6}{3} +b\\10=2+b\\b=10-2\\b=8[/tex]
Then, the line equation is y=1/3x+8
case b)
the slope of a perpendicular line is the "negative reciprocal" of the slope of the original line, that is
[tex]m=-\frac{1}{\frac{1}{3} } \\m=-3[/tex]
Hence, the searched line has the form y=-3x + b. Now, in order to find the y-intercept b, we must use the given point (6,10). Therefore,
[tex]10=-3(6)+b\\10=-18+b\\b=10+18\\b=28[/tex]
Hence, the searced equation is y=-3x+28
# 5
Write an equation in slope-intercept
form to represent the line parallel to
9x + 3y = 8 passing through the point
(-1,-4).
y = -3x - 1
y = -3x - 7
y = 1/3x + 1/3
y = 1/3X -4
Answer:
y = -3x - 1
Step-by-step explanation:
it is the only line that passes through the point (-1, -4)
A dolphin is 13 feet below sea level. A seagull is 3 feet above sea level.
. Write an integer for the position of each animal relative to sea level.
anybody understand this ? please help me .
Answer:its a or b
Step-by-step explanatio
Answer:
The answer is (2)
Step-by-step explanation:
We know that to the distance between two numbers on a number line, we subtract the smaller number from the larger number. For instance, the difference between [tex]5[/tex] and [tex]3[/tex] is simply [tex]5-3[/tex], which is [tex]2[/tex]. With that being said, variables such as [tex]p[/tex] or [tex]q[/tex] differ from a question to another. Sometimes, the [tex]p[/tex] is larger, but sometimes the [tex]q[/tex] is. If we don’t know which one is which, we can subtract them in any order and take the absolute value of that result. If the result of subtraction is positive, great! The absolute value of that is still positive ([tex]5-3=2\\|5-3|=2[/tex]) If it’s not, now it is! (e.g., [tex]|3-5|=2[/tex]! Therefore, the answer is (2) [tex]|p-q|[/tex].
Select the correct answer.
Identify the end behavior and the zeros of function h.
h(x) = –13 – 9x2 + 41 +96
Based on these key features, which statement is true about the graph representing function h?
A. The graph is negative on the intervals (-00, -8) and (-4, 3).
B. The graph is positive on the intervals (-8, –4) and (3, 0).
C. The graph is positive on the intervals (-0, —8)and (-4, 3).
D. The graph is negative on the intervals (-3, 4) and (8,00).
Answer: C. The graph is positive on the intervals (-∞,-8) and (-4,3)
Step-by-step explanation: I guessed on my test and got it right. PLATO
HELP PLEASE the second one is a match question
Answer:
1)Coefficient
2)Dividend
3) Quotient
Step-by-step explanation:
0 2:5 = 1:25
05:8= 20m
A researcher wants to test the relationship between SAT scores and high school GPA. What statistic should be used
Answer: Pearson correlation statistic
Step-by-step explanation:
The Pearson Correlation statistic is used to measure linear association. It simply measures the statistical relationship that exists between two variables that are continuous. Information about both the magnitude and the direction are being provided by the Pearson Correlation statistic.
Since both the SAT scores and the high school GPA has to do with numbers, we are going to use Pearson correlation statistic. Spearman correlation are used for ranking.
at 6:00 PM it’s 24°F at midnight the temperature was 636°F lower than Apple what will the temperature at midnight
Answer:
A)12 F.
Step-by-step explanation:
The pair of polygons is similar. Find the value of x.
A. 2.5 in.
B. 5 in.
C. 35 in.
D. 40 in.
Answer: 40
60÷15=4
10×4=40
I hope this is good enough:
A submarine dives below the surface, heading downward in nine moves. If each move downward was 180
feet where is the submarine after it is finished diving?
The submarine would be blank
feet below sea level, or blank
feet.
Nathan earned $105,70 at his job when he worked for 7 hours. What was his
hourly wage, in dollars per hour?
Answer:
If it is $10,570 then the answer is 1510, but if you made a typo and meant 105,700, then the answer is 15100.
Answer:
Step-by-step explanation:
I divided 105.70 by 7 and got 15.1. So your answer is 15.10 cents I believe
Hope it helps :p
Which investment data is best modeled by an exponential function?
Answer:
Answer is C.
Step-by-step explanation:
Please like and mark brainliest, thanks :)
Exponential functions are functions that increases geometrically. The correct graph that model the investment is the Graph C
Exponential graphExponential functions are functions that increases geometrically. The standard exponential function is expressed as y = ab^x
The correct graph must represents a curve that increases steadily. From the given graph, the correct graph that model the investment is the Graph C
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-4x+6y=-7
-13x-2y=-4
Elimination or substitution
Answer:
substitution
Step-by-step explanation:
If David plays 3 tennis matches every week for 9 weeks,
many matches will he play altogether
Answer:
27
Step-by-step explanation:
3*9=27
hope this helps :3
if it did pls mark brainliest
Answer:
He will have played 27 tennis matches
Step-by-step explanation:
I know he will have played 27 tennis matches because 3 tennis matches every week for 9 weeks that's 3x9 which equals 27.
How do you do these two questions?
Answer:
(x − π)⁷ / 5040
(x − 1)³ / 16
Step-by-step explanation:
Taylor series expansion of a function is:
f(x) = ∑ₙ₌₀°° f⁽ⁿ⁾(x₀) / n! (x − x₀)ⁿ
where f⁽ⁿ⁾(x₀) is the nth derivative evaluated at x₀.
For the first problem, f(x) = sin x and x₀ = π. We want the seventh degree term, so n = 7.
The seventh degree term is therefore: f⁽⁷⁾(π) / 7! (x − π)⁷
Find the seventh derivative of sin x:
f(x) = sin x
f⁽¹⁾(x) = cos x
f⁽²⁾(x) = -sin x
f⁽³⁾(x) = -cos x
f⁽⁴⁾(x) = sin x
f⁽⁵⁾(x) = cos x
f⁽⁶⁾(x) = -sin x
f⁽⁷⁾(x) = -cos x
Evaluated at π, f⁽⁷⁾(x) = 1. So the seventh degree term is (x − π)⁷ / 5040.
For the second problem, f(x) = √x and x₀ = 1. We want the third degree term, so n = 3.
The third degree term is therefore: f⁽³⁾(1) / 3! (x − 1)³
Find the third derivative of √x:
f(x) = √x
f⁽¹⁾(x) = ½ x^-½
f⁽²⁾(x) = -¼ x^-³/₂
f⁽³⁾(x) = ⅜ x^-⁵/₂
Evaluated at 1, f⁽³⁾(x) = ⅜. So the third degree term is (x − 1)³ / 16.
The product of two positive numbers is 48. the larger number is 13 more than the smaller. Find both numbers [Only an algebraic solution will be accepted.]
Answer:
Larger number:
16
Smaller number
3
Step-by-step explanation:
Larger number: 16
Smaller number: 3
Explanation:
Suppose the larger number is
a
and the smaller number is
b
.
You solve the following system of equations:
a⋅b=48
a−13=b
Since b is a −13, you can plug that into a⋅b=48, so...a⋅(a−13)=48
a 2−13a=48
a2−13a−48=0
Factor the polynomial:
(a−16)(a+3)=0
a=16 or a=−3a is positive so a=16.
We can now solve for b by plugging in a, so...16−13=b3=b We have a=16 and b=3, meaning that the larger number is 16 and the smaller number is 3.
The value of the 8 in 89.945 is how many times rhe value of the 8 in 763.186
Answer:
1000x
Step-by-step explanation:
In addition to oxygen, several gases are in air. Carbon dioxide makes up 0.00039 of air. What is 0.00039 written as a percent?
Answer:
0.039%%%%%%%%%%%%%%