Answers
(730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15. This can be obtained by using formula for confidence interval and using statistical table for values.
Find the confidence interval for population variance:The formula for finding the confidence interval for population variance is:
[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]
where n is the size of the sample, (n - 1) is the degrees of freedom, s is the standard deviation, α is the significance level.
Here it is given that,
confidence level = 1 - α = 0.98 significance level = α = 0.02standard deviation = 39 sample size n = 15degrees of freedom (n - 1) = 15 - 1 = 14α/2 = 0.02/2 = 0.01
1 - α/2 = 1 - 0.01 = 0.99
For (n - 1) degrees of freedom,
[tex]\chi^{2}_{\frac{\alpha}{2} }[/tex] = 29.141 , and [tex]\chi^{2}_{1-\frac{\alpha}{2} }[/tex] = 4.660 (Using statistical table)
Using the formula we get,
[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]
[tex]\frac{(14)39^{2} }{29.141} < \sigma^{2} < \frac{(14)39^{2} }{4.660}[/tex]
[tex]730.72 < \sigma^{2} < 4569.53[/tex]
The confidence interval for the population variance is (730.72, 4569.53)
Hence (730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15.
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Related Questions
500 portions of strawberries have been ordered for the tournament, but because of bad weather only
5
6
of the order has been delivered.
10% of those delivered are given to the players and staff.
How many portions of strawberries can be sold?
Answers
We conclude that 375 portions can be sold.
How many portions can be sold?
We know that 500 portions have been ordered, but only 5/6 of that was delivered, so the number of delivered portions is:
p = (5/6)*500 = 416.6
Which we can round to the next whole number, 417.
Now we know that 10% of these are given to the players and staff, then the number of portions that can be sold is the 90% of 417, which is:
N = 417*(90%/100%) = 417*0.9 = 375
We conclude that 375 portions can be sold.
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Problem What is the volume of this rectangular prism?
Answers
Answer:
[tex] \frac{27}{8} cm {}^{3} [/tex]
Is the volume of this right rectangular prism.
Step-by-step explanation:
Rectangular prism volume formula is:-
[tex]v = l \times w \times h \\ v = \frac{3}{2} \times \frac{3}{2} \times \frac{3}{2}apply \: fraction \: rule \\ v = \frac{27}{8} .... \frac{a}{b} \times \frac{c}{d} = \frac{a \times b}{c \times d} [/tex]Answer:
[tex]V=\frac{27}{8}\: cm^3[/tex]
Step-by-step explanation:
The formula to find the volume of a rectangular prism is:
V = length × height × width
Let us find now.
[tex]V = length \:* height \:* width\\\\V =\frac{3}{2} *\frac{3}{2} *\frac{3}{2} \\\\V=\frac{9}{4}*\frac{3}{2} \\\\ V=\frac{27}{8}\: cm^3[/tex]
A teacher wants to split 6 decks of cards between 8 students equally. How many decks of cards will each student get?
Answers
6 decks of cards = 60 cards
---> 60/8 = 15/2 = 7.5
7.5 cards = 0.75 decks of cards
Therefore, each student will get 0.75 decks of cards.
Answer:
1
Step-by-step explanation:
Everyone gets 1 and there's 2 left over
URGENT!!!!!!
Use arrow notation to describe the translation of point P(–5, –4) to point P′(–8, –7).
Answers
The rule of the translation of point P(–5, –4) to point P′(–8, –7) is:
(x,y) -> (x - 3, y - 3).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, from point P to point P', 3 was subtracted from both the x-coordinate and the y-coordinate, hence the rule is given by:
(x,y) -> (x - 3, y - 3).
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I have to be at work at 4 am it takes 34 mins to walk to work from my house what time would i have to leave my house to be at work on time at 4 am
Answers
Answer:
3:26 to be on time!
Step-by-step explanation:
If you leave your house at 3:26 am and then walk 34 minutes it will be 4 am
once you get to work.
distribution has a mean if 18 standard deviation of 4 a value of 24 is how many standard deviations away from the mean
Answers
A value of 24 is 2.5 standard deviations away from the mean
'How to determine the number of standard deviations away from the mean?The given parameters about the distribution are:
Mean = 18
Standard deviation = 4
Value = 24
Let the number of standard deviations away from the mean be x.
The value of x is calculated using
Mean + Standard deviation * x = Value
Substitute the known values in the above equation
18 + 4 * x = 24
Subtract 18 from both sides of the equation
4 * x = 6
Divide both sides of the equation by 4
x = 1.5
Hence, a value of 24 is 2.5 standard deviations away from the mean
So, the complete parameters about the distribution are:
Mean = 18
Standard deviation = 4
Value = 24
24 is 2.5 standard deviations away from the mean
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Astrid is looking for a job at a call center. Call center A offers her $15 per hour and call-center B offers her $.25 per minute.
Which place offers a higher wage?
Answers
Answer: They are the same
Step-by-step explanation: We convert both to $ per hour. Call center A is $15 per hour. Call center B is $.25 per minute. .25 per minute means $1.00 every 4 minutes. There are 15 4 minutes in an hour so they both offer the same wage.
Add the matrices.
What number fills in [?] ?
B
A
4
2
9 -4
3 -2 8
ܚ ܝܪ ܚ
-1
A + B =
25
9 -8
-1 5
596
1 [?]
3
4
82
4
7
-4
Entor
Answers
Answer:
3
Step-by-step explanation:
A + B is calculated by adding the same positions in both matrices.
and position (2, 3) in A+B is therefore the sum of position (2, 3) in A plus the position (2, 3) in B, which is then
-4 + 7 = 3
Finding the sums
Find the sum of the first 7 terms of the following geometric series.
1/36-1/12+1/4-...
what is the sum?
Answers
The sum of the first 7 terms of the geometric series is 15.180
Sum of geometric seriesThe formula for calculating the sum of geometric series is expressed according to the formula. below;
GM = a(1-r^n)/1-r
where
r is the common ratio
n is the number of terms
a is the first term
Given the following parameters from the sequence
a = 1/36
r = -3
n = 7
Substitute
S = (1/36)(1-(-3)^7)/1+3
S = 1/36(1-2187)/4
S = 15.180
Hence the sum of the first 7 terms of the geometric series is 15.180
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Select the correct answer.
Which statement is true about function f, which is shown in the graph?
ƒ(x) = -8x5 + 4x³ + 5x
Answers
Answer:
I think its A
Step-by-step explanation:
2. Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover
Answers
The probability that of 6 randomly selected patients, 4 will recover is 0.03295
The chance of an event occurring is defined by probability.
Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Additionally, the proportion of positive outcomes cannot be negative.
The ratio of good outcomes to all possible outcomes of an event is known as the probability.
Let X represent the binomial random variable that represents the patient count. Let p represent the likelihood that the patient will survive, and q represent the probability that they will pass away. The solution to the problem is q = 75% = 0.75, p = 25% = 0.25, and n = 6.
Required probability = 6C4[tex](0.25)^{4} (0.75)^{2}[/tex]
= 0.03295
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Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, 0) B(6, 0) C(6, 7) D(2, 7)
What is the area of rectangle ABCD?
Answers
Check the picture below.
Answer: 28 [tex]units^{2}[/tex]
Step-by-step explanation:
Can someone help me with this problem from Khan Academy?
Answers
Given that the graph shows P as a function of n, we have:
a. The more hot dogs that is sold, his profit increases.
b. Jimmy sells the hot dog for $1 each.
c. Jimmy needs to sell 16 hot dogs to recover the $8 he invested.
d. He would make a profit of $7.
e. The number of hot dogs he needs to sell is: 20.
What is a Linear Function?A linear function is expressed as, y = mx + b, where y is a function of x, m is the unit rate, and b is the starting value or initial value of the function.
We are given that profit, P, is a function of the number of hot dogs sold, n.
a. The graph of the function slopes upwards, so this means that the more hot dogs that is sold, his profit increases.
b. Cost of 1 hot dog = Unit rate = change in y / change in x = 2 units/2 units
Cost of 1 hot dog = Unit rate = 1
Thus, Jimmy sells the hot dog for $1 each.
c. If you trace profit (P) on the graph when it is $8, the corresponding number of hot dogs, n, would be 16.
So, Jimmy needs to sell 16 hot dogs to recover the $8 he invested.
d. When n = 15, P, from the graph would be 7.
Thus, if Jimmy sells 15 hot dogs, he would make a profit of $7.
e. When P = 12, from the graph, the corresponding n value is 20.
Therefore for Jimmy to make $12, the number of hot dogs he needs to sell is: 20.
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a wooden cube has 6 sides. The sides are labeled A, B, C, D, E, and F. What is the probability of rolling a B? Write your answer as a fraction.
Answers
Answer:
1/6
Step-by-step explanation:
You have six choices and you want to pick only 1 of those choices.
1/6
[tex]\displaystyle\frac{1}{6}[/tex]
Step-by-step explanation:Probability explains the likelihood of an event occurring. The outcome you are finding the probability for is the successful outcome. The sample size is the total number of possible outcomes.
Simple Probability
Simple probability is when there is only one single event. In this situation, the cube is only being rolled once, so it's a simple probability question. To solve this question as a fraction, the numerator should be the number of successful outcomes and the denominator should be the sample size.
Solving for P(B)
Since there are 6 sides with 6 letters, the sample size is 6. So, 6 should be the denominator. We are finding the probability of "B", which means there is 1 successful outcome. Thus, the numerator should be 1.
This means as a fraction the probability is [tex]\frac{1}{6}[/tex].
if x is normally distributed with U = 283 and o = 21 find p(x) is greater than 315
Answers
The probability that the value of p(x) is greater than 315 is 0.063754
How to determine the probability that the value of p(x) is greater than 315?From the question, the given parameters about the distribution are
Mean value of the set of data = 283Standard deviation value of the set of data = 21The actual data value = 315The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (315 - 283)/21
Evaluate the difference of 315 and 283
z = 32/21
Evaluate the quotient of 32 and 21
z = 1.524
The probability that the value of p(x) is greater than 315 is then calculated as:
P(x > 315) = P(z > 1.524)
From the z table of probabilities, we have;
P(x > 315) = 0.063754
Hence, the probability that the value of p(x) is greater than 315 is 0.063754
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Please help me l don’t understand
Answers
a. Let [tex]d[/tex] be the number of daytime calls Eshwa makes, and [tex]e[/tex] the number of evening calls. Then the cost [tex]C[/tex] (in pence) of making [tex]d+e[/tex] calls is
[tex]C = \boxed{50d + 40e}[/tex]
b. £1 = 100p, so the cost [tex]C'[/tex] (in £) is 1/100 of the cost found in part (a),
[tex]C' = \dfrac{50d + 40e}{100} = \boxed{\dfrac d2 + \dfrac{2e}5}[/tex]
c. If Eshwa makes 30 of each type of call in a month, then the total cost (in £) is
[tex]C' = \dfrac{30}2 + \dfrac{2\cdot30}5 = \boxed{27}[/tex]
c2. If Eshwa makes 20 daytime calls and 50 evening calls, then the total cost (in £) is
[tex]C' = \dfrac{20}2 + \dfrac{2\cdot50}5 = \boxed{30}[/tex]
d. Let [tex]e=40[/tex] and [tex]C'=42[/tex]. Solve for [tex]d[/tex].
[tex]42 = \dfrac d2 + \dfrac{2\cdot40}5[/tex]
[tex]42 = \dfrac d2 + 16[/tex]
[tex]\dfrac d2 = 26[/tex]
[tex]d = \boxed{52}[/tex]
Which of the following are polynomials?
A. x^2 + x + 1/x^2 + 1
B. 2/x^3 + x + 1/2
C. 2/3x^2 + x + 1
D. x^2/3 + 0x + 1
E. x^3 + 2x + square root of 2
Answers
Answer: C, E
Step-by-step explanation:
These are polynomials by the definition of a polynomial.
Which linear system has this matrix of constants? `[[12],[11],[4]]` a, b, c or d
IMAGE ATTACHED
Answers
The following linear system has [[12], [11], [4]] matrix of constants,
x + y + z = 12
x - y = 11
x - y + z = 4
(Option D)
Verification of the Choice:
The given linear system is,
x + y + z = 12
x - y = 11
x - y + z = 4
This can be written in the form of matrix as follows,
[tex]\left[\begin{array}{ccc}1&1&1\\1&-1&0\\1&-1&1\end{array}\right][/tex] [tex]\left[\begin{array}{}x&y&z\end{array}\right][/tex] = [tex]\left[\begin{array}{}12&11&4\end{array}\right][/tex]
Hence, option D is the correct linear system as it contains the desired matrix.
About the Other Options:
The RHS matrix in option A would be,
[tex]\left[\begin{array}{}26&17&23\end{array}\right][/tex] which is not the desired matrix.
Similarly, the linear systems in the options B and C contain the matrix [tex]\left[\begin{array}{}23&17&26\end{array}\right][/tex] and the matrix [tex]\left[\begin{array}{}4&11&12\end{array}\right][/tex] on the RHS of the equality, which are not desired.
Thus, option D is correct.
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Find all values of x in the interval [0, 2π] that satisfy the equation. 7 sin(2x) = 7 cos(x)
Answers
Answer:
x = {π/6, π/2, 5π/6, 3π/2}
Step-by-step explanation:
The equation can be solved using a double-angle trig identity and factoring.
SimplifyDividing the equation by 7 and substituting for sin(2x), we have ...
7sin(2x) = 7cos(x)
sin(2x) = cos(x)
2sin(x)cos(x) = cos(x)
2sin(x)cos(x) -cos(x) = 0
cos(x)(2sin(x) -1) = 0
Zero product ruleThe product of factors is zero when one or more of the factors is zero.
cos(x) = 0 ⇒ x = {π/2, 3π/2}
2sin(x) -1 = 0 ⇒ x = arcsin(1/2) = {π/6, 5π/6}
Solutions in the given interval are ...
x = {π/6, π/2, 5π/6, 3π/2}
__
Additional comment
When the equation is of the form f(x) = 0, then the x-intercepts of f(x) are its solutions. We can rearrange this one to ...
sin(2x) -cos(x) = 0
The solutions identified above match those shown in the graph.
Find the mean for the scores 3,820, 5,500, 8,560, 4,400, 5,350
Answers
Answer:
5,526
Step-by-step explanation:
Mean of scores = Total Value of Scores / Number of Values
= [tex]\frac{3820+5500+8560+4400+5350}{5} \\[/tex]
= 5,526
Answer:5526
Step-by-step explanation: Add everything up and divide by 5 because there are 5 numbers
What is the missing factor in the equation? Assume x * 0 and y* 0.
(5x²)(7) = 3xV²
5y
10
O
O
3x
लौजे अने
5y
4x
O 2xy²
5
O 9x³y
25
Answers
Answer:
[tex]\sf b) \quad \dfrac{y^3}{4x}[/tex]
Explanation:
[tex]\sf \left(\dfrac{6x^2}{5y}\right) \left(?}\right) = \left(\dfrac{3xy^2}{10}\right)[/tex]
cross multiply variables
[tex]\sf ? = \left(\dfrac{3xy^2 (5y)}{10(6x^2)}\right)[/tex]
distribute inside parenthesis
[tex]\sf ? = \left(\dfrac{15xy^3}{60x^2}\right)[/tex]
remove parenthesis and simplify
[tex]\sf ? = \dfrac{y^3}{4x}[/tex]
Consider the given statement.
If it is not Monday, then there are students in the gym.
For each statement below, determine whether it is equivalent to the given statement, the negation of the given statement, or neither of these.
Statement Equivalent Negation Neither
It is not Monday and there are not students in the gym.
It is Monday or there are students in the gym.
If there are not students in the gym, then it is Monday.
There are not students in the gym or it is not Monday.
Answers
Answer:
NegationStatementEquivalentNeitherStep-by-step explanation:
If it is not Monday, then there are students in the gym.
Negation: It is not Monday and there are not students in the gym.
Statement: It is Monday or there are students in the gym.
Equivalent: If there are not students in the gym, then it is Monday.
Neither: There are not students in the gym or it is not Monday.
need heeeelp please
Answers
Answer:
7.61577310586
Step-by-step explanation:
Pythagoras Theorem 7 squared + 3 squared= 49+9=58
[tex]\sqrt{58}[/tex]
What is the total number of common tangents that can be drawn to the circles?
Answers
The total number of common tangents that can be drawn to the circles is 1
What are the tangent lines?The tangent lines of a circle are the lines drawn, that touch the circle at only one point
How to determine the total number of common tangents that can be drawn to the circles?The complete question is added as an attachment
From the attached figure, we have the following highlights:
The circles have different radiiThe smaller circle is completely inside the bigger circleBoth circles have one point of intersectionThe one point of intersection is the only point where both circles can have common tangents
Since there is only one point of intersection, then the number of common tangents on the circles is 1
Hence, the total number of common tangents that can be drawn to the circles is 1
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Two regular 6-sided dice are tossed. Compute the probability that the sum of the pips on the upward faces of the 2 dice is the following. 8
Answers
Answer: 5/36
Step-by-step explanation:
Need help with this question
Answers
Answer:
y=-1/2n+44
Step-by-step explanation:
The number of bean stalks, n, represents the x values
The yield, y, represents the y values
After reading the problem, we have two coordinates: (30,29) and (32, 28) Because this problem is asking for y=mn+b, we have to find the slope. How do we find the slope? We do so by using the slope formula y2-y1/x2-x1. Now let's input the coordinates into this formula.
1.) 28-29/32-30 = -1/2
Let's plug -1/2 into y=mn +b
2.) y=-1/2n+b
Now we have to find what b ( y intercept) equals. To find B, we plug a coordinate into x and y. Let's use (30,29)
3.) 29 = -1/2(30)+b
29 = -15 +b
44 = b
We have now found the linear relationship form for this problem: y=-1/2n +44
The radioactive substance uranium-240 has a half-life of 14 hours. The amount At of a sample of uranium-240 remaining (in grams) after t hours is given by the following exponential function.
a(t)=2400(1/2)^t/14
Find the initial amount in the sample and the amount remaining after 40 hours.
Round your answers to the nearest gram as necessary.
Answers
The initial amount in the sample and the amount remaining after 40 hours are 2400 grams and 331 grams respectively.
How to determine the amountFrom the information given, we have the function to be;
a(t)=2400(1/2)^t/14
Where
a(t) is the final amountt represents time'I4' is the half life of the radioactive substance, Uranium - 240To determine the initial amount, we have that t = 0
Substitute into the function, we have
[tex]A(t) = 2400[/tex] × [tex]\frac{1}{2} ^\frac{0}{14}[/tex]
[tex]A (t) = 2400[/tex] × [tex]\frac{1}{2} ^0[/tex]
[tex]A (t) = 2400[/tex]
The initial amount is 2400 grams
For the amount remaining after 40 years, t = 40 years
A(t)=2400(1/2)^t/14
Substitute into the function, we have
[tex]A(t) = 2400[/tex] × [tex]\frac{1}{2} ^\frac{40}{14}[/tex]
[tex]A(t) = 2400[/tex] × [tex](0. 5) ^2^.^8^5^7[/tex]
[tex]A(t) = 2400[/tex] × [tex]0. 1380[/tex]
A(t) = 331. 26
A(t) = 331 grams in the nearest gram
Thus, the initial amount in the sample and the amount remaining after 40 hours are 2400 grams and 331 grams respectively.
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Si un buzo se sumerge 4 metros luego sube 2 metros y finalmente desciende 5 metros más, ¿a qué profundidad se encuentra al final de su recorrido ?
Answers
Así, concluimos que la posición final del buzo será 7 metros bajo la superficie del agua.
¿a qué profundidad se encuentra al final de su recorrido?Primero, vamos a definir la superficie del agua como el 0 metros.
Sí sabemos que primero el buzo se sumerge 4 metros, entonces en este punto la posición del buzo es:
P = 0m - 4m = -4m
Luego el buzo sube 2 metros, entonces la nueva posición será:
P = -4m + 2m = -2m
Finalmente, el buzo desciende otros 5 metros, entonces la posición final del buzo será:
P = -2m - 5m = -7m
Así, concluimos que la posición final del buzo será 7 metros bajo la superficie del agua.
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express 350 as a product of prime factors
Answers
Answer:
2^1 × 5^2 × 7^1 = 350
Step-by-step explanation:
2, 5, 7 are prime
first step is to divide the number 350 with the prime factor 2
continue dividing the number 175 by the next smallest prime factor
stop until you can't divide anymore
https://www.cuemath.com/numbers/factors-of-350/
Evaluate (f + g)(x) if f(x) = 2x and g(x) = 3X - 2
when x = 3
Answers
Answer:
13
Step-by-step explanation:
→ Substitute 3 into 2x
2 × 3
→ Evaluate
f ( x ) = 6
→ Substitute x = 3 into 3x - 2
3 × 3 - 2
→ Evaluate
7
→ Find the sum of the 2 results
13
When x = 3, the value of (f + g)(x) is 13.
To evaluate (f + g)(x) when f(x) = 2x and g(x) = 3x - 2, we substitute the given functions into the expression (f + g)(x).
(f + g)(x) = f(x) + g(x)
Substituting the given functions:
(f + g)(x) = 2x + (3x - 2)
Simplifying the expression:
(f + g)(x) = 2x + 3x - 2
Combining like terms:
(f + g)(x) = 5x - 2
Now, to find the value of (f + g)(x) when x = 3, we substitute x = 3 into the expression:
(f + g)(3) = 5(3) - 2
Simplifying further:
(f + g)(3) = 15 - 2
(f + g)(3) = 13
Therefore, when x = 3, the value of (f + g)(x) is 13.
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