Answer:
623
Step-by-step explanation:
Given that margin of error (E) = 3 unit, standard deviation (σ) = 29, sample size (n) = ?
a) The confidence (C) = 99% = 0.99
α = 1 - C = 1 - 0.99 = 0.01
α/2 = 0.01 / 2 = 0.005
From the normal distribution table, The z score of α/2 (0.005) is the critical value and it corresponds to the z score 0.495 (0.5 - 0.005) which is 2.58.
[tex]critical\ value = z_{\frac{\alpha}{2} }=z_{0.005}=2.58\\[/tex]
b) The margin of error (E) is given as:
[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\\\\sqrt{n}= z_{\frac{\alpha}{2} }*\frac{\sigma}{E }\\ \\n=( z_{\frac{\alpha}{2} }*\frac{\sigma}{E })^2\\\\Substituting:\\\\n=(2.58*\frac{29}{3} )^2=622.0036\\\\\\n=623(to\ the \ next\ whole\ number)[/tex]The minimum sample size (n) is 623
Approximate the stationary matrix S for the transition matrix P by computing powers of the transition matrix P.
P = [0.31 0.69
0.18 0.82]
P^4 = ______
(Type an integer or decimal for each matrix element. Round to four decimal places as needed.)
Continue taking powers of P until S can be determined
S = ______
(Type an integer or decimal for each matrix element. Round to four decimal places as needed.)
Answer:
S = [0.2069,0.7931]
Step-by-step explanation:
Transition Matrix:
[tex]P=\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
Stationary matrix S for the transition matrix P is obtained by computing powers of the transition matrix P ( k powers ) until all the two rows of transition matrix p are equal or identical.
Transition matrix P raised to the power 2 (at k = 2)
[tex]P^{2} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
[tex]P^{2} =\left[\begin{array}{ccc}0.2203&0.7797\\0.2034&0.7966\end{array}\right][/tex]
Transition matrix P raised to the power 3 (at k = 3)
[tex]P^{3} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
[tex]P^{3} =\left[\begin{array}{ccc}0.2203&0.7797\\0.2034&0.7966\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
[tex]P^{3} =\left[\begin{array}{ccc}0.2086&0.7914\\0.2064&0.7936\end{array}\right][/tex]
Transition matrix P raised to the power 4 (at k = 4)
[tex]P^{4} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
[tex]P^{4} =\left[\begin{array}{ccc}0.2086&0.7914\\0.2064&0.7936\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
[tex]P^{4} =\left[\begin{array}{ccc}0.2071&0.7929\\0.2068&0.7932\end{array}\right][/tex]
Transition matrix P raised to the power 5 (at k = 5)
[tex]P^{5} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
[tex]P^{5} =\left[\begin{array}{ccc}0.2071&0.7929\\0.2068&0.7932\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
[tex]P^{5} =\left[\begin{array}{ccc}0.2069&0.7931\\0.2069&0.7931\end{array}\right][/tex]
P⁵ at k = 5 both the rows identical. Hence the stationary matrix S is:
S = [ 0.2069 , 0.7931 ]
Find the area under the standard normal curve between z=−0.89 and z=2.56. Round your answer to four decimal places, if necessary.
Answer:
0.8080
Step-by-step explanation:
A suitable probability calculator gives that area as 0.8080.
In general, what would every child function have in common with the parent function f (x)= x?
Step-by-step explanation:
If f(x) =x, is the father function, then all it's child function would be equally inclined to x and y-axis respectively.
If f(x) =x, is the father function, then all its child functions would be equally inclined to the x and y-axis respectively.
How is each function in a family related to the parent function?Each family of capabilities has a determining feature. A discern function is the best function that also satisfies the definition of a certain sort of function. As an instance, whilst we think about the linear capabilities which make up our own family of capabilities, the parent feature could be y = x.
What key attributes are common among parent functions?Key commonplace points of linear determine features encompass the reality that the equation is y = x. Domain and variety are actual numbers. Slope, or fee of alternate, is steady.
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What is the GIM of a strip mall with annual income of $547,500 and a value of $6,345,000?
Answer:
11.6Step-by-step explanation:
GIM means Gross Income Multiplier and it is a method used for valuating a property or an investment. It is expressed mathematically as the ratio of the property's value/sales price and its gross annual income.
GIM = Value of an investment/Gross annual income.
Given the annual income = $547,500 and Value = $6,345,000;
GIM = $6,345,000/$547,500
GIM = 11.589
GIM ≈ 11.6
Hence, the Gross Income Multiplier of the strip mall is approximately 11.6.
GIM has no units.
can some one plz help me Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 4.
One of the equations of ellipse is in a form of the lengths of its axes. If we have the length of its major axis as 2a and the length of its minor axis as 2b then, the values of a and b are,
2a = 16, a = 16/2 = 8
2b = 4, b = 4/2 = 2
Given that we have the major axis as vertical, the equation for ellipse is,
y²/a² + x²/b² = 1
Substituting,
y²/8² + x²/2² = 1
Simplifying,
y² + 16x² = 1
Answer: y² + 16x² = 1
Hope this helped and if it did please give me brainliest, it will help me a lot. :)
Have a good day!
Find the probability of each event. A basketball player has a 50% chance of making each free throw. What is the probability that the player makes at least seven out of eight free throws?
Hey there! I'm happy to help!
We want to find the probability that the player makes at least seven out of eight free throws. First, we find the probability of them making seven free throws.
[tex]\frac{1}{2}^7=\frac{1}{128}[/tex]
Then, we find the probability of them making eight, which is another possibility that fits this.
[tex]\frac{1}{2}^8=\frac{1}{256}[/tex]
Now, we add the probability of these two events happening.
[tex]\frac{1}{128}+\frac{1}{256}=\frac{3}{256}[/tex]
Therefore, the probability that the player makes at least seven of eight free throws is 3/256 or about 1.17%
Have a wonderful day! :D
What are the positive and negative square roots of 1?
Answer:
Positive is 1
Negative is-1
Step-by-step explanation:
Which statement best explains the relationship between lines PQ and RS? They are parallel because their slopes are equal. They are parallel because their slopes are negative reciprocals. They are not parallel because their slopes are not equal. They are not parallel because their slopes are negative reciprocals.
Answer:
They are not parallel because their slopes are not equal
Step-by-step explanation:
From the diagram attached, The line PQ has point P at (-5, 3) and point Q at (5, 1).
For line RS, point R is at (-4, -2) and point S is at (0, -4).
Two lines AB and CD are said to be parallel to each other if they have the same slope, i.e if the slope of AB is m1 and the slope of CD is m2, m1 = m2. When two lines are parallel, they can never intersect.
The slope (m) of of a line given two points on the line is calculated using:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For line PQ has point P at (-5, 3) and point Q at (5, 1), the slope is given as:
[tex]m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{1-3}{5-(-5)}=-\frac{1}{5}\\[/tex]
For line RS, point R is at (-4, -2) and point S is at (0, -4), the slope is given as:
[tex]m_2=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-(-2)}{0-(-2)}=-1[/tex]
Since the slope of PQ (-1/5) and the slope of line RS (-1) are not equal, therefore the lines are not parallel
Answer:
They are not parallel because their slopes are not equal.
Step-by-step explanation:
The first person to answer this was correct, please mark them brainliest.
which formulas can be used to find the surface area of a regular pyramid where p is the perimeter of the base, s is the slant height, BA is the base area, and LA is the lateral area click all that apply options: A. SA= 1/2BA + 1/2ps B. SA= BA-LA C. SA= BA+LA D. SA= BA • LA E. SA= BA + 1/2ps
Answer:
C and E
Step-by-step explanation:
He got it on ap.ex
The area of the pyramid can be found using the formula SA = BA + LA and SA= BA + 1/2ps option (C) and (E) are correct.
What is a square pyramid?In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the center of the square.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a pyramid with a square base:
The perimeter of the base is p
The slant height is s.
The base area is BA
The lateral area is LA.
We can find the area of the pyramid as follows:
SA = BA + LA
SA= BA + 1/2ps
Thus, the area of the pyramid can be found using the formula SA = BA + LA and SA= BA + 1/2ps option (C) and (E) are correct.
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The table shows the cost, C, in dollars, to rent a car from Carl's Car Rentals. Determine the following: a) What is the fixed cost? b) What is the variable cost? c) Write an equation relating your answer from part (a) and part (b) [be sure to use the variables stated in the table]. d) What kind of variation is this relationship showing? e) Calculate the cost of renting a car for a day and driving a total of 800km.
Answer:
a) Fixed cost = $50
b) Total variable cost is $15, while variable cost per unit is $0.15.
c) C = 50 + d0.15
d) Direct variation
e) The cost of renting a car for a day and driving a total of 800km is $170,
Step-by-step explanation:
a) What is the fixed cost?
Fixed cost is a cost that does not change with the level of activity. Fixed is incurred whether there is an activity, or there is no activity at all, that is, when the activity is zero.
Since cost, C, is equal to $50 when distance, d (km), is equal to zero in the table, the fixed cost is therefore equal to $50, i.e.:
Fixed cost = $50
b) What is the variable cost?
Variable cost is a cost that changes as the level of activity changes. From the table, the variable cost can be obtained by deducting the fixed cost from the total cost. This can be calculated using any of the distance, d (km), in the table.
Using the distance of 100 as an example, the total variable cost can be obtained as follows:
Variable cost = Total Cost at 100 distance - Fixed cost = $65 - $50 = $15
Note that variable cost per distance at 100 distance can be obtained as follows:
Variable cost per distance = $15 / 100 = $0.15
c) Write an equation relating your answer from part (a) and part (b)
Since,
C = Cost
d = distance (km)
Fixed cost = $50
Variable cost per distance = $0.15
Therefore, suppressing the dollar sign for simplicity purpose, an equation relating the above can be given as follows:
C = 50 + d0.15 ............................................. (1)
d) What kind of variation is this relationship showing?
This is a direct variation.
Direct variation is a variation in which an increase in one variable will lead to an increase in another variable.
For example in equation (1), a increase in d which is multiplied by $0.15 will lead to an increase in C.
e) Calculate the cost of renting a car for a day and driving a total of 800km.
This implies that d = 800.
Substituting d = 800 into equation (1), we have:
C = 50 + (800 * 0.15) = 170
Therefore, the cost of renting a car for a day and driving a total of 800km is $170.
what is 5/4 divided by 10 equal
Answer:
[tex]\boxed{\frac{1}{8} }[/tex]
Step-by-step explanation:
[tex]\frac{5}{4} / 10[/tex]
Changing "division" into multiplication and inverting the term after it:
[tex]\frac{5}{4} * \frac{1}{10}[/tex]
=> [tex]\frac{1*1}{4*2}[/tex]
=> 1/8
Answer:
1/8
Step-by-step explanation:
Well to do 5/4 ÷ 10 let's set up the following.
[tex]\frac{5}{4} / \frac{10}{1}[/tex]
Then we use the keep, change, and flip rule.
So keep 5/4 change the / to a * and flip the 10/1 ro a 1/10.
[tex]\frac{5}{4} * \frac{1}{10}[/tex]
Now we multiply them to get,
5/40
simplified
1/8
Thus,
the answer is 1/8.
Hope this helps :)
Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to approximate the sum of the series with an error of less than 0.0001.
Answer:
yeyyyaya
Step-by-step explanation:
Kelly bought Mason’s home for $255,500. Mason had prepaid the annual property taxes of $2,650. If closing costs are calculated on a 365-day year, and the transaction closes on March 5, how much will Kelly owe Mason for property taxes? Carry numbers out four decimal places, but round to two decimal places for your final answer. The proration is calculated up to the day of closing, meaning that the buyer owns the day of closing. Be sure to include the last day of the year in your calculations.
Answer:
$2192.60
Step-by-step explanation:
March 4 is day 63 of the year. So, the amount of tax that Kelly needs to refund to Mason is the tax for the remaining 365 -63 = 302 days of the year.
Kelly will owe Mason ...
(302/365)($2650) = $2192.6027 ≈ $2192.60
which of the following is the correct graph of the linear equation below? y+3=-2/3(x-4)
Answer:
see details.
Step-by-step explanation:
Graphs from question not yet uploaded, so read attached graph to make a match.
PLEASE HELP!!! Select the three statements that give benefits of having a savings account. A. When I withdraw money from my savings account too many times, I can be charged a fee. B. When I put money in a savings account, the bank will pay me interest. C. If there were an emergency, I would have the money to cover expenses. D.When I use a savings account, my money is insured by the FDIC up to $250,000.
Answer:
answer is B
Step-by-step explanation:
Solve: 5x=110. (Round to three decimal places.)
Hey there! Welcome to Brainly! I'm happy to help!
In equations, letters like x or y are called variables. They represent a number that we do not know yet, or they can almost be seen as a question mark in an equation. For example, 1+?=2. We know that this ? represents the number 1, and the same would go if you put a variable in there. If you have 1+x=2, you can figure out that x=1!
Our equation is 5x=110. When you see a number next to a variable, that number is called the coefficient. It is a number that multiplies a variable. So, our coefficient is 5. This means that five is multiplied by x to equal 110.
5·x=110
What if we don't know off the top of our heads what we multiply 5 by to get to 110? It was easy with 1+1=2, but this is trickier. Here's how to figure it out.
We want to get the x all by itself on one side of the equation. Then, we will see what x equals.
To do this, we use inverse operations. I will show you below with our 1+x=2 example.
1+x=2
We have a positive one plus an x equals two. We could visualize this like this.
+1+x=2
What we want to do is move the 1 to the other side of the equation so that x is by itself. So, what's the opposite of adding? Subtracting!
However, we don't just subtract the 1 from the left side, but we do it from the right side! You have to do the inverse operation on both sides to find the answer.
So, let's subtract 1 from both sides.
+1+x-1=2-1
x=1
We see that x equals 1, and if we plug this into the equation 1+x=2, we see that it is correct.
Now, with our problem, we need to divide, because that is the opposite of multiplication. We need to divide both sides by 5 to isolate the x. Let's do it!
5x÷5=110÷5
x=22
We see that 5×22 is equal to 110, so this is correct! Now you can solve for variables in equations!
Have a wonderful day!
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor completely and then place the factors in the proper location on the grid. 4y2 + 25y + 6
Answer:
(4y +1)(y +6)
Step-by-step explanation:
We can rewrite the middle term and factor by grouping.
4y^2 + 25y + 6 = (4y^2 +24y) +(y +6)
= 4y(y +6) +1(y +6)
= (4y +1)(y +6)
The grade point average collected from a random sample of 150 students. Assume that the population standard deviation is 0.78. Find the margin of error if cequals0.98.
Answer:
15%
Step-by-step explanation:
To calculate the margin of error, we can adopt this formula
Margin of error = critical value* (standard deviation/sqrt of sample size)
Where critical value is 2.33, sd is 0.78 and sample size is150.
Thus, we have:
Margin of error = 2.33*(0.78/√150)
Margin of error = 2.33*(0.78/12.2474)
Margin of error =2.33*0.06369
Margin of error = 0.1484 which is a 15% margin of error
find dy/dx if x=at⁴, y = at³
Answer:
The answer for dy/dx is 3/4t .
Step-by-step explanation:
First, you have to differentiate x and y expressions in term of t :
[tex]x = a {t}^{4} [/tex]
[tex] \frac{dx}{dt} = 4a {t}^{3} [/tex]
[tex]y = a {t}^{3} [/tex]
[tex] \frac{dy}{dt} = 3a {t}^{2} [/tex]
Next, we can assume that dy/dt ÷ dx/dt = dy/dx. So we have to substitute the expressions :
[tex] \frac{dy}{dt} \div \frac{dx}{dt} = \frac{dy}{dt} \times \frac{dt}{dx} = \frac{dy}{dx} [/tex]
[tex] \frac{dy}{dx} = 3a {t}^{2} \div 4a {t}^{3} [/tex]
[tex] \frac{dy}{dx} = 3a {t}^{2} \times \frac{1}{4a {t}^{3} } [/tex]
[tex] \frac{dy}{dx} = \frac{3}{4t} [/tex]
I need help with this quickly, it would be very much appreciated.
Answer:
complementary because 2 angles that add up to 90º is a complementary angle and x=9 :)
Step-by-step explanation:
90=46+5x-1
45=5x
x=9
Answer:
x = 9 Complementary
Step-by-step explanation:
The angles are compplementary cause the angle add up to 90°
Well to find x we need to make the following equation,
46 + (5x - 1) = 90
We need to simplify and combine like terms,
46 - 1 = 45
45 + 5x = 90
-45 to both sides
5x = 45
Divide 5 by both sides
x = 9
Thus,
x is 9.
Hope this helps :)
A swimming pool is circular with a 30-ft diameter. The depth is constant along east-west lines and increases linearly from 2 ft at the south end to 7 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.) ft3
Answer:
Volume of water in the pool is 3,182 ft^3
Step-by-step explanation:
In this question, what we want to calculate is the volume of water in the pool.
We proceed as follows;
diameter of pool = 30ft
depth: 2 to 7ft linearly
average depth = (2 + 7)/2 = 9/2 = 4.5 ft
Volume = area * average depth
V = pi * radius^2 * 4.5
where radius = diameter/2 = 30/2 = 15 ft
V = pi * 15^2 * 4.5
V = 22/7 * 225 * 4.5
V = 3,182.14 ft^3
which is 3,182 ft^3 to nearest whole number
The volume of water in the pool is; Volume = 3181 ft³
We are given;
Diameter of swimming Pool; d = 30 ft
Thus; radius; r = d/2 = 30/2 = 15 ft
We are told that the depth is constant along east-west lines and increases linearly from 2 ft at the south end to 7 ft at the north end.
Thus, average depth is;
h_avg = (2 + 7)/2
h_avg = 4.5 ft
Formula for area is; A = πr²
Thus;
A = π × 15²
A = 225π
Formula for volume here is;
Volume = Area × depth
Volume = 225π × 4.5
Volume = 3180.86 ft³
Approximating to a whole number gives;
Volume = 3181 ft³
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What is the anwer? plz help. 2(4x+2) = 4x - 12(x-1)
Answer:
x = 1/2
Step-by-step explanation:
2(4x+2) = 4x - 12(x-1)
Distribute
8x +4 = 4x - 12x +12
Combine like terms
8x + 4 = -8x +12
Add 8x to each side
8x+4+8x = -8x+12 +8x
16x+4 = 12
Subtract 4 from each side
16x +4-4 = 12-4
16x = 8
Divide by 16
16x/16 =8/16
x = 1/2
Answer:
x = 1/2
Step-by-step explanation:
2(4x+2) = 4x - 12(x-1)
Expand brackets.
8x + 4 = 4x - 12x + 12
Subtract 4 on both sides.
8x = 4x - 12x + 12 - 4
Subtract 4x and add 12x on both sides.
8x - 4x + 12x = 12 - 4
Combine like terms.
16x = 8
Divide both sides by 16.
x = 8/16 = 1/2
Find the value of y........
Answer:
hope this is right y=74
Step-by-step explanation:
have not done this since two years ago so...
but anyway 148-180 = 32
32 is that angle
if this were a right triangle my answer would be different but 148/2 still completes this triangle and somewhat makes sense.
The correct answer is 90.
Thank you for the help!!
Answer:
B. 5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
You know that the empty barrel is 1/4 of the full barrel. Find 1/4 of 20 to get 0.25 x 20 = 5
Two points on line p have
coordinates (2, 1) and (5, 3).
The slope of the line is?
A. 2
B. 3/2
C. 1
D. 2/3
E. 4
Answer:
D. ⅔
Step-by-step explanation:
I hope it helps :)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\ m = \frac{3 - 1}{5 - 2} = \frac{2}{3} \\ m = \frac{2}{3} [/tex]
. (08.03 LC) Determine the factors of x2 − 12x − 20. (5 points) (x − 2)(x + 10) (x − 10)(x + 2) (x − 5)(x + 4) Prime
Answer:
prime
Step-by-step explanation:
We're looking for 2 numbers with a sum of -12 and product of -20 but unfortunately there aren't any numbers that do so, therefore the answer is prime.
Answer:
Prime
Step-by-step explanation:
which linear inequality is represented by the graph
Answer:
y > 2x + 1
Step-by-step explanation:
(1 is the y intercept) 2/1 is the gradient so 2 up and 1 across
4x + 12 = 20y Solve for x.
Answer:
x=5y-3
Step-by-step explanation:
[tex]4x+12=20y\\4x=20y-12\\x=\frac{20y-12}{4} \\x=\frac{20y}{4}- \frac{12}{4} \\x=5y-3[/tex]
What is the answer? What is A?
Answer:
35 degree angle a cute angle
Answer:
Step-by-step explanation:
A and B are supplementary angles since the lines are parallel
A + B = 180
6x-18 + 14x+38 = 180
Combine like terms
20x +20 = 180
Subtract 20 from each side
20x+20 -20 =180-20
20x = 160
Divide by 20
20x/20 =160/20
x = 8
Calculate the amount of leather needed to manufacture a basketball if it has a radius of 11.14 cm. I need ASAP please and thank uuu
Answer:
Step-by-step explanation:
A basketball is basically a sphere, so it suffices to calculate the surface are of the ball to determine the amount of required material. Given a sphere of radius r we have that the surface area is [tex]4\pi r^2[/tex]
In this case, r = 11.14 cm. So the area is aproximately 1159.48 squared cm. (1159.48 = [tex]4\pi (11.14)^2[/tex])