For all values of x, y, and z, the expression 56x + 40y - 48z = 8(7x + 5y - 6z) holds true.
Explain expression using an example.As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.
Indeed, for all values of x, y, and z, the expression 56x + 40y - 48z = 8(7x + 5y - 6z) holds true.
We can simplify both sides of the equation to understand why:
56x + 40y - 48z = 8(7x + 5y - 6z)
56x + 40y - 48z = 56x + 40y - 48z
As we can see, the equation is true for all values of x, y, and z because both sides are identical.
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The Khan Shatyr Entertainment Center in Kazakhstan is the largest tent in the world. The spire on top is 60 m in length. The distance from the center of the tent to the outer edge is 97.5 m. The angle between the ground and the side of the tent is 42.7°.
Find the total height of the tent (h), including the spire.
Find the length of the side of the tent (x)
i. The total height of the tent including the spire is 150 m.
ii. The length of the side of the tent x is 132.7 m.
What is a trigonometric function?Trigonometric functions are required functions in determining either the unknown angle of length of the sides of a triangle.
Considering the given question, we have;
a. To determine the total height of the tent, let its height from the ground to the top of the tent be represented by x. Then:
Tan θ = opposite/ adjacent
Tan 42.7 = h/ 97.5
h = 0.9228*97.5
= 89.97
h = 90 m
The total height of the tent including the spire = 90 + 60
= 150 m
b. To determine the length of the side of the tent x, we have:
Cos θ = adjacent/ hypotenuse
Cos 42.7 = 97.5/ x
x = 97.5/ 0.7349
= 132.67
The length of the side of the tent x is 132.7 m.
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please find the midpoint of the following line and arc using straightedge-compass-construction method
The midpoint of a line or arc can be found using straight edge-compass-construction method by drawing two perpendicular bisectors. The intersection of these bisectors is the midpoint.
To find the midpoint of a line segment, first draw a straight line passing through both endpoints of the segment using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the line segment. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the line segment. The intersection of these bisectors is the midpoint of the line segment.
To find the midpoint of an arc, first draw a chord that intersects the arc at two points using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the chord. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the chord. The intersection of these bisectors is the center of the circle that the arc belongs to. Draw a line from the center of the circle to the midpoint of the chord. This line will intersect the arc at its midpoint.
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--The question is incomplete, answering to the question below--
"find the midpoint of a line and arc using straight edge-compass-construction method"
PLEASE HELP !!!! HELP!!label each equation is proportionality or non proportional Help
y=9/x
y=x-12
h=3d
f=1/3e
Answer:
y=9/x => proportional
y = x - 12 ==> non-proportional
h = 3d ==> proportional
f = 1/3 e = proportional
Step-by-step explanation:
A proportional equation is of the general form
y = kx (directly proportional) or
y = k/x (inversely proportional)
k is known as the constant of proportionality
y = 9/x ==> k = 9 proportional
y = x - 12 cannot be expressed as y = kx or y = k/x
h = 3d ==> k = 3 proportional
f = 1/3 e ==> k = 1/3 proportional
fine the exact value of sin(45-30)
ne al Compute the derivative of the given function. TE f(x) = - 5x^pi+6.1x^5.1+pi^5.1
The derivative of f(x) is
[tex]f'(x) = -5pi x^(pi-1) + 6.1 * 5.1x^(5.1-1) + 5.1pi^(5.1-1)[/tex].
What is derivative?The derivative of a function is a measure of how that function changes as its input changes. Derivatives are also used in calculus to find the area under a curve, or to solve differential equations.
In this case, the function f(x) is a polynomial, which means it is a combination of terms of the form [tex]ax^b[/tex], where a and b are constants. The derivative of f(x) can be calculated by taking the derivative of each term in the function and then combining them together.
The derivative of a term [tex]ax^b[/tex] is [tex]abx^(b-1)[/tex]. For the first term of f(x),[tex]-5x^pi[/tex], the derivative is [tex]-5pi x^(pi-1)[/tex]. For the second term, [tex]6.1x^5.1[/tex] the derivative is[tex]6.1 * 5.1x^(5.1-1)[/tex]. For the third term, [tex]pi^5.1[/tex], the derivative is [tex]5.1pi^(5.1-1)[/tex].
Combining these terms together, the derivative of f(x) is
[tex]f'(x) = -5pi x^(pi-1) + 6.1 * 5.1x^(5.1-1) + 5.1pi^(5.1-1)[/tex].
This answer is the derivative of the given function. This is how the function changes as its input changes.
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The derivative of f(x)= [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] is [tex]-5\pi x^{\pi -1}[/tex]+ [tex]6.1*5.1x^{5.1-1}[/tex] +5.1[tex]\pi^{5.1-1}[/tex] which can be calculated with the power rule.
What is derivative?The derivative of a function is a measure of how that function changes as its input changes. Derivatives are also used in calculus to find the area under a curve, or to solve differential equations.
The derivative of the given function f(x) = [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] can be calculated with the power rule, which states that the derivative of xⁿ is nx⁽ⁿ⁻¹⁾
To calculate the derivative of the given function, we begin by applying the power rule to each term.
The first term is [tex]-5^{\pi }[/tex] which has a derivative of [tex]-5\pi x^{\pi -1}[/tex].
The second term is [tex]6.1x^{5.1}[/tex] which has a derivative of [tex]6.1*5.1x^{5.1-1}[/tex].
The third term is [tex]\pi^{5.1}[/tex], which has a derivative of 5.1[tex]\pi^{5.1-1}[/tex].
Therefore, the derivative of the given function
f(x)= [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] is [tex]-5\pi x^{\pi -1}[/tex]+ [tex]6.1*5.1x^{5.1-1}[/tex] +5.1[tex]\pi^{5.1-1}[/tex].
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Question:
Compute the derivative of the given function.
f(x) = - [tex]5x^{\pi }[/tex]+[tex]6.1x^{5.1}[/tex]+[tex]\pi^{5.1}[/tex]
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 9 feet. Container B has a diameter of 8 feet and a height of 20 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.
After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?
Step-by-step explanation:
the volume of container B is Travers from A to B.
so, the volume of the empty space in A is exactly the volume of container B.
the volume of a cylinder is
base area × height = pi×r² × height.
the reside is as always half of the diameter.
r = 8/2 = 4 ft
the volume of the empty space in A = the volume of container B =
= pi×4² × 20 = pi×16 × 20 = 320pi = 1,005.309649... ≈
≈ 1,005.3 ft³
C Select the correct answer. Which equation is equivalent to the given eq -4(x - 5) + 8x = 9x - 3
Answer:
-4(x - 5) + 8x = 9x - 3
Simplifying the left side:
-4x + 20 + 8x = 9x - 3
4x + 20 = 9x - 3
Subtracting 4x from both sides:
20 = 5x - 3
Adding 3 to both sides:
23 = 5x
Dividing both sides by 5:
x = 23/5
Therefore, the equation equivalent to the given equation is:
5x - 23 = 0
There are N distinct types of coupons, and each time one is obtained it will, independently of past choices, be of type i with probability P_i, i, .., N. Hence, P_1 + P_2 +... + P_N = 1. Let T denote the number of coupons one needs to select to obtain at least one of each type. Compute P(T > n).
If T denote the number of coupons one needs to select to obtain at least one of each type., P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}
The problem of finding the probability P(T > n), where T is the number of coupons needed to obtain at least one of each type, can be solved using the principle of inclusion-exclusion.
Let S be the event that the i-th type of coupon has not yet been obtained after selecting n coupons. Then, using the complement rule, we have:
P(T > n) = P(S₁ ∩ S₂ ∩ ... ∩ Sₙ)
By the principle of inclusion-exclusion, we can write:
P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}
where the outer sum is taken over all even values of k from 0 to N, and the inner sum is taken over all sets of k distinct indices.
This formula can be computed efficiently using dynamic programming, by precomputing all values of Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ} for all x from 1 to N, and then using them to compute the final probability using the inclusion-exclusion formula.
In practice, this formula can be used to compute the expected number of trials needed to obtain all N types of coupons, which is simply the sum of the probabilities P(T > n) over all n.
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can you find the slope of the given graph?
slope of graph=?
The slope of the graph f(x) = 3x² + 7 at (-2, 19) is -12
What is the slope of a graph?The slope of a graph is the derivative of the graph at that point.
Since we have tha graph f(x) = 3x² + 7 and we want to find its slope at the point (-2, 19).
To find the slope of the graph, we differentiate with respect to x, since the derivative is the value of the slope at the point.
So, f(x) = 3x² + 7
Differentiating with respect to x,we have
df(x)/dx = d(3x² + 7)/dx
= d3x²/dx + d7/dx
= 6x + 0
= 6x
dy/dx = f'(x) = 6x
At (-2, 19), we have x = -2.
So, the slope f'(x) = 6x
f'(-2) = 6(-2)
= -12
So, the slope is -12.
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The definition of differentiable also defines an error term E(x,y). Find E(x,y) for the function f(x,y)=8x^2 − 8y at the point (−1,−7).E(x,y)=
The value of error term E(x,y) = 8x^2 - 8x - 56.
The definition of differentiability states that a function f(x,y) is differentiable at a point (a,b) if there exists a linear function L(x,y) such that:
f(x,y) - f(a,b) = L(x,y) + E(x,y)
where E(x,y) is an error term that approaches 0 as (x,y) approaches (a,b).
In the case of the function f(x,y) = 8x^2 - 8y, we want to find E(x,y) at the point (-1,-7).
First, we need to calculate f(-1,-7):
f(-1,-7) = 8(-1)^2 - 8(-7) = 56
Next, we need to find the linear function L(x,y) that approximates f(x,y) near (-1,-7). To do this, we can use the gradient of f(x,y) at (-1,-7):
∇f(-1,-7) = (16,-8)
The linear function L(x,y) is given by:
L(x,y) = f(-1,-7) + ∇f(-1,-7) · (x+1, y+7)
where · denotes the dot product.
Substituting the values, we get:
L(x,y) = 56 + (16,-8) · (x+1, y+7)
= 56 + 16(x+1) - 8(y+7)
= 8x - 8y
Finally, we can calculate the error term E(x,y) as:
E(x,y) = f(x,y) - L(x,y) - f(-1,-7)
= 8x^2 - 8y - (8x - 8y) - 56
= 8x^2 - 8x - 56
Therefore, the error term E(x,y) for the function f(x,y) = 8x^2 - 8y at the point (-1,-7) is E(x,y) = 8x^2 - 8x - 56.
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An initial deposit of $800 is put into an account that earns 5% interest, compounded annually. Each year, an additional deposit of $800 is added to the account.
Assuming no withdrawals or other deposits are made and that the interest rate is fixed, the balance of the account (rounded to the nearest dollar) after the seventh deposit is __________.
The balance of the account after the seventh deposit can be calculated using the formula below:
A = P (1 + r/n)ⁿ
where:
A = the balance of the account
P = The initial deposit of $800
r = the interest rate of 5%
n = the number of times the interest is compounded annually
n = 1
Therefore, the balance of the account after the seventh deposit is:
A = 800 (1 + 0.05/1)⁷
A = 800 (1.05)⁷
A = 800 (1.4176875)
A = 1128.54
Rounded to the nearest dollar, the balance of the account after the seventh deposit is $1128.
Alexander and Rhiannon left school at the same time. Alexander travelled 14 km home at an average speed of 20 km/h. Rhiannon travelled 10 km home at an average speed of 24 km/h. a) Who arrived home earlier? b) How much earlier did this person arrive at home? Give your answer to the nearest minute.
Rhiannon arrived home approximately 17 minutes earlier than Alexander.
What is the average?This is the arithmetic mean and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
According to the given information:To solve this problem, we can use the formula:
time = distance / speed
a) The time it took Alexander to get home is:
time_Alexander = 14 km / 20 km/h = 0.7 hours
The time it took Rhiannon to get home is:
time_Rhiannon = 10 km / 24 km/h = 0.41667 hours
Since Rhiannon's time is smaller than Alexander's, Rhiannon arrived home earlier.
b) The time difference between their arrivals is:
time_difference = time_Alexander - time_Rhiannon = 0.7 hours - 0.41667 hours = 0.28333 hours
To convert this to minutes, we can multiply by 60:
time_difference_in_minutes = 0.28333 hours x 60 minutes/hour ≈ 17 minutes
Therefore, Rhiannon arrived home approximately 17 minutes earlier than Alexander.
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Find the sum of 67 kg 450g and 16 kg 278 g?
Dividing sin^2Ø+cos^2Ø=1 by ____ yields 1+cot^2Ø=csc^2Ø
a.cot^2Ø
b.tan^2Ø
c.cos^2Ø
d.csc^2Ø
e.sec^2Ø
f.sin^2Ø
To obtain the required equation we divide the equation by sin²Ø.
What are trigonometric functions?The first six functions are trigonometric, with the domain value being the angle of a right triangle and the range being a number. The angle, expressed in degrees or radians, serves as the domain and the range of the trigonometric function (sometimes known as the "trig function") of f(x) = sin. Like with all other functions, we have the domain and range. In calculus, geometry, and algebra, trigonometric functions are often utilised.
The given equation is:
sin²Ø+cos²Ø=1
To obtain the required equation we divide the equation with sin²Ø:
sin²Ø/sin²Ø +cos²Ø/ sin²Ø = 1/sin²Ø
1 + cot²Ø = csc²Ø
Hence, to obtain the required equation we divide the equation by sin²Ø.
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Find the center and radius of the circle whose equation is x^2+y^2+4y=32
Answer:
center: (0, -2)
radius: 6
Step-by-step explanation:
You have to "complete the square" this allows you to fold up the expressions and put the equation in a standard kinda of format where you can pick the center and radius right out of the equation.
see image.
BRAINEST IF CORRECT! 25 POINTS.
What transformation of Figure 1 results in Figure 2?
Select from the drop-down menu to correctly complete the statement.
A ______ of Figure 1 results in Figure 2.
Answer:
its reflection
Step-by-step explanation:
a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.
Answer:
It is Reflection. Check if it is in the list.
A contestant on a game show has a 1 in 6 chance of winning for each try at a certain game. Which probability models can be used to simulate the contestant’s chances of winning?
Select ALL of the models that can be used to simulate this event.
A) a fair six-sided number cube
B) a fair coin
C) a spinner with 7 equal sections
D) a spinner with 6 equal sections
E) a bag of 12 black chips and 60 red chips
Answer:
I'm pretty confident that the answer is E
Martin has a spinner that is divided into four sections labeled A, B, C, and D. He spins the spinner twice. PLEASE ANSWER RIGHT HELP EASY THANK UU
Drag the letter pairs into the boxes to correctly complete the table and show the sample space of Martin's experiment..
The diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.
Explain about the sample space of an event?A common example of a random experiment is rolling a regular six-sided die. For this action, all possible outcomes/sample space can be specified, but the actual result on any given experimental trial cannot be determined with certainty.
When this happens, we want to give each event—like rolling a two—a number that represents the likelihood of the occurrence and describes how probable it is that it will occur. Similar to this, we would like to give any event or group of outcomes—say rolling an even number—a probability that reflects how possible it is that the occurrence will take place if the experiment is carried out.Martin features a spinner with four compartments marked A, B, C, and D.
To get the correct result of the filling, first take the value of the horizontal bar and write the value from the corresponding vertical bar where both column are meeting.
Thus, the diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.
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(b) Write 5 as a percentage.
Answer:
5 as a percentage of 100 is 5/100 which is 5%
Find the total labour charges for a job that takes; 2 1/2hours Time (h) 1/2 1 2 3 4 Charges 1,200 1400 1 800 2,200 2,600
Answer:
The total labor charges for the job are P3,500.
Step-by-step explanation:
To find the total labor charges for a job that takes 2 1/2 hours, we need to look at the labor charges for each hour and a half-hour fraction and add them up.
For the first hour, the charges are P1,200. For the second hour, the charges are P1,400. For the third hour (the half-hour fraction), the charges are P1,800 / 2 = P900.
So, the total labor charges for 2 1/2 hours of work are
P1,200 + P1,400 + P900 = P3,500
Therefore, the total labor charges for the job are P3,500.
10 POINTS!! ASAP please help me find the area and also the outer perimeter!!!
Answer:
area of semi circle =pi r^2/2
3.14*6*6/2=56.2
area of rectangle=lb
=20*12=240
240+56.2=296.2
rounding it it will become 300 ft sqr
perimeter of rectangle without including 4th side=20+12+20=52
perimeter of semicircle=pi r+d (d is not needed here)
3.14*6=18.84
so total perimeter=52+18.84=70.84ft
Step-by-step explanation:
6TH GRADE MATH PLS HELP TYSM
Answer:
m = 1
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-1,0) (0,1)
We see the y increase by 1 and the x increase by 1, so the slope is
m = 1
The lunch special at Maria's Restaurant is a sandwich and a drink. There are 2 sandwiches and 5 drinks to choose from. How many lunch specials are possible?
Answer:
the question is incomplete, so I looked for similar questions:
There are 3 sandwiches, 4 drinks, and 2 desserts to choose from.
the answer = 3 x 4 x 2 = 24 possible combinations
Explanation:
for every sandwich that we choose, we have 4 options of drinks and 2 options of desserts = 1 x 4 x 2 = 8 different options per type of sandwich
since there are 3 types of sandwiches, the total options for lunch specials = 8 x 3 = 24
If the numbers are different, all we need to do is multiply them. E.g. if instead of 3 sandwiches there were 5 and 3 desserts instead of 2, the total combinations = 5 x 4 x 3 = 60.
For this question's answer, there are 2 x 5 = 10 lunch specials are possible.
The number of lunch specials possible are 10.
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]
If the order matters, then each of those choice of k distinct items would be permuted k! times.
So, total number of choices in that case would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items (all distinct).
We are given that;
Number of sandwiches=2
Number of drinks=5
Now,
To find the total number of lunch specials, we need to multiply the number of choices for sandwiches by the number of choices for drinks.
Number of sandwich choices = 2
Number of drink choices = 5
Total number of lunch specials = 2 x 5 = 10
Therefore, by combinations and permutations there are 10 possible lunch specials.
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can you find c and b?
c=?
b=?
The value of the constant c that makes the following function are c = 0.
What is constant ?Constant is a term used to describe a value that remains unchanged or fixed throughout a program or process. It can be a numeric value, a character value, a string, or a Boolean (true/false) value. Common examples of constants include physical constants, mathematical constants, and programming-language keywords.A constant is a value that does not change, regardless of the conditions or context in which it is used. Common examples of constants include mathematical values such as pi (3.14159), physical constants such as the speed of light (299,792,458 m/s), and other constants such as the universal gravitational constant (6.67408 × 10−11 m3 kg−1 s−2).
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Therefore, c must equal 0 in order for the two sides of the function to be equal. and The one with the greater absolute value is b = 10.
What is function?A function is a block of code that performs a specific task. It is a subprogram or a set of instructions that can be used multiple times in a program.
27. For the function to be continuous at x = 7, the limit of the function as x approaches 7 from the left must equal the limit of the function as x approaches 7 from the right.
This means that the value of y as x approaches 7 must be the same on both the left and right sides of the point.
Since the left side of the function is y = c*y + 3, the right side of the function must also be equal to y = c*y + 3.
Therefore, c must equal 0 in order for the two sides of the function to be equal.
28. In order for the function to be continuous at x = 5, the value of y at x = 5 must be the same on both the left and right sides of the point.
Since the left side of the function is y = b - 2x, the right side of the function must also be equal to y = b - 2x.
Therefore, b must equal 10 in order for the two sides of the function to be equal.
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Complete Question:
Alberto believes that because all squares can be called
rectangles, then all rectangles must be called squares.
Explain why his reasoning is flawed. Use mathematical
terminology to help support your reasoning.
Alberto's statement is flawed because all squares can be called rectangles, but not vice versa
Reason why Alberto's statement is flawedAlberto's reasoning is flawed because all squares can be called rectangles, but not all rectangles are squares.
While it is true that squares meet the definition of rectangles, not all rectangles meet the definition of squares.
A square is a special type of rectangle with all sides equal in length.
Therefore, Alberto's argument violates the logical concept of implication, where the truth of one proposition (squares can be called rectangles) does not necessarily imply the truth of the converse (all rectangles must be called squares).
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please assist with this question...
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
(a)
the experimental probability is just using the actual experience to predict any future results.
the total number of cases was 20, and the number of desired cases (yellow) was 12.
so, the experimental probability of landing on yellow is
12/20 = 3/5 = 0.600
(b)
the theoretical probability of a totally fair spinner landing on yellow is 2 out of 5 possibilities, so
2/5 = 0.4000
(c)
the correct statement is the first one.
with a more or less balanced (fair) spinner the experimental numbers should get closer and closer to the theoretical numbers, the more spins we make.
In a survey of 124 pet owners, 44 said they own a dog, and 58 said they own a cat. 14 said they own both a dog and a cat. How many owned neither a cat nor a dog?
Step-by-step explanation:
See Venn diagram below
A special bag of Starburst candies contains 20 strawberry, 20 cherry, and 10 orange. We will select 35 pieces of candy at random from the bag. Let X = the number of strawberry candies that will be selected. a. The random variable X has a hypergeometric distribution with parameters M= , and N= n= b. What values for X are possible? c. Find PCX > 18) d. Find PX = 3) e. Determine E[X] or the expected number of strawberry candies to be selected. f. Determine Var[X]. The Binomial Distribution input parameters output The mean is The number of trials n is: The success probability p is: Binomial Probability Histogram dev. is: 1 Enter number of trials Must be a positive integer. Finding Probabilities: 0.9 0.8 Input value x fx(x) or P(X = x) Fx(x) or P(X 3x) 0.7 0.6 Input value x fx(x) or P(X = x) Fx(x) or P(X sx) 0.5 0.4 Input value x fx(x) or PCX = x) Fx(x) or P(X sx) 0.3 0.2 0.1 Input value x fx(x) or PCX = x) Fx(x) or P(X sx) 0 0 0 0 0 0 0 0 0 0 0
It involves selecting 35 candies from a bag containing 20 strawberry, 20 cherry, and 10 orange Starburst candies. X is the number of strawberry candies selected. X has a hypergeometric distribution, with possible values from 0 to 20. P(X > 18) is 0.0125, and probability mass function P(X = 3) is 0.0783. The expected value of X is 14, and the variance of X is approximately 5.67.
X has a hypergeometric distribution with parameters M=40 (20+20), N=50 (20+20+10), and n=35.
X can take on values from 0 to 20, since there are only 20 strawberry candies in the bag.
Using the cumulative distribution function for the hypergeometric distribution, we have P(X > 18) = 0.0125.
Using the probability mass function for the hypergeometric distribution, we have P(X = 3) = 0.0783.
The expected value of X is E[X] = np = 35(20/50) = 14.
The variance of X is Var[X] = np(1-p)(N-n)/(N-1) = (35)(20/50)(30/49)(40/49) ≈ 5.67.
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Suppose that, for budget planning purposes, the city in Exercise 24 needs a better estimate of the mean daily income from parking fees.
a) Someone suggests that the city use its data to create a confidence interval instead of the interval first created. How would this interval be better for the city? (You need not actually create the new interval.)
b) How would the interval be worse for the planners?
c) How could they achieve an interval estimate that would better serve their planning needs?
d) How many days' worth of data should they collect to have confidence of estimating the true mean to within
a) As per the given budget, the amount of interval that would be better for the city is 95% confidence interval.
b) The interval that be worse for the planners is depends on sample size
c) They achieve an interval estimate that would better serve their planning needs is depends on margin of error
d) The number of days worth of data should they collect to have confidence of estimating the true mean to 30 days
To obtain a better estimate, the city can create a confidence interval, which is a range of values that is likely to contain the true population mean with a certain degree of confidence.
However, there are also some disadvantages to using a confidence interval. The interval estimate may be wider than a point estimate, which means that the budget planners may have to allocate a larger budget to account for the uncertainty in the estimate.
To achieve a better interval estimate, the city could increase the sample size or reduce the variability of the data. Increasing the sample size reduces the margin of error and increases the precision of the estimate.
Finally, to determine how many days' worth of data the city should collect to estimate the true mean with a certain degree of confidence, the city would need to consider the desired level of precision, the variability of the data, and the desired level of confidence.
Typically, a larger sample size will provide a more accurate estimate, but this also depends on the variability of the data. In general, a sample size of at least 30 is recommended for a reasonably accurate estimate.
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A baseball team plays in a stadium that holds 60000 spectators. With the ticket price at $9 the average attendance has been 23000. When the price dropped to $7, the average attendance rose to 30000. Assume that attendance is linearly related to ticket price. What ticket price would maximize revenue?
Answer:
Step-by-step explanation:
We can start by assuming that the relationship between the ticket price and attendance is linear, so we can write the equation for the line that connects the two data points we have:
Point 1: (9, 23000)
Point 2: (7, 30000)
The slope of the line can be calculated as:
slope = (y2 - y1) / (x2 - x1)
slope = (30000 - 23000) / (7 - 9)
slope = 3500
So the equation for the line is:
y - y1 = m(x - x1)
y - 23000 = 3500(x - 9)
y = 3500x - 28700
Now we can use this equation to find the attendance for any ticket price. To maximize revenue, we need to find the ticket price that generates the highest revenue. Revenue is simply the product of attendance and ticket price:
R = P*A
R = P(3500P - 28700)
R = 3500P^2 - 28700P
To find the ticket price that maximizes revenue, we need to take the derivative of the revenue equation and set it equal to zero:
dR/dP = 7000P - 28700 = 0
7000P = 28700
P = 4.10
So the ticket price that would maximize revenue is $4.10. However, we need to make sure that this price is within a reasonable range, so we should check that the attendance at this price is between 23,000 and 30,000:
A = 3500(4.10) - 28700
A = 5730
Since 23,000 < 5,730 < 30,000, we can conclude that the ticket price that would maximize revenue is $4.10.
