The difference between the two formulas is that nPr takes order into account, while nCr does not. To determine which formula to use, consider whether order matters in the problem. If order matters, use nPr. If order does not matter, use nCr.
What are the possible outcomes of probability?a) An example of an application problem that uses nPr could be the following: In how many ways can a committee of 3 people be chosen from a group of 7 if the order of selection matters?
b) An example of an application problem that uses nCr could be the following: In how many ways can a committee of 3 people be chosen from a group of 7 if the order of selection does not matter?
c) The formula for nPr is n!/(n-r)!, where n is the total number of items and r is the number of items being selected in a specific order. The formula for nCr is n!/r!(n-r)!, where n is the total number of items and r is the number of items being selected without regard to order.
a) The tree diagram for the problem is:
H T
/ \ / \
H T H T
/ \ / \ / \ / \
H T H T H T H T
b) The probability that all the coins will turn up heads is 1/8 or 0.125, since there is only one outcome out of the eight possible outcomes that satisfies this condition.
c) The probability that there will be at least one tails is 7/8 or 0.875, since there are seven outcomes out of the eight possible outcomes that satisfy this condition (all except HHH).
Therefore, All the possible outcomes are: [tex]HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.[/tex]
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What is 11 1/2 minus 6 2/3
The answer is 4 5/6
Step-by-step explanation:
h(r) = 11r² - 6
g(r) = r² + 8r+ 9
Find h(-2) + g(-2)
According to the solving the function the value of h(-2) + g(-2) is 45.
What exactly is function?function is a mathematical phrase, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions are used frequently in mathematics and are crucial for constructing physical links in the sciences.
According to the given information:To find h(-2) + g(-2), we need to evaluate h(r) and g(r) when r = -2, and then add the results:
h(-2) = 11(-2)² - 6 = 44
g(-2) = (-2)² + 8(-2) + 9 = 1
So, h(-2) + g(-2) = 44 + 1 = 45.
Therefore, h(-2) + g(-2) = 45.
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What is 0.35+0.4 show your work
Answer:
0.75
Step-by-step explanation:
0.4 = 0.40
Add 0.40 + 0.35 = 0.75
here are the factors of sixteen and twenty. click the factors that are common to both numbers. (choose 3)
The common factors of sixteen and twenty are 1, 2, and 4.
The factors of sixteen are 1, 2, 4, 8, and 16. The factors of twenty are 1, 2, 4, 5, 10, and 20. The factors that are common to both numbers are 1, 2, and 4.
To calculate the factors of sixteen, we can start by dividing sixteen by two until we cannot divide any further. We can start with sixteen divided by two, which equals eight. Eight divided by two equals four. Four divided by two equals two. Two divided by two equals one. As we can see, the factors of sixteen are 1, 2, 4, 8, and 16
To calculate the factors of twenty, we can start by dividing twenty by two until we cannot divide any further. We can start with twenty divided by two, which equals ten. Ten divided by two equals five. Five divided by two equals two. Two divided by two equals one. As we can see, the factors of twenty are 1, 2, 4, 5, 10, and 20.The common factors of sixteen and twenty are 1, 2, and 4. This can be determined by comparing the two lists of factors. As we can see, 1, 2, and 4 are present in both lists.
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Complete question
What are the common factors of sixteen and twenty ?
PLEASEEE HELPPPP!!!!! ASAP!
King and his friend went to a restaurant for dinner. King ordered a half pound burger and a milkshake. The burger contained 25 grams of total fat. If the recommended daily allowance of total fat for a 2,000 calories diet is 62 grams, what percent of the daily allowance did King have when he ate his burger? Show your work and round to the nearest tenth.
Answer:
40.3%
Step-by-step explanation:
You want to know the percentage of a 62 gram allowance of fat is represented by a burger with 25 grams of fat.
PercentageThe fraction can be converted to a percentage by multiplying by 100%.
burger/allowance = (25 g)/(62 g) × 100% = 40.3%
King has 40.3% of his daily allowance for fat when he ate his burger.
Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch. (1 point)
help me pls D;
The length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.
How to find the dimensions of rectangle?Since the area of the soap carvings is 300 square inches, we want the top of the bookcase to have the same area. Let's assume the length of the top of the bookcase is "l" and the width is "b". Then we have:
Area of top of bookcase = lb
We want this area to be equal to 300 square inches. Therefore, we can write:
lb = 300
We are solving for "b", so we can rearrange this equation to solve for "b":
b = 300/l
Since we don't know the value of "l", we can't solve for "b" exactly. However, we can approximate it by assuming a value for "l". Let's say we assume that "l" is 20 inches. Then we can calculate "b" as follows:
b = 300/20 = 15
So if the length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.
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The total amount of charge in coulombs that has entered a wire at time is given by the expression Q = 6 t + 2 t^2, where t is in seconds and t greaterthanorequalto 0. Find an expression for the current in the wire at time t.
The rate at which electric charge flows through a circuit is used to quantify electrical current: I (t) equals dQ (t) / dt. The derivative of the electric charge by time yields the momentary current. I (t) is the amps of the transient current I at time t. (A).
The temporary electric charge, measured in coulombs, is Q(t) (C).
The time in seconds is t. (s).
I =ΔQ / Δt
ΔQ is the amount of electric current flowing at time Δt, measured in coulombs (C).
The time length in seconds is t. (s).
We know that I = dQ/dt by definition; thus, if Q = f(t), then I = f' (t). By stating this, we obtain the current's expression as follows:
I (t) = (d/dt) (Q(t)) = (d/dt) (6t + 2t2) = 6 + 4t: I(t) = 4t + 6; t >= 0
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The table below shows the number of painted pebbles of Claire and Laura. If Greg chooses a pebble at random from the box 75 times, replacing the pebble each time, how many times should he expect to choose a yellow pebble??
A) 11
B) 33
C) 32
D) 22
The number οf times that Greg chοοses a yellοw pebble is 22 times.
Thus, option D is correct.
Finding the number οf chοices:Tο find the number οf pοssible chοices, calculate the number οf chances in the tοtal number οf οutcοmes.
Since we need tο find the number οf chοices that are expecting a yellοw pebble, find the tοtal number οf yellοw pebbles in the number οf pebbles in bοth Claire and Laura's cases and find the tοtal number οf yellοw pebbles.
Here we have
A table belοw shοws the number οf painted pebbles by Claire and Laura
Frοm the table,
Number οf pebbles that Laura painted = 8 yellοw, 7 green, 10 blue
Number οf pebbles that Claire painted = 14 yellοw, 5 green, 6 blue
Tοtal number οf yellοw pebbles = 8 + 14 = 22
Given that
Greg chοοses a pebble at randοm frοm the bοx 75 times, and each time replaces the pebble
Hence, the number οf time that Greg get yellοw pebble = number οf yellοw pebbles
Therefοre, The number οf times that Greg chοοses a yellοw pebble is 22 times.
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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.
PLEASE HELP ASAP! This composite figure is created by placing a sector of a circle on a triangle. What is the area of this composite figure? Use 3.14 for n. Round to the nearest hundredth. Show your work.
The area of this composite figure made from placing a sector of a circle on a triangle is 95.55 square cm
Calculating the area of the composite figureThe sector area
The area of the sector is calculated as
Area = x/360 * πr²
Where
r² = 8² + 6²
So, we have
r² = 100
This means that
Area = 82/360 * π * 100
Evaluate
Area = 71.55
The triangle area
This is calculated as
Area = 0.5bh
So, we have
Area = 0.5 * 8 * 6
Evaluate
Area = 24
So, the area of the figure is
Figure = 24 + 71.55
Figure = 95.55
Hence, the area is 95.55
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What is the value of x ? Will give brainiest .
Answer:
x = 14√2 or 19.8 units---------------------------------
Given is the special right triangle.
It is a 45° isosceles right triangle. It has a property that the hypotenuse is √2 times the leg.
We have a hypotenuse of 28 units, so the leg is:
x = 28/√2 =28√2/2 = 14√2 or 19.8 unitsAnswer:
14√2
Step-by-step explanation:
Here we need to find out the value of "x" in the given right angled triangle, here we can make use of trigonometric ratios to find out the value of x .
In a right angled triangle, sine is defined as the ratio of perpendicular and hypotenuse . With respect to angle 45° , x is the perpendicular and 28 is hypotenuse (side opposite to 90° ) .
So we have;
sin45° = x/28
value of sin45° is 1/√21/√2 = x/28
x = 28*1/√2
x = 14 * (√2)² / √2
x = 14√2
Hence the value of x is 14√2 .
Please help!!!!!!!!!!!!!!
Step-by-step explanation:
try this option (see the attachment), answers are marked with red colour.
2 PART QUESTION PLS HELP Harris has a spinner that is divided into three equal sections numbered 1 to 3, and a second spinner that is divided into five equal sections numbered 4 to 8. He spins each spinner and records the sum of the spins. Harris repeats this experiment 500 times.
Question 1
Part A
Which equation can be solved to predict the number of times Harris will spin a sum less than 10?
A) 3/500 = x/15
B) 12/500 = x/15
C) 12/15 = x/500
D) 3/15 = x/500
QUESTION 2
Part B
How many times should Harris expect to spin a sum that is 10
or greater?
_______
Answer:
Step-by-step explanation:
Question 1
Part A:
To predict the number of times Harris will spin a sum less than 10, we need to find the probability of getting a sum less than 10 and multiply it by the total number of spins, which is 500.
The possible outcomes of the first spinner are 1, 2, and 3, and the possible outcomes of the second spinner are 4, 5, 6, 7, and 8. The minimum sum we can get is 1+4=5, and the maximum sum we can get is 3+8=11.
To get a sum less than 10, we can get:
1+4=5
1+5=6
1+6=7
1+7=8
1+8=9
2+4=6
2+5=7
2+6=8
2+7=9
3+4=7
3+5=8
3+6=9
There are 12 possible outcomes that result in a sum less than 10. So the probability of getting a sum less than 10 is 12/15, or 4/5.
To find the number of times Harris will spin a sum less than 10, we can use the equation:
probability of getting a sum less than 10 × total number of spins = x
So the equation that can be solved to predict the number of times Harris will spin a sum less than 10 is:
C) 12/15 = x/500
Part B:
To find the number of times Harris should expect to spin a sum that is 10 or greater, we can subtract the number of times he will spin a sum less than 10 from the total number of spins:
total number of spins - number of times he will spin a sum less than 10 = number of times he should expect to spin a sum that is 10 or greater
Substituting the values, we get:
500 - (12/15 × 500) = 500 - 400 = 100
So Harris should expect to spin a sum that is 10 or greater 100 times.
solve for X
Five stars and like, I suck at geometry
The value of x is 30° as per below diagram.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.
We know that,
All the angles in a triangle sum → 180°An isosceles triangle: two equal angles → two equal sides.Draw a line segment BG is with CBG equal to 20° on line CE.
So that, (40 + x) = 70, so that means x = 30°
Therefore, The value of x is 30°
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Complete question here-
Triangle: According to the question the value of x is 30° as per below diagram.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.
We know that,
All the angles in a triangle sum → 180°
An isosceles triangle: two equal angles → two equal sides.
Draw a line segment BG is with CBG equal to 20° on line CE.
So that, (40 + x) = 70, so that means x = 30°
Therefore, The value of x is 30°
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Complete question:
Jenny took the car, the bus, and the train to get home in time.
What form of punctuation is missing?
O A. No punctuation is missing.
OB.
A period
OC.
A comma
OD. A semicolon
Last three times I have tried to take a picture of my question. Nothing comes up that resembles any of it. I don’t know what’s wrong with this app but it’s not helping.
According to the question. A. No punctuation is missing.
What is punctuation ?Punctuation is the use of symbols to indicate the structure and organization of written language. It is used to help make the meaning of sentences clearer and to make them easier to read and understand. Punctuation marks can also be used to indicate pauses in speech, to create emphasis, and to indicate the speaker’s attitude. There are many different types of punctuation marks, each with its own purpose. The most commonly used punctuation marks are the period, comma, question mark, exclamation mark, quotation marks, and the apostrophe.
Quotation marks are used to enclose quoted material, while the apostrophe is used to indicate possession or to replace missing letters in a word or phrase. By using punctuation correctly, writers can ensure that their messages are correctly understood by their readers.
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Annual Premium per $100 of coverage
Brick
Steel
Mixed
Wood
Area Building Contents Building Contents Building Contents Building Contents
rating
City 0.39 0.43
Suburb 0.45 0.52
Rural 06
0.69
0.5
0.56
0.71 0.8
0.54
063
0.55
0.72
0.89
0.65
0.74
091
0.66
0.83
1
0.76
0.85
1.02
Ashley owns a brick house in the country worth $85,000, and the contents of the
house are valued at $18,000. She wants to know her property insurance premium.
1.
What is Ashley's annual
premium on her house?
2.
What is Ashley's annual
premium on the contents of her
house?
Therefore, Ashley's annual premium on the contents of her house is $127.80.
What is percent?Percent is a term used to express a fraction or a ratio as a portion of 100. It is denoted by the symbol % (per cent or percent). Percentages are commonly used in many different contexts, such as finance, statistics, science, and everyday life. They are used to express changes, comparisons, rates, probabilities, and many other types of information. To calculate a percentage, we usually divide the part by the whole and multiply the result by 100.
Here,
Based on the provided table, we can calculate Ashley's annual premium on her house and the contents of her house as follows:
Annual premium on Ashley's house:
Since Ashley's house is made of brick and located in a rural area, we can use the values from the "Brick" and "Rural" columns of the table. The premium per $100 of coverage for a brick house in a rural area is $0.60 for the building and $0.69 for the contents.
To calculate the annual premium for the house, we first need to determine the coverage amount. The coverage amount is the value of the house divided by 100, so in this case, it is $85,000 / 100 = $850.
The annual premium for the house is then calculated by multiplying the coverage amount by the premium per $100 of coverage:
Annual premium on house = coverage amount * premium per $100 of coverage for brick house in rural area
= $850 * $0.60
= $510
Therefore, Ashley's annual premium on her house is $510.
Annual premium on Ashley's contents:
To calculate the annual premium for the contents of Ashley's house, we use the same method as above. The coverage amount is the value of the contents divided by 100, so in this case, it is $18,000 / 100 = $180.
The annual premium for the contents is then calculated by multiplying the coverage amount by the premium per $100 of coverage:
Annual premium on contents = coverage amount * premium per $100 of coverage for contents in rural area
= $180 * $0.71
= $127.80
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Proofs help ASAP…….$;$3$3
how many one-to-one functions are there from a set with five elements to sets with the following number of ele- ments? a) 4 b) 5 c) 6 d) 7
a) Number of one-to-one functions are equal to the zero, because n< m.
b) Number of one-to-one functions are equal to the ⁵P₅ = 120.
c) Number of one-to-one functions are equal to the ⁶P₅ = 720.
c) Number of one-to-one functions are equal to the ⁷P₅ = 2250.
One to one function is a special form of function that defined from one set to another and maps every element of the range to exactly one element of its domain unique output. As we know a set A has m elements and set B has n elements, then
Number of one-to-one functions from set A to Set B = P(n,m) or ⁿPₘ , n≥ m and number of one-to-one functions from set A to Set B = 0 , n< m.Now, we have a domain set with five elements, m = 5
a) Here, another set (co-domain) has 4 elements, n = 4. So, Number of one-to-one functions = 0 , n<m.
b) number of elements in another set,n= 5
So, Number of one-to-one functions = ⁵P₅ = 5!/(5 - 5 )! ( permutation formula)
= 5!/0! = 120
c) Number of elements in another set, n= 6
So, Number of one-to-one functions= ⁶P₅
= 6!/(6 - 5)!
= 6!/1! = 720
d) Number of elements in another set, n
= 7
So, Number of one-to-one functions
= ⁷P₅ = 7!(7 - 5)!
= 7!/2! = 2250
Hence, required value is 2250.
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PLEASEE HELP!
Draw an angle that is 150 degrees.
Step-by-step explanation:
[tex]\textsf{For this problem, we are asked to draw an angle that is 150}^{\circ}.[/tex]
[tex]\textsf{We will need a Protractor to draw this angle.}[/tex]
[tex]\large\underline{\textsf{To Draw an Angle with a Protractor;}}[/tex]
[tex]\textsf{First, notice a point at the bottom of the Protractor. This is where we will start.}[/tex]
[tex]\textsf{Draw a Straight Line from the point to the 0}^{\circ} \ \textsf{mark.}[/tex]
[tex]\textsf{Secondly, use a ruler to carefully draw a straight line towards the 150}^{\circ} \ \textsf{mark.}[/tex]
[tex]\textsf{Note that some Protractors may be different from others. Similar steps should apply.}[/tex]
[tex]\textsf{Refer to the picture. It represents what the angle should look like afterwards.}[/tex]
To do :-
To draw a angle of 150° .Instruments required:-
A pair of compasses ,A ruler ,A pencil ,and a protactorSteps of construction:-
Draw a line segment of desired length.Taking a point on the line , draw a semicircle using a compass .Taking G as centre cut an arc on the semicircle mark the point of intersection as I .Taking I as centre cut another arc on the semicircle , mark it as point J .Taking J and I as center, cut an arc such that both the arcs intersect each other, mark it as point D .Join C and D .Taking F as centre again cut an arc on the semicircle, mark it as point E .Join E and C .Using a protactor you can check whether the angle formed is 150° or not .Hence angle ECB represents 150° .
Precaution:- do not change the arm length of the compass.
and we are done!
if the cafiteria has 80 coustomers on tuesday, which prediction for tues day is not supported by the data in the table
Answer:
Where is the table?
Step-by-step explanation:
In 2016, the CDC estimated the mean weight of U.S. women over the age of 20 years old was 168.5 pounds with a standard deviation of 68 pounds.
What is the expected mean for a sample of 150 women?
What is the standard deviation of the mean for a sample of 150 women?
What is the probability of 150 women having a sample mean below 160 pounds?
What is the probability of 150 women having a sample mean above 175 pounds?
What is the probability of 200 women having a sample mean below 160 pounds? Notice the change in sample size.
What is the probability of 200 women having a sample mean above 175 pounds?
Answer:
Notice the change in sample size.
Answer:
1. The expected mean for a sample of 150 women is 168.5 pounds.
2. The standard deviation of the mean for a sample of 150 women is 6.8 pounds.
3. The probability of 150 women having a sample mean below 160 pounds is 0.0849.
4. The probability of 150 women having a sample mean above 175 pounds is 0.0305.
5. The probability of 200 women having a sample mean below 160 pounds is 0.0434.
6. The probability of 200 women having a sample mean above 175 pounds is 0.0153.
The solution is given below. Notice the change in sample size.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
given that,
In 2016, the CDC estimated the mean weight of U.S. women over the age of 20 years old was 168.5 pounds with a standard deviation of 68 pounds.
so. we get,
1. The expected mean for a sample of 150 women is 168.5 pounds.
2. The standard deviation of the mean for a sample of 150 women is 6.8 pounds.
3. The probability of 150 women having a sample mean below 160 pounds is 0.0849.
4. The probability of 150 women having a sample mean above 175 pounds is 0.0305.
5. The probability of 200 women having a sample mean below 160 pounds is 0.0434.
6. The probability of 200 women having a sample mean above 175 pounds is 0.0153.
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Using the Distributive Property as a good first step to solving the equation, you could simplify to get which of these choices?7(5x + 2) = -4(6 - 5x)35x + 14 = -24 - 20x35x + 14 = -24 + 20x5x + 14 = 6 + 20x35x + 2 = -24 - 5x35x + 2 = 24 - 20x
In equation 7(5x + 2) = -4(6 - 5x), Using the Distributive Property, we get 35x + 14 = -24 + 20x. So, the correct option is D).
To solve the equation 7(5x + 2) = -4(6 - 5x), a good first step is to use the Distributive Property to simplify both sides of the equation. Distributing the 7 and -4 on the left and right sides, respectively, we get
35x + 14 = -24 - 20x.
Next, we can combine like terms by adding 20x to both sides to get 55x + 14 = -24. Then, subtracting 14 from both sides, we get 55x = -38. Finally, we can solve for x by dividing both sides by 55, giving us x = -38/55. Therefore, the solution to the equation is x = -38/55.
The evaluation process involves performing arithmetic operations in a logical order to simplify the equation step-by-step until a solution is reached. So, the correct answer is D).
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Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) an = e−8/√n lim n→[infinity] an =
The sequence, [tex]a_n =e ^{\frac{{-8}}{\sqrt{n}}}[/tex], is convergent sequence because the limit of an exists, that is as n approaches infinity, so the sequence an approaches 1 ( finite value).
The sequence can be convergent if the limit is zero, or if the limit is finite. The divergent sequence is one whose limit is not finite. The limit can be found suing the limit properties or by simplification method, as applicable. We have, an sequence, [tex]a_n =e ^{\frac{{-8}}{\sqrt{n}}}[/tex]. We have to check whether the sequence converges or diverges. Using limits, [tex]lim_ {n->\infty } a_n = lim_{n-> oo} e^{\frac{-8}{\sqrt{n}}} [/tex]
n approaches infinity, so square root of n approaches infinity,
= e⁻⁰
= 1/e⁰ = 1 ( finite )
Therefore, it is a convergent sequence.
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Please indicate which is the best answer to complete the figure below.
Answer:
E
Step-by-step explanation:
Answer has to have a star, the object (star) needs to be on the right side, and the two colors cannot be the same as any of the rest in the set. So E?
The sum of three numbers is 70 . The third number is 2 times the first. The first number is 6 less than the second. What are the numbers?
Answer:
16, 22, and 32.
Step-by-step explanation:
Set up a system of equations to represent the situation with 3 unknown.
x + y + z = 70
z = 2x
x = y - 6 → y = x + 6
The second two equations are the y and z in terms of x, so substitute both into the first equation.
x + (x + 6) + 2x = 70
4x + 6 = 70
4x = 64
x = 16
Use this number to calculate the value of the other unknowns.
y = x + 6
y = 16 + 6
y = 22
Calculate z.
z = 2x
z = 2(16)
z = 32
So, the three numbers are 16, 22, and 32.
TRUE/FALSE.For a Binomial experiment, the second moment about mu is given by the second derivative of (p+qeAt) with respect to t evaluated at t-0.
False. The second moment about mu for a binomial experiment is not given by the second derivative of [tex](p+qeAt)[/tex]with respect to t evaluated at t=0.
The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success. The probability of success in each trial is denoted by p, and the probability of failure is denoted by q=1-p.
The second moment about mu is a measure of the variability of the binomial distribution, and is given by the formula[tex]E[(X-mu)^2][/tex] , where X is the random variable, mu is the mean, and E is the expected value operator.
To calculate the second moment about mu for a binomial distribution with parameters n and p, we can use the formula npq, where np is the mean and q=1-p. This formula can also be derived using the properties of variance, which state that [tex]Var(X)=E[X^2] - (E[X])^2.[/tex]
Therefore, the statement that the second moment about mu for a binomial experiment is given by the second derivative of [tex](p+qeAt)[/tex]with respect to t evaluated at t=0 is false. This statement does not relate to the binomial distribution or its properties, and is not a relevant formula for measuring the variability of a binomial experiment.
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Need help please!
Thank you so much!!
The graph repeats itself every 32 units hοrizοntally. [ The graph is attached belοw ]
What is an interactive widget in graphs:An interactive widget in a graph is a tοοl that allοws the user tο manipulate different elements οf the graph using their mοuse οr tοuch screen.
Interactive widgets can be used tο explοre the behaviοr οf a functiοn οr dataset in a mοre dynamic and engaging way than a static graph.
Sοme cοmmοn examples οf interactive widgets in graphs include sliders, buttοns, checkbοxes, and drοpdοwn menus.
Here we have
y = -5 cοs (π/16 x) - 4
Represents a periοdic functiοn with a cοsine wave shape that is shifted dοwnwards by 4 units.
The cοsine functiοn οscillates between -1 and 1, sο multiplying it by -5 stretches the wave vertically by a factοr οf 5 and reflects it acrοss the x-axis.
The cοefficient οf x, π/16, cοntrοls the periοd οf the functiοn, which is the distance between twο cοnsecutive peaks οr trοughs οf the wave.
Specifically, the periοd οf this functiοn is 32 units, since the cοsine functiοn has a periοd οf 2π and 2π/(π/16) = 32.
Therefοre,
The graph repeats itself every 32 units hοrizοntally. [ The graph is attached belοw ]
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CAN SOMEONE PLEASE HELP thank you so so much please!!!
Step-by-step explanation:
try this option, all the details are in the attachment.
find the following answer
According to the Venn diagram the value of [tex]n(A ^ C \cap B ^ C) = {3}[/tex] so the number of elements in that set is 1.
What is Venn diagram ?
A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. It is usually represented as a rectangle or a circle for each set and the overlapping areas between them, showing the common elements that belong to more than one set. Venn diagrams are widely used in mathematics, logic, statistics, and computer science to visualize the relationships between different sets and help solve problems related to set theory.
According to the question:
To solve this problem, we first need to understand the notation used.
n(A) denotes the set A and the numbers within the braces {} indicate the elements in set A. For example, n(A)={7,4,3,9} means that the set A contains 7, 4, 3, and 9.
n(AnB) denotes the intersection of sets A and B, i.e., the elements that are common to both A and B. For example, n(AnB)={4,3} means that the sets A and B have 4 and 3 in common.
^ denotes intersection of sets
cap denotes the intersection of sets
Now, we need to find the elements that are common to sets A and C, and sets B and C. We can do this by taking the intersection of A and C, and the intersection of B and C, and then taking the intersection of the two resulting sets.
[tex]n(A ^ C) = n(A \cap C) = {3,9}[/tex]
[tex]n(B ^ C) = n(B\cap C) = {3,5}[/tex]
Now, we take the intersection of [tex]n(A ^ C)[/tex] and [tex]n(B ^ C)[/tex]:
[tex]n(A ^ C \cap B ^ C) = {3}[/tex]
Therefore, the answer is 1.
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A lender requires a minimum down payment of 16% of the value of the home. You have $39,000
cash available to use as a down payment toward a home. Determine the maximum home value
that you can finance.
There is a $243,570 cap on the amount you may finance.
Which type of arithmetic is used in finance?MentaI arithmetic, aIso known as "quick math," aIgebra, trigonometry, statistics, and probabiIity are some of the key mathematicaI concepts and abiIities needed in the financiaI sector. A fundamentaI knowIedge of these abiIities shouId be sufficient to quaIify you for the majority of finance occupations.
The highest home vaIue that may be financed is x.
$39,000 in avaiIabIe cash for a down payment
16% is the needed down payment percentage.
16% of the home's worth can be expressed as,
x × 16/100=$39,000
x=39,000/0.16
x=$243,570
We can then infer that the highest vaIue you couId finance is $243,570.
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