₁₁C₈ * ₄C₃ as related to permutations is ₁₁P₈ / 8! * ₄P₃ / 3!
Further explanation of combination and permutationThe term combination refers to a method of choosing where order does not matter. an instance forming 3 letter word from ABC. the combination is ₃C₃ = 1
In permutation, order matters hence in choosing or making selection specific order should be followed. an instance here is arranging the 3 letters word from ABC. ₃P₃ = 6
ABCACBBACCABBCACBAAll the items above are different permutations however for combination they are same.
The difference mathematically is dividing by the number of arrangements
₃C₃ = 3! / (3!(3-3)!) = 3! / (3!* 0!) = 3! / 3! = 1
₃P₃ = 3! / (3-3)! = 3! / (0!) = 3! / 1 = 3! = 6
Therefore ₃C₃ = ₃P₃ / 3!
similarly
₁₁C₈ * ₄C₃ = ₁₁P₈ / 8! * ₄P₃ / 3!
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Solve for x.
please help! giving 20 points
Find the values of x and y.
Answer: The correct answer is x = 50
Step-by-step explanation:
The sum of angles in a triangle = 180 degrees
This is a right-angled triangle, so one of the angles is 90 degrees + x +y
Therefore: 90 + y + x = 180
Substitute the variables:
90 + 40 + x = 180
130 + x =180
Subtract 130 from each side:
(-130) 130 + x =180 (-130)
x = 50
The annual average price per square foot for office space in a city was $30.18 in 2004, and it was $66.85 in 2015.
(a) Find an exponential function of the form f(t)=y0b^t to model these data in which t=0 corresponds to 2004.
The exponential model of the given data is f(t) = 30.18 × 1.06^t.
What are the rules of exponents?Some of the rules of exponents are as follows,
The product of two exponents having the same power is equal to the power of their base multiplied.
The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.
Given that,
The average price for office space in 2004 is $30.18.
The average price for office space in 2015 is $66.85.
Suppose the average price in 2004 is taken as y₀.
The given situation can be represented in the form of exponential function f(t) = y₀b^t as,
Take t = 0 for 2004
Then, f(0) = y₀b^0
⇒ f(0) = y₀ = $30.18.
Then, at 2015, t = 12. Substitute the respective values to get,
f(12) = 30.18 × b^12
⇒ 66.85 = 30.18 × b^12
⇒ b^12 = 66.85 / 30.18
⇒ b = 1.06
Thus in exponential form the given situation can be written as,
f(t) =30.18 × 1.06^t
Hence, the given data can be modeled in exponential function as f(t) =30.18 × 1.06^t.
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Please Help 2
Find (fxg)(x) if f(x)=x2+2+4 and g (x)=x-2
Answer:
x³ - 8
Step-by-step explanation:
is a gas station sells 8 bags of chips for $12, what is the unit price
The ratio shows how many times one value is contained in another value.
8 bags of chips = $12
1 bag of chips = $1.5
The unit price of a bag of chips is $1.5
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
There are 4 black and 3 white marbles in a bag.
The ratio of black and white marbles in the bag is 4:3.
We have,
8 bags of chips = $12
Divide both sides by 8.
1 bag of chips = $12/8
1 bag of chips = $3/2
1 bag of chips = $1.5
This means,
1 bag of chips costs $1.5
Thus,
The unit price of a bag of chips is $1.5
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In how many ways can a person order one ice cream cone with 3 different flavors of ice cream if there are 11 flavors to choose from and it matters to the person how the 3 flavors are stacked on the one cone? That is, which flavor is on top, middle, and bottom.
Answer:
I think the answer is 33?
One card is drawn from a well-shuffled deck of fifty-two cards (no jokers).
(a) Find the probability of drawing a card below a 6 (count an ace as high). (Enter your answer as a fraction.)
(b) Find the odds of drawing a card below a 6 (count an ace as high).
(c) Use the Law of Large Numbers to interpret both the probability and the odds of drawing a card below a 6 (count an ace as high).
(Refer to the picture attached for answer choices)
Probability of drawing a card below a 6 (count an ace as high) is 4/13
Total number of outcome : n(S) = 52
(a) In a deck number of card below a 6 (counting ace as high) is {5 , 4 , 3, 2}
so , n(E) = 4 × 4 = 16
The probability of drawing a card below a 6 (count an ace as high) = P(E)
[tex]P(E) =\frac{n(E)}{n(s)}[/tex] =16/52
P(E) = 4/13
(b) Probability of drawing a card below a 6 (count an ace as high) is 4/13
Hence , the odds of drawing a card below a 6 (count an ace as high). is 0.308
(c) we should expect to draw a card below a 6 about four times out of every 13 attempts .Also, we should expect to draw a card below or 6 four times for every nine times we draw a 6 or above is the law of large number to interpret both the probability and odds of drawing a card below 6
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Myles has 12 markers and 20
pencils. What is the greatest
number of groups that can be
made with equal number of
markers and pencils?
In linear equation, No of marker is 5 and no of pencil is 3 .
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). For the purpose of resolving systems involving two linear equations, this form is also highly helpful.Myles has 12 markers and 20 pencils.
take LCM of 12 and 20 = 60
no of 12 markers = 5
no of 20 pencils = 3
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How do I solve this question
The partial fraction of the compound fraction [tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex] is [tex]\frac{6}{x - 5}[/tex] [tex]-\frac{5}{x - 3}[/tex]
What is a partial fraction?Partial Fractions are the fractions that are formed when a complex rational expression is split into two or more simpler fractions.
When fractions become too cumbersome to solve we split them into simpler units called partial fractions so that mathematical operations can easily be carried out on them.
[tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex] can be split into the form, [tex]\frac{A}{x - 3} + \frac{B}{x - 5}[/tex]
where A and B are constants.
so,
[tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex] = [tex]\frac{A}{x - 3} + \frac{B}{x - 5}[/tex]
taking the LCM of the denominators of the split fractions, we have
(x-3)(x-5)
multiply A by x -5 and B by x - 3
fraction becomes
[tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex] = [tex]\frac{A(x - 5) + B(x - 3)}{(x - 3)(x - 5)}[/tex]
since the denominators of the Left hand side and right hand side are same, we equate the numerators
A(x - 5) + B( x - 3) = x + 7
Using the cover up rule method,
to find A, we substitute x = 3 into the equation so that B becomes zero
A(3 - 5) = 3 + 7
-2A = 10
A = 10/-2
A = -5
To find A put x = 5 so that A = 0
B(5 - 3) = 5 = 7
2B = 12
B = 12/2 = 6
Substituting B and A into the partial fractions above
we have,
[tex]\frac{6}{x - 5}[/tex] [tex]-\frac{5}{x - 3}[/tex]
In conclusion the partial fractions are [tex]\frac{6}{x - 5}[/tex] [tex]-\frac{5}{x - 3}[/tex]
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The meteorologist at Channel 8 News predicted that a snowstorm would drop 7 inches of
snow. After the storm, she reported that the actual snowfall was 4 inches. What is the
percent error for the meteorologist's prediction?
If necessary, round your answer to the nearest tenth of a percent.
%
THE percent error is, 5
what is percent error?Percent error calculates the difference between an estimate and a right value and expresses it as a percentage. Analysts can use this statistic to determine how big the error is in relation to the actual number. It is also referred to as % error and percentage error.The estimate and accurate values in this situation might be any of the following:a measurement, an approximation, a value obtained experimentally, or a guess.Correct Value: A number that has been established or is widely regarded as accurate. It might serve as a standard measurement for something tested as a measurement system. Or a value that is theoretically valid and is known, like a circle's circumference.hence,THE percent error is, 5
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why are 0.8 and 0.80 are equivalent?
0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.
In mathematics, the decimal representation of numbers allows for the use of trailing zeros after the decimal point. When a decimal number has trailing zeros, such as in the case of 0.8 and 0.80, they are considered equivalent because they represent the same value.
The trailing zeros after the decimal point do not change the numerical value of the number. The number 0.8 represents eight tenths, and adding a trailing zero to make it 0.80 does not change its value; it still represents eight tenths. The zero after the decimal point in 0.80 is simply a placeholder, indicating that there are no hundredths or smaller fractional parts.
It is common to use trailing zeros in decimal representations to indicate the precision or accuracy of a measurement. For example, if a measurement is known to be accurate to two decimal places, it is common to represent it as 0.80 rather than 0.8 to indicate the level of precision.
Therefore, mathematically speaking, 0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.
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Solve the system by back substitution.
- 2x - 4y - z- 3w = -5
-2y - 12z - 4w = - 16
5z +5w=10
4w =12
Answer:
y=8 x=-19.5
Step-by-step explanation:
Start from the bottom equation and work your way upSolve the fourth equation for w-5w=-15-5w/(-5)=-15/(-5)w = 3 Then use that value of w to plug into the third equation. Notice we're going backwards or up the chain of equations. After w is replaced, solve for zz+w = 2z+3 = 2z+3-3 = 2-3z = -1 Now use z = -1 and w = 3 to plug into the second equation. Solve for y-2y-12z-4w = -16-2y-12(-1)-4(3) = -16-2y+12-12 = -16-2y = -16-2y/(-2) = -16/(-2)y = 8
Use y = 8, z = -1, w = 3 to plug into the first equation. Solve for x:
2x+4y+z+3w=12x+4(8)+(-1)+3(3)=12x+32-1+9=12x+40=12x+40-40=1-402x=-392x/2=-39/2x = -39/2 The value of x as a fraction is x = -39/2The value of x in decimal form is x = -19.5
Determine whether the ratios are equivalent.
85: 210 and 340: 735
These are equivalent. I hope this helps a ton. I had this question on a test. Tell me if its wrong or not. <:
A frozen yogurt stand charges per ounce of frozen yogurt purchased. There is an extra charge for a waffle bowl. The total cost (c), in dollars, for f ounces of frozen yogurt in a waffle bowl, is described by the function c = 0.45f + 1.
Which statement is true?
A.
The cost of 0.45 ounce of frozen yogurt in a waffle bowl is $1.
B.
Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.
C.
Each ounce of frozen yogurt costs $0.45 and a waffle bowl is $1 extra.
D.
The cost of 0.45 ounce of frozen yogurt in a waffle bowl is $1.45.
Answer:
$0.45 and a waffle bowl is $1 extra.
Step-by-step explanation:
The flower box is 5 ft long, and its ends are in the shape of a trapezoid. The upper and lower bases of the trapezoid measure 18 in. and 10 in., respectively, and the height is 9 in. Find the volume of the flower box.
The volume of the flower box is 7560 cubic inches
How to determine the volume of the box?The given parameters in the question are:
Length = 5 ft
Upper and lower bases = 18 inches and 10 inches
Height = 9 inches
The volume of the box can be calculated using the following volume equation
Volume = 0.5 * Height * Length * (Sum of the bases)
Substitute the known values in the above equation So, we have the following equation
Volume = 0.5 * 9 inches * 5 feet * (18 inches + 10 inches)
Convert feet to inches
Volume = 0.5 * 9 inches * 60 inches * (18 inches + 10 inches)
Evaluate
Volume = 7560 cubic inches
Hence, the volume is 7560 cubic inches
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Find the slope using points: (0, - 3) and (- 4, 2)
Answer:
-5/4
Step-by-step explanation:
slope
[tex]\frac{y2-y1}{x2-x1}\\\\ \frac{2-(-3)}{-4-0}=\frac{5}{-4}\\ \\slope = \frac{-5}{4}[/tex]
Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 12% for 6 months. Calculate the simple interest using I = prt. $69 $90 $420 $1,080
The simple interest that Oliver needs to pay is $ 90
Calculating Simple interest:Simple interest is nothing but interest on a loan at a rate. The formula for Simple interest is given below
Simple interest, I = ptr
where p = principal amount
t = time period in years
r = rate of interest in decimals
Here we have
Oliver borrowed $1,500 to purchase a riding lawn mower
The rate of interest r = 12%
=> 12/100 = 0.12 (in decimals )
The time period given = 6 months = 0.5 years [ 6/12 = 0.5 ]
From the above formula,
The simple interest, I = ptr
=> I = $1,500(0.12) (0.5) = $ 90
Therefore,
The simple interest that Oliver needs to pay is $ 90
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I need the answer fast please
What is the value of X?
Answer:
x=28
Step-by-step explanation:
angle b and angle c are the same measure because it is a iso triangle.
you know triangle sum is 180 so 3x+2(x+20)=180. simplify it to 5x=140
divide both sides by 5
x=28
Answer:
x = 28
Step-by-step explanation:
The triangle is isosceles, meaning that the two base angles (x + 20) are congruent. We can then create an equation that states: (x + 20) + (x + 20) + 3x = 180. Simplifying this, we get 5x + 40 = 180. We can then use reverse order of operations to solve it. Subtract 40 from both sides to get 5x = 140. We will then divide both sides by 5 to get x by itself, getting us the equation x = 28.
An exam has four multiple choice problems, each with five possible answers. If you guess on each problem, what is the probability of getting at least one answer correct? Round your answer to the nearest whole percent.
1/2 is the probability of getting at least one answer correct
How to find the probability of getting at least one answer correct?
Given that: the exam has 4 multiple choice with 5 possible answers. This means there are 20 possible choices ( 5×4 = 20).
That means each problem has a probability of 1/20 correct answer. The probability of getting at least one answer means you either get one, two, three or four correct answers. Thus:
P (at least one correct) = P(1) + P(2) + P(3) + P(4)
= 1/20 + 2/20 + 3/20 + 4/20
= (1+2+3+4)/20
= 10/20
= 1/2
Therefore, the probability of getting at least one answer correct is 1/2
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The probability of getting at least one answer correct is equal to 7
How to calculate for the probabilityThat I guess at least one answer correctly means that I could get all four answers correct or three answers correct or two answers correct or only one answer correct. The probability of getting any one answer is 1/4 and probability of not getting an answer is 1 - 1/4=3/4. Or implies addition.
probability of getting all four answers correct = 1/4 +1/4 + 1/4 + 1/4 = 4/4 = 1
probability of getting three answers correct = 1/4 +1/4 + 1/4 + 3/4 = 6/4 = 3/2
probability of getting two answers correct = 1/4 +1/4 + 3/4 + 3/4 = 8/4 = 2
probability of getting all four answers correct = 1/4 +3/4 + 3/4 + 3/4 = 10/4 = 5/2
The probability of getting at least one answer correct = 1 + 3/2 + 2 + 5/2
The probability of getting at least one answer correct = (2 + 3 + 4 + 5)/2
The probability of getting at least one answer correct = 14/2
Thefore, the probability of getting at least one answer correctly is the whole number 7
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The radius of the circle below is 27 mm.
Calculate the area of the circle.
Give your answer in mm² to 1 d.p.
27 m
84.78 mm² is area of circle .
What is a circle ?
A circle is a closed, two-dimensional object in which all points in the plane are equally spaced apart from the center.Having no sides or edges, a circle is a figure with a round shape. A closed, two-dimensional curved form is what is meant by the term "circular" in geometry.radius of the circle = 27 mm
area of the circle = πr²
= 3.14 * 27
= 84.78 mm²
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Select all of the descriptions which describe a transformation of the graph of f(x) = x that could result in the graph of g(x) = 7x.
A: The graph is translated 7 units to the right.
B: The graph is rotated about (0, 0), becoming steeper.
C: The graph is reflected across the x−axis.
D: The graph is vertically shrunk.
E: The graph is translated 7 units up.
F: The graph is vertically stretched.
Answer:
A,C,D
Step-by-step explanation:
Let a=2 b=5 c= -3
8b-4b=4b Please help quick!!!!!
Answer:
40-20= 20
Step-by-step explanation:
8(5)- 4(5)= 4(5)
40-20=20
The ages of people visiting a senior center one afternoon are recorded in the line plot
Does the data contain an outlier? If so, explain its meaning in this situation.
A: No, there is no outlier. This means that the data was not collected correctly, as there would be lots of age ranges at the center.
B: No, there is no outlier. This means that the people at the center were all seniors around the same age.
C: Yes, there is an outlier of 85. This means that one person was age 85, which is 15 years older than the next closest age.
D: Yes, there is an outlier of 105. This means that someone at the center is 105 years old.
Answer:
b
Step-by-step explanation:
The correct option is (b) The data does not contain an outlier. This means that the people at the center were all seniors around the same age.
What is an Outlier in a Dataset?Outlier in a data set is simply the extremely low data point or an extremely high data point compared to other points in the dataset.
It will stand out from the other values in the dataset.
The line plot shows the ages of people visiting a senior center one afternoon.
The data points are,
70, 70, 70, 75, 75, 80, 80, 85, 90, 90, 95, 95, 95, 100.
If there is an outlier in the set, it would be extremely low or high compared to other points.
But there are no such points.
So there are no outliers.
This means that people visited at the center were all seniors around the same age.
Hence the correct option is (b).
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help, please !!!!!!!! **50points**
Answer:Answer: SAS
Step-by-step explanation:
20. In Problem 14 in Chapter 11, we described a study
showing that students are likely to improve their test
scores if they go back and change answers after
reconsidering some of the questions on the exam
(Johnston, 1975). In the study, one group of students
was encouraged to reconsider each question and
to change answers whenever they felt it was appropri-
ate. The students were asked to record their original
answers as well as the changes. For each student, the
exam was graded based on the original answers and on
the changed answers. For a group of n = 40 students,
suppose that 26 had higher scores for the changed-
answer version and only 14 had higher scores for
the original-answer version. Is this result significantly
different from chance? Use a two-tailed test with
α = .01.
Everyone at Colin's school wore either brown or red for school spirit day. 126 out of the 600 students at the school wore brown. What percentage of the students wore brown?
Write your answer using a percent sign (%).
Answer:
21%
Step-by-step explanation:
126 out of 600=126/600
=0.21 *100 for
21%
A missile was fired from a submarine from 200 feet below sea level. If the missile reached a height of 15900 feet before exploding, what was the change in the altitude of the missile?
The required change in height of the missile is 16100 feet.
Given that,
A missile was fired from a submarine from 200 feet below sea level. If the missile reached a height of 15900 feet before exploding, the change in the altitude of the missile is to be determined.
Change in defined as when the object is in one state but after a certain period of time, the state of the object changes is called change of the state.
here,
The height attained by the missile above sea level is 15900 feet.
The height attained by the missile below the seal level is 200 feet.
Change in height = 15900- (-200) = 15900 + 200 = 16100.
Thus, the required a change in height of the missile is 16100 feet.
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3/5 of a fruit punch is orange juice.
What percentage of the fruit punch is orange juice?
60% of the fruit punch is orange juice.
In this question, we have been given 3/5 of a fruit punch is orange juice.
We need to find the percentage of the fruit punch is orange juice.
3/5 of a fruit punch is orange juice, means 3 of 5 fruit punch is orange juice.
Using the percentage formula,
3/5 * 100
= 0.6 * 100
= 60%
Therefore, 60% of the fruit punch is orange juice.
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For the given ratio of orange juice , the percentage of the orange juice from the given fruit juice is equal to 60%.
As given in the question,
Ratio of orange juice in the given fruit juice = 3/5
From the given ratio it indicates out of 5 fruits 3 are orange
Percentage of fruit punch is orange juice in the given juice is equal to
= ( 3 / 5 ) × 100
= ( 3 × 100 ) / 5
= 300 / 5
= 60%
60% of the fruit punch is orange juice.
Therefore, for the given ratio of orange juice , the percentage of the orange juice from the given fruit juice is equal to 60%.
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The sum of two numbers is 14 and the difference between the numbers is 20. What could one of the numbers be?
The number will x=17 and y=-3 as the sum of two numbers is 14 and the difference between the numbers is 20.
What is arithmetic operation?The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out by the arithmetic operators. One operand is added to the other in addition. On the provided operands, the operator is accustomed to performing mathematical operations like addition, subtraction, multiplication, division, modulus, etc. Examples of arithmetic operators include: 5 + 3 = 8, 5 - 3 = 2, 2 * 4 = 8, etc.
Here,
x+y=14
x-y=20
subtract equation,
2y=-6
y=-3
x+y=14
x-3=14
x=17
The result will be x=17 and y=-3 because the sum of the two numbers is 14 and their difference is 20.
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