The value of [tex]tan^{-1}(0.2)[/tex] = -0.19739 + ... i.e. [tex]tan^{-1} (0.2)= (0.2) - \frac{(0.2)^{3} }{3} +\frac{(0.2)^{5} }{5} -\frac{(0.2)^{7} }{7}+...[/tex]
The power series of [tex]tan^{-1}(x)[/tex] obtained in example 6 is called the Gregory's series. The Gregory series is an infinite series of fractions or rational numbers
After the Scottish mathematician James Gregory (1638-1675) who had anticipated some of Newton's discoveries we have shown that the Gregory's series is valid when -1 < x < 1.
But it turns out (although it isn't easy to prove) that it is also valid when:
x = 1 or ≠ 1.
According to Example 6, The radius of convergence of the series for
[tex]1/(1 +x^{2} )[/tex] is 1, the radius of convergence of this series for [tex]tan^{-1}(x)[/tex] is also 1.
[tex]tan^{-1} x = x - \frac{x^{3} }{3} +\frac{x^{5} }{y} -\frac{x^{7} }{y} +....[/tex]
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grandma famous punch uses a ratio of 5 cups of cranberry juice and 2 cups of sprite. if she needs a total of 56 cups of famous punch how amy cups of cranberry and how many cups of sprite to make 56 cups of punch
You will need 280 cups of cranberry juice and 56 cups of Sprite to make 56 cups of the famous punch.
What is the ratio definition?
A ratio is a mathematical comparison of two or more values or quantities. It is usually written as a fraction, with the first value or quantity being the numerator and the second value or quantity being the denominator.
To make 56 cups of famous punch using the ratio of 5 cups of cranberry juice to 2 cups of Sprite, you can use the following method:
Write the ratio of cranberry juice to Sprite as a fraction: 5 cups cranberry juice / 2 cups sprite
Multiply the fraction by the desired number of cups of punch: (5 cups cranberry juice / 2 cups sprite) x 56 cups punch
Simplify the equation by cross-multiplying: 5 cups cranberry juice x 56 cups punch = 2 cups sprite x 56 cups punch
Solve for the number of cups of cranberry juice: 5 cups cranberry juice x 56 cups punch = 280 cups of cranberry juice
To find the amount of Sprite use the ratio 5:2, meaning you have to use 2 cups of sprite for every 5 cups of cranberry juice. So use 280/5*2 = 56 cups of sprite
Hence, you will need 280 cups of cranberry juice and 56 cups of Sprite to make 56 cups of the famous punch.
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A dozen mangos and a pizza cost $2.70.
Half a dozen mangos and 2 pizzas cost $3.75.
What is the cost of a pizza?
Answer the question and show steps.
Select the law that shows that the two propositions are logically equivalent. -((w V p) ^(-91q1w)) -(w V p) v-(-91qAw) a. DeMorgan's law b. Distributive lawc. Associative law d. Complement law
The rule demonstrating the logical equality of the two claims. -((w V p) ^(-91q1w)) DeMorgan's law has the form -(w V p) v-(-91qAw).
What is meant by DeMorgan's law?By using their opposites, De Morgan's Laws explain how mathematical assertions and concepts are connected. The intersection and union of sets are connected by complements according to De Morgan's Laws in set theory. The De Morgan's Laws are rules of propositional logic that use negation to connect conjunctions and disjunctions of propositions.The complement of the intersection of the complements of two sets A and B is equal to the complement of the union of two sets A and B, according to De Morgan's first law. According to De Morgan's Law, "(P and Q)" and "not (not P or not Q)" are logically equal. If they are logically similar, then it should follow that "(P and Q)" implies "not (not P or not Q)," and "not (not P or not Q)" implies "(P and Q)".To learn more about DeMorgan's law, refer to:
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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 9 cubic feet and the volume of each large box is 12 cubic feet. A total of 20 boxes of paper were shipped with a combined volume of 216 cubic feet. Graphically solve a system of equations in order to determine the number of small boxes shipped, x,x, and the number of large boxes shipped, yy.
The number of large box is 12 and small box is 8.
What is cube?
The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.
Given :
The volume of small box is 9 cubic feet
The volume of the large box is 12 cubic feet
The volume of all box is 216 cubic feet
There are 20 boxes of paper shipped.
Total Volume covered by small box will be 9x
Total Volume covered by large box will be 24x
Total volume shipped = 216
9x + 24x = 216
33x = 216
x = 6
So The number of large box is 12 and small box is 8.
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Please help me!! It is 5 questions
1. 80 people attended only the FSU-Butler game.
2. 165. Since it's not possible to have negative number of people, the answer is 0.
3. 210 people attended at least two of these games.
4. 340 people attended the Marist and Butler games, but not the North Carolina State game.
5. 365 people attended the North Carolina State or the Butler game
How do you calculate this vendiagram? We know that 215 people attended the FSU-Butler game, and that 70 of them also attended the NC State game and 65 of them also attended the Marist game. So, 215 - 70 - 65 = 80 people attended only the FSU-Butler game.We know that 460 people were surveyed in total, and 190, 215, and 220 attended the Marist, Butler and NC State games respectively. The number of people who attended at least one of these games is 190 + 215 + 220 = 625. Thus, 460 - 625 = -165. Since it's not possible to have negative number of people, the answer is 0.We know that 65 people attended the Marist and NC State games, 70 people attended the NC State and Butler games, and 65 people attended the Butler and Marist games. 10 people attended all three games. So, 65 + 70 + 65 + 10 = 210 people attended at least two of these games.We know that 190 people attended the Marist game, 215 people attended the Butler game, and 65 people attended both the Marist and Butler games. So, 190 + 215 - 65 = 340 people attended the Marist and Butler games, but not the North Carolina State game.We know that 220 people attended the North Carolina State game and 215 people attended the Butler game. 70 people attended both the North Carolina State and Butler game. So, 220 + 215 - 70 = 365 people attended the North Carolina State or the Butler game.To learn more about venn diagram refer
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based on your calculated values, what can we say about the percentage of students using ipads in public school districts?
Relative to the mean, there are some school districts where many students are using ipads.
What is called the mean?
The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. It is sometimes referred to as the "average" and is the most widely used central tendency metric.
Simply dividing the total number of values in a data set by the sum of all of the values yields it. The calculation can be performed on unprocessed data or data that has been combined into a frequency table.
By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.
Mean: The "average" number; found by adding all data points and dividing by the number of data points. Example: The mean of 4, 1, and 7 is ( 4 + 1 + 7 ) / 3 = 12 / 3 = 4 (4+1+7)/3 = 12/3 = 4 (4+1+7)/3=12/3=4left parenthesis, 4, plus, 1, plus, 7, right parenthesis, slash, 3, equals, 12, slash, 3, equals, 4.
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write an equivalent expression for 4(w-5)
Answer:
4w - 20
Step-by-step explanation:
hope this help i guess
A 400 g sample is composed of 100 g of cesium (Cs) and 300 g of iodine (1).
What is the percent by mass of Cs in the sample?
A. 50.0%
B. 70.0%
C. 25.0%
D. 75.0%
Answer: C. 25%
Step-by-step explanation: This is a basic probability problem. First, you must find the total which is in question. 400 grams is the total in this case. The Cs make up 100 grams of this. Next, you put the part over the whole, and divide. 100/400= 0.25. When you want to find the probability with the probability sign, you move the decimal place two points to the right and then add the sign. Hence, 25%.
The length of a piece of string is x cm long. Another piece measures x+5cm long. If the second piece is 20% longer than the first,calculate the value of x.
Answer:
x = 25 cm
Step-by-step explanation:
20% =
20/100 = 0.20
20% longer =
20% + 100% =
120% =
120/100 = 1.20
Hence, x+5 is 1.20 times that of x:
x * 1.20 = x + 5
1.2x = x + 5
1.2x - x = 5 ==> subtract x on both sides to move x to one side of the
equation
1.2x - 1x = 5 ==> 1x = x
(1.2 - 1)x = 5 ==> distribution property
0.2x = 5
x = 25 ==> multiply both sides by 5 ( 0.2 * 5 = 1 )
A recipe for soup calls for 6 tablespoons of lemon juice and cup of olive oil. The given recipe serves 4 people, but a cook wants to make a larger batch that serves 40
a) How many cups of lemon juice will the chef need for the larger batch?
b) How many pints of olive oil will the chef need for the larger batch?
a) The chef needed
(Type a whole number,
cups of lemon juice for the larger batch.
proper fraction, or a mixed number.)
b) The chef needed
pints of olive oil for the larger batch.
(Type a whole number, proper fraction, or a mixed number.)
The chef needed a) 3¾ cups of lemon juice and b) 20 pints olive oil for the larger batch.
What is mixed fraction?A mixed fraction is one that has both its quotient and remainder represented. A mixed fraction like 2 1/3 is one where the remainder is 1 and the quotient is 2. Therefore, a mixed fraction is made up of both a whole number and a correct fraction.
The recipe was for 4 person, but now here are 40
The scale multiple is = 40/4
= 10
a) As 1 cup = 16 tablespoon
The number of tablespoon of lemon required for 40 men = 6 × 10
= 60
Converting to cup = 60/16
= 3¾ cups
b) As 1 cup = 0.5 pints
The number of cups of olive oil required for 40 men = 1 × 10
= 10
Converting to pints = 10/0.5
= 20 pints
Thus, The chef needed 3¾ cups of lemon juice and 20 pints olive oil for the larger batch.
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Two factory outlets F_2 and F_2 in New York and Los Angeles sell sofas (S), chairs (C), and tables (T) with a profit of $35, $62, and $30, respectively. Let the sales in a certain week be given by the matrix A = [S 400 C 60 T 240] F_1 Introduce a "profit vector" such that the components of = give the total profits of F_1 and F_2
The total profit of F_1 in the week was $25920 and the total profit of F_2 in the week was $0.
The profit vector can be expressed as p = [35 62 30]. The total profit of F_1 and F_2 can be calculated by multiplying the matrix A by the vector p. The result, Ap, is a vector whose components give the total profits of the two stores in the week.
For example, the total profit of F_1 can be calculated as Ap_1 = [35 62 30] * [400 60 240] = [14000 3720 7200] = 25920.
Similarly, the total profit of F_2 can be calculated as Ap_2 = [35 62 30] * [0 0 0] = [0 0 0] = 0.
Therefore, the total profit of F_1 in the week was $25920 and the total profit of F_2 in the week was $0.
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44+ 7/8r when r = -1/2
[tex]44+\cfrac{7}{8}r\implies 44+\cfrac{7}{8}\left( -\cfrac{1}{2} \right)\implies 44-\cfrac{7}{16}\implies \cfrac{(16)44~~ - ~~(1)7}{\underset{\textit{we'll use this LCD}}{16}} \\\\\\ \cfrac{704~~ - ~~7}{16}\implies \cfrac{697}{16}\implies 43\frac{9}{16}[/tex]
The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 20.
According to the standard deviation rule, ____% of people have an IQ between 80 and 120. Do not round.
Using the Empirical Rule, it is discovered that the proportion of people in a population with IQs ranging from 80 to 120 is 0.95 = 95%.
What is Empirical Rule?It specifies the following for a normally distributed random variable:
68% of the measurements are within one standard deviation of the mean.
95% of the measurements are within 2 standard deviations of the mean.
99.7% of the measurements are within 3 standard deviations of the mean.
Given a mean of 100 and a standard deviation of 20, we can calculate:
80 = 100 - 2 x 20.
120 = 100 + 2 x 20.
Because these are both the most extreme values within two standard deviations of the mean, then the proportion of people in a population with IQ scores between 80 and 120 is 0.95 = 95%.
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a segment is created from points a and b. to copy segment ab, which of the following needs to be identified for the construction? the distance between point a and a point not on the segment the midpoint of points a and b the midpoint between point b and a point not on the segment the distance between points a and b
The correct answer among the following option is , the distance between point a and b of segment ab.
What are Points?
A point is denoted by a dot(.). A point represents position only. It has no size.
Points given in the question are a and b.
What is Line Segment?
A line segment is a part of line with a definite start point and a definite end point.
Their are infinite number of point between the end and start point of the segment.
For the construction,
To copy the segment ab, The distance between the two points a nd b is required.
To calculate the distance, Use the distance formula if the co-ordinates of point a and b are given.
The distance can also be measured using a measuring instrument like
a ruler, A measuring tape if the co-ordinates are not given.
As the distance between both the points a and b is known, A new segment can be drawn of the same distance as ab using two new points and can be named cd or a'b'.
To copy the segment ab, The distance between the point a and b is required.
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Answer:the distance between points a and b
Step-by-step explanation: took the test and got it right
Recall the equation for a circle with centre (h,k) and radius r. At what point in the first quadrant does the line with equation y=1.5x+5 intersect the circle with radius 5 and centre (0,5)?
The equation for the circle is (x-h)^2 + (y-k)^2 = r^2. Substituting the values, we get (x-0)^2 + (y-5)^2 = 25.
Substituting y=1.5x+5 into the equation, we get (x-0)^2 + (1.5x+5-5)^2 = 25
Simplifying, we get 1.5x^2 +15x+25=25
Solving, we get x=1.
Therefore, the point of intersection is (1,1.5).
The line y=1.5x+5 intersects the circle with radius 5 and centre (0,5) at the point (1,1.5) in the first quadrant.
The equation for a circle with centre (0,5) and radius 5 is (x-0)^2 + (y-5)^2 = 25. When this equation is combined with the line equation y=1.5x+5, it can be solved to find that the line intersects the circle at the point (1,1.5), which is located in the first quadrant.
The equation for the circle is (x-h)^2 + (y-k)^2 = r^2. Substituting the values, we get (x-0)^2 + (y-5)^2 = 25.
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regina takes yoga classes 2days a week at the community center
The option that will cost less money from Regina is $8 a class.
How to calculate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
Since the cost for the classes at the community center is $72, plus an additional one-time fee of $12 to rent
the yoga equipment used in class. The amount will be:
= $72 + $12
= $84
The other cost at $8 a class for 2 weeks will be:
= $8 × 10 days
= $80
The second option is cheaper.
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Yoga classes are offered 2 days a week for 6 weeks
at both the community center and the local gym.
The cost for the classes at the community center is
$72, plus an additional one-time fee of $12 to rent
the yoga equipment used in class. The cost at the
local gym is $8 a class. Regina wants to know which
class she can take for less money.
Simplify the following expression. 7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}
The term, [tex]\frac{1}{49}[/tex] is simplified form of the expression [tex]7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}[/tex].
What is simplest form?The top and bottom of a fraction are said to be in its simplest form if they only share the number one. For the top & bottom to remain whole numbers, you cannot divide them further.
Additionally, lowest terms, or simple form, may be used.
The simplest form of a fraction, for instance, is 4/5. Apart from 1, there isn't a number that divides both 4 and 5. Not in its simplest form is the fraction 3/6. Numerator & denominator can both be divided by 3.
Given to simplify the expression
[tex]7^{-\dfrac{5}{6}} \ \cdot\ 7^{-\dfrac{7}{6}}[/tex]
[tex]7^{(-\dfrac{5}{6}-\dfrac{7}{6})}[/tex]
[tex]7^{(\dfrac{-5-7}{6})}[/tex]
[tex]7^{(\dfrac{-12}{6})}[/tex]
[tex]7^{(-2)}[/tex]
[tex]\dfrac{1}{7} \times \dfrac{1}{7}[/tex]
[tex]\dfrac{1}{49}[/tex]
Thus, [tex]\frac{1}{49}[/tex] is simplified form of the expression [tex]7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}[/tex].
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The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65° E, and the two towers are 29 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80° E from the Pine Knob and S 70° E from Colt Station (see figure). Find the distance of the fire from each tower. (Round your answers to two decimal places.)
From Pine Knob:
The distance of the fire from each tower is:
i. From Pine Knob: 41 kilometers
ii. From Colt Station: 15 kilometers
What is Bearing?Bearing as a topic in mathematics can be used to determine the exact position or location of an object considering its angle of position and distance to a reference point.
Considering the given question; let the distance of the fire (F) from Pine knob (PK) be represented by x, and that from Colt Station (CS) be represented by y.
Angle at PK = 80 - 65
= 15^o
Angle at CS = 65 + 70
= 135^o
Angle at F can be determined as;
15 + 135 + F = 180 (sum of angle in a triangle)
150 + F = 180
F = 30^o
So that applying the Sine rule to determine the distances of the fire from PK and CS, we have;
a/Sin A = b/Sin B = c/Sin C
29/Sin 30 = y/Sin 15 = x/ Sin 135
29/Sin 30 = y/Sin 15
y = (29*Sin 15)/ Sin 30
= 7.5052/ 0.5
= 15.0104
y = 15 kilometers
29/Sin 30 = x/Sin 135
x = (29*Sin 135)/ Sin 30
= 20.5059/ 0.5
= 41.0118
x = 41 kilometers
Therefore, the distance from Pine Knob to the fire is 41 kilometers. While the distance from Colt Station to the fire is 15 kilometers.
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A ball has a radius of 3 in how much air can the ball hold
Answer:
v = 113.04 [tex]units^{3}[/tex]
Step-by-step explanation:
v = 4/3[tex]\pi r^{3}[/tex]
v = 4/3[tex]\pi 3^{3}[/tex]
v = 113.04 [tex]units^{3}[/tex]
I need help on getting an answer for "Y"
Answer: 50
Step-by-step explanation:
You can plug in 4 for any of the equations given.
y = 10 + 10(4)
y = 10 + 40
y = 50
OR
y = 30 + 5(4)
y = 30 + 20
y = 50
Answer:
y = 50
Step-by-step explanation:
Since x = 4, plug the value into either equation.
[tex]y =10+10x\\y = 10 + 10(4)\\y=10+40\\y=50[/tex]
Therefore, y equals 50.
75% of the Pottery Club members paid their $5.00 dues. If there are 48 members, how many members paid?
Answer:
36 members paid the total money that would be made would be $180
Step-by-step explanation:
48*75%=36
36*5=180
If f(x) = 5x²-3x + 3, find f'(1).
[tex]f(x)=5x^2-3x+3\implies \left. \cfrac{df}{dx}=10x-3 \right|_{x=1}\implies 10(1)-3\implies 7[/tex]
A poll is given, showing 80% are in favor of a new building project.If 9 people are chosen at random, what is the probability that exactly 3 of them favor the new building project?
help quick!!!!!!
Answer: 30%
Step-by-step explanation:
because e9 people are chosen and 9 divided by 3 is 3 and 3 x 10 =30
What is 2×21 using the distributive property
Answer:
42 is the answer
Step-by-step explanation:
for distributive property of multiplication you could use...
2 x 3 x 7
as 3 x 7 is 21
(07.04 mc) which of the following is the solution to the differential equation dy over dx equals 2 times x times y all over quantity x squared plus 1 end quantity comma with the initial condition y(3)
The solution to the differential equation with the initial condition given is y(x)= (x² + 1)⁴.
Step 1: The given differential equation is dy/dx = 2xy/(x² + 1). Rearranging the equation, we get dy = 2xy dx/(x² + 1).
Step 2: Integrating both sides, we get ∫dy = ∫2xy dx/(x² + 1). On the left side, we have ∫dy = y + C, where C is the constant of integration. On the right side, we have ∫2xy dx/(x² + 1) = x² y + C.
Step 3: Substituting the initial condition y(3) = 6 in the solution, we get 6 = 3² y + C. Solving for C, we get C = 6 - 9y.
Step 4: Substituting C = 6 - 9y in the solution, we get y(x) = (x² + 1)⁴
The solution to the differential equation with the initial condition given is y(x)= (x² + 1)⁴.
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What is the sum of 3+3+
Answer:
0
Step-by-step explanation:
I believe this is correct. Since they don't have the same sign then you will just have to subtract them.
Answer: 6
Step-by-step explanation:
Queen Laetitia is sorting her gem collection. She starts by placing some of her
diamonds into two boxes. In every box after the first two, the Queen puts as many
diamonds as in the previous two boxes combined. If there are 30 diamonds in the
fourth box, and 128 diamonds in the seventh box, how many diamonds did
Queen Laetitia place in the tenth box?
Answer:
Step-by-step explanation:
Let's represent the missing number with "---" -- so we have so far:
--- --- --- 30 --- --- 128 --- --- ?
Now, let's say 5th position number is x and 6th position number is y
So, we have 30 + x = y and x+ y = 128
Combining these 2 equation, we get: x + 30 + x = 128 or x = 49, so y = 79
thus from 4th position, the series can be written as
30, 49, 79, 128, 207, 335, 542....
Thus, at 10th position we will have 542 !!!
Assume that 13% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below.
a) The first lefty is the fifth person chosen.
b) There are some lefties among the 5 people.
c) The first lefty is the second or third person.
d) There are exactly 3 lefties in the group.
e) There are at least 3 lefties in the group.
f) There are no more than 3 lefties in the group.
The first lefty is the fifth person chosen is7.45%
There are some lefties among the 5 people is, 50.16%
What is probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability. A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.The first lefty is the fifth person chosen is
[tex](.87)^4(.13)=.07447=7.45 \%[/tex]
There are some lefties among the 5 people is,
[tex]$$1-(.87)^5=.50157=50.16 \%$$[/tex]
The first lefty is the second or third person.
[tex]$(.87)(.13)+(.87)^2(.13)=.211497=21.15 \%_0$[/tex]
There are exactly 3 lefties in the group.
[tex]$(5, .13,3)=.0166=1.66 \%$[/tex]
There are at least 3 lefties in the group,
[tex]1 \text { - binomadf }(5, .13,2)=.0179=1.79 \%[/tex]
There are no more than 3 lefties in the group
[tex]\text { binomcdf }(5, .13,3)=.9987=99.87 \%[/tex]
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Answer all of these I forgot them
A function built from pieces of different functions over different intervals.
How does one locate the piecewise specified formula?Finding a Piecewise Function’s Equation: Find the equation for both y=mx+b lines. If there is an O, the equation is > or; if there is a •, the equation is or. In the equation, the line represents X.
A piecewise function is one that is constructed from parts of distinct functions at different intervals. For example, we may write a piecewise function f(x) that returns -9 when -9 x -5, 6 when -5 x -1, and -7 when -1.
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1/4(x - 12) use your understanding of writing expressions to translate the expression
The expansion of 1/4(x - 12) is x/4 - 3
What is expansion of expression?In order to expand and simplify an expression, we need to multiply out the parentheses and then simplify the resulting expression by collecting the like terms. Expanding brackets (or multiplying out) is the process by which we remove parentheses. It is the reverse process of factorisation.
For example 4(3-y) can be expanded by multiplying the factor 4 by 3 and y = 12- 4y
Similarly the expression 1/4(x - 12) can be expanded by firstly multiply the factor ¼ by x and 12
therefore 1/4(x - 12) = 1/4×x -12×1/4
= x/4 - 3
Therefore the expansion of 1/4(x - 12) is x/4 -3
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