The additive counterpart of given expressions are (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.
When two numbers may be added together or multiplied, regardless of the order in which they are entered, the result is said to be commutative. There are different formulas available for the conversion of multiplicative expressions to their additive counterparts.
a) The first expression is a²b³. This expression is written as aabbb. This is of the form ab and its corresponding additive counterpart is of the form a+b.
Then, a+a+b+b+b=2a+3b.
b) The second expression is a⁻²(b⁻¹c)². This expression is of the form a⁻¹ and its corresponding additive counterpart is of the form -a.
Then,
[tex]\begin{aligned}a^{-2}(b^{-1}c)^2&=a^{-1}a^{-1}(b^{-1}c)(b^{-1}c)\\&=-a-a-b+c-b+c\\&=-2a+2(-b+c)\end{aligned}[/tex]
c) The third expression is (ab²)⁻³c²=e. This expression is first expanded as, (ab²)⁻¹(ab²)⁻¹(ab²)⁻¹c²=e. Using property, (xy)⁻¹=y⁻¹x⁻¹.
Then,
[tex]\begin{aligned}((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})c^2&=e\\(b^{-2}a^{-1})(b^{-2}a^{-1})(b^{-2}a^{-1})c^2&=e\end{aligned}[/tex]
Also, the additive identity to e is zero. And, aⁿ=na.
Then,
(-2b-a)+(-2b-a)+(-2b-a)+2c=0
Simplifying we get,
-3(a+2b)+2c=0.
The answers are (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.
The complete question is -
Translate each of the following multiplicative expressions into its additive counterpart. assume that the operation is commutative
a. a²b³
b. a⁻²(b⁻¹c)²
c. (ab²)⁻³c²=e
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evaluate the cross product (3iˆ 5jˆ)×(−3iˆ 8jˆ), which expands to −9 iˆ×iˆ 24 iˆ×jˆ−15 jˆ×iˆ 40 jˆ×jˆ. write your answer in vector form physics
The required cross product of given vectors is 39k
What is cross product?Cross product is a parallel procedure on two vectors in three-layered space. It brings about a vector that is opposite to the two vectors. The Vector result of two vectors, an and b, is meant by a × b. Its resultant vector is opposite to an and b. Vector items are additionally called cross items.
According to question:A = 3i + 5j , B = -3i + 8j
Then, cross product of A and B,
A×B = i(5×0 - 8×0) - j(3×0 - (-3)×0) + k(3×8 - (-3)×5)
A×B = i(0) - j(0) + k(24 + 15)
A×B = 39k
Thus, cross product of A and B is 39k
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⠀⠀
Walmart had 200 workers for Black Friday
but had to cut positions for after the
holidays to 152. What percent did the
amount of workers decrease?
Answer:
24%
Step-by-step explanation:
Walmart has 152/200 employees, simplify that to a number over 100, you get 76/100. 100-76=24
Answer:
Step-by-step explanation:
152/200 = .76
100-76 = 24
=24%
Therefore, the percentage the amount of workers decrease is by 24%.
Please do tell if this helps!
is it okay if you can help me out here.
Answer:
Part B:16.5
Step-by-step explanation:
Answer
b
Step-by-step explanation:
A florist has 72 red roses and 40 white roses. If the florist creates the greatest number of identical bouquets possible with a combination of red and white roses without any roses leftover, how many white roses are in each bouquet?.
The number of white roses left in each bouquet is 5.
Explain the term Greatest Common Factor?A group of numbers' greatest common factor (GCF) is the biggest factor that almost all numbers have in common. The biggest number it is a factor for two or more integers is known as the GCF.You must identify the most prevalent common factor for this task (GCF).
The actions are:
1. Divide the supplied numbers into prime factors.2. Select the usual ones, then multiply them.The florist's stock of 72 red roses with 40 white roses reveals what the most common factor is, which is:
72 = 2×2×2×3×3 = 2³×3²
40 = 2×2×2×5 = 2³×5
GCF = 2³
Divide this number of white roses in the first bouquet (40 roses) first by Greatest Common Factor to get how many white roses are in each arrangement.
The result is:
= 40 white roses / 8
= 5 white roses
Thus, number of white roses left in each bouquet is 5.
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Overall, 148 6th-grade scholars voted in the class president election. How many votes did each class president candidate receive?
The number of votes that each class president candidate receive is 59.2 votes and 88.8 votes respectively.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is primarily used to compare and determine ratios and is represented by the symbol %.
The number of votes gotten by each person will be:
A = Percentage × Number of votes
= 40% × 148
= 0.4 × 148.
= 59.2 votes.
B. = Percentage × Number of votes
= 60% × 148
= 0.6 × 148.
= 88.8 votes.
Therefore, A got 59.2 votes and B had 88.8 votes.
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Point O is the incenter of triangle A B C. Lines are drawn from the points of the triangle to point O. Lines are drawn from point O to the sides of the triangle to form right angles and line segments O Q, O R, and O S. Angle O B C is 15 degrees. Angle O C R is 30 degrees.
What is mAngleQOB?
a. 30°
b. 60°
c. 75°
d. 90°
The measure of angle QOB is 75°.
What is right angle?
90 degrees is the angle of a right.
The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol stands for a right angle.
Given:
Point O is the incenter of triangle ABC.
Lines are drawn from the points of the triangle to point O.
Lines are drawn from point O to the sides of the triangle to form right angles and line segments OQ, OR, and OS.
Angle OBC is 15 degrees. Angle OCR is 30 degrees.
OBC= 15
OCR =30
In OBQ
OBQ + QOB + OQB = 180
OBQ= OBC=15
OQB= 90
So,
QOB = 180- OBQ- OQB
= 180-15 -90
= 75
Hence, the measure of angle QOB is 75°.
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Given the piecewise function defined below; answer the questions at the bottom of the page regarding the continuity and differentiability of f at x = 1. In(52 4) + 3 for I < 1 412 for T > 1 f(c) lim f(2) I 1 lim f(z) I f( lim f' (€) I_] lim f' (1) So the function f () is Submnlt Answcr att = [
The given function is neither continuous nor differentiable at x = 1.
Given the piecewise function defined below, the function is not continuous at x = 1 because the left-hand limit is not equal to the right-hand limit. Specifically, the left-hand limit of f(x) as x approaches 1 is 3, while the right-hand limit of f(x) as x approaches 1 is 4. Furthermore, the function is not differentiable at x = 1 because the derivative does not exist at this point. This is because the derivative of the function is discontinuous at x = 1, with a derivative of 0 for x < 1 and a derivative of 1 for x > 1.
Therefore, the function f(x) is not continuous or differentiable at x = 1.
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6.
2x + 5y = -7
7x + y = -8
Answer:
(- 1, - 1 )
Step-by-step explanation:
2x + 5y = - 7 → (1)
7x + y = - 8 → (2)
multiplying (2) by - 5 and adding to (1) will eliminate y
- 35x - 5y = 40 → (3)
add (1) and (3) term by term to eliminate y
(- 35x + 2y) + (5y - 5y) = - 7 + 40
- 33x + 0 = 33
- 33x = 33 ( divide both sides by - 33 )
x = - 1
substitute x = - 1 into either of the 2 equations and solve for y
substituting into (1)
2(- 1) + 5y = - 7
- 2 + 5y = - 7 ( add 2 to both sides )
5y = - 5 ( divide both sides by 5 )
y = - 1
solution is (- 1, - 1 )
Please help me I give points
Answer:
17 degrees
Step-by-step explanation:
<ABD = 25. We know that ABD has a right triangle included. Therefore we know that 25 + 90 + <A = 180.
Therefore 115 + <A = 180.
<A = 65 degrees.
This means that part of <A = 65 degrees. The other part of <A is 44 degrees, add the two to find the whole of angle A.
65 + 44 = 109.
Angle CAD would be congruent to angle C due to alternate interior angles. meaning <C is 44 degrees. Since the angles in a triangle add up to 180 you can write the equation:
109 + 44 + <B = 180.
Combine the like terms.
163 + <B = 180.
Subtract to find angle B.
<B = 17
Complete the table: Rashida bought 3 tickets to a concert for $75. Using this rate, determine how much 1 ticket will cost? and how much 5 tickets will cost? Please write the answer like it is in the block.
In this case we are multiplying the numbers and dividing them.
Fist we got to work with are numbers given the equation.
Given:
[tex]1, 5[/tex]
Therefore, the equation is:
[tex]75 / 3\\5x3[/tex]
75 / 3 = 255 x 25 = 125Therefore, the correct answers are 1 = 25, 5 = 125 and 3 = 75
10. Find the slope of the line.
Answer: y = 1.75x - 1
Step-by-step explanation: The slope of the line is 1.75
What is the range of g(x)=-1/2 |x-6|+1? A. (-∞, 1] B. [1, ∞) C. [6, ∞) D. (-∞, ∞)
PLEASE HELP RIGHT NOW!
The required range of the given function g(x) = -1/2 |x-6| + 1 will be g(x) ≤ 1 or in internal notation form as (-∞, 1]. which is the correct answer would be an option (A).
The function is given in the question below as:
g(x) = -1/2 |x-6| + 1
We have to determine the range of the given function.
As per the given question, we have
⇒ g(x) = -1/2 |x-6| + 1
The range of an absolute function of the form:-
c|ax+b|+k is :f (x) ≤ k
In this case k = 1
⇒ g(x) ≤ 1
[tex]\mathrm{Range\:of\:}-\frac{1}{2}\left|x-6\right|+1:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\le \:1\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:1]\end{bmatrix}[/tex]
Therefore, the required range of the given function will be g(x) ≤ 1 or in internal notation form as (-∞, 1].
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If x varies inversely as y and x=32 when y=3,find y when x=11
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{llll} \textit{"x" varies}\\ \textit{inversely with "y"} \end{array}\implies x=\cfrac{k}{y}\hspace{5em}\textit{we also know that} \begin{cases} x=32\\ y=3 \end{cases} \\\\\\ 32=\cfrac{k}{3}\implies 96=k\hspace{10em}\boxed{x=\cfrac{96}{y}} \\\\\\ \textit{when x = 11, what's "y"?}\qquad 11=\cfrac{96}{y}\implies y=\cfrac{96}{11}[/tex]
a rancher has 80 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). what dimensions should be used so that the enclosed area will be a maximum?
If a rancher has 80 feet of fencing with which to enclose two adjacent rectangular corrals, then for the maximum area the dimensions will be 10 feet and 40/3 feet
From the given figure
4x + 3y = 80 feet
3y = 80 - 4x
y = (80 - 4x) / 3
The area of the rectangle
A = length × width
A = 2x × y
= 2x × (80 - 4x) / 3
Apply distributive property
= (160/3)x - (8/3)x^2
For the maximum area differentiate the values
0 = 160/3 - 16/3x
16/3x = 160/3
x = 160/3 ÷ 16/3
x = 160/3 × 3/16
x = 10 feet
The value of y = (80 - 4x) / 3
y = (80 - 4(10))/3
y = (80-40) / 3
y = 40/3 feet
Therefore, the dimensions are 10 feet and 40/3 feet
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is the sum of a certain pair of integers odd? (1) the difference between the integers is odd. (2) one of the integers is even and the other is odd.
For first case, It is even integer. The difference of odd integers is always even integer. For second case, It is odd integer. The difference of an odd and even integers is always odd integer.
What is integer?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers.
Here,
a. If there is an odd pair of integers,
for example,
=3 and 5
The difference,
5-3=2
It is even integer. The difference of odd integers is always even integer.
b. If one integer is even and other is odd,
for example,
=6 and 3
The difference,
6-3=3
It is odd integer. The difference of an odd and even integers is always odd integer.
It is an even integer in the first scenario. Odd integer differences always result in even integer differences. It is an odd integer in the second case. An odd integer is always the difference between an odd and an even integer.
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dr. rhodes notices an interaction in his factorial study. in describing this, which statement might he use to explain the link between independent variable a and independent variable b in predicting the dependent variable?
For the factorial study, Dr Rhodes can use the statement b) effect of variable A depends on variable B
In a factorial study, two intervention comparisons are undertaken side by side. As a result, in addition to behavioral treatment or standard medical care, individuals may be randomly randomized to receive either aspirin or a placebo. In factorial designs, three different sorts of outcomes are pertinent: main effects, interaction effects, and simple effects.
The primary effect is the impact of one independent variable on the dependent variable, averaged over the values of the other independent variable. Dr Rhodes can forecast the relationship between independent variables A and B using the assumption that the effect of variable A depends on variable B.
Complete question
Dr. Rhodes notices an interaction in his factorial study. In describing this, which statement might he use to explain the link between Independent Variable A and Independent Variable B in predicting the dependent variable? TRUE OR FALSE
Variable A cancels out Variable B.
The effect of Variable A depends on Variable B.
The effect of Variable A is confused by Variable B.
Variable A mainly affects Variable B.
The effect of Variable A is mediated by Variable B.
The effect of Variable A depends on Variable B.
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Assume that the height of your cylinder is 6 inches. Consider A as a function of r, so we can write that as A(r)=2πr2+12πr. What is the domain of A(r)? In other words, for which values of r is A(r) defined?
Can 'r' be 0? No, because a cylinder wouldn't exist otherwise. Because a radius on Earth cannot be endlessly vast, the highest limit would be constrained. But it is hard to say what is excessive, so I'd probably just say that the domain is r > 0.
What do you mean by a domain?
The set of values that can be plugged into a function's domain are called its parameters. The x values for a function like f are contained in this set. The collection of values that the function assumes is known as its range. Following the insertion of an x value, the function outputs this set of values. The domains of f(x)=x2 and g(x)=1/x, respectively, are all real numbers with the exception of x=0.
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Triangle ABCis transformed with the center of dilation at the origin.
Pre-image: △ABC with vertices A(−3, 4), B(−1, 12), C(4, −2)
Image: △A′B′C′with vertices A′(−0.6, 0.8), B′(−0.2, 2.4), C′(0.8, −0.4)
What is the scale factor of the dilation that maps the pre-image to the image?
Enter your answer in the box.
Answer:
take any point on the triangle and any point on the image: for now let's take point A(-3,4) A`(-0.6
Step-by-step explanation:
sf =3/4
scale factor=5
It is a function written as f(x)=b^x where bis greater than 0, b is not equal to 1, and x is any real number.
The function with the following formula is an exponential function with base b:
Given: f(x) = b^x, where b > 0, b ≠ 1 is a real number.
If r is a rational number, we can determine what b means.
An exponential function's domain is all real numbers since b^x may be defined for all real values r.
Now, all you need to know is that any positive number b^x and any real number r can be used to approximate the value of b using this approximation.
B can be any real number greater than 0 in the range.
An exponential function is always positive. And if in addition 0 < b < 1, f is a decreasing function.
Hence, f(x) decreases as x increases.
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The unit rate for inches
per centimeter is 0.39.
Answer:
The inches unit number 0.39 in converts to 1 cm, one centimeter. It is the EQUAL length value of 1 centimeter but in the inches length unit alternative.
Step-by-step explanation:
A tack of heet of tiue paper i about 2. 5 inche high each heet i about 0. 01 inch thick how many heet are in the tack
Using simple mathematical operations, we can conclude that there are 250 sheets in a stack.
What are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.
The quantity of operands affects the operation's arity.
The order of operations refers to the rules that govern how to solve an expression with several operations.
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).
So, the number of sheets in the stack is represented by n.
According to the information provided, a stack of tissue paper is roughly 2.5 inches high.
The thickness of each sheet is roughly 0.01 inches. Determine the number of sheets in the stack, please.
N sheets' thickness would be.
We'll now compare the thickness of n sheets to the thickness of the stack as follows:
0.01n = 2.5
Now, solve for n as follows:
0.01n/0.01 = 2.5/0.01
n = 250
Therefore, using simple mathematical operations, we can conclude that there are 250 sheets in a stack.
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Joey is considering two bowling membership plans. The plans are detailed here. Plan 1: $30 for a monthly pass and a $3 fee for each bowling visit Plan 2: $10 for each bowling visit Select the equation for Plan 1.
y = -10
y = 10x
y = 30x +3
3x+30
Answer:
This equation represents Plan 1, since it shows that the cost to join the plan is $30 and the cost for each bowling visit is $3.
Step-by-step explanation:
Answer: 3x + 30
Step-by-step explanation: the $3 fee depends on how many times joey goes bowling so it will be 3x + the flat $30 per month
what is the largest area of a rectangle that can be inscribed in a semicircle of radius 6? round to the nearest whole numb
The area of the largest rectangle is 46.47 square root.
Consider a semi-circle with a rectangle ABCD inscribed in it.
Let, O = centre of the semi-circle
A and B lies on the base of the semi-circle
OA = OB = x
D and C lie on the semi-circle
BC = AD = y
AB = CD = 2x
By Pythagorean theorem,
CB² + OB² = OC²
⇒ y² + x² = (6)²
⇒ y² = 36 - x²
⇒ y = √(36 - x²)
Now, area of rectangle in terms of x,
Area, A = 2x × y
= 2x × √(36 - x²)
Differentiating,
A' = 2 × √(36 - x²) - 2x²/(36 - x²)
When x = 0, y = 6 and when x = 6, y = 0, area = 0.
It implies that area is maximum when the value of x lies between 0 and 6.
This will occur where A’ = 0.
⇒ 2 × √(36 - x²) - 2x²/(36 - x²) = 0
⇒ 2 × √(36 - x²) = 2x²/(36 - x²)
On simplification, we get,
⇒ 2 × (36 - x²) = 2x²
⇒ 36 - x² = x²
⇒ 2x² = 36
⇒ x² = 36/2
⇒ x = √36/2
Now, y = √(36 - x²) becomes
⇒ y = √(36 - (√36/2)²)
⇒ y = √(36 - 36/2)
⇒ y = √(96 - 36)/2
⇒ y = √60/2
Maximum area = 2xy
= 2(√36/2)(√60/2)
= 46.47
Therefore, the area of the largest rectangle = 46.47 square units.
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Given are five observations collected in a regression study on two variables.
xi 2 6 9 13 20
yi 7 18 9 26 23
(a) Compute b0 and b1 (to 1 decimal).
b1
b0
(b) Complete the estimated regression equation (to 1 decimal).
Y^ =_ + _ x
(c) Use the estimated regression equation to predict the value of y when x = 6 (to 1 decimal).
Y^ = _?
a) The coefficients of the regression equation are given as follows:
b1 = 0.9. b0 = 7.6.b) The regression equation is defined as follows: y = 0.9x + 7.6.
c) The estimate of y when x = 6 is given as follows: y = 13.
How to obtain the regression equation?The slope-intercept definition of the regression equation is given as follows:
y = b1x + b0.
In which the parameters are given as follows:
b1 is the slope.b0 is the intercept.The points from the table in this problem are given as follows:
(2,7), (6, 18), (9,9), (13, 26), (20,23).
Inserting these points into a linear regression calculator, the equation is given as follows:
y = 0.9x + 7.6.
Then the estimate of the value of y when x = 6 is obtained as follows:
y = 0.9(6) + 7.6 = 13.
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the circumference of the base of a 5 -foot-high cylinder is 46 inches. what is the volume of the cylinder? (use the formula v
The volume of the cylinder is 10,099.09 inches³.
Here we have to find the volume of the cylinder.
Given data:
Circumference = 46 inches
height(h) = 5 foot = 12 × 5 = 60 inches
Circumference = 2πr
46 = 2 ×π × r
r = 23/π
The formula for the volume of the cylinder = πr²h
Volume = π( 23/π)² 60
= 529× 60 / π
= 10,099.09 inches³
Therefore the volume is 10,099.09 inches³.
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taxes: the internal revenue service reports that the mean federal income tax paid in the year 2010 was $8040. assume that the standard deviation is $5000. the irs plans to draw a sample of 1000 tax returns to study the effect of a new tax law. part: 0 / 50 of 5 parts complete part 1 of 5 (a) what is the probability that the sample mean tax is less than $7900? round the answer to at least four decimal places. the probability that the sample mean tax is less than $7900 is .
The probability for sample mean tax is less than $7,900 is 0.1894.
How to calculate the probability?
μ = population mean = 8,040
σ = standard deviation = 5,000
n = amount of sample = 1,000
[tex]\bar x[/tex] = sample mean = 7,900
The probability for sample mean tax can be calculated using z test formula.
P(x < 7,900) = P(z < [tex]\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex] )
= P(z < [tex]\frac{7,900 - 8,040}{\frac{5,000}{\sqrt{1,000}}}[/tex])
= P(z < [tex]\frac{-140}{\frac{5,000}{31.622}}[/tex])
= P(z < -0.88)
Using z table for P(z < -0.88). So,
= 0.1894
Thus, the probability is 0.1894 for sample tax mean is less than $7,900.
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if four residential fires are idpenently reported on a single day, what is the probability that two are in family homes, one is in an apartment, and one is in another type of dwelling
The probability that out of four residential fires who independently reported on a single day, two are in family homes, one is in an apartment, and one is in another type of dwelling is 0.0895 or 8.95%.
The multinomial distribution deals specifically with events that have multiple discrete outcomes. The multinomial distribution is not limited to events with only discrete outcomes.
We have given that
The National Fire Incident Reporting Service stated, among all residential fires.
Let consider the number of events ,
X₁---> fires residential who are in home
X₂--> fires residential who are in appartment
X₃--> fires residential who are in another type of dwelling
The probability of ae X₁ occured (p₁)
= 73% = 0.73
The probability of event X₂ occured (p₂) = 20% =0.20
The probability of event X₃ occurred (p₃) = 7% = 0.07
Four residential fires are independently reported on a single day.
we have to calculate probability that two are in family homes, one is in an apartment, and one is in another type of dwelling?
Now, Using the Multinomial distribution,
X₁= 2 , X₂= 1, X₃ = 1 and n = 4
P( X₁, X₂,-----,Xₙ ) =( n!/(X₁! X₂! ----Xₙ!) )( p₁ˣ₁ × p₂ˣ₂ × ----× pₙˣₙ)
P( 2,1,1) = 4!/2! 1! 1! ( 0.73² × 0.2× 0.07¹)
= 12 ( 0.014 × 0.5329)
= 0.0895272
Hence, the required probability is 0.089..
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Complete question:
The National Fire Incident Reporting Service stated that, among residential fires, 73% are in family homes, 20% are in apartments, and 7% are in other types of dwellings.
a) If four residential fires are independently reported on a single day, what is the probability that two are in family homes, one is in an apartment, and one is in another type of dwelling?
Factor the polynomial function over the complex numbersf(x)=x^4+9x^3+15x^2+9x+14
The polynomial function over the complex numbers is,
(x + 1i) ( x - 1i) (x+ 7) ( x + 2).
What is factoring a polynomial?
Factorization of polynomials, also known as polynomial factorization, is a mathematical and computer algebraic technique that combines irreducible factors with coefficients in the same domain to produce a polynomial with coefficients in a given field or in integers.
Consider, the given polynomial
f(x) = x^4 + 9x^3 + 15x^2 + 9x + 14
We can use a factoring "trick" here....write this as
x^4 + 9x^3 + 14x^2 + x^2 + 9x + 14 = 0 factor by grouping
x^2 ( x^2 + 9x + 14) + 1 ( x^2 + 9x + 14) = 0
(x^2 + 1) (x^2 + 9x + 14) = 0
(x^2 + 1) (x^2 + 9x + 14) = 0
⇒ (x^2 + 1) = 0, (x^2 + 9x + 14) = 0
x^2 = -1, x^2 + 7x + 2x + 14 = 0
x = ±i , x(x + 7) + 2(x + 7) = 0
x = ±i , (x + 7)(x + 2) = 0
⇒ (x + i)(x - i)(x + 7)(x - 7) = 0
(x + 1i) ( x - 1i) (x+ 7) ( x + 2) = 0
Hence, the polynomial function over the complex numbers is,
(x + 1i) ( x - 1i) (x+ 7) ( x + 2).
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What is the unit rate for 20 pounds for $4.00? Which answer is correct?
(1): 5 pounds/$1.00
(2): 4 pounds/$1.00
(3): 1 pound/$4.00
(4): 1 pound/$5.00
What is the unit rate for 20 pounds for $4.00? Which answer is correct?
(1): 5 pounds/$1.00
(2): 4 pounds/$1.00
(3): 1 pound/$4.00
(4): 1 pound/$5.00
determine the equation of the ellipse with foci (2,4)(2,4) and (2,-8)(2,−8), and co-vertices (10,-2)(10,−2) and (-6,-2)(−6,−2).
The equation of the ellipse with given foci (2,4) and (2,-8) and co-vertices (10, -2) and ( -6 , -2) is equal to (x - 2)²/40 + ( y + 2)²/36 = 1.
As given in the question,
Given foci of the ellipse :
( 2,4) and ( 2, -8)
Co-vertices of the ellipse :
( 10,-2) and (-6 , -2)
From the given foci and vertices ,
Centre 'c' = 2
b = 6
( h, k) = (2, -2)
a² = c² + b²
⇒a² = 4 + 36
⇒a = √40
⇒a = 2√10
Equation of the ellipse is given by:
( x - h)²/ a² + (y - k)²/b² =1
⇒( x - 2)²/ (2√10)² + (y + 2)²/6² = 1
⇒( x - 2)²/ 40 + (y + 2)²/36 = 1
Therefore, equation of the ellipse is equal to (x - 2)²/ 40 + (y +2)²/36 = 1.
The complete question is:
Determine the equation of the ellipse with foci (2,4) and (2,−8), and co-vertices (10,−2) and(−6,−2).
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