Answer:
I'm going to help you figure this out because I am actually on the same assignment. If you do not understand what it is asking, it is not asking you to break down the function notation, it is simply asking you to substitute (X) with 2,3,4,5,and 6 and then to solve it on each line
A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected (without replacement).
Answer:
The probability of getting two good coils is 77.33%.
Step-by-step explanation:
Since a batch consists of 12 defective coils and 88 good ones, to determine the probability of getting two good coils when two coils are randomly selected (without replacement), the following calculation must be performed:
88/100 x 87/99 = X
0.88 x 0.878787 = X
0.77333 = X
Therefore, the probability of getting two good coils is 77.33%.
The sum of two numbers is 85. If four times the smaller number is subtracted from the larger number, the result is 5. Find the two numbers.
The larger number is
The smaller number is
Answer:
the larger number is 69
the smaller number is 16
Step-by-step explanation:
x is the smaller number
y is the larger number
x + y = 85
y - 4x = 5
y = 5 + 4x
x + 5 + 4x = 85
5x = 80
x = 16
y = 69
T=3 and t=5 to determine if the expression 4(t+3) and 4 t+12 are equivalent
4. How many square feet of carpet are
needed?
The floor plan below shows the Green family's
basement
28 ft.
12 ft.
121
6 ft.
5 ft.
5 ft.
11 ft.
11 ft.
Answer:
Step-by-step explanation:
It is a 28×12 rectangle, minus a 5×6 cutout.
area of 28×12 rectangle = 336 ft²
area of 5×6 cutout = 30 ft²
area of carpet = 336-30 = 330 ft²
Using the following image, solve for x.
Answer:
please provide an image.
What is the value of x in the figure below? If necessary, round your answer to
the nearest tenth of a unit.
X
15
D 4 B
A. 7.7
B. 3.8
O C. 15
D. 4
Answer:
Step-by-step explanation:
Please Help NO LINKS
[tex]V = 864\pi[/tex]
Step-by-step explanation:
Since one of the boundaries is y = 0, we need to find the roots of the function [tex]f(x)=-2x^2+6x+36[/tex]. Using the quadratic equation, we get
[tex]x = \dfrac{-6 \pm \sqrt{36 - (4)(-2)(36)}}{-4}= -3,\:6[/tex]
But since the region is also bounded by [tex]x = 0[/tex], that means that our limits of integration are from [tex]x=0[/tex] (instead of -3) to [tex]x=6[/tex].
Now let's find the volume using the cylindrical shells method. The volume of rotation of the region is given by
[tex]\displaystyle V = \int f(x)2\pi xdx[/tex]
[tex]\:\:\:\:\:\:\:= \displaystyle \int_0^6 (-2x^2+6x+36)(2 \pi x)dx[/tex]
[tex]\:\:\:\:\:\:\:= \displaystyle 2\pi \int_0^6 (-2x^3+6x^2+36x)dx[/tex]
[tex]\:\:\:\:\:\:\:= \displaystyle 2\pi \left(-\frac{1}{2}x^4+2x^3+18x^2 \right)_0^6[/tex]
[tex]\:\:\:\:\:\:\:= 864\pi [/tex]
Can someone help me out here? Not sure how to solve this problem or where to start either?
Answer:
19.3 miles per gallon
Step-by-step explanation:
First, subtract 54,042.8-53,737.7. The answer is 305.1
Then, find the unit rate. 305.1/15.8
You get 19.31012658. The prompt says to round to the nearest tenth, so round, and you get 19.3.
That's your answer!
We roll a pair dice 10,000 times. Estimate the probability that the number of times we get snake eyes (two ones) is between 280 and 300.
Answer:
0.3573 = 35.7%
Step-by-step explanation:
We roll a pair of dice 10,000 times so the mean and standard deviation is,
μ = 10000/36 =277.7 σ = [tex]\sqrt{10000*\frac{35}{36^{2} } } =16.4[/tex]
[tex]z_{1}[/tex] = (280 - 277.7)/16.4 = .14
[tex]z_{2}[/tex] = (300 - 277.7)/16.4 = 1.35
Probablity (range)
0.3573
Z(low)=0.14 0.555766357
Z(upper)=1.36 0.91304644
Exercise 2.2.3: The cardinality of a power set. (a) What is the cardinality of P({1, 2, 3, 4, 5, 6})
Answer:
Cardinality of the power set of the given set = [tex]2^6=64[/tex]
Step-by-step explanation:
Power set is the set of all the possible subsets that can be formed from the given set including the null set and the set itself.
Example set:
{1,2,3}
All the possible subsets of this set:
{}; {1}; {2}; {3}; {1,2,3}; {1,2}; {1,3}; {2,3}
The power set of the above set is written as:
P({ {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} })
Since the no. of elements in the above power set in this example is 8 therefore its cardinality is 8.
Cardinality of the power set of a given set is expressed by a formula: [tex]2^n[/tex]
where n is the cardinality (no. of elements) of the given set whose power set is to be formed for determining cardinality of the power set.
Hence in the given case, we have n = 6.
09:30 am - 4:30 pm minus 30 minutes?
How many hours is that ?
0.9.30 am to 4.30 p.m. is 7 hours.
If we minus 30 minutes from it then it is 6 hours 30 minutes.
A cookie recipe that yields 24 cookies requires 1 3/4 cups of butter. When the ingredients in this recipe are increased proportionally, how many cups of butter are required for the recipe to yield 72 cookies?
Answer:
5 1/4
Step-by-step explanation:
* is multiplication
1 3/4 is 1.75
so
24/1.75 = 72/×
1.75 * 72 = 24 * x
126 = 24x
24x = 126
x = 5.25 or 5 1/4
Total [tex]5\frac{1}{4}[/tex] cups of butter required to make 72 cookies.
What is unitary method?The unitary method is a process of finding the value of a single unit, and based on this value; we can find the value of the required number of .
According to the given question.
Number of cups or butter required for making 24 cookies = [tex]1\frac{3}{4} =\frac{7}{4}[/tex]
⇒ Number of cups of butter required to make 1 cookie = [tex]\frac{\frac{7}{4} }{24} =\frac{7}{(24)(4)}[/tex]
Therefore,
The number of cups of butter required to make 72 cookies
= [tex]72[/tex] × [tex]\frac{7}{(24)(4)}[/tex]
= [tex]\frac{21}{4}[/tex]
= [tex]5\frac{1}{4}[/tex]
Hence, total [tex]5\frac{1}{4}[/tex] cups of butter required to make 72 cookies.
Find out more information about unitary method here:
https://brainly.com/question/22056199
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The perimeter of a square and rectangle is the same. The width of the rectangle is 6cm and it's area is 16cmsquare less than the area of the square. Find the area of the square
Answer:
Area of square = 100 square cm
Step-by-step explanation:
Let the sides of a square be = a
Perimeter of a square = 4a
Let area of square = [tex]a^2[/tex]
Let the Length of rectangle be = [tex]l[/tex]
Given: width of the rectangle = 6 cm
Area of rectangle = length x breadth
Perimeter of rectangle and square is equal.
That is,
[tex]2(length + width) = 4a\\\\2(l + 6) = 4a\\\\l + 6 = 2a\\\\l = 2a - 6[/tex]
Therefore ,
Area of rectangle
[tex]= Length \times width \\\\= (2a - 6) \times 6\\\\=6(2a - 6)[/tex]
Given area of rectangle is 16 less than area of square.
That is ,
[tex]( 6(2a- 6) ) = a^2 - 16\\\\12a - 36 = a^2 - 16\\\\a^2 - 12a +20= 0\\\\a^2 - 2a -10a + 20 = 0\\\\a(a - 2) - 10(a - 2) = 0\\\\(a -10) ( a-2) = 0\\\\a = 10 , \ a = 2[/tex]
Check which value of 'a ' satisfies the equation:
[tex]\underline {when \ a = 2 }\\\\Length\ of \ rectangle \ l = 2a - 6 = 2 ( 2 ) - 6 = 4 - 6 = - 2. \\\\Length \ cannot \ be \ negative \ number. \\\\ \underline{ when \ a = 10 }\\\\Length \ of \ rectangle \ , l = 2a - 6 = 2 (10) - 6 = 20 - 6 = 14\\\\satisfies \ the \ conditions. \\\\Therefore , a = 10[/tex]
That is , side of the sqaure = 10
Therefore , area of the square = 10 x 10 = 100 square cm.
A club of 10 people wants to choose an executive board consisting of president, secretary, treasurer, and three other officers. In how many ways can this be done
Answer:
The number of ways = 151200
Step-by-step explanation:
Below is the calculation of the number of ways:
Total number of people = 10
Total number of posts = 6
The number of ways = 10P6
The number of ways = [tex]\frac{10!}{10! - 6!}[/tex]
The number of ways = 10 x 9 x 8 x 7 x 6 x 5
The number of ways = 151200
An unconditional acceptance into a graduate program at a university will be given to students whose GMAT score plus 100 times the undergraduate grade point average is at least 1075. Robbin's GMAT score was 800. What must her grade point average be in order to be unconditionally accepted into the program?
Robbin's grade point average must be at least ___ in order to be unconditionally accepted into the program.
Answer:
Robbin's grade point average must be at least 2.75 in order to be unconditionally accepted into the program.
Step-by-step explanation:
An unconditional acceptance into a graduate program at a university will be given to students whose GMAT score plus 100 times the undergraduate grade point average is at least 1075
Considering the GMAT score x, and the GPA y, this situation is modeled by the following inequality:
[tex]x + 100y \geq 1075[/tex]
Robbin's GMAT score was 800.
This means that [tex]x = 800[/tex], and thus:
[tex]x + 100y \geq 1075[/tex]
[tex]800 + 100y \geq 1075[/tex]
[tex]100y \geq 275[/tex]
What must her grade point average be in order to be unconditionally accepted into the program?
Solving the above inequality for y:
[tex]100y \geq 275[/tex]
[tex]y \geq \frac{275}{100}[/tex]
[tex]y \geq 2.75[/tex]
Thus:
Robbin's grade point average must be at least 2.75 in order to be unconditionally accepted into the program.
Tell whether ΔABC and ΔDCB can be proven congruent.
A. Yes, ΔABC and ΔDCB can be proven congruent by SSS.
B. Yes, ΔABC and ΔDCB can be proven congruent by HL.
C. No, ΔABC and ΔDCB aren’t congruent because they share a side.
D. No, there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.
Answer:
D. No, there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.
prove that the square of an odd number is always 1 more than a multiple of 4
Answer:
By these examples you are able to see that the square of an odd number is always 1 more than a multiple of 4.
Step-by-step explanation:
For examples,
Let's consider squares of 3, 11, 25, 37 and 131.
[tex] {3}^{2} = 9[/tex]
8 is a multiple of 4, and 9 is more than 8.
[tex] {11}^{2} = 121[/tex]
120 is a multiple of 4 and 121 is one more than it.
[tex] {25}^{2} = 625[/tex]
624 is a multiple of 4 and 625 is one more than it.
[tex] {37}^{2} = 1369[/tex]
1368 is a multiple of 4 and 1369 is one more than 1368.
[tex] {131}^{2} = 17161[/tex]
17160 is a multiple of 4.
Choose the system of inequalities that best matches the graph below.
Answer:
"D" is the correct answer
Step-by-step explanation:
Change 9/3 to percentage
Answer:
300%
Step-by-step explanation:
because 9/3×100=900/3=300 so it is 300%
Answer:
300%
Step-by-step explanation:
9/3 * 100%
900%/3 = 300%
Suppose a large telephone manufacturer has a problem with excessive customer complaints and consequent returns of the phones for repair or replacement. The manufacturer wants to estimate the magnitude of the problem in order to design a quality control program. How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence
Answer:
80 telephones should be sampled
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
89% confidence level
So [tex]\alpha = 0.11[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.11}{2} = 0.945[/tex], so [tex]Z = 1.6[/tex].
How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence?
n telephones should be sampled, an n is found when M = 0.09. We have no estimate for the proportion, thus we use [tex]\pi = 0.5[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.09 = 1.6\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.09\sqrt{n} = 1.6*0.5[/tex]
[tex]\sqrt{n} = \frac{1.6*0.5}{0.09}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.6*0.5}{0.09})^2[/tex]
[tex]n = 79.01[/tex]
Rounding up(as 79 gives a margin of error slightly above the desired value).
80 telephones should be sampled
For each one of the following statements, indicate whether it is true or false.
(a) If X = Y (i.e., the two random variables always take the same values), then Van X | Y = 0.
(b) If X = Y (the two random variables always take the same values), then Var (X | Y) = Var (X).
(c) If Y takes on the value y, then the random variable Var (X | Y) takes the value E[(X – E[X | Y = y])2 |Y = y].
(d) If Y takes on the value y, then the random variable Var (X | Y) takes the value E[(X - E[X | Y])2 | Y = y].
(e) If Y takes on the value y, then the random variable Var ( X | Y) takes the value E[(X – E[X])2 | Y = y].
Solution :
a). [tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y)$[/tex]
Now, if X = Y, then :
[tex]P(X|Y)=\left\{\begin{matrix} 1,& \text{if } x=y \\ 0, & \text{otherwise }\end{matrix}\right.[/tex]
Then, E[X|Y] = x = y
So, [tex]$\text{Var} (X|Y) =E((X-X)^2 |Y)$[/tex]
[tex]$=E(0|Y)$[/tex]
= 0
Therefore, this statement is TRUE.
b). If X = Y , then Var (X) = Var (Y)
And as Var (X|Y) = 0, so Var (X|Y) ≠ Var (X), except when all the elements of Y are same.
So this statement is FALSE.
c). As defined earlier,
[tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y=y)$[/tex]
So, this statement is also TRUE.
d). The statement is TRUE because [tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y=y)$[/tex].
e). FALSE
Because, [tex]$\text{Var} (X|Y) =E ((X-E(X|Y=y))^2 |Y=y)$[/tex]
Tell whether the following two triangles can be proven congruent through SAS.
A.Yes, the two triangles are congruent because they’re both right triangles.
B.Yes, the two triangles are congruent because two sides and their included angle are congruent in both triangles.
C.No, the two triangles can only be proven congruent through SSS.
D.No, the two triangles can only be proven congruent through AAA.
Answer:
C.No, the two triangles can only be proven congruent through SSS.
Calculate the sample mean and sample variance for the following frequency distribution of hourly wages for a sample of pharmacy assistants. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Hourly Wages (in Dollars) Class Frequency 10.01 - 11.50 44 11.51 - 13.00 27 13.01 - 14.50 38 14.51 - 16.00 33 16.01 - 17.50 40
Answer:
[tex]\bar x = 13.739[/tex]
[tex]\sigma^2 = 4.923[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{cc}{Class} & {Frequency} & 10.01 - 11.50 & 44 & 11.51 - 13.00 & 27 & 13.01 - 14.50 & 38 & 14.51 - 16.00 & 33 & 16.01 - 17.50 & 40 \ \end{array}[/tex]
Required
The sample mean and the sample variance
First, calculate the midpoints
[tex]x_1 = \frac{10.01 + 11.50}{2} = 10.755[/tex]
[tex]x_2 = \frac{11.51 + 13.00}{2} = 12.255[/tex]
And so on...
So, the table becomes:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {x} & 10.01 - 11.50 & 44 & 10.755 & 11.51 - 13.00 & 27 & 12.255 & 13.01 - 14.50 & 38 & 13.755 & 14.51 - 16.00 & 33 & 15.255 & 16.01 - 17.50 & 40 & 16.755 \ \end{array}[/tex]
So, the sample mean is:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
[tex]\bar x = \frac{44 * 10.755 + 27 * 12.255 + 38 * 13.755 + 33 * 15.255 + 40 * 16.755}{44 + 27 + 38 + 33 + 40}[/tex]
[tex]\bar x = \frac{2500.41}{182}[/tex]
[tex]\bar x = 13.739[/tex]
The sample variance is:
[tex]\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}[/tex]
[tex]\sigma^2 = \frac{44 * (10.755 - 13.739)^2 + 27 * (12.255 - 13.739)^2+ 38 * (13.755 - 13.739)^2 + 33 * (15.255 - 13.739)^2+ 40 * (16.755- 13.739)^2}{44 + 27 + 38 + 33 + 40-1}[/tex]
[tex]\sigma^2 = \frac{890.950592}{181}[/tex]
[tex]\sigma^2 = 4.923[/tex]
Based on a poll, among adults who regret getting tattoos, 16% say that they were too young when they got their tattoos. Assume that eight adults who regret getting tattoos are randomly selected, and find the indicated probability.
Answer:
The problem is incomplete, but it is solved using a binomial distribution with [tex]n = 8[/tex] and [tex]p = 0.16[/tex]
Step-by-step explanation:
For each adult who regret getting tattoos, there are only two possible outcomes. Either they say that they were too young, or they do not say this. The answer of an adult is independent of other adults, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
16% say that they were too young when they got their tattoos.
This means that [tex]p = 0.16[/tex]
Eight adults who regret getting tattoos are randomly selected
This means that [tex]n = 8[/tex]
Find the indicated probability.
The binomial distribution is used, with [tex]p = 0.16, n = 8[/tex], that is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = x) = C_{8,x}.(0.16)^{x}.(0.84)^{8-x}[/tex]
find from first principle the derivative of 3x+5/√x
Answer:
[tex]\displaystyle \frac{d}{dx} = \frac{3x - 5}{2x^\bigg{\frac{3}{2}}}[/tex]
General Formulas and Concepts:
Algebra I
Exponential Rule [Powering]: [tex]\displaystyle (b^m)^n = b^{m \cdot n}[/tex]Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex] Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{3x + 5}{\sqrt{x}}[/tex]
Step 2: Differentiate
Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle \frac{3x + 5}{x^\bigg{\frac{1}{2}}}[/tex]Quotient Rule: [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})\frac{d}{dx}[3x + 5] - \frac{d}{dx}[x^\bigg{\frac{1}{2}}](3x + 5)}{(x^\bigg{\frac{1}{2}})^2}[/tex]Simplify [Exponential Rule - Powering]: [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})\frac{d}{dx}[3x + 5] - \frac{d}{dx}[x^\bigg{\frac{1}{2}}](3x + 5)}{x}[/tex]Basic Power Rule [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})(3x^{1 - 1} + 0) - (\frac{1}{2}x^\bigg{\frac{1}{2} - 1})(3x + 5)}{x}[/tex]Simplify: [tex]\displaystyle \frac{d}{dx} = \frac{3x^\bigg{\frac{1}{2}} - (\frac{1}{2}x^\bigg{\frac{-1}{2}})(3x + 5)}{x}[/tex]Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle \frac{d}{dx} = \frac{3x^\bigg{\frac{1}{2}} - (\frac{1}{2x^{\frac{1}{2}}})(3x + 5)}{x}[/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle \frac{d}{dx} = \frac{3\sqrt{x} - (\frac{1}{2\sqrt{x}})(3x + 5)}{x}[/tex]Simplify [Rationalize]: [tex]\displaystyle \frac{d}{dx} = \frac{3x - 5}{2x^\bigg{\frac{3}{2}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
What is the point estimate for the number of cars sold per week for a sample consisting of the following weeks: 1, 3, 5, 7, 10, 13, 14, 17, 19, 21?
A.
4.8
B.
5.22
C.
6.38
D.
6.1
Answer: A.
Step-by-step explanation:
Hope this helps!
Identify the transformation that occurs to create the graph of m(x)
m(x)=f(5x)
Answer:
m(x) is a dilation of scale factor K = 1/5 of f(x).
Step-by-step explanation:
The transformation is a horizontal dilation
The general transformation is defined as:
For a given function f(x), a dilation of scale factor K is written as:
g(x) = f(x/K)
If K > 1, then we have a dilation (the graph contracts)
if 0 < K < 1, then we have a contraction (the graph stretches)
Here we have m(x) = f(5*x)
Then we have a scale factor:
K = 1/5
So this is a contraction.
Then the transformation is:
m(x) is a dilation of scale factor K = 1/5 of f(x).
Which statement best describes g(x) = 3x + 6 - 8 and the parent function f(x) = } ?
The domains of g(x) and f(x) are the same, but their ranges are not the same.
* The ranges of g(x) and f(x) are the same, but their domains are not the same.
The ranges of g(x) and f(x) are the same, and their domains are also the same.
The domains of g(x) and f(x) are the not the same, and their ranges are also not the same.
Answer:
In general gf(x) is not equal to fg(x)
Some pairs of functions cannot be composed. Some pairs of functions can be composed only for certain values of x.
Only with they can be composed some values of x are the ranges of g(x) and f(x) are the same, and their domains are also the same. Or else lies inside it.
Step-by-step explanation:
g(x) = 3x + 6 - 8, f(x) = √x.
The domain of a composed function is either the same as the domain of the first function, or else lies inside it
The range of a composed function is either the same as the range of the second function, or else lies inside it.
Or vice versa
Now only positive numbers, or zero, have real square roots. So g is defined only for numbers
greater than or equal to zero. Therefore g(f(x)) can have a value only if f(x) is greater than or
equal to zero. You can work out that
f(x) ≥ 0 only when x ≥3/2
.
-8(9r - 1) - 9(-8r+2)
Simplest form
Answer:
-10
Step-by-step explanation:
Step-by-step explanation:
-8(9r-1)-9(-8r+2)-72r+8-72r-18-72r-72r+8-18-144r-10-(144r+10)hope it helps
stay safe healthy and happy...Two methods, A and B, are available for teaching Spanish. There is a 70% chance of successfully learning Spanish if method A is used, and a 85% chance of success if method B is used. However, method B is substantially more time consuming and is therefore used only 20% of the time (method A is used the other 80% of the time). The following notations are suggested:
A—Method A is used.
B—Method B is used.
L—Spanish was learned successfully. A person learned Spanish successfully.
What is the probability that he was taught by method A?
Answer:
0.7671 = 76.71% probability that he was taught by method A
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Person learned Spanish successfully.
Event B: Method A was used.
Probability of a person learning Spanish successfully:
70% of 80%(using method A)
85% of 20%(using method B)
So
[tex]P(A) = 0.7*0.8 + 0.85*0.2 = 0.73[/tex]
Probability of a person learning Spanish successfully and using method A:
70% of 80%, so:
[tex]P(A \cap B) = 0.7*0.8 = 0.56[/tex]
What is the probability that he was taught by method A?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.56}{0.73} = 0.7671[/tex]
0.7671 = 76.71% probability that he was taught by method A
