Answers
Answer:
The equation is
y=0.5x+2
Related Questions
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.
Answers
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
.
PLSSSSSSSSSSSSS HELp VERY URGENT The graph of F(x), shown below, resembles the graph of G(x) = x^2, but it has been stretched somewhat and shifted. Which of the following could be the equation of F(x)?
Answers
Answer:
Option B
Step-by-step explanation:
Function 'g' is,
g(x) = x²
Since, leading coefficient of this function is positive, parabola is opening upwards.
From the graph attached,
Function 'f' is opening upwards leading coefficient of the function will be positive.
Since, the graph of function 'f' is vertically stretched, equation will be in the form of f(x) = kx²
Here, k > 1
Since, function 'f' is formed by shifting the graph of function 'g' by 1 unit upwards,
f(x) = g(x) + 1
Combining all these properties, equation of the function 'f' should be,
f(x) = 4x² + 1
Option B will be the correct option.
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.
Answers
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.
09:30 am - 4:30 pm minus 30 minutes?
How many hours is that ?
Answers
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.
Exercise 2.2.3: The cardinality of a power set. (a) What is the cardinality of P({1, 2, 3, 4, 5, 6})
Answers
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.
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
Answers
Answer:
Step-by-step explanation:
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
Answers
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.
Answers
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
Answers
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
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).
Answers
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%.
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?
Answers
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
#SPJ3
Identify the transformation that occurs to create the graph of m(x)
m(x)=f(5x)
Answers
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).
determine the general solution of cos2X -7cosX -3=0
Answers
Answer:
x=2pi/3 +2pi n, 4pi/3 +2pi n for all integar of n.
Step-by-step explanation:
Cách tính chu vi hình vuông?
Answers
Answer:
Xin hãy đánh dấu cho tôi là một người tồi tệ nhất
Để tìm chu vi hình vuông, bạn phải nhân 2 cạnh với 4..
Sử dụng công thức
chu vi = 4 * (một mặt)
-8(9r - 1) - 9(-8r+2)
Simplest form
Answers
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...Which expression is equivalent to the following complex fraction?
Answers
Step-by-step explanation:
Option B is correct. Refer to the attachment!
Bryan and his wife, Jane, can afford $2,273 a month for a monthly mortgage payment.
How much money would they be able to borrow for a 30-year fixed mortgage if the APR is 3.8%.
How much money would they make in payments over the life-time of the mortgage?
How much money would they pay in interest over the life-time of the mortgage if they borrowed as much money as they could on the mortgage?
Round your answer to the nearest cent.
Answers
9514 1404 393
Answer:
borrowed amount: $487,812.89total of payments: $818,280.00paid in interest: $380,467.11Step-by-step explanation:
The formula for figuring the amount that can be borrowed (P) is shown on the first line of the attachment. (The second line rounds it to the nearest cent.) In this formula, ...
a = monthly payment, r = annual interest rate, t = number of years
The amounts requested by the problem statement are shown in the attachment, and above. b is the amount that can be borrowed, p is the total of payments, and i is the interest paid. There are 360 monthly payments in 30 years, so the total paid is 360 times the monthly payment amount.
Using the following image, solve for x.
Answers
Answer:
please provide an image.
You’re making 40 servings of English custard. Each serving is 250 ml. The following recipe yields 2 L.
Calculate how much of each ingredient you will need to make enough servings of the custard.
Milk 2 L
Vanilla essence 4 ml
Sugar 200 g
Egg yolks 20
Answers
Answer:
Milk 10 L
Vanilla essence = 20 ml
Sugar = 1kg
Egg yolks 100 yolks
Step-by-step explanation:
2l/250ml = 8 servings per recipe ,
40 servings/8 = 5 "batches"
Milk 2 L * 5 = 10 L
Vanilla essence 4 ml * 5 = 20 ml
Sugar 200 g * 5 = 1000g = 1kg
Egg yolks 20 * 5 = 100 yolks
y is inversely proportional to the square of x. If y=4 when x=6 then what is y when x is 8?
Answers
Step-by-step explanation:
y=k/x
4=k/6 4*6=k =24 . if x=8, y=24/8,y=34. 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.
Answers
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
Which line is parallel to the line that passes through the points (1,7) and (-3, 4)? A. y=--x-5 B. y=+*+1 y=-x-8 O c. D. 11 v==x+3 4
Answers
Answer:
B
Step-by-step explanation:
because
Two cities,a and are mapped on the coordinate plane. How far apart are they from each other?
Answers
Answer:
[tex]\sqrt{97} \\ \sqrt{9^{2}+4^{2} }[/tex]
Step-by-step explanation:
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
Answers
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
Any good tv shows on Netflix
Has to be atleast 3 season long
Answers
I like ncis (also 15 seasons I think)
I like cobra Kai ( 3 season 4 one coming out )
:)
Answer:
Grey's Anatomy
Step-by-step explanation:
Can someone help me out here? Not sure how to solve this problem or where to start either?
Answers
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!
1+1/2+1/4+1/8+1/16+1/32+1/64
if you continue adding on fractions according to this pattern, when will you reach a sum of 2?
Answers
Answer: You will never reach a sum of 2. You would need infinitely many terms to sum up.
============================================================
Explanation:
We have this sequence
1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, ...
which is geometric with the following properties
a = first term = 1r = common ratio = 1/2 = 0.5Notice how we multiply each term by 1/2 to get the next term. Eg: (1/4)*(1/2) = 1/8 or (1/16)*(1/2) = 1/32.
Since r = 0.5 is between -1 and 1, i.e. -1 < r < 1 is true, this means that adding infinite terms of this form will get us to approach some finite sum which we'll call S. This is because the new terms added on get smaller and smaller.
That infinite sum is
S = a/(1-r)
S = 1/(1-0.5)
S = 1/0.5
S = 2
So if we keep going with that pattern 1+1/2+1/4+... and do so forever, then we'll reach a sum of 2. However, we cannot go on forever since it's asking when we'll reach that specific sum. In other words, your teacher wants finitely many terms to be added.
In short, we'll never actually reach the sum 2 itself. We'll just get closer and closer.
Here's a list of partial sums
1+1/2 = 1.51+1/2+1/4 = 1.751+1/2+1/4+1/8 = 1.8751+1/2+1/4+1/8+1/16 = 1.93751+1/2+1/4+1/8+1/16+1/32 = 1.968751+1/2+1/4+1/8+1/16+1/32+1/64 = 1.9843751+1/2+1/4+1/8+1/16+1/32+1/64+1/128 = 1.99218751+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 = 1.99609375We can see that we're getting closer to 2, but we'll never actually get there. We'd need to add infinitely many terms to get to exactly 2.
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.
Answers
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.
Choose the system of inequalities that best matches the graph below.
Answers
Answer:
"D" is the correct answer
Step-by-step explanation:
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?
Answers
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
