Each line of a computer printout contains 72 characters. A: how many characters can print in a 75-line report? B:The computer printer can print 135 characters each second. How long will it take to print this report.
5 pages X 60 minutes = 300 pages per hour
It will take 1 hour to print 300 pages on a printer that prints at 5 pages per minute. Do you have enough ink to print 300 pages?
Two datasets arranged in descending order are: {8, x, 4,1) and (9. y, 5,2). If the medians of
the two given datasets are equal, what is the value of (y – x)??
Answer
Answer:
Legon fo)
Step-by-step explanation:
Answer:
Step-by-step explanation:
Dataset 1 (in increasing order)
{1, 4, x, 8}
Dataset 2 (in increasing order)
{2, 5, y, 9}
Median of dataset 1
[4 + x] / [2]
Median of dataset 2
[5 + y] / [2]
since the medians of the two given sets of data are the same,
=> [4 + x] / [2] = [5 + y] / [2]
=> 2(5 + y) = 2(4 + x)
=> 10 + 2y = 8 + 2x
=> 2y - 2x = 8 - 10
=> 2y - 2x = - 2
=> 2(y - x) = - 2
=> [2(y - x)] / [2] = [- 2] / [2]
denominators and numerators cancel out
=> (y - x) = - 1
Therefore, (y - x) ² = (-1)²
=> (y - x) ² = 1
Suppose that a scarf company estimates that its monthly cost is
C(a)=500x2 + 300 and its monthly revenue is
R(x) = -0.523 +6002-200+300, where x is in thousands of
scarves sold. The profit is the difference between the revenue and the cost.
What is the profit function, P(x)?
The profit function is P(x) = -500.523x^2 + 600x - 200.
To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).
Given:
Cost function: C(a) = 500x^2 + 300
Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300
Profit function, P(x), is obtained by subtracting the cost function from the revenue function:
P(x) = R(x) - C(a)
P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)
Simplifying the expression:
P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300
P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300
P(x) = -500x^2 - 0.523x^2 + 600x - 200
Combining like terms:
P(x) = (-500 - 0.523)x^2 + 600x - 200
Simplifying further:
P(x) = -500.523x^2 + 600x - 200
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PLEASE HELPP! f(x)= -3x + 3
Which of the graphs represent the inverse of the function F??
Answer:
Answer is Y
Step-by-step explanation:
If $5.00 were invested at 3% interest 600 years ago, how much would that investment be worth today?
Simplify the expression. 20 • 5–2
a) 25
b) –500
c) –200
d) 4/5
Answer: D) 4/5
Hope this helps :)
angle abc and angle cbd are supplementary angles the measure of angle cbd is 41 degrees what is the measure of angle abc
Answer:
139
Step-by-step explanation:
180-41=139
F(x-3)=x^2-1. F(0)=?
The answer is f(x−3)=x2
How many does 3/4 go into 2 2/3?
Answer:
(3/4)*(x) = 2/3
Step-by-step explanation:
If you make an equation (3/4)*(x) = 2/3 then the x would represent how many 3/4ths will be equal to 2/3rds since multiplying by that number x represents is like adding up how many of the 3/4ths you need to equal what’s on the other side of the equals sign - so from there you just solve the equation for x..
Answer:
3 times at most
Step-by-step explanation:
\(2\frac{2}{3}\div\frac{3}{4}\)
\(\frac{8}{3}\div\frac{3}{4}\)
\(\frac{8}{3}*\frac{4}{3}\)
\(\frac{32}{9}\)
\(3\frac{5}{9}\)
Therefore, 3/4 goes into 2 2/3 three times at most
I will mark brainiest if you can answer the question correctly!! :)
7. Write the equation of the quadratic given the following 3 points.
(0, -1), (4,51), (-2,9)
A) y = 3x2 - X-1
B) y = 3x2 + x - 2
C) y = 2x2 + x - 1
D) y = 3x2 + x - 1
Answer:
D
Step-by-step explanation:
Sub (0, -1) into 4 choices, Only A, C, D work.
Sub (-2, 9) into A, C, not work.
Sub (4, 51) into D for checking, it works
Sumita buys a set of earphones for £7.23. She pays with £10. How much change does she get?
Sumita get £2.77 amount in change for buys a set of earphones.
Since, We know that;
Subtraction in mathematics means that is taking something away from a group or number of objects.
And, When you subtract, what is left in the group becomes less.
We have to given that;
Sumita buys a set of earphones for £7.23.
And, She pays with the amount £10.
Since, When you subtract, what is left in the group becomes less.
Here, To find the amount to get amount of change.
Hence, We can formulate;
To find the change amount we can subtract cost of earphone from pay amount which she pay.
Thus, WE get;
The Change Amount getting by her is,
⇒ Amount = £10 - £7.23
⇒ Amount = £2.77
Therefore, We get;
⇒ Amount = £2.77
That is,
£2.77 amount in change for buys a set of earphones.
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Recently many airlines have had cancel flight in a single day republic airlines had to cancel 416 flights representing 15.1% of the airlines scheduled flights. How many flights were originally scheduled?
The number 2755 flights were scheduled.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Recently many airlines have had to cancel flights in a single day.
Republic airlines had to cancel 416 flights representing 15.1% of the airlines' scheduled flights.
The number of flights scheduled,
= 416 x 100/ 15.1
= 41600/15.1
= 2754.96
≈ 2755
Therefore, 2755 flights were scheduled.
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60ft by 60ft wall and a mirror that’s 60ft by 20ft the mirror covers wat percent of the wall?
Answer:
okay, so we have a wall that is 60 ft. The area of the wall because the wall is a square is just side squared. So the area of the wall is \(60^{2}\), which is 30 600 square feet. The mirror is 20 ft by 60 ft. So the area of the mirror, because its a rectangle is length times width, so that's 20 a 60 so 20 x 60 is gonna give me 1200 square feet. So if we take the area of the mirror and put that over the area, the wall we get 1200 over 30 600, which reduces to one over three. So the mirror is one third the area of the wall.
Step-by-step explanation:
Graph the system of equations on your graph paper to answer the question.
{y=x−4y=−x+6
What is the solution for this system of equations?
Answer: (5 , 1)
Step-by-Step explanation:
hihi your problem is a system of question y = x-4 and y = -x+6 okay so graph them both normally and then find the point where they intersect which is gonna be a coordinate point, and that's your solution !!
y = x-4
the y intersect is going to be 4
the slope is a positive 1 , going up to the right, through the positive quadrant, line is facing to the right
y = -x+6
the y intersect is going to be -6
the slope is going to be a -1 , following up the opposite way the line is going to face the left
once you graph them both you'll see the point of intersection, the solution
make sure you drew your lines very clearly !!!!
the solution is x = 5 and y = 1 which is also (5 , 1)
hopefully this was helpful !
If 450 birds have to fit evenly into 18 enclosures and there are 3 enclosures in each section of the zoo how many birds are in each section of the zoo?
Answer:There are 75 birds in each section.
Step-by-step explanation:450 birds divided by 18 enclosures is 25 birds in each enclosure. 25 birds times 3 enclosures is 75 birds in each section.
Tony invested $9538 in an account at 8% compounded daily. Identify the compound
interest C after 1 years.
9514 1404 393
Answer:
$794.30
Step-by-step explanation:
The account balance for principal P invested at rate r compounded daily for t years is ...
A = P(1 +r/365)^(365t)
We have P=$9538, r=0.08, t=1, and we want the value of P-A, the interest earned.
P-A = P(1 +0.08/365)^365 -1) = $9538(1.08327757 -1) ≈ $794.30
The interest earned in one year is $794.30.
Evaluate the function f(x) at the given numbers (correct to six decimal places).
f(x) =
x2 − 2x
x2 − 4
,
x = 2.1, 2.05, 2.01, 2.001, 2.0001,
1.9, 1.95, 1.99, 1.999, 1.9999
x f(x)
2.1
0.512195
Correct: Your answer is correct.
2.05
0.5062
Incorrect: Your answer is incorrect.
2.01
0.5012
Incorrect: Your answer is incorrect.
2.001
0.5000
Incorrect: Your answer is incorrect.
2.0001
0.500012
Correct: Your answer is correct.
x f(x)
1.9
0.487179
Correct: Your answer is correct.
1.95
0.493670
Incorrect: Your answer is incorrect.
1.99
0.498746
Incorrect: Your answer is incorrect.
1.999
0.499874
Incorrect: Your answer is incorrect.
1.9999
0.499987
Correct: Your answer is correct.
Answer:
\(f(2.1) = 0.512195\)
\(f(2.05) = 0.506173\)
\(f(2.01)=0.501247\)
\(f(2.001) = 0.500125\)
\(f(2.0001) = 0.500012\)
\(f(1.9) = 0.487179\)
\(f(1.95) = 0.493671\)
\(f(1.99) = 0.498747\)
\(f(1.999) = 0.499875\)
\(f(1.9999) = 0.499987\)
Step-by-step explanation:
Given
\(f(x) = \frac{x^2 - 2x}{x^2 - 4}\)
Solve for f(x) for all given values of x
First, we need to simplify f(x)
\(f(x) = \frac{x^2 - 2x}{x^2 - 4}\)
\(f(x) = \frac{x(x - 2)}{x^2 - 2^2}\)
\(f(x) = \frac{x(x - 2)}{(x- 2)(x + 2)}\)
\(f(x) = \frac{x}{x + 2}\)
When \(x = 2.1\)
\(f(x) = \frac{x}{x + 2}\)
\(f(2.1) = \frac{2.1}{2.1 + 2}\)
\(f(2.1) = \frac{2.1}{4.1}\)
\(f(2.1) = 0.512195\)
When \(x = 2.05\)
\(f(x) = \frac{x}{x + 2}\)
\(f(2.05) = \frac{2.05}{2 + 2.05}\)
\(f(2.05) = \frac{2.05}{4.05}\)
\(f(2.05) = 0.506173\)
When \(x = 2.01\)
\(f(x) = \frac{x}{x + 2}\)
\(f(2.01)=\frac{2.01}{2.01 +2}\)
\(f(2.01)=\frac{2.01}{4.01}\)
\(f(2.01)=0.501247\)
When \(x = 2.001\)
\(f(x) = \frac{x}{x + 2}\)
\(f(2.001) = \frac{2.001}{2.001 +2}\)
\(f(2.001) = \frac{2.001}{4.001}\)
\(f(2.001) = 0.500125\)
When \(x = 2.0001\)
\(f(x) = \frac{x}{x + 2}\)
\(f(2.0001) = \frac{2.0001}{2.0001 + 2}\)
\(f(2.0001) = \frac{2.0001}{4.0001}\)
\(f(2.0001) = 0.500012\)
When \(x = 1.9\)
\(f(x) = \frac{x}{x + 2}\)
\(f(1.9) = \frac{1.9}{1.9 + 2}\)
\(f(1.9) = \frac{1.9}{3.9}\)
\(f(1.9) = 0.487179\)
When \(x = 1.95\)
\(f(x) = \frac{x}{x + 2}\)
\(f(1.95) = \frac{1.95}{1.95 + 2}\)
\(f(1.95) = \frac{1.95}{3.95}\)
\(f(1.95) = 0.493671\)
When \(x = 1.99\)
\(f(x) = \frac{x}{x + 2}\)
\(f(1.99) = \frac{1.99}{1.99 + 2}\)
\(f(1.99) = \frac{1.99}{3.99}\)
\(f(1.99) = 0.498747\)
\(f(x) = \frac{x}{x + 2}\)
When \(x = 1.999\)
\(f(x) = \frac{x}{x + 2}\)
\(f(1.999) = \frac{1.999}{1.999 + 2}\)
\(f(1.999) = \frac{1.999}{3.999}\)
\(f(1.999) = 0.499875\)
When x = 1.9999
\(f(x) = \frac{x}{x + 2}\)
\(f(1.9999) = \frac{1.9999}{1.9999 + 2}\)
\(f(1.9999) = \frac{1.9999}{3.9999}\)
\(f(1.9999) = 0.499987\)
Note that all values of f(x) are approximated to 6 decimal places
What's the inverse of ƒ(x) = x – 20?
Therefore , the solution of Inverse function comes out to be of x-20 equals to x+20
What is the inverse symbol?A function f has an inverse function only if for every y in its range there is only one value of x in its domain for which f(x)=y. This inverse function is unique and is frequently denoted by f−1 and called “f inverse.” For an overview into the idea of an inverse function, see the function machine inverse.Steps for finding the inverse of a function fReplace f(x) by y in the equation describing the function. Interchange x and y. In other words, replace every x by a y and vice versa.
Here,
Solve for y.
Replace y by f-1(x).
y=x-20
x=y-20
Solve for y,x = y-20
x+20
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Answer:
ƒ^(-1)(x) = x + 20
Step-by-step explanation:
To find the inverse of the function ƒ(x) = x - 20, we need to switch the roles of x and y and solve for y.
Let's start by replacing ƒ(x) with y:
y = x - 20
Next, swap x and y:
x = y - 20
Now, solve for y by isolating it:
x + 20 = y
Therefore, the inverse of the function ƒ(x) = x - 20 is given by:
ƒ^(-1)(x) = x + 20
Whats the difference between the lowest temperature -8 and the highest 7
Answer:
-15
Step-by-step explanation:
8+7=15
so
-8-7 = -15
Evaluate each expression.Round your answers to the nearest thousandth. Do not do any intermediate computations (THIS IS ONE QUESTION I DO AN ONLINE MATH PROGRAM WHERE THIS IS CONSIDERED ONE QUESTION)
Explanation
let's remember some properties of the exponents
\(\begin{gathered} (\frac{a}{b})^n=\frac{a^n}{b^n} \\ (\frac{a}{b})^{-n}=\frac{n^n}{a^n} \\ a^m*a^n=a^{m+n} \end{gathered}\)hence
Step 1
\(\begin{gathered} 3.2^{1.5} \\ 3.2^{1.5}=3.2^1+3.2^{0.5} \\ 3.2^{1.5}=3.2+\sqrt{3.2} \\ 3.2^{1.5}=5.72 \end{gathered}\)Step 2
\(\begin{gathered} (\frac{3}{5})^{-0.85} \\ (\frac{3}{5})^{-0.85}=\frac{5^{0.85}}{3^{0.85}}=1.54373 \\ (\frac{3}{5})^{-0.85}=1.544 \end{gathered}\)so, the answer is
\(\begin{gathered} 3.2^{1.5}=5.72 \\ (\frac{3}{5})^{-0.85}=1.544 \end{gathered}\)I hope this helps you
solve and show steps :
9514 1404 393
Answer:
-(5√7 +9√35)/380
Step-by-step explanation:
The denominator is made rational by multiplying numerator and denominator by the conjugate of the denominator.
\(\dfrac{\sqrt{7}}{5-9\sqrt{5}}=\dfrac{\sqrt{7}}{5-9\sqrt{5}}\cdot\dfrac{5+9\sqrt{5}}{5+9\sqrt{5}}=\dfrac{5\sqrt{7}+9\sqrt{35}}{5^2-9^2\cdot5}=\boxed{-\dfrac{5\sqrt{7}+9\sqrt{35}}{380}}\)
_____
Additional comment
This process takes advantage of the factoring of the difference of squares:
a² -b² = (a -b)(a +b)
The method is used to eliminate complex numbers and square roots from denominators.
A recipe calls for 4 cups of pecans for every 5 cups of walnuts. How many cups of pecans should be added to 8 cups of walnuts?
A. 1.6 cups
B. 2.5 cups
C. 6.4 cups
D. 10 cups
Which choice correctly expresses the number below in scientific notation?
Answer:
B. 4.62 x 10^5 is scientific notation of 462000
Find the 66th
term in the following
arithmetic sequence
-92, -85, -78, -71, ...
Answer:
The \(66\)th term is \(363\).
Step-by-step explanation:
To find the \(n\)th term, the formula is \(7n - 99\). Since we want to find the \(66\)th term, we can plug \(n\) for \(66\). So our expression is now \(7 \cdot 66 - 99 =\) \(66\)th term. Solving this we have
\(462 - 99 = 66\text{th term}\\363 = 66\text{th term}\\\). Therefore, the \(66\)th term is \(\boxed{363}\).
Answer:
a₆₆ = 363
Step-by-step explanation:
the nth term of an arithmetic sequence is
\(a_{n}\) = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 92 and d = a₂ - a₁ = - 85 - (- 92) = - 85 + 92 = 7 , then
a₆₆ = - 92 + (65 × 7)
= - 92 + 455
= 363
write an interval to describe the set of values.
The intervals are denoted as:
Closed intervals = [a, b]
This interval includes a and b.
Open intervals = (a, b)
This interval does not include a and b.
The interval that denotes the values between -4 and 3 on the given number line is [-4, 3].
What are intervals?
The intervals are numbers or values between two given point
The intervals are denoted as:
Closed intervals = [a, b]
This interval includes a and b.
Open intervals = (a, b)
This interval does not include a and b.
We have
A number line.
The set of values that is in the blue line is from -4 to 3.
This means that the blue line includes values from -4 to 3.
There are infinite numbers between -4 to 3.
The blue line denoted that the values -4 and 3 are also included.
The interval that denotes the values between -4 and 3 is:
= [-4, 3]
Thus,
The interval that denotes the values between -4 and 3 on the given number line is [-4, 3].
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A fair die with its faces numbered from 1 to 6 will be rolled. Which of the following is the best interpretation of the probability that the number landing face up will be less than 3?
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 1/3
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 1/2
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3
For three rolls of the die, a number less than 3 will land face up one time.
It will take three rolls of the die before a number less than 3 lands face up for the first time.
The best interpretation of the probability that the number landing face up will be less than 3 is \(\frac{1}{3}\).
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is \(\frac{1}{3}\).
As per the given question a fair die with its faces numbered from 1 to 6 will be rolled.
Here we have to calculate the probability that the number landing face up will be less than 3.
The event of the number landing face up will be less than 3 is exhaustive, mutually exclusive, and independent face of a die = 6
(1, 2, 3, 4, 5, 6)
Favorable number of faces of a die = 2
(1, 2)
Since the number landing faces up will be less than 3.
Therefore the probability that the number landing face up will be less than 3
\(=\frac{\text { Favourable Number }}{\text { Total Number }}$\)
\(& =\frac{2}{6} \\\)
\(& =\frac{1}{3}\)
Therefore the best interpretation of the probability that the number landing face up will be less than 3 is \(\frac{1}{3}\)
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The long-run relative frequency of a number less than 3 landing face up is 2/3.
The best interpretation of the probability that the number landing face up will be less than 3 is that for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3. This can be expressed mathematically as P(x<3) = 2/3, where P(x) is the probability of the number landing face up being less than 3.
For a single roll of the die, the probability of a number less than 3 landing face up is 1/2. This is because there are three numbers (1,2,3) which are less than 3, and 6 possible outcomes. Therefore, the probability of any one of those three numbers landing face up is 3/6, or 1/2.
For multiple rolls of the die, the probability of a number less than 3 landing face up is the sum of the probabilities of each of those three numbers landing face up. This can be expressed mathematically as P(x<3) = (1/2) + (1/2) + (1/2), or 2/3.
Therefore, for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3.
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Find the missing numbers
Based on the information provided, the missing number would be number 6.
How to find the missing numbers?When it comes to finding missing numbers, the first step is to decipher or identify the pattern. This can be either a sequence of numbers or the application of a specific mathematical operation such as subtraction or addition.
In this case, we can see there is a sequence of numbers that seems to go from 1 to 9. However, if you check carefully, the number 6 is missing, which is the number you need to add.
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Calculate 1 + 3 + 5 +...+ (2n - 1) for several natural numbers n.
Answer:
The solutions for 1 + 3 + 5 +...+ (2n - 1), for the first 10 natural numbers are given in the explanation section below.
Step-by-step explanation:
To calculate 1 + 3 + 5 +...+ (2n - 1) for several natural numbers n, we will use several natural numbers to represent n.
For n= 1,
2n - 1 = 2(1) - 1 = 2 - 1 = 1
Hence, 1 = 1
For n = 2,
2n - 1 = 2(2) - 1 = 4 - 1 = 3
Hence, 1 + 3 = 4
For n = 3,
2n - 1 = 2(3) - 1 = 6 - 1 = 5
Hence, 1 + 3 + 5 = 9
For n = 4,
2n - 1 = 2(4) - 1 = 8 - 1 = 7
Hence, 1 + 3 + 5 + 7 = 16
For n = 5,
2n - 1 = 2(5) - 1 = 10 - 1 = 9
Hence, 1 + 3 + 5 + 7 + 9 = 25
For n = 6,
2n - 1 = 2(6) - 1 = 12 - 1 = 11
Hence, 1 + 3 + 5 + 7 + 9 + 11 = 36
For n = 7,
2n - 1 = 2(7) - 1 = 14 - 1 = 13
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
For n = 8,
2n - 1 = 2(8) - 1 = 16 - 1 = 15
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64
For n = 9,
2n - 1 = 2(9) - 1 = 18 - 1 = 17
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81
For n = 10,
2n - 1 = 2(10) - 1 = 20 - 1 = 19
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100
HELP Find the value of x in each case. Picture down below
Answer:
11Step-by-step explanation:
Use the triangle in the middle. It has interior angles:
F = 180 - 147 = 33E = 180 - 4xxUse the sum of the three interior angles and find the value of x:
33 + 180 - 4x + x = 18033 - 3x = 03x = 33x = 11Angle F and G are Colinear pairs
<F=180-147=33°Now we know
Sum of two interior angles=Exterior angle
\(\\ \sf\longmapsto 33+x=4x\)
\(\\ \sf\longmapsto 4x-x=33\)
\(\\ \sf\longmapsto 3x=33\)
\(\\ \sf\longmapsto x=\dfrac{33}{3}\)
\(\\ \sf\longmapsto x=11\)
What would the image below look like after a rotation of 909, centered 6. at the origin? D с C. 1 A A D. В. e A
during the rotaion with 90 degrees the coordinates are transform into
(x,y) change to (-y,x)
In the given graph:
The coordinates of A is (-3,0), T(-1,-1), C(-4,-3)
So, after the rotaion to 90 degree
\(\begin{gathered} (x,y)\rightarrow(-y,x) \\ A(-3,0)\rightarrow A^{\prime}(0,-3) \\ B(-1,-1)\rightarrow B^{\prime}(1,-1) \\ C(-4,-3)\rightarrow C^{\prime}(3,-4) \end{gathered}\)Plot them on the graph:
This graph is similar to the graph C
so, the image after rotaion to 90 degree is C
Answer: C)