Answer:
Range: {-1, 0, 5/7, 4/5, 1, 2}
Step-by-step explanation:
We know that:
f(x) = (x + 1)/(2x - 1)
And:
f: A ⇒ B
where:
A={-1,0,1,2,3,4}
B= {-1,0,4/5,5/7,1,2,3,}
We want to find the range of f(x).
The range of f(x) will be the set of the outputs of f(x) (and because f goes from A to B, we will only take the outputs that belong to B).
Then we only need to evaluate all the values of A in f(x), and see if the output belongs to B.
we have:
f(x) = (x + 1)/(2x - 1)
f(-1) = (-1 + 1)/(2*-1 - 1) = 0 (this does belong to B)
f(0) = (0 + 1)/(2*0 - 1) = -1 (this does belong to B)
f(1) = (1 + 1)/(2*1 - 1) = 2 (this does belong to B)
f(2) = (2 + 1)/(2*2 - 1) = 1 (this does belong to B)
f(3) = (3 + 1)/(2*3 - 1) = 4/5 (this does belong to B)
f(4) = (4 + 1)/(2*4 - 1) = 5/7 (this does belong to B)
So the range of f(x) is the set with all these outputs, which is:
Range: {-1, 0, 5/7, 4/5, 1, 2}
A person's email for one day contained a total of 78 messages. The number of spam
messages was two less than four times the number of other messages. How many of
the email messages were spam?
Answer:
62 of the email messages were spam
Step-by-step explanation:
Let the number of spam and other messages be s and o respectively.
Total number of messages= 78
s +o= 78 -----(1)
s= 4o -2 -----(2)
Substitute (2) into (1):
4o -2 +o= 78
Simplify:
5o -2= 78
+2 on both sides:
5o= 78 +2
5o= 80
Divide both sides by 5:
o= 80 ÷5
o= 16
Since s +o= 78, s= 78 -o.
s= 78 -16
s= 62
1/6+4/18 in simplest form
Answer:
7/18
Step-by-step explanation:
1/6 x 3 = 3/18
3/18 + 4/18 = 7/18
Answer:
7/18
Step-by-step explanation:
Make the denominators the same!
You can turn 1/6 into 3/18 by multiplying the numerator and denominator by 3. Then you add the numerators of 3/18 and 4/18 together to get 7/18.
It can't be simplified any further :)
Using a profit P1 of $5,000, a profit P2 of $4,500, and a profit P3 of $4,000, calculate a 95% confidence interval for the mean profit per customer that SoftBus can expect to obtain. (Round your answers to one decimal place.) Lower Limit Upper Limit
Answer:
Confidence Interval
Lower Limit = $4,233.3
Upper Limit = $4,766.7
With 95% confidence, the mean profit per customer that SoftBus can expect to obtain is between $4,233.30 and $4,766.7 based on the given sample data.
Step-by-step explanation:
The z-score of 95% = 1.96
Profit Mean Square Root
Difference of MD
P1 $5,000 $500 $250,000
P2 4,500 0 0
P3 4,000 -500 $250,000
Total $13,500 $500,000
Mean $4,500 ($13,500/3) $166,667 ($500,000/3)
Standard Deviation = Square root of $166,667 = 408.2
Margin of error = (z-score * standard deviation)/n
= (1.96 * 408.2)/3
= 266.7
= $266.7
Confidence Interval = Sample mean +/- Margin of error
= $4,500 +/- 266.7
Lower Limit = $4,233.3 ($4,500 - $266.7)
Upper Limit = $4,766.7 ($4,500 + $266.7)
There is a language with 12 distinct letters. How many words that are less than four letters long can possibly be formed? (Assume any combination of letters is valid and letters can be repeated). Can you help me out with this one?
Answer:
1884
Step-by-step explanation:
1)If you hear the condition "less than four letters" it means that each word can consist of 3,2 or 1 letter. Firstly, consider the easiest situation with the word from one letter. There are 12 letters, so there are 12 words from one letter.
Then the words from two letters. The first letter of such a word can be chosen in 12 means(because 12 letters are available), then the second letter can be chosen in 12 means too. 12*12=144 words with 2 letters. (Multiplying, not adding, because each two words form one combination).
Then for the words from three letters, use the same rule, 12 means for the first letter, 12 means for the second letter, 12 means for the third letter. 12*12*12=1728 words.
Having particular words from 1,2,3 letters add them to get total quantity of words: 12+144+1728=1884words,that is the answer.
5x-22 3x +105 x minus 22 3 X + 10
-291x+10
:)))))) Have fun
Joe used a project management software package and has determined the following results for a given project.: Expected completion time of the project = 22 days Variance of project completion time = 2.77 What is the probability of completing the project over 20 days?
Answer:
0.1151 = 11.51% probability of completing the project over 20 days.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Expected completion time of the project = 22 days.
Variance of project completion time = 2.77
This means that [tex]\mu = 22, \sigma = \sqrt{2.77}[/tex]
What is the probability of completing the project over 20 days?
This is the p-value of Z when X = 20, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 22}{\sqrt{2.77}}[/tex]
[tex]Z = -1.2[/tex]
[tex]Z = -1.2[/tex] has a p-value of 0.1151.
0.1151 = 11.51% probability of completing the project over 20 days.
use induction method to prove that 1.2^2+2.3^2+3.4^2+...+r(r+1)^2= n(n+1)(3n^2+11n+10)/12
Base case (n = 1):
• left side = 1×2² = 4
• right side = 1×(1 + 1)×(3×1² + 11×1 + 10)/12 = 4
Induction hypothesis: Assume equality holds for n = k, so that
1×2² + 2×3² + 3×4² + … + k × (k + 1)² = k × (k + 1) × (3k ² + 11k + 10)/12
Induction step (n = k + 1):
1×2² + 2×3² + 3×4² + … + k × (k + 1)² + (k + 1) × (k + 2)²
= k × (k + 1) × (3k ² + 11k + 10)/12 + (k + 1) × (k + 2)²
= (k + 1)/12 × (k × (3k ² + 11k + 10) + 12 × (k + 2)²)
= (k + 1)/12 × ((3k ³ + 11k ² + 10k) + 12 × (k ² + 4k + 4))
= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)
= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)
On the right side, we want to end up with
(k + 1) × (k + 2) × (3 (k + 1) ² + 11 (k + 1) + 10)/12
which suggests that k + 2 should be factor of the cubic. Indeed, we have
3k ³ + 23k ² + 58k + 48 = (k + 2) (3k ² + 17k + 24)
and we can rewrite the remaining quadratic as
3k ² + 17k + 24 = 3 (k + 1)² + 11 (k + 1) + 10
so we would arrive at the desired conclusion.
To see how the above rewriting is possible, we want to find coefficients a, b, and c such that
3k ² + 17k + 24 = a (k + 1)² + b (k + 1) + c
Expand the right side and collect like powers of k :
3k ² + 17k + 24 = ak ² + (2a + b) k + a + b + c
==> a = 3 and 2a + b = 17 and a + b + c = 24
==> a = 3, b = 11, c = 10
A 10-item statistics quiz was given to 30 students. The table below gives the scores received along with the corresponding frequencies.
A 2-column table with 6 rows. Column 1 is labeled score with entries 5, 6, 7, 8, 9, 10. Column 2 is labeled Frequency with entries 1, 2, 5, 5, 7, 10.
What was the mean score on the quiz?
7.5
8.5
9
10
Answer:
Should be (B).
8.5
ED2021
Answer: B
Step-by-step explanation:
Hello people can you please help me on this
Step-by-step explanation:
Step 1: Complete the first equation
0.1 is a tenth, therefore if we have 15.3 then we have 153 tenths.
Step 2: Complete the second equation
15.3 / 3 = 5.1
0.1 is a tenth, therefore if we have 5.1 then we have 51 tenths.
Step 3: Complete the third equation
15.3 / 3 = 5.1
Muka saved 476.60. He gave Kelvin 429.10 and bought T-Shirt for 432.05, how much money he has left over
Find the measure of the missing angles.
Answer:
b = 53
c = 53
Step-by-step explanation:
Alright so we already know that b and c are going to have the same angle measures. We can find b by subtracting 180 degrees to 127. Why you may ask? Its because when b and 127 are added together its obvious that it creates a straight line (supplementary angle). This means that two angles will sum up to 180 degrees. We can create an easy equation and solve for b.
127 + b = 180
b = 53 and c = 53
Best of Luck!
Two lines, A and B, are represented by equations given below:
Line A: y = x − 2
Line B: y = 3x + 4
Which of the following shows the solution to the system of equations and explains why?
(−3, −5), because the point does not lie on any axis
(−3, −5), because the point satisfies both equations
(−4, −8), because the point satisfies one of the equations
(−4, −8), because the point lies between the two axes
9514 1404 393
Answer:
(b) (−3, −5), because the point satisfies both equations
Step-by-step explanation:
Any solution to a system of two equations must satisfy both equations. The only reasonable explanation of "why" is the one associated with the answer shown above.
7 people can pave a driveway in 9 hours. how long will it take for 11 people to pave a driveway?
Answer:
Step-by-step explanation:
If 7 people can pave the drive in 9 hours, we can use that information in equation form to find out how long it would take 1 person to pave the drive alone.
[tex]\frac{7}{x}=\frac{1}{9}[/tex] and cross multiply
x = 63. That means that it would take 1 person, working alone, 63 hours to get the job done. If that be the case, and assuming that the 2 added people work at the same rate as do the first 9, we simply divide that time alone into 11 parts.
It would take 11 people [tex]5.\bar{27}[/tex] hours to pave that driveway.
(07.04 MC)
Jim is designing a seesaw for a children's park. The seesaw should make an angle of 30' with the ground, and the maximum height
to which it should rise is 2 meters, as shown below:
1
2 meters
30
What is the maximum length of the seesaw? (6 points)
Select one:
a. 3.00 meters
b. 3.5 meter
C. 4,00 meters
d 4.5 meters
The maximum length of the seesaw is option c 4.00 meters.
What is a right-angled triangle?A right-angled triangle is one in which one of the angles is equal to 90 degrees. A 90 degree angle is called a right angle, which is why a triangle made up of right angle is termed a right angled triangle.
What are hypotenuse, height of a right-angled triangle?A right-angled triangle has three sides- hypotenuse, base and height. Hypotenuse is the longest and also the opposite side of the right angle of the triangle, base and height of a right triangle are always the sides adjacent to the right angle.
How to measure the hypotenuse of a right-angled triangle?The formula for measuring the hypotenuse is,
Height / Hypotenuse = Sinθ , where θ is the angle opposite to the height of the triangle.
In the given question, the seesaw should make an angle of 30° with the ground and the maximum height it should rise is 2 meters so the height here is 2 meters. So the seesaw will make a right angled triangle.
Height = 2 meters, θ = 30°,
Now using the formula,
2 / Hypotenuse = Sin30°
Rearranging we get,
Hypotenuse = 2 / Sin30°
The value of Sin30° is 1/2 and putting the value we get,
Hypotenuse = 2 / (1/2)
= 2 × 2
= 4 meters.
Therefore, the maximum length of the seesaw (that is the hypotenuse ) is 4 meters.
To learn more about right-angled triangles and finding sides of it click here-brainly.com/question/10331046
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Which of the following is equivalent to 5 + 5x > 8(x-1) ?
-3x > -12
3x 13
3x < 6
-4X > -12
5+5x>8(x-1)
5+5x>8x-8
5x-8x>-8+5
-3x>-3
5 + 5x > 8(x-1) is equivalent to -3x > -13.
How to estimate the equivalent function to 5 + 5x > 8(x-1) ?Let, the expression be 5 + 5x > 8(x-1)
By applying Multiplicative Distribution Law, we get
5 + 5x > 8x - 8
Rearrange unknown terms to the left side of the equation, then
5x - 8x > -8 - 5
Combine like terms, we get
-3x > -8 - 5
Calculate the sum or difference
-3x > -13
Divide both sides of the inequality by the coefficient of the variable, then we get
[tex]$x < \frac{-13}{-3}$[/tex]
Determine the sign for multiplication or division:
[tex]$x < \frac{13}{3}$[/tex]
Therefore, the correct answer is -3x > -13.
Complete question:
Which of the following is equivalent to 5 + 5x > 8(x - 1)?
-3x > -12
3x < 13
3x < 6
-4x > -12
To learn more about algebraic expression
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Samantha bought m candies at the store. There are n candies in a pound, and each pound costs c dollars. Write an expression for how much Samantha paid.
Answer:
total = m/n * c
m/n gives u the number of pounds u have bought, multplied by the cost of the candies per pound gives u the total amount of money she paid
Find the 97th term of the arithmetic sequence 17, 26,35,...
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The answer of your question is in the attachment..!!
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Nine Increased by the product of a number and 4 is greater than or equal to -15
Use the variable y for the unknown number
Answer:
9+4y ≥ -15
y ≥ -6
Step-by-step explanation:
Nine Increased by the product of a number
9+4y
is greater than or equal to -15
9+4y ≥ -15
Subtract 9 from each side
9-9+4y ≥ -15-9
4y ≥ -24
Divide by 4
4y/4 ≥ -24/4
y ≥ -6
Write an equation for the following: y varies directly with x. Find K
when x=4 and y=5.
Answer:
4/5
Step-by-step explanation:
y varies as x
y=kx
k=x/y
Intelligence quotients (IQs) on the Stanford-Binet intelligence test are normally distributed with a mean of 100 and a standard deviation of 16.
Use the 68-95-99.7
Rule to find the percentage of people with IQs between 84 and 116.
Answer:
Approximately 68% of people have IQs between 84 and 116.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 100, standard deviation of 16.
Percentage of people with IQs between 84 and 116.
84 = 100 - 16
116 = 100 + 16
So within 1 standard deviation of the mean, which, by the Empirical Rule, is approximately 68%.
Find X please
15 POINTS WORTH
Answer and Step-by-step explanation:
To find x, we must find the interior angles first, then we can find the value of x.
To find the interior angle, we need to use the exterior angle. We subtract the exterior angle from 180 to get the interior angle.
180 - 157 = 23
180 - 78 = 102
Now we need to find the last interior angle.
180 - 23 - 102 = 55
Now to find x.
180 - 55 = 125
x = 125
#teamtrees #PAW (Plant And Water) #ALM (All Lives Matter)
I hope this helps!
Answer:
the value of x is 124
Step-by-step explanation:
find area and perimeter of shaded area and the perimeter is not 96
Answer:
picture not clear what is the length
what is 127/14 simplified?
Answer:
9 1/14
Step-by-step explanation:
127 ÷14
127 divided by 14 equals
9 with a remainder of 1
Use the Pythagorean Theorem to find the length of the indicated side of the following right triangle. (NOTE: The square-like symbol indicates a 90-degree angle.)
Pythagorean Theorem: a^2 + b^2 = c^2
a = 5
b = ?
c = [tex]\sqrt{61}[/tex]
5^2 + b^2 = ([tex]\sqrt{61}[/tex])^2
25 + b^2 = 61
b^2 = 36
b = 6
Hope this helps!
I need you guy’s help answer thanks so much
PLEASE HELP FAST!! WILL GIVE FIRST PERSON THAT RESPONDS A HIGH RATING AND POINTS!
Answer:
Step-by-step explanation:
3
What is the largest value of A according to the division operation given above?
A)300 B)314 C)400 D)450
Answer:
Hello,
Answer B
Step-by-step explanation:
Since A=15*20+B and B<15
The max for B is 14
==> 300+14=314
A boat travels 400 kilometers in 9.6 hours (with a constant speed). How much time will it take to travel 138 kilometers? (round to the nearest tenth of an hour)
Step-by-step explanation:
here's the answer to your question
Help me please and thank you
Answer:
D. 3
Step-by-step explanation:
Answer:
3
step by step explanitation
The number formed by adding 1 to the greatest 8 – digit number is?
Answer:
the answer would be 100,000,000
Greatest 8 Digit Number: 99,999,999
Adding 1 = 99999999+1
= 100,000,000
Must click thanks and mark brainliest
