We can conclude the proof of inequality : 3 (m + n)! ≥ m! + n! below.
What is factorial?In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Mathematically, we can write -
[tex]$n! = n \times (n-1) \times \dots \times 1[/tex]
Given is the inequality -
3 (m + n)! ≥ m! + n!
We have -
3 (m + n)!
3 {(m + n)(m + n - 1)(m + n - 2) ....... (3)(2)(1)}
3 {m² + mn - m + nm + n² - n}(m + n + 2) ...... (3)(2)(1)
3 {m² + n² - m - n + 2mn}(m + n + 2) ........ (3)(2)(1)
3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1)
Now, for (m! + n!) --
(m! + n!) = m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)
It can be seen that -
3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1) ≥
m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)
Hence, it can be seen that -
3 (m + n)! ≥ m! + n!
Therefore, we can conclude that 3 (m + n)! ≥ m! + n!.
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Drag each question to the correct location on the table.
Classify the questions as statistical or not statistical.
Each of the questions should be correctly classified as statistical or not statistical as follows:
Not statistical question: "How many hours did I jog yesterday?"Not statistical question: "How many students in my class can swim?"Not statistical question: "How many students in my class watch television?"Statistical question: "How many hours a day do the students in my class watch television?"Statistical question: "How many TV shows did each student in my class watch yesterday?"Statistical question: "How many days a week did each student in my class go swimming in the last month?"What is a statistical question?In Mathematics, a statistical question can be defined as a type of question in which the resulting answer is in the form of an average, percentage, or a range such as "How many TV shows did each student in my class watch yesterday?"
What is a non-statistical question?A non-statistical question simply refers to a question that is not non-statistical and it can be defined as a type of question which has an exact or fixed answer such as "How many students in my class can swim?"
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Can somebody help me please
Answer:
[tex] \frac{34.25}{6.5} [/tex]
Mieko said that the difference between the longest rose and the shortest rose is 1 inch. Is she correct?
Use the drop-down menus to show and explain your answer.
Mieko is Choose
The longest rose is
Choose:
inches, and the shortest rose is
Choose...
So, the difference is
Choose...
inch
Review progress
Question 7
of 7
Bac
HELP WHO EVER SNSWERS FIRST I WILL MARK BRAINLYEST
Answer:
Step-by-step explanation:
lol no
speeeed brainlest
eeee
The foot of a ladder is placed 7 meters from a wall. If the top of the ladder rests 9 meters up on the wall, how long is the ladder?
Answer:
8 meters
step-by-step explanation:
8 is in between 9 and 7
Y
P
Q
S
R
Part A
Rectangle PQRS is rotated 90° counterclockwise about the origin to create rectangle PQR'S' (not shown). What are the coordinates of point R?
0 (-7,6)
O (7,6)
• (-6,7)
O (6,7)
Part B
Answer:
The coordinates of point R are (7,6), second option
Step-by-step explanation:
Coordinates of point R:
The coordinates of point R are , so (6,-7).
90° counterclockwise rule:
The rule for a rotation of 90º counterclockwise is given by:
(x,y) -> (-y,x)
What are the coordinates of point R?
(6,-7) -> (-(-7),6) = (7,6).
The coordinates of point R are (7,6), second option
find the value of x thanks! :D brainliest will be awarded!
Answer:
19
Step-by-step explanation:
point y is 90
x is 3x - 5
w is 2x
so
3x - 5 + 2x = 90
5x - 5 = 90
5x = 95
x = 19
Given the relation x = y 2 − 1, identify the x- and y- axis intercepts.
The effectiveness of two types of textbook is compared. A class of 30 students is randomly divided into two groups. One group uses digital textbooks and the other group uses paper textbooks. A summary of their test scores at the end of the session is given below. Digital Textbook: Paper Textbook: Construct a 90% confidence interval for the difference in scores between the two groups assuming underlying normal distributions with equal variance. Find the lower bound of the confidence interval (round off to first decimal place).
Answer:
- 18.377
Step-by-step explanation:
n1 = 17 ; xbar1 = 78.4 ; s1² = 90.3
n2 = 13 ; x2bar = 92 ; s2² = 107.8
Confidence interval :
(x1 - x2) ± Tcritical * sqrt[(sp²/n1 + sp²/n2)]
Pooled variance = Sp² = (df1*s1² + df2*s2²) ÷ (n1 + n2 - 2)
df = n - 1
Sp² = (16*90.3 + 12*107.8) / 28
Sp² = 97.8
Tcritical, 90%, df = n1 + n2 - 2 = 28 (1 - tail)
Tcritical = 1.313
(78.4-92)±1.313*sqrt[(sp²/n1 + sp²/n2)]
Margin of Error = Tcritical * sqrt[(sp²/n1 + sp²/n2)] Margin of Error = (1.313 * √(97.8/17 + 97.8/13)) = 4.7771473
Lower boundary :
(78.4-92) - 4.7771473
-13.6 - 4.7771473
= −18.3771473
= - 18.377
The temperature is dropping at a rate of five degrees per hour.
Let d represent the number of degrees the temperature drops.
Lett represent the number of hours that pass.
Which is the independent variable?
the number of hours
the number of degrees the temperature drops
the rate at which the temperature drops
the day of the week
Help me plz I’ll give Brainlyest
Answer:
the rate at which the temperature drops
the day of the week
Step-by-step explanation:
Since we can choose the number of hour, it is dependent on us.
If we set time = 2, then it would 5 x 2 = 10 degree
Similarly, if we change time, the temperature changes. Thus, it is dependent.
Temperature is dropping at a rate of five degrees per hour.
If t = 1, T = 5*1 = 5°, rate = 5
if t = 2, T = 5*2 = 10°, rate = 5
if t = 3, T = 5*3 = 15°, rate = 5
Notice that rate doesnt change, even the temperature and time changes.
Thus, rate is independent.
can you help me for this math?
Answer:
3
Step-by-step explanation:
27-6=7q
21/7=q
3=q
hope it helps
27 = 7q + 6
=> 27 - 6 = 7q
=> 21 = 7q
=> 21/7 = q
=> 3 = q
So, q = 3.
Will someone please help me with finding the median
Answer:
remember this rhyme
Step-by-step explanation:
hey diddle diddle,
the median in the middle
you add and divide for the mean
the mode is the one you see the most
and the range is the differences between.
for median put them in order and then it's the one in the middle
so what you have to do is you have to get all the numbers put them in least to greatest order and slowly you're going to mark one off on the side and then on the other side Mark went off and keep on doing that until you get into the middle and then that should be your median
29. For all values of X,
x^2+2x+4 = (x + 2)^2 + a(x+2) + b,
where a and b are constants. What is the value
of a?
(A) -2
(b) - 1
(c) 0
(d) 1
find the test statictis
Answer:
5
Step-by-step explanation:
Solve for X
Pls help
Answer:
xxxtentacion=6&20
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
The sum of any two intieior angles in a triangle equal to the opposite angle.
So 30 + 5X + 15 = 9X - 3
Solving for X
48 = 4X
X = 12
6. Name the polygon. Write whether it is regular
or not regular
Answer:
this shape is a pentagon. this is a regular shape because all the sides are even and all the angles on the inside are also even.
Step-by-step explanation:
pls mark brainliest!
A light bulb consumes 5400 watt-hours in 3 days and 18 hours. How many watt-hours does it consume per day?
We are given:
Time period: 3 days and 18 hours
Energy consumed in given time period: 5400 watt-hours
Converting time to hours:
We know that one day is 24 hours
So, 3 days = 72 hours
Time period = 3 days + 18 hours
Time period = 72 hours + 18 hours
Time period = 90 hours
Converting to days
Time period = 3.75 days
Watt-hour consumption in a day:
Consumption = 5400 watt-hours / 3.75 days
Consumption = 1440 watt-hours/day
During the last class period of the semester, each student in a graduate computer science class with 10 students is required to give a brief report on his or her class project. The professor randomly selects the order in which the reports are to be given. Two students have been working on similar projects and would like to give their reports consecutively. What is the probability that this will happen
Answer:
Probability = 1/5
Step-by-step explanation:
Total ways of arrangement for 10 students = 10 !
Ways to arrange 2 students consecutively & other 8 students = 9 ! x 2
( As 9! to arrange 9 units, as 2 considered together ; & 2 for arranging 2 consecutive students - respectively )
So, Probability = Favourable outcomes / Total outcomes
= ( 2 x 9! ) / 10! = ( 2 x 9 x 8 x ..... 2 x 1 ) / 10 x 9 x ....... 2 x 1)
= 2 / 10 = 1/5
In 2012, the population of Cincinnati, Ohio, was 296,550 with a population density of approximately 3800 people per square mile. What is the approximate land area of Cincinnati in square miles to the nearest whole number?
Answer:
≈ 78mi^2
Step-by-step explanation:
To find approximate land area:
296,550/3,800 = 78.039
Round to nearest whole number:
Area = 78
Which of the following would not be an example of a compound event?
(1) having a coin land on heads three consecutive times
(2) pulling a king out of a deck of cards
(3) missing two free throws in a row
(4) answering four true/false questions correctly by guessing
The only option that is not a compound event is; (2) pulling a king out of a deck of cards
How to identify a compound event?Compound probability is defined as a mathematical term that relates to the likeliness of two independent events occurring.
Thus, a simple event has only one outcome while a compound event involves the probability of more than one outcome
1) For a coin to land on heads three consecutive times means that there can only be three possible independent outcome and so this is a compound event.
2) Pulling a king out of a deck of cards is a simple event and not compound because it has only one outcome.
3) This is a compound event because we are dealing with two independent probabilities.
4) This is a compound event because we are dealing with two independent events which are true or false answers.
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Abigail goes to a restaurant and the subtotal on the bill was x dollars. A tax of
6% is applied to the bill. Abigail decides to leave a tip of 22% on the entire bill
(including the tax). Write an expression in terms of x that represents the total
amount that Abigail paid.
Answer:
Step-by-step explanation:
Total after tax:
x(1+0.06)
x(1+0.06)
x(1.06)
x(1.06)
1.06x
1.06x
{Total after tip:}
Total after tip:
1.06x(1+0.22)
1.06x(1+0.22)
1.06x(1.22)
1.06x(1.22)
1.2932x
1.2932x
I need help finding the median :)
Answer:
15
Step-by-step explanation:
<4?
What is the solution of 3+
X-2
X-3
O x <3
O XS3
Ox>3
0 x23
Answer:
x < 3
Step-by-step explanation:
3 + x-2/x-3 ≤ 4, x ≠ 3
3 + x-2/x-3 -4 ≤ 0
-1 + x-2/x-3 ≤ 0
-(x-3) + x-2/x-3 ≤ 0
1/x-3 ≤ 0
x-3 < 0
x < 3, x ≠ 3
x < 3
x<3 is the solution of the equation 3 + (x-2) / (x-3) ≤ 4.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given equation can be rewritten as 3 + (x-2) / (x-3) ≤ 4.
To solve for x, we need to multiply both sides by (x-3)
3(x-3) + (x-2) ≤ 4(x-3).
3 + x-2/x-3 -4 ≤ 0
Solve the above equation.
-1 + x-2/x-3 ≤ 0
-(x-3) + x-2/x-3 ≤ 0
1/x-3 ≤ 0
x-3 < 0
x < 3
Hence, x<3 is the solution of the equation 3 + (x-2) / (x-3) ≤ 4.
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Correct Answer= Brainliest
Answer:
49
Step-by-step explanation:
Convert the dot plot into numbers
40, 40, 40, 45, 45, 50, 55, 55, 60, 60
Add all together
40+40+40+45+45+50+55+55+60+60 =490
Divide by amount of numbers there are
Amount of numbers = 10 --> 490/10 = 49
Mean = 49
Peter and his four brothers combined all of their money to buy a video game. If 30% of the total money is Peter's, and $6.00 of the total money is Peter's, how much do all five brothers have combined?
A.
$26.00
B.
$20.00
C.
$14.00
D.
$1.80
Why is the discriminant a useful tool to use when solving quadratic equations?
An experienced census official feels that she can accurately estimate the number of inhabitants of a city block by simply noting the size of the block and the types of buildings (single family homes, apartments, businesses, etc.) that are found on the block. This procedure, if accurate, would be much quicker and cheaper than visiting each residence and taking a survey of its inhabitants. The data below are estimates of block populations provided by the official for 10 blocks in a large city, and the actual numbers of inhabitants for the same 10 blocks. Inhabitants of City Blocks Estimate 193 86 81 87 223 226 151 126 120 76 Actual 163 140 150 179 204 128 73 89 136 145 Step 1 of 2: Find the value of the test statistic for testing whether there is a linear relationship between the actual number of inhabitants and the estimated number. Round your answer to two decimal places, if necessary.
Answer:
035
Step-by-step explanation:
193
86
81
87
223
226
151
126
120
76
Y:
163
140
150
179
204
128
73
89
136
145
Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127
The test statistic :
T = r² / √(1 - r²) / (n - 2)
Sample size, n = 10
Hence,
T = 0.127² / √(1 - 0.127²) / (10 - 2)
T = (0.016129 / 0.3506905)
T = 0.3506905
The value of the test statistic to 2 decimal places is 0.35
A company that makes fasteners has government specifications for a self-locking nut. The locking torque has both a maximum and minimum specified. The offsetting machine used to make these nuts has been producing nuts with an average locking torque of 8.62 in-lb and variance of 4.49 squared in-lb. Torque is normally distributed. If the upper specification is 13.0 in-lb and the lower specification is 2.25 in-lb, what percent of these nuts will meet the specification limits
Answer:
97.95% of these nuts will meet the specification limits.
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.
The offsetting machine used to make these nuts has been producing nuts with an average locking torque of 8.62 in-lb and variance of 4.49 squared in-lb.
This means that [tex]\mu = 8.62, \sigma = \sqrt{4.49}[/tex]
Torque is normally distributed. If the upper specification is 13.0 in-lb and the lower specification is 2.25 in-lb, what percent of these nuts will meet the specification limits?
The proportion is the p-value of Z when X = 13 subtracted by the p-value of Z when X = 2.25. So
X = 13
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13 - 8.62}{\sqrt{4.49}}[/tex]
[tex]Z = 2.07[/tex]
[tex]Z = 2.07[/tex] has a p-value of 0.9808.
X = 2.25
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.25 - 8.62}{\sqrt{4.49}}[/tex]
[tex]Z = -3.01[/tex]
[tex]Z = -3.01[/tex] has a p-value of 0.0013.
0.9808 - 0.0013 = 0.9795
0.9795*100% = 97.95%
97.95% of these nuts will meet the specification limits.
Solve for x and show your steps. Is the solution extraneous? Check your work to show how you extraneous or not.
1 1x + 5 = 7
For the given issue, x has a value of 4. The offered solution is the solution extraneous .
What does the mathematical concept of superfluous mean?When we solve equations, we often obtain values that aren't actually the answer to the equation.
What makes an equation unnecessary?A root of a transformed equation that isn't a root of the previous iteration because it was left out of the original equation's domain is known as a extraneous solution.
According to the given information:√(11x + 5) = 7
(11x + 5) = 7²
11x + 5 = 49
11x = 49 - 5
11x = 44
x = 4
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I NEED HELP FAST PLS
Answer:
234 feet cubed
Step-by-step explanation:
6 1/2 * 8 = 52
52 * 4 1/2 = 234