Answers
Answer:
3
Step-by-step explanation:
Factorial means multiply that number and all numbers below it
3! = 3*2*1 = 6
0! =1
2! = 2*1 = 2
1! =1
6*1
------
2*1
6/2 =3
Related Questions
Rationalize the denominator of $\displaystyle \frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}$, and write your answer in the form\[
\frac{A\sqrt{2} + B\sqrt{3} + C\sqrt{7} + D\sqrt{E}}{F},
\]where everything is in simplest radical form and the fraction is in lowest terms, and $F$ is positive. What is $A + B + C + D + E + F$?
Answers
9514 1404 393
Answer:
57
Step-by-step explanation:
Apparently, you want to simplify ...
[tex]\displaystyle \frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}[/tex]
so the denominator is rational. It looks like the form you want is ...
[tex]\dfrac{A\sqrt{2} + B\sqrt{3} + C\sqrt{7} + D\sqrt{E}}{F}[/tex]
And you want to know the sum A+B+C+D+E+F.
__
We can start by multiplying numerator and denominator by a conjugate of the denominator. Then we can multiply numerator and denominator by a conjugate of the resulting denominator.
[tex]\displaystyle =\frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}\cdot\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{\sqrt{2} + \sqrt{3} - \sqrt{7}}=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\\\\=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\cdot\frac{\sqrt{6}+1}{\sqrt{6}+1}=\frac{(1+\sqrt{6})(\sqrt{2}+\sqrt{3}-\sqrt{7})}{10}\\\\=\frac{\sqrt{2}+\sqrt{3}-\sqrt{7}+2\sqrt{3}+3\sqrt{2}-\sqrt{42}}{10}=\frac{4\sqrt{2}+3\sqrt{3}-\sqrt{7}-\sqrt{42}}{10}[/tex]
Comparing this to the desired form we have ...
A = 4, B = 3, C = -1, D = -1, E = 42, F = 10
Then the sum is ...
A +B +C +D +E +F = 4 + 3 -1 -1 +42 +10 = 59 -2 = 57
The sum of interest is 57.
Computers from a certain manufacturer have a mean lifetime of 62 months, with a standard deviation of 12 months. The distribution of lifetimes is not assumed to be symmetric. Between what two lifetimes does Chebyshev's Theorem guarantee that we will find at least approximately 75% of the computers
Answers
Answer:
Between 38 and 86 months.
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question:
Mean of 62, standard deviation of 12.
Between what two lifetimes does Chebyshev's Theorem guarantee that we will find at least approximately 75% of the computers?
Within 2 standard deviations of the mean, so:
62 - 2*12 = 38
62 + 2*12 = 86
Between 38 and 86 months.
Find an odd natural number x such that LCM (x, 40) = 1400
Answers
Answer:
175.
Step-by-step explanation:
40 = 2*2*2*5
1400 = 2*2*2*5*5*5*7
So by inspection we have x = 5*5*7 = 175
A rectangular board is 1400 millimeters long and 900 millimeters wide. What is the area of the board in square meters? Do not round your answer.
=__M
Answers
Answer:
1260000 millimeters
Step-by-step explanation:
You multiply 1400mm x 900mm and this is the correct answer.
Hope it helps c:
The area of the rectangular board which is 1400 millimeters long and 900 millimeters wide is 1.26 square meters.
What is the area of a rectangular board?If x and y be the length and width of a rectangular board respectively, then the area of that rectangular board is xy square unit.
How to solve this problem?Since 1000 millimeters = 1 meter.
i.e. 1 millimeter = 1/1000 meter.
Now, length of the board = 1400 millimeters = 1400/1000 meters = 1.4 meters
Width of the board = 900 millimeters = 900/1000 meters = 0.9 meter
Area of the board = 1.4 * 0.9 = 1.26 square meters.
Therefore, the area of the rectangular board which is 1400 millimeters long and 900 millimeters wide is 1.26 square meters.
Learn more about area here -
https://brainly.com/question/6843862
#SPJ2
By examining past tournaments, it's possible to calculate the probability that a school wins their first game in the national college basketball tournament. Each school's rank going into the tournament is a strong indicator of their likelihood of winning their first game.
Find the linear regression equation that models this data.
Answers
The linear regression model which models the data is :
y = -6.41053X + 103.83509
Obtaining the regression equation could be performed using either the formula method or using technology (excel, calculator, online regression calculators )
Using technology :
• Enter the data into the columns provided ;
The regression equation obtained for the data is : y = -6.41053X + 103.83509
Where ;
Slope = -6.41053
Intercept = 103.83509
X = Rank
y = probability percentage
Hence, from the linear regression equation obtained, we could see that a negative linear relationship exists between rank and probability as implied from it's negative slope value.
Learn more on linear regression : https://brainly.com/question/12164389
Use the Distributive property to solve this equation
-2(x-4)+8=2
Answers
Answer:
x=7
Step-by-step explanation:
-2(x-4)+8=2(remove brackets by multiplying with -2)
-2x+8+8=2(group like terms and simply)
-2x=2-16(change side change sign)
-2x = -14(divide both sides by -2)
x=7
1/2 of 12=1/4 of?
1/3 of 90=2/3of?
Answers
Answer:
24 and 45
Step-by-step explanation:
Okay, now that I can answer this question with the right answers:
The easy way to do this is to first solve the left hand side of the equation.
1/2 of 12 is the same as 12/2 = 6.
So 6 = 1/4 * x
To solve for that unknown x, just multiply both sides by 4 to cancel out the fraction:
6*4 = 4* 1/4*x
24 = x
For the other equation, do the same thing:
1/3 * 90 = 90/3 = 30
30 = 2/3*x
30*3 = 3* 2/3 *x
90 = 2x
90/2 = 2x/2
45 = x
Find the critical numbers (x-values) of the function y equals 2 x to the power of 5 plus 5 x to the power of 4 minus 19. Enter your answers as a comma-separated list. Round answers to 2 decimal places, if necessary.
Answers
Answer:
[tex]x=0,x=-2[/tex]
Step-by-step explanation:
From the question we are told that:
[tex]y=2x^5+5x^4-19[/tex]
Generally the equation if differentiated is mathematically given by
[tex]y'=10x^4+20x^3-0[/tex]
Where
y'=0
[tex]10x^4+20x^3=0[/tex]
Factorizing,We have
[tex]x=0,x=-2[/tex]
Therefore
The critical points are
[tex]x=0,x=-2[/tex]
20 bottles make 1 fleece jacket how much do 200 make
Answers
Step 1: Write an equation
Before we can write an equation, it’s important to acknowledge what we are trying to solve at this point in the problem.
We should create an equation that will bring us from 20 bottles to 200 bottles. This will tell us how many jackets we will have, since 20 bottles make 1 jacket. This will bring us our answer. Let’s write an equation, with 200 equaling 20 times an unknown number.
20x= 200
Step 2: Solve equation
Now let’s solve for x which will tell us how many jackets we will get. Let’s solve now by isolating x. We need to divide each term by 20.
20x= 200
x= 10
Hope this helps! Comment below for more questions.
If an author wanted to inform readers about the different types of advertisements, how would this shape his essay’s content and delivery? He would take an explanatory tone with readers to reveal the different categories of advertisements. He would take a factual tone to show readers why most advertising is exaggerated or even false. He would take a formal, technical tone telling readers about the amount of advertising they see every day without even noticing it half the time. He would take an amusing tone showing readers the worst advertisments ever created.
Answers
Answer:
a He would take an explanatory tone with readers to reveal the different categories of advertisements
Step-by-step explanation:
a is formal and is the best tone for the paper
A candidate running for public office receives 2,000 of the 8, 000 total votes cast from an election. Name the numerator and denominator
of the fraction that represents the candidate's fraction of the total votes.
Answers
Denominator: 8000
Hope this helps lol
55ml to each container how much to 18 containers
Answers
Answer:
Step-by-step explanation:
770
Answer:
it's very simple!!• 1 container contains =55ml
• So 18 container contains
• 18ml multiply to 55 =
• 990 Answer.
Thank you.please help me with this its really needed
Answers
Answer:
f(x) = log x - 1 --> (10, 0)
f(x) = -(log x - 2) --> (100, 0)
f(x) = log(- x - 2) --> (-3, 0)
f(x) = -log-(x-1) --> (0, 0)
Step-by-step explanation:
An x-intercept is the position where the value of y(in this case f(x)) is 0.
Let's start with the first equation:
f(x) = log x - 1
If f(x) is 0, we would get this equation:
0 = log x - 1
Now, we solve for x:
1 = log x
x = 10
This means the x-intercept is (10, 0).
f(x) = -(log x - 2)
Again, we can set f(x) to 0, and solve for x:
0 = -(log x - 2)
0 = log x - 2
2 = log x
x = 100
This means the x-intercept is (100, 0)
Same process applies for the third:
f(x) = log(- x - 2)
0 = log(- x - 2)
1 = -x - 2
3 = -x
x = -3
(-3, 0)
f(x) = -log-(x-1)
0 = -log-(x-1)
0 = log-(x-1)
1 = -(x-1)
1 = -x + 1
0 = -x
x = 0
(0, 0)
Solve the function.
Plz Help!!
Answers
[tex]1\pm\sqrt{2}i[/tex]
Step-by-step explanation:
We already know that one of the roots is x = -4 so we can factor this out to get
[tex]x^3+2x^2-5x+12=(x+4)(x^2-2x+3)[/tex]
Using the quadratic equation on the 2nd factor, we find the roots are
[tex]x= \dfrac{2\pm\sqrt{(2)^2 - 4(1)(3)}}{2}=1\pm\sqrt{2}i[/tex]
Domain and range problem help please
Answers
Answer:
The domain is the number of copies made (N)
The range is the is the total cost of the books (C)
The domain we know that they made 200 copies, so the domain would be 0-200.
The range would be:
C=10(200)+700
C=200+700
C=900
Range would be 700-900
There are two boxes containing red and blue balls. For box A, there are 3red balls and 7blue balls. For box B, there are 6red balls and 4blue balls. Now randomly pick up one ball from the two boxes, and the selected ball is red. What is the probability that this red ball is from box A
Answers
Answer:
0.3333 = 33.33% probability that this red ball is from box 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: Red ball
Event B: From box A.
Probability of a red ball:
3/10 = 0.3 of 1/2 = 0.5(box A)
6/10 = 0.6 of 1/2 = 0.5(box B). So
[tex]P(A) = 0.3*0.5 + 0.6*0.5 = 0.45[/tex]
Probability of a red ball from box A:
0.3 of 0.5, so:
[tex]P(A \cap B) = 0.3*0.5 = 0.15[/tex]
What is the probability that this red ball is from box A?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.45} = 0.3333[/tex]
0.3333 = 33.33% probability that this red ball is from box A.
a pair of fair dice is rolled anf the sum of the numbers is noted. determine the probability that one die resulted in a 3, given that the sum is 8. g
Answers
Answer:
0.4 = 40% probability that one die resulted in a 3.
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.
Outcomes for the dice:
For the pair of dice:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
So 36 total outcomes.
In this question:
Event A: Sum of 8
Event B: One dice resulting in 3.
Probability of a sum of 8:
These are the following desired outcomes:
(2,6), (3,5), (4,4), (5,3), (6,2)
5 outcomes out of 36, so:
[tex]P(A) = \frac{5}{36}[/tex]
Probability of a sum of 8 and one dice resulting in 3.
(3,5) or (5,3), so 2 outcomes out of 36, and:
[tex]P(A \cap B) = \frac{2}{36}[/tex]
Probability that one die resulted in a 3, given that the sum is 8:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{2}{36}}{\frac{5}{36}} = \frac{2}{5} = 0.4[/tex]
0.4 = 40% probability that one die resulted in a 3.
The claim that 40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available is to be investigated at the 0.02 significance level. If 74 out of the 200 workers sampled said they would return to work, what is our decision
Answers
Answer:
The p-value of the test is of 0.1922 > 0.02, which means that there is not significant evidence to reject the null hypothesis, that is, there is not significant evidence to conclude that the proportion is of less than 40%.
Step-by-step explanation:
Test if the proportion is less than 40%:
At the null hypothesis, we test if the proportion is of at least 0.4, that is:
[tex]H_0: p \geq 0.4[/tex]
At the alternative hypothesis, we test if the proportion is of less than 0.4, that is:
[tex]H_1: p < 0.4[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.4 is tested at the null hypothesis:
This means that [tex]\mu = 0.4, \sigma = \sqrt{0.4*0.6}[/tex]
74 out of the 200 workers sampled said they would return to work
This means that [tex]n = 200, X = \frac{74}{200} = 0.37[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.37 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{200}}}[/tex]
[tex]z = -0.87[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion below 0.37, which is the p-value of z = -0.87.
Looking at the z-table, z = -0.87 has a p-value of 0.1922.
The p-value of the test is of 0.1922 > 0.02, which means that there is not significant evidence to reject the null hypothesis, that is, there is not significant evidence to conclude that the proportion is of less than 40%.
A sum of money increased by its 0.05 in every 6 months after how long time the annual compound interest on Rs. 4000 will be Rs. 1324?
Answers
Answer:
3 x 2 = 6 years to get Rs. 1324
Step-by-step explanation:
This is a mathematical relationship that transcends currencies. In other words, it also applies to Dollars, Pounds and Yen.
“Annual compound interest” is a phrase of dubious meaning. The process is a “compound interest problem”, but the item I think you are looking for is simply the amount of interest.
Month 0: interest: 0 balance: 4,000
Month 6: interest; 200 balance: 4,200
Month 12: interest 210 balance: 4,410 12-month total interest: 410
Month 18: interest: 220.5 balance: 4,630.5 12-month total interest: 430.5
Month 24: interest: 231.525 balance: 4,862.025 12-month total interest: 452.025
Month 30: int: 243.10125 bal: 5,105.12625 12-month total int: 474.35125
Keep expanding this progression until the 12-month total interest meets or exceeds 1324, the answer will be the number of months in the last line.
Use the unit circle to find tan 60°.
a. square root 3/3
c. 2 square root 3/3
b. square root 3/2
d. square root 3
Please select the best answer from the choices provided
A
B
C
D
Answers
the answer is d ( square root 3 )
tan = oposite / adjacent
tan 60° = √3 / 1
= √3
What is the equation of the line that is parallel to the line y = -1/3 x + 4 and passes through the point (6, 5)?
y = x + 3
y = x + 7
y = 3x – 13
y = 3x + 5
Answers
Answer:
x+3
Step-by-step explanation:
that's the line which passes through
Compare the functions shown below:
f(x) = x3 + 2x2 − 4x − 3
g(x) = polynomial graph with x intercepts at negative 2, negative 1, 1, 3, y intercept at 6
h(x) = trig graph with points at 0, 3 and pi over 2, 0 and pi, negative 3 and 3 pi over 2, 0 and 2 pi, 3
Over the interval x = 0 to x = 2π
Which function has the most x-intercepts?
f(x)
g(x)
h(x)
All three functions have the same number of x-intercepts.
Answers
9514 1404 393
Answer:
g(x)
Step-by-step explanation:
f(x) is cubic, so can have at most 3 x-intercepts.
g(x) has 4 x-intercepts listed.
h(x) has 2 x-intercepts listed.
__
g(x) has the most x-intercepts.
Please help! Identify the recursive formula for the sequence 20, 28, 36, 44, . . . .
Answers below in picture:
Answers
Option A
Answered by GauthMath if you like please click thanks and comment thanks
Graphing an integer problem help please
Answers
Answer:
Step-by-step explanation:
Given function is,
h(x) = 1 - 2x
Domain of the function = {-3, -2, 1, 5}
For range of the function,
Substitute the values of 'x' in the function,
h(-3) = 1 - 2(-3)
= 7
h(-2) = 1 - 2(-2)
= 5
h(1) = 1 - 2(1)
= -1
h(5) = 1 - 2(5)
= -9
Therefore, set of range for the function will be {7, 5, -1, -9}
Now plot the ordered pairs,
(-3, 7), (-2, 5), (1, -1), (5, -9)
what is the minimum number of students who must be enrolledin a universitt to guarantee that there are at least two students from the same country
Answers
Answer:
Being that there are 195 countries, there would have to be 390 students
Step-by-step explanation:
Find the value of x.
A. 10
B. 6
C. 14
D. 8
Answers
9514 1404 393
Answer:
B. 6
Step-by-step explanation:
The products of the lengths of the parts of the chord are the same.
7×12 = 14x
7(12)/14 = x = 6 . . . . . divide by 14
Answer:
Option (B)
Step-by-step explanation:
If two chords are intersecting each other at a point insides a circle,
"Product of the measures of the line segments on each chord are equal"
By this property,
MH × HY = TH × HN
By substituting the measures of each segment,
7 × 12 = 14 × ([tex]x[/tex])
[tex]x=\frac{84}{14}[/tex]
[tex]x=6[/tex]
Therefore, Option (B) will be the correct option.
Help me please giving brainliest, look at photo
Answers
Answer:
3x-z+9
Step-by-step explanation:
last option 3x+z+9 .........
If y is 2,851, 1% of Y is
Answers
Excellent question, but let's rephrase it.
Suppose you have a square of surface area of 2851.
What would be a hundredth of such square?
What would be surface area of that hundredth.
Why hundredth? Because percent denotes hundredths cent is a latin word for hundred. You would usually encounter similar word that describes 100 years: century.
Well it is actually very easy. Just divide 2851 into 100 pieces and look at what is the area of one piece.
[tex]2851/100=285.1=y[/tex]
So a single piece has an area of 258.1.
Hope this helps. :)
Question 8 of 53
How much would $700 be worth after 8 years, if it were invested at 5%
interest compounded continuously? (Use the formula below and round your
answer to the nearest cent.)
A(t) = P•e^rt
A. $5887.12
B. $1044.28
C. $6432.11
D. $38,218.71
Answers
9514 1404 393
Answer:
B. $1044.28
Step-by-step explanation:
Putting the given numbers into the given formula, we have ...
A(8) = $700•e^(0.05•8) ≈ $1044.28
C. Find the mean, variance and standard deviation of the following probability distributions. (5 pts.) X 1 6 11 16 21 P(X) 1/7 1/7 2/7 1/7 277 D. Given the population of 5,000 scores with p = 86 and o = 10. How many scores are; (10 pts.) A Between 96 to 1067 B. middle 50% of the distribution? E. How many different samples of size n = 3 can be selected from a population with the following sizes? (5pts)
Answers
(C) You're given a probability mass function,
[tex]P(X=x)=\begin{cases}\frac17&\text{if }x\in\{1,6,16\}\\\frac27&\text{if }x\in\{11,21\}\\0&\text{otherwise}\end{cases}[/tex]
The mean is
[tex]\displaystyle E[X] = \sum_x x\,P(X=x) = \frac{1\times1}7 + \frac{1\times6}7 + \frac{1\times16}7 + \frac{2\times11}7 + \frac{2\times21}7 = \boxed{\frac{87}7} \approx 12.43[/tex]
The variance is
[tex]\displaystyle V[X] = \sum_x x^2\,P(X=x) = \frac{1^2}7 + \frac{6^2}7 + \frac{16^2}7 + \frac{2\times11^2}7 + \frac{2\times21^2}7 = \boxed{\frac{1417}7} \approx 202.43[/tex]
The standard deviation is simply the square root of the variance:
[tex]\sqrt{V[X]} = \boxed{\sqrt{\dfrac{1417}7}} \approx 14.23[/tex]
(D) I'm not entirely sure what is being asked here, so I'm kinda guessing at the meaning. I think the question is saying there is a large set of 5000 test scores that are normally distributed with mean µ = 86 and standard deviation σ = 10.
Let X be the random variable representing these test scores. Then
(D.A)
[tex]P(96 < X < 106) = P\left(\dfrac{96-86}{10} < \dfrac{X-86}{10} < \dfrac{106-86}{10}\right) = P(1 < Z < 2)[/tex]
where Z follows the standard normal distribution with mean 0 and variance 1.
To find the remaining probability, you can use the empirical rule (68/95/99.7) which says
• approximately 68% of a normal distribution lies within 1 standard deviation of the mean; in other words, [tex]P(-1<Z<1)\approx0.68[/tex]
• approximately 95% of the distribution lies within 2 standard deviations; [tex]P(-2<Z<2)\approx0.95[/tex]
The normal distribution is also symmetric about its mean. Taking these facts together, we find
[tex]P(1<Z<2) = \dfrac{P((-2<Z<-1)\text{ or }(1<Z<2))}2 = \dfrac{P(-2<Z<2)-P(-1<Z<1)}2 \approx 0.135[/tex]
So roughly 13.5% of all test scores will fall between 96 and 106, and 13.5% of 5000 is 675. (The actual probability is closer 0.135905, and the projected test score count is closer to 679.)
(D.B) Any 50% of the distribution is still 50% of the distribution, so half of all the test scores would fall in this range. There would be 2500 test scores in that group.
(E) No choices given here...
