A two-digit number is of the number
7
formed by reversing its digits. When the
number is increased by 2 times the sum of
its digits, it becomes 54. Find the number.
Answer:
C
Step-by-step explanation:
The time I spend waiting for the bus on any given day has a distribution with mean 4 min- utes and variance off 0.5 minutes. What is the probability that I spend more than 2 hours and 10 minutes waiting for the bus in one month (30 days)? You may assume that waiting times on different days are independent of each other. HINT: Is there a sum of random variables somewhere in here?
Answer:
0.0049 = 0.49% probability that I spend more than 2 hours and 10 minutes waiting for the bus in one month.
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.
n instances of a normal variable:
For n instances of a normal variable, the mean is:
[tex]M = n\mu[/tex]
[tex]s = \sigma\sqrt{n}[/tex]
Mean of 4 minutes, standard deviation of 0.5 minutes:
This means that [tex]\mu = 4, \sigma = \sqrt{0.5}[/tex]
30 days:
[tex]M = 30(4) = 120[/tex]
[tex]s = \sqrt{0.5}\sqrt{30} = \sqrt{0.5*30} = \sqrt{15}[/tex]
What is the probability that I spend more than 2 hours and 10 minutes waiting for the bus in one month (30 days)?
2 hours and 10 minutes is 2*60 + 10 = 130 minutes, so this probability is 1 subtracted by the p-value of Z when X = 130. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In this context, due to the 30 instances of the normal variable:
[tex]Z = \frac{X - M}{s}[/tex]
[tex]Z = \frac{130 - 120}{\sqrt{15}}[/tex]
[tex]Z = 2.58[/tex]
[tex]Z = 2.58[/tex] has a p-value of 0.9951.
1 - 0.9951 = 0.0049
0.0049 = 0.49% probability that I spend more than 2 hours and 10 minutes waiting for the bus in one month.
A local food bank uses volunteers to staff the kitchen. If there are 30 college students working there out of a total of 100 volunteers, what is the probability that in a sample of 10 volunteers, 4 of them are college students? Four decimal places please!
find the amount of time to the nearest day it would take a deposit of $2500 to grow to $1 million at 2% compounded continuously. find how many days & years
Answer:
Years = natural log (Total / Principal) / Rate
Years = natural log (1,000,000 / 2,500) / .02
Years = natural log (400) / .02
Years = 5.9914645471 / .02
It would take 299.573227355 Years
Source: http://www.1728.org/rate2.htm
Step-by-step explanation:
(x)=4log(x+2) Which interval has the smallest average rate of change in the given function? 1≤x≤3 5≤x≤7 3≤x≤5 −1≤x≤1
Answer:
5≤x≤7
Step-by-step explanation:
For a given function f(x), the average rate of change in a given interval:
a ≤ x ≤ b
is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Here we have:
f(x) = 4*log(x + 2)
And we want to see which interval has the smallest average rate of change, so we just need fo find the average rate of change for these 4 intervals.
1) 1≤x≤3
here we have:
[tex]r = \frac{f(3) - f(1)}{3 - 1} = \frac{4*log(3 + 2) - 4*log(1 + 2)}{2} = 0.44[/tex]
2) 5≤x≤7
[tex]r = \frac{f(7) - f(5)}{7 - 5} = \frac{4*log(7 + 2) - 4*log(5 + 2)}{2} = 0.22[/tex]
3) 3≤x≤5
[tex]r = \frac{f(5) - f(3)}{5 - 3} = \frac{4*log(5 + 2) - 4*log(3 + 2)}{2} = 0.29[/tex]
4) −1≤x≤1
[tex]r = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{4*log(1 + 2) - 4*log(-1 + 2)}{2} = 0.95[/tex]
So we can see that the smalles average rate of change is in 5≤x≤7
Turn 43 1/23 into an improper fraction
Answer:
990/23
Step-by-step explanation:
Step 1
Multiply the denominator by the whole number
23 × 43 = 989
Step 2
Add the answer from Step 1 to the numerator
989 + 1 = 990
Step 3
Write answer from Step 2 over the denominator
990/23
I hope this answer helps you out! Brainliest would be appreciated.
what is b x b equialent to?
Answer:
b^2
Step-by-step explanation:
You're going to add the exponents from b x b, both carry a 1 in their powers (or exponents)
so b^1 + b^1 = b^2
Answer:
b^2
Step-by-step explanation:
b*b = b^2
The maximum and minimum Values of a quadratic function are called as______of the function.
Answer:
the answer is B ...Extreme Values
look at the image below
Answer:
SA = 153.9m^2
Step-by-step explanation:
SA = 4[tex]\pi[/tex][tex]r^{2}[/tex]
r = 3.5
SA = 4[tex]\pi[/tex][tex](3.5)^{2}[/tex]
SA = 4[tex]\pi[/tex](12.25)
SA = 49[tex]\pi[/tex]
SA = 153.9m^2
Please help me answer this question?
Answer:
2+2
Step-by-step explanation:
2 + 4!
3-5
3_4
3-6
2-5
2+5
2_3
2-5
Answer:
(A) 12x³ - 12x
(B) -288
(C) y = -288x - 673
(D) x = 0, 1, -1
Step-by-step explanation:
See images. If it's not clear let me know.
in a survey of 90 students, the ratio of those who work outside the home to those who don't is 6:4. How many students work outside the home according to this survey? SHOW ALL WORK! AND ONLY ANSWER IF YOU KNOW THE ANSWER!
9514 1404 393
Answer:
54
Step-by-step explanation:
The fraction of the total that work outside the home is ...
outside/(outside +inside) = 6/(6+4) = 6/10
Then the number of those surveyed who work outside the home is ...
(6/10)(90) = 54 . . . work outside the home
Use the given information to find the number of degrees of freedom, the critical values χ2L and χ2R, and the confidence interval estimate of σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Nicotine in menthol cigarettes 99% confidence; n=23, s=0.28 mg.
df = (Type a whole number.)
χ2L = (Round to three decimal places as needed.)
χ2R = (Round to three decimal places as needed.)
The confidence interval estimate of σ is __ mg < σ < __ mg. (Round to two decimal places as needed.)
Answer:
χ²R = 8.643
χ²L = 42.796
0.20 < σ < 0.45
Step-by-step explanation:
Given :
Sample size, n = 23
The degree of freedom, df = n - 1 = 23 - 1 = 22
At α - level = 99%
For χ²R ; 1 - (1 - 0.99)/2= 0.995 ; df = 22 ; χ²R = 8.643
For χ²L ; (1 - 0.99)/2 = 0.005 ; df = 22 ; χ²L = 42.796
The confidence interval of σ ;
s * √[(n-1)/χ²L] < σ < s * √[(n-1)/χ²R)]
0.28 * √(22/42.796) < σ < 0.28 * √(22/8.643)
0.2008 < σ < 0.4467
0.20 < σ < 0.45
Using Eulers formula, how many edges does a polyhedron with 9 faces and 14 vertices have?
F + V = E + 2
SolutionF = 9V = 14E = ?Substuting the values⇨ 9 + 14 = E + 2
⇨ 23 = E + 2
⇨ 23 - 2 = E
⇨ 21 = E
Hence , the number of edges in polyhedron is 21.
The number of edges of a polyhedron with 9 faces and 14 vertices have will be 21.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
here, we have,
Using Euler's formula, the number of the edges does a polyhedron with 9 faces and 14 vertices have
We know the formula for the edges of the polyhedron will be
By Euler's Formula
F + V = E + 2
The number of faces, vertices, and edges of a polyhedron are denoted by the letters F, V, and E.
Then we have
Solution
F = 9
V = 14
E = ?
Substuting the values
⇨ 9 + 14 = E + 2
⇨ 23 = E + 2
⇨ 23 - 2 = E
⇨ 21 = E
Hence , the number of edges in polyhedron is 21.
More about the polygon link is given below.
brainly.com/question/17756657
#SPJ2
In the statements below, V is a vector space. Mark each statement true or false. Justily each answer a. The set R is a two-dimensional subspace of R3.Choose the correct answer below O A. False, because R2 is not closed under vector addition. O B. True, because R2 is a plane in R3 Ос. False, because the set R2 is not even a subset of R3 OD. True, because every vector in R2 can be represented by a linear combination of vectors inR3 b. The number of variables in the equation Ax 0 equa's the dimension of Nul A. Choose the correct answer below O A. False, because the number of free variables is equal to the dimension of Nul A. O B. True, because the number of variables in the equation Ax 0 equals O C. True, because the dimension of Nul A equals the largest any solution to O D. False, because the number of plvot columns is equal to the dimension of Nud A. c. A vector space the number of columns in A and the number of columns in A equa's the dimension of Nul A. number of Os in any solution to the equation Ax -b, and the equation Ax- 0 always has the trivial solution, so the number of variables is infinite-dimensional if it is spanned by an infinite set Choose the correct answer below O A. True, because the dimension of a vector space is equal to the number of elements in a set that spans O B. Faise, because a basis for the vector space may O C. True, because the dimension of a vector space number of O D. Faise, because all vector spaces are finite-dimensional. d. If dim Van and it S spans V, then S is a basis of V. Choose the correct answer below. the vector space. have only finitely many elements, which would make the vector space finite-dimensional is the number of vectors in a basis for that vector space, and a vector space spanned by an infinite set has a basis with an infinite number of vect O A. False, because the set S must have less than n elements O B. True, because if a vector space is finite-dimensional, then a set that spans t is a basis of the vector space O C. False, in order for S to be a basis, it must also have n elements O D. True, because if a set spans a vector space, regardiess of the dimension of the vector space, then that setis a basis of the vector spaoe e. The only three-dimensional subspace of R3 is R3 itself. Choose the correct answer below Faise, because False, because any subspaces of R3 which contain three-element vectors are three-dimensional, but most of these most three-dimensional subspaces of R3 are spanned by a linearly dependent set of tree vectors, but R can only be sparned by thre Inearly independent vectors subspaces do not contain all of R
D. True, because any three linearly dependent vectors in R3 span all of R3, so there is no three-dmensional subspace of R' that is not R
Answer:
A. False
B. True
C. False
D. True
Step-by-step explanation:
Only three dimensional subspace for R3 is R3 itself. In a 3 d subspace there are 3 basis vectors which are all linearly independent vectors. Dimension of a vector is number of subspace in that vector. Finite set can generate infinite dimension vector space.
2 cans of beans cost 98¢ how many cans can you buy for $3.92?
Which letter on the diagram below represent a diameter of the circle
Answer:
where is your diagram?
Step-by-step explanation:
f(x)=3(x+5)+4/xwhat is f (a+2) solve this problem with showing the work
A sample of 45 bottles of soft drink showed a variance of 1.1 in their contents. The process engineer wants to determine whether or not the standard deviation of the population is significantly different from 0.9 ounces. What is the value of the test statistic
Answer:
The value of the test statistic is 59.75.
Step-by-step explanation:
The test statistic for the population standard deviation is:
[tex]\chi^2 = \frac{n-1}{\sigma_0^2}s^2[/tex]
In which n is the sample size, [tex]\sigma_0[/tex] is the value tested and s is the sample standard deviation.
A sample of 45 bottles of soft drink showed a variance of 1.1 in their contents.
This means that [tex]n = 45, s^2 = 1.1[/tex]
The process engineer wants to determine whether or not the standard deviation of the population is significantly different from 0.9 ounces.
0.9 is the value tested, so [tex]\sigma_0 = 0.9, \sigma_0^2 = 0.81[/tex]
What is the value of the test statistic
[tex]\chi^2 = \frac{n-1}{\sigma_0^2}s^2[/tex]
[tex]\chi^2 = \frac{44}{0.81}1.1 = 59.75[/tex]
The value of the test statistic is 59.75.
Help me because I dont understand
Answer:
105 sq ft + 31 sq ft
Step-by-step explanation:
= 136 sq ft
Hope it helps✌✌
In 1815, Sophie Germain won a mathematical prize given by the Institut de France for her work on the theory of elasticity. The prize was a medal made of 1 kilogram of gold. How much is the medal worth today in U.S. dollars and in euros
Answer:
gold price : $58.72/gram
$58,720 per kilo(1000) grams
Step-by-step explanation:
Prove that A.M, G.M. and H.M between any two unequal positive numbers satisfy the following relations.
i. (G.M)²= (A.M)×(H.M)
ii.A.M>G.M>H.M
Answer:
See below
Step-by-step explanation:
we want to prove that A.M, G.M. and H.M between any two unequal positive numbers satisfy the following relations.
(G.M)²= (A.M)×(H.M) A.M>G.M>H.Mwell, to do so let the two unequal positive numbers be [tex]\text{$x_1$ and $x_2$}[/tex] where:
[tex] x_{1} > x_{2}[/tex]the AM,GM and HM of [tex]x_1[/tex] and[tex] x_2[/tex] is given by the following table:
[tex]\begin{array}{ |c |c|c | } \hline AM& GM& HM\\ \hline \dfrac{x_{1} + x_{2}}{2} & \sqrt{x_{1} x_{2}} & \dfrac{2}{ \frac{1}{x_{1} } + \frac{1}{x_{2}} } \\ \hline\end{array}[/tex]
Proof of I:[tex] \displaystyle \rm AM \times HM = \frac{x_{1} + x_{2}}{2} \times \frac{2}{ \frac{1}{x_{1} } + \frac{1}{x_{2}} } [/tex]
simplify addition:
[tex] \displaystyle \frac{x_{1} + x_{2}}{2} \times \frac{2}{ \dfrac{x_{1} + x_{2}}{x_{1} x_{2}} } [/tex]
reduce fraction:
[tex] \displaystyle x_{1} + x_{2} \times \frac{1}{ \dfrac{x_{1} + x_{2}}{x_{1} x_{2}} } [/tex]
simplify complex fraction:
[tex] \displaystyle x_{1} + x_{2} \times \frac{x_{1} x_{2}}{x_{1} + x_{2}} [/tex]
reduce fraction:
[tex] \displaystyle x_{1} x_{2}[/tex]
rewrite:
[tex] \displaystyle (\sqrt{x_{1} x_{2}} {)}^{2} [/tex]
[tex] \displaystyle AM \times HM = (GM{)}^{2} [/tex]
hence, PROVEN
Proof of II:[tex] \displaystyle x_{1} > x_{2}[/tex]
square root both sides:
[tex] \displaystyle \sqrt{x_{1} }> \sqrt{ x_{2}}[/tex]
isolate right hand side expression to left hand side and change its sign:
[tex]\displaystyle\sqrt{x_{1} } - \sqrt{ x_{2}} > 0[/tex]
square both sides:
[tex]\displaystyle(\sqrt{x_{1} } - \sqrt{ x_{2}} {)}^{2} > 0[/tex]
expand using (a-b)²=a²-2ab+b²:
[tex]\displaystyle x_{1} -2\sqrt{x_{1} }\sqrt{ x_{2}} + x_{2} > 0[/tex]
move -2√x_1√x_2 to right hand side and change its sign:
[tex]\displaystyle x_{1} + x_{2} > 2 \sqrt{x_{1} } \sqrt{ x_{2}}[/tex]
divide both sides by 2:
[tex]\displaystyle \frac{x_{1} + x_{2}}{2} > \sqrt{x_{1} x_{2}}[/tex]
[tex]\displaystyle \boxed{ AM>GM}[/tex]
again,
[tex]\displaystyle \bigg( \frac{1}{\sqrt{x_{1} }} - \frac{1}{\sqrt{ x_{2}}} { \bigg)}^{2} > 0[/tex]
expand:
[tex]\displaystyle \frac{1}{x_{1}} - \frac{2}{\sqrt{x_{1} x_{2}} } + \frac{1}{x_{2} }> 0[/tex]
move the middle expression to right hand side and change its sign:
[tex]\displaystyle \frac{1}{x_{1}} + \frac{1}{x_{2} }> \frac{2}{\sqrt{x_{1} x_{2}} }[/tex]
[tex]\displaystyle \frac{\frac{1}{x_{1}} + \frac{1}{x_{2} }}{2}> \frac{1}{\sqrt{x_{1} x_{2}} }[/tex]
[tex]\displaystyle \rm \frac{1}{ HM} > \frac{1}{GM} [/tex]
cross multiplication:
[tex]\displaystyle \rm \boxed{ GM >HM}[/tex]
hence,
[tex]\displaystyle \rm A.M>G.M>H.M[/tex]
PROVEN
Diane must choose a number between 49 and 95 that is a multiple of 2, 3, and 9. Write all the numbers that she could choose. If
there is more than one number, separate them with commas?
The set of numbers that Diane can choose is:
{54, 60, 66, 72, 78, 84, 90}
Finding common multiples of 2, 3, and 6:
A number is a multiple of 2 if the number is even.
A number is a multiple of 3 if the sum of its digits is multiples of 3.
A number is a multiple of 6 if it is a multiple of 2 and 3.
Then we only need to look at the first two criteria.
First, let's see all the even numbers in the range (49, 95)
These are:
{50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94}
All of these are multiples of 2.
Now we need to see which ones are multiples of 3.
To do it, we sum its digits and see if that sum is also a multiple of 3.
50: 5 + 0 = 5 this is not multiple of 3.
52: 5 + 2 = 7 this is not multiple of 3.
54: 5 + 4 = 9 this is multiple of 3, so 54 is a possible number.
And so on, we will find that the ones that are multiples of 3 are:
54: 5 + 4 = 9.
60: 6 + 0 = 6
66: 6 + 6 = 12
72: 7 + 2 = 9
78: 7 + 8 = 15
84: 8 + 4 = 12
90:9 + 0 = 9
Then the numbers that Diane could choose are:
{54, 60, 66, 72, 78, 84, 90}
If you want to learn more about multiples, you can read:
https://brainly.com/question/1553674
A sample of 375 college students were asked whether they prefer chocolate or vanilla ice cream. 210 of those surveyed said that they prefer vanilla ice cream. Calculate the sample proportion of students who prefer vanilla ice cream.
Answer:
The sample proportion of students who prefer vanilla ice cream is 0.56.
Step-by-step explanation:
Sample proportion of students who prefer vanilla ice cream:
Sample of 375 students.
Of those, 210 said they prefer vanilla ice cream.
The proportion is:
[tex]p = \frac{210}{375} = 0.56[/tex]
The sample proportion of students who prefer vanilla ice cream is 0.56.
Simplify the given expression.
Answer:
8x-21
----------------------
(2x-7)(2x+7)
Step-by-step explanation:
7 4
----------- + ------------
4x^2 -49 2x+7
Factor ( notice that it is the difference of squares)
7 4
----------- + ------------
(2x)^2 - 7^2 2x+7
7 4
----------- + ------------
(2x-7)(2x+7) 2x+7
Get a common denominator
7 4(2x-7)
----------- + ------------
(2x-7)(2x+7) (2x-7)(2x+7)
Combine
7 +4(2x-7)
----------------------
(2x-7)(2x+7)
7 +8x-28
----------------------
(2x-7)(2x+7)
8x-21
----------------------
(2x-7)(2x+7)
Answer:
(8x - 21) / (2x + 7)(2x - 7)
Step-by-step explanation:
7 / (4x^2 - 49)+ 4 / (2x + 7)
= 7 / (2x + 7)(2x - 7) + 4 / (2x + 7)
LCM = (2x + 7)(2x - 7) so we have
(7 + 4(2x - 7) / (2x + 7)(2x - 7)
= (8x - 21) / (2x + 7)(2x - 7).
If y = ax^2 + bx + c passes through the points (-3,10), (0,1) and (2,15), what is the value of a + b + c?
Hi there!
[tex]\large\boxed{a + b + c = 6}[/tex]
We can begin by using the point (0, 1).
At the graph's y-intercept, where x = 0, y = 1, so:
1 = a(0)² + b(0) + c
c = 1
We can now utilize the first point given (-3, 10):
10 = a(-3)² + b(-3) + 1
Simplify:
9 = 9a - 3b
Divide all terms by 3:
3 = 3a - b
Rearrange to solve for a variable:
b = 3a - 3
Now, use the other point:
15 = a(2)² + 2(3a - 3) + 1
14 = 4a + 6a - 6
Solve:
20 = 10a
2 = a
Plug this in to solve for b:
b = 3a - 3
b = 3(2) - 3 = 3
Add all solved variables together:
2 + 3 + 1 = 6
PLEASE HELPPPPPPPPPPPPPP
Answer:
False
Step-by-step explanation:
To find the inverse of a function, switch the variables and solve for y.
The inverse of f(n)=-(n+1)^3:
[tex]y=-(n+1)^3[/tex]
[tex]n=-(y+1)^3[/tex]
[tex]\sqrt[3]{n} =-(y+1)[/tex]
[tex]\sqrt[3]{n} =-y-1[/tex]
[tex]\sqrt[3]{n} +1=-y[/tex][tex]-(\sqrt[3]{n} +1)=y[/tex]
[tex]-\sqrt[3]{n} -1=y[/tex]
Answer:
False
Step-by-step explanation:
Find the missing segment in the image below
Answer:
Step-by-step explanation:
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:Mark Brainliest please
Answer is 4.86 which is rounded to 5
Step-by-step explanation:
Cos 40 degree = VW/7
0.694 =VW/7
0.694 * 7 =VW
4.858 =VW
VW=4.86 is the answer
 Solve each system by graphing.
9514 1404 393
Answer:
(x, y) = (4, -4)
Step-by-step explanation:
A graphing calculator makes graphing very easy. The attachment shows the solution to be (x, y) = (4, -4).
__
The equations are in slope-intercept form, so it is convenient to start from the y-intercept and use the slope (rise/run) to find additional points on the line.
The first line can be drawn by staring at (0, -2) and moving down 1 grid unit for each 2 to the right.
The second line can be drawn by starting at (0, 2) and moving down 3 grid units for each 2 to the right.
The point of intersection of the lines, (4, -4), is the solution to the system of equations.
0.14 converted as a fraction simplest form.
Answer: 7 / 50
Step-by-step explanation:
Given
0.14
Convert to 100-denominator fraction
= 14 ÷ 100
= 14/100
Divide both numerator and denominator by 2
=(14 ÷ 2) / (100 ÷ 2)
=7 / 50
Hope this helps!! :)
Please let me know if you have any questions
