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}
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Use the discriminant to
determine the number
of real solutions to the
equation.
Зm2 = -6
Answer:
m=-1 I think
Step-by-step explanation:
What percent of 30 is 3?
Answer:
10%
Step-by-step explanation:
3/30 × 100 = 100
Therefore 3 is 10% of 30
3 is 10 percent of 30.
To determine what percent of 30 is 3, we can use the concept of finding a proportion or ratio.
The proportion can be set up as follows:
3 is what percent of 30?
Let x represent the unknown percentage.
Using the formula for finding the percentage, we can write:
x/100 = 3/30
To simplify the equation, we divide both sides by 3:
x/100 = 1/10
To isolate x, we multiply both sides by 100:
x = (1/10)100
Simplifying the expression, we have:
x = 10
Therefore, 3 is 10% of 30.
To understand this calculation, we can interpret it as follows: If we consider 30 as the whole or 100%, then 3 is a fraction of that whole. By dividing 3 by 30 and multiplying by 100, we find that 3 is equivalent to 10% of 30.
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solve the equation simultaneously. Y=x² + 2x + 1, Y= x²+2x - 2.. Solve for the values of X and Y.
The two functions should never intersect.
Since y = y, we can equate the other side of both equations together.
x^2 + 2x + 1 = x^2 + 2x - 2
Rearrange the equation to bring all the terms to one side.
0 = x^2 - x^2 + 2x - 2x - 2 - 1
0 = -3
You can see that does not make sense, so we can conclude that there are no points of intersection between the two functions.
I also graphed the functions. In the first pic you can see that the red is between the blue and they don't intersect. In the second pic I zoomed in so you can see the right side of the graph going up to y = 600 and the red is still between the blue.
Write each word phrase as an algebrale
expression for exercises 66-69
66) ten less than a number
67) the product of x andy
The algebraic expression for ten less than n
66) ten less than a number
Let the number be n
= n - 10
67) the product of x and y
= x × y or xy
68) The algebraic expression for ten less than n
= n - 10
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Define limit and it's types.
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value.
g(x) , one may look at how big f(x) and g(x) are. For example: If f(x) is close to some positive number and g(x) is close to 0 and positive, then the limit will be ∞. If f(x) is close to some positive number and g(x) is close to 0 and negative, then the limit will be −∞.
A. X is a random variable denotes number of customers visiting a local coffee shop, which follows a Poisson distribution. The mean number of customers per 10 minutes is 6.
a. What is the probability that there are 8 or less customers in the next 20 minutes?
b. What is the probability that there are more than 4 customers in the next 10 minutes?
B. X is a random variable denotes number of customers visiting a local coffee shop, which follows a Poisson distribution. The mean number of customers per 6 minutes is 6?
a. What is the probability the associate have to wait less than 1 minute to have the next customer showing up?
C. X is a random variable denotes number of customers visiting a local coffee shop, which follows a Poisson distribution. The mean number of customers per 6 minutes is 12?
a. What is the probability the associate have to wait more than 1 minutes to have the next customer showing up?
A
(a) You're looking for
[tex]P(X\le 8) = \displaystyle \sum_{x=0}^8 P(X=x)[/tex]
where
[tex]P(X=x) = \begin{cases}\dfrac{\lambda^x e^{-\lambda}}{x!}&\text{if }x\in\{0,1,2,\ldots\}\\0&\text{otherwise}\end{cases}[/tex]
Customers arrive at a mean rate of 6 customers per 10 minutes, or equivalently 12 customers per 20 minutes, so
[tex]\lambda = \dfrac{12\,\rm customers}{20\,\rm min}\times(20\,\mathrm{min}) = 12\,\mathrm{customers}[/tex]
Then
[tex]\displaystyle P(X\le 8) = \sum_{x=0}^8 \frac{12^x e^{-12}}{x!} \approx \boxed{0.155}[/tex]
(b) Now you want
[tex]P(X\ge4) = 1 - P(X<4) = 1 - \displaystyle\sum_{x=0}^3 P(X=x)[/tex]
This time, we have
[tex]\lambda = \dfrac{6\,\rm customers}{10\,\rm min}\times(10\,\mathrm{min}) = 6\,\mathrm{customers}[/tex]
so that
[tex]P(X\ge4) = 1 - \displaystyle \sum_{x=0}^3 \frac{6^x e^{-6}}{x!} \approx \boxed{0.849}[/tex]
B
(a) In other words, you're asked to find the probability that more than 1 customer shows up in the same minute, or
[tex]P(X > 1) = 1 - P(X \le 1) = 1 - P(X=0) - P(X=1)[/tex]
with
[tex]\lambda = \dfrac{6\,\rm customers}{6\,\rm min}\times(1\,\mathrm{min}) = 1\,\mathrm{customer}[/tex]
So we have
[tex]P(X > 1) = 1 - \dfrac{1^0 e^{-1}}{0!} - \dfrac{1^1 e^{-1}}{1!} \approx \boxed{0.264}[/tex]
C
(a) Similar to B, you're looking for
[tex]P(X \le 1) = P(X=0) + P(X=1)[/tex]
with
[tex]\lambda = \dfrac{12\,\rm customers}{6\,\rm min}\times(1\,\mathrm{min}) = 2\,\mathrm{customers}[/tex]
so that
[tex]P(X\le1) = \dfrac{2^0e^{-2}}{0!} + \dfrac{2^1e^{-2}}{1!} \approx \boxed{0.406}[/tex]
1. On the set of axes below, graph . State the roots of
Is this question complete?
what is the answer to 5- -8
Answer:
13
5 - -8
When you subtract a negative number it changes to an addition so 5- -8 becomes 5 + 8 which equals 13.
How many oxygen atoms O are there when there are 6 sulfur atoms?
Answer:
There are 12 oxygens for 6 sulfur
Suppose that 17 inches of wire costs 68 cents.
At the same rate, how much (in cents) will 39 inches of wire cost?
cents
Х
5
?
Answer:
5
Step-by-step explanation:
17 inches is equal to 39 inches and it's answer is 5
Cost of 17 inches of wire = 68 cents
Cost of 1 inch of wire
= 68 cents/17
= 4 cents
Cost of 39 inches of wire
= 4 cents × 39
= 156 cents
= $1.56
yes it's surprisingly for highschool can someone help I just can't figure it out
22
Step-by-step explanation:
For simplicity, let
x = teary smiley
y = tongue smiley
z = plain smiley
So now our system of equations is
[tex]x + x + x = 12\:\:\:\:\:\:(1)[/tex]
[tex]y + z + x = 18\:\:\:\:\:\:\:(2)[/tex]
[tex]z + z + y = 22\:\:\:\:\:\:\:(3)[/tex]
[tex]z + y + 2x= ??\:\:\:\:\:\:(4)[/tex]
From Eqn(1), we plainly see that
[tex]3x = 12 \Rightarrow x = 4[/tex]
Now subtract Eqn(2) from Eqn(3) to get
[tex](2z + y) - (y + z + x) = 22 - 18[/tex]
[tex]\Rightarrow z - x = 4[/tex]
But we know that [tex]x = 4[/tex], which then gives us [tex]z = 8.[/tex]
Using the values of [tex]x[/tex] and [tex]z[/tex] in Eqn(2), we find that [tex]y = 6.[/tex] Now that we the values of all the variables, use them in Eqn(3) and we'll get
[tex](8) + (6) + 2(4) = 22[/tex]
13 is subtracted from the product of 4 and a certain number. The result is equal to the sum of 5 and the original number. Find the number.
Answer:
The number is 6.
Step-by-step explanation:
[tex]4x-13=x+5\\3x-13=5\\3x=18\\x=6[/tex]
Find an equation of the line through the given pair of points. (-7,-5) and (-1,-9) The equation of the line is (Simplify your answer. Type an equation using x and y as the variables. Use integers or fractions for any numbers in the equation.) please help
Answer:
The equation of the line is y = -2/3x - 29/3
Step-by-step explanation:
The slope of these points (-7,-5) and (-1,-9) is m = -2/3
Once you plug that into the y = mx + b equation, you can see that the y-intercept is -29/3.
Put all of that into the y = mx + b equation and you'll get --> y = -2/3x - 29/3
How??????????????????????
Answer:
y=-1/3x+7
Step-by-step explanation:
y=mx+c
m=-1/3, c=7
y=-1/3x+7
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.
Write these numbers in expanded form 132 480 302
Step-by-step explanation:
132 = 100×1+3×10+2×1
480 = 100×4+8×10+0×1
302 = 100×3+0×10+2×1
How many terms of the series 2 + 5 + 8 + … must be taken if their sum is 155
9514 1404 393
Answer:
10
Step-by-step explanation:
The sum of terms of an arithmetic series is ...
Sn = (2a +d(n -1))·n/2 = (2an +dn^2 -dn)/2
For the series with first term 2 and common difference 3, the sum is 155 for n terms, where ...
155 = (3n^2 +n(2·2 -3))/2
Multiplying by 2, we have ...
3n^2 +n -310 = 0 . . . . . arranged in standard form
Using the quadratic formula, the positive solution is ...
n = (-1 +√(1 -4(3)(-310)))/(2(3)) = (-1 +√3721)/6 = (61 -1)/6 = 10
10 terms of the series will have a sum of 155.
Step-by-step explanation:
[tex]\displaystyle \ \Large \boldsymbol{} S_n=\frac{2a_1+d(n-1)}{2} \cdot n =155 \\\\ \frac{4+3(n-1)}{2} \cdot n =155 \\\\\\ 4n+3n^2-3n=310 \\\\ 3n^2+n-310=0 \\\\D=1+3720=3721=61^2\\\\n_1=\frac{61-1}{6} =\boxed{10} \\\\\\n_2=\frac{-61-1}{3} \ \ \o[/tex]
How many titles are in the nth figure
Please help——- Geometry problem
Thank you.
Answer:
b
Step-by-step explanation:
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{s\sqrt{3} }{2s}[/tex] ( cancel s on numerator/ denominator ), then
sinA = [tex]\frac{\sqrt{3} }{2}[/tex] → b
Identifying equivalent statements and negations of a conditional statement: help
Attached is the photo reference.
Answer:
1: Equal
2: Negation
3: Negation
4: Neither
Step-by-step explanation:
Sorry if I got any of them wrong
The complement of set S is the set of elements in U and ___ in S
9514 1404 393
Answer:
not
Step-by-step explanation:
The complement of set S is the set of elements in U and not in S.
_____
It's a definition.
The mean of 5 conservative odd number is 11, find the numbers
I bet you meant "consecutive". If x is the smallest of the 5 numbers, then the other 4 are x + 1, x + 2, x + 3, and x + 4. If their mean is 11, then
(x + (x + 1) + (x + 2) + (x + 3) + (x + 4))/5
= (5x + 10)/5
= x + 2 = 11
==> x = 9
Then the five numbers are {9, 10, 11, 12, 13}.
Alternatively, since we're talking about an odd number of consecutive integers, the mean among them will always be the number in the middle. So if 11 is the mean, and there are five numbers overall, then we just take the four closest integers to 11, two on either side.
Help!!
A.) show work as you evaluate the composition: (g o g) (2)
B.) show work as you find: f^-1 (x)
C.) show a composition of the two functions f and g. Are they inverse functions, explain using a complete sentence
Answer:
Hello,
Step-by-step explanation:
[tex]A)\\g(x)=\dfrac{x-5}{-3} =\dfrac{-x}{3} +\dfrac{5}{3} \\\\(gog)(x)=g(g(x))=g(\dfrac{-x}{3} +\dfrac{5}{3})\\\\=\dfrac{\dfrac{-x}{3} +\dfrac{5}{3} }{3}+\dfrac{5}{3} \\\\\\=\dfrac{-x}{9} +\dfrac{5}{9} +\dfrac{5}{3}\\\\=-\dfrac{x}{9}+\dfrac{20}{9} \\\\\\(gog)(2)=-\dfrac{2}{9}+\dfrac{20}{9} =\dfrac{18}{9}=2 \\\\[/tex]
[tex]B)\\f(x)=y=-3x-5\\exchanging\ y\ and\ x\\x=-3y-5\\3y=-x-5\\\\y=\dfrac{-x}{3} -\dfrac{5}{3} \\\\f^{-1}(x)=\dfrac{-x}{3} -\dfrac{5}{3} \\\\[/tex]
[tex]C)\\\\(fog)(x)\ must\ be\ equal\ to\ x\\\\\\(fog)(x)=g(f(x))=g(-3x-5)\\\\=\dfrac{-(-3x-5)}{3} +\dfrac{5}{3} \\\\=x+\dfrac{5}{3} +\dfrac{5}{3} \\\\\\=x+\dfrac{10}{3}\ and\ not\ x\ !!!\\[/tex]
f(x) and g(x) are not inverse functions.
Only the top runners in the world can finish a marathon in close to 2 hours. This graph
shows the pace that one such runner followed in a race. What is the unit rate?
Marathon Pace
N
28
24
20
Distance (mi)
10
12
B
8
A
4
0
0 20 40 60 80 100120140
Time (min)
Answer:
the unit rate is 4mi per minute.
Step-by-step explanation:
if you find the slope between point A and point B, you see that the line rises at 4 mi (distance) per minute (time). thus the unit rate is 4mi per minute. please correct me if I'm wrong, I hope this answer helps.
What is the smallest number that has both 6 and 9 as a
factor?
A 54
B 12
C 36
D 18
Answer:
yep it's D
Step-by-step explanation:
For each of the indicates values given for x and y, determine which expression has a greater value (x+y)^2 or (x-y)^2
if Albert gives 30$ to George both of them will have the same amount of money.if George give 50$ to Albert,Albert will have 5 times as much money as George. how much money do both of them have altogether
Step-by-step explanation:
let George money will be X and Albert be Y
30$+x=y
x-50$=5y
30+x=y
x=y-30
(y-30)-50=5y
y-80=5y
y-5y=80
-4y=80
y=-20
x=-50
Answer:AlBERT=150; GEORGE=90
Albert-30=George+30....(.1)eq
A=(G+60)
#2 (G-50)5=A+50......(.2)eq
substitute result of #1 for A
5G-250=(G+60)+50
4G=360
G=90
substitute $90 into equation #1
A=90+60=150
Therefore Albert has $150, George has $90, and their total is $240
Which is the graph of f(x) = 1/4(4)*?
5
40.4)
5 4 3
(4,4)
4 *04)
3
2
(2,1)
1
3 2
2
2
3.2)
(1.1)
543-24
1 2 3 4
-5 -4 -3 -2 -14
2 3
1 2 3
4 5
х
-5 -4 -3 -2 -14
-2
- 2
-3
-2
-3
-3
4
4
-5
-5
45
o
o
5
(2.4)
Answer:
(2,3)
Step-by-step explanation:
The graph of the given function is attached to the solution.
What is function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given is a function f(x) = 1/4(4)ˣ, we need to graph this,
Put x = 0
f(x) = 1/4
(0, 1/4)
Put x = 1
f(x) = 1
(1, 1)
Put x = 2
f(x) = 4
(2, 4)
Plot these points on a graph, the graph will be the graph of the function,
Since, the function is an exponential function therefore, we will get a curve.
Hence, the graph of the given function is attached to the solution.
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√10 Multiple √15 is equal to
(a) 6√5
(b) √30
(c) √25
step by step
Solve :-
Answer:
Answer is 5√6 ( none of the objectives )
Step-by-step explanation:
[tex] \sqrt{10} \times \sqrt{15} \\ = \sqrt{150} \\ = \sqrt{25 \times 6} \\ = \sqrt{25} \times \sqrt{6} \\ = 5 \times \sqrt{6} \\ = 5 \sqrt{6} [/tex]
Together, Emily and Charlotte have a total of 60 strawberries. Emily sats 4 times the amount that Charlotte eats. How many strawberries does Charlotte eat?
Answer choices:
A. 6
B. 8
C. 10
D. 12
E. 14
F. 15
Answer:
12
Step-by-step explanation:
Since Emily eats four times the amount that Charlotte eats, then Emily will eat: = (4 × x) = 4x. Therefore, Charlotte eats 12 strawberries
