Answer:
the probability is [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
there are 4 numbers on a 12 sided die that can be divided by 3: 3, 6, 9, and 12.
so the probability would be [tex]\frac{4}{12}[/tex], or [tex]\frac{1}{3}[/tex]
Using the concept of probability. The chances of having a value which is divisible by 3 is 1/3
Recall :
Probability = required outcome / Total possible outcomesTotal possible outcomes = Sample space = 12
Required outcome = numbers divisible by 3 :
(3, 6, 9, 2) = 4 outcomesP(number divisible by 3) = 4 / 12 = 1/3
Therefore, the probability of having a number which is divisible by 3 is 1/3
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Which one of the following options is true when considering the expansion of
the binomial expression (x + y)6?
A. The first term of the expansion of (x + y)^6 is x3y3.
B. The coefficients of the expansion of (x + y) are: 1,6, 15, 15, 6, 1.
c. The expansion of (x + y)^6 will yield 7 terms.
D. The sum of the exponents of each term of the expansion of
(x + y)^6 is 5
Answer:
c The expansion of (x + y)^6 will yield 7 terms
Step-by-step explanation:
(x + y)^6 =
x^6 +6x^5y + 15x^4y^2 + 20x^3y^3 + 15x^2y^4 + 6xy^5 + y^6
so its a no on A
its a no on B because its missing a 20
its a yes on c
its a no on d because the sum is 6
so c
(e) Dhanu plays with his model railway from 06 50 to 11 15. He then rides his bicycle for 3 hours. Find the ratio time playing with model railway : time riding bicycle. Give your answer in its simplest form.
Answer:
53:36
Step-by-step explanation:
53:36
265:180
The ratio of time Dhanu spent playing with model railway to the time riding bicycle is 53 : 35.
What is the ratio of the time spent playing with model railway to the time riding bicycle ?Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
Time spent playing with the model railway = 4 hours 25 minutes.
Converting the time to minutes = (4 x 60) + 25 = 265 minutes
Time in minutes spent riding a bicycle = 60 x 3 = 180
Ratio of the minutes - 265 : 180
53 : 35
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A company uses two vans to transport
workers from a free parking lot to the
workplace between 7:00 and 9:00 a.m.
One van has 6 more seats than the other.
The smaller van makes two trips every
morning while the larger one makes only
one trip. The two vans can transport 57
people, maximum.
How many seats does the larger van have?
Answer:
The larger van has 23 seats
Step-by-step explanation:
Create a system of Equations:
1. Define variables.
> let x=small van and y=larger van
2. create 2 equations based on the information given.
> y = 6 + x
> 2x + y = 57
3. Use any method to solve
Substitution: 2x + (6 + x) = 57. x=17
now plug x in to the original equation to solve for y (the larger van)
y = 6 + 17 and y = 23
Elimination: 2y = 12 + 2x
y = 57 - 2x
3y = 69 and y = 23
Question 4 Multiple Choice Worth 4 points)
(01.02 LC)
What is the solution for the equation 6x - 8 = 4x?
Answer:
Algebra
Step-by-step explanation:
(+) it's the same thing btw6x -8 = 4x
(collect like terms) meaning the numbers with x go over the " = " sign
making it = -8 = 4x -6x
the signs change when it crosses over so it becomes that
-8 = -2x
-8 ÷ -2 = 4 (cause - ÷ by - is + )
What is the interval of increase f(x)=3x^2-6x
Answer:
F(g(×)1=3(6+2)-5=18×+6-5=18×+1
Step-by-step explanation:
so correct answer is the last one pa brainliest plss
Solve the qn in attachment .
Answer:
[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]
Step-by-step explanation:
The given expression to us is ,
[tex]\implies \dfrac{\frac{ 3}{x-1} -4 }{ 2 -\frac{2}{x-1}}[/tex]
Now take the LCM as ( x - 1 ) and Simplify , we have ,
[tex]\implies \dfrac{\frac{ 3 -4(x-1) }{x-1} }{ \frac{2-2(2x-1)}{x-1}}[/tex]
Simplifying further , we get ,
[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]
Hence the second option is correct.
Answer:
[tex] \frac{ \frac{3}{x - 1} - 4}{2 - \frac{2}{x - 1} } \\ = \frac{ \frac{3 - 4(x - 1)}{x - 1} }{ \frac{2(x - 1)}{x - 1} } \\ = \frac{3 - 4x + 4}{2x - 2} \\ \frac{ - 4x + 7}{2(x - 1)} \\ option \: b \: is \: your \: answer \\ thank \: you[/tex]
A bag contains 13 blue marbles, 12 red marbles, 6 yellow marbles, and 8 green marbles. What is
the probability of picking a red marble, putting that one back and then picking another red
marble?
4. Assume you have the same bag of marbles as the previous question. What is the probability of
selecting a yellow marble, then another yellow marble, then a red marble, and finally another
yellow marble, without replacing in between?
Answer:
12 in 29. uou add all the number together then and it is 12 red marbles in 29 chancesso you take one marble out and put the exact marble back in having no effect.
write an expression for 15 divided by a number
show your work
Answer:
15/X
Step-by-step explanation:
a number divided by 15
15/X
Use the quadratic formula to find the solution to the quadratic equation given
below.
X^2-x+1/4=0
Answer:
[tex]\displaystyle x=\frac{-1}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]\displaystyle x=\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]Step-by-step explanation:
Step 1: Define
Identify
x² + x + 1/4 = 0
↓ Compare to Standard Form
a = 1, b = 1, c = 1/4
Step 2: Solve for x
Substitute in variables [Quadratic Formula]: [tex]\displaystyle x=\frac{-1 \pm \sqrt{1^2 - 4(1)(\frac{1}{4})}}{2(1)}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle x=\frac{-1 \pm \sqrt{1 - 4(1)(\frac{1}{4})}}{2(1)}[/tex][√Radical] Multiply: [tex]\displaystyle x=\frac{-1 \pm \sqrt{1 - 1}}{2(1)}[/tex][√Radical] Subtract: [tex]\displaystyle x=\frac{-1 \pm \sqrt{0}}{2(1)}[/tex][√Radical] Evaluate: [tex]\displaystyle x=\frac{-1 \pm 0}{2(1)}[/tex]Simplify: [tex]\displaystyle x=\frac{-1}{2(1)}[/tex]Multiply: [tex]\displaystyle x=\frac{-1}{2}[/tex]In an office there was a small cash box.One day ann took half of the money plus$1 more.Then dan took half of the remaining money plus$1 more.Stan then took the remaining $11.How many dollars were originally in the box?
Answer:
this as a equation looks like this
-1/2x+1+x=11
1/2x=10
x=20
Hope This Helps!!!
20 dollars were originally in the box
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
In an office there was a small cash box.
One day ann took half of the money plus$1 more
Then dan took half of the remaining money plus$1 more
Stan then took the remaining $11
-1/2x+1+x=11
Subtract 1/2x from both sides
1/2x=10
Multiply 2 on both sides
x=20
Hence, 20 dollars were originally in the box
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Laura bought some movie tickets. The graph represents
the
proportional relationship between the cost and the number of movie
tickets. Find the cost of seven tickets
Answer:
it must be 85 (approx.)
Step-by-step explanation:
Summer school math problem
Hello!
4/18 = 6/27 ?
4 × 27 = 18 × 6
108 = 18 × 6
108 = 108 => 4/18 = 6/27
4/6 = 16/36 ?
4 × 36 = 6 × 16
144 = 6 × 16
144 ≠ 96 => 4/6 ≠ 16/36
3/4 = 9/12 ?
3 × 12 = 4 × 9
36 = 4 × 9
36 = 36 => 3/4 = 9/12
5/9 = 8/12 ?
5 × 12 = 9 × 8
60 = 9 × 8
60 ≠ 72 => 5/9 ≠ 8/12
Good luck! :)
y =2/3x + 20
when x = 21
Answer:
34
Step-by-step explanation:
First we need to do 2/3*21, which equals 14 as 3 and 21 can be simplified to 1 and 7. 7 * 2/1= 14. Then we add the 20 to 14, 20+14= 34
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{y = \dfrac{2}{3}x + 20}[/tex]
[tex]\mathsf{y =\dfrac{2}{3}(21) + 20}[/tex]
[tex]\mathsf{\dfrac{2}{3}(21) + 20 = y }[/tex]
[tex]\mathsf{\dfrac{2}{3}(21)=\bf14}[/tex]
[tex]\mathsf{14 + 20 = y}[/tex]
[tex]\mathsf{14 + 20 = \bf 34}[/tex]
[tex]\huge\checkmark\boxed{\huge\textsf{y = 34}}\huge\checkmark[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf y = 34}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\huge\text{Amphitrite1040:)}[/tex]
Find the domain and range for each of the relations described by the sets of
ordered pairs below.
4. (-1, 2), (2, 51), (1,3), (8, 22), (9,51)
Domain:
Range:
Answers:
Domain = {-1, 2, 1, 8, 9}
Range = {2, 51, 3, 22}
==================================
Explanation:
The domain is the set of allowed inputs of a function. So it's the set of possible x values. We simply list the x coordinates of each point to form the domain.
The range is the set of possible y values or y outputs. So we simply list the y coordinates of the points. We toss out any duplicates. Since order doesn't matter in a set, we can have the values listed any way we want.
Side notes:
This is a function since we don't have any repeated x values between any of the points. This graph passes the vertical line test.This function is not one-to-one because we have y = 51 correspond to multiple x values (x = 2 and x = 9 simultaneously). This graph fails the horizontal line test.The x-intercept, or zero, of function g is x = . Function g is over the interval [-5, 5]. As the value of x approaches positive infinity, the value of g(x) approaches infinity.
Answer:
boom box second one one my bad just need points my g
Step-by-step explanation:
Answer:
3
decreasing
negative
Step-by-step explanation:
The graph of function g crosses the x-axis at (3,0), so there is a zero at x = 3.
As the values of x increase, the values of g(x) decrease, so function g is decreasing along all intervals, including the interval [-5, 5].
As the values of x approach positive infinity, cube root functions either approach positive infinity or negative infinity. Since this function is decreasing, the values of g(x) approach negative infinity.
How do I simplify the expression
solve the logarithmic equation
[tex] log_{6}(2x - 6) + log_{6}x = 2[/tex]
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
We want to solve the equation:
[tex]\displaystyle \log_6(2x-6)+\log_6x=2[/tex]
Recall the property:
[tex]\displaystyle \log_bx+\log_by=\log_b(xy)[/tex]
Hence:
[tex]\log_6(x(2x-6))=2[/tex]
Next, recall that by the definition of logarithms:
[tex]\displaystyle \log_b(a)=c\text{ if and only if } b^c=a[/tex]
Therefore:
[tex]6^2=x(2x-6)[/tex]
Solve for x. Simplify and distribute:
[tex]36=2x^2-6x[/tex]
We can divide both sides by two:
[tex]x^2-3x=18[/tex]
Subtract 18 from both sides:
[tex]x^2-3x-18=0[/tex]
Factor:
[tex](x-6)(x+3)=0[/tex]
Zero Product Property:
[tex]x-6=0\text{ or } x+3=0[/tex]
Solve for each case. Hence:
[tex]x=6\text{ or } x=-3[/tex]
Next, we must check the solutions for extraneous solutions. To do so, we can simply substitute the solutions back into the original equations and examine its validity.
Checking x = 6:
[tex]\displaystyle \begin{aligned} \log_{6}(2(6)-6)+\log_{6}6&\stackrel{?}{=} 2 \\ \\ \log_6(12-6)+(1)&\stackrel{?}{=}2 \\ \\ \log_6(6)+1&\stackrel{?}{=}2 \\ \\ 1+1=2&\stackrel{\checkmark}{=}2\end{aligned}[/tex]
Hence, x = 6 is indeed a solution.
Checking x = -3:
[tex]\displaystyle\begin{aligned} \log_6(2(-3)-6) + \underbrace{\log_6-3}_{\text{und.}} &\stackrel{?}{=} 2\\ \\ \end{aligned}[/tex]
Since the second term is undefined, x = -3 is not a solution.
Therefore, our only solution is x = 6.
Answer:
x = 6
Step-by-step explanation:
The given logarithmic equation is ,
[tex]\implies log_{6}(2x - 6) + log_{6}x = 2[/tex]
We can notice that the bases of both logarithm is same . So we can use a property of log as ,
[tex]\bf \to log_a b + log_a c = log_a {( ac)} [/tex]
So we can simplify the LHS and write it as ,
[tex]\implies log_{6} \{ x ( 2x - 6 )\} = 2 [/tex]
Now simplify out x(2x - 6 ) . We get ,
[tex]\implies log_6 ( 2x^2 - 6x ) = 2 [/tex]
Again , we know that ,
[tex]\bf \to log_a b = c , a^c = b [/tex]
Using this we have ,
[tex]\implies 2x^2 - 6x = 6^2 \\\\\implies 2x^2 - 6x -36 = 0 [/tex]
Now simplify the quadratic equation ,
[tex]\implies x^2 - 3x - 18 = 0 \\\\\implies x^2 -6x + 3x -18=0\\\\\implies x( x -6) +3( x - 6 ) = 0 \\\\\implies (x-6)(x+3) = 0 \\\\\implies x = 6 , -3 [/tex]
Since logarithms are not defined for negative numbers or zero , therefore ,
[tex]\implies 2x - 6 > 0 \\\\\implies x > 3 [/tex]
Therefore the equation is not defined at x = -3 . Hence the possible value of x is 6 .
[tex]\implies \underline{\underline{ x \quad = \quad 6 }}[/tex]
Solve the system of equations.
−5x−3y−9=0
4x−18y−54=0
y=? x=?
Answer:
Step-by-step explanation:
Eq. 1 ) −5x−3y−9=0
Eq. 2) 4x−18y−54=0
there are two routes to solve this, Substitution or elimination, I'll go for the 2nd one because I can see that the y values are a multiple of each other :)
6 *( −5x−3y−9=0 )
Eq. 3) -30x -18y =54
subtract Eq. 2 from Eq. 3 :)
-30x -18y =54
-( 4x−18y=54)
-34x = 0
so according to the equations then x =0 but, that's not really a full answer, so now we should go back and try the other method, substitution,
then:
-5x = 9 +3y
x = - 9/5 + (-3/5)y
now plug that into Eq. 2
4( - 9/5 + (-3/5)y ) - 18y = 54
-36/5 + (-12/5)y -18y = 54
(-12/5)y - (90/5)y = 54+36/5
-(102/5)*y =270/5+36/5
-(102/5)y = 306/5
y = (-5/102)*(306/5)
y = -306/102
y = -3
then plug in for either equation
-5x-3( -3) = 9
-5x + 9 = 9
-5x = 0
x = 0
now we have the full answer
check it by plugging in both x and y into the 2nd equation
4(0) - 18(-3) = 54
54= 54
this seems good
solve |5x+30|=10x ......
Answer:
Option A
Step-by-step explanation:
We need to solve out ,
[tex]\implies |5x + 30| = 10x [/tex]
We can write it as ,
[tex]\implies 5x + 30 = \pm 10x [/tex]
On simplyfing further,
[tex]\implies 5x + 30 = 10x \quad or \quad 5x +30=-10x [/tex]
On solving the above equation , we will get ,
[tex]\implies \boxed{ x = 6,-2}[/tex]
Now we know that the value of modulus is never negative so when we will put x is equal to 2 on the RHS we will get -20 which is not possible . Therefore , the extraneous root is -2 .
Option A is correct .
the ratio of boys to girls is 4 :3,if there are 24boys and how many girls will be there?
Answer:
There are 18 girlsStep-by-step explanation:
explanation given in the image ❣️◕Jess bregoli◕❣️#keep learning!!Can somebody please help meee
Answer:
Top one: y= 3/1+2
bottom: y= -1/1+4
I need help pls !!!!!!!
i need help trying to solve this question to the nearest tenth of a degree
Which linear inequality represents the graph below? (-2, 3) & (0, -2)
Answer:
no hablo inglés wey perdón corona y gracias
Which is true about this triangle?
Answer:
C=32°
because sum of three angles of triangles is 180°
Which shows the correct solution of the equation + so, when 6-30?
Answer:
-24
Step-by-step explanation:
rest 6 minus 30 and it give you -24
What is a set ? Give an example of a set .
Answer: 24
Step-by-step explanation:
Choose the correct answer from the given four options:In an AP if a = –7.2, d = 3.6, an = 7.2, then n
2
4
3
5
Answer:
n=5
Step-by-step explanation:
by using
n=(an-a)/a+1
substituting values
n= 7.2-(-7.2)/3.6 +1
n=5
an apple farm costs $5 to get in and $0.75 per pound of apples, what is the y intercept? (Number answer only, no symbols)
Answer:
(0, 5).
Step-by-step explanation:
$5 is the base fee, so when x = 0, y = 5. 0.75 won't come into play yet.
Please help me with this
Answer:
x = 23
Step-by-step explanation:
if line j is parallel to line k then
5x + 9 + 33 + x = 180 add like terms
6x + 42 = 180 subtract 42 from both sides
6x = 138 divide both sides by 6
x = 23