Answer:
The probability that the outcome of the roll is an even sum or a sum that is a multiple of 3
P( E∪F) [tex]= \frac{24}{36}[/tex]
Step-by-step explanation:
Given Each number cube has sides numbered 1 through 6
Two distinct number cubes are rolled together
Total number of exhaustive cases n(S) = 36
Let 'E' be the event of getting sum is even
n(E) = {(1,3),(1,5), (2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4), (4,6),(5,1),(5,3),(5,5),(6,2),(6,4),(6,6)} = 17
[tex]P(E) = \frac{n(E)}{n(S)} = \frac{17}{36}[/tex]
Let 'F' be the event of getting sum that is a multiple of '3'
n(F) = {(1,2),(1,5),(2,1),(2,4),(3,3),(3,6),(4,2),(4,5),(5,1),(5,4),(6,3),(6,6) = 12
[tex]P(F) = \frac{n(E)}{n(S)} = \frac{12}{36}[/tex]
n((E∩F) = {(2,4),(3,3),((4,2),(5,1),(6,6)} =5
[tex]P(En F) = \frac{n(En F)}{n(S)} = \frac{5}{36}[/tex]
The probability that the outcome of the roll is an even sum or a sum that is a multiple of 3
P( E∪F) = P(E) + P(F) - P( E∩F)
[tex]\frac{17}{36} +\frac{12}{36} - \frac{5}{36} = \frac{24}{36}[/tex]
The numbers x and y are inversely proportional. When the sum of x and y is 42, x is twice y. What is the value of y when x = -8? PLEASE HELP
Answer:
y= -4
Step-by-step explanation:
x+y=42. We know that x plus y equals 42.
x=2y . We also know that x equals twice y.
2y+y=42. Since we know that x=2y, we're going to replace x with 2y from the original equation, simplified would be 3y=42.
y=14. 3y=42 simplified is y=14, this is because we divided both sides by 3 (since 3 and 42 are both divisible by 3) (btw divisible by 3 simply means that it can be divided by 3)
x+14=42. Now that we know what y equals, let's replace y with 14 from the original equation.
x=28. Now that we know that x=28 and y=14, we know that y is always x/2.
When x=-8, we divide it by 2 and get, -4.
Not absolutely positive as this was all mental math, but hope this helps! :)
The value of the variable y at x = -8, will be negative 49.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
The numbers x and y are inversely proportional. Then we have
y ∝ 1/x
y = k/x ...1
When the sum of x and y is 42. Then the equation will be
x + y = 42 ...2
x is twice y. Then the equation will be
x = 2y ...3
From equations 2 and 3, we have
2y + y = 42
3y = 42
y = 14
Then the value of x will be
x = 2(14)
x = 28
Then the value of k will be
14 = k / 28
k = 392
Then the equation will be
y = 392 / x
Then the value of the variable y at x = -8, will be
y = 392 / (-8)
y = -49
Thus, the value of the variable y at x = -8, will be negative 49.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ5
What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4)?
Answer: 5x + 2y = -2
Step-by-step explanation:
Change 5x+2y=12 to slope intercept: 2y = 12 - 5x, y = -5x/2 + 6
A parallel line has the same slope, so the line we try to find is y = -5x/2 + b.
Substitute (-2, 4) in and get 4=5+b, so b = -1.
Therefore the answer is y = -5x/2 - 1, or if you want it in the original form it would be 2y = -5x - 2 ---> 5x+2y = -2.
Hope that helped,
-sirswagger21
Can someone help me please
Answer:
AA similarity
Step-by-step explanation:
Respective angles of both triangles are 40°, 50° and 90°
AA similarity is the case:
If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.A survey of 720 adults nationwide asked, "What irks you most about the actions of other motorists?" The response "tailgaters" was given by 231 people. What percent of those surveyed were most irked by tailgaters? Round to the nearest tenth of a percent
Answer: 32.08%
Step-by-step explanation:
From the question, a survey of 720 adults nationwide asked, "What irks them most about the actions of other motorists? and the response "tailgaters" was given by 231 people.
The percentage of people that responded with tailgaters will be the number of people who responded with tailgaters divided by the total survey of adults asked and then multiplying by 100. This can be mathematically written as:
= 231/720 × 100
= 32.08%
HELLPPP LOTS OF POINTSS
Answer:
B.
Step-by-step explanation:
Lines EI and HG would be parallel if the two triangles are congruent. The first option is not correct since we can not determine if that statement is true. The third option is not correct since points E, F, and G are not collinear or not in the same line. The last option is not correct because we can not determone that statement. The second option would be correct since the two lines never intersect.
Answer:
I'm not sure if we're supposed to find all the statements that apply but if so then the answer would be B, C, and D. If we're not to find all the statements then the best answer would be D.
Step-by-step explanation:
When triangles are similar it would mean that when you put their lines in a fraction like choice D you can find what the other value for a side of a triangle that's missing. I don't exactly know how to explain but I'm pretty sure that's the answer if you're not supposed to pick all true statements. Hopefully this helps!
What value of n makes the statement true?
6x^n• 4x^2=24x^6
n =
Answer:
n =4
Step-by-step explanation:
6x^n• 4x^2=24x^6
Combine like terms
24 x^n *x^2 = 24 x^6
We know that a^b * a^c = a^(b+c)
24 x^(n +2) = 24 x^6
Divide each side by 24
x^(n +2) = x^6
The bases are the same so the exponents are the same
n+2 = 6
Subtract 2
n+2-2 = 6-2
n=4
Answer:
4
Step-by-step explanation:
just did it
factorise 6 x ^2 + 17 X + 5
Answer:
( 3x + 1) (2x+5)
Step-by-step explanation:
6 x ^2 + 17 X + 5
We break the 6 into 3 and 2
(3x ) (2x )
We need the middle term to be 17
( 3x + 1) (2x+5)
3*5+2 = 17 so it works
The length of a rectangle is 20 units more than its width. The area of the rectangle is x4−100.
Which expression represents the width of the rectangle?
1. x2−10 because the area expression can be rewritten as (x2−10)(x2+10) which equals (x2−10)((x2−10)+20).
2. x2+10 because the area expression can be rewritten as (x2+10)(x2−10) which equals (x2+10)((x2+10)−20).
3. x2−30 because the area expression can be rewritten as (x2+10)(x2−10) which equals (x2+10)((x2−30)+20).
4. x2+30 because the area expression can be rewritten as (x2−10)(x2+10) which equals (x2−10)((x2+30)−20).
Answer:
[tex]1. x^2-10[/tex] because the area expression can be rewritten as [tex](x^2-10)(x^2+10)[/tex]which equals [tex](x^2-10)((x^2-10)+20).[/tex]
Step-by-step explanation:
Area of the rectangle [tex]=(x^4-100)[/tex]
[tex]x^4-100=(x^2)^2-10^2\\$Applying difference of two squares: a^2-b^2=(a-b)(a+b)\\(x^2)^2-10^2=(x^2-10)(x^2+10)[/tex]
Since the length of a rectangle is 20 units more than its width.
[tex]Width: x^2-10\\Length=x^2+10=x^2-10+20[/tex]
The correct option is therefore 1.
Answer:
x2−10 because the area expression can be rewritten as (x2−10)(x2+10) which equals (x2−10)((x2−10)+20).Step-by-step explanation:
The area of the rectangle is [tex]x^{4} -100[/tex], which can be factored as [tex](x^{2} +10)(x^{2} -10)[/tex], because it's the difference of two perfect squares.
But, we know that [tex]l=20+w[/tex], where [tex]l[/tex] is the length and [tex]w[/tex] is the width.
Additionally, [tex]l=x^{2} -10+20[/tex] and [tex]w=x^{2} -10[/tex], which means [tex]l=x^{2} +10[/tex].
Therefore, the right answer is A.
the slope of the line below is -2. which of the following is the point-slope form of the line? 4, -8
Answer:
D
Step-by-step explanation:
Point: (4,-8)
Slope: -2
y-y1=m(x-x1)
y+8=-2(x-4)
f(n) = 4(n-1) + 7
fine the first three(3) terms in the sequence show all work
Answer:
f(n) = 4(n-1) + 7
First term
f(1) = 4(1-1) +7 = 0 + 7 = 7
Second term
f(2) = 4(2-1) + 7
= 4(1) + 7 = 4 + 7 =11
Third term
f(3) = 4(3-1) + 7
= 4(2) + 7
= 8 + 7 = 15
Therefore the first three terms of the sequence are 7, 11 and 15.
Hope this helps
can someone help me to find TSA of this figure?
Answer :
is approximately 100 cm ²
Step -by-step explanation
[tex]r \: = 10 \\ l \: = 21.81 \\ T.S.A \: of a \: cone\: = \pi \times r(r + l)[/tex]
[tex] \frac{22}{7} \times 10(10 + 21.81) \\ \frac{22}{7} \times 10(31.81) \\ \frac{22}{7} \times 318.1[/tex]
[tex] \frac{22}{7} \times 318.1 \\ = 999.7 \\ = 100 {cm}^{2} [/tex]
Which procedure justifies whether Negative 3 x (5 minus 4) + 3 (x minus 6) is equivalent to Negative 12 x minus 6? The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (2) minus 6 = negative 30. The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (3) minus 6 = negative 42. The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (negative 2) minus 6 = 18. The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (1) minus 6 = negative 18.
Answer:
The correct option is;
The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 - 6) = negative 18 and Negative 12 (1) minus 6 = negative 18
Step-by-step explanation:
The parameters given are;
First expression 3 × X × (5 - 4) + 3 ×(X - 6)
Second expression -12 × X - 6
Therefore;
For the first expression, for all X, e have;
3 × X × 1 + 3 ×(X - 6) = -3·X + 3·X -18 = -18
The second expression gives -12·X - 6
When both expressions are equal, we have;
-12·X - 6 = -18
∴ X = (-18 + 6)/(-12) = 1
Hence the correct option is that the expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 - 6) = negative 18 and Negative 12 (1) minus 6 = negative 18.
Answer:
The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (2) minus 6 = negative 30
Or
Answer A
Step-by-step explanation:
Apparently, we're trying to see if ...
-3(x)(5 -4) + 3(x -6) = -12(x) -6
by evaluating the expressions for x=2:
-3(2)(5-4) +3(2 -6) ?= -12(2) -6
-6 -12 ?= -24 -6
-18 ≠ -30 . . . . . . . . . shows expressions are not equivalent
Find the slope of the line that goes through the points (12,-12) and (-3,13).
slope,m=________
Enter your answer as an integer or a reduced fraction in the form A/B
Answer:
-5/3
Step-by-step explanation:
The slope of a line is found by
m = (y2-y1)/(x2-x1)
= (13- -12)/(-3 -12)
= ( 13+12) / (-15)
25/-15
-5/3
The right answer is -5/3
please see the attached picture for full solution
Hope it helps..
Good luck on your assignment..
The point R is halfway between the integers on the number line below and represents the number ____. (Use the hyphen for negative numbers and write the answer as a decimal, such as -6.4).
Number line from negative 10 to positive 10 in increments of 1 is shown. In between the whole numbers, there should be a tick mark. Only the whole numbers are labeled. A point labeled R is placed halfway between the 3rd and 4th tick marks to the left of 0.The point R is halfway between the integers on the number line below and represents the number ____. (Use the hyphen for negative numbers and write the answer as a decimal, such as -6.4).
Number line from negative 10 to positive 10 in increments of 1 is shown. In between the whole numbers, there should be a tick mark. Only the whole numbers are labeled. A point labeled R is placed halfway between the 3rd and 4th tick marks to the left of 0.
Answer: - 2.5
Step-by-step explanation:
The point R is - 2.5,
The numbers on the number line are arranged sequentially and in regular increment of 1 with only the integer numbers being displayed and ticked. The point R sits directly in between - 3 and - 2. Therefore, to accurately obtain the position of the blue dot, we take the average of both positions binding the blue dot. That is - 3 and - 2
Average = ( - 3 + - 2) / 2
Average = - 5 / 2 = - 2.5
Answer: yea it it - 2.5 i just did that test and got it right <3
Step-by-step explanation:
a rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation(x+5) x=104 represents the situation, where x represents the width of the rectangle. (x+5) x=104 x2+5x-104=0. Determine the solutions of the equation. What solution makes sense for the situation?
Answer:
x=8
Step-by-step explanation:
Area of a rectangle=length×width
Area=104
Width=x
Length=5+x
104=x*(5+x)
104=5x+x^2
104-5x-x^2=0
x^2+5x-104=0
Can also be written as
-x^2-5x+104=0
Solve the quadratic equation using formula
−x2−5x+104=0
using the Quadratic Formula where
a = -1, b = -5, and c = 104
x=−b±√b2−4ac/2a
x=−(−5)±√(−5)2−4(−1)(104)/2(−1)
x=5±√25−(−416)/−2
x=5±√441/−2
The discriminant b^2−4ac>0
so, there are two real roots.
Simplify the Radical:
x=5±21/−2
x=-26/2 or 16/2
x=-13 or 8
The value of x can't be negative
So, x=8 is the answer
Help me!
A spinner can land on either red or blue. You spin the spinner and then roll a six-sided number cube.
What is the sample space of outcomes?
{(R, 1), (R, 2), (R, 3), (R, 4), (R, 5), (R, 6), (B, 1), (B, 2), (B, 3), (B, 4), (B, 5), (B, 6)}
{(R, B), (B, R), (R, 1), (B, 2), (R, 3), (B, 4), (R, 5), (B, 6)}
{BR, 123456}
{1, 2, 3, 4, 5, 6, B, R}
A sample set contains every possible outcome.
The answer would be:
(R, 1), (R, 2), (R, 3), (R, 4), (R, 5), (R, 6), (B, 1), (B, 2), (B, 3), (B, 4), (B, 5), (B, 6)}
The sample space of the outcomes is {(R, 1), (R, 2), (R, 3), (R, 4), (R, 5), (R, 6), (B, 1), (B, 2), (B, 3), (B, 4), (B, 5), (B, 6)}
How to determine the sample spaceThe sample space of the spinner is:
S1 = {R, B}
The sample space of the six-sided number cube is:
S2 = {1,2,3,4,5,6}
When the two sample spaces are merged together, we have:
S = {(R, 1), (R, 2), (R, 3), (R, 4), (R, 5), (R, 6), (B, 1), (B, 2), (B, 3), (B, 4), (B, 5), (B, 6)}
Hence, the sample space of the outcomes is (a)
Read more about sample space at:
https://brainly.com/question/5750471
A large rectangle is made up of 3 smaller identical rectangles, the perimeter of one small rectangle is 21cm. What is the perimeter of the large rectangle.
Answer:
63 units
Step-by-step explanation:
If the perimeter of 1/3 of the rectangle is 21, multiply 21 by 3 to find the perimeter of the entire rectangle.
21 x 3 = 63
Select all of the equations for which x = -4 *
1 point
x + 4 = 0
-3x = 12
x - 4 = -8
x + 4 = 4
Answer:
x + 4 = 0. / -3x = 12. / x - 4 = -8
Step-by-step explanation:
x + 4 = 0
-4. -4
x = -4
-3x = 12
÷-3. ÷-3
x = -4
x - 4 = -8
+ 4. +4
x = -4
x + 4 = 4
-4. -4
x = 0
Explain why a sample of 30 dentists from a large city taken to estimate the median income of all residents of that large city is not representative
Answer: Because all individuals in the sample have the same job, so the sample is biased.
Step-by-step explanation:
Ignoring the fact that 30 is a small sample for a large city, we already know that all the people in the sample has the same profession.
Now, we can expect that two dentists win have around the same income, but not all the residents in the city are dentists
A lot of them work in fast food, others may be lawyers, others may be freelancers.
We have a lot of jobs where the income does not coincide with the average income of a dentist, so with the sample of 30 dentists we are not actually representing all the other possible jobs that there are in the city.
If we want a sample that represents the income of all the residents, we should have a random sample (so the sample is not biased, like in this case).
The volume of a sphere is 45001 m3. Find the length of the radius
of the great circle.
Answer:
[tex]\large \boxed{\text{22.07 m}}[/tex]
Step-by-step explanation:
The formula for the volume (V) of a sphere is:
V = ⁴/₃πr³
We can use this equation to calculate the radius (r).
[tex]\begin{array}{rcl}45001 & = & \dfrac{4}{3} \pi r^{3}\\\\33750 & = &\pi r^{3}\\10740 & = &r^{3}\\r & = & \textbf{22.07 m}\\\end{array}\\\text{The radius of the great circle is $\large \boxed{\textbf{22.07 m}}$}[/tex]
£620 is divided between Malachy, Paul & Brian so that Malachy gets twice as much as Paul, and Paul gets three times as much as Brian. How much does Paul get?
Answer:
Step-by-step explanation:
What is the nth term rule of the linear sequence below? − 4 , − 1 , 2 , 5 , 8 ,
Answer:
a
n
=
3
n
−
7
Step-by-step explanation:
If jasmine gets $3.00 every time her song gets 1500 streams how much money would she have if she got 3 million streams
Answer:
$2000
Step-by-step explanation:
3,000,000/1500=$2000
n+n+n=1 what is n?????
Answer:
1/3
Step-by-step explanation:
If you add all the n's, it would make 3n=1. Divide both sides by 3 and get n=1/3
Answer:
0.333 or 1/3
Step-by-step explanation:
0.333*3=1
Elsa used the multiplication table below to write ratios that are equivalent to StartFraction 12 Over 4 EndFraction.
A multiplication table.
One number is missing from the equivalent ratio, as shown.
StartFraction blank Over 12 EndFraction
What is the missing number?
6
18
24
36
Answer:18
Step-by-step explanation:because it was in the same column
Answer:
Its actually 24 because 4 times 6 is 24 and 12 times 2 is 24
Please help.. I don't understand.. Please show workings
[tex]answer \\ = £59.25 \\ please \: see \: the \: attached \: picture \: for \: \\ full \: solution \\ hope \: it \: helps[/tex]
Find the value of x.
Answer:
x = -7
Step-by-step explanation:
Make an equation:
3x + 33 = 12
3x = -21
x = -7
Answer:
x = -7
Step-by-step explanation:
form an equation.
14 + x + 2x + 19 = 12
like terms together;
x + 2x = 12 - 14 - 19
simplify;
3x = -21
divide both sides by 3;
x = -7
3× + y = 8, 4× - 3y=2
Answer:
x=2
y=2
Step-by-step explanation:
You can use the process of elimination
x can't be 3 because than the first question would be 9+y=8 which is even bigger than the answer.
So now, we try 2. x=2
6+y=8 which =
6+2=8
So y must be two
Then we try it on the
Second one.
8-6=2 which makes sense.
Hope it helps
Answer:
x = 2
y = 2
Step-by-step explanation:
3x + y = 8..…...(1)× -3
4x - 3y = 2......(2)× 1
-9x - 3y = -24.......(3)
4x - 3y = 2..…..........(4)
Cancel -3y - 3y
-9x - 4x = -24 - 2
-13x = -26
Divide both sides by -13
x = 2
Substitute for the value of y
3x + y = 8
3(2) + y = 8
6 + y = 8
y = 8 - 6
y = 2
Given the range {-1, 5, 9), what is the domain for the relation y = x + 3?
Answer:
yes
Step-by-step explanation:
because it happens that way that it wants
Answer:
The answer is {-4,2,6}
Step-by-step explanation:
I am sorry if i had more time i would explain but i gotta go.
PLZ PLZ HELP QUICK PLZ PLZA
circle with radius of
3
cm
3cmstart color #1fab54, 3, start text, c, m, end text, end color #1fab54 sits inside a
8
cm
×
7
cm
8cm×7cmstart color #11accd, 8, start text, c, m, end text, times, 7, start text, c, m, end text, end color #11accd rectangle.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
Answer:
27.73 cm^2
Step-by-step explanation:
Answer:
Guys its 27.73- Please trust me i have done this one on khan multiple times
Step-by-step explanation:
Please please please like my answer or vote one of my answers brainliest.
