The probability notation for the probability for choosing a green marble is [tex]P(G)=\frac{n(G)}{n(T)}[/tex], where [tex]n(G)[/tex] denotes the number of green marbles and [tex]n(T)[/tex] denotes the number of total marbles in the bag (or from wherever we are choosing).
The probability of occurrence of an event is the ratio of the number of favorable outcomes and the total number of outcomes, where the favorable outcomes are the outcomes that implies the occurrence of the event.
Here, the event is "choosing a green marble". So, the number of green marbles in the bag is the number of favorable outcomes and the total number of marbles in the bag is the total number of outcomes.
Denoting [tex]G[/tex] as the event of "choosing a green marble", the notation [tex]P(G)[/tex] denotes the probability of event [tex]G[/tex], that is, probability of choosing a green marble.
Denoting [tex]n(G)[/tex] and [tex]n(T)[/tex] as the number of green marbles and total number of marbles respectively, by the definition, the probability notation for the probability for choosing a green marble is given as [tex]P(G)=\frac{n(G)}{n(T)}[/tex].
Learn more about probability notation here:
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pls helpppp
The length of the diagonal of a square is 12 cm. Let the side of the square = x cm. Make an equation in x and solve it to find the side length of the square. Hence calculate the area of the square in cm².
Answer:
2x²=12*12
x²=144/2
x=√72
x=8.48528137424
One side of square is 8.48528137424 cm
Geometry, please answer question ASAP
Answer:
I think the shape above has an order of 5 because it has a reflectional symmetry of 5.
I hope this helps
Please help a-e I will rate and like response. Thank u
Answer:
VOLUME OF RIGHT CIRCULAR CONE=≈74.93136cm^3
VOLUME OF SPHERE: ≈523.6cm^3
Simplify the radical sqrt(18d ^ 9); 3sqrt(2a ^ 7); 2a ^ 3 * sqrt(3); a ^ 4 * sqrt(18a); 3a ^ 4 * sqrt(2a)
Answer:
The answer above is completely correct, but it may help the student to see how to reach it:
We seek a square root of
3
−
2
√
2
. This must have the form
a
+
b
√
2
.
(
a
+
b
√
2
)
2
=
a
2
+
2
a
b
√
2
+
2
b
2
So
a
2
+
2
b
2
=
3
and
2
a
b
=
−
2
⇒
a
b
=
−
1
These are two simultaneous equations for
a
and
b
.
Rearrange the second:
b
=
−
1
a
Substitute into the first:
a
2
+
2
a
2
=
3
a
4
+
2
=
3
a
2
a
4
−
3
a
2
+
2
=
0
Note that this is a quadratic in
a
2
:
(
a
2
)
2
−
3
(
a
2
)
+
2
=
0
Factorise:
(
a
2
−
2
)
(
a
2
−
1
)
=
0
This gives us two possible solutions for
a
2
:
2
and
1
, and so the four solutions for
a
:
±
√
2
and
±
1
.
We are looking for integer solutions for
a
, and so
±
1
are possible solutions. But the other two are possible too - they can simply be folded in to the
√
2
term. This wouldn't have been possible if we'd had the root of some other number in the solution for
a
, but this solution is a special case.
Now use the second equation to deduce the four equivalent solutions for
b
:
b
=
−
1
a
b
=
¯¯¯¯¯
+
1
√
2
=
¯¯¯¯¯
+
1
2
√
2
and
¯¯¯¯
+
1
.
So we have the four solution pairs
(
a
,
b
)
:
(
√
2
,
−
1
2
√
2
)
(
−
√
2
,
1
2
√
2
)
(
1
,
−
1
)
(
−
1
,
1
)
This is a bit suspicious - we expect only two solutions, positive and negative square roots, so we wonder if some of these are identical to each other: When we substitute them in to our desired expression
a
+
b
√
2
, we get:
√
2
−
1
2
√
2
√
2
=
−
1
+
√
2
−
√
2
+
1
2
√
2
√
2
=
1
−
√
2
1
−
√
2
−
1
+
√
2
So the two solutions with
√
2
are identical to the two simpler solutions, so we can get rid of them. We now have two solutions, positive and negative square roots:
1
−
√
2
−
1
+
√
2
When we take the written square root of a quantity, it is implied that the desired root is the positive root, the "principal value" of the square root function. So we take the single solution that comes from
a
=
+
1
:
1
−
√
2
Double check: Make sure that this produces the desired answer:
(
1
−
√
2
)
2
=
1
−
2
√
2
+
2
=
3
−
2
√
2
I think this will help you
What is the sign of y + x?
y
0
Choose 1 answer:
Positive
B
Negative
Zero
Answer:
C
Step-by-step explanation:
As y is zero, y/x will be zero
If it takes a team of three painters to paint a 7-room house in a day, how many painters are required to paint a 14-room house in a day?
Answer: 6 Painters
Step-by-step explanation:
Total painters needed to paint 7-room house = 3 painters
Rooms painted by each painter = 3/7
Total painters needed to paint 14-room house = 3/7×14
= 42/7
= 6 painters
Therefore it will require 6 painters to paint 14-room house
please click thanks and mark brainliest if you like :)
Analyze the diagram below and complete the instructions that follow.
10
6
B.
'C С
8
Find sin ZA
A 3
5
B. 4
C 1
Answer:
B. 4/5
Step-by-step explanation:
Sin = Opposite/Hypotenuse
Sin∠A = 8/10 = 4/5
How do you solve combination (working together) rate problems example, if john can do a particular job in 4 hours, but Mitch can do the same job in 3, how long will it take them to do the same job if they work together?
3 hours and 30 minutes as ambod will work half the time
Simply Square Roots of 45
[tex] \sqrt{45} [/tex]
Answer:
[tex] 3\sqrt{5} [/tex]
Step-by-step explanation:
Find the largest factor of 45 that is a perfect square.
The factors of 45 are 1, 3, 5, 9, 15, 45.
The largest perfect square is 9.
Now breakup 45 into a product which has 9 as a factor.
45 = 9 * 5
[tex] \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5} [/tex]
If A=(prime number less than 10)list the element of set A and find n(A)
WILL GIVE BRAINLIEST:
Elanor wants to estimate the number of frogs in a reservoir.
She catches 90 frogs from the reservoir and marks them with a non-harmful dye.
Elanor then returns the frogs to the reservoir.
The next day she catches another 70 frogs and 10 of these are marked with the dye.
Work out an estimate for the total number of frogs in the reservoir.
Answer:
approximately 150 frogs
Step-by-step explanation:
To find your estimate, you have to add 90 + 60 because from the 70 that Elanor caught the second day, 10 of them were the ones that she had caught the day before so you have to do 70 - 10 = 60. Therefore, 90 + 60 = 150 estimated frogs.
Someone please helppp
Answer:
k = 5/6
Step-by-step explanation:
First, we can make this have the form of a quadratic function, or ax²+bx+c=0. To do this, we can first subtract 10x from both sides to get
(2k+1)x²-8x=-6
Next, we can add 6 to both sides, resulting in
(2k+1)x²-8x+6 = 0
For a quadratic function of form ax²+bx+c=0, we can see that a=2k+1, b=-8, and c=6. We can then apply the quadratic equation, or
x= (-b ± √(b²-4ac))/(2a) to get our roots to be
x= (8 ± √(64-4(6)(2k+1)))/(2*(2k+1))
= (8 ± √(64-(48k+24)))/(4k+2)
= (8 ± √(40-48k))/(4k+2)
For the roots to be equal, we must have the two roots equal to each other. We can write this as
(8 + √(40-48k))/(4k+2) = (8 - √(40-48k))/(4k+2)
multiply both sides by (4k+2) to remove the denominator
8+√(40-48k) = 8 - √(40-48k)
subtract 8 from both sides to isolate the square roots
√(40-48k) = - √(40-48k)
The only number that is equal to its negative self (and is real) is 0. Therefore, √(40-48k) = - √(40-48k) = 0, so we have
√(40-48k) = 0
square both sides to remove the square root
40-48k = 0
add 48k to both sides to isolate the k and its coefficient
40 = 48k
divide both sides by 48 to isolate k
k = 40/48 = 5/6
what is 2/5 divided by -1/2 minus 3/2
Answer:
[tex] - \frac{23}{10} [/tex]
Step-by-step explanation:
[tex] \frac{2}{5} \div \frac{ - 1}{2} - \frac{3}{2} [/tex]
➡️ [tex] - \frac{2}{5} \times 2 - \frac{3}{2} [/tex]
➡️ [tex] - \frac{4}{5} - \frac{3}{2} [/tex]
➡️ [tex] - \frac{23}{10} [/tex]
Please help answer!!!!
Answer:
? = 4
Step-by-step explanation:
You are in the third quadrant. You want the answer to come out to the equivalent of 225o or pi + pi/ 4 = 5/4 * pi
x - pi/2 = 5/4 pi
x = 5/4 pi + pi/2
x = 5/4 pi + 2*pi / 4
x = 7/4 pi
? = 4
Ok ong i'm struggling and need help i've been up all night- Ill give brainlyest!!
Solve the following problems below. Find the variable and show your work
1.) 7(6x-1)+x=36
2.) 11-2(8+3p)=7²
3.) 1/4(5b+11)=19
4.) 2/7(4m-18)=12
Answer:
1- 91315Step-by-step explanation
- 7(6x-1)+x=36
=> 42x - 7 + x = 36=> 43x - 7 = 36=> 43x = 36 + 6 = 43=> x = 43 / 43 = 1- 11-2(8+3p)=7²
=> 11 - 16 - 6p = 7^2=> 11 - 16 - 6p = 49=> -5 - 6p = 49=> -6p = 49 + 5 = 54=> p = (54) / (-6) = - 9- 1/4(5b+11)=19
=> (5/4)b + (11/4) = 19=> (5/4)b = 19 - (11/4) = 65 /4=> b = (65/4) / (5/4) => (65/4) * (4/5) = 13- 2/7(4m-18)=12
=> (8/7)m - (36/7) = 12=> (8/7)m = 12 + (36/7) = 120/7=> m = (120/7) / (8/7) = 120 /8 = 15
type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar
Step-by-step explanation:
The first piece wise function is from interval (-3,-1). The line during this interval isnt constant so this means that f(x) must be a linear equation along interval -3 to -1. The line has a slope of 1. And if we keep continuing, our y intercept will be 3. So we can say that
[tex]f(x) = x + 3 \ : if \: - 3 \leqslant x < - 1[/tex]
Foe the 2nd, the interval is between -1 and 1.
The line is constant so f(x) is going to be equal to one y value. The y value is passed through is 5 so we can say that
[tex]f(x) = 5 \: if \: - 1 \leqslant x \leqslant 1[/tex]
If T is the midpoint of SU what are ST, TU, and SU?
a. ST = 7, TU = 63, and SU = 126
b. ST = 63, TU = 63, and SU = 126
c. ST = 80, TU = 80, and SU = 160
d. ST = 18, TU = 18, and SU = 36
Answer:
B
Step-by-step explanation:
As T is the midpoint of SU, ST=TU. 9x=5x+28, 4x=28, x=7. ST=TU=63 and SU=126
What is the volume of this figure?
Step-by-step explanation:
3 x 3 x 3 = 27
2 x 2 x 2 = 8
6 x 10 x 2 = 120
27+8+120=155m³
ground of the following nearest tens and Place a 7639. b_4325671
Answer:
a)7640
b)4325670
Step-by-step explanation:
when rounding off a number one of the factors to consider is the number before the number you are supposed to round off,if the number is greater than 5 or equal to then you can go ahead and add a 1 to the number you have to round off.but if the number before is less than 5 you just have to leave the number the way it is.in this case for the first question you can see that the tens number is 3 and the number before is greater than 5 so you can add a 1 to the 3 to make it 4, bringing the answer to 7640 the 9 becames a zero..for the second one you can see that the number before the tens number is less than 5 so you can't add a 1 to it leaving the answer as 4325670..
I hope this helps
The points (3,6) and (5,12) lie on the graph of a linear equation. Is (4,8) a solution of the same linear
equation? Explain.
After finding the equation of the line, it is found that:
Since replacing x by 4 and y by 8 in the equation of the line does not result in an identity, (4,8) is not a solution of the same linear equation.
------------------------
Equation of a line:
The equation of a line is given by:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
------------------------
Finding the slope:
Given two points (x,y), the slope is given by change in y divided by change in x.
Points (3,6) and (5,12)Change in y: 12 - 6 = 6Change in x: 5 - 3 = 2Slope: [tex]m = \frac{6}{2} = 3[/tex]Thus:
[tex]y = 3x + b[/tex]
------------------------
To find the y-intercept, we replace one of the points into the equation. I will replace (3,6). Thus:
[tex]6 = 3(3) + b[/tex]
[tex]b = 6 - 9 = -3[/tex]
Thus, the equation of the line is:
[tex]y = 3x - 3[/tex]
------------------------
Is (4,8) a solution of the same linear equation?
We have to replace x by 4 and y by 8, and see if it results in an identity. So
[tex]8 = 3(4) - 3[/tex]
[tex]8 = 12 - 3[/tex]
[tex]8 \neq 9[/tex]
Since replacing x by 4 and y by 8 in the equation of the line does not result in an identity, (4,8) is not a solution of the same linear equation.
A similar problem is given at https://brainly.com/question/16024991
Find the x- and y-intercepts of the graph of – 10x + 3y = 10. State your
answers as whole numbers or as improper fractions in simplest form.
M
I hope you see what I did there. if you still confused, comment and I'll help
help help help
From the top of a lighthouse was 60 m above sea level. A ship located 1200 m
from the shore could spot the lighthouse. What was the angle of depression from
the top of the lighthouse to the ship?
Answer:
I think 60 - 1200 but i am not conform
The angle of depression from the top of the lighthouse to the ship is 0.04998 radians.
Given that, the top of a lighthouse was 60 m above sea level. A ship located 1200 m from the shore could spot the lighthouse.
We need to find the angle of depression from the top of the lighthouse to the ship.
What is the angle of depression?The angle is formed by the line of sight and the horizontal plane for an object below the horizontal.
Now, sin b=60/1200
⇒sin b=1/20
⇒sin b=0.05
⇒b=0.04998 radians
Now, b=x=0.04998 radians
Therefore, the angle of depression from the top of the lighthouse to the ship is 0.04998 radians.
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Evaluate the integral by interpreting it in terms of areas Draw a picture of the region the integral
Answer:
Step-by-step explanation:
The picture is below of how to separate this into 2 different regions, which you have to because it's not continuous over the whole function. It "breaks" at x = 2. So the way to separate this is to take the integral from x = 0 to x = 2 and then add it to the integral for x = 2 to x = 3. In order to integrate each one of those "parts" of that absolute value function we have to determine the equation for each line that makes up that part.
For the integral from [0, 2], the equation of the line is -3x + 6;
For the integral from [2, 3], the equation of the line is 3x - 6.
We integrate then:
[tex]\int\limits^2_0 {-3x+6} \, dx+\int\limits^3_2 {3x-6} \, dx[/tex] and
[tex]-\frac{3x^2}{2}+6x\left \} {{2} \atop {0}} \right. +\frac{3x^2}{2}-6x\left \} {{3} \atop {2}} \right.[/tex] sorry for the odd representation; that's as good as it gets here!
Using the First Fundamental Theorem of Calculus, we get:
(6 - 0) + (-4.5 - (-6)) = 6 + 1.5 = 7.5
The value of the integral [tex]\int\limits^3_0 {|3x-6|} \, dx[/tex] is -9/2.
The given integral is [tex]\int\limits^3_0 {|3x-6|} \, dx[/tex]
We have to find the value of this integral.
We know that ∫xⁿ dx= xⁿ⁺¹/n+1
So, [tex]\int\limits^3_0 {|3x-6|} \, dx[/tex] = 3x²/2 -6x (from 0 to 3)
Apply the limits.
=3(3)²/2-6(3)
=27/2-18
=27-36/2
=-9/2.
Hence, the value of the integral [tex]\int\limits^3_0 {|3x-6|} \, dx[/tex] is -9/2.
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What do you notice about the absolute value of the
difference between the two numbers of -5 and -1
Dr. Perry conducts a study in which she evaluates the effectiveness of an adult literacy program. The study is both quantitative and qualitative in nature, and the 30 participants are treated as equal researchers in the study. What research method is Dr. Perry MOST likely to use
The method is Dr. Perry most likely to use is Participatory action research.
Participatory action research is a type of research characterized by :
Qualitative and quantitative method Active participation of the community involved in the researchAdditionally, in this type of research, the community involved is treated as researchers and their contributions are taken into account in the result of the same.
According to the above, the type of research suitable for Dr Perry's study is participatory action research, since it includes all the factors that Dr Perry takes into account for her research such as quantitavie/qualitative method and active participation from the community involved.
On the other hand, case study, naturalistic observation, and focus group are not the correct options because they use other methods in which the studied community does not actively participate.
Learn more in: https://brainly.com/question/15930435
Note:
This question is incomplete because the options are missing. Here are the options.
A. Case study
B. Naturalistic observation
C. Participatory action research
D. Focus group
A package of 4 red,white and blue hats costs $8. What is the unit rate
Answer:
$2/ hat
Step-by-step explanation:
Find the unit rate:
$ to hats
8 to 4
Divide by four to get the unit rate; over 1
2 to 1
So, $2 per hat
Hope this helps!
If the areas of two similar triangles are equal, prove that they are congruent
Refer the attached image for the answer
HOPE SO IT HELPS YOU
yx(y+1) + 4x(y + 1) - 5(y + 1) factor
( yx + 4x - 5 )( y + 1 )
.....................................
Simplify this Algebraic equation with steps
-6q +7 -2 +4q
Answer:
-2q+5
Step-by-step explanation:
-6q +7 -2 +4q
Combine like terms
-6q+4q+7-2
-2q+5
Answer:
= solution,
= -6q + 7 - 2 +4q
= -6q + 4q +7 -2
= - 2q + 5
✌✌✌✌
construct a quadrilateral PQRS such that PQ=RS=7.3cm,angle Q=60°,QR=5cm and angle R=135°.
Answer:
is your answer how are you
