The probability that both the balls are red = [tex]\bold{\frac{11}{20}}[/tex]
What is probability?"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
Formula of the probability of an event A is:P(A) = n(A)/n(S)
where, n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.
What is the formula of combination?"[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]"
For given question,
a bag contains 12 red, 3 white and 1 blue balls.
Total balls = 12 + 3 + 1
Total = 16
Two balls are drawn from a bag.
The number of possible ways of drawing 2 balls from the bag are:
Using combination formula,
[tex]^{16}C_2\\\\=\frac{16!}{2!(16-2)!}\\\\ =\frac{16!}{2!\times 12!}\\\\ =120[/tex]
So, n(S) = 120
Two balls are drawn with replacement from a bag.
We need to find the probability that both are red.
Let event A: both the balls are red
[tex]\Rightarrow n(A)=^{12}C_2[/tex]
Using combination formula,
[tex]^{12}C_2\\\\=\frac{12!}{2!\times (12-2)!}\\\\= \frac{12!}{2!\times 10!}\\\\ =66[/tex]
Using probability formula,
[tex]\Rightarrow P(A)=\frac{n(A)}{n(S)}\\\\\Rightarrow P(A)=\frac{66}{120}\\\\\Rightarrow P(A)=\frac{11}{20}[/tex]
Therefore, the probability that both the balls are red = [tex]\bold{\frac{11}{20}}[/tex]
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Derive the equation of the parabola with a focus at (2,4) and a directrix of y=8
Answer:
The equation of the parabola with a focus at (2,4) and a directrix of y=8 is,
48-8y=(x-2)²
HELP NEEDED PLEASE :(
Identify the center and the radius of a circle that has a diameter with endpoints at (5, 8)
and (7,6).
Answer:
Centre is,
((5+7)/2,(8+6)/2)
or, (12/2,14/2)
or, (6,7)
radius is,
[√{(5-7)²+(8-6)²}]/2
= [√(2²+2²)]/2
= [√(4+4)]/2
= [√8 ]= [2√2]/2 = √2
The center of a circle = (6, 7)
the radius of a circle = [tex]\sqrt{2}[/tex] units
What is the distance formula?"The distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex] is given by [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_2)^2}[/tex]"
What is midpoint formula?"The coordinates of the midpoint of the line segment having endpoints [tex](x_1,y_1),(x_2,y_2)[/tex] is given by [tex]m=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex] "
What is diameter of circle?"It is the line segment through the center and touching two points on its edge. "
For given question,
The diameter of circle has endpoints at (5, 8) and (7,6).
Let [tex](x_1,y_1)=(5,8),(x_2,y_2)=(7,6)[/tex]
First we find the length of the diameter of the circle.
Using the distance formula,
[tex]\Rightarrow d=\sqrt{(x_2-x_1)^2+(y_2-y_2)^2} \\\\\Rightarrow d=\sqrt{(7-5)^2+(6-8)^2} \\\\\Rightarrow d=\sqrt{2^2+(-2)^2}\\\\\Rightarrow d=\sqrt{4+4}\\\\\Rightarrow d=2\sqrt{2}~units[/tex]
We know that the diameter = 2 × radius
⇒ radius (r) = [tex]\frac{2\sqrt{2} }{2}[/tex]
⇒ r = [tex]\sqrt{2}[/tex] units
We know that the midpoint of the diameter is the center of the circle.
Using midpoint formula the center of the circle would be,
[tex]\Rightarrow O=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\\\\Rightarrow O=(\frac{5+7}{2} ,\frac{8+6}{2} )\\\\\Rightarrow O=(\frac{12}{2} ,\frac{14}{2} )\\\\\Rightarrow O=(6,7)[/tex]
Therefore, the center of the circle is (6,7)
Hence, the center of a circle = (6, 7)
the radius of a circle = [tex]\sqrt{2}[/tex]
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2. A dolphin leaps 5 feet in the air at the same time an orca whale dives 12 feet below the water. How far apart are the whale and the dolphin?
write your answer in simplest radical form
Answer:
n = 8√2
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 60°
Opposite = 4√6
Hypothenus = n =?
The value of n can be obtained by using the sine ratio as illustrated below:
Sine θ = Opposite / Hypothenus
Sine 60 = 4√6 / n
√3/2 = 4√6 / n
Cross multiply
n × √3 = 2 × 4√6
n × √3 = 8√6
Divide both side by √3
n = 8√6 / √3
Rationalise
n = 8√6 / √3 × (√3/√3)
n = 8√(6×3) / 3
n = 8√18 / 3
Recall
√18 = √(9×2) = √9 × √2 = 3√2
Thus,
n = 8√18 / 3
n = 8 × 3√2 / 3
n = 8√2
f (x) = 3r + 6. Find the inverse of f(x).
Answer:
The inverse is 1/3x -2
Step-by-step explanation:
f (x) = 3x + 6
y = 3x+6
Exchange x and y
x = 3y+6
Subtract 6 from each side
x-6 = 3y+6-6
x-6 = 3y
Divide by 3
1/3x - 6/3 = y
1/3x -2 = y
The inverse is 1/3x -2
find the missing length indicated
============================================================
Explanation:
Let y be the length of the vertical dashed red line in the drawing. More specifically, this dashed line is an altitude.
Along the top, the entire segment is 400 units long. The right piece is 144 units long, so the left piece is 400-144 = 256 units long.
The triangles are similar, allowing us to set up a proportion like so:
144/y = y/256
144*256 = y*y
36864 = y^2
y^2 = 36864
y = sqrt(36864)
y = 192
So this is the length of that vertical dashed red line.
--------------------------------
Now shift your attention solely on the smaller triangle on the right side. It is a right triangle with legs 144 and 192. The hypotenuse is x.
We can use the pythagorean theorem to find x.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
x = sqrt( 144^2 + 192^2 )
x = 240
240.
Let y be the length of the vertical dashed red line in the drawing. More specifically, this dashed line is an altitude.
Along the top, the entire segment is 400 units long. The right piece is 144 units long, so the left piece is 400-144 = 256 units long.
The triangles are similar, allowing us to set up a proportion like so:
144/y = y/256
144*256 = y*y
36864 = y^2
y^2 = 36864
y = sqrt(36864)
y = 192
So this is the length of that vertical dashed red line.
Now shift your attention solely to the smaller triangle on the right side. It is a right triangle with legs 144 and 192. The hypotenuse is x.
We can use the Pythagorean theorem to find x.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
x = sqrt( 144^2 + 192^2 )
x = 240
What is Pythagorean Theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
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1.) Three numbers form a geometric sequence whose common ratio is 0.5. If the first is reduced to 10 more than one quarter its value, the second decreased by 10, and the third increased by 10 more than twice its value, the resulting three numbers form an arithmetic sequence. Determine the original three numbers.
Let x be the first number in the sequence, so the first three numbers are
{x, 0.5x, 0.5²x}
Then
{x/4 + 10, 0.5x - 10, 2(0.5²x) + 10}
is arithmetic, so there is some constant c such that
0.5x - 10 = x/4 + 10 + c ==> x/2 - 10 = x/4 + 10 + c
2(0.5²x) + 10 = 0.5x - 10 + c ==> x/2 + 10 = x/2 - 10 + c
Solve the second equation for c :
x/2 + 10 = x/2 - 10 + c
c = 20
Substitute this into the first equation and solve for x :
x/2 - 10 = x/4 + 10 + 20
x/4 = 40
x = 160
Then the terms are
{160, 80, 40}
how many cubic meters of gravel are in the back of a full dump truck that measures 7m wide by 4m tall by 16m long
Answer:
Step-by-step explanation:
Assuming the gravel reaches the top of the walls and no higher, the volume is 7×4×16 = 448 m³
Answer:
hello thereee
now vol of truck = l b h = 7 * 4 * 16 = 448 m^3
( 448m^3 is final ans...
glad for brainliest.... hope that helps <3
Need help plz + will give brainlest
Thanks in advance
Answer:
it is D.
Step-by-step explanation:
if ella earns x dollars, she is taxed x%. How much money should she earn to maximize her income?
Answer:
just devide it. after that ÷ with 100 per time
2. About how much is 123.1 do you weigh in pounds? Estimate if you don't know☺ Find an online converter and find out how many kilograms that is.
Answer:
123.1 pounds is vary long, and I don't want to repeat, so 55.8372207 repeat.
Step-by-step explanation:
If you have any questions regarding my answer, tell me them in the comments, and I will come answer them for you. Have a good day.
Which side of XYZ is the longest?
A. xy
B. xz
C. yz
D. cannot be determined
Answer:
the answer is x because its small
Answer:
Step-by-step explanation:
It’s Xy
8. Solve the following triangle for all missing sides and angles.
Part 1: Find the measure of angle B
Part 2: Use the law of sines to find the length of side A
Part 3: Use any method to find the length of side c
Answer:
Parte1 :
∡B= 180 - (42 + 83)= 55°
Parte2 :
Using the law of sines : [tex]\frac{sin 42}{a} = \frac{sin 55}{175}[/tex] ⇔ [tex]a = sin42 \frac{175}{sin 55}[/tex] ⇔ a= 142.95
Parte3 :
Using the same law : [tex]c = sin 83\frac{a}{sin 42}[/tex] or [tex]c= sin 83\frac{175}{sin 55}[/tex] ⇔ c= 212.04
Help very confusing to me???!
Answer:
Heyy mate... here's ur ans ;)
they asked us to apply pythagarus theorem becoz that theorem proves
that it is rectangle so lets get started
( p - perpendicular / b - base / h - hypotenuse )
a) =>
B = 8.1 m
P = 6.3 m
H = 10.15m
Now applying thm => H^2=p^2+b^2
(8.1)^2 + (6.3)^2 = (10.15)^2
65.61 + 39.69 = 103.02
so now LHS = 105.3 and RHS = 103.02 hence
LHS not equal to RHS
so is not rectangle
b) =>
B = 14.4
P = 5.2
H = 15.31
Now applying thm => H^2=p^2+b^2
(5.2)^2 + (14.4)^2 = (15.31)^2
27.04 + 207.36 = 234.39
LHS = 234.4 and RHS = 234.39
just taking approximation rhs is 234.4
hence
LHS = RHS
so it is a rectangle
please mark it brainliest <3
An exponential function f(x) = ab^xpasses through the points (0, 2) and (3, 54). What are the values of a and
b?
a=
b =
Answers:
a = 2
b = 3
=======================================================
Explanation:
Plug in x = 0 and y = 2 to find that
y = a*b^x
2 = a*b^0
2 = a*1
2 = a
a = 2
Then plug in x = 3 and y = 54 to determine the value of b
y = a*b^x
y = 2*b^x
54 = 2*b^3
2b^3 = 54
b^3 = 54/2
b^3 = 27
b = (27)^(1/3)
b = 3
So we have y = a*b^x update to y = 2*3^x
In a class of 70 pupils, 36 like tasty time , 34 like ice-
cream, 6 like both tasty time }
draw a Venn diagram to show the data.
find how
many
like neither tasty time nor ice-cream
Step-by-step explanation:
I think this might be the correct answer
The number of pupils that like neither tasty-time nor ice cream is 6 if in a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty times.
What is the Venn diagram?It is defined as the diagram that shows a logical relation between sets.
The Venn diagram consists of circles to show the logical relation.
We have:
In a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty time.
Total = 70 pupils
Number of like tasty time = 36
Number of like ice cream = 34
Number of like both = 6
Let x be the total number of pupils that like neither tasty-time nor ice cream
The number of pupils that like ice cream only = 34 - 6 = 28
The number of pupils that like tasty-time only = 36 - 6 = 30
From the Venn diagram:
28 + 30 + 6 + x = 70
x = 70 - 64
x = 6
Thus, the number of pupils that like neither tasty-time nor ice cream is 6 if in a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty times.
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Ron has 22 coins with a total value of $ 1.85. The coins are nickels (5 cents) and dimes (10 cents). How many of each coin does he have?
Please help asap and thank you in advance!!
Answer:
18 dimes and 1 nickle
Step-by-step explanation:
This is because 18 time 10 is 180 and one of 5 add it and this is $1.85
Remeber a dollar is 100 cents
Find the value of
[tex] {z}^9{ \times {z}^10 = {z}^x [/tex]
Step-by-step explanation:
Just use the Law of Indices.
Complete the equation describing how x
and y are related.
х у
y = [ ? ]x
-2
-1
0
1
2
3
-6
-3
0
3
6
9
Enter the answer that
belongs in [?]
Answer:
y=3x
Step-by-step explanation:
-6/-2=3, -3/-1=3, 3/1=3. 6/2=3
The length of a rectangle is twice its width. If the area of the rectangle is 72in², find its perimeter
Let breadth be x
Length=2x[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]
[tex]\\ \sf\longmapsto 72=2x(x)[/tex]
[tex]\\ \sf\longmapsto 2x^2=72[/tex]
[tex]\\ \sf\longmapsto x^2=\dfrac{72}{2}[/tex]
[tex]\\ \sf\longmapsto x^2=36[/tex]
[tex]\\ \sf\longmapsto x=\sqrt{36}[/tex]
[tex]\\ \sf\longmapsto x=6[/tex]
Length=6×2=12inBreadth=6in[tex]\\ \sf\longmapsto Perimeter=2(L+B)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(12+6)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(18)[/tex]
[tex]\\ \sf\longmapsto Perimeter=36in[/tex]
Find the length represented by x for each pair of similar triangles.
18cm, 9cm, and x
30cm, 15cm, and 25cm
Answer:
15 cm
Step-by-step explanation:
Since the traingles are similar, we can find the ratio between the side lengths, and it will be the same for each side.
We can use the side length 9 and 15 to find this ratio. 15/9=5/3. So, the ratio of a side length of the larger triangle to the smaller one is 5/3, so our equation becomes 5/3 = 25/x. Use any method you like to find that x=15.
Hope this helped,
~cloud
Find the sum of ∑4/k=1 (-4k)
Answer:
Hello,
Answer C: -40
Step-by-step explanation:
[tex]\displaystyle \sum_{k=1}^4\ (-4k)\\\\=-4*\sum_{k=1}^4\ k\\\\=-4*4*\dfrac{1+4}{2} \\\\=-4*5*2\\\\=-40\\[/tex]
How many 4-digit passcodes can be created if each digit can be any number, 0-9?
6,561
10,000
40
5,040
Answer:
6,561
that's a good number
0 thru 9 is 10 numbers.
Each digit can be 1 of 10 numbers:
Total combinations = 10 x 10 x 10 x 10 = 10,000
Answer: 10,000
!!!!PLEASE HELP!!!!
What is the following quotient?
2
√13+ /11
O 13-2./11
13+ 11
6
13+ V11
12
√13 - 1
(D)
Step-by-step explanation:
Multiply and divide the fraction by the conjugate:
[tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}×\dfrac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}[/tex]
[tex]= \dfrac{2(\sqrt{13} - \sqrt{11})}{(\sqrt{13})^2 - (\sqrt{11})^2}[/tex]
[tex]=\dfrac{2(\sqrt{13} - \sqrt{11})}{2}[/tex]
[tex]=\sqrt{13} - \sqrt{11}[/tex]
Find the missing side or angle.
Round to the nearest tenth.
b=15 a=30 c=29 a=[?]. Acellus plz
Answer:
∠ A ≈ 79.0°
Step-by-step explanation:
Using the Cosine rule to find the angle
cosA = [tex]\frac{b^2+c^2-a^2}{2bc}[/tex]
= [tex]\frac{15^2+29^2-30^2}{2(15)(29)}[/tex]
= [tex]\frac{225+841-900}{870}[/tex]
= [tex]\frac{166}{870}[/tex] , then
A = [tex]cos^{-1}[/tex] ([tex]\frac{166}{870}[/tex] ) ≈ 79.0° ( to the nearest tenth )
A hunter walks 400m Up a hill which slopes at an angle of 20 to the horizontal. Calculate,correct to the nearest metre, the: a. horizontal distance he covered b.vertical height through which he rises.
let y be the horizontal distance and x the vertical
y/400 = cos 20
y=400 cos20
y=376m
x/400 =sin20
x=400sin20
x=137m
if 25 liters of milk can make 8 tin of cheese how many liters of milk would b needed to make 11 tin of cheese?
Answer:
Step-by-step explanation:
34.375 Liters of milk make 11 tins of cheese. Assuming that milk is available in whole liters only, 35 Liters of milk are needed.
Graph y=|x|+5, how does it compare to parent graph y=|x|
9514 1404 393
Answer:
it is shifted 5 units upward
Step-by-step explanation:
The y-coordinate is a measure of the distance above the x-axis. When 5 is added to a y-coordinate, the point is shifted 5 units upward.
The function y = |x| +5 adds 5 units to the y-value of every point of the graph of y = |x|. The graph of y=|x|+5 is shifted 5 units upward from the parent graph.
Find the value of each determinant
Answer:
−4304
Step-by-step explanation:
1. The given determinant is :
[tex]\begin{vmatrix}7 &31 \\ 142& 14\end{vmatrix}[/tex]
We need to find its determinant . It can be solved as follows :
[tex]\begin{vmatrix}7 &31 \\ 142& 14\end{vmatrix}=7(14)-142(31)\\\\=-4304[/tex]
So, the value of determinant is equal to −4304.
Answer:
A= -4269
B= 1768
C= 647.36
Step-by-step explanation:
4) If the perimeter of a square is 48cm",
What is the length of each side?
Simplify your answer.
Answer:
If the total perimeter of square is 48 cm, then the length of one side is equal to 48 divided by 4, since all sides of a square are the same.
So, the correct answer is 12.
Let me know if this helps!
The length of each side is 12cm.
Explanation:
The perimeter of a square is calculated by the formula:
P = 4a , where P = perimeter, and a = length of any side, all sides being equal in a square.
From the given data we write:
48 = 4a
Divide both sides by
4.12 = a
The length of each side is 12cm.
