An economist is studying the linear relationship between the selling price p, of a
mobile phone and the number of persons buying the phone x. The table of values
illustrates her findings. Write the equation that represents the relationship between the
number of persons buying the phone and the price of the phone.
Answers
Answer:
The equation that represents the number of persons buying the phone and the price of the phone is y = -0.75·x + 60
Step-by-step explanation:
The given data are as follows
x, p($)
10, 52.5
25, 41.25
40, 30
60, 15
We note that a plot of the given points give a straight line graph indicating a linear relationship
The rate of change of p($) with x is given by slope, m in the following relation;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Which gives;
[tex]Slope, \, m =\dfrac{41.25-52.5}{25-10} = \dfrac{30-41.25}{40-25} = \dfrac{15-30}{40-60} =-0.75[/tex]
Therefore, to write the equation in slope and intercept form, we have;
From the first point with coordinates (52.5, 10), we have
y - 52.5 = -0.75×(x - 10)
y = -0.75·x + 7.5 + 52.5 = -0.75·x + 60
The equation that represents the number of persons buying the phone and the price of the phone is y = -0.75·x + 60.
Related Questions
Why is the information in the diagram enough to determine that △LMN ~ △PON using a rotation about point N and a dilation? because both triangles appear to be equilateral because∠MNL and ∠ONP are congruent angles because one pair of congruent corresponding angles is sufficient to determine similar triangles because both triangles appear to be isosceles, ∠MLN ≅ ∠LMN, and ∠NOP ≅ ∠OPN
Answers
Answer:
The correct option is;
Because ∠MNL and ∠ONP are congruent angles
Step-by-step explanation:
From the diagram shown in the question, ∠MNL and ∠ONP are vertically opposite angles as they are formed by crossing of the lines LP and MO making them congruent, that is ∠MNL ≅ ∠ONP
Given that two angle of triangle LMN are congruent to two angles of triangle PON , then by the Angle Angle (AA) rule of similarity, triangle LMN and PON are similar.
The information in the diagram enough to determine that △LMN ~ △PON because∠MNL and ∠ONP are congruent angles.
What are Congruent angles?These are referred to angles which have an equal measure. From the diagram ,vertically opposite angles are formed by crossing of the lines LP and MO thus,we can deduce that ∠MNL and ∠ONP are congruent angles.
This means that there is enough information to determine that △LMN ~ △PON using a rotation about point N and a dilation.
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Find the measure of AngleJ, the smallest angle in a triangle with sides measuring 11, 13, and 19. Round to the nearest whole degree. 30° 34° 42° 47°
Answers
Answer:
34°
Step-by-step explanation:
The law of cosines is good for finding angles when only sides are known. We'll use the conventional sides a, b, c, and angles A, B, C. Yes, we know the problem statement calls the smallest angle "J". We trust you can make the translation.
a² = b² +c² -2bc·cos(A) . . . . . for sides a, b, c and angle A
Solving for the angle, we get ...
A = arccos((b² +c² -a²)/(2bc))
Filling in the numbers with "a" being the shortest side, we have ...
A = arccos((13² +19² -11²)/(2·13·19)) = arccos(409/494)
A ≈ 34.113°
The smallest angle, ∠J, is about 34°.
Answer:
b
Step-by-step explanation:
A swimming pool can be emptied in 6 hours using a 10-horsepower pump along with a 6-horsepower pump. The 6-horsepower pump requires 5 hours more than the 10-horsepower pump to empty the pool when working by itself. How long will it take to empty the pool using just the 10-horsepower pump?
Answers
Answer: 10 hours
Step-by-step explanation:
The 10hp pump takes x hours to empty the pool which means it gets [tex]\dfrac{1}{x}[/tex] of the job done in one hour.
The 6hp pump takes x+5 hours to empty the pool which means it gets [tex]\dfrac{1}{x+5}[/tex] of the job done in one hour.
Together, they can get [tex]\dfrac{1}{x}+\dfrac{1}{x+5}[/tex] of the job done in one hour.
It is given that together they get the job done in 6 hours which means they get [tex]\dfrac{1}{6}[/tex] of the job done in one hour.
10 hp pump + 6 hp pump = Together
[tex]\dfrac{1}{x}\quad +\quad \dfrac{1}{x+5}\quad =\quad \dfrac{1}{6}[/tex]
Multiply by 6x(x+5) to eliminate the denominator:
[tex]\dfrac{1}{x}(6x)(x+5) +\dfrac{1}{x+5}(6x)(x+5) = \dfrac{1}{6}(6x)(x+5)[/tex]
Simplify and solve for x:
6(x + 5) + 6x = x(x + 5)
6x + 30 + 6x = x² + 5x
12x + 30 = x² + 5x
0 = x² - 7x - 30
0 = (x - 10)(x + 3)
0 = x - 10 0 = x + 3
10 = x -3 = x
Since the number of hours cannot be negative, disregard x = -3.
So, the only valid answer is x = 10.
Solve the equation in the interval from 270° to 810°
Your answer should be in degrees
cos(x)=1
Choose all answers that apply
A. 0°
B.90°
C.360°
D.540°
E. 720°
F.1080°
Answers
Answer:
the answer should be C,E please give brainliest
Step-by-step explanation
Answer:
C. 360
E. 720
Step-by-step explanation:
note: 2pi radians = 360 degrees.
Cos(x) = 1 whenever x = 2k pi where k is an integer, thus
This translates to
cos(x) = 1 when x=0, 360, 720, 1080, ... degrees.
Between 270 and 810, the angles that satisfy cos(x) = 1 are
360 and 720.
So choose C and E
Please factorise the equations in the doc bellow ASAP. please show full working
Answers
Answer:
b. x² + 8x + 12 =
1. use the factoring X (see attachment)
2. 6 x 2 = 12; 6 + 2 = 12
3. (x + 6)(x + 2) = 0
4. x = -6, -2
c. x² + 13x + 12 =
1. 12 x 1 = 12; 12 + 1 = 13
2. (x + 12)(x + 1) = 0
3. x = -12, -1
c. x² + x - 12 =
1. 4 · (-3) = -12; 4 - 3 = 1
2. (x +4)(x - 3) = 0
3. x = -4, 3
f. x² + 15x + 36 =
1. 12 x 3 = 36; 12 + 3 = 15
2. (x + 12)(x + 3) = 0
3. x = -12, -3
hope this helps :)
Answer:
b) - (x + 2)(x + 6)
c) - (x + 12)(x + 1)
c) - (x - 3)(x + 4)
f) - (x + 12)(x + 3)
Step-by-step explanation:
Well to factor the given info we need to find the factors.
b)
[tex]x^2 + 8x + 12[/tex]
So 6*2 = 12
6x + 2x = 8x
x*x = x^2
Factored - (x + 2)(x + 6)
c)
[tex]x^2 + 13x + 12[/tex]
Well x*x = x^2
and 12*1 = 12
12x + x = 13x
Factored - (x + 12)(x + 1)
The second c)
[tex]x^2 + x - 12[/tex]
Well x*x = x^2
-3*4 = -12
-3x + 4x = x
Factored - (x - 3)(x + 4)
f)
[tex]x^2 + 15x + 36[/tex]
So x*x = x^2
12*3 = 36
12x + 3x = 15x
Factored - (x + 12)(x + 3)
Thus,
everything factored is (x + 2)(x + 6) , (x + 12)(x + 1) , (x - 3)(x + 4) ,
(x + 12)(x + 3).
Hope this helps :)
Express the complex number in trigonometric form. 5 - 5i
Answers
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Lets do this step by step.
This is the trigonometric form of a complex number where [tex]|z|[/tex] is the modulus and [tex]0[/tex] is the angle created on the complex plane.
[tex]z = a + bi = |z| (cos ( 0 ) + I sin (0))[/tex]
The modulus of a complex number is the distance from the origin on the complex plane.
[tex]|z| = \sqrt{a^2 + b^2}[/tex] where [tex]z = a + bi[/tex]
Substitute the actual values of a = -5 and b = -5.
[tex]|z| = \sqrt{(-5) ^2 + (-5) ^2}[/tex]
Now Find [tex]|z|[/tex] .
Raise - 5 to the power of 2.
[tex]|z| = \sqrt{25 + (-5) ^2}[/tex]
Raise - 5 to the power of 2.
[tex]|z| = \sqrt{25 + 25}[/tex]
Add 25 and 25.
[tex]|z| = \sqrt{50}[/tex]
Rewrite 50 as 5^2 . 2 .
[tex]|z| = 5\sqrt{2}[/tex]
Pull terms out from under the radical.
[tex]|z| = 5\sqrt{2}[/tex]
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
[tex]0 = arctan (\frac{-5}{-5} )[/tex]
Since inverse tangent of [tex]\frac{-5}{-5}[/tex] produces an angle in the third quadrant, the value of the angle is [tex]\frac{5\pi }{4}[/tex] .
[tex]0 = \frac{5\pi }{4}[/tex]
Substitute the values of [tex]0 = \frac{5\pi }{4}[/tex] and [tex]|z| = 5\sqrt{2}[/tex] .
[tex]5\sqrt{2} ( cos( \frac{5\pi}{4}) + i sin (\frac{5\pi}{4}))[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
The complex number (5 - 5i) in trigonometric form is
5√2 [cos(-π/4) + i sin(-π/4)]
What is an imaginary number?An imaginary number is denoted by i.
The value of i is √-1.
We have,
To express the complex number (5 - 5i) in trigonometric form,
We first need to find its modulus (r) and argument (θ).
The complex number (a - bi) in trigonometric form is
|r| [cosФ + i sinФ]
Now,
Modulus (r).
|r| = √(5² + (-5)²)
= √(50)
= 5√(2)
And,
Argument (θ).
θ = [tex]tan^{-1}[/tex](-5/5)
= -π/4
(since the complex number is in the fourth quadrant)
Therefore,
The complex number (5 - 5i) in trigonometric form is
5√2 [cos(-π/4) + i sin(-π/4)]
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A certain quantity grows exponentially over time. The initial quantity at t = 0 is 2,000. The quantity
grows by a factor of 20%. What is the quantity at t = 8?
A 0.00512
B. 8,599.63392
C. 10,319.56070
D. 12,383.47284
Answers
Answer:
B
Step-by-step explanation:
using the equation y=2000*1.2^8 we can get the exact value of y which aligns with b
Find the value of this expression if x=3 x^2 + 3/x-1
Answers
Answer: 9
Step-by-step explanation:
[tex]3^2 + \frac{3}{3}-1\\\\=9+1-1\\\\=9[/tex]
Calculate the area of triangle RST. a = 38.
Answers
Answer:
722 √(3) square units
Step-by-step explanation:
Mathematically, the area of a triangle is 1/2 * b * h
But in this question, we have the base which is a while the height is absent
We can use trigonometric ratios since we are given the angle to find the value of the height.
Since we are dealing with the opposite and the adjacent, the correct trigonometric identity to use is the tangent
Mathematically;
Tan 60 = h/a
where h represents the height which we want to calculate
h = a tan 60
But tan 60 = √(3)
So h = a √(3)
Now the area of the triangle will be;
A = 1/2 * a * a √(3)
But a has a value of 38 units.
Substituting this value, we have ;
A = 1/2 * 38 * 38 √(3)
A = 19 * 38√(3)
A = 722 √(3) square units
Find the center and radius of x^2 – 18x + y^2 -10y = -6. part two write x2 – 18x + y2 -10y = -6 in standard form
Answers
Answer:
see explanation
Step-by-step explanation:
I will begin with part two, first.
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius.
Given
x² - 18x + y² - 10y = - 6
Using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 9)x + 81 + y² + 2(- 5)y + 25 = - 6 + 81 + 25, that is
(x - 9)² + (y - 5)² = 100 ← in standard form
with centre = (9, 5 ) and r = [tex]\sqrt{100}[/tex] = 10
dilate the given triangle with a magnitude of 3 [3 6 3 -3 3 3]
Answers
Answer:
The coordinates of the triangle, (3, 6), (3, -3), and (3, 3), dilated by a magnitude of 3 is;
(9, 18), (9, -9), and (9, 9)
Step-by-step explanation:
The vertices of the given triangle are;
(3, 6), (3, -3), and (3, 3)
A dilation with a magnitude of 3 can be found as follows;
For each value of the x, and y-coordinates of the vertices, we multiply by the magnitude of dilation
As an example, the coordinate of the points on a line, (x₁, y₁) and (x₂, y₂), dilated by a scale factor of m, will become, (m·x₁, m·y₁) and (m·x₂, m·y₂)
Therefore, we have foe a magnitude of 3;
(3, 6), (3, -3), and (3, 3) becomes, (3×3, 3×6), (3×3, 3×(-3)), and (3×3, 3×3)
(9, 18), (9, -9), and (9, 9).
Answer:
(9, 18), (9, -9), and (9, 9)
Step-by-step explanation:
Mayelle earns $18,000 a year. After a raise, she earns $19,500. What is the percent of increase in pay? Round to the nearest tenth of a percent
Answers
Answer:
8.3 %
Step-by-step explanation:
Mayelle earns $18000 per year. Mayelle earning is increased by $19500, to calculate the percentage increase in earnings, we divide the difference between earnings after increase and earnings before increase by the earnings before increase and then multiply the result by 100. The percentage increase is given by:
Increase in pay = (Earnings before increase - earnings after increase) / Earnings before increase × 100%
Increase in pay = ($19500 - $18000)/ $18000 × 100% = 8.3 %
What is the vertical height, h?
Answers
Answer:
6.2Step-by-step explanation:
s = 10 so ¹/₂s = 5
Pythagorean theorem:
[tex]h^2+(\frac12s)^2=8^2\\\\h^2+5^2=8^2\\\\h^2=64-25\\\\h^2=39\\\\h=\sqrt{39}=6.2449979....\approx6.2[/tex]
Consider the matrix A = \begin{pmatrix} 7 & 9 & -3 \\ 3 & -6 & 5 \\ 4 & 0 & 1 \end{pmatrix} ⎝ ⎛ 7 3 4 9 −6 0 −3 5 1 ⎠ ⎞ . What is the value of minor M_{11}M 11 ? 5 -6 0 -4
Answers
Answer:
The value of M₁₁ is -6.
Step-by-step explanation:
The minor, [tex]M_{ij}[/tex] is the determinant of a square matrix, say P, formed by removing the ith row and jth column from the original square matrix, P.
The matrix provided is as follows:
[tex]A=\left[\begin{array}{ccc}7&9&-3\\3&-6&5\\4&0&1\end{array}\right][/tex]
The matrix M₁₁ is:
Remove the 1st row and 1st column to form M₁₁,
[tex]M_{11}=\left|\begin{array}{cc}-6&5\\4&0\end{array}\right|[/tex]
Compute the value of M₁₁ as follows:
[tex]M_{11}=\left|\begin{array}{cc}-6&5\\4&0\end{array}\right|[/tex]
[tex]=(-6\times 1)-(5\times 0)\\\\=-6-0\\=-6[/tex]
Thus, the value of M₁₁ is -6.
How to subtract LCD - 13/20 - 2/5
Answers
Answer: 13/20 - 2/5 = 1/4 ( Using LCD)
Step-by-step explanation:
Given: 13/20 - 2/5 = ? Use LCD
1) First we need find the least common multiple of the denominator (20 and 5) which is 20.
2) Since we know the least common multiple we know need to switch the two fractions up but since one of the denominator is already 20 ( 13/20) we now need to fix the other fraction (2/5).
3) We need to make it the same for both fractions so we want the same denominator as the first fraction (20) so we multiply 5 by 4 since 5 x 4 = 20 and we get 20, while also doing the same thing with the numerator. So we times 2 by 4 and we get 8.
4) Now our two fractions are now 13/20 and 8/20.
5) Our next step is to subtract the numerator, so its 13-8 which we get 5.
6) So now we have 5/20 and we want to simply to the smallest fraction so we find a number that is divisible and can make the smallest fraction which is 5.
5/5 and 20/5 and we get 1/4.
A pair of dice is rolled. What is the probability that the sum is 9? a 1/36 b 1/18 c 1/9 d 2/9
Answers
A right triangle has a height of 18 inches and a base of 12 inches find the area of the triangle in square inches find the area of the triangle in square inches
Answers
Answer: 108 square inches
Step-by-step explanation:
The formula for any square is base*height/2. The formual to find the area of a square is base*height. If you draw out a square and cut it in half diagonaly, you get a right triangle. That is why you divide it by 2. (sorry if the explanation was clunky/ hard to understand)
1. You would multiply 18*12 which equals 216.
2. Divide 216 by 2. 216/2= 108.
The answer is 108. Hope this helped you:)
The area of the triangle is 108 square inches.
What is the area of the triangle?The area of the triangle is defined as the product of half the base and the height of the triangle.
The area of the triangle = 1/2 x b x h
If we draw out a square and cut it in half diagonaly, you get a right triangle. That is why we need to divide it by 2.
The area of the triangle = 1/2 x b x h
The area of the triangle = 1/2 x 12 x 18
= 216/2= 108.
The area of the triangle is 108 square inches.
Learn more about the area;
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There are 238 juniors at a high school The ratio of boys to girls in the junior class is 3:4. How many juniors are girls?
Answers
Explanation:
Find the girls in junior class:
238 x 4/7 = 136
Answer:
59.5
Step-by-step explanation:
I know there cannot be half a human running around the school, and I don't exactly remember if you round up or down, but there are a total of 238 juniors in the school. you divide 238 by 4. the girls represent one fourth of the juniors, and the boys represent three fourths. thank you, please mark brainliest!
An electronics company designed a cardboard box for its new line of air purifiers. The figure shows the dimensions of the box.
The amount of cardboard required to make one box is___square inches.
a)130
b)111
c)109
d)84
Answers
Answer:
130
Step-by-step explanation:
just did test on plato/edmentum..it was correct
84 (the answer above) is incorrect
Answer:
Hi sorry for late respond but the answer in 130!!
Step-by-step explanation:
15 POINTS! three times X is 13 less than Y. the sum of X and two times y is 12 write two equations and graph to find the value of Y. A. y=-7 B. y=2 C. y=7 D. y=-2
Answers
x + 2y = 12
x + 2(3x + 13) = 12
x + 6x + 26 = 12
7x = -14
x = -2
y = 3(-2) + 13
y = 7
It would be answer C
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The value of y is 7.
The graph of the two-equation is given below.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
3x = y - 13 ____(1)
x + 2y = 12 _____(2)
From (1) we get,
x = (y - 13)/3 _____(3)
Putting (3) in (2) we get,
(y - 13)/3 + 2y = 12
y - 13 + 6y = 36
7y = 36 + 13
7y = 49
y = 7
The graph of the equation is given below.
Thus,
The value of y is 7.
The graph of the two-equation is given below.
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Solve this application problem using a system of equations: Dan and June mix two kinds of feed for pedigreed dogs. They wish to make 70 pounds of feed worth $0.30 per pound by mixing Feed A worth $0.26 per pound with Feed B worth $0.40 per pound. How many pounds of the cheaper kind should they use in the mix
Answers
Answer:
50 pounds
Step-by-step explanation:
Dan and june mix two kind of feed for pedigreed dogs
Feed A worth is $0.26 per pound
Feed B worth is $0.40 per pound
Let x represent the cheaper amount of feed and y the costlier type of feed
x+y= 70..........equation 1
0.26x + 0.40y= 0.30×70
0.26x + 0.40y= 21.........equation 2
From equation 1
x + y= 70
x= 70-y
Substitutes 70-y for x in equation 2
0.26(70-y) + 0.40y= 21
18.2-0.26y+0.40y= 21
18.2+0.14y= 21
0.14y= 21-18.2
0.14y= 2.8
Divide both sides by the coefficient of y which is 0.14
0.14y/0.14= 2.8/0.14
y= 20
Substitute 20 for y in equation 1
x + y= 70
x + 20= 70
x= 70-20
x = 50
Hence Dan and june should use 50 pounds of the cheaper kind in the mix
Two cards are selected at random from a standard deck of cards. What is the probability that you select a king or a queen? (If your answer will reduce, you should reduce it.) Also show you're work
Answers
Answer:
2/13
Step-by-step explanation:
In a standard deck of cards, there are 52 cards total, 4 kings, and 4 queens.
Probability is calculated by (number of favorable outcomes)/(number of possible outcomes), so our probability would be 8/52, which can be simplified to 2/13.
Hope this helps!
Manuela solved the equation 3−2|0.5x+1.5|=2 for one solution. Her work is shown below.
3−2|0.5x+1.5|=2
−2|0.5x+1.5|=−1
|0.5x+1.5|=0.5
0.5x+1.5=0.5
0.5x=−1
x=−2
What is the other solution to the equation?
x=−6
x=−4
x=2
x=4
Answers
Answer:
X= -4
X=-2
Step-by-step explanation:
for
|a|=b
assume
a=b and a=-b
so
3-2|0.5x+1.5|=-2
minus 3 both sides
-2|0.5x+1.5|=-1
divide both sides by -2
|0.5x+1.5|=0.5
set negative and postivive
0.5x+1.5=0.5 and 0.5x+1.5=-0.5
solve each
0.5x+1.5=0.5
minus 1.5 both sides
0.5x=-1
times - 2 both sides
x=-2
other
0.5x+1.5=-0.5
minus 1.5 from oth sides
0.5x=-2
times 2 both sides
x=-4
the solutions are x=-2 and x=-4
Answer:
x=-4
Step-by-step explanation:
A box contains 5 yellow toys and 4 red toys. Two toys are selected with replacement.
- Draw a tree diagram showing all outcomes and probabilities
-Find the probability that:
A. Two toys of the same colour will be picked
B. Toys of different colours will appear
C. A red toy will be picked first
D. At least one red toy will be picked
-if there was no replacement, find the probability that:
A. Two toys of the same colours will be picked
B. Toys of different colours will appear
C. A red toy will be picked first
D. At least one red toy will be picked
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Yellow (Y) toys = 5
Red (R) toys = 4
Total toys = yellow + red = (5 +4) = 9
WITH REPLACEMENT :
Probability that two toys of same color will be picked.
From the tree diagram.
Two toys of the same color
a.)P(Y, Y) + P(R, R) = (25/81) + (16 / 81) = 41/81
b) toys of different color :
P(Y, R) + P(R, Y) = (20/81) + (20/81) = 40/81
c.) A red toy will be picked first :
P(R, Y) = 20/81
d.) Atleast one red toy will be picked
P(Y, R) + P(R, Y) + P(R, R)
20 /81 + 20/81 + 16/81 = 56/81
2) WITHOUT REPLACEMENT :
a.)P(Y, Y)+P(R, R) = (20/72) + (12/72) = 32/72 = 4/9
b) P(Y, R)+P(R, Y) = (20/72)+(20/72)= 40/72 = 5/9
c) p(R, Y) = 12/72 = 1/6
d) P(Y, R) + P(R, Y) + P(R, R) = 20/72 + 20/72 + 12/72 = 52/72 = 13/ 18
List the coordinates of FOUR vertices that create the feasible region on the graph. Submit your answer in the form of FOUR ordered Pairs (x, y)
Answers
Answer:
see below
Step-by-step explanation:
The feasible region is the shaded area. We just need to find the coordinates of its vertices. These are (200, 200), (300, 0), (500,0) and (300, 200).
Suppose we have three urns, namely, A B and C. A has 3 black balls and 7 white balls. B has 7 black balls and 13 white balls. C has 12 black balls and 8 white balls. We first choose one urn from A, B and C. Then we randomly pick up two balls from that urn without replacement. Let Ai, i 1,2,3 denote the event that the urn we choose is A, B and C respectively. Suppose P(A1): P(A2): P(A3) =1:2:2. Compute :
(a) The probability that the first ball is black.
(b) The probability that the first ball is black given that the second ball is white.
Answers
Answer:
a. 11/25
b. 11/25
Step-by-step explanation:
We proceed as follows;
From the question, we have the following information;
Three urns A, B and C contains ( 3 black balls 7 white balls), (7 black balls and 13 white balls) and (12 black balls and 8 white balls) respectively.
Now,
Since events of choosing urn A, B and C are denoted by Ai , i=1, 2, 3
Then , P(A1 + P(A2) +P(A3) =1 ....(1)
And P(A1):P(A2):P(A3) = 1: 2: 2 (given) ....(2)
Let P(A1) = x, then using equation (2)
P(A2) = 2x and P(A3) = 2x
(from the ratio given in the question)
Substituting these values in equation (1), we get
x+ 2x + 2x =1
Or 5x =1
Or x =1/5
So, P(A1) =x =1/5 , ....(3)
P(A2) = 2x= 2/5 and ....(4)
P(A3) = 2x= 2/5 ...(5)
Also urns A, B and C has total balls = 10, 20 , 20 respectively.
Now, if we choose one urn and then pick up 2 balls randomly then;
(a) Probability that the first ball is black
=P(A1)×P(Back ball from urn A) +P(A2)×P(Black ball from urn B) + P(A3)×P(Black ball from urn C)
= (1/5)×(3/10) + (2/5)×(7/20) + (2/5)×(12/20)
= (3/50) + (7/50) + (12/50)
=22/50
=11/25
(b) The Probability that the first ball is black given that the second ball is white is same as the probability that first ball is black (11/25). This is because the event of picking of first ball is independent of the event of picking of second ball.
Although the event picking of the second ball is dependent on the event of picking the first ball.
Hence, probability that the first ball is black given that the second ball is white is 11/25
Circle C is shown. Radius A has a length of r. In circle C, r = 32 units. What is the area of circle C? 32Pi units squared 64Pi units squared 256Pi units squared 1024Pi units squared
Answers
Answer:
A = 1024 pi units^2
Step-by-step explanation:
If r = 32 units, we can find the area
A = pi r^2
A = pi ( 32) ^2
A = 1024 pi units^2
The area of the circle C is 1024π square units.
What is area?Area is the amount of space occupied by a two-dimensional figure.
What is the formula for the area of circle?The formula for the area of circle is given by
[tex]Area = \pi r^{2}[/tex]
Where,
r is the radius of the circle
According to the question.
We have the radius of circle, r = 32 units
Therefore,
The area of the circle C is given by
[tex]Area = \pi (32)^{2}[/tex]
⇒ [tex]Area = 1024\pi[/tex] square units
Hence, the area of the circle C is 1024π square units.
Find out more information about area of circle here:
https://brainly.com/question/16969543
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An electronics store is having a back-to-school sale. Blake is interested in purchasing a new computer, and the one he’s been wanting to buy currently has a manufacturer’s rebate of $100. The store is also offering a 10% discount with a school ID, which Blake carries regularly in his wallet. Part A Suppose f(x) = x − 100 and g(x) = 0.9x. Find (f ∘ g)(x).
Answers
Answer:
(f ∘ g)(x) = 0.9x - 100
Step-by-step explanation:
Here in this question, we are interested in calculating (f ∘ g)(x)
From the question, we are given;
f(x) = x -100
g(x) = 0.9x
So (f ∘ g)(x) simply means we shall be representing the x in f(x) with the totality of the value of g(x)
Mathematically, what we are saying is that;
Find (f ∘ g)(x) = 0.9x - 100
PLZ HELP!!!!!!
(06.05 MC)
A group of students were surveyed to find out if they like watching television or reading during their free time. The results of the survey are shown below
90 students like watching television
20 students like watching television but do not like reading
80 students like reading
40 students do not like watching television
Make a two-way table to represent the data and use the table to answer the following questions.
Part A: What percentage of the total students surveyed like both watching television and reading? Show your work. (5 points)
Part B: What is the probability that a student who does not like watching television also does not like reading? Explain your answer. (5 points)
Answers
Answer:
A: 39.1304348% OR 39%
B: 33.3%
Step-by-step explanation:
Part A:
find the total amount of children: 90+20+80+40=230
90-20=50
i got this from taking away the amount that like watching tv and not reading so from this you know 50 of those 90 that like watching tv also like tv and reading.
80-40=40
(same explanation as 90-20=50)
then do 50 +40 which equals 90
now you need to turn it into a percentage.
90/230=
9/23
=39.1304348%
if you need round it, do so!
Part b:
40+20=60
20/60= 2/6
=1/3
=33.3%
25 percent of 510,000
Answers
Answer:
127 500
Step-by-step explanation:
Let x be the missing value.
● 510 000 => 100
● x => 25
x = (25*51000)÷100 = 127 500
Answer:
hope it helps
Step-by-step explanation:
25 percent of 510,000 = 127,500