Answer:
P(A) x P(B) = 35 x 13 = 455
P(A∩B) = 18
=> P(A) x P(B) ≠ P(A∩B).
=> A and B are not independent.
=> Option A (No, because 35(13)≠18) is correct.
Hope this helps!
:)
A and B are not independent because 35(13)≠18), the correct option is A
What is the independent probability?Independent events and probability can be defined as those occurrences that are not dependent on any specific event.
P(A)=35, P(B)=13, and P(A∩B)=18, are A and B independent.
It is to note here that A and B are the odd number outcome and multiples of 3 respectively. So, P (A ∩ B) = 18
P(D│E) = P (D ∩ E)/ P(B)
P(D│E) = 18/13
Here P(D) = P(D│E) = 18/13, which entails that the occurrence of event E will not be affected by the probability of event D’s occurrence.
Taking A and B as independent events, then P(D│E) = P(D).
Here, A and B are not independent because 35(13)≠18), the correct option is A.
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ2
The triangular prism shown below is 6 \,\text{cm}6cm6, start text, c, m, end text wide and 4\,\text{cm}4cm4, start text, c, m, end text deep. The vertical height is 7\,\text{cm}7cm7, start text, c, m, end text. What is the length of the side edge, sss, of the triangular prism? Round your answer to the nearest tenth.
Question :
The triangular prism shown below is 6 cm wide and 4 cm deep. The vertical height is 7 cm. What is the length of the side edge, s, of the triangular prism? Round your answer to the nearest tenth.
Answer: 7.62cm
Step-by-step explanation:
Given the following :
Width = 6cm
Depth = 4cm
Vertical height = 7cm
Splitting the face of the prism into two:
Thus the width becoming 6cm/2 = 3cm and vertical height = 7cm
Using Pythagoras ;
The side edge 's' equals
s^2 = width^2 + height^2
s = √(width^2 + height^2)
s = √(3^2 + 7^2
s = √9 + 49
s = √58
s = 7.62cm
Answer:
7.6
Step-by-step explanation:
the person above is correct, i took the test on khan, but you have to round to the nearest tenth
Which function is the result of vertically shrinking ƒ(x) = (x + 1)2 by a factor of 1∕6?
Question 6 options:
A) ƒ(x) = (6x + 1)2
B) ƒ(x) = (1∕6x + 1)2
C) ƒ(x) = 6(x + 1)2
D) ƒ(x) = 1∕6 (x + 1)2
Answer:
[tex]y=\frac{1}{6}(x+1)^2[/tex] is the result of vertically shrinking
Step-by-step explanation:
Vertical stretch or shrink
[tex]y=c \cdot f(x)[/tex]
a stretch by a factor of c if c>1
a shrink by a factor of c if c<1
c is the factor
We are given that factor = 1/6 <1
So, Vertical shrink
So, [tex]y = \frac{1}{6} \cdot f(x)[/tex]
We are given that [tex]f(x) = (x + 1)^2[/tex]
So,[tex]y=\frac{1}{6}(x+1)^2[/tex]
Option D is true
Hence [tex]y=\frac{1}{6}(x+1)^2[/tex] is the result of vertically shrinking
Answer:
ƒ(x) = (1∕6x + 1)^2
Step-by-step explanation:
What are the domain and range of the logarithmic
function f(x) = log7X? Use the inverse function to
justify your answers.
Answer:
The domain of f is x > 0.
The range of f is all real numbers.
The domain of the inverse function is all real numbers.
The range of the inverse function is y > 0.
The domain of f is the same as the
range of the inverse function.
The range of f is the same as the
the domain of the inverse function.
Step-by-step explanation:
this is the sample answer, make sure you rewrite in your own words!
The domain and the range of a function are the set of input and output values of the function
The domain and the range of the function are set of real numbers greater than 0
The function is given as:
[tex]f(x) = log_7(x)[/tex]
The above function is a logarithmic function.
From the properties of a logarithmic function, we have:
The x-values are always greater than 0The y-values are always greater than 0This means that, the domain and the range of the function are set of real numbers greater than 0
Read more about domain and range at:
https://brainly.com/question/10197594
help me plzzzzzzz!!!!
[tex] {y}^{2} + 14 = 3 {y}^{2} \times 5[/tex]
Answer:
[tex]y=1,\:y=-1[/tex]
Step-by-step explanation:
[tex]y^2+14=3y^2\cdot \:5\\\y^2+14-14=3y^2\cdot \:5-14\\y^2=15y^2-14\\y^2-15y^2=15y^2-14-15y^2\\-14y^2=-14\\\frac{-14y^2}{-14}=\frac{-14}{-14}\\y^2=1\\\\y=\sqrt{1},\:y=-\sqrt{1}\\y=1,\:y=-1[/tex]
Answer:
y = ± 1
Step-by-step explanation:
Given
y² + 14 = 3y² × 5, that is
y² + 14 = 15y² ( subtract y² from both sides )
14 = 14y² ( divide both sides by 14 )
1 = y² ( take the square root of both sides )
± [tex]\sqrt{1}[/tex] = y , that is
y = ± 1
Thus y = - 1 or y = 1
Mr. Blackburn is buying new carpet for his family room and hallway. The floor plan is shown below.
Pls help me ASAP
Answer:
Step-by-step explanation:
3.2 times 1.5 plus 6 times4.2= 30 meters of carpet.
Answer:
He needs 23.7 of carpet
Step-by-step explanation:
multiply 4.2 and 6 which is 25.2. Then subtract 1.5 from 25.2 which is 23.7.
The measure of an angle is 17°. What is the measure of its complementary angle?
Answer:
73°
Step-by-step explanation:
the measure of two complementary angles add up to 90
so We need to solve this equation to get the measure of its complementary angle :
x + 17 = 90
then
x = 90 - 17
= 73
Benny scored 19 points in Mondays basketball game and 46 points in Fridays game.How many points did he score in the last two games?
Answer:
He scored 65 points in his last two games
Step-by-step explanation:
Here, we want to calculate the number of points Benny scored in his last two games.
We must understand that his last two games correspond to the games he played on Monday and on Friday
So to get his total points in the last two games, what we do is that we add both points together
Mathematically, that would be 19 + 46 = 65 points
(x - 3)² + (x - 1)² = 8
Identify the center and radius of each
Answer:
The center is at (3,1) and the radius is [tex]\sqrt{8}[/tex]
Step-by-step explanation:
I am going to assume you meant to write
[tex](x-3)^2+(y-1)^2 = 8[/tex]
Since if both variables were x it would not be a circle:
Then you can find the center and radius using the general formula of a circle:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
where the center is at (h,k) and r is the radius
Therefore:
The center is at (3,1) and the radius is [tex]\sqrt{8}[/tex]
3. Which of the following represents a function?
O (5, 1), (5,2), (5, 3), (5, 4)
O (-1,2), (-2, 1), (-1, -2), (-2,-1)
O (3, 4), (-3, 2), (3, 8), (5,5)
O (2, 3), (4, 3), (-2, -3), (-4,-3)
Answer: D is a function.
Step-by-step explanation:
A function need to have exactly one output to each input.
Answer: D. (2, 3), (4, 3), (-2, -3), (-4,-3)
Step-by-step explanation: This represents a function because they're the opposing of each other. Hope this helps happy holidays! :)
what percent of 420 is 70
Answer:
16.67
Step-by-step explanation:
Answer:
16.67
Step-by-step explanation:
70:420*100 =
(70*100):420 =
7000:420 = 16.67
The dimensions of a chocolate box are: height=x + 2 inches, length=2x+5 inches, and width=4x-1 inches. If the volume of the chocolate box is 605 cubic inches, what is the value of x?
I hope this helps you
Answer:
To begin to answer your question you would need to know that the formula for the volume of a rectangular prism is the following: [tex]V=lwh[/tex]. Now its just a manner of substitutions.
Step-by-step explanation:
[tex]V=605 \text{in}^3[/tex]
Then one can also state the following:
[tex]V=(x+2)(4x-1)(2x+5)[/tex]
Following up with this substitution:
[tex]605=(x+2)(4x-1)(2x+5)[/tex]
Proceeding with a FOIL procedure:
[tex]605=(4x^2+8x-x-2)(2x+5)[/tex]
[tex]605=8x^{3}+34x^{2}+31x-10[/tex]
[tex]0=8x^{3}+34x^{2}+31x-615[/tex]
Using PRZs:
[tex]PRZs=\frac{\text{Factors of Constant Term}}{\text{Factors of Highest Power}}=\frac{\pm 1,\pm 3, \pm 5, \pm 41, \pm 615}{\pm 1, \pm 2, \pm 4, \pm 8}[/tex]
By graphing it one can identify that 3 is a solution so plugging it in and using synthetic division.
[tex]\begin{array}{ccccc}3|& 8 & 34 & 31 & -615\\ \ \ |& & 24 & 174 & 615 \\ & 8 & 58 & 205 &0 \end{array}\\[/tex]
Giving the following the polynomial:
[tex]0=(x-3)(8x^2+58x+205)[/tex]
Now one can evaluate the discriminant of that quadratic:
[tex]58^2-4(8)(205)=-3196[/tex]
Because it is negative one knows that it produces imaginary solutions. Therefore the only real solution is [tex]x=3[/tex]. Therefore the dimension of the box is the following: [tex]5\text{in},11\text{in}, 11\text{in}[/tex]
Solve the right triangle. Round decimal answers to the nearest tenth.
С
12
B
9
A
AB=
m
M
I need help
Answer:
15
Step-by-step explanation:
Use the Pytago theorem.
AB^2=AC^2+BC^2
AB^2= 9^2 + 12^2
= 225
AB = [tex]\sqrt225}[/tex]
= 15
3. Find x, y, and z.
zº
xº
y
18°
64°
Answer:
[tex]y = 18 \: \: degrees[/tex]( vertically opposite angles)
[tex]x = 64 \: \: degrees[/tex]
[tex]y + z + x = 180 \\ 18 + z + 64 = 180 \\ 82 + z = 180 \\ z = 180 - 82 \\ z = 98 \: \: degrees[/tex]
15. Find the largest number which divides 70
and 125 leaving remainders 5 and 8,
respectively
Answer:
13
Step-by-step explanation:
70 - 5 = 65
125 - 8 = 117
Find the Greatest Common Divisor of 65 & 117
65 = 5 * 13
117 = 3 * 3 * 13
GCD = 13
13 is the largest number that divides 70 & 125 and leaves remainders 5 and 8 respectively
− 5/6 x=−10/3 solve for X
Answer:
X = 4
Step-by-step explanation:
-5/6x = -10/3
x = -10/3 * -6/5
x = 60/15
x = 4
Answer:
The result for this equation is [tex]x =4[/tex] .
Step-by-step explanation:
Solve the equation for [tex]x[/tex] :
[tex]-\frac{5}{6}x =-\frac{10}{3}[/tex]
[tex]\frac{-\frac{5}{6}x }{-\frac{5}{6} } =\frac{-\frac{10}{3} }{-\frac{5}{6} }[/tex]
[tex]x = 4[/tex]
So, the answer for this equation is [tex]x =4[/tex] .
1
2
3..
4
5
6
8
9
10
Which set of data does not contain any outliers?
113, 115, 103, 154, 109, 111, 119
141, 151, 111, 142, 149, 140, 150
99, 103, 91, 104, 109, 107, 97
131, 135, 131, 99, 138, 136, 140
Answer:
99, 103, 91, 104, 109, 107, 97
Step-by-step explanation:
The bold is the outlier
113, 115, 103, 154, 109, 111, 119
141, 151, 111, 142, 149, 140, 150
131, 135, 131, 99, 138, 136, 140
What is the area of sector GPH?
Answer:
Area of GPH = pi x 15^2 x 40/360 = 78.54 (yd2)
Hope this helps!
Answer:
78.5 yards²
Step-by-step explanation:
Area of a sector:
Theta/360 × pi × r²
40/360 × 3.14 × 15²
78.5 yd²
At 8:00 am, it is 10 degrees outside. 12 hours later at 8:00 pm, it is -20 degrees outside. What is the difference in temperatures?
Answer:
-30
Step-by-step explanation:
Determine the volume of the cylinder
Answer:
about 904.78
Step-by-step explanation:
πr^2h pi(6)^2 * 8
What is the distance between the points (4, 5) and (10, 13) on a coordinate plane?
A. 10 units
B. 14 units
C. 12 units
D. 8 units
Answer:
10
Step-by-step explanation:
Distance = √(x2-x1)² + (y2-y1)²
d = √(10-4)² + (13-5)²
d = √6² + 8²
d = √36+364
d = √100
d = 10
The amount of money 'y' made at a laundromat after 'x' months can be represented by the linear function: y = 8.50x - 5. After 2 months, the laundromat made 20 dollars, but the linear function predicted they would make 12 dollars. What is the residual value for this data?
Answer:
[tex] \hat y = 8.5*2 -5 = 12[/tex]
And the residual is defined as:
[tex] e_ i = y_i -\hat y_i [/tex]
And replacing we got:
[tex] e_i = 20-12 = 8[/tex]
Step-by-step explanation:
For this case we know that the amount of money 'y' made at a laundromat after 'x' months can be represented by the linear function:
[tex] y = 8.50 x -5[/tex]
And fter two months we know that the laundromat made 20 dollars. And if we use the linear function we got:
[tex] \hat y = 8.5*2 -5 = 12[/tex]
And the residual is defined as:
[tex] e_ i = y_i -\hat y_i [/tex]
And replacing we got:
[tex] e_i = 20-12 = 8[/tex]
9. What is the volume of the given prism? Round the answer to the nearest tenth of a centimeter.
The figure is not drawn to scale.
8.8 cm
/
4.7 cm
13.1 cm
313.3 cm3
436.4 cm
541.8 cm3
681.5 cm3
Answer:
The answer is 541.8 cm³
Step-by-step explanation:
you just have to multiply the measures of each side:
(8.8)(4.7)(13.1) = 541.8
Pleaaaase hellp me will mark u brainly for both answers!!!
Thank u if u do really appreciate it.
Answer:
1. Option A is correct (A = length x width)
2. Option B is correct ( A = base x height/2)
Hope this helps
:)
What is the end behavior of the polynomial function?
Answer:
D) as x approaches neg. infinity, y approaches neg. infinity
Step-by-step explanation:
This is because you get to negative x infinity which is towards the right, you see that the y value is going down sharply as well towards the direction of negative infinity in y direction (x direction is right to left and y direction is up and down)
Answer:
D one Edge 2021 ;))
Step-by-step explanation:
whats the product for (2z-3)^3
Answer:
8z^3-36z^2+54z-27
Step-by-step explanation:
(2z-3)^3
(2z)^3*(2z)^2*3+3*2z*3^2-3^3
8z^3-3*4z^2*3+3*2z*9-27
8z^3-36z^2+54z-27
Answer:
[tex]8z^3-36z^2+54z-27[/tex]
Step-by-step explanation:
[tex](2z-3)^3\\(2z-3)(4z^2-12z+9)\\2z(4z^2-12z+9)-3(4z^2-12z+9)\\8z^3-24z^2+18z-12z^2+36z-27\\8z^3-36z^2+54z-27[/tex]
Someone help me please
Step-by-step explanation:
Step 1: Convert degrees into radians
[tex]\frac{degrees}{1}*\frac{\pi }{180}[/tex]
[tex]\frac{52}{1}*\frac{\pi}{180}[/tex]
[tex]\frac{52\pi}{180}[/tex]
[tex]\frac{13\pi}{45}[/tex]
Step 2: Find the arc length
[tex]S = r\theta[/tex]
[tex]S=(3)(\frac{13\pi}{45})[/tex]
[tex]S = \frac{39\pi}{45}[/tex]
[tex]S=\frac{13\pi}{15}[/tex]
Answer: Option B
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Answer:
D
Step-by-step explanation:
see attachment
V2 is equal to + 2 a s derive
HELP ASAP!
Point A is located at (1, 4), and D is located at (-3, 6). Find the coordinates of the point that lies halfway between A and D. (5 points)
(3, 4)
(-3, 4)
(1, 5)
(-1, 5)
Answer:
I believe the answer is (-1,5)
Step-by-step explanation: because when you draw it out on a coordinate plain (-1,5) lies right in the middle of these two points.
what is the solution of this equqtion? 1w= -17
Answer:
-17
Step-by-step explanation:
1w= -17
(1)(-17)=
-17
Answer:
-17
Step-by-step explanation:
in this situations, we normally divide both sides by the number next to the unknown.
1w is the same as saying w
so,
w = -17
