Answer:
Yes, because the P(A)P(B) = P(A and B)
Step-by-step explanation:
Independent Events are events that occurs simultaneously i.e they occur at the same time. This means that the occurrence of one does not affect the other. If A and B are two events, for the to be independent then;
P(A and) = P(A)P(B)
Given: P(A) = watching a movie = 62% = 0.62
P(B) = going out to dinner = 46% = 0.46
The probability of watching a movie and going out to dinner will be
P(A and B)
P(A and B) = 0.62×0.46
P(A and B) = 0.2852
P(A and B) = 28.52%
Since the probability of watching a movie and going out to dinner is 28.52% which tallies with the question, hence it can be concluded that watching a movie and going out to dinner are independent events.
daniel thinks of a number and subtracts 2
from it. He divides 32 by the result. If
his answer is 4, what number does he
think of
Answer:
the number is 126
Step-by-step explanation:
1) multiply each side by 32: (n-2) / 32 = 4
2) subtract 2 from each side: n-2 = 128
3) n = 126
Answer:
130
Step-by-step explanation:
So basically this number, minus 2, divided by 32 is 4, so lets write the unknown number as x.
So, (x-2)/32 = 4.
First multiply both sides by 32 to get rid of the denominator.
(32)(x-2)/32 = 4(32) x-2 = 128
Now the -2 remains to figure out x, so you add 2 to both sides to get rid of the -2.
So, x-2+2 = 128+2, -2 +2 is 0, and 128 +2 is 130, so you have x = 130.
the first four terms of the sequence an=2n+3are
answer
5,8,11,14
3,5,7,9
1,3,5,7
5,7,9,11
Step-by-step explanation:
Hey, there!!!
Your required answer is optionD.
checking,
The 1st sequences are,
5,8,11,14
here,
now, use formula,
(an = 2n+3) in the sequences,
a1 = 2×1+3=5 = matching
a2= 2×2+3=7 = not matched
a3= 2×3+3= 9 = not matched
a4= 2×4+3=11 = not matched.
For 2nd sequences
3,5,7,9
Use the formula of an term,
a1 = 2×1+3=5 = not matched
a2 =2×2+3=7not matched
a3 = 2×3+3=9= not matched.
For 3rd sequences,
1,3,5,7
a1=2×1+3=5= not matched
a2=2×2+3=7= not matched
a3=2×3+3=9= not matched
a4=2×4+3=11= not matched
Now, for 4th sequences,
5,79,11
a1=2×1+3=5= matching
a2=2×2+3=7= matching
a3= 2×3+3=9= matching
a4=2×4+4=11= matching
Therefore, the answer is option D.
Hope it helps..
1.Solve by factorization method: x+1/x=11 1/11 2.Comment on the nature of roots for 4x^2-5=2(〖x+1)〗^2-7 plz, help...
Answer:
The equation
[tex]4\,x^2-5=2\,(x+1)^2-7[/tex]
can be solved by first expanding all indicated operations, and later when the constant terms disappear, by factoring out 2x , leaving the equation as a product of two factors equal zero, from which it is easy to extract the roots. See below.
Step-by-step explanation:
When solving for x in the following expression, and using factoring to apply at the end the zero product theorem:
[tex]4\,x^2-5=2\,(x+1)^2-7\\4\,x^2-5=2\,(x^2+2x+1)-7\\4\,x^2-5=2\,x^2+4\,x+2-7\\4\,x^2-5=2\.x^2+4\,x-5\\4\,x^2=2\,x^2+4\,x\\4\,x^2-2\,x^2-4\,x=0\\2\,x^2-4\,x=0\\2\,x\,(x-2)=0[/tex]
We observe that for the last product, to get a zero, x has to be zero (making the first factor zero), or x has to be "2" making the binomial factor zero.
Nathan, a tutor, buys 5 calculators for $7.50 each at a store, planning to provide one to each of his clients. However, the next day, he discovers that the same calculators has gone on sale for $5.00 and also discovers that he will only have three tutoring clients instead of five. He returns the five calculators and purchases three calculators at the new sale price. He uses the following expression to determine the amount he should receive back from the store. (5 x $7.50) - (3 x $5.00) Which of the following expressions could Nathan have used. 5 ($7.50 - $5.00). $7.50 - $5.00. (5 x $7.50) - $5.00. (5 x $7.50) - $5.00. 3 ($7.50 - $5.00) +2 x $7.50
Answer: 5 (7.50-3 )
Step-by-step explanation:
Given: Previous price of calculator = $7.50
Number of client =5
Total price = (Number of calculators) x (Price for each calculator)
Total price of 5 calculators = (5 x $7.50)
New price of calculator = $5.00
Number of client =3
Total price of 3 calculators = (3 x $5)
Price will receive = (Total price of 5 calculators) -(Total price of 3 calculators )
= (5 x $7.50) - (3 x $5)
= 5 (7.50-3 )
Required expression: 5 (7.50-3 )
Hong buys candy that costs $5 per pound. He will buy at least 7 lbs of candy. What are the possible amounts he will spend on candy? Use c for the amount (in dollars) Hong will spend on candy. Write your answer as an inequality solved for c.
Step-by-step explanation:
if he buys 7 pounds, it will cost 7×5 = $35
he might buy more than that (and it will then also cost more than that) , but not less than that.
so,
c >= $35
Find the length of the third side. If necessary, round to the nearest tenth.
20
28
Answer:
Submit Answer
attempt 1 out of 2
PLS HELP ASAP
Answer:
b = 19.6
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
20^2+ b^2 = 28^2
400 + b^2 = 784
b^2 = 784-400
b^2 =384
Taking the square root of each side
sqrt( b^2) = sqrt(384)
b =19.59591794
To the nearest tenth
b = 19.6
Answer:
19.6
Step-by-step explanation:
It is a right triangle so use the pythagorean theorem; a^2 + b^2 = c^2
a=20
b=?
c=28 - c is the hypotenuse because it is across from the right angle
20^2 + b^2 = 28^2
400+ b^2 =784
b^2=384
b= 19.595917... or 19.6 (rounded to nearest tenth)
MATH QUESTION : As punishment for bad behavior during recess, Mrs. Busywork asked her class to multiply 10 by 1/3 five times. John, however, notices that it is possible to multiply 10 by a single fraction and still get the same answer as the other students. What is this single fraction?
Answer:
5/3
Step-by-step explanation:
5×(10×1/3)
=10×5/3
=since 5×(10×1/3) gives 50/3 so thus 10×5/3.
The fraction is therefore 5/3
1. Dada a função exponencial abaixo, se x=1, qual valor de imagem? * a) 1 b) -2 c) 0 d) -1
Complete question:
Dada a função exponencial abaixo, se x=1, qual valor de imagem? * a) 1 b) -2 c) 0 d) -1
The function in the image is f(x) = 3^x-1
Answer:
A) 1
Step-by-step explanation:
To solve the exponential function above given that x = 1;
Substitute x = 1 into the exponential function
If x = 1
f(x) = 3^(x - 1)
f(1) = 3^(1 - 1)
f(1) = 3^0
f(1) = 1
For the polynomial, (((x^3)+3x+2)/5)+((5x^2)/2)-(x^6)
a. Determine the coefficient of x^3.
b. Determine the coefficient of x^6.
c. Determine the constant of the term
polynomial.
d. Determine the degree of the polynomial.
Answer:
Hello,
Step-by-step explanation:
[tex](((x^3)+3x+2)/5)+((5x^2)/2)-(x^6)\\\\=\dfrac{x^3}{5} +\dfrac{3*x}{5} +\dfrac{2}{5} +\dfrac{5*x^2}{2} -x^6\\\\\\=-x^6+0x^5+0x^4+\dfrac{x^3}{5} +\dfrac{5*x^2}{2} +\dfrac{3*x}{5}+\dfrac{2}{5} \\\\\\a)\ \dfrac{3}{5} \\\\b)\ -1\\\\c)\\degree=6\\[/tex]
Is this a function or no?
Function
It is a function
If sin 115° ≈ 0.91 and cos 115° = -0.42, then sin -115° =
Answer:
sin -115° = -0.91
Step-by-step explanation:
Point A is (cos 115°, sin 115°). Since cos 115° = -0.42 and sin 115° ≈ 0.91, it means that the coordinates at point A is (-0.42, 0.91).
As for point B which was revolved around -115°,
the coordinates will be similar to point A but you just have to change the negative.
B(cos -115°, sin -115°) = B(0.42, -0.91)
Answer:
PLATO ANSWER
-0.91; -0.42
Step-by-step explanation:
The sine function is an odd function, meaning that sin -x = -sin x. Because sin 115° ≈ 0.91, sin -115° ≈ -0.91.
The cosine function is an even function, meaning that cos -x = cos x. Because cos 115° = -0.42, cos -115° = -0.42.
if line y bisects line AC, AB = 4 - 5x, and BC = 2x+25, find AC
Answer:
4-5x = 2x+25
-5x+4 = 2x+25
-7x = 21
x = -3
4 - 5(-3)
4 + 15
19
AC = 2 x 19
AC = 38
Let me know if this helps!
need help right now please
its 4
x=4
[tex]4^{2}[/tex]-2x4
16-8
=8
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your equation step-by-step.
[tex]x^2 - 2x = 8[/tex]
Step 1: Subtract 8 from both sides.
[tex]x^2 - 2x - 8 = 8 - 8\\x^2 - 2x - 8 = 0[/tex]
Step 2: Factor left side of equation.
[tex]( x+2) ( x - 4) = 0[/tex]
Step 3: Set factors equal to 0.
[tex]x + 2 = 0[/tex] or [tex]x - 4 = 0[/tex]
[tex]x = -2[/tex] or [tex]x = 4[/tex]
Answer : -2 , 4
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
A car is averaging 50 miles per hour. If the car maintains this speed, how many minutes less would a 450-mile trip take than a 475-mile trip?
Answer:
1/2 a minute (30 seconds)
Step-by-step explanation:
475/50=9.5
450/50=9
9-9.5=.5
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
Mrs. barker works 40 hours per week regularly, at a rate of $36.80 per hour. when she works overtime, her rate is time and a half of her regular hourly rate. what is Mrs. Barker hourly overtime rate
Answer:
$55.20 is Mrs. Barker hourly overtime rate.
Step-by-step explanation:
The term "time and a half" in your question means that Mrs. Baker's overtime rate is 1.5 times her usual hourly rate.
So, ----> $36.80 times 1.5 = $55.20
jack wants to run at least 275 miles before the baseball season begins. he has already run 25 miles. he plans to run 2.5 miles each day. at this rate what is the fewest number of days he will need to reach his goal
Hey there! I'm happy to help!
We see that Jack has already run 25 miles.
25
He also wants to run 2.5 miles every day. This means we will multiply 2.5 miles by the number of days he runs. We will call the number of days x.
25+2.5x
And he needs this to equal 275.
25+2.5=275
We subtract 25 from both sides.
2.5x=250
We divide both sides by 2.5
x=100
So, Jack will need to run 100 days to meet his goal.
Have a wonderful day and keep on learning! :D
17. ralph is 3 times as old as sarah. in 4 years ralph will only be twice as old as sara will be then. find ralph’s age now.
Answer:
Sara is now 4, will be 8 in 4 years. Ralph is now 12, will be 16 in 4 years.
Help please, thanks :)
Answer:
х=6
Step-by-step explanation:
[tex]7 + 5(x -3 ) = 22 \\ 7 + 5x - 15 = 22 \\ 5x = 22 - 7 + 15 \\ 5x = 30 \\ x = 6[/tex]
Answer:
C
x=6
Step-by-step explanation:
PLEASE HELP!! what is the equation of a line that is perpendicular to y = 2x + 4 and passes through the point (4, 6)?
Answer:
The answer is B)
[tex]y = - \frac{1}{2}x + 8[/tex]
Answer:
B. y = -[tex]\frac{1}{2}[/tex]x + 8
Step-by-step explanation:
The line is perpendicular to line whose equation is:
y = 2x + 4 and;
passes through point (4,6) .
The product slopes of two perpendicular lines is -1.
The slope of the line whose equation is y = 2x + 4 is; 2
Let the slope of the perpendicular line (l2) be [tex]m_{l2}[/tex]
[tex]m_{l2} * 2 = -1[/tex]
[tex]m_{l2}[/tex] = [tex]-\frac{1}{2}[/tex]
Taking another point xy on line l2;
[tex]\frac{y - 6}{x - 4} = -\frac{1}{2}[/tex]
Cross multiplying this gives;
y = -[tex]\frac{1}{2}[/tex]x + 8 which is the equation of the perpendicular line!
Suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. Give the formula for calculating the size of that population after t years.
Answer:
y = 100(3)^t
Step-by-step explanation:
Use the formula y = P(1 + r)^t where y is the new amount, P is the starting amount, r is the rate as a decimal, and t is the time.
Plug in the values given:
y = 100(1 + 2)^t
y = 100(3)^t
Answer:
Step-by-step explanation:
y = 100(3)^t
A sequence of transformations is described below. A reflection over a line \overleftrightarrow{PQ} PQ P, Q, with, \overleftrightarrow, on top A rotation about the point PPP Another reflection over \overleftrightarrow{PQ} PQ P, Q, with, \overleftrightarrow, on top A rotation about the point QQQ Which of the following must be preserved under this sequence of transformations? Choose 1 answer: Choose 1 answer: (Choice A) A Angle measures only (Choice B) B Segment lengths only (Choice C) C Both angle measures and segment lengths (Choice D) D Neither angle measures nor segment lengths
Answer:
The correct option is;
(Choice C) Both angle measures and segment lengths
Step-by-step explanation:
The given transformations are;
The reflection over the line, [tex]\overleftrightarrow{PQ}[/tex], with, A rotation about the point P. Another reflection over [tex]\overleftrightarrow{PQ}[/tex]. A rotation about the point Q, we have;
The transformations involve changes only in the orientation and location of the pre-image, which remain rigid, therefore, there are no changes in the segment lengths or angle dimensions
Therefore, the correct option is, both angle measures and segment lengths.
(Choice C) C Both angle measures and segment lengths
Every year the Lee family has a big family dinner, and everyone brings a mug to exchange. The mugs are put on wooden hangers on the wall, and each wooden hanger can hold 12 mugs. Last year the family had 15 mugs to hang up. This year the Lee family filled three wooden hangers. How many more mugs were brought to the Lee family dinner this year compared to the previous year? *
Answer:
21 more mugs were brought this year than last year.
Step-by-step explanation:
We can solve by subtracting the initial amount of mugs from the final amount of mugs.
To find the amount of mugs hung up this year, we will use the equation: m = 12w where m = the number of mugs & w = the number of wooden hangers. The 12 represents the amount of mugs per wooden hanger.
We can plug in 3 for w since 3 wooden hangers were filled up and we would get 12(3) = m = 36 mugs
Now we subtract last year's total mugs hung up from this year's total mugs hung up.
We end up with 36 - 15 = 21
Write the parametric equation of the line: 10x - 4y = 20
The parametric equation of the line10x - y = 20 is given as y = 2.5t - 5
Parametric equation
parametric equation are equations where the dependent variable is expressed in terms of independent variable
say dependent variable y = f(t)
independent variable x = t
Given data
10x - 4y = 20
solution
10x - 4y = 20
10x - 20 = 4y
4y = 10x - 5
y = 2.5x - 5
where x = t
y = 2.5t - 5
Read more on parametric equations here: https://brainly.com/question/12953407
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Given the range (1, 1),(4,2), (2, -1), with a coordinate transformation of f(x, y) = (x+1, y-1), what is the
domain?
=============================================
Explanation:
The rule f(x,y) = (x+1,y-1) says to add 1 to the x coordinate and subtract 1 from the y coordinate. So let's say the input point is (7,2). This would move it to (8,1).
Now let's say that you accidentally erased the "(7,2)", but you still have the "(8,1)". You'd have to work through the steps backwards to get back to (7,2)
So you'll effectively use this rule g(x,y) = (x-1, y+1) which is the inverse transformation. Whatever f(x,y) does, the g(x,y) function will undo it and go opposite. We'll subtract 1 from the x coordinate and add 1 to the y coordinate.
------------
So that's what we'll do with the set of points { (1,1), (4,2), (2,-1) }
We have (1,1) become (0,2) after applying the g(x,y) rule
(4,2) becomes (3,3) after using g(x,y)
(2,-1) becomes (1,0) after using g(x,y)
Therefore, the domain is { (0,2), (3,3), (1,0) }
-------------
The mapping diagram is shown below.
Line segment AB has a length of 5 units. It is translated 3 units to the right on a coordinate plane to obtain line segment A'B' . What is the length of A'B' ? (50 points)
2 units
3 units
4 units
5 units
Answer:
5 units is the correct answer
Step-by-Step Explanation:
the translation of ab is a rigid transformation so, the size of the preimage and the size of the image are equal therefore,
ab=a'b'
the length of a'b' is 5 units which is option d.
Twice the difference between a number and 4 is twenty. Find the number.
А. 8
B. 9
C. 12
D. 14
Please help!!!
Answer:
D 14
Step-by-step explanation:
Let x be the number
2(x-4) = 20
Divide each side by 2
2/2(x-4) = 20/2
x-4 = 10
Add 4 to each side
x-4+4 = 10+4
x = 14
Answer:
The number is 14
Step-by-step explanation:
Let's call this unknown number of x:
2×(x – 4) = 20
2x – 8 = 20
2x = 20 + 8
2x = 28
x = 28/2
x = 14
Find the domain for the rational function f of x equals quantity x plus 1 end quantity divided by quantity x minus 2 end quantity.
(−[infinity], 2) (2, [infinity])
(−[infinity], −2) (−2, [infinity])
(−[infinity], 1) (1, [infinity])
(−[infinity], −1) (−1, [infinity])
Answer:
[tex](- \infty, 2), (2, \infty)[/tex]
Step-by-step explanation:
Given the function:
[tex]f(x) = \dfrac{x+1}{x-2}[/tex]
To find:
Domain of the function.
Solution:
First of all, let us learn about definition of domain of a function.
Domain of a function is the valid input values that can be provided to the function for which output is defined.
OR
Domain of a function [tex]f(x)[/tex] are the values of [tex]x[/tex] for which the output [tex]f(x)[/tex] is a valid value.
i.e. The function does not tend to [tex]\infty[/tex] or does not have [tex]\frac{0}0[/tex] form.
So, we will check for the values of [tex]x[/tex] for which [tex]f(x)[/tex] is not defined.
For value to tend to [tex]\infty[/tex], denominator will be 0.
[tex]x-2\neq 0 \\\Rightarrow x \neq 2[/tex]
So, the domain can not have x = 2
Any other value of x does not have any undefined value for the function [tex]f(x)[/tex].
Hence, the answer is:
[tex]\bold{(- \infty, 2), (2, \infty)}[/tex] [2 is not included in the domain].
What are the solutions to 3( x + 2)(x – 9) = 0
Mark Brainliest if correct:
x = -2, 9
Step-by-step explanation:
x2: x + 2 = 0
x = -2
x1: x - 9 = 0
x = 9
x = -2, 9
What is the range of the given function?
{(-2, 0), (-4, -3), (2, -9), (0,5), (-5, 7)}
O {x | x = -5, 4, -2, 0, 2}
{yly = -9, -3, 0, 5, 7}
{x | x = -9, -5, 4, -3, -2,0, 2, 5, 7}
{yl y = -9, -5, 4, -3, -2, 0, 2, 5, 7}
9514 1404 393
Answer:
(b) {yly = -9, -3, 0, 5, 7}
Step-by-step explanation:
The range is the set of y-values in the ordered pairs. It is usually convenient to list a set in alphanumeric order.
The second values of the ordered pairs are 0, -3, -9, 5, 7. So, the range is ...
y ∈ {-9, -3, 0, 5, 7} . . . . . matches the second choice