P(A n B) = P(A|B) * P(B) = (2/3) * (3/4) = 1/2
Therefore, there is a 50% probability that both occurrences A and B will happen. P(A and B)=1/2
What do probability and an example mean?The possibility that something will occur is called the probability. the total number of conceivable outcomes. Because there is only one way to receive a head and there are a total of two possible outcomes, the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). We state P(heads) = 12.
What is the fundamental definition of probability?A probability is a number that expresses the likelihood or chance that a specific event will take place. Probabilities can be stated as percentages ranging from 0% to 100% or as proportions from 0 to 1.
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Write an equation of the line that passes through (-4,-1) and is perpendicular to the line y=x+6
Answer:
y = -x + 5
Step-by-step explanation:
To find the equation of the line that is perpendicular to the line y = x + 6 and passes through the point (-4, -1), we'll use the slope-point form of the equation of a line. The slope of a line perpendicular to y = x + 6 is -1, which we can find using the negative reciprocal of the slope of y = x + 6. The slope of y = x + 6 is 1. The negative reciprocal of 1 is -1.
So the equation of the line perpendicular to y = x + 6 that passes through the point (-4, -1) is given by:
y - (-1) = -1(x - (-4))
Expanding and simplifying the right-hand side, we get:
y + 1 = -x + 4
y = -x + 5
an airline serves a dinner to all the passengers on an airplane. they get their choice of steak or fish. three steak meals and three fish meals are set aside for the six-member crew. if the meals are distributed to the crew members randomly, what is the probability that both pilots get the fish?
I think the answer is
1/5 or 20%
Sorry if I'm wrong
Divide the following fractions!
Answer: a - a / (7a/3 - 21b)
Step-by-step explanation:
First, let's simplify the numerator:
(a^2 - 3ab) / 3b = a^2/3b - 3ab/3b = a^2/3b - a
Next, we'll simplify the denominator:
7a - 21b = 7a/3 - 7b
Now, we can simplify the entire expression:
(a^2/3b - a) / (7a/3 - 7b) = (3b * a^2/3b - 3b * a) / (7a - 21b * 3) = a - a / (7a/3 - 21b)
OATB is a parallelogram. M, N and P are midpoints of BT, AT and MN respectively.
O is the origin and the position vectors of A and B are a and b respectively. Find in
terms of a and/or b:
a) MT
b) TN
C) MN
D) the position vector of P, giving your answer in simplest form.
A parallelogram with vertices O, A, B, and C can be represented as O + a = B, and O + b = A.
What are the responses to other questions?a) MT is the midpoint of BT, which can be represented as (O + b + B)/2 = (O + B)/2 + (b/2). Therefore, MT = (b/2).
b) TN is the midpoint of AT, which can be represented as (O + A)/2 + (a/2). Therefore, TN = (a/2).
c) MN can be represented as B - A = a - b. Therefore, MN = a - b.
d) P is the midpoint of MN, which we already found to be a - b. Therefore, the position vector of P is (a - b)/2.
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You are deciding what carb you want to eat for dinner, and you decide to look at the ratio of cooking times between rice to pasta. Rice takes 20 minutes to cook, and pasta takes 12. What is the ratio of cooking times for the rice to pasta?
(Make sure your ratio is simplified for your final answer)
5 : 3 is the ratio of cooking times for the rice to pasta .
What does a math ratio mean?
When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. A percentage is an equation in which two ratios are made equal to one another.
You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
Rice takes 20 minutes to cook
pasta takes 12
the ratio of cooking times for the rice to pasta = 20 : 12
= 5 : 3
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If F(X)=11x-7, express in terms of P find F(p)
Answer:
Step-by-step explanation:
99.5 x 54 add 10
Answer the attached imagine. Please and thank you.
The solution of the given equation is -4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equations is 3|5 - x| + 2 = 29
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
3|5 - x| =27
5-x=9
x=-4
Therefore, the solution of an equation is -4.
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"Your question is incomplete, probably the complete question/missing part is:"
Find the solution set for the equation below.
3|5 - x| + 2 = 29
there are 8 sprinters in the olympic 100-meter finals. three of the sprinters are americans. the gold medal goes to first place, silver to second, and bronze to third. in how many ways can the medals be awarded if at most one american gets a medal?
The total number of ways medals be awarded when at most one American gets a medal is equal to 40 ways.
Total number of sprinters in the Olympic of 100-meter finals = 8
Total number of sprinters Americans has in Olympic = 3
Number of sprinters of other country = 8 - 3
= 5
Number of medals be awarded = 3
Condition for medals to be awarded :
Possibility for American to get medals at most one:
Either 0 or 1.
Number of ways medals be awarded
= ⁵C₂³C₁ + ⁵C₃³C₀
= (5!/ 3!2!)(3!/2!1!) + ( 5!/ 3!2!)( 3! / 3!0!)
= (10 × 3) + ( 10 × 1 )
= 30 + 10
= 40 ways
Therefore, the number of ways medals be awarded with the given condition is equal to 40.
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What does 5² × 1201 equal to
Answer:
30025
Step-by-step explanation:
5² × 1201
5^2 = 25
25 x 1201 = 30025
Which statement describes the end behavior of a given function? g(x)=x^2 + 5x/3x
Answer:
as x approaches - infinity g(x) approaches - infinity and as x approaches infinity g(x) approaches infinity
Step-by-step explanation:
so the third answer
Find the slope of 5,-7 and 6,-4
The slope from points (5, -7) and (6, -4) is 3.
The slope of a line:The slope of a line represents the stiffness or direction of a line. It is also defined as the change in the y-coordinate with respect to the x-coordinate.
The slope of a line from the points (x₁, y₁) and (x₂, y₂) is given by
Slope of a line (m) = [y₂ - y₁]/[x₂ - x₁]Here we have
Points (5, -7) and (6, -4)
As we slope of the line is [y₂ - y₁]/[x₂ - x₁]
Take (5, -7) = (x₁, y₁) and (6, -4) = (x₂, y₂)
Slope from given points = [-4 - (-7) ]/[6 - 5]
= [-4 + 7) ]/[1] = 3
Therefore,
The slope from points (5, -7) and (6, -4) is 3.
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Eddie made a video. The video included 5-minute introduction followed by short segments. Each segment was 8 minutes long. Eddie's video was 149 minutes long. How many segments were in Eddie's video?
WILL GIVE BRAINLIEST!
Data plans from phone company A costs $50.00 for 10G. Company B charges $65.00 for 12 G. Which is the better rate? PLEASE Show your work!!!!
To find out how much each G costs for each company, we can use this equation:
Total price ÷ Number of G's = Each G's priceFitting the company's number into the equation would look like this:
Company A: 50 ÷ 10 = 5So, company A charges $5 for each G purchased.
Company B: 65 ÷ 12 = 5.42 (Rounded to the nearest hundredth)Company B charges $5.42 for each G purchased.Therefore, company A charges $5 for each G, while company B charges $5.42, making company A have a better rate.
Find the angle, correct to two decimal places, that the lines joining the given points
make with the positive direction of the x-axis:
a (−4, −2), (6, 8)
b (2, 6), (−2, 4)
c (−3, 4), (6, 1)
d (−4, −3), (2, 4)
e (3b, a), (3a, b)
f (c, b), (b, c)
Answer: look at the image, and u better give me brainliest for this
Step-by-step explanation:
Write an indirect proof for the following statement:
A triangle can have at most 1 obtuse angle.
We can prove that the statement is false by contradiction, as if a triangle had two obtuse angles, the sum of the measures of the internal angles of the triangle would be greater than 180º.
What is proof by contradiction?To prove an statement by contradiction, we must simply take an statement that either accepts the statement (true) or rejects (false).
An angle is classified as obtuse if it has a measure that is greater than 90º.
The sum of the measures of the internal angles of a triangle is of 180º, hence if the triangle had two obtuse angles, then the sum of the measures of the internal angles of the triangle would be greater than 180º.
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Amit drives a car daily to his office from his home. The distance is 24 km. On a particular day, he left
his home at 8:15 AM, drove for 5 km at a speed of 60 kmph. After that he was stuck in a traffic jam of 1
km during this stretch he could drive only at a speed of 15 kmph.
(Figure shown above is upto scale) Which of these is the closest to the MINIMUM speed at which he
should drive after the traffic jam to ensure that he reaches the office by 8:45 AM?
(Assuming that he can drive the way he wants to, without any traffic jams.
According to the information, it can be inferred that Amit has to drive at a speed of at least 60 km/h to get to work on time.
How to calculate the speed that Amit must have after the traffic jam to get to work on time?To calculate the speed that Amit must have after the traffic jam to arrive at work on time we must perform the following mathematical operation:
speed = 60 * 5 / 18 m/s = 50 / 3 m/s
distance = 5000m
time = 300 seconds = 5 minutes
According to the above he traveled 5 km distance in 5 minutes. On the other hand to calculate the speed that the rest of the journey must have we must:
speed = 15 * 5 /18 = 25/6 m/s
distance = 1000m
time = 240 seconds = 4 minutes
Distance left = (24km -6km = 18km= 18000m
Time left = 21 minutes = 1260 seconds
Speed = 14.28m/s
Speed = 14.28 × 18/5 kmph
Speed = 51.42 kmph
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Find the inverse of the equation
The inverse of the equation is f-1(x) = 2/(x - 3)
How to determine the inverse of the equationFrom the question, we have the following parameters that can be used in our computation:
f(x) = (3x + 2)/x
Express as
y = (3x + 2)/x
Swap x and y
This gives
x = (3y + 2)/y
So, we have
xy = 3y + 2
This gives
y(x - 3) = 2
Make y the subject
y = 2/(x - 3)
Hence, the inverse is f-1(x) = 2/(x - 3)
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A tennis-playing golfer has $15 to
spend on golf balls x, costing $ 1 each
and tennis balls y, costing 60 cents
each. He must buy at least 16
altogether and he must buy more golf
balls then tennis balls.
a) What is the greatest number of
balls he can buy?
b) After using them, he can sell golf
balls for 10 cents and tennis balls for
20 cents each. What is his maximum
possible income from sales?
(This questions is about inequalities and linear programming)
Maximum possible income from sales is $2.6
What do you understand by Linear Programming?Linear Programming also called linear optimization, is a method to achieve the best outcome(such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear Programming is a special case of mathematical programming (also known as mathematical optimization).
Linear Programming is used in many industries such as energy, telecommunication, transportation and manufacturing.
This linear function or objective function consists of linear equality and inequality constraints.
Given:
$15 to spend on golf balls x costing $1 each and
tennis balls y, 60 cents each.
Buy at least 16 together.
x + y ≥ 16
x + 0.6 ≤ 15
x - y ≥ 1
x = 9 and y = 7
[tex]9 + 0.6 \times 7[/tex]
9 + 4.2
13.2 < 15
x = 10 and y = 8
10 + 0.6 × 8
10 + 4.8
14.8 < 15
Maximum number of golf balls x = 10
And tennis balls y = 8
Greatest number of balls he can buy = 10 + 8 = 18
Maximum possible income = 10×0.1 + 8 × 0.2 = 1 + 1.6 = $2.6
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A local Best Buy sells 8 times as many iPads as target. The difference between their sales is 490 iPads how many did each sell?
Answer:
Step-by-step explanation:
Let's assume the number of iPads sold by Target as "x".
Then, the number of iPads sold by Best Buy would be 8 times this value, which is 8x.
We are given that the difference in their sales is 490 iPads. So we can set up an equation:
8x - x = 490
Simplifying and solving for x:
7x = 490
x = 70
Therefore, Target sold 70 iPads, and Best Buy sold 8 times as many, or 560 iPads.
Two cars, an Audi and a Tesla, travel a 100 mile journey.
Which car is fastest and by how much?
Write Audi or Tesla in the first box and state your answers in mph in the second box
100-
80
60-
40
20
100
Distance from starting point tri
80-
60-
40
20-
N+
Audi
2
2
Distance from starting point (miles)
Time (hours)
Tesla
2.
Time (hours)
Two cars, an Audi and a Tesla, travel a 100 mile journey. The fastest car is Audi by 30mph.
What is distance?While distance and displacement appear to have the same meaning, they actually have very different definitions and implications. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "how much ground an object has covered during its motion."
The formula of the speed is given as:
Speed = distance / time
For Audi:
Speed = 100 / 2 = 50 mph
For Tesla:
Speed = 100 / 5 = 20mph
The difference between their speeds is:
50 - 20 = 30mph
Hence, the fastest car is Audi by 30mph.
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you set up a colorful candy bag for your friend with 4 cherry, 8 orange, 2 lemon, 8 grape, and 6 sour raspberry, hard candies. when they pull out two of them, one for each of you, what is the probability they draw 1 cherry and 1 sour raspberry in either order?
Answer:
Step-by-step explanation:
The total number of candies in the bag is 4 cherry + 8 orange + 2 lemon + 8 grape + 6 sour raspberry = 28 candies.
The probability of drawing a cherry on the first draw is 4/28, and the probability of drawing a sour raspberry on the second draw given that a cherry was drawn first is 6/27 (since there are 27 candies left in the bag after the first draw).
The probability of drawing a sour raspberry on the first draw is 6/28, and the probability of drawing a cherry on the second draw given that a sour raspberry was drawn first is 4/27.
Therefore, the probability of drawing one cherry and one sour raspberry in either order is:
(4/28) * (6/27) + (6/28) * (4/27) = 24/756 + 24/756 = 48/756
So the probability of drawing one cherry and one sour raspberry in either order is 48/756.
Eight bands are to perform at a weekend festival. How many different ways are there to schedule their appearances?
By using the permutation formula, it can be concluded that there are 40320 ways to schedule the bands' appearances.
Permutations are different arrangements of elements formed from n elements, taken from n or some elements. In permutation, arrangement, or order matter.
P(n,r) = n! / (n-r)! where:
n = number of objects
r = number of objects selected
If we want to know the ways to schedule the bands' appearances, it means that the arrangement matter. Thus we have to use the permutation formula:
P(n,r) = n! / (n-r)!
P(8,8) = 8! / (8 - 8)!
= 8!
= 40320 ways
Thus, there are 40320 ways to schedule the bands' appearances.
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write the following as an algebraic equation . Use x as the unknown and use a sum.
Sum of a number and its equivalent to 115.6
The value of unknown number is 57.8.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the unknown number.
Sum of a number and its equivalent to 115.6
The equivalent number value will be also same as the unknown number.
x+x=115.6
2x=115.6
Divide both sides by 2
x=115.6/2
x=57.8
Hence, the value of unknown number is 57.8.
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WILL GIVE brainliest
The value of the equation is A = ( 50.4 )x - ( 35.2 )y - 3
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 8 ( 6.3x - 4.4y ) - 3 be equation (1)
On simplifying the equation , we get
By distributive property ,
A = 8 ( 6.3x ) - 8 ( 4.4y ) - 3
On further simplification , we get
A = ( 50.4 )x - ( 35.2 )y - 3
Hence , the equation is A = ( 50.4 )x - ( 35.2 )y - 3
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suppose that 17 boys and 22 girls are randomly lined up. what is the probability that the 27th person is a boy?
Using probability we know that there is a 43% chance that the 27th person in the line would be a boy.
What is probability?Probability is simply the possibility that something will happen. When we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several.
The study of events that fit into a probability distribution is known as statistics.
So, we know that:
The boys are 17.
The girls are 22.
Probability formula: P(E) = Favourable events/Total events
Then, the probability that the 27th person is a boy:
P(E) = Favourable events/Total events
P(E) = 17/39
P(E) = 0.43
P(E) = 43%
Therefore, using probability we know that there is a 43% chance that the 27th person in the line would be a boy.
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Which fraction of the whole circle is this sector?
The fraction of the whole circle denoting the sector is 23/72.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
The whole circle has an angle of = 360°.
The measure of the sector of the angle is = 115°.
The fractional value of the sector is -
Measure of Sector angle / Measure of whole circle angle
Substitute the value into the expression -
115/360
23/72
Therefore, the fraction is 23/72.
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25 POINTS PLEASE HELP ! Are the expressions [tex]-3^{2}[/tex] and [tex](-3)^{2}[/tex] equivalent? explain
The value of the expressions are not equal
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
p = -3²
q = ( -3 )²
On simplifying the equations , we get
The value of p = -9
The value of q = 9
So , the value of p and q are not equal
Hence , the equations are not equal
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Consider DEF in the figure below.
The perpendicular bisectors of its sides are XW, YW, and ZW. They meet at a single point W.
(In other words, W is the circumcenter of ADEF.)
Suppose YW=24, DZ=66, and FW=74.
Find EY, DW, and DE.
Note that the figure is not drawn to scale.
On solving the provided question, we can say that in the provide quadrilateral DE = 132, DW = 74, EY = 70.
Describe the quadrilateral.In terms of geometry, a quadrilateral is a four-sided polygon with four edges and four corners. Its origins are in the Latin terms quadri and latus (meaning "side"). A rectangle is a two-dimensional form with four sides, four vertices, and four corners.
Two main types of concave and convex exist. Convex quadrilaterals also have a number of subclasses, such as trapezoids, parallelograms, rectangles, rhombuses, and squares. A rectangle is a two dimensional shape with four straight sides. Quadrilaterals come in many various shapes, such as parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
here,in the provide quadrilateral
The perpendicular bisectors of Its sides are X W, Y W, and Z W. They meet at a single point W.
from the question. So EW = DW = FW
and DZ=EZ
SO DE = 2 (DZ) = 2 × 66 = 132
EW = FW = DW = 74.
at At right triangle, EWY.
EW= 74, YW=24
Using Pythagoras theorem,
So EX² = EW²- WY² = 74² - 24² = 4900
EY = √4900 = 70.
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Zara can exchange dollars ($) for pounds (£) at the rate $1 = £0.64. She can exchange dollars ($) for euros (€) at the rate $1 = €0.78. Complete the statement to show the exchange rate between pounds and euros. Exchange rate £1 = €............
Answer:
£1 = €1.21875
Step-by-step explanation:
We have the following exchange rates
$1 = £0.64
and
$1 = €0.78
Equating the two values on the right side since they both convert to $1 gives us
£0.64 = €0.78
Divide both sides by 0.64 to see how much a pound is worth when converted to euros
0.64/0.64 = 0.78/0.64
£1 = €1.21875
Use a sketch to find the exact value of the following expression.
sec[sin^-1(-4/7)]=
The exact value of the expression is 7√33/33
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given expression is sec[sin⁻¹(-4/7)]
We need to fine the exact value of the expression
sec[sin⁻¹(-4/7)]=√1-(-4/7)²/1-(-4/7)²
=√(1-16/49)/1-16/49
=√(1-16/49)/1-16/49
=√33/7/33/49
=√33/7×49/33
=7√33/33
Hence, the exact value of the expression is 7√33/33
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