The cardinality of a set refers to the number of elements in the set. If the set X has cardinality 16 and the set Y has cardinality 24, then the number of elements in set X is 16 and the number of elements in set Y is 2.
If their intersection has cardinality 21, then the number of elements that both sets have in common is 21.To determine the number of elements contained in the union of X and Y, we need to subtract the number of elements in their intersection from the sum of the cardinalities of X and Y. That is,
|X U Y| = |X| + |Y| - |X ∩ Y| = 16 + 24 - 21 = 19
Therefore, the union of X and Y contains 19 elements.
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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
Mr. McBurney loves hisplants. She knows that 25 of the plants in the his greenhouse use 43 gallons of water. However this is not enough for ALL her plants. How much water is necessary to water all the plants in the house? Write an equation to represent the situation, and then find the answer. Explain VERY well.
The equation to represent the situation can be written as:
25 * 43 + (x - 25) * w = total amount of water needed
How to calculate this?Let's call the total number of plants in the greenhouse as "x". Then, the number of plants that use 43 gallons of water is 25, so the rest of the plants use (x - 25) gallons of water.
The equation to represent the situation can be written as:
25 * 43 + (x - 25) * w = total amount of water needed
where "w" is the amount of water used by each plant (not including the 25 plants that use 43 gallons).
To find the answer, we need to know the value of "w". Since we don't know "w", we can't solve for the total amount of water needed.
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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)
What does 5² × 1201 equal to
Answer:
30025
Step-by-step explanation:
5² × 1201
5^2 = 25
25 x 1201 = 30025
if michigan's motor vehicle death rate were proportional to indiana, what would have been the expected number of deaths in michigan? round your answer to the nearest whole number. do not include units with your answer.
The expected number of deaths in Michigan, rounded to the nearest whole number, is 300.
To find the expected number of deaths in Michigan if the motor vehicle death rate were proportional to Indiana, we need to know the population of both states and the actual number of deaths in Indiana. Let's assume that the population of Indiana is 100,000 and the number of deaths is 200.
Since the death rate is proportional, we can use the ratio of deaths to population to find the expected number of deaths in Michigan:
(number of deaths in Michigan) / (population of Michigan) = (number of deaths in Indiana) / (population of Indiana)
Let's assume that the population of Michigan is 150,000. We can then use the above equation to find the expected number of deaths in Michigan:
(number of deaths in Michigan) / 150,000 = 200 / 100,000
(number of deaths in Michigan) = 200 * (150,000 / 100,000) = 300
The expected number of deaths in Michigan, rounded to the nearest whole number, is 300.
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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.
What is the distance between the points?
The formula in finding the distance between two points is given below:
[tex] \boxed{\bold{\:\:d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \:\:}}[/tex]Now, you know the distance formula. So, let us try solving the given problem using the distance formula.
Problem: What is the distance between A(-3, 5) and B(8, 1)?
From inspection on the given problem:
[tex]\sf (x_1, y_1) = (-3, 5)[/tex][tex]\sf (x_2, y_2) = (8, 1)[/tex]Substitute the given values into the distance formula and solve for AB:
[tex]\sf AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex][tex]\sf AB = \sqrt{[8 - (-3)]^2 + (1 - 5)^2}[/tex][tex]\sf AB = \sqrt{(11)^2 + (-4)^2}[/tex][tex]\sf AB = \sqrt{121 + 16}[/tex][tex]\bold{AB = \sqrt{137} \approx 11.7 \: units}[/tex]Therefore, the distance between two points is 11.7 units.
[tex]\\[/tex]
Now, wasn't that easy? Try this sample problem:
Find the distance between P(1, 3) and Q(7, 11).From the sample problem above, you may solve it on your own to enhance your skill on calculating the distance.
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A bicycle store costs $2400 per month to operate. The store pays an average of $50 per bike. The average selling price of each bicycle is $80. How many bicycles must the store sell each month to break even?
2400+60n= store's operating costs
120n=store's profits
120n=2400+60n is the break-even point
60n=2400
n=40 bikes need to be sold monthly to break even.
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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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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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 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.
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
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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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!
how many ways are there to choose 2 items from a set of n items, such that at least one of the items is not the first item in the set?
The number of ways to choose 2 items from a set of n items is
[(n-1)(n-2)]/2.
Combinations:
Combinations represent the choice of items from a predetermined group of items. We're not trying to arrange anything here. We're going to pick them. We use the symbol ⁿCr to represent the number of distinct r-selections or combinations among a set of n objects.
The formula for combinations is given by
ⁿC₂ = n!/ r![n- r]!Here we have
Number of items = n
The number of items that need to be chosen = 2
By given combination formula,
Number of ways are there to choose 2 items from a set of n items
=> ⁿC₂ = n!/ 2![n- 2]!
= (n - 1) × (n - 2) × (n - 3) .... (n - (n-1))/ [ 2! (n -2 - 1) × (n - 2 - 2) ..... ]
= (n - 1) × (n - 2) × (n - 3) .... (n - (n-1))/ [ 2! (n -3) × (n -4) (n -5) ..... ]
= (n - 1)(n-2)/2 × 1
= [(n-1)(n-2)]/2
Therefore,
The number of ways to choose 2 items from a set of n items is
[(n-1)(n-2)]/2
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Express as a single fraction
Expression of given expression as simple fraction is ax/3y.
What is fraction ?Fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Given expression
(ax + ay)/xy² . x²y/(3x + 3y)
simplifying
(ax + ay)/y . x/(3x + 3y)
Factoring out common factors
a(x + y)/y . x/3(x + y)
Simplifying
= ax/3y
Hence, given expression as simple fraction is ax/3y.
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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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Can someone solve this problem (algebra) please! Thanks!
Answer:
Therefore, the height of the traingle is 7.5 cm.
Step-by-step explanation:
1 dm= 10 cm
3.3 dm=3.3×10
=33 cm
(x+4)+(2x-7)+x= (4x-3) cm
4x-3= 33
4x= 36
x=9
2x-7=2×9-7
=18-7
=11
x+4=9+4
=13 [longest side of triangle]
13-5.5=7.5 cm [height of triangle]
Log base 7(log base 2(3x-2))=1
The value of 'x' in the expression [tex]log_{7}(log_2(3x - 2) ) = 1[/tex] is, 1/3.
What is a logarithm?The logarithm is exponentiation's opposite function in mathematics.
This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 100 = 10², the logarithm of 100 in base 10 is 2, or log10 = 2.
Given, A logarithmic expression [tex]log_{7}(log_2(3x - 2) ) = 1[/tex].
[tex]log_7^{log_{7}(log_2(3x - 2) )} = log_71[/tex].
[tex]log_2(3x - 2) = log_71[/tex]. (7⁰ = 1)
[tex]log_2(3x - 2) = 0[/tex].
[tex]\frac{log_23x}{log_22} = 0[/tex].
[tex]log_23x = 0[/tex].
2⁰ = 3x.
1 = 3x.
x = 1/3.
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Cartoon Universe stock lost 12.5% of its value in one day's trading in the stock market. If the stock sold for $28 per share at the end of the day, what was its price at the start of the day?
The actual price of the share at the start of the day will be $224.
What is the percentage?
The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Cartoon Universe stock lost 12.5% of its value in one day's trading in the stock market. If the stock sold for $28 per share at the end of the day.
The actual price of the share will be calculated as:-
12.5% of x = 28
( 12.5 / 100 ) x = 28
x = ( 28 x 100 ) / 12.5
x = $224
Therefore, the share's actual price will be $224 at the start of the trading day.
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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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after the viewing, each student was asked to rate their craving for del taco on a scale of 0 to 10. how many treatments are there?
There probability are 11 treatments, as the scale ranges from 0 to 10.
There are 11 treatments in this experiment, as the scale of craving for Del Taco ranges from 0 to 10. Each student is asked to rate their craving on this scale and the responses are recorded as the treatments. 0 would represent no craving, while 10 would represent the highest level of craving. This experiment allows researchers to measure the level of craving for the food, and the results can then be used to inform decisions about marketing or product development. The treatments are discrete and specific, allowing for a clear comparison between the students. This type of experiment can also be used to measure the effects of different variables on craving levels.
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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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what is the area of the regular octagon shown below?
Answer:
2336
Step-by-step explanation:
2s^2(1+sqrt2)
s=22
968(1+sqrt2)= 2336.96
Store #1 sold packages of eggs 1 dozen (12) for $1.44 a package. Store #2 sold packages of eggs 3 dozen (36) for $4.68. Which has the better price? Show the comparing prices.
Store #1 has the better price amount , as the price per dozen eggs is $1.44, whereas Store #2 is $1.29 per dozen eggs.
Store #1:
Price per egg = $1.44 / 12 = $0.12
Store #2:
Price per egg = $4.68 / 36 = $0.13
Store #1 has the better price as it is cheaper per egg.
Price comparison:
Store #1: $0.12 per egg
Store #2: $0.13 per egg
Store #1 has the better price, as the price per dozen eggs is $1.44, whereas Store #2 is $1.29 per dozen eggs. To compare the prices, we need to calculate the cost per dozen eggs for each store. To do this, we divide the cost by the number of eggs. For Store #1, the cost per dozen eggs is $1.44 divided by 12, which is $0.12. For Store #2, the cost per dozen eggs is $4.68 divided by 36, which is $0.13. Therefore, Store #1 has the better price, as it is cheaper than Store #2. By comparing prices, we can find the best deal for our money. It is important to compare prices to get the best value for our money, as it can help us save money in the long run. Additionally, by comparing prices, we can make sure we are getting the highest quality product at the best price.
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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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On the coordinate plane, what is the distance between (3, -4) and (-3, -4)?
1. what legal description is required in a land survey for a plat plan? 2. what are metes and bounds? sketch an example. 3. what is the rectangular system and how is it used? 4. what is the difference between a plot plan, plat plan and survey plan? provide sketch examples.
1 ) The location of a specific piece of real estate may be determined with accuracy using a legal description of the property. This often employs a combination of alphabetical abbreviations and numbers to find the land and is based on current township grids.
The legal description is a completely unique identification for properties, unlike a property address. It must close, which means the lines describing the start and conclusion must finally come together, in order to be legitimate.
2 ) Metes are a segment of the property line that are established by calculating the separation between two places. It may also establish the orientation of the property plot.
The boundary of a property is referred to as its bounds. Bounds are frequently used to outline larger-scale features.
3 ) A surveying technique called the Public Land Survey System (PLSS) is used to divide real estate into specific plots. It is furthermore frequently called the Rectangular Survey System.
4) A site plan, also known as a plot plan, is a form of drawing used by architects, landscape architects, urban planners, and engineers to represent the current and desired conditions for a specific area, usually a parcel of land that is to be altered.
A land survey plan is a specific map of a piece of land that is made after carefully inspecting and measuring the area. It establishes and defines the positions of boundaries, buildings, physical features, and other important spatial elements.
A plat plan is a scaled-down cadastral map that depicts the divisions of a plot of land.
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Is that a right answer
na
it wants you to factor a 3, and you could get that comon x out of there but it only wants 3, out of that
it would go like this
divide that left side by 3
write it on the right side so it multiplies the 3 back in
3x^2 + 15x = 3(x^2 + 5x)
see how when you distribute that 3 into the right side, you get back the left side?
if you need more help just ask me bro
Hope this helps,
- Jeron :- )