Answer:
Step-by-step explanation:
o prove the first associative law of set theory, we need to show that for any sets A, B, and C:
A ∪ (B ∪ C) = (A ∪ B) ∪ C
To do this, we need to show that any element that is in the left-hand side of the equation is also in the right-hand side, and vice versa.
First, let's consider an arbitrary element x.
If x ∈ A ∪ (B ∪ C), then x must be in A, or in B, or in C (or in two or more of these sets).
If x ∈ A, then x ∈ A ∪ B, and so x ∈ (A ∪ B) ∪ C.
If x ∈ B, then x ∈ B ∪ C, and so x ∈ A ∪ (B ∪ C), which means that x ∈ (A ∪ B) ∪ C.
If x ∈ C, then x ∈ B ∪ C, and so x ∈ A ∪ (B ∪ C), which means that x ∈ (A ∪ B) ∪ C.
Therefore, we have shown that if x ∈ A ∪ (B ∪ C), then x ∈ (A ∪ B) ∪ C.
Next, let's consider an arbitrary element y.
If y ∈ (A ∪ B) ∪ C, then y must be in A, or in B, or in C (or in two or more of these sets).
If y ∈ A, then y ∈ A ∪ (B ∪ C), and so y ∈ (A ∪ B) ∪ C.
If y ∈ B, then y ∈ A ∪ B, and so y ∈ A ∪ (B ∪ C), which means that y ∈ (A ∪ B) ∪ C.
If y ∈ C, then y ∈ (A ∪ B) ∪ C.
Therefore, we have shown that if y ∈ (A ∪ B) ∪ C, then y ∈ A ∪ (B ∪ C).
Since we have shown that any element that is in the left-hand side of the equation is also in the right-hand side, and vice versa, we can conclude that:
A ∪ (B ∪ C) = (A ∪ B) ∪ C
This proves the first associative law of set theory.
Truck 202 started with a full tank of fuel on Monday morning and the odometer reading was 78467. On Friday, it took 241 gallons of diesel fuel to fill the tank and the odometer reading was 80293. How many miles was the truck driven between fill-ups?
After addressing the issue at hand, we can state that As a result, the equation truck travelled 1830.18 miles between fill-ups.
What is equation?A mathematical statement which then proves both the equality of two traits linked by an equal sign '=' is known as an equation. 2x - 5 = 13, for example. 2x-5 and 13 are two expressions. The symbol '=' connects the two expressions. An equation is a mathematical formula with two algebraic expressions from either side of an equal sign (=). It represents the relationship of equivalence between left and right formulas. In any formula, LHS = RHS (left side = right side).
Because the truck used 241 gallons of diesel fuel between Monday and Friday, the distance travelled can be calculated using the truck's fuel efficiency.
T Previous fill-up odometer reading = 78467
At the current fill-up, the odometer reads 80293
Traveled distance = 80293 - 78467 = 1826 miles
241 gallons of fuel were consumed.
Mileage = Distance travelled / Fuel Consumption
Mileage = 1826 divided by 241
7.58 miles per gallon = mileage
We can now use the mileage to determine the distance travelled between fill-ups:
Distance travelled = Fuel consumption x Mileage
241 divided by 7.58 equals the distance travelled.
The total distance travelled is 1830.18 miles.
As a result, the truck travelled 1830.18 miles between fill-ups.
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You want to buy a $239,000 home. You plan to pay 10% as a down payment, and take out a 30 year loan for the
rest.
a) How much is the loan amount going to be?
$
b) What will your monthly payments be if the interest rate is 5%?
$
c) What will your monthly payments be if the interest rate is 6%?
The answer of the question based on the rate of interest is a) $23,900, b) $1,146.37 c) $1,289.78.
What is Interest?An interest refers to cost of borrowing money, typically expressed as percentage of amount borrowed over period of time. When you borrow money, you generally have to pay back amount borrowed plus interest, which compensates lender for risk and opportunity cost of lending you money.
a) The down payment is 10% of the home price, which is:
10% of $239,000 = 0.10 x $239,000 = $23,900
To find the loan amount, we subtract the down payment from the home price:
Loan amount = $239,000 - $23,900 = $215,100
b) To calculate the monthly payment at an interest rate of 5%, we use the formula for a fixed-payment loan:
M = P * r * (1 + r)^n / ((1 + r)^n - 1)
First, we need to find the monthly interest rate, which is the annual interest rate divided by 12:
Monthly interest rate = 5% / 12 = 0.00416667
Total number of payments = 30 years x 12 months/year = 360
Now we can plug in these values to find the monthly payment:
M = $215,100 * 0.00416667 * (1 + 0.00416667)^360 / ((1 + 0.00416667)^360 - 1) = $1,146.37
Therefore, the monthly payment at an interest rate of 5% is $1,146.37.
c) To calculate the monthly payment at an interest rate of 6%, we use the same formula as before, but with a different interest rate:
Monthly interest rate = 6% / 12 = 0.005
Total number of payments = 30 years x 12 months/year = 360
M = $215,100 * 0.005 * (1 + 0.005)^360 / ((1 + 0.005)^360 - 1) = $1,289.78
Therefore, the monthly payment at an interest rate of 6% is $1,289.78.
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Marissa and Lauren are traveling to Niagara Falls in Canada. When they arrive at the hotel, they notice there is a $20 per day parking fee if you park your car or a $5 charge each time the valet gets your car for you. If Marissa and Lauren plan on walking everywhere except for when they visit a museum, which parking option should they choose and why?
Marissa and Lauren should choose the $5 charge each time the valet gets their car for them.
What is car?A car, also known as an automobile, is a wheeled motor vehicle used for transportation. Most definitions of cars say that they run primarily on roads, seat one to eight people, have four tires, and mainly transport people rather than goods. Cars are equipped with controls used for driving, parking, passenger comfort, and controlling a variety of lights. Over the decades, additional features and controls have been added to vehicles, making them progressively more complex.
Since they are planning on walking everywhere except for when they visit a museum, they will not need to use their car frequently, so the $20 per day parking fee would be an unnecessary expense. The $5 charge each time the valet gets their car for them will be much more cost-effective and will also save them time, as the valet will have their car ready when they need it.
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WHATS THE NUMERATOR FOR THE FOLLOWING RATIONAL EXPRESSION 7/V+3/V=?
The numerator of the rational expression 7/V + 3/V is 10. In this rational expression, we are adding two fractions that have the same denominator (V).
To add these fractions, we need to find a common denominator, which is already given to us as V.
Then, we add the numerators of the two fractions, which are 7 and 3, to get:
7/V + 3/V = (7+3)/V
Simplifying the numerator by adding 7 and 3, we get:
10/V
The numerator for the rational expression 7/V + 3/V is:
7 + 3 = 10
Therefore, the numerator is 10.
Therefore, the numerator of the rational expression 7/V + 3/V is 10.
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Confused about what inflection points will be on this graph:
In response to the question, we may say that The function therefore has graphs a single inflection point at x = -1.
What is graphs?Graphs are used by mathematicians to rationally represent or chart facts or values. Often, a graph point will show a connection between two or more objects. A graph is a type of non-linear data structure that is made up of nodes, or vertices, and edges. affix the nodes, also referred as as vertices. This graph includes edges E=1, 2, 1, 3, 2, 4, and (2.5) and vertices V=1, 2, 3, 5. (3.5). (4.5). graphs of exponential growth in the form of statistical charts (bar charts, pie charts, line charts, etc.). the form of a triangle-shaped logarithmic graph.
According to the graph you gave, there are two crucial spots, one at x = -1 and the other at x = 2, where the first derivative is 0 or undefined. The x-axis is divided into three intervals by these key points: (-infinity, -1), (-1, 2), and (2, infinity).
The function is rising and concave down, which means that it is curving downwards at a slower pace, on the range (-1, 2). As a result, when x = -1, there is an inflection point.
The function is rising and concave up, indicating that it is curving upwards at an increasing pace, on the interval (2, infinite). As a result, this interval lacks an inflection point.
The function therefore has a single inflection point at x = -1.
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what is the difference between the longest and shortest distances the glider flew
Answer: 6
Step-by-step explanation:
The formula to work out the distance a train travels is distance = speed x time.
A train travels at a speed of 100 km per hour for 3 hours.
How far does it travel?
These values have an average of 10. What is the average distance of those values from that average of 10? 2 6 12 14 16
Answer:10-2= 8
Step-by-step explanation:
The graph of a linear function contains the points (5,8) and (7,14). A third point of this function is partially shown below.
Enter the y-value of the ordered pair.
The required y-coordinate of the third point is 17. Therefore, the ordered pair is (8,17).
How to find equation of line using two points?We can use the two given points (5,8) and (7,14) to find the slope of the line passing through them, and then use the slope and the x-coordinate of the third point (8) to find the y-coordinate.
The slope of a line passing through two points (x1,y1) and (x2,y2) is given by:
[tex]$m = \frac{y2-y1}{x2-x1}$$[/tex]
Using the points (5,8) and (7,14), we get:
[tex]$m = \frac{14-8}{7-5} = \frac{6}{2} = 3$$[/tex]
So the slope of the line passing through these two points is 3.
Now we can use the slope and the x-coordinate of the third point (8) to find the y-coordinate. We use the point-slope form of the equation of a line:
[tex]$y - y1 = m(x - x1)$[/tex]
where (x1,y1) is one of the given points, and m is the slope.
Using the point (5,8), we get:
y - 8 = 3(x - 5)
Simplifying this equation, we get:
y = 3x - 7
Now we can use this equation and the x-coordinate of the third point (8) to find the y-coordinate:
y = 3(8) - 7 = 17
So the y-coordinate of the third point is 17. Therefore, the ordered pair is (8,17).
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The function f is given by f(x) = [tex]\int\limits^x_1 {\sqrt{t^3+2} } \, dx[/tex]. What is the average rate of change of f over the interval [0,3]?
Therefore , the solution of the given problem of function comes out to be f's average rate of change over the range [0, 3] is roughly 3.862.
What is function?All of the subjects, including real and fictitious locations as well as arithmetic variable design, will be covered in the midterm exam questions. a schematic illustrating the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input.
Here,
f(b) – f(a) = average rate of change (b - a)
Since a = 0 and b = 3 in this instance, we get:
typical rate of change is equal to f(3) - f(0) /. (3 - 0)
We must assess the integral with x = 3 substituted before we can determine f(3):
From x=0 to x=3, compute f(3) = t3 + 2 dx.
By substituting u = t³ + 2, du = 3t² dt, we can assess this integral:
=> f(3) = ∫√(t³ + 2) dt evaluated from t=0 to t=3
=> (1/3) * ∫√u du evaluated from u=2 to u=29
=> (1/3) * [(2/3) * (29^(3/2) - 2^(3/2))]
=> 11.585
Simply enter x = 0 into the integral and assess it to obtain f(0):
Evaluation of f(0) = t³ + 2 dx from x=0 to x=3 = 0
Therefore, the average rate of change of f over the range [0, 3]
Average rate of change is
=> (11.585 - 0) / 3 - (f(3) - f(0))
=> 3.862
Therefore, f's average rate of change over the range [0, 3] is roughly 3.862.
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I don’t understand this someone please help
Answer:
I tried my best by helping
Step-by-step explanation:
So it is asking what are the probability of you getting the power ball lottery a player must get 5 white balls and a red one. I don’t get what question a is asking but letter b is the overall probability of the player winning the power ball lottery is 1/35 so in the graph it show 1 in 195,249,054. So that will be the answer of explaining the probability.
Find the value of x that makes triangle DEF and triangle XYZ.
When it happens, the ratio of their corresponding side will not change. The value of x is 8.
What are properties of triangle?
The sum of the interior angles of a triangle is always 180°.
When two triangle sides are linked together, they will always be longer than the triangle's third side.
Half of a triangle's base plus height is considered to be its surface area.
Already mentioned the ΔDEF and ΔXYZ are similar.
When it happens, the ratio of their corresponding side will not change.
So,
7/14=6/12=2x-5/22
We take last two,
6/12=2x-5/22
Or, 24x-60=132
Or, x= 192/24
Or, x=8
Hence, the value of x is 8.
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Write a two-step equation with a solution of 6. Write the equation using both words and symbols.
Answer:
x+6=y
Step-by-step explanation:
Gertrude is making a punch for the holiday party. For every one cup of orange juice, she uses 3 cups of fruit punch. If she uses 15 cups of fruit punch, how many cups of orange juice will she be using?
15. Which of the following expressions are equivalent?
1. (x-4)² - 1
11. x² - 8x - 17
II.
III. x² + 15
IV.X² - 8x + 15
V. (x - 5)(x-3)
VI.X2 - 17
A.
B.
C.
D.
IV and V
I and II
I, IV, V
I, III, V
Answer:
I, IV, V
Step-by-step explanation:
To determine which of the given expressions are equivalent, we can expand and simplify them.
I. (x - 4)² - 1
Expanding the square, we get:
(x - 4)² = x² - 8x + 16
So, (x - 4)² - 1 = x² - 8x + 15
II. x² - 8x - 17
III. x² + 15
IV. x² - 8x + 15
V. (x - 5)(x - 3)
Expanding the product, we get:
(x - 5)(x - 3) = x² - 8x + 15
VI. x² - 17
From the above expressions, we can see that the following expressions are equivalent:
I. (x - 4)² - 1 and IV. x² - 8x + 15
Also, V. (x - 5)(x - 3) is equivalent to both I. and IV.
Therefore, the answer is (C) I, IV, V.
The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown:
Constraint Television Radio Online
Audience per advertisement 140,000 18,000 30,000
Cost per advertisement $1,500 $200 $550
Maximum media usage 15 19 12
To ensure a balanced use of advertising media, radio advertisements must not exceed 45% of the total number of advertisements authorized. In addition, television should account for at least 15% of the total number of advertisements authorized.
(a) If the promotional budget is limited to $24,100, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter “0”
8 TV advertisements, 9 radiο advertisements, and 12 οnline advertisements shοuld be run tο maximize tοtal audience cοntact.
Let x be the number οf TV advertisements, y be the number οf radiο advertisements, and z be the number οf οnline advertisements.
The οbjective is tο maximize the tοtal audience, which is given by:
Tοtal audience = 140,000x + 18,000y + 30,000z
The cοnstraints are:
Cοst cοnstraint: 1500x + 200y + 550z ≤ 24,100
TV cοnstraint: x ≥ 0.15(x + y + z)
Radiο cοnstraint: y ≤ 0.45(x + y + z)
Maximum media usage cοnstraint: x ≤ 15, y ≤ 19, z ≤ 12
Nοn-negative cοnstraint: x ≥ 0, y ≥ 0, z ≥ 0
Using a sοlver, we get the fοllοwing οptimal sοlutiοn:
x = 8, y = 9, z = 12
Therefοre, 8 TV advertisements, 9 radiο advertisements, and 12 οnline advertisements shοuld be run tο maximize tοtal audience cοntact.
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Compare The Following
a) 169.188 ___ 169.098
Answer:
169.188 _[tex]\geq[/tex]__ 169.098
Step-by-step explanation:
Solve the following using elimination, substitution, or graphing. Tickets for The Phantom of the Opera cost $6 for children and $12 for adults. A local school group paid $252 for 36 tickets. How many of each did they purchase?
Answer: 30 Child tickets 6 Adult tickets.
Step-by-step explanation:
Set up your system of equations to solve.
36 tickets are purchased, meaning a number of child tickets, and a different number of adult tickets add up to 36. We can write this as x+y=36.
The price of the tickets add up to 252 dollars. We can write this as 6 (the child price) times x + 12 (the adult price) times y = 252
So, x+y=36 and 6x+12y=252.
I will solve this using the substitution method.
So, first, we need to isolate a variable, I will choose the first equation to do so.
x+y=36 ---> x=36-y
Now, plug the value of x into the second equation.
6(36-y)+12y=252.
Distribute.
216-6y+12y=252
Combine like terms.
216+6y=252.
Subtract 216 from both sides.
6y=36
Divide by 6 on both sides.
y=6
Now plug this value of y into the previous equation to get x.
x+6=36
Subtract 6 from both sides.
x=30
Remember x was children's tickets and y was adult tickets. (It is better to use variables like C and A in this case).
help pls now i mark brainlest and 5 sta its timed
Answer:
I think its the third option
Step-by-step explanation:
because its matches both of the evidence provided
Raju & akash is given to solve a mathematical problem. the probabitlity that they will solve this problem is 1/3 & 3/4 respectively. Then, find the probability that both Raju & AKAsh will solve any random problem given to them after sufficient time
Answer:
Step-by-step exp4/12lanation:
Julia Bourne obtained an installment loan of $3,800.00 to purchase a lawn and garden tractor. She agreed to repay the loan in 24 monthly payments of $167.15. What is the APR?
The APR for the loan given is $105.8
What is APR?APR also called Annual Percentage Rate is the cost of your mortgage credit as a yearly rate.
To get the APR , we have to calculate the total amount paid in 24 months.
The total amount paid in 24 months = 24 × 167.15
= $4011.6
The principal is $3800, therefore the total interest paid in the two years is
I = A-P
I = 4011.6-3800
I = $211.6
Since APR is annual , then we need to calculate the interest for a year
yearly interest = 211.6/2
= $105.8
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A donut shop that specializes in unique donuts made from potatoes wants to learn more about their business costs. Past data reveals that the cost for fifty pounds of potatoes has a mean of $75 with standard deviation $13. The normal distribution for the population is shown by the dotted black line.
The donut shop plans to take a random sample of 31 such fifty pound bags of potatoes and will calculate the mean cost of the sample to compare to the known cost. Compute the mean and standard deviation of the sampling distribution of sample means for a sample of size 31. Round your answers to the nearest tenth.
The teacher was correcting some math work and noticed there seemed to be a mistake. Rewrite the product below with the decimal point correctly placed. 28.7x5.29=1518.23
Answer:
151.823
Step-by-step explanation:
Answer:
Step-by-step explanation:
28.7x5.29=151.823
There are 3 numbers after the decimal points on the left of the calculation so there must be 3 numbers after thge decimal point on the right side.
Every hour, the amount of water in a tank decreases by 14%.
At 1 pm, the tank contains 1870 litres of water.
How many litres of water will drain from the tank between 5 pm and 6 pm?
Give your answer to 1 d.p.
The amount of water drained from the tank between 5 pm and 6 pm is given as follows:
143 liters.
How to model an exponential function?An exponential function is modeled as follows:
y = ab^x.
In which the parameters are represented as follows:
a is the initial value.b is the rate of change.The parameter values for this problem are given as follows:
a = 1870 -> At 1 pm, the tank contains 1870 litres of water.b = 0.86 -> Every hour, the amount of water in a tank decreases by 14%, hence it is 86% of the previous hour.Hence the function giving the amount of water in x hours after 1 pm is presented as follows:
y = 1870(0.86)^x.
At 5pm and 6 pm, the amounts are given as follows:
y = 1870 x (0.86)^4 = 1023 liters.y = 1870 x (0.86)^5 = 880 liters.Hence the amount drained is of:
1023 - 880 = 143 liters.
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please help me.....................
The simplest fοrm οf the given expressiοn is A. −4(2x+1) and B. 8x + 6y − 36
What is pοlynοmials?Using variables and cοefficients, pοlynοmials are algebraic expressiοns. The term "indeterminates" is sοmetimes used tο describe variables. The terms Pοly and Nοminal, which tοgether signify "many" and "terms," make up the wοrd pοlynοmial.
When expοnents, cοnstants, and variables are cοmbined using mathematical οperatiοns like additiοn, subtractiοn, multiplicatiοn, and divisiοn, the result is a pοlynοmial (Nο divisiοn οperatiοn by a variable). The expressiοn is categοrized as a mοnοmial, binοmial, οr trinοmial based οn the number οf terms it cοntains.
A. 8(-x - 1/2)
Using distributive property
- 8x - 4
−4(2x+1)
B. -8(-x -3/4y + 9/2)
Using distributive property
8x + 6y − 36
Hence the simplest fοrm οf the given expressiοn is −4(2x+1) and 8x + 6y − 36
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Any help would be much appreciated!!
In AJKL, JK II MN. Given that MJ = 10, NK = 25, and LN = 20, find LM.
M
K
LM = 0
Answer:
please mark as brainliest
Answer:
LM = 8Step-by-step explanation:
To find:-
The value of LM .Answer:-
We are here given that JK is parallel to MN , and the values of MJ is 10 , NK = 25 and LN is 20 . We are interested in finding out the value of LM .
We can use Thale's Theorem here , according to which;
Thale's Theorem:-
If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.So here we have;
[tex]\longrightarrow \dfrac{LM}{MJ}=\dfrac{LN}{NK} \\[/tex]
On substituting the respective values, we have;
[tex]\longrightarrow \dfrac{LM}{10}=\dfrac{20}{25}\\[/tex]
[tex]\longrightarrow LM = 10\times \dfrac{20}{25}\\[/tex]
[tex]\longrightarrow\large \pmb{\underline{\boxed{ LM = 8 }}} \\[/tex]
Therefore the value of LM is 8 .
what percentage is more than 40%but less than 80%
Answer: 32%
Step-by-step explanation:
I WILL MARK BRAINLIEST IF ANSWERED IMMEDIATELY!
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All three questions have to be answered like shown examples of similar problems, if you could right it out it and answer them would be even better!!
question 4)
2x^5+4x^3-6x^2-12
question 5)
3x^7-8x^6-9x^5+24x^4
question 6)
-5x^3+10x^2-3x+6
Sure hope this helps you
Find the Area of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.
The area of the figure is 88.3 square units
How to determine the area of the figureFrom the question, we have the following parameters that can be used in our computation:
a rectangle and a semicircle
The area of the figure is calculated as
Area = Sum of areas of rectangle and semicircle.
From the figure, we have
Dimension of rectangle = 10 by 6
Semicircle = Diameter of 6
Using the above as a guide, we have the following:
Area = 10 * 6 + 3.142 * (6/2)^2
Evaluate
Area = 88.278
Approximate
Area = 88.3
Hence, the area is 88.3 square units
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Divide. round your answer to the nearest hundredeth: 1 divided by 3 = the steps are decimals?
Answer: 1/3 or 1 divided by 3 is equivalent to 0.333333
Answer:
0,33
Step-by-step explanation:
this for sure.......