Given:
A = {6, 2, 3, 4}, B = {5, 2, 3}, and C = {1, 2, 3}.
a) To find:
\(A\times(B\cup C)\)First, let us find BUC. We get
\(B\cup C=\mleft\lbrace1,2,3,5\mright\rbrace\)Next, we find
\(\begin{gathered} A\times(B\cup C)=\mleft\lbrace2,3,4,6\mright\rbrace\times\mleft\lbrace1,2,3,5\mright\rbrace \\ =\mleft\lbrace(2,1\mright),(2,2),(2,3),(2,5),(3,1),(3,2),(3,3),(3,5),(4,1),(4,2),(4,3),(4,5),(6,1),(6,2),(6,3),(6,5)\} \end{gathered}\)Hence, the answer is,
\(\lbrace(2,1),(2,2),(2,3),(2,5),(3,1),(3,2),(3,3),(3,5),(4,1),(4,2),(4,3),(4,5),(6,1),(6,2),(6,3),(6,5)\}\)1. A taxi service charges a $ 1.95 flat rate plus $ 0.55 per mile. Jason only has $ 12 to spend on a ride. Which graph best represents the number of miles Jason can afford to travel?
Answer:
B
Step-by-step explanation:
Subtract $1.95 from $12 to account for the flat rate that Jason must pay, then divide that by 0.55, or the per mile charge. The answer, or the highest amount of miles he can go with $12, is 18.27272727. The answer that best represents the number of miles he can go is B because he can go up to 18 miles, including 18 miles, hence the closed circle.
Which problem can be solved by performing this multiplication?
3/4×8/9
Responses
Evan practiced piano this week for 3/4 hour. Last week he practice for8/9 hour. How much longer did Evan practice last week than this week?
Jada rode her bike 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike. How far did Sarah ride her bike?
Amelie drove 3/4 mile. She then drove another 8/9 mile. How many miles did she drive in all?
Three out of 4 containers hold lemonade. Each container holds 8/9 quart of lemonade. How much lemonade do the containers all hold?
The multiplication 3/4×8/9 can be used to address the problem in response (B). which is the correct answer that would be an option (B).
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
As per option (B),
Jada rode her bike for 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike.
Sarah rides her bike = Sarah rode (8/9) of the (3/4) that Jada rode.
Sarah rides her bike = 3/4 × 8/9
Therefore, this problem can be solved by performing the above multiplication.
Hence, the correct answer would be an option (B).
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Tom is applying for a visa.
He has to pay £2,400 for the visa as well as a 8% charge on the visa price for an on-the-day service.
If Tom has 1 year to save, how much money should he save per month to be able to cover his costs?
Round your answer to the nearest £10.
Answer:
100
Step-by-step explanation:
The total amount Tom saved per month is equal to \(\£ 220\) (nearest \(\£10\)).
What is the amount?" Amount is defined as the total of all the given quantities as per given conditions."
According to the question,
The amount required to pay for a visa \(= \£ 2,400\)
Percentage charges on the visa price as day service\(= 8\%\)
Amount as day charge \(= 8\%\) of \(2400\)
\(= \frac{8}{100} \times 2400\\\\= \£192\)
The total amount required for a visa \(= \£ (2400 + 192)\)
\(= \£ 2592\)
Tom has one year to save,
Therefore,
Amount Tom save in one month \(= \frac{2592}{12}\)
\(=\£ 216\)
≈\(\£ 220\) ( round to nearest \(\£ 10\))
Hence, the total amount Tom saved per month is equal to \(\£ 220\) (nearest \(\£10\)).
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Multiply (1.2 ⋅ 10^28) ⋅ (3 ⋅ 10^−19). Express the answer in scientific notation.
3.6 ⋅ 109
3.6 ⋅ 1010
36 ⋅ 109
36 ⋅ 1010
Answer:
3.6 × 10^9
Step-by-step explanation:
When multipliying two numbers in scientific notation, the exponents in the factor of 10 will be added when the two expressions are multiplied.
Thus (1.2 ⋅ 10^28) ⋅ (3 ⋅ 10^−19) = ( 1.2 × 3 )
( 10^28 × 10^-19 ) = 3.6 × 10^(28-19) = 3.6 × 10^9
the area of a triangle is 6 and 3/8 square yards. The height of the triangle is 2 and 1/2 yards. What is the length of the base of the triangle? pls help this is a important question
Solution:
Note that:
Area of triangle = 6 3/8 yd²Height of triangle = 2 1/2 Area of triangle = 1/2 x base x altitudeUse the formula to find the base of the triangle.
1/2 x base x altitude = 6 3/8 yd²=> 1/2 x base x 2 1/2 = 6 3/8 yd²=> 1/2 x base x 5/2 = 6 3/8 yd²=> 5/4 x base = 6 3/8 yd²=> base = 6 3/8 ÷ 5/4 yd=> base = 51/8 x 4/5 yd=> base = 51/2 x 1/5 yd=> base = 51/10 ydThe length of the base is 51/10 yards.
\(\large{|\underline{\mathtt{\red{G}\blue{i}\orange{v}\pink{e}\blue{n}\purple{}\green{}\red{↯}\blue{}\orange{}}}}\)
Area of triangle = 6 3/8 yards²Height of triangle = 2 1/2 yards\(\large{|\underline{\mathtt{\red{T}\blue{o}\orange{\:}\pink{F}\blue{i}\purple{n}\green{d}\red{↯}\blue{}\orange{}}}}\)
Base of triangle = ?\(\large\underline{\underline{\maltese{\blue{\pmb{\sf{\: Explanation :-}}}}}}\)
\( \boxed{\mathfrak{area = \frac{1}{2} \times base \times height}}\)
We are already given the values, Let's plug them and solve for x i.e base
\( \bf\: 6 \frac{3}{8} = \frac{1}{ \cancel2} \times x \times \cancel2 \frac{1}{2} \)
\( \bf \: 6\frac{3}{8} = x \times \frac{1}{2} \)
Convert the mixed number to an improper fraction
\( \bf \: \frac{51}{8} = \frac{1}{2} x\)
Multiply both sides of the equation by 2
\( \boxed{ \tt \: x = \frac{51}{4} }\)
➪ Therefore, The base of the triangle is 51/4 yards...~
Solve the initial-value problem: y" - 4y' + 8y = 0, y(0) = 1, y'(0) = 2.
Answer:
The solution of the problem is \(y(t) = e^{2 t} cos(2 t)\)
Step-by-step explanation:
First we will write the characteristic equation which is
\(x^{2} -4x + 8 = 0\)
Now, we will solve this quadratic equation using the general formula.
Given a quadratic equation of the form, \(ax^{2} +bx +c = 0\), then
From the general formula,
\(x = \frac{-b+\sqrt{b^{2}-4ac } }{2a}\) or \(x = \frac{-b-\sqrt{b^{2}-4ac } }{2a}\)
From the characteristic equation, \(a = 1, b = -4,\) and \(c = 8\)
Hence,
\(x = \frac{-(-4)+\sqrt{(-4)^{2}-4(1)(8) } }{2(1)}\) or \(x = \frac{-(-4)-\sqrt{(-4)^{2}-4(1)(8) } }{2(1)}\)
\(x = \frac{4+\sqrt{-16} }{2}\) or \(x = \frac{4-\sqrt{-16} }{2}\)
\(x = \frac{2+4i }{2}\) or \(x = \frac{2-4i }{2}\)
\(x = 2 + 2i\) or \(x = 2 - 2i\)
That is, \(x\) = \(2\) ± \(2i\)
Then, \(x_{1} = 2 + 2i\) and \(x_{2} = 2 - 2i\)
These are the roots of the characteristic equation
The roots of the characteristic equation are complex, that is, in the form
(\(\alpha\) ± \(\beta i\)).
For the general solution,
If the roots of a characteristic equation are in the form (\(\alpha\) ± \(\beta i\)), the general solution is given by
\(y(t) = C_{1}e^{\alpha t} cos(\beta t) + C_{2}e^{\alpha t} sin(\beta t)\)
From the characteristic equation,
\(\alpha = 2\) and \(\beta = 2\)
Then, the general solution becomes
\(y(t) = C_{1}e^{2 t} cos(2 t) + C_{2}e^{2 t} sin(2t)\)
Now, we will determine \(y'(t)\)
\(y'(t) = 2C_{1}e^{2 t} cos(2 t) - 2C_{1}e^{2t}sin(2t) + 2C_{2} e^{2t}sin(2t) +2C_{2}e^{2t}cos(2t)\)
From the question,
y(0) = 1
and
y'(0) = 2
Then,
\(1 = y(0) = C_{1}e^{2 (0)} cos(2 (0)) + C_{2}e^{2 (0)} sin(2(0))\)
\(1 = C_{1}e^{ 0} cos(0) + C_{2}e^{0} sin(0)\)
(NOTE: \(e^{0} = 1, cos(0) = 1\) and \(sin(0) = 0\) )
Then,
\(1 = C_{1}\)
∴\(C_{1} = 1\)
Also,
\(2 = y'(0) = 2C_{1}e^{2 (0)} cos(2 (0)) - 2C_{1}e^{2(0)}sin(2(0)) + 2C_{2} e^{2(0)}sin(2(0)) +2C_{2}e^{2(0)}cos(2(0))\)\(2 = 2C_{1}e^{0} cos(0) - 2C_{1}e^{0}sin(0) + 2C_{2} e^{0}sin(0) +2C_{2}e^{0}cos(0)\)
\(2 = 2C_{1} +2C_{2}\)
Then,
\(1 = C_{1} +C_{2}\)
\(C_{2} = 1 - C_{1}\)
Recall, \(C_{1} = 1\)
∴ \(C_{2} = 1 - 1 = 0\)
\(C_{2} = 0\)
Hence, the solution becomes
\(y(t) = e^{2 t} cos(2 t)\)
Answer the questions below to find the total surface area of the can.
Ab=3.14xRadious to the power of 2
then to the area of the rectange you do B x H = YOUR ANSWER
what is the answer for the question 2 add 2
Answer:
y dónde está la pregunta de imagen?????????????
solve pls branliest!
Answer:
c,b
Step-by-step explanation:
7 units to the right of 4 means 7 more. the other answers have -4 not 4. and adding -7 is going to the left making the number smaller.
answer is c
again a and d have -4 not 4. adding 7 will move the numbers to the right making it bigger.
answer is choice b
\(\huge\textsf{Hey there!}\)
\(\large\text{SOME FACTS ABOUT NEGATIVE NUMBERS}\\\\\bullet\large\textsf{ Negatives are BELOW 0.}\\\bullet\large\textsf{ Negatives are SMALLER THAN 0.}\\\bullet\large\textsf{ Negatives are on the LEFT SIDE of the number line}\\\\\\\\\\\large\text{SOME FACTS ABOUT POSITIVE NUMBERS}\\\star\large\textsf{ Positives are ABOVE 0}\\\star\large\textsf{ Positives are GREATER/BIGGER THAN 0.}\\\star\large\textsf{ Positives are on the RIGHT SIDE of the number line}\)\(\)
\(\large\text{Part A.}\\\\\large\boxed{\frak{7\ units\ to\ the\ right\ of\ 4\rightarrow \bold{7 + 4} \ because, you\ are\ starting\ at\ 7\ \&}}\\\large\boxed{\frak{\underline{up}\ 4\ spaces}}\\\\\large\boxed{\textsf{ANSWER: C. 4 + 7}}\large\checkmark\)
\(\large\text{Part B}\\\\\large\boxed{\frak{7 \ units\ to \ the\ left \ of \ 4\ is\righrarrow\ \bold{4 + (-7)} \ because, you \ are\ going\ starting \ at} \ 4}}\\\large\boxed{\frak{7\ \& \ going\ down\ -4 \ spaces}}\\\\\large\boxed{\mathsf{Option \ B. \ 4 + (-7)}}\large\checkmark\)
\(\huge\textsf{Good luck on your assignment \& enjoy your day!} \\\\\\\\\frak{Amphitrite1040:)}\)
Harry's amount of money is 75% of Kayla's amount of money
Answer:
Add vaslues
Step-by-step explanation:
How much money does kayla have?
A shoe manufacturer claims that among the general adult population in the United States that the length of the left foot is longer than the length of the right foot. To compare the average length of the left foot with that of the right foot, we will take a random sample of adults and measure the length of the left foot and then the length of the right foot. Based on our sample, does the data indicate that the length of the left foot is greater than the length of the right foot? Is the hypothesis one-tailed or two-tailed?
We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.
How to test the data indicate that the length of the left foot is greater than the length of the right foot?A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.
This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.
A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).
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y=(2x+h)/3 solve for x
Answer: \(x=\frac{3y-h}{2}\)
Step-by-step explanation:
\(y=\frac{2x+h}{3}\\ \\ 3y=2x+h\\\\3y-h=2x\\\\x=\frac{3y-h}{2}\)
M
Check all that apply.
The angles that we have in the image here are:
supplementary angleright angleWhat is a supplementary angle?When two angles are measured, they sum up to 180. They are said to be supplementary angles.
On the question, we have two angles that are 90 degrees on a straight line. Hence they are supplementary.
What is a right angle
This is an angle that is at 90 degrees. We have to two right angles on the diagram that we have here.
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The functions f(x) = −(x − 1^)2 + 5 and g(x) = (x + 2)^2 − 3 have been rewritten using the completing-the-square method. Apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.
If we write a quadratic in vertex form:
\(y=a(x-h)^2+k\)
Then:
\(\bold{a}\) \(\longrightarrow\) is the coefficient of \(x^2\)
\(\bold{h}\) \(\longrightarrow\) is the axis of symmetry.
\(\bold{k}\) \(\longrightarrow\) is the max/min value of the function.
Also:
If \(a > 0\) then the parabola will be of the form \(\cup\) and will have a minimum value.
\(a < 0\) then the parabola will be of the form \(\cap\) and will have a minimum value.
For the given functions:
\(a < 0\)
\(f(x)=-(x-1)^2+5\) this has a maximum value of \(\bold{5}\)
\(a > 0\)
\(f(x)=(x+2)^2-3\) this has a minimum value of \(\bold{-3}\)
Last year at a certain high school, there were 50 boys on the honor roll and 80 girls on the honor roll. This year, the number of boys on the honor roll increased by 20% and the number of girls on the honor roll increased by 10%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
the total number of students on the honor roll increased by 13.8%.
Step-by-step explanation:
Last year, there were a total of 50 + 80 = 130 students on the honor roll.
This year, the number of boys on the honor roll increased by 20%, which means there are now 1.2 * 50 = 60 boys on the honor roll.
The number of girls on the honor roll increased by 10%, which means there are now 1.1 * 80 = 88 girls on the honor roll.
The total number of students on the honor roll this year is 60 + 88 = 148.
The percentage increase in the total number of students on the honor roll is (148-130)/130 * 100% = 13.8%.
Rounding to the nearest tenth, we get that the total number of students on the honor roll increased by 13.8%.
The area of an equilateral triangle (all sides are equal, all angles are equal) varies directly as the square of its perimeter. If the perimeter is 12 inches, the area is 6.9 square inches. What is the area if the perimeter is 21 inches? Round to the nearest whole number.
Answer:
The area of the triangle is 36 square inches. This can be found using the formula A=P2/4, where A is the area and P is the perimeter. Therefore, if the perimeter is 21 inches, the area is (212/4) = 36 square inches.
The wholesale price for a desk is $199. A certain furniture store marks up the wholesale price by 24%. Find the price of the desk in the furniture store.
Round your answer to the nearest cent, as necessary.
Answer:
246.76$
Step-by-step explanation:
199 x .24 =
47.76
199 + 47.76 =
246.76
...................................................................
Answer:
29 degrees
Step-by-step explanation:
Note how both triangles are isosceles triangles, which mean two angles will be equivalent. In the triangle with the marked angle measurement, since the total of angles in a triangle is 180, then the measurement of the unmarked angles have a sum of 180-64, which is 116. Then, as stated before, this triangle is isosceles, so the measurement of each unmarked angle is 116/2, which is 58.
Next, notice how the angle below angle x in that triangle shares a line with one of the 58 degree angles. This means that angle is 180-58, which is 122. Now, since the total of angles in a triangle is 180 and the triangle is isosceles, then angle x is (180-122)/2, which is 58/2, or 29 degrees
The survey provides included 55 students that smoke and 337 who dont find the p os students that dont
As a result, about 85.18% of the students in the survey do not smoke, and the probability of not smoking is 0.8518.
What is percent?Percentages are just fractions with a denominator of 100. We use the percent sign (%) beside a number to indicate that it is a percentage. For instance, if you answered 75 questions correctly out of 100 on a test (75/100), you would have received a 75%. A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The sign "%" represents it.
Here,
The survey included 55 students who smoke and 337 students who do not smoke. The percentage of students who do not smoke can be calculated as follows:
337/(55+337) = 337/392 = 85.18%
So, approximately 85.18% of the students in the survey do not smoke and the probability of student of who don't smoke is 0.8518.
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The following table shows the number and type of properties available in three cities.
City
Key West
Orlando
Miami
Write a matrix that represents the number of each type of property available in Key West.
[ 3 9 13 ] is the Matrix showing all types of property available in key west .
What is matrix ?A matrix is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns to represent a mathematical object or an attribute of such an entity in mathematics.
Calculationgiven in the table that how many types of property are there in the table
its a simple matrix which u can directly see
its a 3 x 1 matrix ...
[3 9 13] this matrix shows the required value
hope this helps...
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Answer: [3 9 13]
Step-by-step explanation:
Gabriella is buying a pair of sneakers for $74.95. She has a coupon that will take $17.50 off the price of the sneakers.
How much will Gabriella pay for her sneakers after the discount?
$57.44
$56.45
$57.45
$56.65
write an equation of a line passing thru the point (-4,-11) and perpendicular to the line 4x+5y= -45
Answer:
y = 5/4x - 6
Step-by-step explanation:
First, put 4x + 5y= -45 in y = mx + b form
4x + 5y= -45
5y = -4x - 45
y = -4/5x - 9
So, the slope is -4/5. Perpendicular lines have a opposite reciprocal slope, so the line's slope will be 5/4
To find the equation of the perpendicular line, plug in the slope and given point into y = mx + b, and solve for b
y = mx + b
-11 = 5/4(-4) + b
-11 = -5 + b
-6 = b
Plug in b and the slope into y = mx + b
y = 5/4x - 6
So, the equation is y = 5/4x - 6
Find the area enclosed by y1 = (x - 1)3 and y2 = x -1.
I wanted to double check the answer. The professor got something completely different.
Find area between two curves
9514 1404 393
Answer:
0.5
Step-by-step explanation:
The "enclosed area" can be taken to mean different things. Here, we consider it to mean the finite area bounded between the two curves, regardless of which curve is higher value than the other.
The area is bounded on the interval [0, 2]. On half that interval y1 > y2; on the other half, y2 > y1. This means the integral of the area between the curves will be different for one part of the interval than for the other. (The curves are symmetric about the point (1, 0).)
The area on the interval [0, 1] is given by the integral ...
\(\displaystyle\int_0^1{(y_1-y_2)}\,dx=\int_0^1{((x-1)^3-(x-1))}\,dx\\\\=\int^1_0{(x(x-1)(x -2))}\,dx=\left.(\frac{x^4}{4}-x^3+x^2)\right|^1_0=\boxed{\frac{1}{4}}\)
The area on the interval [1, 2] is the integral of the opposite integrand, but has the same value.
The positive area over the whole interval from 0 to 2 is 1/4+1/4 = 1/2.
If you simply integrate y2-y1 or y1-y2 over that interval, the result is 0.
I need the answer:’)
Answer:
its D
Step-by-step explanation:
calculator
-4 1/2 divided by (-2 2/3
Answer:
1 11/16
Step-by-step explanation:
Answer:
1 11/16
Step-by-step explanation:
Convert mixed numbers into improper fractions:
-4 1/2
Step 1: whole number x denominator + numerator
-4 x 2 + 1 = -9
Step 2: write that number over your original denominator
-9/2
Step 3: repeat for other fraction
-2 2/3
-2 x 3 + 2 = -8
-8/3
Step 4: copy, dot, flip
-9/2 × -3/8
Step 5: solve
27/16
Step 6: convert back to mixed number
1 11/16
*note* Negative x negative = positive
-35x+85x-24=26 what is x
Answer:
x=1
Step-by-step explanation:
-35x+85x-24=26
Combine like terms
50x -24 = 26
Add 24 to each side
50x-24+24 =26+24
50x = 50
Divide each side by 50
50x/50 = 50/50
x=1
Answer:
x=1
Step-by-step explanation:
subtract 35 from 85 which would equal 50 and then add x
so 50x-24=26
add 24 to 26 because you want x by itself
which would equal 50
50x=50
divide by 50 on both sides
50/50=1
x=1
Simultaneous equation.
I know the final answer i just need the steps
3) x=9, y= -3
4) x=4, y= -2
5) x=3, y=2
6) x=8, y=1
7) x=6, y=8
Answer:
3.You collect
4.Multiply the bottom by 4 and then add
5.Multiply the bottom by -2 and then add
6.Multiply the bottom by 2.Multiply the top by 3 and then add
7.Multiply the top by -3.Multiply the bottom by 2and then add
Step-by-step explanation:
Find the value of the variable in the isosceles trapezoid.
The value of the variable in the isosceles trapezoid is 24.
Calculation of the value of the variable:Since the measure of one angle should be 63 degrees
And, there is the equation 2x + 15 degrees
So for determining the value of x here we have to equate the equation
So,
2x + 15 = 63
2x = 63 - 15
2x = 48
x = 24
Therefore, The value of the variable in the isosceles trapezoid is 24.
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Which inequality is graphed below
Answer:
wheres it at?
Step-by-step explanation:
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Angle ABC and angle CBD are complementary. What is the value of X?
Answer:
26
Step-by-step explanation:
complementary means two angles that add up to 90 degrees
90-38=52
52÷2=26
to check work you can do 26×2 (since there's 2x) = 52
52+38=90