How many subsets of 5 e elements can be made from a set of 7 elements?
Answers
Answer:
seems like this.
Step-by-step explanation:
From set theory, the factorial combinations are 2^N where N are the number of induvidual mambers of the set and that includes the null set. If we require that one element be the minimum to form a set, this eliminates the empty set (and there is only one empty set) so we must subtract one from the formula. The correct answer is therefore 2^N-1. In this case that is 2^5–1 = 31.
Related Questions
Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis.
y = x3/2 y = 27 x = 0.
Answers
Volume of the solid generated by revolving the plane region about the y-axis is \(\frac{6561 \pi}{7}\) .
Given, that y = x3/2, y = 27, x = 0
So, the volume of the solid generated by revolving the region about y axis will be,
\(V=\int_0^92\pi(x)(27-y)dx\)
\(V=\int_0^92\pi x(27-x^{\frac{3}{2}})dx\)
\(V=\left [ 27{\pi}x^2-\frac{4{\pi}x^\frac{7}{2}}{7} \right ]_0^9\)
\(V=\left [ \frac{{\pi}\left(189x^2-4x^\frac{7}{2}\right)}{7} \right ]_0^9\)
\(V=\frac{6561 \pi}{7}\)
The image of the region bounded by plane is attached below.
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The volume of the solid generated by revolving the plane region about the y-axis is approximately 6863.01 cubic units.
To use the shell method to find the volume of the solid generated by revolving the plane region about the y-axis, we need to express the limits of integration and the height of the infinitesimally thin cylindrical shells.
Given the equations:
y = x^(3/2)
y = 27
x = 0
To determine the limits of integration, we need to find the intersection points between the two curves: y = x^(3/2) and y = 27.
Setting the equations equal to each other:
x^(3/2) = 27
Taking the square root of both sides:
x = 27^(2/3)
x = 9
Therefore, the limits of integration are x = 0 and x = 9.
Now, let's consider an infinitesimally thin cylindrical shell with height "h" and radius "r" at some x value between 0 and 9.
The height of the shell, "h", is the difference between the y-values of the two curves:
h = 27 - x^(3/2)
The radius of the shell, "r", is the x-value.
The volume of the shell can be expressed as:
dV = 2πrh dx
To find the total volume, we integrate this expression from x = 0 to x = 9:
V = ∫[0, 9] 2π(27 - x^(3/2))x dx
Now, let's evaluate this integral:
V = 2π ∫[0, 9] (27x - x^(5/2)) dx
Integrating term by term:
V = 2π [(27/2)x^2 - (2/7)x^(7/2)] evaluated from 0 to 9
Plugging in the limits of integration:
V = 2π [(27/2)(9)^2 - (2/7)(9)^(7/2)] - 2π [(27/2)(0)^2 - (2/7)(0)^(7/2)]
Simplifying and evaluating the expression:
V = 2π [(27/2)(81) - (2/7)(3√(9))] - 0
V = 2π [1093.357] ≈ 6863.01 cubic units
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Write each amount as rate
500 words in one minute
Answers
Answer:
500 words per minute.
Step-by-step explanation:
PLZ HELPPP will give BRAINLIEST
Answers
Explanation: If a graph is proportional, it means that but the x coordinate and the y coordinate have the same rate of change
Answer:
True
Step-by-step explanation:
Saying the graph is proportional means that the line crosses through the origin which is (0,0).
write each info entire radical √48
Answers
The value of the radical √48 is 4√3.
Radical is a symbol (√) that denotes square roots and nth roots. The number inside the symbol is called Radicand and the expression containing the radical or a square root is called a Radical expression.
Here, we are given the radical √48
To find the value of the radical, we will factorize 48
i.e., 48 = 2×2×2×2×3
= 16×3
Now, the square root of 48, that is, √48
= \(\sqrt{16\cdot3}\) =\(\sqrt{16} \cdot \sqrt{3}\)
We know 16 is a perfect square of 4, that is, the square root of 16= 4
⇒√16=4
Using this, we have √48= 4√3
The correct answer is 4√3.
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What is the equation of the line that is parallel to the line defined by the equation y = 3x−7 and goes through the point (4, 2)?
Answers
Answer:
\(y-2=3(x-4)\)
Step-by-step explanation:
Pre-SolvingWe are given a line contains the point (4, 2).
We also know that the line is parallel to y= 3x - 7.
We want to write the equation of this line.
Parallel lines have the same slopes.
First, let's find the slope of y = 3x - 7.
3 is in the place of where m (the slope) is, so that means it is the slope of that line.
It is also the slope of the line whose equation we want to write.
The equation of the line can be written in three ways:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept. Standard form, which is ax+by=c, where a, b, and c are free integer coefficients. a and b cannot be 0, and a is usually non-negative as well. Point-slope form, which is \(y-y_1=m(x-x_1)\), where m is the slope and \((x_1, y_1)\) is a point.All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.
SolvingSubstitute 3 as m in \(y-y_1=m(x-x_1)\).
\(y-y_1=3(x-x_1)\)
Now, substitute 4 as \(x_1\) and 2 as \(y_1\).
\(y-2=3(x-4)\)
Topic: parallel and perpendicular lines
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Which of these is an example of being "underwater" on a car?
A. Owing $4400 on a car that's worth $4800
B. Owing $8600 on a car that's worth $8200
C. Owing $7200 on a car that's worth $7500
D. Owing $5700 on a car that's worth $6600
Answers
The required, example of being "underwater" on a car is option B, owing $8600 on a car that's worth $8200.
What is inductive reasoning?Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.
Here,
Being "underwater" on a car means owning more on a car than it is currently worth.
Based on the given options, the example of being "underwater" on a car is option B, owing $8600 on a car that's worth $8200.
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A soccer player stands at one corner of the field and kicks a soccer ball 100 yards to the opposite corner if the field is 80 yards long what is the width
Answers
The width οf the field is 80 yards.
What is the Pythagοrean theοrem?Pythagοras Theοrem is the way in which yοu can find the missing length οf a right angled triangle.
Assuming the field is rectangular, we can use the Pythagοrean theοrem tο sοlve fοr the width:
Let the width οf the field be x. Then, we have a right triangle with legs x/2 and 80/2 = 40 and hypοtenuse 100:
\((x/2)^2 + 40^2 = 100^2\)
\(x^2/4 + 1600 = 10000\)
\(x^2 = 6400\)
\(x = 80\)
Hence, the width οf the field is 80 yards.
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Harper is starting a printing business. She purchases plain t-shirts for $5 dollars each and spends $150 for printing equipment She decides to sell printed shirts for $10 each. How many t-shirts does Harper need to sell so that the amount of money she spends to start her business and the amount of money she earns are the same.
Answers
Answer:
30
Step-by-step explanation:
150/5 = 30
30+30+30+30+30 = 150
2/5 of employees in a company drive to work, 1/3 travel by bus and the rest walk. 1. Find the fraction of who walk.
Answers
Answer:
4/15
Step-by-step explanation:
2/5 drive
1/3 bus
and rest walk
fraction of those who walk is 1-(2/5+1/3)
2/5+1/3=(6+5)/15=11/15
15/15-11/15=4/15
5.4.3
Question 8 of 10
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
OA. x= -8, y = 2
OB. No solution
OC. More than 1 solution
OD. x= 12, y = 3
3y-12x=18
2y-8x=12
SUBMIT
Answers
Answer:
C) More than 1 solution
Step-by-step explanation:
\(3y-12x=18\\2y-8x=12\\\\3(y-4x)=18\\2(y-4x)=12\\\\y-4x=6\\y-4x=6\\\\6=6\)
Therefore, since both sides will always be equal to each other, then there are infinitely many solutions (so C is the best choice)
This diagram shows a pre-image △ABC and its image, △A′′B′′C′′ , after a series of transformations.
Select from the drop-down menus to correctly complete the statements.
△ABC is
1. reflected across the y-axis.
2. rotated 90 degrees counterclockwise about the origin.
3. translated 4 units right
to become △A′B′C′. Then △A′B′C′ is
1. reflected across the x-axis.
2. reflected across the line y = x
3. rotated 90 degrees counterclockwise about the origin
to become △A′′B′′C′′ . Because the transformations are
1. both rigid
2.not both rigid,
The pre-image and image are
1. congruent
2. not congruent
Answers
Using translation concepts, we have that:
△ABC is 3. translated 4 units right to become △A′B′C′. Then, △A′B′C′ is 3. rotated 90 degrees counterclockwise about the origin to become △A′′B′′C′′ .Because the transformations are both rigid, the pre-image and the image are congruent.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
On the translation of △ABC to △A′B′C′, the rule applied to the vertices is:
(x,y) -> (x + 4, y).
Hence it was translated 4 units right.
On the translation of △A′B′C′ to △A′′B′′C′', the rule is given by:
(x,y) -> (-y,x).
Hence it was rotated 90 degrees counterclockwise about the origin.
The triangle keeps the same size after the translations, hence:
Because the transformations are both rigid, the pre-image and the image are congruent.
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Find the surface area of this shape.
Answers
Answer:
54 yds²
Step-by-step explanation:
Area of 1 side: 3*3=9
Number of sides: 6
6*9=54
Answer:
54 square yards
Step-by-step explanation:
This is a cube, as the width, height, and length are all the same. To fine the surface area of a cube, simply find the area of one side and multiply it by six, as a cube has six sides.
\(Area = Width*Height\\Area = 3 * 3\\Area = 9\)
The area of one side of the cube is 9 square yards. Therefore, the surface area of the entire cube is 6 x 9 or 54 square yards.
please help me !!!
Below are two triangles that are drawn to scale.
Find the missing lengths as well as the scale factor.
Numbers may be used once or not at all.
Answers
The scale factor here is 1.5 for both the triangles in the image.
What is scale factor and how to find it?The ratio of any two corresponding lengths in two similar figures is known as the scale factor. In other words, it is the factor that is used to multiply all corresponding lengths between two similar figures in order to convert one to the other.
By identifying two corresponding lengths in both pictures and dividing the length of one by the corresponding length of the other, you may get the scale factor between two identical figures. The scale factor is the outcome. By dividing the length of one corresponding side in one triangle by the length of the corresponding side in the other, for instance, you may determine the scale factor if you have two similar triangles.
The bases in the given figures are in a ration,
10.5/7
=1.5
and since both triangles are similar therefore side would also be in the same ration
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In Math town,60% of the population are males and 30% of them have brown eyes. Of the total math town population 28 % have brown eyes. What percentage of the females in math town have brown eyes?
Answers
25% percent of the females in Math town have brown eyes. To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes
what is percent ?
A percent is a way of expressing a number as a fraction of 100. The symbol for percent is %, which means "per hundred".
In the given question,
Let's assume that there are 100 people in Math town.
60% of them are males, so there are 60 males and 40 females.
Out of the 60 males, 30% have brown eyes, so there are 18 males with brown eyes.
28% of the entire population have brown eyes, so there are 28 people with brown eyes.
To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes:
28 - 18 = 10
So, there are 10 females with brown eyes.
Out of the 40 females in Math town, what percentage have brown eyes?
10 brown-eyed females out of 40 females is:
10/40 = 0.25 or 25%
Therefore, 25% of the females in Math town have brown eyes.
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a total of 700 is invested part of 6% and the remainder at 10% how much is invested at each rate if the annual interest is 520
Answers
To determine the investment at each rate:
A total of $7000 is invested:
part x at 6% and the remainder 7000-x at 10%. How much is invested at each rate if the annual interest is $520
6% = 6/100 = 0.06
10% = 10/100 = 0.1
\(\begin{gathered} 0.06x+0.1(7000-x)=520 \\ 0.06x+700-0.1x=520 \\ 0.06x-0.1x=520-700 \end{gathered}\)\(\begin{gathered} -0.04x=-180 \\ \text{divide both side by -0.04} \\ x=-\frac{180}{-0.04} \\ x=4500 \\ x=\text{ \$4500} \end{gathered}\)x = $4500 -> invested at each 6% rate
while
7000 - x = 7000 - 4500 = $2500 ->invested at each 10% rate
Therefore the invested at each 6% rate = $4500 and invested at each 10% rate = $2500
find the value of a and the value of b :
4x2 - 4x - 15 is a factor of 4x3 + ax2 + bx + 30.
Answers
Step-by-step explanation:
the answer is in the above image
pls give me BRAINLIEST
Need help ASAP
Will mark you brainlist
Answers
Answer:
11.3 and more
Step-by-step explanation:
the area of a trapezoid is given by the formula A= h(a+b)/2. solve for the formula for b.
Answers
The formula is
\(A=\frac{(a+b)\cdot h}{2}\)To solve for b, first, we multiply the equation by 2
\(\begin{gathered} 2A=2\cdot\frac{(a+b)\cdot h}{2} \\ 2a=(a+b)\cdot h \end{gathered}\)Then, we divide the equation by h
\(\begin{gathered} \frac{2A}{h}=\frac{(a+b)h}{h} \\ \frac{2A}{h}=a+b \end{gathered}\)At last, we subtract a from each side
\(\frac{2A}{h}-a=a-a+b\)Hence, the final expression is\(b=\frac{2A}{h}-a\)The table shows three transactions and the resulting account balance in a bank account, except some numbers are missing. Fill in the missing numbers.
Answers
Answer: A
Step-by-step explanation: Pic is attached. Hope this helps.
write the place value of the 5 in each number. a) 1 325
Answers
Answer:
Place Value of 5 in 1325 is 'Thousands'
How many cubes will be needed to construct the 5th "building" in the same pattern?
A. 11
B. 12
C. 13
D. 14
E. 15
Answers
Answer:12
Step-by-step explanation:They are adding three box for every building so is the fifth block you do it
300 + 200 = ????????????????????????
i am gust giving free brainiest i know the answer.
Answers
Answer: 500
Step-by-step explanation:
300
+ 200
500
What is the measure of angle f?
22
39
61
32
Answers
Answer:
22
Step-by-step explanation:
alternate interior angles because upper side is parallel to lower side
About % of babies born with a certain ailment recover fully. A hospital is caring for babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. Is the experiment a binomial experiment?
Answers
Answer:
This is a binomial experiment .
Step-by-step explanation:
As the percent is not indicated the success is the amount of percent (if given) say it is 10 % . So p will be equal to = 0.1 and q will be = 1-0.1= 0.9
and n would be five or any number as a binomial experiment is repeated for a fixed number of times.
And x would take any value of n i.e.
X= 0,1,2,3,4,5
If it is 20 % . So p will be equal to = 0.2 and q will be = 1-0.2= 0.8
The probability is the number of the percent indicated. But as it is not indicated we assume it to be 10 % or 20 % .Or suppose any number for it to be a binomial experiment.
The number of trials n would be fixed .
The success remains constant for all trials.
All trials are independent.
What were the rental rates?
Answers
answer/explanation:
d = daily rental chargem = the charge per mileJon rented a car from a company that charged a daily rental fee and a mileage charge. He rented the car for 6 days and drove 300 miles and was charged $285.6d + 300m = 285His friend Amanda later rented the same car for 7 days and drove 260 miles and was charged $310.7d + 260m = 310by solving the system of equations6d + 300m = 2857d + 260m = 310we findd = $35m = $0.25the daily rental charge is $35.the company charge per mile is $0.25.hope this helps
[~S & (R V S) ] ≡ (Q ⊃ S) where A = T, S = F, R = F, Q = T
Answers
[~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T by substituting the propositional variables.
What is truth table?A truth table is a table used to determine the truth values of a compound proposition, which is a logical statement made up of simpler propositions using logical operators such as "and" (represented by "&"), "or" (represented by "V"), "not" (represented by "~"), conditional (represented by "⊃"), and biconditional (represented by "≡").
According to question:Let's substitute the given truth values for the propositional variables in the given statement:
[~F & (F V F)] ≡ (T ⊃ F)
Using the truth table for conjunction (represented by "&") and disjunction (represented by "V"), we can simplify the left-hand side of the equivalence:
[T & F] ≡ (T ⊃ F)
Using the truth table for conditional (represented by "⊃"), we can simplify the right-hand side of the equivalence:
F ≡ F
Since both sides of the equivalence have the same truth value, the statement is true.
Therefore, [~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T.
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Using 50 random numbers given below, compute the mean and standard deviation. 0.937776 0.270012 0.243785 0.590701 0.824982 0.131805 0.879337 0.741998 0.254683 0.080259 0.419321 0.928220 0.958430 0.980182 0.263900 0.063119 0.762096 0.485612 0.662900 0.362242 0.724796 0.307736 0.305021 0.417052 0.054337 0.323357 0.069662 0.843387 0.353107 0.074262 0.735596 0.175095 0.390508 0.668932 0.029861 0.205228 0.387740 0.962169 0.646565 0.423914 0.754782 0.156719 0.773113 0.546335 0.323573 0.649740 0.214082 0.382383 0.383982 0.030539 Mean = (to 6 decimals) Standard deviation = (to 6 decimals)
Answers
The mean is 0.477514 (rounded to 6 decimal places).
The standard deviation is 0.288919 (rounded to 6 decimal places).
How to Solve the Problem?To calculate the mean and standard deviation, we will use the following formulas:
Mean = (sum of all values) / (number of values)
Standard deviation = sqrt[(sum of (value - mean)^2) / (number of values)]
Using these formulas, we can calculate the mean and standard deviation for the given set of random numbers:
Mean = (0.937776 + 0.270012 + 0.243785 + 0.590701 + 0.824982 + 0.131805 + 0.879337 + 0.741998 + 0.254683 + 0.080259 + 0.419321 + 0.928220 + 0.958430 + 0.980182 + 0.263900 + 0.063119 + 0.762096 + 0.485612 + 0.662900 + 0.362242 + 0.724796 + 0.307736 + 0.305021 + 0.417052 + 0.054337 + 0.323357 + 0.069662 + 0.843387 + 0.353107 + 0.074262 + 0.735596 + 0.175095 + 0.390508 + 0.668932 + 0.029861 + 0.205228 + 0.387740 + 0.962169 + 0.646565 + 0.423914 + 0.754782 + 0.156719 + 0.773113 + 0.546335 + 0.323573 + 0.649740 + 0.214082 + 0.382383 + 0.383982 + 0.030539) / 50 = 0.477514
Therefore, the mean is 0.477514 (rounded to 6 decimal places).
Now we will calculate the standard deviation:
Standard deviation = sqrt[((0.937776 - 0.477514)^2 + (0.270012 - 0.477514)^2 + (0.243785 - 0.477514)^2 + ... + (0.382383 - 0.477514)^2 + (0.383982 - 0.477514)^2 + (0.030539 - 0.477514)^2) / 50] = 0.288919
Therefore, the standard deviation is 0.288919 (rounded to 6 decimal places).
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i Need Help with math whats 69*79/24*1
Answers
Answer:
it. would. be. an. irrational. number. but. 220.54166. if. you. want. it. rounded. it. would. be. 220.5
Step-by-step explanation:
13+t/17
A 13+t=17
B 13t+17
Find the value of t that makes the equation true.
t=
Answers
Answer:
the value of t that makes the equation true is 7x
A number cube is rolled. Event A is rolling an odd number, and event B is rolling a factor of 12. What is P(AU B)?
Answers
Explanation:
A = set of odd numbers = {1,3,5}
B = set of factors of 12 = {1,2,3,4,6}
A U B = union of set A and set B
A U B = {1,3,5} union {1,2,3,4,6}
A U B = {1,3,5, 1,2,3,4,6}
A U B = {1,2,3,4,5,6}
The set union operation combines two sets into one bigger set. Duplicates are tossed out.
There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.
Therefore, the probability event A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.
Side notes:
A U B can be read out as "event A or event B"; so P(A U B) is "the probability event A happens or B happens or both".A intersect B = {1,3} = values that are in both set A and set B at the same time. These are both odd and a factor of 12.