The number of subsets formed is 67,108,864.
What is defined as the subsets?Set 1 is said to be a subset of set 2 if all of its elements are present in it. A set is a clearly defined group of numbers, alphabets, items, or any other items.
If set 1 = A,B,C and set 2 = A,B,C,D,E,F, then set 1 is a subset of set 2 because all of the elements in set 1 are also present in set 2.A subset is a subset of a larger set (another set or the same set). To symbolize a set A as a subset of a larger set B, use the set notation: A ⊆ B.The number of subsets of an n-element set is 2ⁿ.
As a result, the formula for determining the number of subsets of the a set with 'n' components is 2ⁿ.
For the given question;
A={x:x is letters of the alphabet}
Thus, the n = 26 (total letter is English alphabet).
Total subsets = 2ⁿ
Total subsets = 2²⁶ = 67,108,864.
Therefore, the total number of subsets formed by the English alphabet are 2²⁶ = 67,108,864.
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The area of a certain desert (Desert 1) is eight times the area of another desert (Desert 2). If the sum of their areas is
27,000,000 square miles, find the area of each desert.
What is the area of Desert 1?
Answer:
1687500
Step-by-step explanation:
If their sum is 27,000,000 then their are millions of ways to find this answer. like one can be 13500000. But that answer is obviously incorrect. If you divide that by 8, your answer will be 1687500.
x[tex]x/y+y/x/x/y-y/x[/tex]
Answer: 1
Step-by-step explanation:
here only taking the power of x in account
we have
[tex]\frac{x}{y} + \frac{y}{x}-\frac{x}{y} - \frac{y}{x}[/tex]
=0
since [tex]x^{0}[/tex] =1
so solution is 1
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A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0: μ = 12 against H1: μ < 12, using a random sample of four specimens. (a) What is the type I error probability if the critical region is defined as x < 11.5 kilograms? (b) Find β for the case in which the true mean elongation is 11.25 kilograms. (c) Find β for the case in which the true mean is 11.5 kilograms.
The Type I error's computed value is 0.02275 and The Type II error has a computed value of 0.50 based on probability.
What is probability?
The potential or opportunity of an event happening is known as probability. The probability is equal to the variety of possible outcomes. the estimated number of outcomes that could occur.(a) Type I error probability if the critical region is defined as x < 11.5 kilograms
[tex]P(Type\ Error)=P\ xbar < 11.5\ when\ mu=12)\\\\[/tex]
[tex]=P(Z < \frac{11.5-12}{\frac{0.5}{\sqrt{4} } } )\\\\=P(Z < -2)\\\\=0.02275[/tex]
The Type I error's computed value is 0.02275.
Observe that there is a 2.275% likelihood of dismissing the null hypothesis if it is true based on the Type I error probability.
(b) β for the case in which the true mean elongation is 11.25 kilograms.
[tex]b= P(Type II Error)\\\\=P(xbar\geq 11.5\ when\ mu_1\ =11.25)[/tex]
[tex]=P(Z \geq \frac{11.5-12}{\frac{0.5}{\sqrt{4} } } )\\\\=P(Z \geq 1)\\\\= 1-P(Z < 1)\\\\=1-0.8413\\\\=0.1587[/tex]
The Type II error's computed value is 0.1587.
Observe that there is a 15.87% possibility of refusing to disprove the null hypothesis when it is untrue based on the Type II error probability.
(c) β for the case in which the true mean is 11.5 kilograms.
[tex]b= P(Type II Error)\\\\=P(xbar\geq 11.5\ when\ mu_1\ =11.25)[/tex]
[tex]=P(Z \geq \frac{11.5-11.5}{\frac{0.5}{\sqrt{4} } } )\\\\=P(Z \geq 0)\\\\= 1-P(Z < 0)\\\\=1-0.50\\\\=0.50[/tex]
The Type II error has a computed value of 0.50.
Observe that there is a 50% possibility of neglecting to disprove the null hypothesis when it is untrue based on the Type II error probability.
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can someone help me please
Answer:
A(-9/2, 0)B(1, 0)C(0, -9)Step-by-step explanation:
Given the quadratic equation y = 2x² +7x -9, you want the coordinates of the x- and y-intercepts.
X-interceptsThe values of x where y=0 can be found by factoring the equation.
y = (2x +9)(2x -2)/2 = (2x +9)(x -1)
The constants 9 and -2 in the binomial terms are factors of the product of leading and trailing coefficients (2)(-9) = -18. Those factors are chosen because their sum is 7, the middle coefficient.
The x-intercepts are the values of x that make these factors zero:
2x +9 = 0 ⇒ x = -9/2
x -1 = 0 ⇒ x = 1
Points A and B are ...
A(-9/2, 0)B(1, 0)Y-interceptThe y-value at point C is where x=0. It is the constant in the quadratic equation.
y = 2(0²) +7(0) -9 = -9
Point C is ...
C(0, -9)Please help, This is urgent 7th-grade math.
There was 2/3 of a pan of lasagna in the refrigerator. Bill and his friends ate half of what was left. Write a number sentence and draw a model to represent the problem. How much of the pan did they eat?
Explanations/Answers, please!
4(x + 2)-2=6x-21-4+x)
Answer:
3.5 or [tex]\frac{7}2}[/tex]
Step-by-step explanation:
4(x+2)-2=6x-2(4+x)
4x + 8 - 2 = 6x - 8 + 2x
4x + 6 = 8x - 8
14 = 4x
x = 3.5 or [tex]\frac{7}2}[/tex]
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Given the function that g(x) = 2x² − 5x + 1, find each of the following.
-
a) g(0)
b) g(-2)
c) g(4)
d) g(-x)
e) g(1 – t)
Step-by-step explanation:
g(x) = 2x² − 5x + 1
a) g(0)
g(0)=2[tex](0)^{2}[/tex]-5(0)+1
=1
b) g(-2)
g(2)=2[tex](-2)^{2}[/tex]-5(-2)+1
=8+10+1
=19
c) g(4)
g(4)=2[tex](4)^{2}[/tex]-5(4)+1
=32-20+1
=11
d) g(-x)
g(x) = 2x² − 5x + 1
g(-x)=2[tex](-x)^{2}[/tex]-5(-x)+1
=2[tex]x^{2}[/tex]+5x+1
e) g(1 – t)
g(x) = 2x² − 5x + 1
g(1-t)=2[tex](1-t)^{2}[/tex]-5(1-t)+1
=2[tex]t^{2}[/tex]+t-2
A=bh;A=5,h=5
HELP ME
Answer:
b = 1
Step-by-step explanation:
5 = 5b
b = 1
evaluate 2pq - r for p = 3, q = 2 and r = 5
Answer:
7
Step-by-step explanation:
[tex]2 \times p \times q - r\\= 2 \times 3 \times 2 - 5\\= 2 \times 3\\= 6\\= 6 \times 2\\= 12\\= 12 - 5\\= 7[/tex]
Sue has a 8 cups of flour and needs to fill it equally in containers that hold 3/4 of a cup each. How many containers can she fill?
She will need 11 containers.
How to calculate the fraction?From the information, Sue has a 8 cups of flour and needs to fill it equally in containers that hold 3/4 of a cup each.
The containers needed will be:
= 8 ÷ 3/4
= 8 × 4/3
= 32/3
= 11
He will need 11 containers.
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HELP ASAP PLEASE!! FIND THE DOMAIN AND RANGE OF THJS GRAPH
The range is all the y-value or outputs of a function. In the case of a horizontal line, this is only one value.
The range is the y-intercept, -5.
The domain is all x-values or inputs of a function. For this graph, it is all real numbers (as you said).
The domain is all real numbers.
Select the action you would use to solve x-4=16 then select property that justifies the action
The value of x is 64 and the property that justifies that action is the multiplication property of equality.
What is an expression?
It is defined as the combination of constants and variables with mathematical operators.
Mathematical statements are called expressions if they contain at least two terms that are connected by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
As an illustration, the expression x + y is one where x and y are terms with an addition operator in between. There are two types of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.
We have an expression:
x/4 = 16
Apply Multiplication property of equality:
Multiply by 4 on both sides:
(x/4)4 = 16×4
x = 64
Thus, the value of x is 64 and the property that justifies that action is the multiplication property of equality option (1) is correct.
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55) Lenny has $3.69 in pennies,
dimes, and quarters. The number
of pennies is three more than
the number of dimes. The number
of quarters is twice the number
of dimes. How many each coin does
he
have?
Answer:
For each coin he has 6 dimes, 12 quarters, and 9 pennies.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify using order of operations. Show all of your work and do ONE operation at a time to receive all possible points. 90 ÷ [ 10 + ( 3 2 − 4 ) ]
2.368
Given expression is
90 ÷ [ 10 + ( 3 2 − 4 ) ]
According to BODMAS rule we simplify this expression
The order of operations consist of evaluate the parenthesis, then the exponents, the multiplication, the division, and as last the addition and subtraction.
90 ÷ [ 10 + ( 3 2 − 4 ) ]= 90 ÷ [ 10 + 28 ]
= 90 ÷ [ 38]
= 90 ÷38
= 2.368
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33. How many 3-cup servings are in 4 cups? A. 2 B. 3 C. C. 4 D. 12
K
Pedro has scores of 85, 84, 69, and 82 after four tests. What score must he make on his fifth test to have an average of 79 or greater?
The score that Pedro needs on his fifth test to get an average of at least 79 is
(Round to the nearest integer as needed.)
Answer: x > 75
Step-by-step explanation:
(85+84+69+82+x)/5 > 79
85+84+69+82+x > 395
x > 75
Which number has a 4 that is 10 times greater than the 4 in 542?
A. 5,420
B. 54.2
C. 5.42
D. 0.542
Answer:
A. 5,420
Step-by-step explanation:
4 in 542 is in the tens place and 4 in 5,420 is in the hundreds.
The number A. 5420 has a 4 that is 10 times greater than the 4 in 542.
What is the standard decimal form of numbers?The standard decimal form of numbers is written in base 10 as there are 10 different numbers from 0 to 9.
Each digit has a face value and a place value.
The expanded form of 542 is 5×100 + 4×10 + 4.
So, 10 times greater than it should be a multiple of 100 or a digit in the hundreds place.
From the given options the number 5420 in the expanded form is,
5×1000 + 4×100 + 2×10 + 0.
So, The number 5420 has a 4 that is 10 times greater than the 4 in 542.
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Use the diagram to find the measures of the lengths of the
sides. The perimeter of the trapezoid on the right is 67
inches.
The length of all four sides of the Isoclesles Trapezium is 67 inches.
What is an area of a Trapezium?Area of a Trapezium is (1/2)(a+b)h.Where and b are the parallel sides of the trapezium and h is the distance between the two parallel side
We know that for a plane 2D figure perimeter is the sum of the lengths of all the sides.
Given an isosceles Trapezium with a perimeter of 67 inches,
As the sides are given in variables we can equate the sum of all the sides with the given perimeter and obtain the value of x.
∴ (x + 1.5x + 2.5x - 5 + x) = 67.
6x = 67 + 5.
6x = 72.
x = 12.
So, the measure of lengths of four sides are [ 12 + 1.5(12) + 2.5(12) - 5 + 12) which is ( 12 + 18 + 30 - 5 + 12 ) = 67 inches.
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Some one pls help me will give Brainly
Answer:
100 miles
Step-by-step explanation:
We need to read the graph to determine the answer.
The input is 10 hours
Using the x, go up until you hit the red line and read the y value
The y value is 100 miles
A cone has a volume of 9 pi in cubed and a diameter of 6 in . Wilson states that a cylinder
Answer:
ok then what's the correct answer?
Step-by-step explanation:
Simplify: 2.4 × 10-4
The four is a exponent
Answer: 20
Step-by-step explanation:
Multiply 2.4*10-4
Calculate 24-4
the answer is (12x^10000)/5
What number can be divided into 2 equal groups without a remainder?
Answer:
Step-by-step explanation:
When we divide one number by another and there is no remainder, the divisor A the quotient are the of the first number.
8/2=4
There are 20 flowers in a bouquet, and 2 of them are roses. What percent of the flowers are roses?
Answer: 10%
Step-by-step explanation:
Larry put $1,287 into a savings account 8 years ago. • The account earned 4% simple annual interest. • He made no additional deposits or withdrawals. Based on this information, what is the balance in dollars and cents in Larry's savings account at the end of these 8 years? Record your answer in the boxes below. Be sure to use the correct place value.
The balance in Larry's savings account at the end of these 8 years is 1698 dollars and 84 cents
What is the balance in dollars and cents in Larry's savings account at the end of these 8 yearsThe given parameters are
Principal, P = 1287
Rate, R= 4%
Time, T = 8
The balance in dollars and cents in Larry's savings account at the end of these 8 years
Balance = P * PRT
This gives
Balance = 1287 + 1287 * 4% * 8
Evaluate
Balance = 1698.84
Hence, the balance in Larry's savings account at the end of these 8 years is 1698 dollars and 84 cents
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Suppose that the functions r and s are defined for all real numbers x as follows.
r(x)=x-2
s(x)=3x+6
Write the expressions for (r+s) (x) and (r-s)(x) and evaluate (r·s)(−1).
(r+s)(x) =
(r-s)(x) =
(r.s) (-1) =
Assume that the following definitions of the functions r and s apply to all real numbers x. r(x)=x-2s(x)=3x+6 Evaluate (rs)(1) and write the equations for (r+s)(x) and (r-s)(x). r+s(x) = r-s(x) = r.s(-1) =
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
The types of functions can be broadly classified into four types. Based on Element: One to one Function, many to one function, onto function, one to one and onto function, into function.
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A passbook savings account has a rate of 10%. Find the effective annual yield, rounded to the nearest tenth of a percent, if the interest is compounded monthly.
Effective Annual Yield : 10.5%
Effective Annual Yield
In the case of monthly there are 12 months in a year. Therefore, making n=12. So, the effective annual yield if the interest 10% is compounded monthly is given as r=10, n=12;
[tex]Y= (1 +\frac{r}{n}) ^{n}-1 = (1 +\frac{0.1}{12}) ^{12}-1\\ =(1 +0.00833) ^{12}-1\\ =(1.00833) ^{12}-1\\ = 1.10466 -1\\ = 0.10466[/tex]
But, this is decimal form, to convert it to the percentage form we have to multiply the decimal form by 100 and finally, place "%" after the last digit of the number. That is,
Y= 0.10466× 100%
Y=10.46% or 10.5%
Effective Annual Yield : 10.5%
6) Four pieces measuring 29.cm, 19.62cm, 32.49cm and 24.74cm are cut from a board that is 200cm long. Allowing 1cm for waste in cutting, what is the length of the remaining piece?
The Remaining length of the cardboard piece is 94.15 cm.
According to the statement
We have to find that the length of the remaining piece.
So, For this purpose, we know that the
Length is defined as the measurement or extent of something from end to end.
From the given information:
Four pieces measuring 29.cm, 19.62cm, 32.49cm and 24.74cm are cut from a board that is 200cm long.
Then
Total length of the four pieces become:
Four pieces length = 29+19.62+ 32.49 + 24.74
Four pieces length = 105.85 cm
Then the
Remaining length of the cardboard piece = total length - length of the four pieces.
Remaining length of the cardboard piece = 200 - 105.85
Remaining length of the cardboard piece = 94.15cm.
So, The Remaining length of the cardboard piece is 94.15 cm.
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Completa la tabla.
Número - opuesto - valor - absoluto
-5
10
-56
34
La tabla completa es:
Numero opuesto valor absoluto.
-5 5 5
10 -10 10
-56 56 56
34 -34 34
¿Como completar la tabla?
En este caso tenemos la tabla:
Numero opuesto valor absoluto.
-5
10
-56
34
Para completar la tabla debemos encontrar los opuestos de esos numeros, el opuesto de cualquier numero real es un número con el mismo valor absoluto pero distinto signo, entonces podemos completar la tabla:
Numero opuesto valor absoluto.
-5 5
10 -10
-56 56
34 -34
Ahora debemos encontrar los valores absolutos, eso es el mismo número pero en forma positiva, completando eso obtendremos:
Numero opuesto valor absoluto.
-5 5 5
10 -10 10
-56 56 56
34 -34 34
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3x+4=2x+8 solve linear equation
Answer:
3x±4=2x±8
3x-2x=8-4
x=4
Step-by-step explanation:
Hope its helpful for you
Find all points having a -coordinate of whose
distance from the point is .
The points which are a distance of 13 units from (12,5) are (0,0)and (24,0).
The distance between two point with co-ordinates ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) is calculated by the distance formula [tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
All points on the x-axis have their y-coordinates equal to 0. So let the point (a,0) be a point on the x-axis such that the distance from (12,5) to (a,0) is 13 units.
Let us substitute the values into the distance formula to calculate the values of a so that we can find the two points.
[tex]13=\sqrt{(12-a)^2+(5-0)^2}[/tex]
Squaring both sides we get:
[tex]or,13^2=144-24a+a^2+25\\or,169-144-25-24a+a^2\\or,a^2-24a=0\\or,a(a-24)=0[/tex]
Now either a=0 or (a-24)=0
Therefore either a=0 or a=24.
Therefore the two points (0,0) and (24,0) .
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