Therefore , the solution to the given problem of mean comes out to be the sample size yields the equivalent number of households is 30.
What is mean?Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the total number of values in the dataset by the total number of values in the dataset. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the numbers in a set of data and dividing the total by the total number of numbers.
Here,
Given:
Mean = 2
Four pets are two standard deviations away from the mean, and one standard deviation equals one pet.
We can determine that at least
100 (1-1k2)% = 100 (1-1/4)% = 75%
is within 2 standard deviations of the mean using Chebyshev's Rule with
k = 2.
The percentage times the sample size yields the equivalent number of households:
=> 75% x 40 = 30
Therefore , the solution to the given problem of mean comes out to be the sample size yields the equivalent number of households is 30.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Simplify the complex numbers using de Moivre's Theorem and match them with their solutions 2(3+1) 2. cos(20°) + sin(20°)] 2[ coo(4)+isin(7)]* (-1+i) -41 (1+1) -16 4+4731 Reset Next
The complex numbers are solved using De Moivre's Theorem and then are matched with their respective solutions.
What is De Moivre's Theorem?
De Moivre's formula, also known as the theorem and identity of de Moivre, says that for any real number x and integer n, holds -
(cos x + i sin x)^n=cos nx + i sin nx
where i is the imaginary unit (i^2 = 1).
Also, [r(cos x + i sin x)]^n = r^n(cos nx + i sin nx) or [r cis x]^n = [r^n cis nx].
The first complex number is (1+i)^5.
Solve using De Moivre's formula -
(1+i)^5 = [√2{(1/√2)+(i/√2)}^5]
=(√2)^5[cos(π/4)+i sin(π/4)]^5
=(√2)^5[cos(5π/4)+i sin(5π/4)]
=(√2)^5[(-1/√2)-(i/√2)]
=4(-1-i)
=-4-4i
The second complex number is (-1+i)^6.
Solve using De Moivre's formula -
(-1+i)^6=(1-i)^6
=[√2{(1/√2)-(i/√2)}^6]
=(√2)^6[cos(-π/4)+i sin(-π/4)]^6
=(√2)^6[cos(-6π/4)+i sin(-6π/4)]
=8(0+1i)
=8i
The third complex number is 2[cos(20)+i sin(20)]^3.
Solve using De Moivre's formula -
2[cos(20)+i sin(20)]^3=2^3[cos(60)+i sin(60)]
=8[(1/2)+{(√3)i/2}]
=4+4√3i
The last complex number is 2[cos(π/4)+i sin(π/4)]^4.
Solve using De Moivre's formula -
2[cos(π/4)+i sin(π/4)]^4=2^4[cos(4π/4)+i sin(4π/4)]
=16[cos(π)+i sin(π)]
=16(-1+i(0)]
=-16
Therefore, the complex numbers are solved using the theorem.
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CORRECT ANSWER WITH **STEPS** GETS BRAINLIEST
for the following questions, determine what values of x makes the rational expression equal to zero.
1. x+6 / x-4
2. (x+4)(x-2) / (x+6)
3. 2x+10 / 3x-12
thanks.
Answer:
see explanation
Step-by-step explanation:
if the denominator of a rational expression is zero then the expression will be undefined.
the numerator is the part of the rational expression that makes it zero.
solve the numerators in each to find values of x
1
[tex]\frac{x+6}{x-4}[/tex]
x + 6 = 0 ( subtract 6 from both sides )
x = - 6 ← value that makes expression equal to zero
2
[tex]\frac{(x+4)(x-2)}{x+6}[/tex]
(x + 4)(x - 2) = 0
equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 2 = 0 ⇒ x = 2
x = - 4 and x = 2 make the expression equal to zero
3
[tex]\frac{2x+10}{3x-12}[/tex]
2x + 10 = 0 ( subtract 10 from both sides )
2x = - 10 ( divide both sides by 2 )
x = - 5 ← value that makes expression equal to zero
Answer:
1) x = -6
2) x = -4 and x = 2
3) x = -5
Step-by-step explanation:
A rational expression is undefined when the denominator equals zero.
A rational expression equals zero when the numerator equals zero.
Question 1Given rational expression:
[tex]\dfrac{x+6}{x-4}[/tex]
Set the numerator to zero and solve for x:
[tex]\implies x+6=0[/tex]
[tex]\implies x=-6[/tex]
Question 2Given rational expression:
[tex]\dfrac{(x+4)(x-2)}{x+6}[/tex]
Set the numerator to zero:
[tex]\implies (x+4)(x-2)=0[/tex]
Apply the zero-product property and solve for x:
[tex]\implies x+4=0 \implies x=-4[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
Question 3Given rational expression:
[tex]\dfrac{2x+10}{3x-12}[/tex]
Factor the numerator and denominator:
[tex]\dfrac{2(x+5)}{3(x-4)}[/tex]
Set the numerator to zero and solve for x:
[tex]\implies 2(x+5)=0[/tex]
[tex]\implies x+5=0[/tex]
[tex]\implies x=-5[/tex]
3y2 + 4ab + 7y2 + ab
Answer:
Combine like terms:
10y2 + 5ab
Step-by-step explanation:
Is your simplified algebraic expression.
S2 Alg I Unit 3B Common Unit Assessment (MC&CR) / 5 of 11
If (x - 3)2 = 5, what vakies of x make the quadratic equation TRUE?
O A. 3+5
ОВ.
+
3
O C. -5+3
O D. -3 + 5
help! what is the missing length?
Answer:
Hello! answer: 30
Step-by-step explanation:
32 × 30 = 960 HOPE THAT HELPS!
please help and explain
Which represents the value of x?
Maksim was asked on a test "What is the domain of the function: f(x) = √(x - 2)? Explain." Maksim responded with "The function f(x) = √(x - 2) has a domain of all real numbers because any number can be put in for x." Explain if Maksim's answer and explanation were correct. Make sure to use at least two pieces of evidence to support your claim. If he is wrong, state the actual domain.
Answer:
Maksim's answer and explanation are not correct
The actual domain is 2 < x < Infinity
Step-by-step explanation:
The domain of a function is the set that is made up of the possible inputs of the function
The given function is f(x) = √(x - 2)
Maksim's response for the domain of f(x) is x ∈ R ('x' is a member of the set of all real numbers
The function is not defined when x < 2, at which the expression, x - 2, will become negative, and for which the square root of the negative number is imaginary
Therefore, the domain for which the function is defined is all real numbers larger than 2, which can be presented as follows;
The domain of f(x) = 2 < x < ∞
Therefore Maksim is wrong as the actual domain is limited to 2 < x < ∞.
How is the relationship between the formula for the volume of a cone and the formula for the volume of acylinder
The total number of books sold from 2010-2015 from
Amazon can be modeled by the function
3
2
f(x) = 40x + 8x + 14824x + 33000and the number of kinds
of books at Amazon from that same time period can be modeled
as g(x): =
10x + 22, where x is the number of years since
2010. What is the average number of each kind of book
Amazon sold?
Answer:
If you want to find out how many print copies the book is selling, just click the Paperback or Hardcover edition of the book on Amazon, scroll down to Product Details on that page, and find the Amazon Best Sellers Rank for the print edition.
Step-by-step explanation:
Se seleccionan un grupo de datos de 120 personas donde 40 tienen una estatura promedio de 1.70 y 50 tienen una estatura de 1.68 y 10 están entre las dos estaturas: encuentre la probabilidad de los faltantes estén en las estaturas.
what are u saying ????????/?
i can't read spanish
Jack invested some money in a bank at a fixed rate of interest compounded annually. The equation below shows the value of his investment after x years: f(x)
Equation = P(1+r)^x, where P is the initial amount invested, r is the fixed interest rate, and x is the number of years.
It is important to note that the equation provided is the formula for compound interest. P is the initial principal, r is the annual interest rate, and x is the number of years the money is invested. The equation gives the total amount of money in the account after x years.
It should be also noted that the interest rate is given as a decimal and not a percentage.
For example, if the interest rate is 5%, then r = 0.05.
In order to use this equation, the value of P, r and x should be known
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The linear function F is defined as f(x) = -2x + 3. Consider the graph of y = f(x) in the xy-Plane.
If the function g(x) = f (x) + k, where k = 2, describe the changes to the slope and y-intercept of this transformation.
The changes to the slope and to the intercept of the linear function after the transformation g(x) = f(x) + k, in which k = 2, are given as follows:
The slope remains constant.The intercept is increased by two.What is the definition of a linear function?The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope.b is the y-intercept.The function f(x) in this problem is given as follows:
f(x) = -2x + 3.
Meaning that it has a slope of -2 and and intercept of 3.
The function g(x) is defined as follows:
g(x) = f(x) + k.
Since k = 2, we have that:
g(x) = f(x) + 2
g(x) = -2x + 3 + 2
g(x) = -2x + 5.
Hence the slope and the intercept are given as follows:
Slope of -2, which is the same as f(x).Intercept of 5, which is an increase of 2 compared to the intercept of f(x).More can be learned about linear functions at https://brainly.com/question/24808124
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Shondra borrowed $200 for the books she needed for her second semester of college. The finance charge on the loan was $12, and the term of the loan was 21 days. What was the APR of Shondra's loan?
Answer:
the Annual percentage rate of shondra loan is 104.28%
Step-by-step explanation:
Given that
The borrowed amount is $200
The finance charge is $12
And, the term of the loan is 21 days
We need to find out the APR of the loan
so,
= (($12 ÷ $200) × 365) ÷ 21 × 100
= 104.28%
hence, the Annual percentage rate of shondra loan is 104.28%
If total employee benefits are calculated as a percentage of their gross pay, which of the following employees receives the largest percentage of their gross pay in employee benefits?
Answer: the answer is the option
Employee B: gross pay $32,900, total job benefits $34,000
hope this helped you
028)
the cost to insure jewellery is a fixed amount plus a percentage of the value of the jewellery. it costs 32$ to insure 1000$ worth of jewellery or 44.5$ to insure 3500$ worth of jewellry.what is the fixed amount to insure jewellery?
i wrote jewellery so much it isnt a word anymore send help ( explanatio ) asap!
Answer:
The fixed cost to insure jewellery is $0.602.
Step-by-step explanation:
We can use the information provided to set up a system of two equations in two variables, and then use the system to solve for the fixed cost of insuring the jewellery. Let x be the fixed cost and y be the percentage of the value of the jewellery. Then we can write the following two equations:
1000x + 1000y = 32 (1) (cost equation for insuring $1000 worth of jewellery)
3500x + 3500y = 44.5 (2) (cost equation for insuring $3500 worth of jewellery)
We can use either of these equation to solve for the fixed cost(x), to do that we can first solve for y from either of the equation, and then substitute it in other equation.
From equation (1)
y = (32 - 1000x) / 1000
then substitute this in equation (2)
3500x + 3500((32-1000x) / 1000) = 44.5
3500x + 32 - 3500x =44.5 - (1000x)
-20x = -12.05
x = 0.602 $
So, the fixed cost to insure jewellery is $0.602.
That means you have to pay $0.602 as a fixed cost, in addition to 0.01(y) as a percentage of the value of jewellery to insure it.
What is the difference?
X/x^2-16 - 3/x-4
Answer:
B
Step-by-step explanation:
From a group of 5 counselors and 8 teachers, 3 counselors and 2 teachers will be selected to attend a conference. In how many ways can the selection be made?
A.
38
B.
3360
C.
280
D.
240
Sugar cookies make up 38% of all sales for a local baker's cookie sales. If the baker sold 133 sugar cookies, how many total cookies did the baker sell?
The total number of cookies baker sold in all are 350 cookies.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, sugar cookies make up 38% of all sales for a local baker's cookie sales.
Let the total number of cookies be x.
Now, 38% of x=133
38/100 ×x=133
x=13300/38
x=350
Therefore, the total number of cookies baker sold in all are 350 cookies.
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(2×/×+3)- (×/×-3)=(3÷3-×)
Answer:
x = 6
Step-by-step explanation:
(2×/×+3)- (×/×-3)=(3÷3-×)
2x/x+3-x/x+3= 1-x
2 + 3 - 1 + 3 - 1 = x
8-2 = x
x = 6
Select the interval where f is negative.
Answer: A
Step-by-step explanation:
Based on the graph, we know that it is negative if it is under the x-axis. It is also indicated by the negative labels.
A: correct
Looking at choice A, it says the interval is from -4<x<-2. This means we have to find x=-4 and x=-2. On the graph, that interval is below the x-axis, so it is negative.
B: incorrect
Looking at choice B, it says the interval is from -1<x<1. This means we have to find x=-1 and x=1. On the graph, that interval is above the x-axis, so it is positive, not negative.
C: incorrect
Looking at choice C, it says the interval is from 2<x<4. This means we have to find x=2 and x=4. On the graph, that interval is above the x-axis, so it is positive, not negative.
Therefore, A is the correct answer.
22 - {[(87 - 32) divided by 5] × 2}
22 − ( ( ( 87 − 32 ) ÷ 5 ) × 2 )
Simplify each term.
22 − 22
Subtract 22 from 22 .
= 0
What is m
A- 28
B- 31
C- 62
D- 90
E- 118
Answer:
D. 90
Step-by-step explanation:
If a triangle is inscribed inside of a circle, using the diameter as the hypotenuse, then the opposite angle of the hypotenuse is equal to 90 °
Because ΔABC is inscribed inside of the circle using the diameter it is a right triangle.
∠ABC is the angle opposite of the diameter therefore ∠ABC = 90°
I need help with this geometry!
Answer:
[tex]7.8(sin23^o)[/tex]
Step-by-step explanation:
[tex]Sin23=\frac{opp}{hyp}[/tex]
[tex]Sin23=\frac{BC}{7.8}[/tex]
[tex]0.3907=\frac{BC}{7.8}[/tex]
[tex]BC=3.04746[/tex]
----------------------
hope it helps...
have a great day!!
What is an equivalent expression example?
A given set of expressions are known as equivalent expression if and only if the result after evaluating those expression is the same number.
Example,
3 + 2 = 5
4 + 1 = 5
5 + 0 = 5
These three are equivalent as because the sum of all of them is same , i.e., 5.
An equivalent expression is an expression which consists of variables, coefficients, constants, and mathematical functions such as addition, subtraction, multiplication, and division.
In general, if two objects are identical, they are then called as identical.
These expressions are also known as duplicates of each other though they look different but they are same.
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What are the 3 types of translations in math?
NEED HELP ASAP DUE SOON!!!! This scatter plot shows the relationship between the amount of time, in hours, spent working on an essay and the grade, as a percent, earned.
Enter the approximate slope of the estimated line of best fit.
Answer:
5 % per hour
Step-by-step explanation:
Pick two of the grid points the line seems to go through. I'm using (0, 50) and (4, 70).
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{70-50}{4-0}=\frac{20}{4}=5[/tex]
please help me again thank you
Answer:
The answer is 28.26 hope that helps
A group consisting of 14 aggressive zombies quadruples in size every hour. Which equation matches the number of zombies after 6 hours?
The exponential equation that matches the number of zombies after 6 hours is the possible option;
Z = 14 × 4⁶
What is an exponential equation?An exponential equation is one in which the argument is an index or power of a constant.
The initial number in the group of zombies = 14
The amount by which the group increases every hour = The group quadruples every hour
The required equation; The equation that matches the number of zombies after 6 hours
The information in the question indicates that the sequence is a exponential, which can be presented using the following equation;
Z = a·rⁿ
Where;
Z = The number of zombies after n hours
a = The first term = The initial number of zombies in the group = 14
r = The common ratio = The amount that multiplies members of the group every hour = 4
n = The number of hours after which the number in the group is evaluated
Therefore, after 6 hours, n = 6, and we get;
a₆ = 14 × 4⁶ = 14 × 4⁵ = 14336
The equation from the possible options, obtained from a similar question posted online, that matches the number of zombies after 6 hours is therefore;
Z = 14 × 4⁶
The possible options are;
Z = 4·(14)⁶
Z = 4·(1 + 14)⁶
Z = 14·(1 + 4)⁶
Z = 14·(4)⁶
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Algebra: PLEASES QUICK DUE SOON!!!
In Completing the Square problems, what formula do you use to find c?
Answer:
Solve the equation
x2−(3+1)x+3=0
by the method of completing the square. i dont know if its right
Step-by-step explanation:
Consider the equation -5+10x+3=5x+6. How many solutions are there?
One
None
Infinitely many