Answer:
[tex]49x^{6}[/tex][tex]y^{8}[/tex]
Step-by-step explanation:
1. Factor 2401 into its prime factors
2401 = 74
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
2401 = 74
No factors remain inside the root!!
To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
49 = 72
At the end of this step the partly simplified SQRT looks like this:
49√(x^12y^16)
2. Rules for simplifying variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) √(x8)=x4
(3.2) √(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
(4.1) √(x5)=x2•√(x)
(4.2) √(x-7)=x-3•√(x-1)
Applying these rules to our case we find out that
SQRT(x12y16) = x6y8
Combine both simplifications:
sqrt (2401x12y16) =
49x6y8
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In the figure to the right, it AC=22 and BC=19, what is the radius?
Triangle A'B'C' is a reflection of triangle ABC across line l. Select all statements that must be true.
A Line l bisects segment AB.
B Line l bisects segment CC’.
C Angle ABC is 60 degrees.
D Line BB’ is perpendicular to line l.
E Angle ABC is congruent to angle A’ B’ C’.
F Triangles ABC and A’ B’ C’ are congruent.
G Segment BC is congruent to segment B’ C’.
H The distance from point A to line l is the same as the distance from point A’ to line l.
Answer:
A, B, D, E, F, G, H
Step-by-step explanation:
If triangle A'B'C' is a reflection of triangle ABC across line l, the following statements must be true:
A. Line l bisects segment AB.
B. Line l bisects segment CC’.
D. Line BB’ is perpendicular to line l.
E. Angle ABC is congruent to angle A’ B’ C’.
F. Triangles ABC and A’ B’ C’ are congruent.
G. Segment BC is congruent to segment B’ C’.
H. The distance from point A to line l is the same as the distance from point A’ to line l.
Statements C and H are not necessarily true. The angle ABC may not be 60 degrees, and the distance from point A to line l may not be the same as the distance from point A’ to line l.
10 students have volunteered for a committee. 7 of them are seniors and 3 of them are juniors. 1) how many ways are there to select a committee of 8 students? 10!/(8!2) 2) how many ways are there to select a committee with 3 seniors and 5 juniors? 7!/(3!/4!)*(3!/(5!/(2)!)) 3) suppose the committee must have 8 students (either juniors or seniors) and that one of the 8 must be selected as chair. how many ways are there to make the selection?
(a) The number of ways of selecting a committee of 8 students = 45.
(b) The number of ways to select a committee with 3 seniors and 2 juniors are 105.
(c) The number of ways to select a committee having 8 students (either juniors or seniors) and that one of the 8 must be selected as chair = 360 ways
What is combination?
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Given that 10 students have volunteered for a committee. 7 of them are seniors and 3 are juniors.
a) Need to find the number of ways of selecting a committee of 8 students
The number of ways of selecting a committee of 8 students = [tex]10_C_8[/tex]
[tex]10C_8= \frac{10!}{8!(10-8)!}= \frac{10!}{8!(2!)}=45[/tex]
The number of ways of selecting a committee of 8 students = 45.
(b) Need to find the number of ways to select a committee with 3 seniors and 2 juniors
The number of ways to select a committee with 3 seniors and 2 juniors
= [tex]7_C_3(3_C_2)[/tex]
[tex]7_C_3*3_C_2 = \frac{7!}{3!*4!} *\frac{3!}{2!*1!} = 35 * 3 = 105[/tex]
The number of ways to select a committee with 3 seniors and 2 juniors are 105.
(c) Need to find the ways to make the select the committee must have 8 students (either juniors or seniors) and that one of the 8 must be selected as chair.
Number of ways = [tex]10_C_8*8_C_1[/tex]
[tex]10_C_8*8_C_1 = \frac{10!}{8!*2!} *\frac{8!}{7!*1!} = 45*8 = 360[/tex]
The number of ways to select a committee having 8 students (either juniors or seniors) and that one of the five must be selected as chair = 360 ways.
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a child finds a stack of old magazines in the basement and picks one out at random. find the probability that the magazine is a sports magazine if the pile consists of 25 sports magazines, 11 news magazines, and 2 travel magazines. (round your answer to three decimal places.)
The probability of the magazine is a sports magazine is 0.065.
What do you mean by probability?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
According to data in the given question,
We have the given information:
The number of sports magazines = 25
The number of news magazines = 11
The number of travel magazines = 2
Now, we will calculate the probability of the magazine is a sports magazine,
Total number of magazine = 25+11+2 = 38
To find the probability that the random selected magazine is a sports magazine divide the amount of sports magazines by the total amount of magazines:
P( sports magazine ) = Number of sports magazine/Total number of magazine
[tex]=\frac{25}{38}\\ =0.065[/tex]
Therefore, the required probability is 0.065.
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10. The bottom of a 23-foot straight ladder is set into the ground 7 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach? Show your work. Round your answer to the nearest tenth.
Answer:
4√130 or just √480
Step-by-step explanation:
You set up each number for pythagorean theorem as a squared plus b squared equals c squared. Then you solve for b squared and simplify into radical form, or...
your answer is 21.9
Select the correct answer from each drop-down menu. Find the average rate of change of the function f(x), represented by the graph, over the interval [-4, -1]. Average rate of change plotted on coordinate plane linear graph. A solid boundary line intersects X-axis at unit minus 2.5 and Y-axis at unit 5. The Y-value for x= minus 1 is 3 and for x= minus 4 is minus 3. Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula . The value of f(-1) is . The value of f(-4) is . The average rate of change of f(x) over the interval [-4, -1] is .
The average rate of change of f(x) over the interval [-4, -1], with coordinates, (-4, -3) and (-1, 3) is 2
How can the average rate of a function over an interval be found?The average rate of change of a function over an interval is found from the change in the output values of the function over the period indicated, divided by the change in the input values of the function over the specified interval.
Average rate of change = [tex]\dfrac{\Delta y}{\Delta x}[/tex]
The interval over which the average rate of change of the function is required = [-4, -1]
The formula for the average rate of change over the interval, [-4, -1], can be presented as follows;
Average rate of change = [tex]\dfrac{\Delta y}{\Delta x}[/tex] = [tex]\dfrac{f(-1) - f(-4)}{\left(-1 - (-4)\right)}[/tex]
The coordinates of the points of the graph of the function in the indicated range are; (-1, 3), and (-4, -3)
f(-1) = 3, f(-4) = -3, therefore;
Average rate of change = [tex]\dfrac{3 - (-3)}{-1 - (-4)}[/tex] = 2
The average rate of the function over the specified interval is 2
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explain how you could use a regression model to estimate the wage gender gap using the data on earnings of men and women. what are the dependent and independent variables?
A regression model could be used to estimate the wage gender gap by comparing the earnings of men and women.
Regression is a statistical technique used in the fields of finance, investing, and other areas that aims to assess the nature and strength of the relationship between one dependent variable and another. In this case, the dependent variable would be the gender gap in wages and the independent variable would be the earnings of men and women. The regression model would be used to calculate the difference between the two variables, which would indicate the wage gender gap.
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how many ways are there to seat n couples around a circular table such that no couple sits next to each other?
2n(n−1)! ways n couples around a circular table such that no couple sits next to each other.
What is combination?
The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant."Combining these two words indicates "Selection of things," where the order of the items is irrelevant.Depends on how you consider two ways as different ways.
If the seats are in fixed positions, then there are two possible seatings as the couple can swap with each other. In this case, choose a seat as reference. Swapping is available in each couple or between couples, on seat 0 and 2N sit one couple or different couples. So the answer is 2n+1n!If you consider seats as all same, pick a couple as reference. Still, husband can sit either on clockwise of his wife or counterclockwise. The remaining n−1 couples can choose their seats at will. In this case the answer is 2n(n−1)! when n>1. When n=1 there’s only 1 since the relative position becomes unimportant in this case.In case you still feel confused, take 2 for example. We have plan AaBb, AabB, aABb and aAbB
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There are 1,200 bacteria in a lab dish. The population decreases 10% per day. Calculate the average rate of change in the decrease in population for days 1 to 3 with the decrease for days 4 to 6.
The population decreases more quickly from day 1 to day 3 than from day 4 to day 6.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The total number of bacteria in lab dish is 1200
The population decreases 10% per day
In first day:
10/100×1200=120
120 bacteria decreased in lab
1200-120=1080
In second day:
0.1×1080=108
1080-108=972
In third day
0.1×972=97.2
972-97.2=874.8
In fourth day
0.1×874.8=87.48
874.8-87.48=787.32
In fifth day
0.1×787.32=78.732
787.32-78.732
708.588
The population decreases more quickly from day 1 to day 3 than from day 4 to day 6.
Hence, the population decreases more quickly from day 1 to day 3 than from day 4 to day 6.
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A swimming pool is on sale for $875.50. If the sale price is discounted 15% from the original price, what was the original price?
The original price of the swimming pool is $1030.
How to calculate the value?From the information, the swimming pool is on sale for $875.50 and the sale price is discounted 15% from the original price.
Let the original price be x.
This will be illustrated as:
(x - 15% × x) = 875.50
x - 0.15x = 875.50
0.85x = 875.50
Divide
x = 875.50 / 0.85
x = 1030
The original price is $1030.
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Simplify the rational expression. State any excluded values. x^2-64/16x-2x^2
Answer:
The answer is -x^2-4x
Step-by-step explanation:
how much does each apple cost?
Apples
4 for $2
Find the volume of a right circular cone that ha a height of 16. 4 in and a bae with a radiu of 20 in
Answer: V=πr2h
3
Step-by-step explanation: Your spelling is a bit off
△abc is similar to △lmn. also, angle b measures 35° and angle c measures 95°. what is the measure of angle l? enter your answer in the box. the measure of angle l = °
The measure of the angle I= is 50 degree
What is an example of geometry?A triangle has three sides and a total interior angle of 180 degrees. Four-sided shapes like a square, rectangle, or quadrilateral have a total interior angle of 360 degrees. Other polygons have different angles and different numbers of sides, such as the pentagon, hexagon, heptagon, and octagon.
Is geometry easier than algebra?Compared to algebra, geometry requires less math, and the math that is needed is simpler. Geometry, on the other hand, necessitates the memorization of numerous rules and formulas, which for some students can be more challenging than fundamental algebra. Ask your teacher for assistance if you need it in a math class.
The ratio of the respective sides is proportional when two triangles are comparable to one another.
Additionally, the corresponding angles coincide.
Given in this case are B= 35° and C= 95°
the angle sum property now
A + B + C = 180°
A + 35 + 95 = 180
A + 130 = 180
130 is subtracted from both sides, giving us
A = 180 - 130
A = 50°.
Now
ABC and LMN
Consequently, in terms of similarity
A = L
But A = 50°.
Thus, L = 50°.
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you have a box with a square base and no top. the surface area of the box is 220 ????????????????2. find the maximum volume.
The required maximum volume of the box would be 85184 cube units.
The surface area of a box is the total area of all of the box's faces. For a box with a square base and no top, the surface area is equal to the sum of the areas of the four sides and the bottom.
To find the maximum volume of such a box, we can first find the length of one side of the square base. We can do this by dividing the given surface area by the number of sides of the box.
In this case, the box has 4 sides plus the bottom, so the length of one side is 220 / 5 = 44.
We can now use the length of one side to find the maximum volume of the box. The volume of a box with a square base and no top is equal to the length of one side cubed.
The length of one side is 44, so the maximum volume of the box is :
⇒ 44 × 44 × 44 = 85184.
Therefore, the maximum volume of the box is 85184 cube units.
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Given: < 2. Choose the solution set. {x | x < 10/11} {x | x > 10/11} {x | x > 22/5} {x | x < 22/5}.
The solution set is {x | x < [tex]\frac{22}{5}[/tex]}.of the given evaluation.
What is a Solution Set?
The solution set of an equation is, however defined as the set of all solutions that satisfy the equation and since that set has no members the solution set is empty.
Given: [tex]\frac{5x}{11}[/tex][tex]< 2[/tex]
= [tex]5x < 22[/tex]
= [tex]x < \frac{22}{5}[/tex]
Hence, the correct solution set is {x | x < [tex]\frac{22}{5}[/tex]}.
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Evaluate each general power function at the indicated values.
1.
f(x) = x^n, where n is even
f(1) = ?
f(-1) = ?
2.
g(x) = x^n, where n is odd
g(1) = ?
g(-1) = ?
Step-by-step explanation:
remember, an exponent n just means that the base is multiplied by itself n times.
so, e.g.
a³ = a×a×a = (a×a)×a
a⁶ = a×a×a×a×a×a = (a×a)×(a×a)×(a×a)
as you can see, any even exponent can be written as products of squares.
and any odd (uneven) exponent can be written as product of squares multiplied by one base.
a square of a real number is always positive. therefore, an even exponent of a real number is always positive.
and an odd exponent has the sign of the base (as the result of these multiplications is the product of the squares, that are always positive and one instant of the base, and +×+ = +, +×- = -).
and 1^n = 1
no matter how often I multiply 1 by 1, I get 1 as result.
also : -×- = +
1.
f(x) = x^n, n is even
f(1) = 1^n = (1×1)×(1×1)×...×(1×1) = 1×1×1×...×1 = 1
f(-1) = (-1)^n = (-1×-1)×(-1×-1)×...×(-1×-1) = 1×1×1×...×1 = 1
2.
g(x) = x^n, n is odd
g(1) = (1×1)×(1×1)×...(1×1)×1 = 1×1×1×...×1×1 = 1
g(-1) = (-1×-1)×...×(-1×-1)×-1 = 1×1×...×1×-1 = -1
Use the number line to represent the solution to 2.4x−6>−13.2.
The required solution of the given inequality is given as x > -3.
Given that,
To determine the solution of the given inequality, 2.4x−6>−13.2.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
here,
2.4x−6>−13.2.
2.4x > -7
x > -3
Thus, the required solution of the given inequality is given as x > -3.
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Cynthia Besch wants to buy a rug for a room that is 25 ft wide and 32 ft long. She wants to leave a uniform strip
of floor around the rug. She can afford to buy 330 square feet of carpeting. What dimensions should the rug
have?
If $10,000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
10,000n(x/100)
The reasoning is from the following:The formula for simple rate of interest is F = P(1+rt) whereF = future valueP = present valuer = ratet = time
If $10,000 is invested at x percent simple annual interest for n years, the total amount of interest would be F = 10,000n(x/100)
What is simple interest?Simple interest is calculated based on the principle of a loan or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only charge interest on the principal sum, and a borrower will never be required to pay interest on interest that has already accrued.
F = P(1+rt), formula for simple rate of interest
Here,
=> Future value is F
=> Present value is P
=> Rate is R
=> Time is t
Substituting x for r
And, n for t
Also, 10,000 in for P
F = 10,000(1+xn)
The formula tells us principal + interest,
F = 10,000(xn)
Now, to get the x into terms of a percentage,
F = 10,000(n * x/100)
F = 10,000n(x/100)
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What is the measure of angle o in parallelogram lmno? 35° 75° 105° 155
The measure of angle O in the given parallelogram is equal to 105°.
As given in the question,
Given parallelogram LMNO,
As shown in the attached diagram we have,
Measure of angle L = ( x + 40 )°
Measure of angle O = (3x)°
In the parallelogram LMNO,
LM is parallel to NO .
LO is the transversal.
∠MLO and ∠NOL are interior angles and are supplementary.
m ∠MLO + m ∠NOL = 180°
⇒ ( x + 40 )° + ( 3x )° = 180°
⇒ 4x° = 180° - 40°
⇒x = 140° / 4
⇒ x = 35°
Measure of ∠O = 3x°
= 3(35°)
= 105°
Therefore, the measure of ∠O in the parallelogram LMNO with the given conditions is equal to 105°.
The complete question is :
What is the measure of angle O in parallelogram LMNO?
Diagram of parallelogram LMNO is attached.
m∠O = ?
a. 35° b. 75° c. 105° d. 155°
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Answer: 105 degrees
Step-by-step explanation:
edge 2023, (Proving a Quad. is a Parallelogram)
Please Help! - Algebra
Zachary purchased a computer for $1,800 on a payment plan. Two months after he purchased the computer, his balance was $1,540. Three months after he purchased the computer, his balance was $1,410. What is an equation that models the balance y after x months?
Using an exponential decay equation, the function that models the balance is y = 1800(1 + 0.081)⁻ˣ at a rate of 8.1%
Exponential FunctionExponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.
In mathematics, an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
To solve this problem, we need to find the rate at which the payment is calculated on.
The general equation for an exponential decay is given as
A = P(1 + r)⁻ˣ
x = timer = rateSubstituting the values and solving for r
1540 = 1800(1 + r)⁻²
r = 0.081
r = 8.1%
Comparing the third month to ascertain values
1410 = 1800(1 + r)⁻³
r = 0.081
r = 8.1%
The rate which the payment is calculated is 8.1%
An exponential equation that models the balance after y months will be
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50 POINTS! PLEASE HURRY!
f(x) = x2. What is g(x)?
Answer: g(x) = -x^2 -3
Step-by-step explanation:
We know that the y-intercept is -3, so we can eliminate the first 2 answers. For the last two answers, c is wrong because it is a negative slope and if we square root it, it will become a positive slope our graph slope is not positive, so the answer is d.
a grandfather, two fathers and two sons bought passage for a voyage together and everyone paid for one berth each. how many berths did they buy in total?
Grandfather, two fathers and two sons purchased a total of three tickets.
What is a Mathmatical riddle?
Children must convert a few lines from a real-life incident into the appropriate set of mathematical equations in order to solve a math mystery. Mathematical riddles can be cracked by kids utilizing logic, inventive problem-solving, and common sense.
All three tickets:
Grandfather and His Son's Father
Father and his father's son.
Son.
Two fathers and two sons, then.
As a result, a total of 3 tickets were purchased by a grandfather, two fathers and two sons.
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E-tech initiatives limited plans to issue $500,000, 10-year, 4 percent bonds. Interest is payable annually on december 31. All of the bonds will be issued on january 1, 2022. Show how the bonds would be reported on the january 2, 2022, balance sheet if they are issued at 97. (deductions should be indicated by a minus sign. ).
The preparation of the bond that should be reported on the balance sheet is presented below:
E-tech initiatives limited plans to issue $500,000, 10-year, 4 percent bonds. Interest is payable annually on december 31. All of the bonds will be issued on january 1, 2022.
We need to present it on balance sheet balance sheet if they are issued at 97.
E-Tech Initiatives Limited
Partial balance sheet
As on January 2, 2019
Liabilities
Long term Liabilities
Bond Payable $500,000
Add: Premium on Bond $10,000 ($510,000 - $500,000)
Carrying value $510,000 ($500,000 * 97%)
Therefore, The preparation of the bond that should be reported on the balance sheet is presented above.
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E ≠ V + Ir
Solve for r
Answer:
r ≠ E – V/r
Step-by-step explanation:
E ≠ V + Ir
E – V ≠ Ir
divide both sides by I
E – V/I ≠ r
r ≠ E – V/r
i hope i helped
an instructor has given a short quiz consisting of two parts. for a randomly selected student, let and . suppose that the joint pmf of and is given in the accompanying table.
Random variable
a. E (X+ Y) = 14.10
E|(X – Y)| = 5.1
b. E[max(X ,Y )] = 9.60
E[min(x, y)] = 4.5
Conversely, once Y=y is observed, we would more likely be interested in the quantity E(X∣Y=y)=ρy which is a scalar.
Maybe this seems like needless complication, but regarding E(X∣Y) as a random variable in its own right is what makes things like the tower-law E(X)=E[E(X∣Y)] make sense - the thing on the inside of the braces is random, so we can ask what its expectation is, whereas there is nothing random about E(X∣Y=y).
a. E (X+ Y)
=∑∑( x +y)p(x ,y)
= (0+0)(0+2) + (0 + 5)(.06) + … + (10 + 15)(.01)
= 14.10
E|(X – Y)| = ∑∑ |x – y| p(x,y)
= |(0-0)|(0.02) + |(0-5)|(0.06) + ……+ |(10-15)|(0.01)
= 5.1
b.
E[max(X ,Y )] = ∑∑max(x+y).p (x ,y)
= (0)(.02) + (5)(.06) +…+(15)(.01)
= 9.60
E[min(x, y)] = ∑∑ min (x,y) p(x,y)
= 0(0.02) + 0(0.06) + ……+ 10(0.14) + 10(0.01)
= 4.5
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What are the equations to the slopes of 1/5, 3/5, and 6/5?
Answer:
1/ y= 1/5x
2/ y= 3/5x
3/ y= 6/5x
Step-by-step explanation: Our original equation is y=mx+b
Where m is the slope and b is the y-intercept. Since there is no y-intercept, so we just say it is 0 and only put in the slope to the equation.
exhibit 12-2 last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. a random sample of 300 students taken from this year's student body showed the following number of students in each class. freshmen 83 sophomores 68 juniors 85 seniors 64 we are interested in determining whether there has been a significant change in the distribution of class between the last school year and this school year. refer to exhibit 12-2. if the distribution is the same as the previous year, the expected number of freshmen is . a. 30 b. 10 c. 90 d. 83
Option D is the correct answer.
What is distribution?
To “distribute” means to divide something or give a share or part of something.
From the given information , 83 + 68 + 85 + 64 = 300 students.
30 % = freshmen, 24% =sophomores, 26% = juniors , 20% = seniors
Class Observed frequency Expected proportion
Freshman 83 0.30
Sophomores 68 0.64
juniors 85 0.26
seniors 64 0.20
Total 300 1
The expected number of students in freshman class can be calculated as
Expected Frequency = Total number of value x Expected Proportions
= 300 x 0.30
= 90
Therefore, the expected number of students in freshman class = 90
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The odds in favor of Michael Jordan making a free throw were 21:4. Find the probability of Michael Jordan missing a free throw.
Give answer as a decimal rounded to the nearest hundredth.
The probability that Jordan misses a free throw is 0.16
How to determine the probability that he misses?From the question, we have the following parameters that can be used in our computation:
Odds in favour = 21 : 4
Represent the odds as a fraction
So, we have the following representation
Odds in favour = 21/4
To convert the odds to probability, we make use of the following equation
Probability = Numerator/(Numerator + Denominator)
Substitute the known values in the above equation, so, we have the following representation
Probability = 21/(21 +4)
Evaluate the sum
Probability = 21/25
The probability that he misses is
Misses = 1 - 21/25
Evaluate the probability
Misses = 4/25
So, we have
Misses = 0.16
Hence, the probability is 0.16
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