In the equation [tex](2x^{9} y^{n})(4x^{2}y^{10}) = (8x^{11}y^{20})[/tex] value of n = 10
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.
[tex](2x^{9} y^{n})(4x^{2}y^{10}) = (8x^{11}y^{20})[/tex]
exponents multiplied with the same base: am * an = a{m + n}
On the powers of x, use the Rule of Multiplying Exponents.
⇒ x⁹ * x² = x⁹⁺² = x¹¹
The powers of y operate similarly.
⇒ [tex]y^{n} * y^{10} = y^{n + 10} = y^{20}[/tex]
Since y¹⁰⁺¹⁰ = y²⁰
Therefore in the given equation, the value of n = 10
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Minh paints 12 rooms to paint 3 he needs 2 cans of paint . He wants to know how many cans he needs in all. Which tools would be appropriate for Minh to use to solve the problem? Choose all that apply
Minh can use unitary method to determine how many cans he will need in all to paint the 12 rooms, which will give a total of 8 cans as requirement. The tools he'll need for the same are : counters, pencil and paper.
In its simplest form, the unitary procedure is used to determine the value of a single unit from a given multiple.
How to calculate the value of one pen, for example, if 40 cost Rs. 400. To finish it, using the unitary method. Additionally, after the value of a single unit has been established, we can multiply that value by the quantity of additional units required to establish the value of the additional units.
This is typically how the concepts of ratio and proportion are used. The unitary method entails calculating the value of a single unit before calculating the value of the required number of units.
Given, He requires 2 paint cans to paint 3 rooms.
Once more, he will require 2/3 of a can of paint to paint 1 room.
He will thus require cans of paint to paint 12 rooms, which equals (2/3)*23 = 8.
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Help find X-coordinate
The value of x coordinate be 0 or -2.
Given,
Vertex of the graph, f(x) = x² + 2x + 2
We have to find the x coordinate.
Here,
f(x) = x² + 2x + 2 is in the form of quadratic equation.
So, we can find x coordinate by using quadratic formula.
Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Here,
a = 1, b = 2 and c = 2
So,
[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
= [tex]\frac{-2(+-)\sqrt{2^{2}-4(1)(2) } }{2(1)}[/tex]
= [tex]\frac{-2(+-)\sqrt{4-8} }{2}[/tex]
= (-2±(-√4)) ÷ 2
= (-2±(-2)) ÷ 2
Solve for.
-2 + (-2) / 2 = -2 -2 / 2 = -4/2 = -2
Solve for,
-2 - (-2) / 2 = -2 + 2 / 2 = 0
That is,
The value of x coordinate be 0 or -2.
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A bagel shop sold S plain bagels and 13 rye bagels. What is the ratio of the number of rye bagels to the number of plain bagels sold?
We can conclude that (B) 13 : 8 is the ratio of Rye bagels to Plain bagels.
What is the ratio?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8. Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B).So, the ratio of Rye bagels to Plain bagels:
Rye bagels = 13Plain bagels = 8Then,
Rye bagels: Plain bagels13 : 8Therefore, (B) 13 : 8 is the ratio of Rye bagels to Plain bagels.
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The correct question is given below:
A bagel shop sold 8 plain bagels and 13 rye bagels. What is the ratio of the number of rye bagels to the number of plain bagels sold?
Home Depot wants to buy a new line of fertilizers. Manufacturer A offers a 22/14 chain discount. Manufacturer B offers a 25/8 chain
discount. Both manufacturers have the same list price.
a. What is the percentage of discount for both manufacturers?
Note: Do not round intermediate calculations. Round your final answers to the nearest hundredth percent.
Manufacturer A
Manufacturer B
Percentage of
Discount
%
%
b. What manufacturer should Home Depot buy from?
Manufacturer B
Manufacturer A
(a) The percentage of discounts for manufacturers A and B is 32.92% and 31%, respectively.
(b) The Home Depot should buy from manufacturer A.
Home Depot wants to buy a new line of fertilizers.The manufacturer A offers a chain discount of 22/14.The manufacturer B offers a chain discount of 25/8.The list price of the manufacturers is the same.Let the list price be "x".For manufacturer A:The price after the first discount is x*(1-22%).The price after first and second discount is x*(1-22%)(1-14%).The price is 0.6708x.The total discount is 1-0.6708.The total discount percentage is 32.92%.For manufacturer B:The price after the first discount is x*(1-25%).The price after first and second discount is x*(1-25%)(1-8%).The price is 0.69x.The total discount is 1-0.69.The total discount percentage is 31%.Home Depot should buy from manufacturer A due to the greater discount.To learn more about percentage, visit :
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Rewrite as equivalent rational expressions with denominator (3x-8)(x-5)(x-3)
we have the expression
[tex]\frac{4}{3x^2-23x+40}[/tex]Rewrite as equivalent rational expressions with denominator (3x-8)(x-5)(x-3)
In this problem
3x^2-23x+40=3(x-5)(3x-8)
so
[tex]\frac{4}{3x^2-23x+40}=\frac{4}{3\mleft(x-5\mright)\mleft(3x-8\mright)}[/tex]Multiply by (x-3)/(x-3)
[tex]\frac{4}{3(x-5)(3x-8)}\cdot\frac{(x-3)}{(x-3)}=\frac{4(x-3)}{3(x-5)(3x-8)(x-3)}[/tex]Part 2
we have the expression
[tex]\frac{9x}{3x^2-17x+24}[/tex]we have that
3x^2-17x+24=3(3x-8)(x-3)
so
[tex]\frac{9x}{3x^2-17x+24}=\frac{9x}{3\mleft(3x-8\mright)\mleft(x-3\mright)}=\frac{3x}{(3x-8)(x-3)}[/tex]Multiply the expression by (x-5)/(x-5)
[tex]\frac{3x}{(3x-8)(x-3)}\cdot\frac{(x-5)}{(x-5)}=\frac{3x(x-5)}{(3x-8)(x-3)(x-5)}[/tex]This season, the probability that the
Yankees will win a game is 0.6 and the
probability that the Yankees will score 5 or
more runs in a game is 0.61. The
probability that the Yankees win and score
5 or
more runs is 0.51. What is the
probability that the Yankees would score
fewer than
5 runs when they lose the
game? Round your answer to the nearest
thousandth.
Answer:
0.156
Step-by-step explanation:
P(A & B) = P(A) * P(B)
P(Yankess score less than 5 and lose) = P(score less than 5) * P(lose)
0.39 * 0.4 = 0.156
show work help plsss
The required quotient is 6.5625 when -5 2/8 is divided by (-4)/5.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.
The quotient is given in the question:
-5 2/8 ÷ (-4)/5
-(42/8) / (-4)/5
Reciprocal the term in the denominator
-(42/8) × -(5)/4
210/32
6.5625
Therefore, the required quotient is -5 2/8 ÷ (-4)/5 = 6.5625.
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An election ballot asks voters to select five city commissioners from a group of eighteen candidates. In how many ways can this be done?
Number of ways to select five city commissioners from a group of eighteen candidates is equal to 8568.
As given in the question,
Total number of candidates = 18
An election ballot asks voters to select five city commissioners from 18 candidates
Number of ways to select 5 city commissioners from a group of 18 candidates
= ¹⁸C₅
= ( 18!) ) / (5!)(18 - 5)!
= (18!) / (5!)(13!)
= ( 18 ×17×16×15×14×13! ) / ( 5×4×3×2×1 )( 13! )
= 8568
Therefore, number of ways to select five city commissioners from a group of eighteen candidates is equal to 8568.
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a skydiver is falling at about 176 ft per second. how many feet per second is he falling?
Now multiply 176 by 60 and that is the answer, Khalil :=)
Step-by-Step Example: Sketch a graph for a situation.
A carnival game booth begins the evening with 40 prizes.
In the first 30 minutes that the booth is open, no one wins
a prize. In the next hour, 8 prizes are won. In the next 45
minutes, 10 prizes are won. During the next 45 minutes,
the booth owner brings in 16 additional prizes. In the next
2 hours, 12 prizes are won. An hour later, 4 prizes are
won, and the carnival closes for the evening.
Sketch a graph that shows the number of prizes the booth
had over the time it was open.
By using the method subtraction, Total prizes are left over are 52- 34= 18
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.
Given that,
A carnival game booth begins the evening with 40 prizes.
In the first 30 minutes that the booth is open, no one wins
a prize.
In the next hour, 8 prizes are won. In the next 45
minutes, 10 prizes are won.
During the next 45 minutes, the booth owner brings in 16 additional prizes.
In the next 2 hours, 12 prizes are won.
An hour later, 4 prizes are won, and the carnival closes for the evening.
Total prizes are 52 prizes.
Total prizes given are 34 prizes
Total prizes are left over are 52- 34= 18
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Ration of adults to children is 16to 10 40 adults
A relationship between two quantities that is typically stated as the product of their respective quotients.
The ratio of red to blue marbles, or 6:4, is, for instance, 6:4 if a box contains six red and four blue marbles. Decimal or percentage expressions of ratios are also possible. This implies that there would be 10 children for every 16 adults.
The number of children there would be for 40 adults can be calculated by dividing 40 by 16, then multiplying the result by 10.
40/16=2.5
2.5×10=25
25 kids.
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the gcf of (x-8) (x+1) and (x+1)
The two numbers are:
[tex](x-8)(x+1);(x+1)[/tex]The greatest common factor is the product of common factors.
F(x)=1/2x4x domain:(0,1,2,)
Dion has a pizza with a diameter of 10 1/3 in. Is the square box song big enough to fit the pizza inside?
justify your answer
yes, the square box song big enough to fit the pizza inside.
what is square?
A square is a regular quadrilateral , which means that it has four equal sides and four equal angles.
we have that,
the diameter of the pizza is
D = 10 1/3in
the wide of the square box is
b=10.38in
we know that
for the pizza to fit inside the box ,it must be fulfilled that
D ≤ b
convert 10.38 in to fraction number
10.38 (100/100)= 1.038/100=519/50
convert 101/3 in to an improper fraction
10 1/3 = 10+3+1/3=31/3
multiply the diameter of the pizza by 50 both numerator and denominator =31+50/50+3= 1.550/150 in
multiply the wide of the box by 3 both numerator and denominator 1.550/150in ≤ 1.557 /150 in
therefore
the pizza fit inside the box .
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what is the method used to complete the table?
Answer:
see attached
Step-by-step explanation:
You want to finish filling the given 2-way table.
TotalsAny single missing value in a row or column will be the value that makes the total correct for that row or column. Filling the single missing values will fill enough of a row or column with two or more missing values so that the remaining missing values can be filled the same way.
It is basically a series of subtraction problems.
For example, the upper left cell is filled with 20 -4 = 16, so the total on that row is 16+4=20.
a student computes -8-2(-3) by writing -10(-3)=30 how would you help this student?
Answer:
-2
Step-by-step explanation:
You want to help a student evaluate -8-2(-3).
Order of operationsThe given expression consists of a sum of a number and a product. The first operation to be performed is to find the product:
-8-2(-3) = -8 +6
Then the sum can be performed:
-8 +6 = -2
The student should be reminded to identify the parts of the expression and use the order of operations to evaluate them.
Katie earns $549 each week working her full time job. Her employer has a 14.3% tax deduction on all monies earned each week. Calculate the tax deduction Katie paid for that week.
The tax deduction Katie paid for that week will be $78.5.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Katie earns $549 each week working her full-time job. Her employer has a 14.3% tax deduction on all monies earned each week.
The deduction will be calculated as follows:-
Deduction = ( 549 x 14.3 ) / 100
Deduction = 7850.7 / 100
Deduction = $78.50
Therefore, the tax deduction Katie paid for that week will be $78.5.
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(2y-1)+3y+5
please help
Answer:
5y + 4; y = -4/5
Step-by-step explanation:
combine like terms
add 2y+3y together, and -1+5
5y+4=0
-4 -4
5y= -4
/5 /5
y= -4/5
ve the system and find the numbers.
11) One number is four more than a second number. Two times the first number is 4 more than four
times the second number.
A) 7 and 3
C) 6 and 2
D) - 6 and -10
B) 5 and 1
Answer:
6 and 2
Step-by-step explanation:
Let the first and second numbers be x and y respectively.
x = 4 + y..... (1)
2x = 4 + 4y...... (2)
Using the substitution method from Eqn(1) into (2)
Anywhere we see x in Eqn(2) we substitute it with 4 + y
I. E. 2(4 + y) = 4 + 4y
8 + 2y = 4 + 4y
Collect like terms.
8 - 4 = 4y - 2y
4 = 2y
.: y = 2
Put y = 2 in Eqn(1), and we have;
x = 4 + 2
x = 6.
.: the first number is 6 and the second number is 2.
Option C is correct.
Given the relation R {(4,2), (3,6), (x,8), (1,4)} Which value of x would make this relation a function?
(1) 4
(2) 3
(3) 1
(4) 0
Answer:
SOLUTION
TO CHOOSE THE CORRECT
OPTION
Given the relation R = {(6,4), (8,-1), (x,7), (-3,-6)}. Which of the following values for x will make relation R a function
(a) 8
(b) 6
(c) -3
(d) 1
CONCEPT TO BE IMPLEMENTED
FUNCTION
Let A and B are two non empty sets. A Mapping (function ) f from A to B is a rule that assigns to each element x of A a definite element y in B
EVALUATION
Here the given relation
R = {(6,4), (8,-1), (x,7), (-3,-6)}
Take A = {6,8,x,-3}
B={-6, -1, 4,7}
In order to satisfy all requirement for R to be mapping is R will have to assign to each element x of A a definite element y in B
Since R has mapped 6, 8, -3 already
So R can not map 6, 8, - 3 again
So R can not be any of 6, 8, - 3
.'. X = = 1
FINAL ANSWER
The correct option is (d) 1
1. . A relation R in the set of real numbers R defined as R = {(a,b): √a = b} is a
function or not. Justify
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2. Let R be a relation on a collection of sets defined as follows,
R={(A,B)|ACB}
Then pick out the correct statement(s).
Which point is part of the solution set of the inequality x < -12?
Answer:
all the number to the left of -12 on a number line. -12 is not a solution. If we were graphing this, we would have an open circle above -12 on a number line and the dark ray points to the left of -12
Step-by-step explanation:
Lines l and m are parallel. Which of the following pairs of angles are alternate interior angles?
The pairs of angles that are alternate interior angles will be angle 6 and angle 8.
What are alternate interior angles?When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairings of that transversal. Alternate interior angles are what they are termed.
Angles that are exterior to the lines, have different vertices, and sit on different sides of the transversal are referred to as alternate exterior angles. In other words, eight angles are created when a transversal intersects two parallel lines.
These van be illustrated in angle 6 and 8
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Lines l and m are parallel. Which of the following pairs of angles are alternate interior angles? ∠1 and ∠4 ∠2 and ∠3 ∠6 and ∠8
If $2,000 is invested at 11% annual interest compounded quarterly, what is the account balance after 10 years, assuming no additional deposits or withdrawals are made?
Answer:
$5,919.75
Step-by-step explanation:
What is Annual Compound Interest?
Annual compound interest is represented by this formula:
[tex]A = P ( 1 + \frac{r}{n}) ^{(n)(t)}[/tex]
A= Final value (including interest)P = principal/original amount: $2000r = rate as a decimal: 0.11n= number of times compounded yearly: quarterly: 4t= numbers of years borrowed for: 10You have been giving all the information needed to solve this equation, so plug in what you have. and solve for A.
[tex]A = (2000)( 1 + \frac{0.11}{4} )^{(4)(10)}[/tex]
[tex]A = (2000) (1.0275)^{40}[/tex]
[tex]A = (2000) (2.9598739872)\\[/tex]
[tex]A = 5919.74797[/tex]
Round your answer to the nearest hundred, and the account balance after 10 years should be $5,919. 75
I need help with my math
The definition of the slope can be interpreted by the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]selcect two points from the graph
(0,-2)
(0,-4)
replace the points into the formula
[tex]\begin{gathered} m=\frac{(-4)-(-2)}{0-0} \\ m=\frac{-4+2}{0} \\ m=\frac{-2}{0} \\ m=\text{IND} \end{gathered}[/tex]Since any number divided by 0 is indetermined, the slope of the line is undefined.
Which of the following parent functions has a domain of all real values of x
and a range of 0?
there are 248 students in a large-lecture history course. on the first exam, 12% got an A, 28% a B, 41% a C, 11% a D, and the rest failed. Based on these results, whats the probability that a randomly selected student will (a) Get better than a C on the second test? (b) Fail the second test? (c) Not get an A on the second test
Assuming that the scores on the first exam are a representation for the ones in the second exam, we will see that the probabilities are:
a) P = 40%b) P = 8%c) P = 88%How to get the probabilities?First we want to get the probability that a randomly selected student gets better than a C on the second test.
We assume the percentages for the first test can be applied for the second, so, the ones that got better than a C on the first exam are:
A: 12%
B: 28%
Then the probability is:
P( more than a C) = 12% + 28% = 40% (or 0.40 in actual probability notation)
b) Now we want to find the probability of fail.
The percentage that failed the first test is:
100% - 12% - 28% - 41% - 11% = 8%
So 8% of the students failed the first exam, this means that the probability that a randomly selected student fails the second exam is:
P = 8% or 0.8 in decimal notation.
C) 12% of the students tgot an A, so the probability that a randomly selected student does not get an A is:
P = 100% - 12% =88%
or 0.88 in decimal notation.
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How can you use compatible numbers when you divide decimals
Division is opposite of multiplication. If 3 groups of 4 make 12 in the multiplication, 12 divided into the 3 equal groups give 4 in each group in division. The main goal of dividing is to see how many equal groups are formed or how many are in the each group when sharing fairly.
How to divide the compatible numbers?In divisions involving fractions, numerator is called the dividend while the denominator is called the divisor while the answer is called the quotient.
Now, when Dividing decimal by a whole number, it means the decimal is the numerator while the whole number is the denominator.
The first step is to estimate quotient by approximating the dividend and divisor to the nearest compatible numbers. For example; 6.5/9
The nearest compatible number for numerator is 6 while for the denominator it is 10. Thus, we have;
7/10 = 0.7
Second step is to perform division with original numbers. This gives us;
6.5/9 = 0.722
Third step is to compare the both answers to see if our estimate makes sense.
Using compatible numbers gave us quotient of 0.7 while the normal division gave us a quotient of 0.722
Since both the quotient are very close, then it means our estimated quotient is okay.
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Consider the incomplete paragraph proof.
Given: P is a point on the perpendicular bisector, l, of MN.
Prove: PM = PN
Line l is a perpendicular bisector of line segment M N. It intersects line segment M N at point Q. Line l also contains point P.
Because of the unique line postulate, we can draw unique line segment PM. Using the definition of reflection, PM can be reflected over line l. By the definition of reflection, point P is the image of itself and point N is the image of ________. Because reflections preserve length, PM = PN.
Since we see that P is a point on the perpendicular bisector, l, of MN, we have proven the required PM = PN by the definition of reflection, we can conclude that point P is the image of itself , while point N is the image of M .
How to Interpret the Perpendicular Bisector?We are given :
P is a point on the perpendicular bisector, l, of MN.
Now, we want to prove the assertion that PM = PN
A Reflection is defined as a transformation in which a given figure is the mirror image of the other. This means that every point on the new image is a mirror reflection of itself .
From the question, we can say that by the definition of reflection, we can conclude that point P is the image of itself , while point N is the image of M .
The perpendicular bisector, l is acting as a Line of symmetry which is also called axis of reflection.
Now, due to the fact that reflections preserve lengths in transformation, it means that we have; PM = PN.
Therefore, we see that point N is the image of M .
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Answer:
Point M
Step-by-step explanation:
what is the z-score of the value 9 rounded to the nearest tenth?
Please, let me know if you have any question anytimeGiven:
mean = μ = 8
standard deviation = σ = 0.7
random value = x = 9
Then, the formula to calculate the z score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substitute the values:
[tex]z=\frac{9-8}{0.7}=\frac{1}{0.7}=1.428\approx1.4[/tex]Answer: 1.4
find x if AC=15 , AB=x+14 , and BC= x+13
Given the information, we have the following:
Now, since AC=15, we have the following expression:
[tex]\begin{gathered} AB+BC=AC \\ \Rightarrow(x+14)+(x+13)=15 \end{gathered}[/tex]Solving for x we get:
[tex]\begin{gathered} (x+14)+(x+13)=15 \\ \Rightarrow2x=15-14-13=-12 \\ \Rightarrow2x=-12 \\ \Rightarrow x=\frac{-12}{2}=-6 \\ x=-6 \end{gathered}[/tex]Therefore, x=-6