ADBA. 9°B. 10°C. 81°D. 91°99⁰CABCD is a quadrilateral. If mZC = (x²)°, find mZC..
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Since ABCD is a quadrilateral, the sum of internal angles is equal to 360°.
Using this property, let's find the measure of angle C:
[tex]\begin{gathered} A+B+C+D=360°\\ \\ 90+99+C+90=360\\ \\ C+279=360\\ \\ C=360-279\\ \\ C=81° \end{gathered}[/tex]The measure of angle C is 81°, therefore the correct option is C.
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A car depreciates by 20% each year after it is purchased. The table below shows the value of the car over the first three years. 1 2 G Year Value of Car $12,000 $9600 $7680 a) Write an equation to represent this sequence. b) What will be the value of the car after 8 years?
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The value of the car depreciates by 20% each ear, meaning after one year the price of the car is 80% of the original price.
In our case, the initial price of the car is $12,000; therefore after one year, its price will be
[tex]12000\times\frac{80}{100}=12000\times0.8[/tex]after 2 years
[tex](12000\times0.8)\times\frac{80}{100}=12000\times0.8\times0.8[/tex]after three years
[tex]12000\times0.8\times0.8\textcolor{#FF7968}{\times0.8}[/tex]and therefore, after n years
[tex]12000\times0.8^{n-1}[/tex]Hence, after 8 years n= 8; therefore,
[tex]12000\times0.8^7=2516.6[/tex]To conclude, the value of the car after 8 years will be $2516.6.
what are the theorems I feel like I got at least 1 wrong already ╥﹏╥
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. Mr. Hawkins wants to buy 2 shirts that are $40 each. The store was having a Buy-One-Get-One 50% Off sale! Mr. Hawkins also had a 10% off coupon and will have to pay 6% sales tax. How much did he spend?
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for the shirts $60 with the 10% discount $54 and 6% on taxes }$57.24
So the answer is $57.24
Tell whether the following situation can be modeled by a linear function, an exponential function, a quadratic function or neither. The speed of a ball after a golfer hits it
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Given the statement:
Speed of a ball after a golfer hits it
Let's determine whether the situation can be modeled using a linear, exponential or quadratic function.
After a golfer hits a ball, the ball starts from the initial position(rest), goes up and also comes down.
The movement of the ball will form a parabola.
A graph that has the shape of a parabola is the graph of a quadratic function.
The speed of ball after it is hit reduces with time.
A quadratic function has the form:
[tex]f(x)=ax^2+bx+c[/tex]Therefore, the speed of the ball after it is hit by a golfer can be modeled using a quadratic function
ANSWER:
Quadratic function
What is the coefficient of the x^2 term of the polynomial that would result from the following multiplication?(-2x + 4)(-4x + 9)The coefficient of the x^2 term is
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To answer the question we first have to do the multiplication.
[tex]\begin{gathered} (-2x+4)(-4x+9)=8x^2-18x-16x+36 \\ =8x^2-34x+36 \end{gathered}[/tex]From the result we see that the coefficient of the x^2 term is 8.
Identify the images that represents a rigid transformations. LIST the card number of each rigid transformation card and EXPLAIN why each is a rigid transformation.
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The first one is a rigid transformation because it is a translation
The second one is not a rigid transformation because the size of the original image changes
The third one is a rigid transformation, because it is a reflection about the y axis
The fourth one is a rigid transformation because it is a rotation
The fifth one is a rigid transformation because it is a rotation
The sixth one is not a rigid transformation because the size of the original image changes
The seventh one is not a rigid transformation because the size of the original image changes
The eighth one is a rigid transformation, because it is a reflection about the y axis
The ninth one is a rigid transformation because it is a translation
A 30-foot tree casts a 12-foot shadow as shown inthe picture.30 ftx12Find the angle of elevation to the nearest tenth.12.850°68.2°90°
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Since the triangle has a right angle, we can conclude that the diagram is of a right triangle.
When dealing with right triangles, there are some useful formulas that are known as 'Trigonometric Identities'. There are a lot of them but we will need only one of those to solve the problem, that's the equation below:
[tex]\tan (\theta)=\frac{O}{A}[/tex]Where θ is the angle, O is the length of the opposite side to the angle, and A the adjacent side to the angle.
Therefore, in the case of our problem,
[tex]\begin{gathered} \theta=x,O=30ft,A=12ft \\ \Rightarrow\tan (x)=\frac{30}{12}=2.5 \end{gathered}[/tex]Solving for x, we get
[tex]x=\tan ^{-1}(2.5)=1.1902\text{rad}[/tex]And we can transform radians into degrees,
[tex]\Rightarrow x\approx68.2[/tex]Thus, the answer is the third option. 68.2°
I am having trouble understanding where to begin with determining the zeros and their multiplicities for a factored polynomial. f(x)=(x-5)^5*(x+1)^7
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A zero of a polynomial f(x) is a value of x such that f(x)=0.
When a polynomial is written as the product of binomial factors, we can easily find its zeroes by looking at the values of x which make each binomial equal to 0. In this case:
[tex]f(x)=(x-5)^5(x+1)^7[/tex]Notice that this polynomial is composed by two different binomial factors:
[tex]\begin{gathered} x-5 \\ x+1 \end{gathered}[/tex]If any of those factors are equal to 0, the whole polynomial will be equal to 0 since the product of 0 times any algebraic expression is always equal to 0.
Then. the zeroes of the function are the values of x such that:
[tex]\begin{gathered} x-5=0 \\ or \\ x+1=0 \end{gathered}[/tex]Solving each equation for x, we can see that the zeroes of the polynomial are x=5 and x=-1.
On the other hand, the multiplicity of those zeroes is equal to the exponent of the corresponding binomial. The exponent of (x-5) is 5, then the multiplicity of the x=5 zero is 5.
Similarly, the multiplicity of the x=-1 zero is 7.
Therefore, the zeroes of the polynomial f(x)=(x-5)^5*(x+1)^7 and their multiplicities are:
[tex]\begin{gathered} x=5,\text{ multiplicity: 5} \\ x=-1,\text{ multiplicity: 7} \end{gathered}[/tex]
the first three terms of a sequence are given round to the nearest thousandth(if necessary). 413,405,397,...Find the 48th term
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37
1) Examining the sequence we can notice that
413-405 = 8
405 -397 =8
So, this is an Arithmetic Sequence whose common difference is -8
2) Therefore, we can write one Explicit Formula so that we can find out the 48th term
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ a_{48}=413+(48-1)(-8) \\ a_{48}=413\text{ +47(-8)} \\ a_{48}=413+(-376) \\ a_{48}=413-376\text{ =37} \end{gathered}[/tex]3) Hence, the 48th term of that Arithmetic Sequence is 37
wy IWPLAYER Determine whether each number is prime or not prime. Drag each numar to the appropriate box. 9 13 33 43 69 Prime Not Prime Review progress Question 2 of 5
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Prime numbers have two factors only 1 and itself
Ex: 5 is a prime number because it has just 2 factors 1 and 5
3 is a prime number because it has 2 factors 1 and 3
9 is not a prime number because it has 1, 3, 9 as factors
13 is a prime number because it has only 2 factors 1 and 13
23 is a prime number because it has only 2 factors 1 and 23
33 is not a prime number because it has 1, 3, 11, 33 as factors
43 is a prime number because it has 2 factors only 1 and 43
69 is not a prime number because it has 1, 3, 23, 69 as factors
The football teams consists of 15 seniors and 7juniors. The coach has decided to randomly choose 4players to represent the team at this year's pep rally.What is the probability that one senior and 3 juniorswill be chosen?
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SOLUTION
The team consists of 15 seniors. Probability of choosing 1 senior becomes
[tex]\begin{gathered} \text{Probability = }\frac{\exp ected\text{ outcome}}{\text{total outcomeP}} \\ P(S)=\frac{1}{15} \end{gathered}[/tex]The team also consists of 7 juniors. Probability of choosing 3 juniors
[tex]P(J)=\frac{3}{7}[/tex]And the probability that one senior and 3 juniors will be chosen becomes
[tex]\begin{gathered} P(S\text{ and J) = P(S) }\times P(J) \\ =\frac{1}{15}\times\frac{3}{7} \\ =\frac{1}{5}\times\frac{1}{7} \\ =\frac{1}{35} \end{gathered}[/tex]Hence the answer is
[tex]\frac{1}{35}[/tex]Consider the following quadratic equation. -2x^2 - 4x = - 5STEP 1 of 2: Find the values of a, b, and c that should be used in the quadratic formula to determine the solution of the quadratic equation. a = -2 b = -4 c = 1STEP 2 of 2: Use the discriminate, b^2 - 4ac, to determine the number of solutions of the given quadratic equation. Then solve the quadratic equation using the formula X = (Formula to use is in the pic attached)
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Given the equation:
[tex]-2x^2-4x=-5[/tex]STEP 1 of 2:
To solve the equation using the formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]We need to find the values of a, b, and c.
To do that, the equation must be in the form:
[tex]ax^2+bx+c=0[/tex]Let's rearrange the terms of the given equation:
[tex]-2x^2-4x+5=0[/tex]Now we can identify the values
a = -2, b = -4, c = 5
STEP 2 of 2: Calculate the value of the discriminant:
[tex]\begin{gathered} d=b^2-4ac \\ d=(-4)^2-4\cdot(-2)\cdot5=16+40=56 \end{gathered}[/tex]Since the discriminant is positive, the equation has two real solutions. Using the formula:
[tex]x=\frac{-(-4)\pm\sqrt[]{56}}{2\cdot(-2)}=\frac{4+\sqrt[]{56}}{-4}=\frac{4\pm7.483}{-4}[/tex]We have two solutions:
x = -2.87
x = 0.87
If we wanted to express the solutions in radical form, then we must simplify the expression:
[tex]x=\frac{4+\sqrt[]{56}}{-4}[/tex]Since 56 = 4 x 14 :
[tex]\begin{gathered} x=\frac{4\pm\sqrt[]{4\cdot14}}{-4} \\ \text{Separating the roots:} \\ x=\frac{4\pm2\sqrt[]{14}}{-4} \\ \end{gathered}[/tex]Dividing by -2:
[tex]x=\frac{-2\pm\sqrt[]{14}}{2}[/tex]Separating the solutions:
[tex]\begin{gathered} x_1=\frac{-2+\sqrt[]{14}}{2} \\ x_2=\frac{-2-\sqrt[]{14}}{2} \end{gathered}[/tex]Which is a better deal? Martha sells apples in 5 lb bags for $4.00 OR Steve sells apples in 3 lb bags for $2.25
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Maria's deal is a better deal
Explanations:First Deal: Martha sells apples in 5 lb bags for $4.00
Price of a 5 lb bag of apples = $4
Price of a 1 lb of apples = $4 /5 = $0.8
Second deal: Steve sells apples in 3 lb bags for $2.25
Price of a 3 lb bag of apples = $2.25
Price of 1 lb of apples = $2.25 / 3 = $0.75
The deal with the highest price per pound is the better deal
Maria sells at a higher price per pound than Steve, therefore, Maria's deal is better
3/2 gallon of water fills 4/5 of a pitcher.How many gallons can fill a full pitcher. Write a division equation to match this problem then explain what it's value represents in the context.
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Answer
(15/8) gallons of water will fill one full pitcher.
Explanation
Let the amount of gallons that will fill a full pitcher be x gallons
(3/2) gallons = (4/5) of the pitcher
x gallons = 1 pitcher
Converting the fractions into decimals for easier solving
(3/2) = 1.5
(4/5) = 0.8
1.5 gallons = 0.8 of the pitcher
x gallons = 1 pitcher
We can form a mathematical relationship by cross multiplying
(0.8) (x) = (1) (1.5)
0.8x = 1.5
Divide both sides by 0.8
0.8x ÷ 0.8 = 1.5 ÷ 0.8
x = 1.875 gallons = (15/8) gallons
Hope this Helps!!!
Find the length of side x in simplest radical form with a rational denominator.45°V545°X
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Since we have two angles of 45° and a right angle, we can deduce the opposite and the adjacent side are the same.
Using the pythagoras theorem we have,
[tex]\begin{gathered} a^2+b^2=c^2 \\ x^2+x^2=\sqrt[]{5}^2\text{ Adding like terms we have} \\ 2x^2=5\text{ Isolating x, we get.} \\ x^2=\frac{5}{2}\text{ finding the root we have} \\ x=\sqrt[]{\frac{5}{2}}=\frac{\sqrt[]{5}}{\sqrt[]{2}} \end{gathered}[/tex]Then, we have to find the simplest radical form, with the rational denominator. Rationalizing we have.
[tex]\frac{\sqrt[]{5}}{\sqrt[]{2}}=\frac{\sqrt[]{5}}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}}=\frac{\sqrt[]{5\cdot2}}{\sqrt[]{2\cdot2}}=\frac{\sqrt[]{10}}{\sqrt[]{4}}=\frac{\sqrt[]{10}}{2}[/tex]The final answer is
[tex]x=\frac{\sqrt[]{10}}{2}[/tex]Find the average rate of change of f(x) = 2x ^ 2 - 8x from x = 2 to x = 5 .
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Remember that
The average rate of change of the function f(x) is given by the formula
[tex]\frac{f(b)-f(a)}{b-a}[/tex]where
a=2
b=5
f(a)=f(2)=2(2)^2-8(2)=-8
f(b)=f(5)=2(5)^2-8(5)=10
substitute
[tex]\frac{10-(-8)}{5-2}=\frac{18}{3}=6[/tex]The average rate of change is 6Given the points A and BThe coordinates of point A = ( 3 , 1 )The coordinates of point B = (-1 , -1)The midpoint of AB = ([?],[ ])The midpoint of ab?
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Given the points A and B
The coordinates of point A = ( 3 , 1 )
The coordinates of point B = (-1 , -1)
The midpoint of AB, is the point C
C will be calculated as following :
[tex]C=\frac{A+B}{2}=\frac{(3,1)+(-1,-1)}{2}=\frac{(3-1,1-1)}{2}=\frac{(2,0)}{2}=(1,0)[/tex]so, the midpoint of AB = (1 , 0 )
In a photography club, about 48% of the members are girls. If there are 26 members who are girls, explain how you can use mental math to estimate the total number of people in the photography club.
To estimate the total number of people in the photography club, begin by rounding 48% to , 1 of 6.
Select Choice
% and round 26 to , 2 of 6.
Select Choice
. Since this is about , 3 of 6.
Select Choice
of the members in the club, then , 4 of 6.
Select Choice
+ , 5 of 6.
Select Choice
or , 6 of 6.
Select Choice
people is the approximate number of people in the club.
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From the given data , 26 girls represents the 48% of the members in a club then estimating total number of people in the club are 325 /6 approximately equal to 54.
As given in the question,
Let x represents the total number of members present in the club
Given:
48% of the total members present in the club are girls
Total number of girls present in club are 26
Required expression to estimate total number of members present in the club
48% of x = 26
⇒( 48 /100) × x = 26
⇒ x = (26 ×100) /48
⇒ x = 325 /6
⇒ x≈ 54 (approximately)
Therefore, as 26 girls represents the 48% of the members in a club then estimating total number of people in the club are 325 /6 approximately equal to 54.
The complete question is:
In a photography club, about 48% of the members are girls. If there are 26 members who are girls, explain how you can use mental math to estimate the total number of people in the photography club.
Learn more about estimate here
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Determine if the expression - m²/7 is a polynomial or not.
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SOLUTION
We want to determine if
[tex]\frac{m^2}{7}[/tex]is a polynomial, now this can be written as
[tex]\frac{1}{7}m^2[/tex]Since the coefficient is a fraction, but the exponent which is 2 is not a fraction or a negative number, it is a one term polynomial known as monomial.
Hence it is a polynomial called a monomial
Since the highest power is 2
It is a polynomial of degree 2
I need help I'm confused about how to get my inequality
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The inequality is 11.25x + 14.75 ≤ 80. And the number of people will be 5.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
A gathering of companions needs to go to the entertainment mecca. They have something like $80 to spend on stopping and confirmation. Stopping is $14.75, and tickets cost $11.25 per individual, including the charge.
Let 'x' be the number of people. Then the inequalities are written as,
11.25x + 14.75 ≤ 80
Simplify the equation, then the value of 'x' is given as,
11.25x + 14.75 ≤ 80
11.25x ≤ 65.25
x ≤ 5.8
The number of people will be 5.
More about the inequality link is given below.
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Find the area of a square with sides 17 meters long.
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Given:
Length of one side of the square, L = 17 meters
Let's find the area of the square.
To find the area of a square, apply the formula:
[tex]\text{Area}=L^2[/tex]Where:
L is length of one side of the square = 17 meters
Hence, we have:
[tex]\text{Area}=L^2=17^2=17\ast17=289m^2[/tex]Therefore, the area of the square is 289 square meters.
ANSWER:
289
2 17 The area of the trapezoid below is 420 cm Find the height Round to the nearest tenth if the answer is in decimal form.
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Consider that the area of a trapezium is given by,
[tex]\text{Area}=\frac{1}{2}\times(\text{sum of parallel sides)}\times\text{ height}[/tex]According to the given problem,
[tex]\begin{gathered} \text{Area}=\frac{17}{420} \\ \text{Parallel sides=}\frac{2}{7},\text{ }\frac{1}{5} \end{gathered}[/tex]Substitute the values and solve for the height as,
[tex]\begin{gathered} \frac{17}{420}=\frac{1}{2}\times(\frac{2}{7}+\frac{1}{5})\times h \\ \frac{17}{210}=(\frac{17}{35})\times h \\ h=\frac{35}{210} \\ h=\frac{1}{6} \\ h\approx0.2 \end{gathered}[/tex]Thus, the height of the trapezium is 0.2 cm approximately.
BD and AC on dining room levels of .0 identify each are as a major
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The measure of the minor arc is less than 180 degrees
The measure of the major arc is greater than 180 degrees
So Arc BA is a minor arc
[tex](BA)=44[/tex]The measure of the circle is 360 degree, then
[tex]m(\text{ACB)}=360-44=316[/tex]BD is the diameter of the circle, then it divides the circle into two equal parts
[tex]m(\text{BCD)}=\frac{360}{2}=180[/tex]The length of the arc DE can be found using this rule
[tex]\begin{gathered} \text{Arc(DE)}=\frac{120}{360}\times2\times\pi\times r \\ \text{Arc(DE)}=\frac{1}{3}\times2\times\pi\times2=\frac{4}{3}\pi=4.18879 \end{gathered}[/tex]Need help solving this problem without giving the answer: The Distance on a map between lake view and bay Cove is 4.5 inches. The map key says 0.5 inches on the map is equivalent to 1 mile. What is the actual distance between lake view and bay cove?
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
lake view ===> bay Cove
distance (map) = 4.5 in
map ratio:
0.5 in = 1 mile
Step 02:
real distance:
[tex]\text{real distance = 4.5 in }\cdot\text{ }\frac{1\text{ mile }}{0.5\text{ in}}[/tex]real distance = 9 miles
The answer is:
real distance = 9 miles
Before your trip to the mountains, your gas tank was ; full. When you returned home, the gas gaugeregistered ; of a tank. If your gas tank holds 18 gallons, how many gallons did you use to drive to themountains and back home?
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To determine the total gallons used in the trip, let's solve the following first.
1. Initial gallon before the trip.
If the tank is 18 gallons when full and before the trip, it was 7/9 full, then, let's multiply 18 and 7/9 to get the exact number of gallons before the trip.
[tex]18\times\frac{7}{9}=\frac{18}{1}\times\frac{7}{9}=\frac{126}{9}=14gal[/tex]Hence, initially, there were 14 gallons before the trip.
2. Number of gallons after the trip
If the tank is 18 gallons when full and after the trip, it was now 1/3 of a tank, then, let's multiply 18 and 1/3 to get the exact number of gallons left after the trip.
[tex]\frac{18}{1}\times\frac{1}{3}=\frac{18}{3}=6gal[/tex]After the trip, we have 6 gallons of gas remaining in the tank.
So, this means, 14 gal - 6 gal = 8 gallons of gas was used in driving to the mountain and back home.
If you can do your homework at a rate of 5.5 minutes for every problem,how many problems could be done after 4.81 hours? Round to a wholenumber.
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we have to change 4.81 hours to minutes, so we get that
[tex]4.81\text{ hours=}4.81\cdot60=288.6\text{ minutes}[/tex]And now we have to divide 288.6 minutes by 5.5
[tex]\frac{288.6}{5.5}=52.47\approx52[/tex]So 52 problems could be solved in 4.81 hours
Observe that: 6= 1 X2 X3; 24 = 2 X 3 X 4; 60 = 3 X 4 X 5 - Note also that: 6 = 23 - 2 ; 24 = 33 - 3 ; 60 = 43 - 4 (a) Write down the first number larger than 60 that is the product of three consecutive integers. (b) Write down the smallest 4-digit number that is the product of three consecutive integers. (c) Prove algebraically that any number that can be written in the form n - n can be expressed as the product of three consecutive integers.
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Answer:
a) 120
b) 1320
c)
[tex]\begin{equation*} n^3-n=(n-1)*n*(n+1) \end{equation*}[/tex]Explanation:
Given:
a) From the above, we can see the first three numbers that are products of three consecutive integers. The numbers are 6, 24, and 60.
The next number will be;
[tex]120=4*5*6[/tex]So the first number that is larger than 60 that is the product of three consecutive numbers is 120
b) The first 4-digit number that is a product of three consecutive integers is 1320 as can be seen below;
[tex]1320=10*11*12[/tex]So 1320 is the smallest 4-digit number that is the product of three consecutive integers.
c) We can go ahead and prove as shown below;
[tex]\begin{gathered} n^3-n=n(n^2-1)=n(n^2-1^2)=n(n+1)(n-1)=(n-1)*n*(n+1) \\ \therefore n^3-n=(n-1)*n*(n+1) \end{gathered}[/tex]For example, if n = 2, we'll have;
[tex]\begin{gathered} 2^3-2=(2-1)*2*(2+1) \\ 8-2=1*2*3 \\ 6=6 \end{gathered}[/tex]last year 4822 people took a licensing exam at a test center and 3028 people passed. what was the pass rate? (round answer as a % rounded to the nearest whole #)
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
total people = 4822
passed people = 3028
pass rate = ?
Step 02:
pass rate = passed people / total people * 100 %
= 3028 / 4822 * 100 %
= 62.8 %
The answer is:
The pass rate was 63%
Tracy read 1/2 of her new book on Tuesday. She would like to read 1/4 of what remains this weekend. What fraction of the whole book will she read this weekend
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Tuesday = 1/2 of the book
Weekend = 1/4 of what remains
First, calculate the remain after Tuesday:
1-1/2 = 1/2
Multiply the amount read by the remain:
1/2 x 1/4 = 1/8
Fraction of the whole book: 1/8
n is between m and o if mn =14 and mo =36 then no = what
Answers
Given MN=14, MO=36.
N is between M and O.
The figure is :
Thus NO=MO-MN
Putting the values,
[tex]NO=36-14=22[/tex]Thus the answer is NO=22.