Answer:
Hi,
Step-by-step explanation:
Let's make group of 3 numbers
1+2-3=0
4+5-6=3
7+8-9=6
...
97+98-99=96
s=1+2-3+....+97+98-99=0+3+6+..+96=3*(0+1+2+3+...+32)
=3*(32+0)*33/2
=1584
Prove that an integer consisting of 3n ones is divisible by 3n (e.g. 111 is divisible by 3, 111,111,111 is divisible by 9, etc.) Prove it by induction. Notice, that while the number with a sum of digits divisible by 3 is itself a multiple of 3 and the number with a sum of digits divisible by 9 is itself a multiple of 9, it is NOT true that the number with a sum of digits divisible by 27 is necessarily a multiple of 27.
For proof of 3 divisibility, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.
Integers divisible by 3The proof for divisibility of 3 implies that an integer is divisible by 3 if the sum of the digits is a multiple of 3.
Proof for the divisibility111 = 1 + 1 + 1 = 3 (the sum is multiple of 3 = 3 x 1) (111/3 = 37)
222 = 2 + 2 + 2 = 6 (the sum is multiple of 3 = 3 x 2) (222/3 = 74)
213 = 2 + 1 + 3 = 6 ( (the sum is multiple of 3 = 3 x 2) (213/3 = 71)
27 = 2 + 7 = 9 (the sum is multiple of 3 = 3 x 3) (27/3 = 9)
Thus, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.
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Which of the following shows the true solution to the logarithmic equation 3 log Subscript 2 Baseline (2 x) = 3
x = negative 1
x = 1
x = negative 1 and x = 1
x = 0, x = negative 1, and x = 1
The value of x is 1 , option B is the correct answer.
What is an Equation ?When two algebraic expressions are equated using an equal sign , the mathematical equation formed is called an Equation.
The equation is given by 3log₂(2x)=3
3log₂(2x)=3
log₂(2x) = 3/3
log₂(2x) = 1
The base of the logarithm is 2
it can also be written as
[tex]\rm 2^{log_{2}(2x)} = 2 ^1[/tex]
2x = 2
x = 1
Therefore the value of x is 1 , option B is the correct answer.
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Jamaal bounces on a trampoline. His height, as a function of time, is modeled by = -16x^2+20x+4.
Which statement best describes the function?
Answer:
B. The function is nonlinear.
Step-by-step explanation:
A linear function graphs as a straight line. It is a polynomial function of degree 1. Any function that is not a linear function is a nonlinear function.
__
degreeThe function given is a polynomial function of degree 2. (Its highest-degree term is x^2, which has an exponent of 2.)
categorizationSince the degree is not 1, the function is nonlinear.
_____
Additional comment
A polynomial function will never be "linear at some points and nonlinear at other points." Such a description might apply to a piecewise-defined function.
You have been given data about gas prices in 15 states.
2018 Gas Price Data
Max: $2.42
Min: $2.03
Mean: $2.098
Median: $2.06
Mode: $2.04
Variance: 0.0121
Standard Deviation: $0.1098
What does the range, standard deviation, and variance say about gas prices in 2018?
The range, standard deviation, and variance say about gas prices in 2018 discussed below
What is standard deviation and variance?Variance is the average squared deviations from the mean, while standard deviation is the square root of this number.
As the variance in 2018 is 0.0121.
A model with low variance means sampled data is close to where the model predicted it would be.
As the standard deviation in 2018 is 0.1098.
Low standard deviation means data are clustered around the mean
A small range means low variability in a distribution.
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A landscaping company has giving quotes to 2 different customers the first customer quote is $287 to install 13 bushes and 7 trees and the second customer' quote is $392 to install 8 bushes and 12 trees
The cost of installing a bush is $7 and the cost of installing a tree is $28
How to determine the cost of bushes and trees?Represent the trees with t and the bushes with b.
So, we have the following equations:
13b + 7t = 287
8b + 12t = 392
Make t the subject in 13b + 7t = 287
t = (287 - 13b)/7
Substitute t = (287 - 13b)/7 in 8b + 12t = 392
8b + 12 * (287 - 13b)/7 = 392
Multiply through by 7
56b + 12 * (287 - 13b) = 2744
Expand
56b + 3444 - 156b = 2744
Collect like terms
56b - 156b = 2744 - 3444
-100b = -700
Divide both sides by -100
b = 7
Substitute b = 7in t = (287 - 13b)/7
t = (287 - 13*7)/7
Evaluate
t = 28
Hence, the cost of installing a bush is $7 and the cost of installing a tree is $28
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Hey i have a question i need help with this it says...
How many cups would give you 2 quarts of water
if you have an awnser for this please let me know
Answer:
8 cups = 2 quarts
Step-by-step explanation:
Answer:
Eight cups will give you 2 quarts of water
a 4 1/2 inch candle burns down in 9 hours. after how many hours will it have burned 4 1/4 inches? use the drop down menu to state your answer as a decimal, mixed number, or improper fraction.
The number of hours it will take to burn 4 1/4 inches of candle is 8.5 hours in decimal.
How to solve fractions?Using ratio to solve, find the ratio of candle length to the time taken to burn down
let
x = time taken by 4 1/4 inches candle4 1/2 : 9 = 4 1/4 : x
9/2 ÷ 9 = 17/4 ÷ x
9/2 × 1/9 = 17/4 × 1/x
1/2 = 17/4x
cross product1 × 4x = 2 × 17
4x = 34
x = 34/4
x = 8.5 hours
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What value of b will cause the system to have an infinite number of solutions? A system of equations. y equals 6 x plus b. negative 3 x plus StartFraction one-half EndFraction y equals negative 3. A coordinate grid with a line labeled negative 3 x plus StartFraction one-half EndFraction y equals negative 3 and passes through the points (1, 0) and (0, negative 6).
The value of b that causes the system of equations to have infinite solutions is -6.
How to find the solution to the given system of equations?For that, we will try solving it first using the method of substitution in which we express one variable in another variable's form and then you can substitute this value in another equation to get a linear equation in one variable.
If there comes a = a situation for any a, then there are infinite solutions.
If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.
In the given problem, our equations are:
y = 6x + b
-3x + (1/2)^y = -3
So the value of b needs to be such that these two equations must be equal.
In the second equation:
[tex](1/2)^y = -3 + 3x\\y = -3^2 + 3x^2 \\y = -6 + 6x[/tex]
Then we must have:
6x - 6 = 6x + b
-6 = b
Thus, the value of b that causes the system to have infinite solutions is -6.
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Answer:
-6
Step-by-step explanation:
trust
If c = 64-d, what is the value of C when D = -1/6
The equation c = 64 - d is a linear equation, and the value of c in the equation is 64 1/6
How to solve the equation?The equation is given as:
c = 64 - d
The value of d is given as:
d = -1/6
Substitute -1/6 for d in c = 64 - d
c = 64 - -1/6
Evaluate the difference
c = 64 1/6
Hence, the value of c in the equation is 64 1/6
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1,8,27; 64; Rule Missing numbers
Answer:
rule: f(n) = n³
missing numbers: 125, 216, 343, 512, 729
Step-by-step explanation:
Your familiarity with the cubes of small integers helps you recognize each of these numbers is a cube. Their sequence is the sequence of cubes of increasing natural numbers.
1 = 1·1·1 = 1³
8 = 2·2·2 = 2³
27 = 3·3·3 = 3³
64 = 4·4·4 = 4³
__
The rule is ...
f(n) = n³
The cubes of 5 through 9 will complete the set of numbers ...
1, 8, 27, 64, 125, 216, 343, 512, 729
How many triangles are there
Answer:
24 trianglesStep-by-step explanation:
in the picture
A grapefruit is 8% heavier than an orange, and an apple is 10% lighter than the orange
By what percent is a grapefruit heavier than an apple?
Answer:
8%+10%=180 180÷100=1.8% grapefruit is heavier than Apple
Which of these is a correct expansion of (3x − 1)(4x² + 5)?
OA. 3x 4x2 + 3x 5+1 4x² +1.5
OB. 3x. 4x² + 3x • 5+ (−1) • 4x² + (−1) • 5
OC. 3x 4x² + (-1). 4x² + 4x².5+ (-1).5
Given: MN is twice the length of
KM and KM = 8. Find the
perimeter of the total figure.
A. 24
B. 28
C. 38
D. 48
MN=2KM
2(8)16MN+KM=24
QP/KJ=MN/MK=24/16=3/2As we can see
QP is almost greater than 3/4th MN
It's atleast 10+ or even 12+
So possible perimeter excluding QJ and KJ is atleast 34 to 36 .
So it can neither be 38 nor 28 .
Only one option yields that's 48(Option D)
SAmina walked nine times round a square Field. If she covered a total distance of 12 96 meters, what is the area of the field?
Find the surface area of the prism //Please answer//
Answer:
358in²
Step-by-step explanation:
9 × 11 = Area of Face One = 99in²
99 × 2 = Face One + Face One on the opposite side = 198in²
4 × 11 = Area of Face Two = 44in²
44 × 2 = Face Two + Face Two on the opposite side = 88in²
9 × 4 = Area of Face Three = 36in²
36 × 2 = Area of Face Three + Face Three on the opposite side = 72in²
Total Surface Area = 198 + 88 + 72 = 358in²
Find the sum of the interior angles of the following polygon
Answer:
540° and x = 85°
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 5 , then
sum = 180° × 3 = 540°
2
sum the interior angles and equate to 540°
x + 115° + 95° + 115° + 130° = 540°
x + 455° = 540° ( sum 455° from both sides )
x = 85°
Enlarge the triangle by scale factor of -1/3
Please help me on this question I will mark you as the brainiest
The attached image represents the triangle after it has been enlarged
How to enlarge the triangle?The given parameters are:
Scale factor, k = -1/3Center, (a,b) = (-1,2)From the graph, the coordinates of the triangle are:
A = (-4,2)
B = (-4,-4)
C = (-1,-4)
The rule of dilation is calculated using:
[tex](x,y) \to (k(x - a) + a, k(y - b) + b)[/tex]
So, we have:
[tex]A' = (-\frac 13(-4 +1) - 1, -\frac 13(2 - 2) + 2)[/tex]
A' = (0, 2)
[tex]B' = (-\frac 13(-4 +1) - 1, -\frac 13(-4 - 2) + 2)[/tex]
B' = (0, 4)
[tex]C' = (-\frac 13(-1 +1) - 1, -\frac 13(-4 - 2) + 2)[/tex]
C' = (-1, 4)
See attachment for the image of the triangle, after it has been enlarged
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NEED HELP ASAP PLEASE
Answer:
y = 2x^2 + 8x + 3
Step-by-step explanation:
Step 1: use the vertex form of the quadratic equation
y = a*(x - h)^2 + k
vertex = (-2, -5) = (h, k)
y = a*(x + 2)^2 - 5
Step 2: determine a using the given point
point = (0, 3)
y = a*(x + 2)^2 - 5
3 = a*(0+2)^2 - 5
3 + 5 = a*(2)^2
8 = a*4
a = 2
vertex equation is now y = 2*(x + 2)^2 - 5
Step 3: simplify vertex equation to standard quadratic equation
quadratic equation = Ax^2 + Bx + C
y = 2*(x + 2)^2 - 5
y = 2*(x^2 + 4x + 4) - 5
y = 2x^2 + 8x + 8 - 5
y = 2x^2 + 8x + 3
What is the mass of hydrogen atoms that is measured at 54 u? the relationship between atomic mass units (u) and grams (g) is 1 u = 1.66 x 10^-24 g.
The mass of hydrogen atoms that measures 54 u is 89.64 x 10^-24
Analysis:
If 1 u = 1.66 x 10^-24, then 54 u = 54 x 1.66 x 10^-24 = 89.64 x 10^-24
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The final exam scores in a statistics class were normally distributed with a mean of 70 and a standard deviation of five. What is the probability that a student scored less than 55% on the exam?
The probability that a student scored less than 55% on the exam is 0.134%.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
We have:
Mean of the sample = 70
Standard deviation = 5
= P(X<55%)
Z = (55-70)/5
Z = -3
P(X < -3)
From the Z table:
P(x<-3) = 0.0013499
or
P(x<-3) = 0.134%
Thus, the probability that a student scored less than 55% on the exam is 0.134%.
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100 points!!!! university data if a student is selected at random, what is the probability that the student receives aid and is a graduate?
Answer:
17.5%
Step-by-step explanation:
1879/10730=17.5%
Answer:
18%
Step-by-step explanation:
Locate the "receives aid" column and "graduate" row. The value 1879 is in this row and column combo.
There are 10730 students total as shown in the bottom right hand corner.
Roughly 1879/10730 = 0.1751 = 17.51% of the students are graduates who receive aid. This rounds to 18%
Please help me!! High School algebra 2 math. Big Ideas Math
Answer:
x = 8
Step-by-step explanation:
Hello!
The missing angle in the triangle can be found by subtracting 90° and 45° from 180°. The missing angle is 45°.
This means that the triangle is isosceles, as there are two congruent base angles, 45° and 45°.
The side lengths opposite these two angles are congruent.
We can see that 8 is opposite 45°, and x is opposite 45°. Therefore, x must be equal to 8.
The value of x is 8.
Answer:
x = 8
Step-by-step explanation:
The interior angles of a triangle sum to 180°.
The given triangle is a right triangle, so the missing angle is 45°
⇒ 180° - 90° - 45° = 45°
As the triangle has 2 equal angles, this means it is an isosceles triangle (with its vertex at the right angle). An isosceles triangle has legs of equal measure, therefore [tex]x=8[/tex].
Proof
This can be proven by using the tan trigonometric ratio to calculate the value of x.
Tan trig ratio
[tex]\sf tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta[/tex] = 45°O = 8A = xSubstituting the given values into the equation and solving for x:
[tex]\implies \tan (45^{\circ})=\dfrac{8}{x}[/tex]
[tex]\implies x=\dfrac{8}{\tan (45^{\circ})}[/tex]
[tex]\implies x=\dfrac{8}{1}[/tex]
[tex]\implies x=8[/tex]
If you bought 4 candies for a
total of $3.28, how much did it
cost you for 3 candies?
Answer:
2.46
Step-by-step explanation:
3.28/4=0.82(for one candy)
0.82×3=2.46(for 3 candies)
Which expression is equivalent to 18x^2√14x^8 / 6√7x^4, if x ≠ 0?
The equivalent expression of [tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex] is [tex]3x^4\sqrt{2}[/tex]
How to determine the equivalent expression?The expression is given as:
[tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex]
Start by dividing 18 by 6
[tex]3x^2\sqrt{14x^8} \div \sqrt{7x^4}[/tex]
Next, divide 14 by 7
[tex]3x^2\sqrt{2x^8} \div \sqrt{x^4}[/tex]
Take the square root of x^8 and x^4
[tex]3x^2 * x^4\sqrt{2} \div x^2[/tex]
Divide x^2 by x^2
[tex]3* x^4\sqrt{2}[/tex]
Evaluate
[tex]3x^4\sqrt{2}[/tex]
Hence, the equivalent expression of [tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex] is [tex]3x^4\sqrt{2}[/tex]
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Answer: B or 3x^4 sqrt 2
explanation: only simplified answer above
How do I solve and find x?
Answer:
x=60
Step-by-step explanation:
First get x all alone on 1 side of the equation. Add 14.5 to both sides of the equation to cancel out the negative. You will then be left with
x/5= 12
Multiply both sides of the equation by 5 to cancel out the division and you'll get x=60
If f(x )= 3/x-3, what is (fof)(x)?
Answer:
the second option is correct.
Step-by-step explanation:
that is the solution above.
Select the correct answer
The function g(x)=x²2 is transformed to obtain function h:
h(x) = g(x − 3).
Which statement describes how the graph of his different from the graph of g?
A. The graph of h is the graph of g vertically shifted down 3 units.
B. The graph of h is the graph of g horizontally shifted right 3 units.
C. The graph of h is the graph of g horizontally shifted left 3 units.
D. The graph of h is the graph of g vertically shifted up 3 units.
Answer:
B
Step-by-step explanation:
h(x) is the same as g(x), just that every y value of g(x) happens now at x instead of at x-3, so 3 units "later", and everything is therefore just moved 3 units to the right.
Use DeMoivre's Theorem to find (3cis*pi/6)^3
The ANSWER is 27i ----- PLEASE EXPLAIN!!!! THANK YOU!!!
The correct value of (3cis(pi/6))³ is 27i.
What is Complex Number?Complex numbers are numbers that consist of two parts — a real number and an imaginary number. Complex numbers are the building blocks of more intricate math, such as algebra.
Given the complex number in polar coordinate expressed as
z = r(cos∅+isin∅)
zⁿ = {r(cos∅+isin∅)}ⁿ
According to DeMoivre’s Theorem;
zⁿ = rⁿ(cosn∅+isinn∅)
Given the complex number;
(3cis(pi/6))³
= {3(cosπ/6 + isinπ/6)}³
Using DeMoivre’s Theorem;
= 3³(cos3π/6 + isin3π/6)
= 3³(cosπ/2 + isinπ/2)
= 3³(0 + i(1))
= 27i
Thus, the correct value of (3cis(pi/6))³ is 27i.
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12. Ben says
"the difference between two consecutive square numbers is always odd."
Is Ben correct?
Answer:
Yes Ben is correct
Step-by-step explanation:
For example:
If n² is the greater of the two consecutive square numbers, then the difference will be 2n-1. So for example, if you have two consecutive squares with the values of 25, and 36, their difference will be 11. Notice though that 11=2×6–1, so it conforms to 2n-1.