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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given that у=6 cm and θ=15 °, work out x rounded to 1 decimal place.
(the diagram is not drawn to scale.)
Using a trigonometric realtion, we can see that x = 23.18cm
How to find the value of x?Here we have a right triangle, we can see that y = 6cm, and the angle theta is 15°.
Notice that y is the opposite cathetus to the known angle, and we want to find the value of x, which is the hypotenuse.
Then we can use the trigonometric relation:
sin(a) = (opposite cathetus)/hypotenuse.
Reaplacing what we know, we will get:
sin(15°) = 6cm/x
Solving that for x:
x = 6cm/sin(15°9
x = 23.18cm
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What is the value of x log3x equals 4
[tex]~~~~\log_3 (x) = 4\\\\\implies x= 3^4 \\\\\implies x= 81[/tex]
5² + 12² =
64a3³
Work out the value of a.
Your final line should say, a =
Answer:
a = 13/4Step-by-step explanation:
√(5²+12²) = ∛(64a³)
√(25+144)=√(64a)
√169 = √(64a)
13 = 4a
a = 13/4
The perimeter of an equilateral triangle is 96 cm. Find the length of the side of the triangle.
Answer:
Answer : Length(l) = 32 cm
Step-by-step explanation:
Given,
Perimeter(P)=96 cm
Length(l)=?
We know that,
P = 3l
96 = 3l
96÷3 = l
32 = l
Therefore, length(l) = 32 cm
I need help! 50 points!
The equation of this sinusoidal function is either
f(x) = a sin(bx) + c
or
f(x) = a cos(bx) + c
Either way, the plot of f9x) has amplitude a, period 2π/b, and midline y = c.
If the period is π/2, then
2π/b = π/2 ⇒ b = 4
If the maximum value is 10 and the minimum value is -4, then
-4 ≤ a sin(4x) + c ≤ 10
-4 - c ≤ a sin(4x) ≤ 10 - c
-(4 + c)/a ≤ sin(4x) ≤ (10 - c)/a
Recall that sin(x) is bounded between -1 and 1. So we must have
-(4 + c)/a = -1 ⇒ a = c + 4
(10 - c)/a = 1 ⇒ a = -c + 10
Combining these equations and eliminating either variable gives
a + a = (c + 4) + (-c + 10) ⇒ 2a = 14 ⇒ a = 7
a - a = (c + 4) - (-c + 10) ⇒ 0 = 2c - 6 ⇒ c = 3
Finally, we have either
f(x) = a sin(bx) + c ⇒ f(0) = c = 3
or
f(x) = a cos(bx) + c ⇒ f(0) = a + c = 3
but the cosine case is impossible since a = 7.
So, the given function has equation
f(x) = 7 sin(4x) + 3
For every 36 minutes of sprinting, Scarlett earned 12 dollars for charity. To find the unit rate of this, I would first need to structure the equation. In this case, I would use division, so my equation would be 36 ÷ 12 = 3. The final answer would be, for every 3 minutes, Scarlett earns $1. is this right? i will give 15 points:)
Answer:
$1 every 3 minutes
Step-by-step explanation:
Cause every 36 minutes Scarlett earns $12 and if you divide 36 by 12 it will give 3 minutes which means she earns $1 per 3 minutes. You're right.
A large bin of Peanut M&M's contains red, yellow, blue, and brown M&M's. Lexi
scoops out a bowl full of M&M's and counts how many of each type she has: 12 red,
7 yellow, 14 blue, and 9 brown.
Luke scoops out a bowl of 36 Peanut M&M's. About how many should he expect to
be blue?
Answer:
About 12 blue m&m’s
Step-by-step explanation:
30 Use the method of completing the square to determine the vertex of f(x) = x² - 14x - 15.
State the coordinates of the vertex.
Answer:
x² - 14x - 15 = (x − 7)² − 64Then the coordinates of the vertex are (7 , -64)Step-by-step explanation:
x² - 14x - 15 = x² - 14x + (49 - 49) - 15
= (x² - 14x + 49) - 49 - 15
= (x² - 14x + 7²) - 49 - 15
= (x − 7)² − (49 + 15)
= (x − 7)² − 64
x² - 14x - 15 = (x − 7)² − 64
Then the coordinates of the vertex are (7 , -64)
Rotate the point (7, 8) around the origin 90 degrees counter clockwise. State the image of the point .
By applying the equation for the rotation around the origin we conclude that the image of the point (7, 8) after rotating 90° counterclockwise is (-8, 7).
How to rotate a point around the origin
In this question we must apply a rigid transformation on a point to find its image, rigid transformations are transformations applied on geometric loci such that Euclidean distances are observed in every point of the loci. A rotation about the origin is a kind of rigid transformation and is defined by the following expression:
(x', y') = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)
Where:
(x, y) - Original point(x', y') - Resulting pointθ - Angle of rotation, in degrees.Please notice that positive values of θ represents a counterclockwise rotation. If we know that (x, y) = (7, 8) and θ = 90°, then the resulting point is:
(x', y') = (7 · cos 90° - 8 · sin 90°, 7 · sin 90° + 8 · cos 90°)
(x', y') = (-8, 7)
By applying the equation for the rotation around the origin we conclude that the image of the point (7, 8) after rotating 90° counterclockwise is (-8, 7).
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6x1 + 9 x 1/10 + 8 x 1/100 + 3 x 1/1000=?
Answer:
6983/1000 OR 6.983
Step-by-step explanation:
6*1=6
9*1/10=9/10
8*1/100=8/100
3*1/1000=3/1000
6+9/10+8/100+3/1000=6983/1000
OR
6.983
help i will give 20 thax
Ty's brother will get 3/4th part of the pizza.
What is Division ?The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing.
Here, Total number of Pizza = 1
Number of parts required = 4
Now, each member will get the part of pizza = 1/4
Total number of brothers = 3
Ty's brother will get pizza = 3 X 1/4
= 3/4
Thus, Ty's brother will get 3/4th part of the pizza.
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Answer:
3/4
Step-by-step explanation:
because there are 4 people so ty get 1/4 and his brothers get the rest.
Please help me with this probability question; I’d really appreciate it!
The attendance at a village fair depends on the weather.
The probability of a high attendance at the fair is 0.9.
This is reduced to 0.4 if it is raining.
The probability of it raining is 0.2.
What is the probability of its raining and there being a high attendance?
0.6
0.08
0.36
0.18
Answer:
B. 0.08
Step-by-step explanation:
In order to solve this problem, we must account for all possibilities. The sum of all posssiblities must sum up to 1.
1 - High Attendance/No Rain
0.9*0.8 = 0.72
2- High Attendance/ Rain
0.4*0.2 = 0.08
3 - Low Attendance/No Rain
0.1*0.8 = 0.08
4 - High Attendance/No Rain
0.6*0.2 = 0.12
Now we answer the question of rain and high attendance.
0.08/1 = 0.08
Figure FGHJ is shown below.
Figure F G H J has 4 sides. Sides F J and G H are congruent and parallel, and sides G F and H J are congruent and parallel. Angles G and J are 130 degrees.
Which names accurately describe figure FGHJ? Select two options.
parallelogram
quadrilateral
rectangle
rhombus
trapezoid
If x and y are complementary angles, then y is a right angle.
right?
5600 to the nearest 1000
Answer:
6000.
Step-by-step explanation:
Hundreds digit is 6 so we round up the thousand digit (5) to get 6000.
PLS HELP
Which shows the following expression after the negative exponents have been eliminated?
Answer:
Option 2
Step-by-step explanation:
Given :
[tex]\frac{xy^{-6} }{x^{-4}y^{2} }[/tex]
=============================================================
Applied Rule :
[tex]\frac{x^{a} }{x^{b} } = x^{a-b}[/tex]
============================================================
Solving :
⇒ To remove negative exponents, bring to the opposite side (e.g. if in the denominator, bring to the numerator)
⇒ [tex]\frac{x(x^{4}) }{y^{2}(y^{6}) }[/tex]
How do I graph this linear function
x < -1
This is how the linear function looks.
Explain the difference between 2(7x-4) and (7x-4)^2
Answer:
2(7x-4) = 7x(2)-4(2) = 14x-8
but
(7x-4)^2 = (7x-4) (7x-4)
Multiply the following
(a) 2.7x4
(b) 0.79x32.4
(c)1.07 x 0.02
(d) 2.3x4.35
(e) 2.5x100
(f) 0.0008x100
g) 0.25x 10000
h)3x0.55
i)0.08x5
j)351.06x4
k)0.3x0.03
l) 21.7x0.1
m) 200.02 x 2.2
Kindly look into this and try to answer all of them this contains 30 points
Find the general solution of the given differential equation. Cos(x) dy dx (sin(x))y = 1
The general solution to the differential equation is y = sinx + c cosx.
What is differential equation?It is defined as the equation which contains functions, derivative of the functions to make an expression.
We have a differential equation:
[tex]\rm cosx\left(\dfrac{dy}{dx}\right)+\left(sinx\right)y\:=\:1[/tex]
Multiply by dx:
(cosx) dy + (sinx) y dx = dx
(cosx) dy = (1 - (sinx) y) dx
After simplification and integrating, we will get:
[tex]\rm y = \dfrac{tan x}{sec x}+ \dfrac{c}{secx}[/tex]
y = sinx + c cosx
Thus, the general solution to the differential equation is y = sinx + c cosx.
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A random number generator is used to create a list of 200 single-digit numbers. of those 200 numbers, 105 are even and ninety-five are odd. seven was generated fifteen times. what is the experimental probability of an odd number other than seven being generated? 40.0% 45.0% 47.5% 52.5%
Using it's concept, it is found that the probability of an odd number other than seven being generated is of 40.0%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For an experimental probability, these number of outcomes are taken from previous trials.
In this problem, 200 numbers have been generated, and 80 are odd numbers that are not seven, hence the probability is given by:
p = 80/200 = 0.4 = 40%.
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Answer:
40
Step-by-step explanation:
What is the measure of major B 84° O 276° O252° O 84° O 168 arc AB? A
Answer:
A - 84°
Step-by-step explanation:
The measure of an arc is equal to the measure of the central angle that intersects it.
The central angle of this circle measures 84° and it intercepts arc AB, meaning arc AB measures 84°
PLS I NEED 100% TO GET A GOOD MATH GRADE THIS YEAR
The following box plot shows the number of years during which 24 schools have participated in an interschool swimming meet:
At least how many schools have participated for 1 year or less? (5 points)
6 schools
8 schools
12 schools
14 schools
Answer:
6 schools
Step-by-step explanation:
I did the same assignment
A bottle contains 1 2/5 litres of orange squash. To make one drink, 1/200 of a litre of squah is needed. How many drinks can be made from the bottle of squash?
Answer:
280 drinks
Step-by-step explanation:
Capacity of bottle [tex]=1\frac{2}{5}=\frac{7}{5}\: l[/tex]Squash needed to make one drink [tex]=\frac{1}{200}\:l[/tex]Total number of drinks [tex]=\frac{7}{5}\div\frac{1}{200}[/tex][tex]=\frac{7}{5}*200[/tex][tex]=7*40[/tex][tex]=280[/tex]Answer:
280 drinks. We need to divide 1 2/5 by 1/200 in order to get this answer.
Find the volume of the following figure.
6 cm3
7 cm3
8 cm3
5 cm3
Answer:
7 cm³
Step-by-step explanation:
Assume each cube has an edge 1 cm in length.
Each cube has volume 1 cm³.
There are 7 cubes.
volume = 7 cm³
What is the solution of 5sin2θ=3 for 0≤θ≤2π? Please help.
Answer:
C) [tex]\theta\approx\{0.3218,1.249,3.463,4.3908\}[/tex]
Step-by-step explanation:
[tex]5\sin2\theta=3;\: 0\leq\theta\leq 2\pi\\\\\sin2\theta=\frac{3}{5}\\ \\2\theta\approx\{0.6436,2.498,6.926,8.7816\}\\\\\theta\approx\{0.3218,1.249,3.463,4.3908\}[/tex]
The mean mass of a squad of 19 rugby players is 87 kg
A player of mass 102 kg joins the squad.
Work out the mean mass of the squad now, in kilograms (kg).
19 players x 87kg = 1653 total kg
1653 kg + 102kg = 1755 kg
1755kg / 20 players = 87.75kg mean mass
Answer: 87.75 kg
Please help me with this!
Answer:
sin(4)
Step-by-step explanation:
sin(-184) is the equivalent to sin(4) (degree), positive and acute angle.
What is the quotient if -3/8 and -1/3
[tex]\left(- \dfrac 38 \right) \div \left(-\dfrac 13 \right)\\\\\\=-\dfrac 38 \times (-3)\\\\\\=\dfrac 98[/tex]
What is the y intercept of this quadratic? (Picture)
Answer:
We know that the y intercept is -3 because that is where it intersects! The point for the y intercept is (0, -3)
Step-by-step explanation: