The value of the double integral ∫∫[tex]\frac{y^{2} }{x^{2} +y^{2} }[/tex] dA is 131.95.
We know that in polar coordinates, the circle become r = 4 and r = 16. These are the limits on the radius. Clearly the limits on the angle are
0 ≤ θ ≤ 2π.
Therefore we get,
∫∫ [tex]\frac{y^{2} }{x^{2} + y^{2} }[/tex] dA = ∫ ∫ r²sin²θ / r² dr dθ
= ∫ sin²θ dθ ∫ r dr
= [ [tex]\frac{1}{2}[/tex]θ - [tex]\frac{1}{4}[/tex]sin(2θ)]₀²ⁿ[ [tex]\frac{1}{2}[/tex] r²]₄¹⁰
= [tex]\frac{1}{4}[/tex] (2π)(10² - 4²)
= 42π
∫∫ [tex]\frac{y^{2} }{x^{2} + y^{2} }[/tex] dA = 131.95.
What is Polar coordinates?
When each point on a plane of a two-dimensional coordinate system is decided by a distance from a reference point and an angle is taken from a reference direction, it is known as the polar coordinate system.
Polar coordinates are useful in calculating the equations of motion from a lot of mechanical systems. Polar coordinate means the magnitude and direction of a vector.
Polar coordinate system of locating points in a plane with reference to a fixed point O and a ray from the origin usually chosen to be the positive x-axis.
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A number is between 10 and 15. It has prime factors of 2 and 3. What is the number?
The number in between 10 and 15 and having prime factors of 2 and 3 is 12.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
The integer between 10 and 15 are,
11,12,13,14
The prime factors of 2 and 3 will be given as,
[tex]2^{a} \times 3^{b}[/tex] where a and b can be positive.
Since, 12 = 2² × 3¹
Thus, 12 is the only number that is the prime factor of 2 and 3 both.
Hence "The number between 10 and 15 and having prime factors of 2 and 3 is 12".
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how healthy are the employees at direct marketing industry? a random sample of 12 employees was taken, and the number of days each was absent for sickness was recorded (for a 1-year period). use these data to create a 95% confidence interval for the population mean days absent for sickness.
The sample mean is 5.0833 and the standard deviation is 3.476 and the confidence interval is (2.87, 7.29).
In the given question, a random sample of 12 employees was taken, and the number of days each was absent for sickness was recorded (for a 1-year period).
Using these data to create a 95% confidence interval for the population mean days absent for sickness
2 5 3 7 10 0 6 8 5 11 3 1
a) We have to find the sample mean and the standard deviation (round to two decimal places).
The sample mean;
X = 2+5+3+7+10+0+6+8+5+11+3+1/12
X = 61/12
X = 5.0833
Now the standard deviation
SD = √[{x(1)-X)^2+(x(2)-X)^2…………….(x(12)-X)^2}/N]
After solving using that formula;
SD = 3.476
b) 95% confidence in interval for the population mean days absent for sickness.
Lower Bound = X - t(α/2)*s/√n
Upper Bound = X + t(α /2)*s/√n
where
α /2 = (1 - confidence level)/2 = 0.025
X = sample mean = 5.083333333
t(α/2) = critical t for the confidence interval = 2.20098516
s = sample standard deviation = 3.476108936
n = sample size = 12
df = n - 1 = 11
Thus,
Lower bound = 2.874719086
Upper bound = 7.291947581
Thus, the confidence interval is (2.87, 7.29).
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The right question is:
How healthy are the employees at direct marketing industry? A random sample of 12 employees was taken, and the number of days each was absent for sickness was recorded (for a 1-year period). Use these data to create a 95% confidence interval for the population mean days absent for sickness.
2 5 3 7 10 0 6 8 5 11 3 1
a) Find the sample mean and the standard deviation (round to two decimal places)
b) 95% confidence in interval for the population mean days absent for sickness.
Differentiate implicitly to find dy/dx. 2x^2+8xy+6y^2+13y-2=0 dy/dx= Find dy/dx using implicit differentiation. 3x^3=2y^2-9y dy/dx= Use implicit differentiation to find dy/dx. 3y^2=5x-2/5x+2 dy/dx
The first derivative of the implicit functions are listed below:
y' = - 4 · (x + 2 · y) / (8 · x + 12 · y + 13) y' = 9 · x² / (4 · y - 9) y' = 23 / (30 · y)How to use implicit differentiation
In this problem we have an implicit function of the form f(x, y) = 0, whose first derivative shall be found by implicit differentiation. Now we proceed to present the procedure. First, write the entire expression:
2 · x² + 8 · x · y + 6 · y² + 13 · y - 2 = 0
Second, use the derivative rules:
4 · x + 8 · y + 8 · x · y' + 12 · y · y' + 13 · y' = 0
4 · x + 8 · y + (8 · x + 12 · y + 13) · y' = 0
y' = - 4 · (x + 2 · y) / (8 · x + 12 · y + 13)
The same procedure is used in the next two implicit functions:
3 · x³ = 2 · y² - 9 · y
9 · x² = 4 · y · y' - 9 · y'
9 · x² = (4 · y - 9) · y'
y' = 9 · x² / (4 · y - 9)
3 · y² = 5 · x - (2 / 5) · x + 2
6 · y · y' = 5 - 2 / 5
6 · y · y' = 23 / 5
y' = 23 / (30 · y)
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An athlete runs 200 metres race in 24 seconds. what is his speed in km/h
Answer:(29.85km/h)
Step-by-step explanation:
1000m=1km
200m=x [x=(200m/1000m)x1km]
x=0.2km
3600second= 1 hour
24 seconds =b [b=(24s/3600s)x1 hour ]
b=0.0067(in 2 decimal place)
velocity in km/h will be
0.2km/0,0067secs
=29.85(in 2 decimal place)
Answer:
speed = 30 km/h
Step-by-step explanation:
We are told that a 200 metres race is run by an athlete in 24 seconds. The question then asks us to calculate the athlete's speed in km/h.
To do this, let's first convert the given data into the required units:
• Converting from metres to kilometres:
To convert from 200 metres to kilometres, we have to divide it by 1000:
200 m = 200 m ÷ 1000 m/km
= 0.2 km
• Converting from seconds to hours:
To convert 24 seconds to hours, we have to divide it by 3600:
24 s = 24 s ÷ 3600 s/h
= [tex]\frac{24}{3600}[/tex] h
Now that we have the data in the appropriate units, we can use the following formula to calculate speed:
[tex]\boxed{\mathrm{speed = \frac{distance}{time}}}[/tex]
⇒ speed = [tex]\mathrm{\frac{0.2 \ km}{24/3600 \ h}}[/tex]
⇒ speed = 30 km/h
Therefore, the speed of the athlete is 30 km/h.
Find X and Y I WILL MARK BRAINLIEST
Answer:
x = 40°
y = 35°
Step-by-step explanation:
Let us take two triangles ∆ABC and ∆ADE
We know that, in a triangle the sum of all angles is equal to 180°
So,
For the traingle ABC
m∠A = 80°m∠B = 60°m∠C = x°Now,
m∠A + m∠B + m∠C = 180°
80° + 60° + x° = 180°
140° + x° = 180°
x° + 140° - 140° = 180° - 140°
x = 40°
For the triangle ADE
m∠A = 80°m∠D = 65°m∠E = y°Now,
m∠A + m∠D + m∠E = 180°
80° + 65° + y° = 180°
145° + y° = 180°
y° + 145° - 145° = 180° - 145°
y = 35°
Thus, The value of x and y is 40° and 35° respectively
Find the slope of the line that contains the following points: (-7, 8) and (12, 8)
The slope of the line that contains the points: (-7, 8) and (12, 8) is 0
How to calculate the slope of the line?From the question, the points are given as
(-7, 8) and (12, 8)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (-7, 8) and (12, 8)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (-7, 8) and (12, 8)
Substitute the known values in the above equation
So, we have the following equation
Slope = (8 - 8)/(12 + 7)
Evaluate
Slope = 0
Hence, the slope of the line is 0
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10 less than a number
If a+ß+0 =πº, prove that: sin(a+ß-0) + sin(B+0-a) + sin(0+a-B) = 4sina.sinß.sin0
Answer: A+B+C=π⇒A+B=π−C
Step-by-step explanation: I think not sure hope this helps :)
Hi!, may I ask how this is meant to be solved? Studying for finals!
The slopes of the lines are 2/3, 5, 5/6 and 1 respectively
How to find the slope of a line?
The slope of a line is a measure of its steepness or incline. It is defined as the ratio of the vertical change (called the "rise") to the horizontal change (called the "run") between two points on the line.
The slope of a line can be expressed using the following formula:
Slope = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are two points on the line.
1. P₁(0,2) and P₂(3,4):
Slope = (4-2)/(3-0) = 2/3
2. P₁(1,2) and P₂(3, 7):
Slope = (7-2)/(3-2) = 5/1 = 5
3. P₁(-1,1) and P₂(5,6):
Slope = (6-1) / (5-(-1)) = 5/6
4. P₁(-1,-2) and P₂(10,11)
Slope = (11-(-1)) / (10-(-2)) = 12/12 = 1
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A ladder is leaning against a vertical wall makes an angle of 20° with the ground. The foot of the ladder is 3 m from the wall. Find the length of ladder (Round to the nearest whole number).
If you choose the 20 degree acute angle, the distance between the foot of the ladder and the wall represents the [Select] leg. Since we are given the [Select] leg and solving for the hypotenuse, we need to use [Select] to solve for the length of the ladder. The length of the ladder when solved is [Select] meters.
Options for blank #1: adjacent, opposite, hypotenuse
Options for blank #2: adjacent, opposite, hypotenuse
Options for blank #3: sine, cosine, tangent
Options for blank #4: 3, 1, 9, 4
The length of the ladder is approximately 3 m. The correct option is the first option 3
Calculating the length of a ladderFrom the question, we are to calculate the length of the ladder.
From the given information,
The ladder makes an angle 20° with the ground
and
The foot of the ladder is 3 m from the wall
This scenario gives a right triangle where the hypotenuse is the ladder and the adjacent is the distance of the foot of the ladder from the wall.
Let the length of the ladder be x
Thus,
Using SOH CAH TOA
We can write that
cos 20° = 3 / x
x = 3/(cos 20°)
x = 3.19
x ≈ 3 m
Hence, the length is approximately 3 m
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write an equation for the graph shown in the form $y=ax b.$
The required straight equation will be y = -0.5x + 27.5 passes through the points (-5, 0) and (5, 2).
What are equations in a straight line?
A straight line's equation is given by y=mx+c, where c is the height at which the line intersects the y-axis (often referred to as the y-intercept) and m is the gradient.
According to the given graph,
We can see two points are (-5, 0) and (5, 2)
The linear equation will be: y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Here
x₁ = -5, y₁ = 0
x₂ = 5, y₂ = 2
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]
Substitute values in the equation, we get
⇒ y - 0 = (2 - 0)/(8-4)(x-(-5))
⇒ y - 30 = (2)/(-4)(x + 5)
⇒ y - 30 = -1/2(x + 5)
⇒ y = (-1/2)x - 5/2 + 30
⇒ y = -0.5x + 27.5
Thus, the required equation will be y = -0.5x + 27.5 passes through the points (-5, 0) and (5, 2).
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Write an equation for the graph shown in the form y=ax+b.
what assumption is checked when looking at a qqplot in a one-way anova model? select one: a. independence assumption b. identically distributed assumption c. normality assumption d. equal variances among the groups
Therefore, option (c)normality assumption is checked when looking at a Q–Q plot in one-way ANOVA model.
What is Q–Q plot ?In statistics, a Q–Q plot is a probability plot, a graphical method for comparing two probability distributions by plotting their quantiles against each other. A point on the plot corresponds to one of the quantiles of the second distribution plotted against the same quantile of the first distribution
Here,
normality assumption is checked when looking at a Q–Q plot in one-way ANOVA model.
Explanation: The core tenet of the assumption of normality states that the sample mean distribution (across independent variables) is normal. Technically speaking, the Assumption of Normality asserts that the mean's sampling distribution or the distribution of means among samples is normal.
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evaluate √24−x when x = 6. write the answer in simplified radical form.
Given √24−x when x = 6 in simple radical form is 3*√2.
What is radical form?Simply put, simplifying a radical eliminates the need to find any further square roots, cube roots, fourth roots, etc.
Additionally, it entails eliminating any radicals from a fraction's denominator.
The square root of 2 or root 2 is represented using the square root symbol √ and written as √2 whose value is 1.414.
So, we have:
√24−x when x = 6
Thus we must now calculate the square root of 18.
The square root, if you're allowed to use a calculator, is 4.242.
If not, however, let's come as close as we can:
√(9 * 2)
Since 3 is the square root of 9:
3*√2
Therefore, given √24−x when x = 6 in simple radical form is 3*√2.
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how to find asymptotes of a rational function
Step-by-step explanation:
you devide the upper half of a fraction with the part under it. for example
6x2+x+1
_______=6. that is asymptote
x2+2
when you multiply 6 and lower half of a fraction you get 6x2+12
if you substract that from 6x2+x+1 you get x-11
if you make x-11=0 the number that x represents is the point where the function crosses the asymptote
An arithmetic sequence has first term 13 and common difference 6. Find the 25th term
of the sequence.
Answer:
a₂₅ = 157
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 13 and d = 6 , then
a₂₅ = 13 + (24 × 6) = 13 + 144 = 157
HELP MEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
t ≈ 7.7
Step-by-step explanation:
r ^nt
A = P ( 1 + ------- )
n
A = 3000
P = 1500
n = 12
r = 0.09
t = ?
0.09
3000 = 1500 ( 1 + ------- ) ^(12)(t)
12
0.09
3000 = 1500 ( 1 + ------- ) ^(12)(t)
÷1500 ÷1500 12
0.09
2 = ( 1 + ------- ) ^(12)(t)
12
Change into logs and divide
log 2
---------------------- = 12t
0.09
log (1 + ----------)
12
multiply both sides by (1/12)
log 2
(1/12) ---------------------- = 12t (1/12)
0.09
log (1 + ----------)
12
7.7304805 = t
7.7 ≈ t
I hope this helps!
SHOW WORK FOR BRAINLIST DUE TODAY
The transformations from the parent function are
Translation left by 3 unitsReflection across the x-axisTranslation down by 4 unitsThe graph of the absolute functionFrom the question, we have the following parameters that can be used in our computation:
g(x) = -|x + 3| - 4
The above function is an absolute value function
Next, we plot the graph using a graphing calculator
See attachment for the graph
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = |x| --- the parent function of an absolute value function
g(x) = -|x + 3| - 4 -- the transformed function
First, we have the transformation to be:
From f(x) = |x| to f'(x) = |x + 3|
This means the function is translated left by 3 units
Next, we have:
From f'(x) = |x + 3| to f'(x) = -|x + 3|
This means the function is reflected across the x-axis
Lastly, we have:
From f'(x) = -|x + 3| to g(x) = -|x + 3| - 4
This means the function is translated down by 4 units
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please help ASAP will give brainlest IF correct, and if you answer first! thanks sm
Answer:
x = 50
Step-by-step explanation:
we have 110, so
180 - 110 = 70
sum of all angles is 180
60 + 70 + x = 180
x = 180 - 60 - 70
x = 50
It is given that p : q : r = 0.8 : 4 : 0.2.Calculate the percentage of r of the total of p,q and r.
A.1%
B.4%
C.20%
D.25%
Answer:
B) 4%
Step-by-step explanation:
The total is
.8 + 4 + .2 = 5
[tex]\frac{r}{t}[/tex] = [tex]\frac{.2}{5}[/tex] = 0.04 = 4% To change a decimal to a percent multiply by 100%
what is the probability that a person selected at random will live on campus or have a low intention of attending the fair?
The probability that a person selected at random will live on campus OR have a low intention of attending the Fair is 0.584.
The data of Intention of Attending the Fall Career Fair is given below:
High Medium Low TOTAL
On Campus 99 102 22 223
Off Campus 78 80 43 201
>20 mi. Away 18 32 26 76
TOTAL 195 214 91 500
We have to find the probability that a person selected at random will live on campus OR have a low intention of attending the Fair.
Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = P(on campus) + P(low) - P(on campus and low)
Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = 223/500 + 91/500 - 22/500
Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = 292/500
Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = 0.584
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The right question is:
The data shown below is for a sample of LSU students to evaluate their intention of attending the Fall 2023 Career Fair based on where they live.
Intention of Attending the Fall Career Fair
High Medium Low TOTAL
On Campus 99 102 22 223
Off Campus 78 80 43 201
>20 mi. Away 18 32 26 76
TOTAL 195 214 91 500
What is the probability that a person selected at random will live on campus OR have a low intention of attending the Fair?
Please help. Math- Thank you
The simplified expression, when using the Quotient rule is b. 1 / 8⁴.
What is the Quotient Rule ?The Quotient Rule allows us to be able to carry out operations on quotients. The rule is such that when dividing quotients with the same base, you should subtract the quotients. For multiplication, you add the quotients.
8 ⁵ / 8 ⁹ will therefore be:
= 8 ⁵ ⁻ ⁹
= 8 ⁻⁴
8 ⁻⁴ is the equivalent of 1 / 8⁴ because when a number is taken to a negative power, then that number becomes a denominator to 1.
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The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes 8 hours for a car moving at 45 mph How long does the trip take for a car moving at 30 mph?
Time ∝ 1/Speed
Time = k/Speed
k = Time x Speed
The time taken for the trip for the car moving at 30 mph is 12 hours.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 7 is an equation.
We have,
Time ∝ 1/Speed
This can be written as,
Time = k/Speed
k = Time x Speed
Now,
The trip takes 8 hours for a car moving at 45 mph.
This means,
k = 8 x 45
k = 360
Now,
The time taken at the speed of 30 mph.
Time = k / Speed
Time = 360/30
Time = 12 hours
Thus,
The time taken for the trip for the car moving at 30 mph is 12 hours.
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The tree diagram represents an
experiment consisting of two trials.
.5 - A - A - .4 - c
.5 - B - .3 - c
.7 - D
P(A) =
Answer:
P(A) =0.5 obviously since it didn't say like P(AC) or P(AD)
At a store, a shirt was marked down in price by $10.00. A pair of pants doubled in price. Following these changes, the price of every item in the store was cut in half. write two different expressions that represent the new cost of the items, using s for the cost of each shirt & P for the cost of a pair of pants. Explain the different information each one shows.
The required new price of the shirts and pair of paints is given as y = [s - 10]/2 and y = [2p]/2 respectively,
Given that,
At a store, a shirt was marked down in price by $10.00. A pair of pants doubled in price. Following these changes, the price of every item in the store was cut in half.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
let y be the total cost for each different item
cost of the shirt = s - 10 and pair of pants = 2p
According to the question,
y = s - 10 / 2 and y = 2p / 2
Thus, the required new price of the shirts and pair of paints is given as y = [s - 10]/2 and y = [2p]/2 respectively,
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In ΔWXY, \overline{WY} WY is extended through point Y to point Z, \text{m}\angle YWX = (3x+17)^{\circ}m∠YWX=(3x+17) ∘ , \text{m}\angle XYZ = (10x-5)^{\circ}m∠XYZ=(10x−5) ∘ , and \text{m}\angle WXY = (3x+2)^{\circ}m∠WXY=(3x+2) ∘ . Find \text{m}\angle WXY.m∠WXY
The value of ∠WXY = 20.
What is Exterior angle theorem?
The exterior angle theorem describes the connection between the two remote angles in a triangle and the external angle created by an extended side outside the triangle.
Given: Measure of angle YWX = (3x + 17) °
Measure of angle WXY = (3x + 2) °
Measure of angle XYZ = (10x − 5) °
Therefore, m∠XYZ = m∠YWX + m∠WXY (exterior angle theorem)
⇒ (10x − 5) ° = (3x + 17) ° + (3x + 2) °
Solve for x,
⇒ 10x - 5 = 3x + 17 + 3x + 2
⇒ 10x - 6x = 17 + 7
⇒ 4x = 24
⇒ x = 6
∴ ∠WXY = (3x + 2) = 18 + 2 = 20
Hence, value of ∠WXY = 20.
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what is the rate of change?
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{50}~,~\stackrel{y_1}{45})\qquad (\stackrel{x_2}{70}~,~\stackrel{y_2}{61}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{61}-\stackrel{y1}{45}}}{\underset{run} {\underset{x_2}{70}-\underset{x_1}{50}}} \implies \cfrac{ 16 }{ 20 } \implies {\Large \begin{array}{llll} \cfrac{4 }{ 5 } \end{array}}[/tex]
Evaluate the expression.343 ^ { 4 / 3 }
In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. the expression.343 ^ { 4 / 3 } is 7,625
In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 = 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.The expression 343^ {4/3} can be broken down into 343 to the power of 4 divided by 3. Before we evaluate the expression, we must understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 can be calculated using the formula 343 x 343 x 343 x 343. This results in 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.
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2x2+89+765-78
i'm lesbian what you gonna say? thats what i thought
have a nice day
Answer: 780
Step-by-step explanation:
Two times 2 is 4
4 + 89 = 93
93 +765 = 858
858 - 78 = 780
please help me find the answer
Answer:
the last one is obviously represent a linear of function
What equals number nineteen
13+16 are the numbers that equals to 19.
What is equal number?The equal sign in the mathematics describes by equality between the values,. Of the equations, or expressions are the written on both sides. There symbol for equal to is two be the small horizontal lines placed to parallelly. We place the to the 'equal to' sign is between two things that are to the same or equal.
As we know,
If two things are equal or if one thing is equal to the another, they are the same or in the size, number, standard, or values .
As per the question we have to find equal number of 19.
So 13+6 are the equal number that equals to 19.
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