still 7 inches since translation and rotation do not affect area, angles and the length of the sides. Therefore, if you look at the angles, CA will be the same as DF
Convert to polar form
Y=x^2-64/16
To convert the expression, Y=x^2-64/16 into the polar form, we would have: r = 2 / √(sin^2θ + cos^2θ).
How to convert into the polar formThe polar form of a mathematical expression is a way of representing complex numbers using their magnitude and angle.
For a complex number z = a + bi, where a and b are real numbers, its polar form is given by z = r(cosθ + i sinθ), where r is the magnitude of z and θ is the angle that z makes with the positive real axis.
So, for the given expression, the polar form can be converted this way:
r^2 sin^2θ = r cos^2θ - 4
r^2(sin^2θ + cos^2θ) = 4
r = 2 / √(sin^2θ + cos^2θ)
Therefore, the polar form is r = 2 / √(sin^2θ + cos^2θ).
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A wall is 2000 sq ft. A gallon of paint covers 400 sq ft. Complete the conversion factor: 1 gallon / ? sq ft
To cover a 2000 sq ft wall, we will need 5 gallons of paint.
what is area?
Area is the measure of the size of a two-dimensional surface or region, expressed in square units. It is a fundamental concept in geometry and is used to quantify the amount of space inside a shape, such as a square, rectangle, triangle, or circle. The unit of measurement for area varies depending on the system used, but in the International System of Units (SI), the standard unit of area is the square meter (m²). In everyday life, we often use other units of area such as square feet, square inches, or square centimeters.
To find the conversion factor, we need to divide the number of square feet by the number of square feet covered by one gallon of paint:
Conversion factor = 1 gallon / (400 sq ft/gallon)
So, for a wall that is 2000 sq ft, we can use this conversion factor to find the number of gallons of paint needed:
Number of gallons = (2000 sq ft) / (400 sq ft/gallon) = 5 gallons
Therefore, to cover a 2000 sq ft wall, we will need 5 gallons of paint.
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1.) Write a48 as a product of two powers with the same
base in four different ways. Only use positive exponents.
The given exponents term can be written in the form of [tex](a^{4})^{12}[/tex] .
What about exponents?
Exponents are a mathematical operation that involves multiplying a base number by itself a certain number of times. Exponents are often referred to as powers, and the base number is raised to a power, which is usually represented by a superscript number. For example, 2^3 means 2 raised to the power of 3, which is 2 x 2 x 2 = 8.
Exponents are commonly used in many areas of mathematics, including algebra, calculus, and geometry. They are used to represent very large or very small numbers, to simplify calculations, and to express repeated multiplication in a more compact form. Exponents can also be negative or fractional, allowing for the representation of roots and other mathematical concepts.
According to the given information:
In the given question [tex](a^{48} )[/tex] can be written as,
[tex](a^{4})^{12}[/tex] = [tex](a^{4})^{12} = a^{48}[/tex]
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The table below shows the numbers of two to five bedroom houses in the Belmont Neighborhood. What is the mean number of bedrooms in a house in this neighborhood?
Number of bedrooms Frequency
2 7
3 35
4 56
5 27
The mean number of bedrooms in a house in this neighborhood will be: 3.824.
How to determine the mean number of bedroomsIn order to find the mean number of bedrooms in a house in the Belmont Neighborhood, we need to calculate the weighted mean by multiplying each number of bedrooms by their respective frequency.
Next, we will add the products, and then divide by the total frequency. So we can start as follows:
(2 * 7) + (3 * 35) + (4 * 56) + (5 * 27) = 14 + 105 + 224 + 135 = 478
Total frequency = 7 + 35 + 56 + 27 = 125
Therefore, the mean number of bedrooms = 478 / 125 approximately 3.824
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An investment opportunity is offering an annual interest rate of 12% compounded continuously.
How much should you invest initially if you want to have fifteen thousand dollars after nine years?
Do not include a dollar sign in your answer. Round your answer to the nearest cent.
I
Answer:
data given
interest rate 12%
amount to be received 15ooo
time9years
Step-by-step explanation:
from
A=p[1+r/100]^n
where
A is amount
p is principal
r is rate interest
n number of interist period
now,
15000=p[1+12/100]^8
15000/1.12^8 =p×1.12^8/1.12^8
p=6058.24
p=6058)
: .you should invest 6,058
The amount to be invested initially if you want to have fifteen thousand dollars after nine years is $3947.18.
How to find the compound interest?If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
We are given that:
A=15000
r=0.12
t=9
We need to find P. You can do this by rearranging the formula:
P=ertA
Then plug in the given values and use a calculator:
P=e0.12×915000
P≈3947.18
Therefore, by the given interest rate the answer will be $3947.18.
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F(x)=2/3x-1 show creat points to graph
Label values on thex&y axis
To create points for the graph of f(x) = (2/3)x - 1, we can choose values of x and calculate the corresponding values of f(x). See explanation below and attached graph.
What is the explanation for the above response?To create points for the graph of f(x) = (2/3)x - 1, we can choose values of x and calculate the corresponding values of f(x). For example:
When x = -3, f(x) = (2/3)(-3) - 1 = -3 - 1 = -4When x = -2, f(x) = (2/3)(-2) - 1 = -2 1/3When x = -1, f(x) = (2/3)(-1) - 1 = -1 2/3When x = 0, f(x) = (2/3)(0) - 1 = -1When x = 1, f(x) = (2/3)(1) - 1 = -1/3When x = 2, f(x) = (2/3)(2) - 1 = 1/3When x = 3, f(x) = (2/3)(3) - 1 = 1So, we have the following points for the graph: (-3, -4), (-2, -2 1/3), (-1, -1 2/3), (0, -1), (1, -1/3), (2, 1/3), (3, 1).
We can now plot these points on a graph, with x-values on the horizontal axis and f(x) values on the vertical axis. We can label the horizontal axis as "x" and the vertical axis as "f(x)" or "y".
Note that the graph of f(x) = (2/3)x - 1 is a straight line with slope 2/3 and y-intercept -1.
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The volume of a cube is increasing at a rate of 56 in^3/sec. At what rate is the length of each edge of the cube changing when the edges are 4 in. long? (Recall that for a cube,
V = x^3.)
Answer:
Step-by-step explanation:
Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.
We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.
First, we differentiate the volume equation with respect to time t:
V = x^3
dV/dt = d(x^3)/dt
Using the chain rule:
dV/dt = 3x^2 * (dx/dt)
Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:
56 = 3 * (6)^2 * (dx/dt)
Solving for dx/dt:
56 = 108 * (dx/dt)
dx/dt = 56 / 108
dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)
So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.
f(x) = x2 + 4; interval [0, 5]; n = 5; use left endpoints
Therefore, the Left Riemann Sum for this function, interval, and number of subintervals is 50.
The left endpoint rule is what?The top-left corner of these rectangles touched the y=f(x) curve. In other words, the value of f at the subinterval's left endpoint determined the height of the rectangle over that subinterval. This technique is called the left-endpoint estimate because of this.
With left endpoints and n = 5 subintervals, we may use the Left Riemann Sum formula to approximate the area under the curve of f(x) = x2 + 4 over the range [0, 5]:
Left Riemann Sum = ∑[i=1 to n] f(x_i-1) Δx
In this case, a = 0, b = 5, n = 5, and we will use the left endpoints, so:
Δx = (5 - 0)/5 = 1
Using the left endpoints, the subintervals and their left endpoints are:
[0,1],[1,2],[2,3],[3,4],[4,5]
[tex]so,\; x_0 = 0, x_1 = 1, x_2 = 2, x_3 = 3, x_4 = 4.[/tex]
Now we can calculate the Left Riemann Sum:
Left Riemann Sum= [tex]f(x_0)\Delta x + f(x_1)\Deltax + f(x_2)\Deltax + f(x_3)\Deltax + f(x_4)\Deltax[/tex]
= f(0)×1+f(1)×1+f(2)×1+f(3)×1 + f(4)×1
= 4+5+8+13+20
= 50
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The expression below is equal to -20g plus a constant term. -8(2.5g-4.25)+5.25 What is the value of the constant term?
Answer:
We can simplify the expression -8(2.5g-4.25)+5.25 by distributing the -8:
-8(2.5g-4.25)+5.25 = -20g + 34 + 5.25
Simplifying further, we can combine the constant terms:
-8(2.5g-4.25)+5.25 = -20g + 39.25
So the value of the constant term is 39.25.
Landon and Maria are meeting at the library to work on their history project. Maria walks 9 blocks east and 3 blocks north to get to the library from her house. Landon walks 5 blocks south and 7 blocks west to get to the library from his house. The map below shows the location of the library and Landon's and Maria's houses. To the nearest block, how far is Landon's house from Maria's house if Maria could walk in a straight line?
To the nearest block, Landon's house is at distance of 12 blocks away from Maria's house if Maria could walk in a straight line.
What is Pythagoras theorem?A basic mathematical theorem relating to the sides of a right-angled triangle is known as Pythagoras' theorem. The square of the length of the hypotenuse, the side that faces the right angle, is said to be equal to the sum of the squares of the lengths of the other two sides, known as the legs, in a right triangle.
This can be written in mathematical notation as:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the legs of the right triangle.
In this case, we can consider the straight line between Maria's house and Landon's house as the hypotenuse of a right triangle, with the distances they walked as the other two sides. We can use the distance formula to find the lengths of those sides:
Distance walked by Maria = √(9² + 3²) = √90 ≈ 9.49 blocks
Distance walked by Landon = √(5² + 7²) = √74 ≈ 8.60 blocks
Now we can use the Pythagorean theorem to find the distance between their houses:
Distance between houses = √(9.49² + 8.60²) ≈ 12.46 blocks
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3. Assess the quantity of mass in twenty-six point seven ounces in terms of milligrams. MUST SHOW
ENGINEERING METHOD BELOW.
What is your calculated answer most closely to?
a. 0.562 mg
b. 1.562 mg
c. 2.562 mg
d. 3.562 mg
The unit twenty-six point seven ounces in terms of milligrams is 756932.3
Converting the unit to milligramsTo convert ounces (oz) to milligrams (mg), we can use the following conversion factor:
1 oz = 28,349.5 mg
Therefore, to convert 26.7 oz to mg, we can multiply 26.7 by the conversion factor as follows:
26.7 oz × 28,349.5 mg/oz = 756932.3 mg
So, there are approximately 756932.3 milligrams in 26.7 ounces of mass.
Comparing the calculated answer with the options given, we see that the answer is closest to 756,498.15 mg, which is not one of the options.
Therefore, we cannot choose any of the options given.
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If you are performing a left-tailed z-statistic test with a sample size n = 85 and a 0.01 significance level, what is the critical value?
If your calculated value of the z-statistic is z = −1.95, what is your conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis)?
This null hypothesis prompt is actually straight forward. Note that where the above conditions exist, we must NOT reject the null hypothesis due to the values of the z-statistics and the significance level.
What is a nyll hypothesis?The idea that there is no influence on the population is known as the null hypothesis. We can reject the null hypothesis if the sample contains sufficient data to refute the assertion that there is no impact in the population (p≤α ).
So to determine whether or not to accept or reject the null hypothesis, we must determine dthe z-score.
To find the the critial value for a left-tailoed test, where the signifiance level is 0.01, note that we must find the z-score that leaves 1% of the area in the left tail.
Using the standard distribution table, the z-score for 0.01 left tail is about -2.33.
Since
z-satistics which is equal to -1.95 (as given) is greater than the z-score, we must NOT reject the null hypothesis.
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which of these is another way to write the function g(x)= 3x
Answer:
y=9 (3x/9-2) + 18=3x
Step-by-step explanation:
If you horizontally…
Check the picture below.
so following the template below, a shift 2 units to the left, means C=2
[tex]G(x)=\sqrt{x+2}[/tex]
Please help will mark Brainliest
Step-by-step explanation:
5 cos (307) = 3
5 sin (307) = -4
just plot the point ( 3, -4 ) Done.
Answer:
The point is (3, -4) because 5 cos [307] = 3 and 5 sin [307] = -4
100 Points! Algebra question. Write a quadratic equation in standard form with -1/2, 3/4 as its roots. Photo attached. Thank you!
Answer:
Step-by-step explanation:
Given:-
•α=
•β=
To Find:-
♦The Quadratic Equation using the Given details?
AnsWer:-
↓Quadratic Formula↓
→k[x²-(α+β)x+αβ]
→α+β=+
•Take LCM•
→α+β=+
→α+β=
→αβ=×
→αβ=
↑Using these Values in The Formula↑
→k[x²-(x)+() ]
★Let k=8★
→8[x²-(x)+() ]
→8x²-(-2x)+(-3)
→8x²+2x-3=quadratic Equation
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. There is no shaded bar above 60 to 69. A shaded bar stops at 4 above 70 to 79, at 4 above 80 to 89, at 6 above 90 to 99, at 6 above 100 to 109 and at 10 above 110 to 119. The graph is titled Temps in Beach Town.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Sunny Town is symmetric
Mean, because Sunny Town is skewed
Median, because Beach Town is skewed
Mean, because Beach Town is symmetric
Answer:
Whats the question?
Step-by-step explanation:
plsssssssss 2/7=4/5+9q
Answer: q= -2/35
Step-by-step explanation:
Rearrange terms 2 Subtract from both sides 3.Simplify the expression Subtract the numbers Subtract the numbers 4 Divide both sides by the same factor 5 Simplify the expression Divide the numbers Cancel terms that are in both the numerator and denominator Move the variable to the left
Answer:
q = -2/35
Step-by-step explanation:
2/7 = 4/5 + 9q
(2/7) - (4/5) = 9q
(10/35) - (28/35) = 9q
-18/35 = 9q
(-18/35) / 9 = q
(-18/(35*9)) = q
-18/315 = q
q = -2/35
Check:
2/7 = 4/5 - 9*2/35
2/7 = 4/5 - 18/35
10/35 = 28/35 -18/35
10 = 28 -18
Kelly is on a quiz bowl team. She answers her quiz bowl questions correctly two-thirds of the time.
Which is a way you could simulate the probable outcomes of this event with a six-sided number cube?
A)correct: a roll of 6
incorrect: a roll that is not 6
B)correct: a roll of an even number
incorrect: a roll of an odd number
C)correct: a roll of a number less than 3
incorrect: a roll of a greater than, or equal to, 3
D)correct: a roll of a number that is not divisible by 3
incorrect: a roll of a number that is divisible by 3
Answer:
To simulate the probable outcomes of this event with a six-sided number cube, you can place the numbers 1-6 on the faces in the following order: 1, 4, 3, 2, 5, 6. Then roll the cube and use the following outcomes:
a) Correct: a roll of 6 Incorrect: a roll that is not 6
b) Correct: a roll of an even number Incorrect: a roll of an odd number
c) Correct: a roll of a number less than 3 Incorrect: a roll of a greater than or equal to 3
d) Correct: a roll of a number that is not divisible by 3 Incorrect: a roll of a number that is divisible by 3
Step-by-step explanation:
what is 4361 divided by 7
Triangle PQR is rotated 180 degrees clockwise about the origin to produce the image Triangle P’Q’R’. Which of the following statements is TRUE abóyate Triangle P’Q’R’.
Answer:
Step-by-step explanation:
We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is: P (1, 4) → P' (-1, -4) Q (3, 1) → Q' (-3, -1) R (2, -1) → R' (-2, 1) Thus, the new position of ∆PQR is ∆P’Q’R’.
What are the solutions to the quadratic equation below?
10x17x+3=0
O A.
x=-
x=-- and x = -1/
5
O B. x=² and x = 1/
X
O C. x=
3
10
15
and x = 1
OD. x=3 and x = 1
Answer:
The given quadratic equation is: 10x^2 + 7x + 3 = 0.
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 10, b = 7, and c = 3.
Substituting these values into the formula, we get:
x = (-7 ± sqrt(7^2 - 4(10)(3))) / 2(10)
x = (-7 ± sqrt(49 - 120)) / 20
x = (-7 ± sqrt(-71)) / 20
Since the square root of a negative number is not a real number, this quadratic equation does not have any real solutions. Therefore, none of the options (A), (B), (C), or (D) are correct.
Using a table, find the range of the function for the given domain:
f(x)=2x+7 with domain: x = {2, 3, 5, 9}
A. y = {9, 10, 12, 16}
B. y = {11, 13, 17, 25}
C. y = {4, 6, 10, 18}
D. y = {-11, -13, -17, -25}
f(x)=2x+7
domain: x = {2, 3, 5, 9}
Explanation:Replace each x value and solve for y
x=2
f(2)= 2(2) + 7 = 4 + 7 = 11
x=3
f(3)= 2(3) + 7 = 6 + 7 = 13
x=5
f(5)= 2(5) + 7 = 10 + 7 = 17
x=9
f(9)= 2(9) + 7 = 18 + 7 = 25
Answer:B. y = {11, 13, 17, 25}We can find the range of the function by plugging in each value in the domain into the function and listing the output values:
When x = 2, f(2) = 2(2) + 7 = 11
When x = 3, f(3) = 2(3) + 7 = 13
When x = 5, f(5) = 2(5) + 7 = 17
When x = 9, f(9) = 2(9) + 7 = 25
Therefore, the range of the function for the given domain is y = {11, 13, 17, 25}.
Hence, the correct answer is B. y = {11, 13, 17, 25}.
Given the figure below .find X and Y to three significant digits.Write your answer in the answer box provided below
Check the picture below.
Make sure your calculator is in Degree mode.
[tex]\cos(25^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{12}}\implies 12\cos(25^o)=x\implies \boxed{10.876\approx x} \\\\[-0.35em] ~\dotfill\\\\ \sin(25^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{12}}\implies 12\sin(25^o)=z \\\\[-0.35em] ~\dotfill\\\\ \sin(50^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{y}}\implies y=\cfrac{z}{\sin(50^o)}\implies y=\cfrac{12\sin(25^o)}{\sin(50^o)}\implies \boxed{y\approx 6.62}[/tex]
Which expression represents the phrase The sum of w and twenty
A. 20w
B. w + 20
C. w^20
D. 20 x w
Brenda is fishing from a small boat. Her fishing hook is 12 feet below her, and a fish is swimming at the same depth as the hook, 16 feet away. How far away is Brenda from the fish?
Answer:
We can use the Pythagorean theorem to solve this problem. Let's call the distance Brenda is away from the fish "x". Then, we have a right triangle with legs of length 12 and x, and a hypotenuse of length 16. So:
x^2 + 12^2 = 16^2
Simplifying:
x^2 + 144 = 256
x^2 = 112
Taking the square root of both sides:
x ≈ 10.6 feet
Therefore, Brenda is approximately 10.6 feet away from the fish.
how can you tell if a quotient is less than 1'.
Answer:
Step-by-step explanation:
Okay so when a smaller number is divided by a larger number, the quotient is less than 1. Hope this helps Bye sisters slay.
Use the information below to determine the new coordinates of the image under the given translation.
Triangle ABC with vertices
A(0, 7), B(7, 3),
and C(1, 4): (x, y) → (x − 3, y - 4)
The new triangle A'B'C' after the translation is A'(-3, 3), B'(4, -1), and C'(-2, 0).
What is translation?A shape is translated when it is moved up, down, left or right without turning. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.
To perform the given translation (x, y) → (x − 3, y - 4) on the triangle ABC with vertices A(0, 7), B(7, 3), and C(1, 4), we need to apply the same transformation to each vertex of the triangle and obtain their new coordinates.
For vertex A(0, 7), the transformation gives:
(x, y) → (x − 3, y - 4)
(0, 7) → (0 - 3, 7 - 4)
The new coordinates of A are (-3, 3).
For vertex B(7, 3), the transformation gives:
(x, y) → (x − 3, y - 4)
(7, 3) → (7 - 3, 3 - 4)
The new coordinates of B are (4, -1).
For vertex C(1, 4), the transformation gives:
(x, y) → (x − 3, y - 4)
(1, 4) → (1 - 3, 4 - 4)
The new coordinates of C are (-2, 0).
Therefore, the new triangle A'B'C' after the translation is A'(-3, 3), B'(4, -1), and C'(-2, 0).
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Is a measure of 30 inches "far away" from a mean of 15 inches? As someone with knowledge of statistics, you answer "it depends" and request the standard deviation of the underlying data.
(a) Suppose the data come from a sample whose standard deviation is 3 inches. How many standard deviations is inches from 15 inches?
(b) Is 30 inches far away from a mean of 15 inches?
(c) Suppose the standard deviation of the underlying data is 10 inches. Is 30 inches far away from a mean of 15 inches?
Hence, 30 inches deviate by 1.5 standard deviations from the 15-inch mean as the underlying data's standard deviation is 10 inches.
what is standard deviation ?The standard deviation of statistics is a measurement of how much a group of data values deviate from their mean (average) value. While a significant standard deviation suggests that the pieces of information are dispersed throughout a broader range of values, a low standard deviation suggests that the data points are generally close to the mean.
given
a) If the sample's standard deviation is 3 inches, then the number of standard deviations from the mean of 15 inches that are 30 inches is:
z = (30 - 15) / 3 = 5
b) The context of the data and the standard deviation will determine whether 30 inches is distant from a mean of 15 inches.
A departure of 15 inches from the mean, meanwhile, can be viewed as being significantly off the mean if the standard deviation is minimal.
c) If the underlying data's standard deviation is 10 inches, then the number of standard deviations from the mean of 15 inches that are 30 inches is:
z = (30 - 15) / 10 = 1.5
Hence, 30 inches deviate by 1.5 standard deviations from the 15-inch mean as the underlying data's standard deviation is 10 inches.
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What number increased by 3.5% of itself equals 621?
Answer:
Step-by-step explanation:
We need to find a number which increased by 3.5 of itself equals 621.
Let that number be x.
x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.
x(1+3.5) = 621
x(4.5) = 621
x = 621/4.5
x = 138
Therefore the required number is 138.
Answer: 138
Step-by-step explanation:
We need to find a number which increased by 3.5 of itself equals 621.
Let that number be x.
x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.
x(1+3.5) = 621
x(4.5) = 621
x = 621/4.5
x = 138
Therefore the required number is 138.