Answer: The square root of 216 is equal to approximately 6.485281.
Step-by-step explanation:
The square root of 216 is equal to the number that, when multiplied by itself, gives 216. The value of the square root of 216 can be found using several methods, including estimation, the long division method, and a calculator. Here, I'll provide a step-by-step explanation using estimation.
Step 1: Estimate the value of the square root.
One way to estimate the value of the square root of 216 is to find two perfect squares that are close to 216, and whose square roots are therefore close to the square root of 216. In this case, the perfect squares closest to 216 are 144 (12^2) and 225 (15^2). Since 216 is closer to 144, the square root of 216 is likely to be closer to 12 than to 15.
Step 2: Refine the estimate.
To refine the estimate of the square root of 216, we can average the two closest perfect squares and their square roots. In this case, the average of 12 and 15 is 13.5, and this is a better estimate of the square root of 216 than either 12 or 15 alone.
Step 3: Improve the estimate using a more precise method.
One method for finding an even more precise estimate of the square root of 216 is to use the Newton-Raphson formula for finding square roots. This formula involves repeatedly applying the following equation:
x_n+1 = (x_n + n/x_n) / 2,
where x_n is the nth estimate of the square root, and n is the number whose square root we are trying to find (in this case, n = 216). We can start with an initial estimate, such as x_0 = 13.5, and iterate the formula until the estimate converges to a desired level of precision.
Step 4: Use a calculator or other tools to find the exact value.
Finally, we can use a calculator or computer program to find the exact value of the square root of 216 to as many decimal places as desired. The exact value of the square root of 216 is equal to approximately 6.485281.
List the steps for rewritten
fractions as repeating decimals
(include an example as needed)
The graph of the rational function f(z) is shown. Which of the following statements are true?
Select all that apply.
Of(x) has end behavior as z → ∞, y → 0
O f(x) has a domain of all real numbers
□ f(x) > 0 on the intervals (-∞, -2) and (2, ∞)
Of(x) has an end behavior as zoo, y → 00
Of(x) <0 on the intervals [-2, 2]
Of(x) has vertical asymptotes x = -2 and x = 2
Of(x) has a horizontal asymptote y=-1
Answer:
x{27}=69+420
Step-by-step explanation:
The equation, A equal to 2,400 plus quantity 1 plus 0.031 over 4 end quantity all raised to the power of 4 times t, represents the amount of money earned on a compound interest savings account. What does the value 0.031 represent?
The value 0.031 represents the interest rate, which means the annual compounded interest rate is 3.1%.
The value 0.031 represents the interest rate, which means the annual compounded interest rate is 0.31%.
The value 0.031 represents the investment period, which means the investment is invested for 0.031 years.
The value 0.031 represents the investment period, which means the investment is invested for 3.1 years
In The equation, A equal to 2,400 plus quantity 1 plus 0.031 over 4 end quantity all raised to the power of 4 times t, represents the amount of money earned on a compound interest savings account, A. The value 0.031 represents the interest rate, which means the annual compounded interest rate is 3.1%.
What is the compound interest equation?The general compound interest equation is given as:
Formula:
A = P(1 + r/n)^nt
A = final amount or future value
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Compounding interest involves computing interest on both the principal and the accumulated interest.
On the other hand, the simple interest method does not compute interest on accumulated interest.
Thus, the correct representation of the value 0.031 is the compound interest rate as 3.1%.
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Use the information to answer the question.
Akeem, Diego, and Lily are each making banana bread. Lily uses
3½ cups
cups of flour more than Akeem. She uses 1 cups of flour less than Diego.
How many more cups of flour does Diego use than Akeem? Move numbers to the boxes to show the answer. If there is no whole number,
place a 0 in the first box.
The number of cups of flour that Diego uses more than Akeem will be 4 ½.
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
Akeem, Diego, and Lily are each making banana bread. Lily uses 3 ½ cups of flour more than Akeem. She uses 1 cup of flour less than Diego.
L = 3 ½ + A ...1
L = D - 1 ...2
From equations 1 and 2, then we have
D - 1 = 3 ½ + A
D = 4 ½ + A
The number of cups of flour that Diego uses more than Akeem will be 4 ½.
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which measures are used in the five-number summary?
Select all that apply
a. standar deviation
b. first quartile
c.minimum value
d. median
e.maximum value
f. third quartile
g. interauqrtile range
h. variance
i.mode j.mean
Five number summary consist of b. First quartile, a. Standard deviation, c. Minimum value, e. Maximum value i Mode, h. Variance, f. Third quartile, j. Mean, g. interquartile range, d. median.
If the data are graphed symmetrically, the distribution demonstrates 0% skewness regardless of how long or fat the tails are. When the median of a data set is utilized, 50% of the data points in the collection have values lower than or equal to the median, and 50% of them have values greater than or equal to the median. The middle score in the set is known as the median. The first step in calculating the median is to order the data points from smallest to greatest. The median in an odd-numbered set will be the value that falls exactly in the middle of the list. You must determine the average of the two middle numbers in a set of even numbers. The average is determined by summing up each value individually and dividing that sum by the total number of observations.
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QUIZ 4-2: PARALLEL LINES & TRANSVERSALS
Identify each angle pair, and tell whether each set is congruent or
supplementary.
1. Type:
or
2. Type:
or
3. Type:
supplementary?
supplementary?
or supplementary?
21 and 27
21 and 23
22 and 2
1. <1 and <7 are supplementary.
2. <1 and <3 are supplementary.
3. <2 and <6 are congruent angles.
What are Supplementary Angles and Congruent Angles?Supplementary angles are two angles that add up to 180 degrees. In other words, they are angles that "complete" each other, forming a straight line. If two angles are supplementary, they are said to be "supplementary to each other."
Congruent angles are angles that have the same measure. They are written with the symbol "≅" and are read as "is congruent to." Two angles are congruent if they have the same degree measure.
1. Angles 1 and 7 add up to 180 degrees, therefore, they are supplementary.
2. Also, angles 1 and 3 are supplementary.
3. Angles 2 and 6 are corresponding angles, therefore, they are congruent angles.
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In a lab, a substance was cooled by 18 °C over a period of 3 hours at a constant rate. What
was the change in temperature each hour?
The change in temperature each hour is 6 °C.
What is Unit Rate?Unit rate is the amount of one quantity for a unit amount of the other quantity.
In other words it compares 1 unit of some quantity with different amount of another quantity
Given that,
In a lab, a substance was cooled by 18 °C over a period of 3 hours at a constant rate.
Since the rate at which the substance is cooling down is constant,
Amount by which substance cooled down in 3 hours = 18 °C
Amount by which substance cooled down in 1 hour = 18 °C / 3 = 6 °C, which is the unit rate.
Hence the unit rate of the change in temperature is 6 °C per hour.
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How do you double integrate in polar coordinates?
Double integration in polar coordinates involves integrating a function over a two-dimensional region in the polar coordinate system. This is done by setting up a double integral in terms of r and θ, and integrating first with respect to r and then with respect to θ.
Double integration in polar coordinates involves integrating a function over a two-dimensional region in the polar coordinate system. The steps to double integrate a function in polar coordinates are as follows:
1. Determine the limits of integration for r and θ. These limits define the region over which the function will be integrated. Typically, the limits are determined by the boundaries of the region in the xy plane.
2. Write the function to be integrated in terms of r and θ. The function must be expressed in polar coordinates for integration in polar coordinates.
3. Set up the double integral by writing the function in polar coordinates, multiplying by the appropriate factors of r and integrating with respect to r first and then θ.
4. Integrate the function with respect to r, using the limits of integration for r determined in step 1.
5. Integrate the result from step 4 with respect to θ, using the limits of integration for θ determined in step 1.
The general form of a double integral in polar coordinates is:
∫∫f(r, θ)r dr dθ
where f(r, θ) is the function to be integrated, and r and θ are the polar coordinates.
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Please helppppp meeeeeeee
Answer:
I Also need the answer plese helep ussss
Step-by-step explanation:
A is the point with (2,9) and B is the point with coordinates (10,1) calculate the length of the line segment AB
Using the distance formula we can conclude that the measure of line AB is 64 units.
What is the distance formula?Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.
The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula.
The Pythagorean theorem can be rewritten as d=(((x 2-x 1)2+(y 2-y 1)2) to calculate the separation between any two locations.
So, the formula is:
d = √(x2-x1)² + (y2-y1)²
Now, insert values as follows:
d = √(x2-x1)² + (y2-y1)²
d = √(10-2)² + (1-9)²
d = √(8)² + (-8)²
d = √64+64
d = √128
d = 64 units
Therefore, using the distance formula we can conclude that the measure of line AB is 64 units.
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PLS HELP ME THIS IS HARD
Answer: The first answer
Step-by-step explanation:
x commision/15,000 = $360 comission/4500
what number is greater than 7/2
Answer:
A) √(13)
Step-by-step explanation:
We can more clearly see the difference in the values of the numbers if we convert/approximate them all to a decimal form.
7/2 = 3.5
A) √(13) ≈ 3.6 > 3.5
B) ∛(27) = 3 < 3.5
C) 3.4 < 3.5
D) π ≈ 3.1 < 3.5
From these approximations, we can see that A) √(13) is the only answer choice that evaluates to greater than 7/2.
Is t-test better than ANOVA?
Answer:
t-test is less likely to commit an error. ANOVA has more error risks. Sample from class A and B students have given a mathematics course may have different mean and standard deviation.
Step-by-step explanation:
have a nice day
Find the perimeter of a circle with a diameter of 7. 8 yds
If a sphere has a volume of 100in^3 what is the length of the radius
Answer:
Step-by-step explanation:
v=(4/3)*pi*r^3
100=(4/3)*pi*r^3
r=2.879
How to calculate the volume of water in your pool?
Answer:
Step-by-step explanation:
The volume of water in a pool can be calculated using the following formula:
Volume (in gallons) = Length (in feet) x Width (in feet) x Average Depth (in feet) x 7.5
For example, if your pool is 20 feet long, 15 feet wide, and has an average depth of 5 feet, the volume of water in your pool would be:
20 x 15 x 5 x 7.5 = 5625 gallons
Note: If you prefer metric units, the formula for volume in liters would be:
Volume (in liters) = Length (in meters) x Width (in meters) x Average Depth (in meters) x 1000
It's important to note that this formula assumes a standard rectangular or square pool shape. If your pool has a more complex shape, you may need to measure the volume in smaller sections and add the volumes together to get the total volume.
a smoothie is made of 60% fruit and 40% water. if 4 cups of smoothie is to be made, how many cups of smoothie mixture should be fruit?
The cups of smoothie mixture should be fruit is 2.4
How many cups of smoothie mixture should be fruit?To find how many cups of the smoothie mixture should be fruit when 4 cups of smoothie are to be made, we can use proportions.
Let's call the number of cups of fruit needed x.
So, we have
x = percentage of fruit * number of cups
Substitute the known values in the above equation, so, we have the following representation
x = 60% * 4
Evaluate
x = 2.4
Hence, 2.4 cups of the smoothie mixture should be fruit to make 4 cups of smoothie with a 60% fruit and 40% water ratio.
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A 210-N force is applied to the top of a piston, and the force produces 320 kPa of pressure. What is the area of the piston?
The area of the piston is 0.00065625 m².
What is the relation between force, pressure and area?A force can push or pull anything. An object can change its speed, direction of motion, or shape when a force is applied to it.
The amount of force acting on a given area is measured by its pressure.
Using the formula pressure = force area, pressure may be computed. As a result, a force exerted across a smaller area will result in more pressure.
Given that, force is applied to the top of a piston = 210N
And the force produces pressure = 320 kPa = 320,000 Pa
We know that, pressure = force/ area
So that, Area = force/ pressure
Area of Piston = 210 / 320,000 Pa
Area of Piston = 0.00065625 m²
So that The area of the piston is 0.00065625 m².
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Solve the problem pls
Answer:
x = 2
Step-by-step explanation:
7 [tex]\frac{1}{3}[/tex] x - 5 [tex]\frac{1}{2}[/tex] = 4x + 1 [tex]\frac{1}{6}[/tex] ( change mixed numbers to improper fractions )
[tex]\frac{22}{3}[/tex] x - [tex]\frac{11}{2}[/tex] = 4x + [tex]\frac{7}{6}[/tex]
multiply through by 6 ( the LCM of 3, 2, 6 ) to clear the fractions
44x - 33 = 24x + 7 ( subtract 24x from both sides )
20x - 33 = 7 ( add 33 to both sides )
20x = 40 ( divide both sides by 20 )
x = 2
Find the percent change from the first value to the second.
48;60
The change is (select)
V
by. %
The percent change from the first value to the second is 20%.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Given;
The first number= 48
The second number= 60
Now, difference=60-48=12
Here,
=(60-48) x 100/48
=1200/48
=20
Therefore, the percentage change will be 20%.
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A store charges a restocking fee for any returned item based upon the item price. An item priced at 200 has a fee of 12. An item priced at 150 has a fee of 9. If you return an item that has an original price I’d 180, how much is the restocking fee
The restocking fee of item priced 180 is $10.8.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Given that,
An item priced at 200 has a fee of 12.
An item priced at 150 has a fee of 9.
Let the restocking fee of item priced 180 be x.
Now, 200:12 :: 150:9 :: 180:x
50/3 :: 50/3 :: 180/x
50x=540
x=54/5
x=10.8
Therefore, the restocking fee of item priced 180 is $10.8.
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regroup the like terms?
The arrangement and simplification of like term gives 1/4 x + 3/4 x - 1/2 x + 1 - 2/3.
What are like terms?The term "like terms" in algebra refers to terms that have the same variable raised to the same power. Only the numerical coefficients can vary in terms that are similar to algebra.
Given:
Expression: 1/4 x + 1 + 3/4 x -2/3 - 1/2 x
As, like terms have variables then
1/4 x + 3/4 x - 1/2 x + 1 - 2/3
Now, applying the operation as
= x(1/4 + 3/4- 1/2) + 1 - 2/3
= x(4/4 - 2/4) + 3/3 - 2/3
= 2/4 x + 1/3
= 1/2 x + 1/3
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Nicholas is driving his car at a constant rate of 55 miles per hour.
Select whether Nicholas could achieve the distances listed in the
given times.
165 miles in 3 hours
240 miles in 4 hours
330 miles in 6 hours
504 miles in 9 hours
Using the distance, time, and speed formulas, Nicholas could only achieve the distances listed in the given times for:
A) 165 miles in 3 hoursC) 330 miles in 6 hours.What are the distance, time, and speed formulas?The distance, time, and speed formulas show that:
Speed = distance ÷ time.Distance = speed × timeTime = Distance ÷ speed.Constant driving rate (Speed) = 55 mph
Distance Time Speed
165 miles 3 hours 55 mph (165/3)
240 miles 4 hours 60 mph (240/4)
330 miles 6 hours 55 mph (330/6)
504 miles 9 hours 56 mph (504/9)
Thus, using the distance, time, and speed formulas, we can conclude that Nicholas could not achieve the distances in B and D but only in A and C.
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Please help me solve this and tell me the steps.
The solution to the given fraction polynomial is expressed as; (x - 4)/(x + 4)
How to solve Fraction Polynomials?The polynomial fraction expression is;
[(6x² - x - 1)/(3x² + 25x + 8)] * [(x² + 4x - 32)/(2x² + 7x - 4)]
Let us reduce each of the terms to their factors;
6x² - x - 1 = (3x + 1)(2x - 1)
3x² + 25x + 8 = (3x + 1)(x + 8)
x² + 4x - 32 = (x - 4)(x + 8)
2x² + 7x - 4 = (2x - 1)(x + 4)
Thus, we now have;
[(3x + 1)(2x - 1)/((3x + 1)(x + 8))] * [((x - 4)(x + 8))/(2x - 1)(x + 4))]
Common terms will cancel out to get;
(x - 4)/(x + 4)
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Please give me answers ASAP and show what x stands for!
find the surface area of the cylinder use 3.14 for n
The surface area of the cylinders are 565.2 square yards and 395.64 square cm
Calculating the surface area of a cylinderThe formula for calculating the surface area of a cylinder is expressed as:
S = 2πr(r+h)
where
r is the radius
h is the height
1) Given that r = 6yd and h = 9yd
S = 2(3.14)6(6+9)
S = 565.2 square yd
Hence the surface area of the cylinder is 565.2 square yards
2) Given that r = 3cm and h = 18cm
S = 2(3.14)3(3+18)
S = 395.64 square cm
Hence the surface area of the cylinder is 395.64 square cm
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figure out what’s wrong with it
find the value of a and b such that
x^2+2x-7=(x+a)^2+b
The value of a and b are 1 and -8 respectively.
What are Quadratic Expressions?Quadratic expressions are polynomial expressions of second degree.
The general form of a quadratic expression is ax² + b x + c.
The given quadratic expression is x² + 2x - 7.
We have to write this in the form (x + a)² + b.
We have the algebraic identity a² + 2ab + b² = (a + b)²
x² + 2x - 7 = x² + 2x - 7 + 1 - 1
= (x² + 2x + 1) - 7 - 1
= (x + 1)² - 8, which is in the form (x + a)² + b.
a = 1 and b = -8
Hence the value of a is 1 and the value of b is -8.
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How Many 2 Cups In Pound?
Converting 1 pound to 2 cups is mainly used for cooking and baking. One pound equals two cups.
Pound:
A pound is a unit of mass used to measure the weight of dry ingredients. It is expressed in "pounds" and equals 16 ounces in the traditional American system. On the other hand, there are two types of pounds used in England, the common American pound (avoirdupois pound) and the British imperial pound, which are slightly different from each other. So remember the pounds used in the recipe book you're working on.
Cups:
Cups are an important tool for measuring ingredients in the kitchen. It is mainly used for measuring the volume of liquid ingredients such as water, milk, butter, etc. or for measuring dry grain or powder ingredients such as coffee beans, chocolate chips, flour, sugar, etc.
There are two types of measuring cups:
Dry measuring cups and liquid measuring cups.Measuring cups are normally supplied with a printed weighing scale. We can fill the cup with ingredients according to this scale. Liquid measuring cups are usually made of a transparent material such as glass or plastic. This makes it easier to fill accurately.
According to the Question:
1 cup = ½ lb
To calculate how many pounds are in a given number of cups, you can do it with the following simple formula:
Pounds = Cups × ½
Or, Pounds = Cups × 0.5
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Use the IQR to determine how many outliers there are in the data set with this
Five Number Summary: 1, 2, 8, 20, 21.
a. 2
b. 3
c. 0
d. 1
===================================================
Explanation:
The five number summary is
MinQ1MedianQ3Maxin that exact order.
A five number summary of 1,2,8,20,21 means:
Min = 1Q1 = 2Median = 8Q3 = 20Max = 21The IQR (interquartile range) is the distance from Q1 to Q3
IQR = Q3-Q1
IQR = 20-2
IQR = 18
The lower fence (L) is then calculated like so
L = Q1 - 1.5*IQR
L = 2 - 1.5*18
L = -25
If any values are smaller than this lower fence of -25, then they are considered small outliers. But we know that min = 1 is the smallest value. This means we do not have small outliers.
Now onto the upper fence (U)
U = Q3 + 1.5*IQR
U = 20 + 1.5*18
U = 47
If any values are larger than 47, then they are considered large outliers. But we know that max = 21 is the largest value. This means we do not have large outliers.
In summary, all of the data values are between min = 1 and max = 21, which guarantees they are definitely in the interval between L = -25 and U = 47.
This is why there are no outliers in this data set.