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Symbolab Derivative Calculator is free online tool for calculating derivatives of functions. It allows users to input the equations and then calculates the derivatives of those equations for the user. This tool is useful for students and professionals who need to calculate derivatives quickly and accurately.
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In general, if the sample size is large, adding an extremely large outlier to a data set will not substantially affect _____ .a. the sample standard deviationb. the sample meanc. the sample mediand. none of the above.
In general, if the sample size is large, adding an extremely large outlier to a data set will not substantially affect sample mean. The correct option is (b) sample mean
The sample size is large, adding an extremely large outlier to a data set will not substantially affect the sample mean.
This is because the sample mean is a measure of central tendency that is influenced by all the values in the dataset, but it is more affected by the values that are closer to it in magnitude. When the sample size is large, the impact of any individual outlier on the overall mean is typically reduced, as the outlier will be more likely to be balanced out by the other values in the dataset.
However, the addition of an extremely large outlier may still have an impact on the sample standard deviation and median, depending on the magnitude and distribution of the other values in the dataset.
Therefore, the correct option is (b) sample mean
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Please help me now this is due
The area below the curve is equal to 10 - 3π / 2 square units. (Correct choice: B)
How to determine the area below a curve
In this problem we need to determine the area below the curve for the interval x ∈ [- 4, 7]. Mathematically speaking, this area can be found by means of definite integrals. Given that we find a piecewise function formed by five expressions, the area is the sum of several subintervals.
The areas can be represented by using the following area formulas:
Triangle
A = 0.5 · w · l
Semicircle
A = 0.5π · R²
Rectangle
A = w · l
Where:
w - Widthl - LengthR - RadiusPlease notice the area above the x-axis is positive and the area below the x-axis is negative. Finally, we find the net area below the curve:
A = 0.5 · 2 · 2 - 0.5π · 2² + 0.5 · 2 · 2 + 2 · 2 + 0.5π · 1² + 1 · 2
A = 2 - 2π + 2 + 4 + 0.5π + 2
A = 10 - 1.5π
A = 10 - 3π / 2
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A block of mass m slides down an inclined plane of inclination θ with uniform speed. The coefficient of friction between the block and the plane is μ. The contact force between the block and the plane is___
the contact force between the block and the plane is equal to the normal force, which is equal to the weight of the block (mg) multiplied by the cosine of the angle of inclination (θ). Therefore, the contact force between the block and the plane is mg cosθ.
The contact force between the block and the plane can be determined by analyzing the forces acting on the block.
First, we need to consider the forces acting on the block in the direction parallel to the inclined plane. Since the block is moving with uniform speed, the forces in this direction must be balanced. The forces in this direction are the force due to gravity acting down the inclined plane (mg sinθ) and the frictional force acting up the inclined plane (μmg cosθ). Therefore, we have:
mg sinθ = μmg cosθ
Simplifying this equation, we get:
μ = tanθ
This means that the coefficient of friction between the block and the plane is equal to the tangent of the angle of inclination.
Next, we need to consider the forces acting on the block in the direction perpendicular to the inclined plane. Since the block is not accelerating in this direction, the forces in this direction must also be balanced. The forces in this direction are the normal force acting up the inclined plane (N) and the force due to gravity acting vertically down (mg cosθ). Therefore, we have:
N = mg cosθ
So, the contact force between the block and the plane is equal to the normal force, which is equal to the weight of the block (mg) multiplied by the cosine of the angle of inclination (θ). Therefore, the contact force between the block and the plane is mg cosθ.
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Triangle LMN is dilated by a scale factor of 1/2 to form triangle LMN what is the measure of side NL?
Answer: Half the side of NL from the original figure.
Step-by-step explanation:
When it is a scale factor of 1/2 all the sides are halved there fore nl is halved.
help pls
The box plot shows the times for sprinters on a track team.
A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 42, 44, 50, 54, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.
What is the value of the upper quartile?
52
53
54
56
The upper quartile of the data set is, 56.
What is mean by Addition?The process for combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
The values of 42, 44, 50, 54, and 56 are all marked by the box plot.
Hence, The value of upper quartile is,
⇒ Upper quartile = 3/4 (n + 1)
Where, n is number of terms.
Hence, We get;
⇒ Upper quartile = 3/4 (5 + 1)
= 3/4 × 6
= 4.5
≈ 5th term
Thus, The value of Upper quartile = 56
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how many reflectional symmetries does this figure have?
The letter "F" has one reflectional symmetry. This symmetry can be seen by drawing a line that divides the letter "F" into two equal parts, such that the left and right sides are mirror images of each other.
This line of symmetry would run vertically down the middle of the letter "F", passing through the crossbar. The letter "F" has one reflectional symmetry. A reflectional symmetry is a type of symmetry where one half of an object is a mirror image of the other half. In the case of the letter "F", a line can be drawn vertically down the middle of the letter, passing through the crossbar, such that the left and right sides of the letter are mirror images of each other. This line is called a line of symmetry. Therefore, the letter "F" has one reflectional symmetry.
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The figure which is missing in the question is attached here-with the answer
The perimeter of a rectangle measures 48 feet. The length is 4 times as long as the width. If 9 1/2 feet is added to the length of the original rectangle, what is the new length of the rectangle?
Since the polygon's perimeter equals the sum of its sides. This means that the perimeter (P) of a rectangle is;
P = the sum of all of its sides.
P = a + b + a + b In a rectangle, the opposite sides are equal.
P = 2(a + b)
Given a rectangle with length 4x and width x, what is its perimeter?
P equals 2(a + b), thus 48 equals 2(x + 4x).
48 = 2(x+4x)
48 = 2(5x)
48 = 10x
x = 4.8
4x = 19
19.2 feet in length and 4.8 feet in width when first built.
The new length would be 9.5+19.2=28.7 if 9 1/2 were added to the previous length.
A new length of 28.7 feet results as a result.
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. The distance from Santa Maria to Los Alamos is 16.25 mi. What is the distance in cm?
Answer: Santa Maria to Los Alamos is approximately 2,612,951.6 centimeters.
Step-by-step explanation:
To convert miles to centimeters, we need to use the following conversion factors:
1 mile = 160,934.4 centimeters
So, to find the distance from Santa Maria to Los Alamos in centimeters, we can use the following calculation:
16.25 miles x 160,934.4 centimeters/mile = 2,612,951.6 centimeters
Therefore, the distance from Santa Maria to Los Alamos is approximately 2,612,951.6 centimeters.
1 mile = 160,934 centimeters
16.25 miles = ?
16.25 * 160,934 = ?
16.25 miles = 2,615,184 centimeters
Use the terms domain, range independent variable and dependent variable to explain how function relates one variable to another variable. Fill in the blanks below: A function is a rule that assigns to each value of the in the unique value of the in tne
A function is a rule that assigns to each value of the independent variable in the domain unique value of the dependent variable in the range.
The domain of a function is defined as the set of all possible values that a function can take as input.
The range of a function is defined as the set of all values of a function that it takes as output.
The variable that represents the input values of a given function is called the independent variable.
The variable that represents the output values of a given function is called the dependent variable.
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How many acre to hectare?
There are 2.47105 acres in 1 hectare.
An acre is a common unit of measurement in the United States and other countries. One acre equals 43,560 square feet (4,047 square metres).
In contrast, a hectare is a metric unit of area that is widely used in many countries. One hectare equals 10,000 square metres (2.47105 acres).
You can use the conversion factor of 1 acre = 0.4047 hectares or 1 hectare = 2.47105 acres to convert acres to hectares.
Simply multiply the number of acres by 0.4047 to convert from acres to hectares. Similarly, multiply the number of hectares by 2.47105 to convert the number of hectares to acres.
To convert a given number of acres to hectares using mathematical terms, you can use the formula:
Hectares = Acres × 0.4047
In this formula, "Acres" is the number of acres you want to convert to hectares, and "Hectares" is the equivalent area in hectares.
Similarly, to convert a given number of hectares to acres using mathematical terms, you can use the formula:
Acres = Hectares × 2.47105
In this formula, "Hectares" is the number of hectares you want to convert to acres, and "Acres" is the equivalent area in acres.
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Rob has $7,869 in an account that earns 13% interest compounded annually.To the nearest cent, how much will he have in 5 years?
Step-by-step explanation:
Principal (P)=$7869
Rate (R)= 13%
Time (T)= 5 years
Compound Interest (CI)=?
We know that,
CI = P { (1+R/100)^T -1}
= $7869 {(1+13/100)^5 -1}
= $7869 {(113/100)^5 -1}
= $7869 {(1.13)^5 -1}
= $7869 {1.84-1}
= $7869 × 0.84
= $6609.96
Compound Amount= CI+p
= $6609.96+7869
= $14478.96
Therefore, he will have $14478.96 after 5 years.
Its in the form of a picture
From the given information the quadrilateral QUAD is a rectangle because opposite sides are of the same length and the adjacent sides are perpendicular to each other.
What is a quadrilateral?
A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry. A closed quadrilateral has four sides, four vertices, and four angles. It is a form of a polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees. The diagonals are obtained by joining the opposing vertices of the quadrilateral.
From finding the lengths of the sides of the quadrilateral, we can see that two sides of the quadrilateral have the same length and the other two sides have the same length.
QU
length = √20
slope = 2
UA
length = √5
slope = -1/2
AD
length = √20
slope = 2
DQ
length = √5
slope = -1/2
Now the lines QU and UA are perpendicular to each other since the product of slopes is -1.
So QU ⊥ UA
similarly,
AD ⊥ UA
AD ⊥ DQ
Also, the lines QU and AD as well as the lines UA and DQ are parallel to each other as the slopes are the same.
Therefore from the given information the quadrilateral QUAD, is a rectangle because opposite sides are of same length and the adjacent sides are perpendicular to each other.
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Its in the form of a picture
The area of the given composite figure is the sum of the areas of triangles and the area of the rectangle, which is 11 sq. units.
What is a composite figure?
Geometric figures can be combined from two or more separate geometric figures. A two-dimensional figure built up of fundamental two-dimensional shapes like triangles, rectangles, circles, semicircles, etc. is known as a composite shape or composite figure. The total of the individual areas will represent the composite shape's area.
The given composite figure can be divided into the shapes given below.
There are 3 right triangles and one rectangle.
The sum of the areas of each shape makes the area of the given composite figure.
Δ ARC
base RC, b = 3
Height AC, h = 4
Area = 1/2 * b * h = 1/2 * 3 * 4 = 6 sq. units.
Δ RST
base RS, b = 2
Height ST, h = 2
Area = 1/2 * b * h = 1/2 * 2 * 2 = 2 sq. units.
Δ BCK
base BK, b = 1
Height BC, h = 2
Area = 1/2 * b * h = 1/2 * 1 * 2 = 1 sq. units.
Rectangle SCBT
length l = 2
Breadth b = 1
Area = 2 * 1 = 2 sq. units
Therefore the area of the given composite figure is = 6 + 2 + 1 + 2
= 11 sq. units
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Samuel found the difference of the polynomials.
(15x^(2)+11y^(2)+8x)-(7x^(2)+5y^(2)+2x)
Samuel found the difference between the polynomials is 8x² + 6y² + 6x.
What is the polynomials?
An expression that contains coefficients, variables, non-negative integer exponents, and constants is known as a polynomial.
To find the difference between the polynomials, we need to subtract the second polynomial from the first polynomial.
(15x² + 11y² + 8x) - (7x² + 5y² + 2x)
First, we can simplify the coefficients of the like terms by subtracting them:
15x² - 7x² + 11y² - 5y² + 8x - 2x
Simplifying further, we get:
8x² + 6y² + 6x
Therefore, the difference between the polynomials is 8x² + 6y² + 6x.
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on a unit circle, 0=60degrees. Identify the terminal point and tan 0
stop giving wrong answers for points. Seriously.
On a unit circle, Ф = 60°, Then the terminal point and tanФis,
D. (1/2, √3/2), tanФ = √3.
What are periodic functions?A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.
Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.
We know, tanФ = sinФ/cosФ.
From the unit circle, we also know that cos60° = 1/2 and sin60° = √3/2.
So, When Ф = 60°, cosФ = 1/2 and sinФ = √3/2.
Therefore, tan60° = sin60°/cos60°.
tan60° = (√3/2)/(1/2).
tan60° = √3.
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100 points and brainliest!!! multiple choice as well!!!!
Answer:
A. (2,3)
Step-by-step explanation:
2,3 is a solution, because it is marked on the graph. We can also tell because they are solutions for both the marked lines.
Answer:
2,3 is the answer
Step-by-step explanation:
on graph
What is the binomial probability formula used for?
The binomial probability formula calculates the probability of obtaining a specific number of successes in a fixed number of independent trials, each with the same probability of success
The binomial probability formula is used to calculate the probability of obtaining a certain number of successes in a fixed number of independent trials, each with the same probability of success.
The formula is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where:
P(X=k) is the probability of obtaining k successes
n is the total number of trials
p is the probability of success in each trial
(n choose k) represents the number of ways to choose k successes from n trials, and is calculated as n! / (k! * (n-k)!)
Therefore, the uses of binomial probability formula has been explained
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The binomial probability formula is widely used in various fields, including statistics, probability theory, and genetics, to analyze and predict outcomes in situations with binary events.
The binomial probability formula is used to calculate the probability of obtaining a specific number of successes in a fixed number of independent Bernoulli trials. In other words, it helps us determine the likelihood of achieving a certain outcome in a series of experiments, where each experiment can result in one of two possible outcomes (success or failure).
The formula is given by P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where P(X=k) represents the probability of getting exactly k successes, n is the total number of trials, p is the probability of success in a single trial, and (n choose k) is the binomial coefficient.
For example, let's say you flip a fair coin 10 times and want to know the probability of getting exactly 7 heads. In this case, n = 10 (number of trials), k = 7 (number of successes), and p = 0.5 (probability of heads). Plugging these values into the binomial probability formula will give you the desired probability.
The binomial probability formula is widely used in various fields, including statistics, probability theory, and genetics, to analyze and predict outcomes in situations with binary events.
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Bruce's Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon, the cafe sold 57 single-shot espressos and 38 double-shot espressos. What percentage of the espressos sold were single-shot?
Write your answer using a percent sign (%).
Answer: 60%
Step-by-step explanation:
In order to find the percentage, we need to find the sum of the espressos ordered.
57 + 38 = 95
95 will be our denominator, and since we are trying to find the percentage of the single-shot, our numerator is going to be 57 because that is how many sold.
57 / 95
Now we can divide 57 by 95 to get the percent of single shot espressos to get an answer of 60%
i need help on this equation
Answer:
c
Step-by-step explanation:
DO THE MATH!!!!!!!PLEASE
Which equation is correct?
which equation is correct? a. tanx=1/secx b.sinx=1/cosx c.cscx=1/sinx d.cosx=1/cotx
Answer:
Step-by-step explanation:
csc and sin are inverses of one another, therefore, c is the correct statement.
Thoriso can either walk to school at 5 km/h or ride her bicycle at 15 km/h. If she rides her bicycle, it takes her 10 minutes to get to school. how long will it take her if she walks to school
It will take her 30 minutes if she walks to the school.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
The time can be modeled as follows:
t = d/v.
Hence if the velocity decays by a factor of 1/3, the time is tripled, hence the time needed to get to the school walking is given as follows:
t = 10 x 3
t = 30 minutes.
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What expression is equivalent to 3x+3x+3x
Answer:
[tex]\huge\boxed{\sf 9x}[/tex]
Step-by-step explanation:
Given expression:= 3x + 3x + 3x
Take x as common factor
= x(3 + 3 + 3)
= x (9)
= 9x[tex]\rule[225]{225}{2}[/tex]
PLEASE HELP!!!!!!!!!! Use an algebraic method (substitution or elimination) to solve the system of equations. Show your work.
4 − 2 = 16
2 + 3 = 32
The requried solution to the system of equations is x = 7, y = 6.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
To solve the system of equations:
4x - 2y = 16 - - -- - -(1)
2x + 3y = 32 - - - - - - (2)
We can use the method of substitution:
Solve one of the equations for one of the variables in terms of the other variable.
Let's solve the first equation for y:
4x - 2y = 16
-2y = -4x + 16
y = 2x - 8
Substitute the expression found in step 1 into the other equation 2.
2x + 3(2x - 8) = 32
Solve the resulting equation for the remaining variable.
2x + 6x - 24 = 32
8x - 24 = 32
8x = 56
x = 7
Substitute the value of x into one of the original equations to find the value of the other variable.
Using the first equation:
4x - 2y = 16
4(7) - 2y = 16
28 - 2y = 16
-2y = -12
y = 6
Therefore, the solution to the system of equations is x = 7, y = 6.
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In a data set, the number of elements will always be the same as the number of: a. data pointb. independent variable c. dependent variabled.observation
In a data set, the number of elements will always be the same as the number of observations.
How to determine the true statementAn observation is a single measurement or record of a particular variable or event. In a data set, observations are typically organized into rows, with each row representing a single observation.
The number of observations in a data set corresponds to the number of times the data was measured or recorded.
On the other hand, a data point can refer to a single value within a data set, or a combination of values if the data set contains multiple variables.
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what value of h is needed to complete the square for the equation
To complete the square for the equation [tex]x^2 + 8x + 32 = (x - h)^2 + 16[/tex],
we need to choose h = -2.
To complete the square for the given equation
[tex]x^2 + 8x + 32 = (x - h)^2 + 16[/tex],
we need to express the left-hand side of the equation in the form
[tex](x - p)^2 + q[/tex], where p and q are constants.
We can start by expanding the right-hand side of the equation:
[tex](x - h)^2 + 16 = x^2 - 2hx + h^2 + 16[/tex]
Now we can compare the coefficients of [tex]x^2[/tex], x, and the constant term on both sides of the equation:
[tex]x^2 + 8x + 32 = (x - p)^2 + q[/tex]
=> [tex]p^2 = 0[/tex] (since the coefficient of [tex]x^2[/tex] is 1 on both sides)
=> -2hp = 8 (since the coefficient of x is 8 on the left-hand side)
=> h = -2 (solving for h)
=> q = [tex]h^2 + 16[/tex] = 20 (since the constant term on the right-hand side is 16)
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The complete question may be:
What value of h is needed to complete the square for the equation [tex]x^2+8 x+32=(x-h)^2+16[/tex] ?
how many ft in a meter
Answer:
there are 3 feet in one meter.
Step-by-step explanation:
12 inches = 1 foot.
39.3701 inches = 1 meter.
39.3701 ÷ 12 = 3.281.
3.281 is simplified to 3.
There are about 3 feet in 1 meter.
Hope this helped! Have a Good Day!
1.Find the lateral area of a cone with a radius of 7 ft. and a slant height of 13 ft. Use 3.14 for ð and round to the nearest tenth. 439.6 ft2 324.5 ft2 571.5 ft2 285.7 ft2 2.Find the surface area of a square pyramid with a base length of 24 cm and a height of 16 cm. 1056 cm2 1536 cm2 816 cm2 1344 cm2 3.Find the volume of a rectangular prism with the following dimensions: Length = 5 mm Base = 7 mm Height = 3 mm 142 mm2 105 mm2 126 mm2 130 mm2 4.Find the volume of a square pyramid with a base length of 9 cm and a height of 4 cm. 324 cm3 108 cm3 36 cm3 152 cm3 5.Find the volume of a cone with a radius of 10 mm and a height of 6 mm. 628 mm3 600 mm3 1,884 mm3 1,254 mm3 1.D 2.C 3.? 4.? 5.?
All five answers are (1) 285.7 ft2 (2) 1056 cm2 (3) 105 mm3 (4) 108 cm3 (5) 628 mm3 in accordance with the provided assertion.
What in math is a volume?In mathematics, volume refers to the amount of space present within a specific 3D object. As an example, the dimensions of a fish aquarium are three feet long, one foot broad, and two feet height.
By increasing the length, width, and height, or 3x1x2, which also equals six, the volume is determined. Consequently, the fish tank has a 6 cubic foot size.
(1) The lateral area of a cone can be calculated using the formula L = πrℓ, where r is the radius and ℓ is the slant height. Using the given values, we have:
L = π(7)(13) ≈ 285.7 ft²
Rounding to the nearest tenth, the answer is 285.7 ft².
(2) A = B + (1/2)Pl, where B is the base area, P is the base circumference, l is the slope height, and A is the surface area, can be used to determine the surface area of a square pyramid. Since the pyramid's foundation is square, we have:
B = (24)² = 576 cm²
The perimeter of the base is 4 times the base length, so we have:
P = 4(24) = 96 cm
Now we can use the formula to find the surface area:
A = 576 + (1/2)(96)(16) = 1056 cm²
Therefore, the surface area of the square pyramid is 1056 cm².
(3) The volume of a rectangular prism can be calculated using the formula V = lwh,
where
l is the length
w is the base
h is the height
V is the volume.
Substituting the given values, we have:
V = (5)(7)(3) = 105 mm³
Therefore, the volume of the rectangular prism is 105 mm³.
(4) The formula V = (1/3)Bh, where B is the base area, h is the height, and V is the volume, can be used to determine the volume of a square pyramid. Since the pyramid's foundation is square, we have:
B = (9)² = 81 cm²
Now we can use the formula to find the volume:
V = (1/3)(81)(4) = 108 cm³
Therefore, the volume of the square pyramid is 108 cm³.
(5) The volume of a cone can be calculated using the formula V = (1/3)πr2h, where r is the radius, h is the height, and V is the volume. Substituting the given values, we have:
V = (1/3)π(10)²(6) ≈ 628.3 mm³
Rounding to the nearest whole number, the answer is 628 mm³.
Therefore, the volume of the cone is 628 mm³.
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how many billion in a trillion
Answer:
1,000,000,000,000 = 1,000,000,000 × 1,000
Step-by-step explanation:
1,000,000,000,000 = 1,000,000,000 × 1,000One trillion equals a thousand billions, or a million millions.
Which percent accurately reflect the white section in the circle?
A. 38%
B. 48%
C. 62%
D. 68%
The percent that accurately reflects the white section in the circle is 38%. So, the correct option is A).
To find the percentage of the circle that is white, we need to divide the area of the white region by the area of the entire circle and multiply by 100.
Looking at the diagram, we can see that the white region takes up about 3/8 of the circle, or 37.5% (since 3/8 is equal to 0.375 or 37.5%). This is closest to answer choice A, which is 38%.
Therefore, the percent that accurately reflects the white section in the circle is 38%.
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what is 56 as a decimal?
Answer: 56 as a decimal is 0.56
Step-by-step explanation: Just simply add a decimal point in front of 56, and you’ll get 0.56
56 = 0.56
Hope this helps!