The mean of negatively skewed data is smaller than the median. If the data are displayed symmetrically, the distribution is not skewed regardless of tail length or thickness. So, option d. is correct.
What do you mean by skewed curve?A skew curve is a type of statistical distribution in which the data are unevenly distributed. This is often called an asymmetric distribution, meaning that the two halves of the curve look different. A skewed curve can be either positively or negatively skewed, depending on the direction in which the data points are shifted. Positively skewed curves tend to have long tails to the right, while negatively skewed curves tend to have long tails to the left. This type of distribution is common in real-world data such as income and wealth distributions.
A negatively skewed curve is indicated by the negative tail of the chart. This means that the data points are likely to be below average. Therefore, the mean is lower than the mode, which is lower than the median. The mean is the arithmetic mean of all data points, the mode is the most common value, and the median is the midpoint of the data points.
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The right triangle represents a sketch of a wheelchair ramp that meets safety requirements. What is the horizontal distance required for the ramp? Round your answer the nearest tenth
The horizontal distance required for the ramp is 143.5 inches
Consider the following figure.
In right triangle ACB, CB is the horizontal distance,
hypotenuse AB = 144 in.
and the vertical distance AC = 12 in.
We need to find the measure of side CB
Let m be the measure of the horizontal distance CB
Using Pythagoras theorem for right triangle ACB,
(AB)² = (AC)² + (CB)²
Substitute given values in above equation.
(144)² = (12)² + (m)²
20736 = 144 + m^2
20736 - 144 = 144 + m^2 - 144
20592 = m^2
m^2 = 20592
m = 143.5 in.
Therefore, the horizontal distance is 143.5 in.
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What is the value of sin cos theta?
If sinθ⋅cosθ = 1/2, then the value of sinθ + cosθ = √2
We know that the trigonometric sine function is nothinng but the ratio of the length of the opposite side of angle to that of the hypotenuse in a right triangle.
And cosine function (cos function) is the ratio of the length of the adjacent side of angle to that of the hypotenuse.
Given that sinθ⋅cosθ = 1/2
2(sinθ⋅cosθ) = 1 .........(1)
We know that trigonometric identity,
sin(2θ) = 2 sinθ cosθ
so equation (1) becomes,
sin(2θ) = 1
We know that sin(π/2) = 1
Comparing with equation sin(2θ) = 1 we get,
2θ = π/2
θ = π/4
Using trigonometric table,
sin(π/4) = 1/√2
and cos(π/4) = 1/√2
The value of sinθ+cosθ would be,
sin(π/4) + cos(π/4)
= (1/√2) + (1/√2)
= 2/√2
= √2
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The complete question is:
If sinθ⋅cosθ=1/2 find the value of sinθ+cosθ
using multiple properties of exponents simplify the expression
2a^3b^-4/3a^5b^-2
2a³b⁻⁴/3a⁵b⁻² = 2/3(ab)²
What are exponents?The exponent of a number shows how many times the number is multiplied by itself.
Example: 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power."
In general, xⁿ means that x is multiplied by itself for n times.
Properties of exponents:
Law of Product: a ^m × a ^n = a ^(m + n)
Law of Quotient: a ^m/a ^n = a ^(m - n)
Law of Negative Exponent: a^-m = 1/a ^m
Law of Power of a Product: (ab)^m = a ^m . b ^m
Law of Power of a Quotient: (a/b) ^m = a ^m/b ^m
Given expression
2a³b⁻⁴/3a⁵b⁻²
= 2/3 . a³/a⁵ . b⁻⁴/b⁻²
Law of Negative Exponent: [tex]a^{-m} = 1/a^{m}[/tex]
= 2/3 . a³/a⁵ . b²/b⁴
Law of Quotient: [tex]a^{m} /a^{n} = a^{m-n}[/tex]
= 2/3 . a³⁻⁵ . b²⁻⁴
= 2/3 . a⁻² .b⁻²
Law of Power of a Product: [tex]a^{m} .b^{m}= (ab)^{m}[/tex]
= 2/3 . (ab)⁻²
Law of Negative Exponent: [tex]a^{-m} = 1/a^{m}[/tex]
= 2/3 . 1/(ab)²
= 2/3(ab)²
Hence the simplified expression of 2a³b⁻⁴/3a⁵b⁻² is 2/3(ab)².
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Whats 3x+1? for in high school its really hard to solve none of my friend cant do it
As per the zeros of the function, the value of the function 3x + 1 is x = -1/3.
Zeros of the function in math is defined as the values of the variable of the function such that the function equals 0.
Here we have given the function 3x + 1.
Now, we have to equate the function with zero, in order to solve it, then we get,
=> 3x + 1 = 0
Now, we have to subtract 1 on both sider to individualize the x value then we get the rewritten expression as,
=> 3x = -1
Now, we have to divide each side by 3, then we get the value of x as,
=> x = -1/3
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Write an equation of the line that passes through (3,-4) and is perpendicular to y=1/2x+7.
Which graph best represents a function with a domain of all real numbers greater than or
equal to 1 and less than or equal to 2?
The graph best represents a function with a domain of all real numbers greater than or equal to 1 and less than or equal to 2 are area between equation x + y [tex]\geq[/tex] 1 and x + y [tex]\leq[/tex] 2 .
Which function has a domain that includes all real numbers?The collection of all potential inputs for a function is known as its domain. For instance, the domain of f(x)=x2 is all real numbers, and the domain of g(x)=1/x is all real numbers other than x=0.
How do you plot all real values on a graph?The real numbers are all the numbers that make up the real number line, per definition. Thus, all real numbers can be graphed by simply drawing a number line. The number line is a graph of all real numbers since it contains all of the rational numbers.
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Marius buys computers for £915.00 each and sells them for £2081.00 each. What is his total profit on the sale of 13 computers?
Answer:
£15158.00
Step-by-step explanation:
The profit on the sale of 1 computer is the difference between the selling price and the buying price.
Profit on 1 computer:
£2081.00 - £915.00 = £1166.00
The profit on 13 computers is 13 times the profit on 1 computer.
13 × £1166.00 = £15158.00
Answer: £15158.00
How to solve 5x 2 7x 4?
We can solve this equation by using quadratic formula. So we have two solution of given equation.
How do we solve quadratic equation?Write the quadratic equation in standard form a + bx + c = 0. Identify the values of a, b, c. Then write the Quadratic Formula. Then substitute in the values of a, b, c. Then solve and check the solution.
What is quadratic formula?Quadratic formula that gives the solutions of the general quadratic equation a + bx + c = 0 and that is usually written in the form quadratic formula x = [-b ± √(b² - 4ac)] / (2a). So to solve a quadratic equation using quadratic formula just get the equation into standard form a + bx + c = 0 and apply the quadratic formula.
Here we have equation 5-7x+4
where a=5 b= -7 c=4
putting values in the formula
x= -(-7) +[tex]\sqrt{(-7)^2-4(5)(4)/2(5)}[/tex]
x= 7 + [tex]\sqrt{49+80/10}[/tex]
x= 7+[tex]\sqrt{129/10}[/tex]
Hence given values given two solutions.
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Complete question is: How to solve the given quadratic equation?
In δfgh, g = 64 cm, ∠f=131° and ∠g=47°. find the length of f, to the nearest centimeter.
The length of f = 66 centimeters
What is the sine rule for triangle?It is a law that express a relationship between side length of triangle and their opposite angles.
If ABC is triangle, then sine rule can be expressed as
BC/ sin A = AB /sin C = AC /sin B
How can we determine the length of f of the above triangle?Given, a triangle fgh where angle ∠ f = 131° and ∠g = 47°
also, side length, g = 64 cm
the remaining angle ∠ h = 180° - (131°+47°)
∠h = 2°
this is because angle sum of three angle for a triangle is 180 degrees.
what is the length of f?
we know that Δf g h has three side f g, g h and f h.
we denote the side f g = h, side g h = f and side f h = g
according to the sine rule for a triangle
h/ sin h = f /sin f = g /sin g
f/ sin f = g/ sin g
f / sin 131° = 64 / sin 47°
f = (64 × sin 131°) / sin 47°
f = 66 cm
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QUESTION 1 OF 10
If √62-9 =z, what is the value of ?
The required value of z is "i√6" to the given expression√(6/2 - 9) = z.
What is a complex number?A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib, where a, and b are real numbers and i is an imaginary number.
The expression is given in the question, as follows:
√(6/2 - 9) = z
We have to determine the value of z to the given expression.
As per the question, we have
⇒ √(6/2 - 9) = z
⇒ √(3 - 9) = z
⇒ √(- 6) = z
⇒ √(6 × -1 ) = z
⇒ (√6 × √-1 ) = z [∵ imaginary number i = √-1 ]
⇒ (√6 × i ) = z
⇒ z = i√6
Therefore, the required value of z is "i√6" to the given expression.
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Graph the line that passes through the points (9, -1) and (6, 1) and determine the equation of the line.
The equation of the line will be y = -2/3x + 5.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the line passes through points (9, -1) and (6, 1).
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 1 - (-1) / ( 6 - 9 )
Sloe = - 2 / 3
The y-intercept will be calculated as,
y = mx + c
-1 = (-2/3) x 9 + c
c = 5
The equation of the line,
y = mx + c
y = -2/3x + 5
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A jar contains 7 red jelly beans, 2 black jelly beans and 6 green jelly beans. You draw ONE jelly bean. What is the probability of drawing a red bean? a. c. 1 b. d.
Answer:
7/15
Step-by-step explanation:
number of favorable outcomes (red jelly beans) = 7
number of total outcomes (total jelly beans) = 7 + 2 + 6 = 15
probability of red = number of favorable outcomes/number of total outcomes = 7/15
The probability of getting a red jelly bean is 7/15
Total number of jelly beans in the jar (sum of all the jelly beans): 7+6+2= 15
Total number of red jelly beans: 7
Therefore, the probability of getting a red jelly bean= number of red jelly beans/ total number of jelly beans
=7/15
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How do you verify that a dilation is a similarity transformation?
A transformation that alters the size of a figure is called a dilation (similarity transformation). It needs a scale factor of k and a central point. Depending on the value of k, the dilatation is either an enlargement or a decrease. The dilation is an enlargement if |k|>1.
If two figures have the same shape but different sizes, they are said to be comparable. A stiff motion combined with a rescaling constitutes a similarity transformation. In other words, a similarity transformation can change shape without changing location or size.
A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.
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Find the value x that makes the equation true . x + 4 = 12
x = 16
x=8
x=24
x=3
Answer:
x = 8
Step-by-step explanation:
x + 4 = 12
Subtract 4 from both sides
x = 8
Let's check
8 + 4 = 12
12 = 12
So, x = 8 is correct!
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What is dual and complement?
The Boolean dual are created by replacing AND operator with OR operator and the complement is defined as the negation of the statement .
What is Boolean Expression ?
The Boolean Expression is defined as a logical statement that is either TRUE or FALSE . It compares data of any type as long as both the parts of expression have same basic data type.
The Dual of Boolean Expression are calculated by simply replacing AND operator with OR and OR operator with AND .
The Compliment of Boolean Expression is defined as negation of variables with replacement .
For Example : if the statement is [tex]A+B[/tex] ,
then the dual will be [tex]AB[/tex] and the compliment will be [tex]A'B'[/tex] .
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Describe the distribution of the ages of the Best Actor Oscar winners [LINK]:
A) What is the BEST description of the SHAPE?
- The distribution is not skewed
- The distribution is skewed left.
- The distribution is skewed right.
The correct option is option (c)-"The distribution is skewed right."
The distribution of the ages of the Best Actor Oscar winners is slightly skewed to the right.
A histogram of the ages of the Best Actor Oscar winners shows that the majority of the ages are centered around the mean age, with a few ages on the higher end that extend the right tail of the distribution. This creates a small skewness to the right.
The distribution seems to be centered at around 42-43.
The age distribution ranges from about 30 to about 75, without taking into account an outlier.
It's worth noting that the distribution is not extremely skewed, and the majority of the ages are still grouped around the center of the distribution.
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1) state whether the dilation with the given scale factor would be a reduction or an enlargement
k=4
k=1/2
k= .75
k=5/2
Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation.
How do you know if a dilation is an enlargement or reduction?Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation.
A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.
An enlargement (imagine stretching) is a dilation that makes a larger image, whereas a reduction (think shrinking) is a dilation that creates a smaller image. A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.
A transformation called a dilation (similarity transformation) alters the size of a figure. A center point and a scaling factor, k, are necessary. Which kind of dilation it is—an enlargement or a reduction—depends on the value of k. An enlargement results from a dilatation if |k|>1.
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Hi!
ik -2x+9 is x=4.5 so are the number 4.5 apart and if so what do i do after that
The function y = -2x + 9 have ordered pairs (-4, 17), (-2, 13), (0, 9), (2, 5) and (4, 1)
What is an equation?An equation shows how two or more numbers and variables are related to each other.
The standard linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Given that:
y = -2x + 9
When x = -2; y = -2(-2) + 9 = 13
When x = 0; y = -2(0) + 9 = 9
When x = 2; y = -2(2) + 9 = 5
When x = 4; y = -2(4) + 9 = 1
The function y = -2x + 9 is a linear equation
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write an equation in pint-slope form, slope-intercept, and standard form
Slope: -5 (-3,-7)
(-6,10), (-4,18)
(-4,9), (1,14)
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
to get the equation of any straight line, we simply need two points off of it, let's use (-6,10), (-4,18)
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{18}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{18}-\stackrel{y1}{10}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{8}{-4 +6} \implies \cfrac{ 8 }{ 2 } \implies 4[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y -10 = 4 ( x +6) \end{array}} \\\\\\ y-10=4x+24\implies -4x+y=34\implies \stackrel{standard~form}{{\Large \begin{array}{llll} 4x-y=-34 \end{array}}}[/tex]
Dominique decorates a round cake with fruits. The cake has a diameter of 16 inches. She frosts just the top if the cale. How many square inches of the cake are covered with icing?Use 3. 14 for π
The amount of square inches of the cake that are covered with icing is 201.06, calculated by using the formula (π * radius2), with π equal to 3.14 and the radius equal to 8 inches.
1. Use the formula (π * radius2), with π equal to 3.14
2. The radius is half of the diameter, divide the diameter (16 inches) by 2
3. Radius = 16 inches / 2 = 8 inches
4. Calculate π * radius2: 3.14 * (8 inches)2 = 201.06 square inches
π * (8 inches)2
= 3.14 * (64 inches2)
= 201.06 square inches
Dominique is decorating a round cake with fruits and has frosted just the top of the cake. To determine the area of the cake that is covered with icing, we can use the formula (π * radius2). Since the cake is round, we can determine the radius of the cake by dividing the diameter of the cake (16 inches) by 2, resulting in the radius being 8 inches. We can then calculate the area of the cake covered with icing by multiplying π by the radius squared. Using the number 3.14 for π, the calculation is 3.14 * (8 inches)2, which equals 201.06 square inches. Therefore, 201.06 square inches of the cake are covered with icing.
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BRAINLIEST IF U MAKE UR OWN AND ORIGINAL ANSWER!
Question 2(Multiple Choice Worth 1 points)
(01.06 MC)
An equation is shown:
−np − 6 = 3(c − 5)
Which of the following solves for n?
n = the quantity 3 times c minus 21 all over negative p
n = the quantity 3 times c minus 9 all over negative p
n = the quantity 3 times c minus 21 all over p
n = the quantity 3 times c minus 9 all over p
Answer:
Option 2
Step-by-step explanation:
Hello!
We can solve the equation for n by isolating the variable.
Solve for n:-np - 6 = 3(c - 5) Add 6 to both sides-np = 3(c - 5) + 6 Divide both sides by p-n = [tex]\frac{3(c - 5) + 6}{p}[/tex] Expand the parenthesis-n = [tex]\frac{3c - 15 + 6}{p}[/tex] Combine Like terms-n = [tex]\frac{3c - 9}{p}[/tex] Divide both sides by -1n = [tex]-\frac{3c - 9}{p}[/tex]The answer would be the second option: "n = the quantity 3 times c minus 9 all over negative p."
The intensity level of sound, L measured in decibels (dB), is a function of the sound
intensity, S watts per square metre (W m-2). The intensity level is given by the following
formula.
(a) An orchestra has a sound intensity of 6. 4 × 10-3 Wm-2. Calculate the intensity level, L of
the orchestra.
(b) A rock concert has an intensity level of 112 dB. Find the sound intensity, S
(a) If an orchestra has a sound intensity of [tex]6.4 \times 10^-^3\ Wm^{-2[/tex], then
the intensity level of sound, L, is 98.062 dB.
(b) If a rock concert has an intensity level of 112 dB, then the sound intensity, S, is [tex]10^{-0.8}\ Wm^{-2[/tex].
Sound intensity, also known as acoustic intensity, is defined as the dominion ferried by sound waves per unit area in a direction perpendicular to that area.
Given that the intensity level of sound, L, measured in decibels (dB), is a function of the sound intensity, S, watts per square meter ([tex]Wm^{-2[/tex]) as
[tex]L = 10log_{10}(S\times10^1^2), S\geq 0[/tex]
(a) If an orchestra has a sound intensity of [tex]6.4 \times 10^-^3\ Wm^{-2[/tex], then
the intensity level of sound,
[tex]L = 10log_{10}(6.4\times10^{-3}\times10^1^2)[/tex]
[tex]= 10log_{10}(6.4\times10^9)\\= 10(log_{10}6.4\ +\ log_{10}10^9 )\\= 10(0.8062\ +\ 9)\\=10 \times 9.8062\\= 98.062\ dB[/tex]
(b) If a rock concert has an intensity level of 112 dB, then
[tex]112 = 10log_{10}(S\times10^1^2)\\log_{10}(S\times10^1^2) = \frac{112}{10}\\log_{10}(S\times10^1^2)= 11.2\\S\times10^1^2 = 10^{11.2}\\S = \dfrac{10^{11.2}}{10^1^2} \\S = 10^{-0.8}\ Wm^{-2[/tex]
The sound intensity is [tex]10^{-0.8} Wm^{-2[/tex].
Hence, (a) L = 98.062 dB and (b) S [tex]= 10^{-0.8}\ Wm^{-2[/tex].
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35% of ____ = $3.50 find the unknown number
Answer:
10
Step-by-step explanation:
35% of x = 3.5 To change a percent to a decimal, divide by 100%
.35x = 3.5 Divide both sides by 3.5
[tex]\frac{.35x}{.35}[/tex] = [tex]\frac{3.5}{.35}[/tex]
x = 10
Check:
.35 x 10 = 3.3.5 = 3.5
Answer:
10
Step-by-step explanation:
Let the unknown number be x.
35% of x = 3.50
35/100 * x = 3.50
35x = 3.50 * 100
35x = 350
x = 350/35
x = 10
Hence, the unknown number is 10.
=Round each number to five decimal places: a. 23.54 b. 0.916?
Therefore the rounded numbers are 23.54 and 0.9160.
Define rounded numbers.An integer containing one or more "0"s at the end in a certain base is said to be round. In this way, 590 is more rounded than 592 but less rounded than 600. A round number is frequently understood to stand for a value or values close to the nominal value given in both formal and informal language.
What is integer?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold mathbb Z.
a. To round 23.54 to five decimal places, we look at the sixth decimal place, which is 4. Since 4 is less than 5, we leave the fifth decimal place as is, and the number rounded to five decimal places is 23.54.
b. To round 0.916 to five decimal places, we look at the sixth decimal place, which is 1. Since 1 is greater than or equal to 5, we increase the fifth decimal place by one, and the number rounded to five decimal places is 0.9160.
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Please help quickly!
Use the figure below to answer questions 18-21
Answer:
Step-by-step explanation:
18. m∠1 = 104°
19. m∠2 = 79°
20. m∠3 = 65°
21. m∠5 = 73°
A newsletter publisher believes that more than 47% of their readers own a personal computer. Is there sufficient evidence at the 0.05 level to substantiate the publisher's claim?
There is no sufficient evidence that we can use in order to substantiate the claim of the publisher,
How to write the hypothesisThe null hypothesis H0: p = 0.47
The alternative hypothesis is H1: p > 0.47
The question requires us to test the fact that more than 47 percent of the readers have their own personal computer. This is therefore the claim that is to be tested here.
There is no sufficient evidence to substantiate the claim because of the lack of certain details that would have been used to carry out the hypothesis test.
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Please its due today
a) The domain and the range of the function are given as follows:
Domain: [-4,5).Range: [0,9].b) The zero of the function is given as follows: (3,0).
c) The behaviors are given by these following intervals:
Increasing: (-4,0) U (3,5).Decreasing: (0,3).Constant: DNE.d) The extremas are given as follows:
Relative minimum: (3,0).Relative maximum: (0,9).e) The function is neither even nor odd.
What are the features of the function?The domain of a function is the set that contains all the input values for the function, hence in the graph it is given by the values of x.
The range of a function is the set that contains all the output values for the function, hence in the graph it is given by the values of y.
The zeros are the points of the function at which it either crosses or touches the x-axis.
The function is increasing when the graph is moving up, and decreasing it the graph is moving down.
The extremas are given as follows:
Relative minimum: function changes from decreasing to increasing.Relative maximum: function changes from increasing to decreasing.The function is classified as even, odd or neither as follows:
Even: f(x) = f(-x) for all values of x.Odd: f(-x) = -f(x) for all values of x.Neither: none of the two above statements are true.More can be learned about functions at https://brainly.com/question/24808124
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How do you find the y-intercept without a calculator?
In the equation y = mx + c if we substitute the value of x as zero we will get a point on the y axis given by y =(m × 0) + c ⇒ y = c. Therefore the point of the line on the y axis is (0, c) and so c is also called the y -intercept of the line.
Now, According to the question:
i) from the general equation of line we know that any line can be represented in the form y = mx + c , where m is a constant and is called the slope of the line and c is also a constant and is the y-intercept.
ii) In the equation y = mx + c if we substitute the value of x as zero we will get a point on the y axis given by y =(m × 0) + c ⇒ y = c. Therefore the point of the line on the y axis is (0, c) and so c is also called the y intercept of the line.
iii) If for example we have the line 3y = 6x + 12 then we first get this equation of the line to match the general form of the equation of the line, that is y = mx + c. Therefore dividing both the left and the right sides of the given equation of the line by 3 we get y = 2x + 4 which matches with the general form of the equation for line and we see that the slope of the given line is m = 2 and the y intercept is given by c = 4.
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What is the perimeter of a regular pentagon inscribed in a circle with radius 1 meter
Answer:
Step-by-step explanation:
The perimeter of a regular pentagon is equal to the sum of the lengths of its sides. The length of each side of a regular pentagon inscribed in a circle with radius 1 meter can be found using the formula: side length = 2 * radius * sin(180/number of sides).
For a regular pentagon, the number of sides is 5. Plugging this into the formula gives us:
side length = 2 * 1 * sin(180/5) = 2 * 1 * sin(36) = 2 * 0.587785 = 1.175570
So the perimeter of the regular pentagon is equal to 5 * 1.175570 = 5.877849 meters.
The rate of growth dP / dt of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days (0 ? t ? 10) as shown below.
dP/dt=k \sqrt{t}
The initial size of the population is 300. After 1 day the population has grown to 600. Estimate the population after 8 days. (Round your answer to the nearest whole number.)
The population of bacteria after 8 days is 7088
Here, we have been given an equation for the rate of growth of a population of bacteria
dP/dt = k√t
where P is the population size
and t is the time in days (0 ≤ t ≤ 10)
We rewrite above equation as,
dP = k√t dt
Integrating both sides, we get,
P = (2/3) × kt^(3/2) + C
We find the value of C.
For t = 0, P = 300 as the initial size of the population is 300.
Substitute t = 0 in above equation.
300 = 0 + C
C = 300
So, the above equation becomes,
P = 300 + (2/3) × kt^(3/2) .......(1)
Now we find the value of k.
After 1 day the population has grown to 600.
substitute t = 1, P = 600 in equation (1)
600 = 300 + (2/3) × k
(2/3)k = 300
k = 900/2
k = 450
So, the equation of population of bacteria after time t is:
P = 300 + [(2/3) × 450 × t^(3/2)]
P = 300 + 300 × t^(3/2)
P = 300 (1 + t^(3/2))
To find the population after 8 days, substitute t = 8
P = 300 (1 + 8^(3/2))
P = 7088.22
P ≈ 7088
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