A human hair is approximately 40 microns (um) wide. If 1 um is equal to 10
-6
meters (m),
and 1 nanometer (nm) is equal to 10-9m, then how many nanometers wide is a human hair?
A
0.0004 nm
B
0.004 nm
C
4,000 nm
D
40,000 nm

Answer:

x = 25

Step-by-step explanation:

you need x on its own, so just divide both sides by 3, and you get 25.

Therefore ,the speed at height 40 feet in the air = 16*40=640 feet/sec

A mathematical function from one set X to another gives each element of X exactly one element of the other. The sets X and Y, respectively, represent the function's domain and codomain.

Here,

the given function is

f(t)=−8\(t^{2}\)+25

Therefore, the speed of the ball can be calculated by using derivative of f(t)

f(t)=−8\(t^{2}\)+25

Differentiating f(t) w.r.t  t

=> d(f(t)/dt=-8*2t

=> d(f(t)/dt=-16t

Therefore the speed at height 40 feet in the air = 16*40=640 feet/sec

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The area of the circle r = 18 sinθ as an integral in polar coordinates is 81π.

We must evaluate the integral of the function r = 18sinθ with respect to θ in order to determine the circle's area in polar coordinates, where r stands for the radius and θ for the angle.

The whole revolution of the circle should be covered by the limits of integration for θ. Our bounds of integration will be 0 to 2π(or 0 to 360 degrees), which is the range of a whole revolution.

The following is the formula for the area in polar coordinates:

A = (1/2)\(\int[a, b] r^2 d\theta\)

A = 0 and b = 2 in this instance. The radius at every given angle is represented by the function r = 18sinθ, which must be squared to get r².

We can now determine the area:

A = (1/2) \(\int[0, 2\pi] (18sin\theta)^2 d\theta\)

Simplifying the integrand:

A = (1/2) \(\int[0, 2\pi] 324sin^2\theta d\theta\)

Using the trigonometric identity sin²θ = (1/2)(1 - cos2θ):

A = (1/2) \(\int[0, 2\pi] 324(1/2)(1 - cos2\theta) d\theta\)

A = (1/4) \(\int[0, 2\pi] (162 - 162cos2\theta) d\theta\)

Integrating term by term:

A = (1/4) [162θ - 81sin2θ] evaluated from 0 to 2π

Plugging in the limits:

A = (1/4) [(162(2π) - 81sin(4π)) - (162(0) - 81sin(0))]

Simplifying further:

A = (1/4) [324π - 0 - 0 - 0]

A = (1/4) (324π)

Finally, we can calculate the area:

A = 81π

Therefore, the area of the circle r = 18sinθ in polar coordinates is 81π square units.

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Answer:

False.

Step-by-step explanation:

The statement "(dbl num, 2)" does not correctly represent rounding the value of "dbl num" to two decimal places. The correct notation for rounding a number to two decimal places is typically represented as "round(dbl num, 2)" or "dbl num rounded to 2 decimal places."

:)

The graph of the equation x+y = 8 will be a straight line.

Graphical representation refers to the use of charts and graphs to visually display, analyse, clarify, and interpret numerical data, functions, and other qualitative structures.

Given an equation, x+y = 8

when x = 0, y = 8 → (0,8)

when y = 0, x = 8 → (8,0)

Hence, The graph of the equation x+y = 8 will be a straight line.

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Answer:

0.4 grams

Step-by-step explanation:

40/100 = 0.4

We're asked to find inverse of the function,

\(\longrightarrow\rm{f(x)=\dfrac{e^x-e^{-x}}{e^x+e^{-x}}+2}\)

Take \(\rm{y=f(x).}\)

\(\longrightarrow\rm{y=\dfrac{e^x-e^{-x}}{e^x+e^{-x}}+2}\)

Subtract 2.

\(\longrightarrow\rm{y-2=\dfrac{e^x-e^{-x}}{e^x+e^{-x}}}\)

We apply componendo - dividendo rule.

\(\rm{\dfrac{a}{b}=\dfrac{c}{d}\quad\iff\quad\dfrac{b+a}{b-a}=\dfrac{d+c}{d-c}}\)

Thus,

\(\longrightarrow\rm{\dfrac{y-2}{1}=\dfrac{e^x-e^{-x}}{e^x+e^{-x}}}\)

\(\Longrightarrow\rm{\dfrac{1+(y-2)}{1-(y-2)}=\dfrac{(e^x+e^{-x})+(e^x-e^{-x})}{(e^x+e^{-x})-(e^x-e^{-x})}}\)

\(\longrightarrow\rm{\dfrac{y-1}{3-y}=\dfrac{2e^x}{2e^{-x}}}\)

\(\longrightarrow\rm{\dfrac{e^x}{e^{-x}}=\dfrac{y-1}{3-y}}\)

\(\longrightarrow\rm{e^{2x}=\dfrac{y-1}{3-y}}\)

\(\longrightarrow\rm{(e^x)^2=\dfrac{y-1}{3-y}}\)

Take square root.

\(\longrightarrow\rm{e^x=\sqrt{\dfrac{y-1}{3-y}}}\)

Take natural logarithm.

\(\longrightarrow\rm{x=\log_e\sqrt{\dfrac{y-1}{3-y}}}\)

\(\longrightarrow\rm{x=\dfrac{1}{2}\log_e\left(\dfrac{y-1}{3-y}\right)}\)

Now take \(\rm{x=f^{-1}(y).}\)

\(\longrightarrow\rm{f^{-1}(y)=\dfrac{1}{2}\log_e\left(\dfrac{y-1}{3-y}\right)}\)

Replace y by x and finally we get,

\(\longrightarrow\rm{\underline{\underline{f^{-1}(x)=\dfrac{1}{2}\log_e\left(\dfrac{x-1}{3-x}\right)}}}\)

This is the inverse of the given function.

The confidence interval is 0.039. This means that the value lies between the range of -0.039 and 0.039. Therefore, we can express the confidence interval as the mean plus or minus the margin of error.

This will give us a range in which the true population mean lies.Let's assume that the mean is 0.259. Then the lower limit of the range is given by:Lower limit = 0.259 - 0.039 = 0.22 And the upper limit of the range is given by:Upper limit = 0.259 + 0.039 = 0.298Therefore, the confidence interval is: 0.22 to 0.298Now we can see that option A is the correct answer: 0.259+0.22.

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The given equation is a recursive formula where a subscript i equals the product of a subscript i-1 and 2, with the initial value of a subscript 1 being -4a.

The equation represents a recursive relationship between the terms of the sequence. Starting with the initial term, a subscript 1, the subsequent terms are determined by multiplying the previous term, a subscript i-1, by 2. This recursive formula can be written as a subscript i = a subscript i-1 * 2.

Given that a subscript 1 = -4a, we can use this initial value to find the subsequent terms of the sequence. To calculate a subscript 2, we substitute i = 2 into the formula:

a subscript 2 = a subscript 2-1 * 2 = a subscript 1 * 2 = -4a * 2 = -8a.

Similarly, for a subscript 3:

a subscript 3 = a subscript 3-1 * 2 = a subscript 2 * 2 = -8a * 2 = -16a.

By applying the recursive formula repeatedly, we can generate the terms of the sequence. Each term is obtained by multiplying the previous term by 2.

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The area of the figure is 528units²

The space enclosed by the boundary of a plane figure is called its area. The area is measured in square units.

The figure contains several rectangles by dividing it into different shapes.

The first part is a rectangle;

area = l×w

= 16×8 = 128 units²

for the second part ;

area = l× w

= 8× 24

= 192 units²

for the third part

The area of the whole rectangle

= l×w

= 8× 24

= 192 units²

area of the cut out section

= 12 × 4 = 48 units²

Therefore area of the figure = 128+192+192-48

= 528 units²

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The probability of choosing a uni-color pair of socks from the bag is 199/799.

The probability of choosing a uni-color pair of socks from a large bag with 100 pairs of each of red, blue, black, and white socks is calculated as follows:

Step 1: Calculate the total number of socks in the bag.
There are 100 pairs of each color, and each pair consists of 2 socks, so there are 100 x 2 = 200 socks of each color.
The total number of socks in the bag is 200 x 4 = 800 socks.

Step 2: Calculate the probability of choosing a uni-color pair of socks.
The probability of choosing a red sock on the first draw is 200/800 = 1/4.
The probability of choosing another red sock on the second draw is 199/799.
The probability of choosing a red pair is (1/4) x (199/799) = 199/3196.

Similarly, the probability of choosing a blue pair, a black pair, or a white pair is also 199/3196.

The probability of choosing a uni-color pair is the sum of the probabilities of choosing a red pair, a blue pair, a black pair, and a white pair.

So the probability of choosing a uni-color pair is (199/3196) x 4 = 796/3196 = 199/799.

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The second step when evaluating the given expression is to subtract 6 from 18, simplifying the expression within the parentheses to 12.

The second step when evaluating the expression 3 + (18 - 6) + 20 + 4 is to perform the operation within the parentheses, specifically the subtraction inside the parentheses.

Let's break down the expression step by step:

1. Start with the expression: 3 + (18 - 6) + 20 + 4

2. The expression inside the parentheses is 18 - 6. To simplify this, we subtract 6 from 18, which equals 12.

3. Now, we rewrite the expression with the simplified part: 3 + 12 + 20 + 4

4. At this point, the expression consists of addition operations only. When evaluating an expression with multiple addition operations, we start from the left and work our way to the right, performing the addition operation between two numbers at a time.

5. The first addition operation is between 3 and 12. Adding these two numbers gives us 15.

6. We rewrite the expression again, replacing the addition of 3 and 12 with the result: 15 + 20 + 4

7. Now, we perform the next addition operation between 15 and 20, resulting in 35.

8. We rewrite the expression once more: 35 + 4

9. Finally, we perform the last addition operation between 35 and 4, resulting in 39.

Therefore, the second step when evaluating the given expression is to subtract 6 from 18, simplifying the expression within the parentheses to 12.

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The simplest form of the rational expression (x² + 4 · x + 4) / (x² + 3 · x + 2) + (x + 8) / (x² - 5 · x - 6) by algebra properties is (x³ - 2 · x² + 5 · x + 20) / (x³ - 4 · x² + x + 6).

In this question we need to simplify a rational expression by means of algebra properties. First, write the entire expression:

(x² + 4 · x + 4) / (x² + 3 · x + 2) + (x + 8) / (x² - 5 · x - 6)

Second, factor all numerators and denominators:

(x + 2)² / [(x + 2) · (x + 1)] + (x + 8) / [(x - 3) · (x - 2)]

Third, simplify each term:

(x + 2) / (x + 1) + (x + 8) / [(x - 3) · (x - 2)]

Fourth, use the properties for the addition of fractions with different denominator:

[(x + 2) · (x - 3) · (x - 2) + (x + 1) · (x + 8)] / [(x + 1) · (x - 3) · (x - 2)]

Fifth, expand and simplify the resulting expression:

[(x² - 4) · (x - 3) + x² + 9 · x + 8] / [(x + 1) · (x² - 5 · x + 6)]

(x³ - 4 · x - 3 · x² + 12 + x² + 9 · x + 8) / (x³ - 5 · x² + 6 · x + x² - 5 · x + 6)

(x³ - 2 · x² + 5 · x + 20) / (x³ - 4 · x² + x + 6)

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A sampling distribution is the probability distribution of a statistic for all random samples of n observations from a population. The term "sampling distribution" refers to the probability distribution of a statistic, such as the mean or standard deviation, that arises from random sampling of a fixed-sized sample from a population.

It is essential to understand this concept because it allows us to make inferences about the population parameter using information from the sample statistic. The standard deviation of the sampling distribution is known as the standard error of the statistic, and it measures how much the statistic varies across all possible samples of the same size from the population. In short, the sampling distribution is a theoretical distribution that helps us to understand the properties of the statistic and make inferences about the population parameter based on sample data.

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Answer:

D

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is true!

Let's say we subtract 6 from both sides

-2x -6< 0                       Now Let's add 2x to both sides

-2x + 2x - 6 < 0 + 2x

- 6 < 2x                         We did so we would be dividing by a number greater than 0.                         Divide by + 2

-6/2 < 2x / 2

-3 < x                            Notice you still get the open end of the inequality sign closest to the x without changing the direction of the inequality.

Answer:

if i am right it 260

Step-by-step explanation:

Answer:

Experimental study

Step-by-step explanation:

The probability that the second card is higher in rank than the first card can be calculated using the fact that the probability of drawing a higher card is equal to the probability of drawing a lower card.

Let's denote P(higher) as the probability of the second card being higher than the first, P(lower) as the probability of the second card being lower than the first, and P(same) as the probability of the second card being the same rank as the first.

Using this notation, we can express the probability of the second card being higher in rank than the first as follows:

P(higher) = 1 - P(lower) - P(same)

Therefore, the probability that the second card is higher in rank than the first card is 1 minus the probability of the second card being lower than the first card minus the probability of the second card being the same rank as the first card.

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Answer:

26 this is because 4x5=20 then add the triangle which is 3x4 ÷ 2 equalling 26

Answer:

Step-by-step explanation:

(5+8)/2 = 13/2 = 6.5

6.5*4 = 26m²

The formula for the area of a trapezoid is the same as a trapezium :

(a+b)/2 *h = Area

Step-by-step explanation:

Ratio of pink to blue eraser = 4/12 = 1/3

= 1:3

Answer:

1:3

Step-by-step explanation:

The ratio of pink:blue erasers is 4:12. Then you simplify, 4 and 12 both have 4 in common. 4 goes into 4 one time, and 4 goes into 12 three times. So your simplified answer is 1:3.

The speed of the wave is 7 m/s and the direction is positive x direction.

Speed wave:

Speed Wave is the distance a wave travels in a given time by Meters covered per second. Wave velocity is related to wavelength and wave frequency by the following equations:

                Speed = Wave length × Frequency

This equation can be used to calculate the wave velocity if the wavelength and frequency are known.

On comparing the given statement with  :

y(x ,t) = sin (14πt - 2πx +π/4)

The given travelling wave travels towards positive x direction.

Now, By comparing the equation, We get :

W =14 π          k = 2π             ϕ = π/4

Speed wave , V = W/k

                          = 14π / 2π

                          = 7 m/s.

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Answer:

A. 360 \(m^2\)

Step-by-step explanation:

(10 x 13) + (8 x 13) + (6 x 13) + 2(1/2(6 x 8))

= 130 + 104 + 78 + (6 x 8)

= 312 + 48

= 360 \(m^2\)

Answer:

1/3

Step-by-step explanation:

I think not sure.

\(7p - 4p - p \\ \\ 7p - 5p \\ \\ 2p.\)

Solution is : 2p .

Applying the inscribed angle theorem, m(CB) = 80°.

The inscribed angle theorem states that the measure of the inscribed angle is equal to one-half the measure of the intercepted arc or the arc it subtends.

Given the following:

m<DCB = 140°

m<BCE = 180 - m<DCB = 180 - 140 = 40°

Measure of intercepted arc CB = 2(m<BCE) [according to the inscribed angle theorem]

m(CB) = 2(40)

m(CB) = 80°

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Answer:

Yes. The rule is that any 2 sides of a triangle should be larger than the third. Therefore, it is possible to have lengths of 18, 19, and 7.

yes it can be

because the triangle inequality theorem described that for any triangle the sum of the length of two sides are always grater than the third side

then 18, 19, 7 can the three side of a triangle