f'(x) = 0 * x^(-2) + (-2/x^3) = -2/x^3.
So, the derivative of f(x) = 2/x^2 is f'(x) = -2/x^3.
To find f'(x) for the function f(x) = x + 2, we can use the power rule for derivatives.
The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = n*x^(n-1).
In this case, the function f(x) = x + 2 can be written as f(x) = x^1 + 2.
Applying the power rule, we differentiate each term separately:
f'(x) = d/dx (x^1) + d/dx (2)
The derivative of x^1 is 1x^(1-1) = 1x^0 = 1.
The derivative of a constant term like 2 is 0, as the derivative of a constant is always 0.
Therefore, f'(x) = 1 + 0 = 1.
So, the derivative of f(x) = x + 2 is f'(x) = 1.
To find f'(x) for the function f(x) = 2/x^2, we can use the power rule and the constant multiple rule.
The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = n*x^(n-1).
The constant multiple rule states that if we have a function of the form f(x) = cg(x), where c is a constant, then the derivative is given by f'(x) = cg'(x), where g'(x) is the derivative of g(x).
In this case, the function f(x) = 2/x^2 can be written as f(x) = 2 * x^(-2).
Applying the power rule and the constant multiple rule, we differentiate each term separately:
f'(x) = d/dx (2 * x^(-2))
Applying the constant multiple rule, the derivative of 2 is 0, as it is a constant term.
Applying the power rule, the derivative of x^(-2) is (-2) * x^(-2-1) = (-2) * x^(-3) = -2/x^3.
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If a ring costs a jeweler $2100, at what price should it be sold to yield a profit of 50% on the selling price?
which of the following is most likely the next step in the series
Answer:
A.
Step-by-step explanation:
Let's think of this as a clock. We can see that the 2 lines start in the same place, around 3 o'clock. Next, one of the line segments shifts down to around 6 o'clock. Next, it shifts to about 9 o'clock. Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.
We can also just use a regular circle, with one of the line segments moving 90 degrees each time.
Hope this helps! :)
reduce 205/246 to its lowest term
For the weight of the box that she measured, Beatriz determined the margin of error as 23.5 pounds to 24.5 pounds. What was the greatest possible error for her actual measurement?
Beatriz measured the weight of a box and determined the margin of error as 23.5 pounds to 24.5 pounds. The range of the margin of error is 1 pound, which means that the actual weight of the box could be off by a maximum of 1 pound.
Beatriz measured the weight of a box and determined the margin of error as 23.5 pounds to 24.5 pounds. The greatest possible error for her actual measurement can be determined by finding the range of the margin of error.
The range of the margin of error can be determined by finding the difference between the upper limit and the lower limit. Therefore, the range of the margin of error is 24.5 - 23.5 = 1 pound.
This means that the actual weight of the box could be off by a maximum of 1 pound. This is the greatest possible error for her actual measurement.
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Fabian is painting a wall that is 16 feet wide and 9 feet high. The wall has a window in it that is 4 feet
wide by 2 feet high. What is the total area of the remaining wall that needs to be painted?
O 144 ft²
O 50 ft²
O 136 ft²
O 152 ft²
Answer:
136 [tex]ft^{2}[/tex]
Step-by-step explanation:
Find the area of the wall and subtract out the area of the window
16 x 9 = 144
4 x 2 = 8
144 - 8 = 136
Helping in the name of Jesus.
What are the next four terms of the sequence -22, -6, 2, 6, 8,
Answer:
9, 9.5, 9.75, 9.875
Step-by-step explanation:
Notice the following pattern:
[tex]-22+16=-22+2^4=-6\\-6+8=-6+2^3=2\\2+4=2+2^2=6\\6+2=6+2^1=8[/tex]
Therefore, the next four terms will be:
[tex]8+2^0=8+1=9\\9+2^{-1}=9+0.5=9.5\\9.5+2^{-2}=9.5+0.25=9.75\\9.75+2^{-3}=9.75+0.125=9.875[/tex]
Rachel wants to reflect AABC across the y=x line and then reflect the image across the y - axis. Is there a single transformation that would be equivalent to this?
A single 180-degree rotation about the origin is equivalent to the sequence of reflections mentioned, as it accomplishes the same changes to the shape's orientation and coordinates.
Yes, there is a single transformation that is equivalent to reflecting AABC across the y=x line and then reflecting the image across the y-axis. This single transformation is known as a 180-degree rotation about the origin.
When you reflect AABC across the y=x line, each point is transformed to its corresponding point on the opposite side of the line. This reflection effectively swaps the x-coordinates with the y-coordinates for each point, resulting in a new shape.
Now, when you reflect the newly formed image across the y-axis, you essentially negate the x-coordinates of each point. This is equivalent to rotating the shape 180 degrees about the origin.
A 180-degree rotation about the origin involves flipping the shape by exchanging the x and y coordinates and taking their negatives. This transformation achieves the same result as reflecting across the y=x line and then reflecting across the y-axis.
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Correct answer please
Answer:
50.75
Step-by-step explanation:
We have:
[tex]E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\[/tex]
[tex]=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74[/tex]
An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of the residents of a state if you want to be 95% confident that the sample mean is within 4 IQ points of the true mean.
What is the required sample size?
Answer:
55
Step-by-step explanation:
[tex]\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow[/tex]
Make sure to always round up the required sample size to the nearest integer!
national Bureau of statistics reported that approximately 30% of the population are unemployed. In conducting a random telephone surveys, what is the probability of getting two or fewer unemployed people in a sample of 20? “Binomial distribution”
Change 4630 Litres to kiloliters 2 express 2Liters 360 milliliters in milliliters (3) express 2700 gram to the nearest 0.1kg (4) Change 2.705kg to the nearest 0.01kg (5) Express 9.597kg to the nearest kilograms.
Answer:
1) 4630 L = 4.63 kL
2) 2 L 360 mL = 2360 mL
3) 2700 g = 2.7 kg (rounded to nearest 0.1 kg)
4) 2.705 kg = 2.71 kg (rounded to nearest 0.01 kg)
5) 9.597 kg = 10 kg (rounded to nearest kg)
Select the equation you could use to find the perimeter of the rectangle.
horizontal rectangle with side lengths labeled 9 feet, 9 feet, 4 feet and 4 feet
P = 9 x 9 x 4 x 4
P = 9 x 4
P = 9 + 9 + 4 + 4
P = 9 + 4 + 4
Answer:
P = 9 + 9 + 4 + 4
Step-by-step explanation:
P=2(lxw) or l+l+w+w
Therefore, 9+9+4+4 is right.
Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.
f(x)= 1= ² + 4
X-4
To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:
[tex]f(g(x)) = f(x - 4) = (x - 4)^2 + 4[/tex]
To simplify this expression, we can expand the square:
[tex]f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20[/tex]
Therefore, f(g(x)) simplifies to[tex]x^2 - 8x + 20.[/tex]
Next, let's find g(f(x)). We substitute f(x) into the function g(x):
[tex]g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2[/tex]
Hence, g(f(x)) simplifies to 1/x^2.
In summary, f(g(x)) simplifies to[tex]x^2 - 8x + 20[/tex], and g(f(x)) simplifies to 1/x^2.
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PLS HELP ITS DUE TODAY
Isabella filled her pool with water at a constant rate. The table compares the remaining volume of water left to fill the pool (in liters) and the time since Isabella started filling the pool (in minutes). Time (minutes) Water (liters)
2 184
7 94
12 4
How fast did Isabella fill her pool? l
________liters per minute
Answer:
18
Step-by-step explanation:
Look at the values
2 184
7 94
Difference in volume: 184 liters - 94 liters = 90 liters
Difference in time: 7 minutes - 2 minutes = 5 minutes
rate in liters/minute: (90 liters) / (5 minutes) = 18 liters/minute
If angle C is 48 and angle B is 11x-5 and angle A is 9x-3, Find angle A.
Answer:
60°
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180°.
To find the measure of m∠A, we can write the following equation based on the above mentioned information:48° + 11x - 5 + 9x - 3 = 180°
Add like terms.40° + 20x = 180°
Subtract 40 from both sides.20x = 140°
Divide both sides with 20.x = 7
To find m∠A, replace x with 7:
m∠A = 9x - 3
9×7-3 = 60°
Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. Answer the following questions. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z=?
Step-by-step explanation:
To convert all pulse rates of women to z-scores, we use the formula:
z = (x - μ) / σ
where x is the pulse rate, μ is the mean, and σ is the standard deviation.
Substituting the given values, we get:
z = (x - 77.5) / 11.6
Therefore, after converting all pulse rates of women to z-scores, the mean will be 0 and the standard deviation will be 1.
Question 6
a) Given (t² + 2ty)y' = y²; where y(1) = 1, show that it is homogenous and find its degree.
b) Find the implicit and the explicit solution to the IVP in Q6.(a).
Formula Table
f(t) (Source) (K, m, a, b, given.)
Ke^at
Kmt^m + ... + Ko
K₁ cos(bt) + K₂ sin(bt)
(Kmt^m+ + ... + Ko)e^at
(K₁ cos(bt) + K₂ sin(bt))e^at
(Kmt^m+ + ... + Ko)(K₁ cos(bt) + K₂ sin(bt)
yp(t) (Guess) (k not given)
ke^at
kmt^m + ... + ko
k₁ cos(bt) + k₂ sin (bt)
(kmt^m + ... + ko)e^at
(k₁ cos(bt) + k₂ sin(bt))e^at
(kmt^m +... + ko) (k₁ cos(bt) + k₂ sin (bt))
TABLE 1. List of sources f and solutions yp to the equation L(yp) = f.
a) The solution to the function is t²(du/dt) + 2tu - u² = 0 and can be expressed in the form F(t, u, du/dt) = 0 which confirms it is homogeneous
b) The implicit solution is t/y + 1/t = 2ln|t| + C₁ and the explicit solution is y = (t + 1)/(2ln|t| + C₁)
Understanding Homogenous Functiona) To show that the given differential equation is homogeneous, we need to verify that it can be written in the form:
F(x, y, y') = 0
where F is a homogeneous function of degree zero.
Given:
(t² + 2ty)y' = y²
Let's rearrange the equation:
(t² + 2ty)y' - y² = 0
Now, let u = y/t. We can rewrite y' in terms of u:
y' = du/dt
Substituting these values into the equation, we get:
(t² + 2ty)(du/dt) - (y/t)² = 0
Expanding the equation:
t²(du/dt) + 2ty(du/dt) - (y²/t²) = 0
Now, let's substitute u = y/t into the equation:
t²(du/dt) + 2tu - u² = 0
We can see that this equation is of the form F(t, u, du/dt) = 0, which is homogeneous. Therefore, the given differential equation is homogeneous.
To find the degree of the equation, we need to determine the power of t in each term. Looking at the equation:
t²(du/dt) + 2tu - u² = 0
The highest power of t is 2, which means the degree of the equation is 2.
b) To find the implicit and explicit solutions to the initial value problem (IVP), we need to solve the homogeneous differential equation and apply the initial condition y(1) = 1.
Let's solve the homogeneous equation:
t²(du/dt) + 2tu - u² = 0
We can rewrite it as:
du/u² - dt/t² = -2dt/t
Integrating both sides:
∫(du/u²) - ∫(dt/t²) = -2∫(dt/t)
This simplifies to:
-1/u - (-1/t) = -2ln|t| + C₁
1/u + 1/t = 2ln|t| + C₁
Since u = y/t, we substitute u back:
1/(y/t) + 1/t = 2ln|t| + C₁
t/y + 1/t = 2ln|t| + C₁
This is the implicit solution to the given initial value problem.
To find the explicit solution, we need to solve for y in terms of t. Let's rearrange the equation:
t/y = 2ln|t| + C₁ - 1/t
Multiply both sides by y:
t = y(2ln|t| + C₁ - 1/t)
Now, let's simplify:
t = 2yln|t| + C₁y - 1
Rearranging the equation:
2yln|t| + C₁y = t + 1
Factoring out y:
y(2ln|t| + C₁) = t + 1
Dividing both sides by (2ln|t| + C₁), assuming C₁ ≠ -2ln|t|, we get:
y = (t + 1)/(2ln|t| + C₁)
This is the explicit solution to the given initial value problem.
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Please explain how to do it too ill give brainliest
Answer:
x = 90
Step-by-step explanation:
The given diagram shows a circle with intersecting chords, KM and JL.
To find the value of x, we can use the Angles of Intersecting Chords Theorem.
According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.
Let the point of intersection of chords KM and JL be point P.
As the chords are straight lines, angle x° forms a linear pair with angle JPM.
Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.
From inspection of the given diagram:
[tex]m\overset\frown{JM}=30^{\circ}[/tex][tex]m\overset\frown{LK}=(2x - 30)^{\circ}[/tex]Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):
[tex]\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}[/tex]
As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:
[tex]\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}[/tex]
Therefore, the value of x is 90, which means that the two chords intersect at right angles.
A pool measuring 18 meters by 24 meters is surrounded by a path of uniform width, as
shown in the figure. If the area of the pool and the path combined is 1672 square meters,
what is the width of the path?
Answer:
10 meters
Step-by-step explanation:
You want the width of the path surrounding an 18 meter by 24 meter pool if the total area of pool and path is 1672 square meters.
AreaThe total area of the rectangular shape is the product of its length and width:
A = LW
1672 = (24 +2x)(18 +2x)
418 = (12 +x)(9 +x) . . . . . . . . divide by 4
418 = 108 +21x +x² . . . . . . eliminate parentheses
420.25 = 110.25 +21x +x² . . . . . . add 2.5 to complete the square
20.5 = (10.5 +x) . . . . . . . . . . take the positive square root
10 = x . . . . . . . . . . . . . . subtract 10.5
The width of the path is 10 meters.
__
Additional comment
The attached graph shows the two solutions of the original equation written so the solutions are the x-intercepts:
(24 +2x)(18 +2x) -1672 = 0
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Given that cos0 = 8/17 and sin0 = -15/17. What is the value of tan0?
The value of tan 0 is -15/8.
The tangent is a periodic function that is defined by a unit circle. It is the ratio of the opposite side to the adjacent side of a right-angled triangle that contains the angle in question as one of its acute angles. The value of the tangent function can be positive, negative, or zero, depending on the quadrant in which the angle is located.
The given values are
cos0 = 8/17
sin0 = -15/17
We can use the trigonometric identity of tan = sin/cos to find the value of tan 0.
Substituting the given values, we get
tan 0 = sin 0 / cos 0
= (-15/17) / (8/17)
=-15/8
Therefore, the value of tan 0 is -15/8.
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need help with this question ASAP
The angle of elevation of the sun to the nearest degree is: 34°
How to find the angle of elevation?The angle of elevation is defined as an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is referred to as an angle of elevation.
There are three main trigonometric ratios which are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
In this case, the dimensions given will warrant the use of the tangent function to get:
tan θ = 101/147
tan θ = 0.6871
θ = tan⁻¹(0.6871)
θ = 34°
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What is lim x-1 x3-1/x-1
Answer:
Step-by-step explanation:
[tex]\lim_{x\to 1} \frac{x^3-1}{x-1} \\= \lim_{x \to 1} \frac{(x-1)(x^2+x+1)}{(x-1)} \\= \lim_{x \to 1} (x^2+x+1)\\=(1)^1+1+1\\=1+1+1\\=3[/tex]
By first finding tan, calculate the size of angle
0.
Give your answer in degrees to the nearest
integer.
13 cm
9 cm
0
Not drawn accurately
Tan (θ) = 13/9
θ = 55.305°
write equation line passing through (3,7) (-5,-1)
Answer:
Step-by-step explanation:
First find the slope using m = (y2-y1)/(x2-x1)
m = (-1-7)/(-5-3)
= -8/-8
= 1
y = mx + b
find the y-intercept
use 1 of the 2 points
Let's try (3,7)
7 = 1(3) + b
b = 4
Equation of the line is y = x + 4
The equation is:
y = x + 4Work/explanation:
First, we will use the slope formula and determine the slope:
[tex]\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
where m = slope.
Plug in the data
[tex]\sf{m=\dfrac{-1-7}{-5-3}}\\\\\\\sf{m=\dfrac{-8}{-8}}\\\\\\\sf{m=1}[/tex]
The slope is 1; the equation so far is y = 1x + b or y = x + b.
Plug in the point:
[tex]\sf{7=3+b}[/tex]
[tex]\sf{3+b=7}[/tex]
Solve for b
[tex]\sf{b+3=7}[/tex]
[tex]\sf{b=4}[/tex]
So the y-intercept is 4; we plug that in and see that the equation is y = x + 4.
Hence, the equation is y = x + 4.a triangle is shown drag graphs to the table to ahow the image of the triangle after it is reflected over the x-axis, the y-axis, or the line y = x.
The graphs have been correctly dragged to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, and the line y = x.
How to reflect the triangle based on the transformation rule?By applying a reflection over the x-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;
(x, y) → (x, -y)
(1, -3) → (1, -(-3)) = (1, 3)
(3, -2) → (3, -(-2)) = (3, 2)
(4, -5) → (4, -(-5)) = (4, 5)
By applying a reflection over the y-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;
(x, y) → (-x, y)
(1, -3) → (-1, -3)
(3, -2) → (-3, -2)
(4, -5) → (-4, -5)
By applying a reflection over the line y = x to the coordinates of this triangle, we have the following coordinates of the image triangle;
(x, y) → (y, x)
(1, -3) → (-3, 1)
(3, -2) → (-2, 3)
(4, -5) → (-5, 4)
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tan(x-1) ( sin2x-2cos2x) = 2(1-2sinxcosx)
[tex]\huge\blue{\fbox{\tt{Solution:}}}[/tex]
We can simplify the expression using trigonometric identities.
First, we can use the double angle formula for sine to write sin(2x) = 2sin(x)cos(x).
Next, we can use the double angle formula for cosine to write cos(2x) = cos^2(x) - sin^2(x) = 1 - 2sin^2(x). Rearranging this equation gives 2sin^2(x) - 2cos^2(x) = -cos(2x) + 1.
Substituting these identities into the original expression gives:
tan(x-1) ( sin2x-2cos2x) = tan(x-1) [2sin(x)cos(x) - 2(1 - 2sin^2(x))]
= 2tan(x-1)sin(x)cos(x) - 2tan(x-1) + 4tan(x-1)sin^2(x)
We can use the identity tan(x) = sin(x)/cos(x) to simplify this expression further:
2tan(x-1)sin(x)cos(x) - 2tan(x-1) + 4tan(x-1)sin^2(x)
= 2sin(x)cos(x)/(cos(x-1)) - 2sin(x)/(cos(x-1)) + 4sin^2(x)/(cos(x-1))
Multiplying both sides of the equation by cos(x-1) gives:
2sin(x)cos(x) - 2sin(x) + 4sin^2(x)cos(x-1) = 2(1-2sin(x)cos(x))
Expanding the left-hand side of the equation gives:
2sin(x)cos(x) - 2sin(x) + 4sin^2(x)cos(x) - 4sin^2(x) = 2 - 4sin(x)cos(x)
Simplifying this equation gives:
4sin^2(x) - 2sin(x) - 2 = 0
This is a quadratic equation in sin(x), which can be solved using the quadratic formula.
What is the formula to find the perimeter of a rectangle?
P = l + w + w
P = l + l + w + w
P = w + w + l
P = l + l + l + w
Answer:
it answer is
P=2(l+b)
P=l + l + b + b
The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift. Apportion 16 salespeople using Jefferson's method given the information below.
Shift Morning Midday Afternoon Evening
Average number of customers 125 280 460 560
Salespeople to assign
What modified divisor did you use?
a) Using the standard divisors according to Jefferson's apportionment method, the number of salespeople assigned to work each shift is as follows:
Shift Morning Midday Afternoon Evening Total
Number of
salespeople assigned 1 3 5 7 16
b) The modified or adjusted divisor used represents the average number of customers for each shift divided by the standard divisor.
What is the standard divisor?The standard divisor shows the ratio of the total population to the number of seats.
The standard divisor gives an insight about the number of people each seat represents.
Standard divisor = Total number of customers / Total number of salespeople
The total number of customers = 1,425
The number of salespeople = 16
a) Standard divisor = 1,425 ÷ 16
= 89.0625
Shift Morning Midday Afternoon Evening Total
Average number of
customers 125 280 460 560 1,425
Standard divisor 89.0625 89.0625 89.0625 89.0625
b) Modified divisor 1.4035 3.1438 5.165 6.288
Number of
salespeople assigned 1 3 5 7 16
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SOMEONE PLEASE ANSWER FAST!!! 20 POINTS
Find the probability that a randomly
selected point within the square falls in the
red-shaded area.
First, find the area of the red-shaded region.
3
3 5
Ashaded
The probability that a randomly selected point within the square falls in the red-shaded square is 0.36
Finding the probabilityFrom the question, we have the following parameters that can be used in our computation:
Red square of length 3White square of length 5The areas of the above shapes are
Red square = 3² = 9
White square = 5² = 25
The probability is then calculated as
P = Red square/White square
So, we have
P = 9/25
Evaluate
P = 0.36
Hence, the probability that a randomly selected point within the square falls in the red-shaded square is 0.36
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on : to show More... Then click on √x to enter your answers using the Math Equation editor. Question 5 A frog with bionic legs leaps from a stump with an initial velocity of 64 ft/sec. It is determined that the height of the frog as a function of time can by modeled by h (t) = − 16t² +64t + 3. What is the height of the stump? O 3 ft -3 ft O 16 ft O 64 ft ◄ Previous 1 pts M Next ▸
The height of the stump is 3 ft.
The given equation represents the height of the frog, h(t), as a function of time, t. To find the height of the stump, we need to determine the height when the time, t, is equal to 0.
In the equation h(t) = -16t² + 64t + 3, we substitute t = 0:
h(0) = -16(0)² + 64(0) + 3
Since any term multiplied by zero is zero, we can simplify further:
h(0) = 0 + 0 + 3
Therefore, the height of the stump, at time t = 0, is 3 ft. This means that when the frog initially leaps from the stump, the height of the stump itself is 3 ft.
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