\(f(x)=\dfrac{4}{5}x-2\\\\\\f(3)=\dfrac{4}{5}\cdot3-2=\dfrac{12}{5}-2=\dfrac{12}{5}-\dfrac{10}{5}=\boxed{\frac{2}{5}}\)
. Write the equation of a line with a slope of 4 passing through the point (3, 1). Write the
equation in slope-intercept form.
Answer:
y = 4x - 11
Step-by-step explanation:
The general equation of the slope-intercept form of a line is given by:
y = mx + b, where
(x, y) are any point on the line,m is the slope,and b is the y-intercept.We can find b, the y-intercept of the line, by plugging in 4 for m and (3, 1) for (x, y) in the slope-intercept form:
1 = 4(3) + b
1 = 12 + b
-11 = b
Thus, the y-intercept is -11.
Thus, the equation of the line with a slope of 4 passing through the point (3, 1) in slope-intercept form is y = 4x - 11
The answer is:
y = 4x - 11Work/explanation:
First, we will write the equation in point slope:
\(\sf{y-y_1=m(x-x_1)}\)
where m = slope;
(x₁,y₁) is a point on the line.
Plug in the data:
\(\sf{y-1=4(x-3)}\)
Simplify
\(\sf{y-1=4x-12}\)
Add 1 on each side
\(\sf{y=4x-12+1}\)
\(\sf{y=4x-11}\)
Hence, the equation is y = 4x - 11.Heeeelp please, Can be zero or not?
with all steps and explanay.
The value of integral is 3.
Let's evaluate the integral over the positive half of the interval:
∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx
Let u = 4 + 3sin(x), then du = 3cos(x) dx.
Substituting these expressions into the integral, we have:
∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du
Using the power rule of integration, the integral becomes:
∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]
Evaluating the definite integral at the limits of integration:
(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))
(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0
So, the value of integral is
= 3-0
= 3
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Answer:
\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)
Step-by-step explanation:
First, compute the indefinite integral:
\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)
To evaluate the indefinite integral, use the method of substitution.
\(\textsf{Let} \;\;u = 4 + 3 \sin x\)
Find du/dx and rewrite it so that dx is on its own:
\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)
Rewrite the original integral in terms of u and du, and evaluate:
\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)
Substitute back u = 4 + 3 sin x:
\(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)
Therefore:
\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)
To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.
Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.
\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)
Therefore, the curve of the function is:
Below the x-axis between -π and -π/2.Above the x-axis between -π/2 and π/2.Below the x-axis between π/2 and π.So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.
Integrate the function between -π and -π/2.
As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:
\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)
Integrate the function between -π/2 and π/2:
\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)
Integrate the function between π/2 and π.
As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:
\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)
To evaluate the definite integral, sum A₁, A₂ and A₃:
\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)
Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:
\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)
Therefore, the given expression cannot be zero.
Write .000594 in scientific notation
Answer:5.94 × 10^-4
Step-by-step explanation:
a salesman earns 25% commission he sells amount to 2450 shillings after giving a buyers 2% discount . calculate his commission. Suppose all the goods were sold at marked price , what would be is earnings?
Answer:
Step-by-step explanation:
A) Commission = 2450 shillings * 25 % = 2450 shillings * (25/100) = 2450 shillings * (0.25) = 612.50 shillings
Commission = 612.50 shillings
B) If the total sale is 2,450.00 shillings, after the seller gives buyers a 2% discount. We must re-enter the discount:
2,450.00 shillings = X - X * 2% = X - 0.02 X --->
------> 0.98 X = 2,450.00 shillings
------>X= 2,450.00 / 0.98
------> X = 2,500.00 shillings
NEW COMMISSION = 2,500.00 shillings * 25 % = 2,500.00 shillings *(25/100) =2,500.00 shillings * (0.25) = 625 shillings
NEW COMMISSION = 625 shillings
what are the coordinates of point b on ac such that ab=2/5ac
Answer:
\((-\frac{36}{7},\frac{40}{7})\)
Step-by-step explanation:
Coordinates of points A and C are (-8, 6) and (2, 5).
If a point B intersects the segment AB in the ratio of 2 : 5
Then coordinates of the point B will be,
x = \(\frac{mx_2+nx_1}{m+n}\)
and y = \(\frac{my_2+ny_1}{m+n}\)
where \((x_1, y_1)\) and \((x_2,y_2)\) are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.
For the coordinates of point B,
x = \(\frac{2\times 2+(-8)\times 5}{2+5}\)
= \(-\frac{36}{7}\)
y = \(\frac{2\times 5+5\times 6}{2+5}\)
= \(\frac{40}{7}\)
Therefore, coordinates of pint B will be,
\((-\frac{36}{7},\frac{40}{7})\)
Point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid. The distance between the two points is ____. (Input numbers and decimal point only, such as 8.2.) (Please walk me through how you got your answer!)
Answer:
\( RT = 1.1 \)
Step-by-step explanation:
Distance between R(3, 1.3) and T(3, 2.4):
\( RT = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
\( RT = \sqrt{(3 - 3)^2 + (2.4 - 1.3)^2} \)
\( RT = \sqrt{(0)^2 + (1.1)^2} \)
\( RT = \sqrt{0 + 1.21} = \sqrt{1.21} \)
\( RT = 1.1 \)
Help
Find a if A = 8a
Answer:
a(A) = 0
Step-by-step explanation:
At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph?
A) approximately 16%
B) at most 34%
C) at most 2.5%
D) at most 13.5%
The percentage of players serves were between 115 mph and 145 mph is approximately 16%.
Given :
The statistician reported that the mean serve speed was 100 miles per hour
the standard deviation of the serve speeds was 15 mph
Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric
To find :
What percentage of the player's serves were between 115 mph and 145 mph?
Solution :
μ =100
σ = 15
P ( 115 < x <145)
= P ( \(\frac{115-100}{15}\) < x-μ /6 <\(\frac{145-100}{15}\) )
= P ( \(\frac{15}{15}\) < z < \(\frac{15}{15}\) )
= p ( 1<z<3)
= p( z<3)-p(z-1)
=0.9987-0.8413
=0.1574
p ( 115<xx<145)= 15.74 %
p( 115<x<145)= approximately 16%
The percentage of players serves were between 115 mph and 145 mph is approximately 16%.
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Help please with the last part? Tap on it
The slope of the line below is -4. Which of the following is the iS point-slope
form of the line?
\ (2, -8)
O A. y+ 8 = -4(x-2)
O B. y+ 2 =-4(x-8)
• C. y-8 = -4(x+ 2)
• D. y- 2=-4(x+ 8)
Correct option is A, the iS point-slope form of the line is y+ 8 = -4(x-2). A straight line's equation can be written as both a point slope form and a slope intercept form.
What does "point-slope form of the line" refer to?A line equation written using a single line point and the slope of the line is the simplest definition of the term "point-slope form." The slope is expressed in point form as the ratio of the change in y values to the change in x values, also known as the rise over run (x, y).
The point slope form is useful when there is a slope and one or more points are present. Standard form is often easier to employ while doing algebraic computations. Depending on our needs or our level of expertise, we can alter the form of an equation. Both the point slope form and the slope intercept form can be used to express the equation for a straight line. The point slope form highlights any point on the line as well as the slope. The slope and y-intercept of a line are only shown in slope intercept form.
Given,
the slope of line = - 4 and point = (2,-8)
The equation of line = y - yo = m (x - xo)
where m = slope and x,y are coordinates
y + 8 = - 4 (x - 2)
y + 8 = - 4x + 8
y = - 4x
Therefore, the correct answer is option A, y+ 8 = -4(x-2)
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You are given that z > 2. Write an inequality for each expression.
a) 2z+ 9
b) 3(z - 4)
c) 4+2z
d) 5(3z-2)
a) The inequality for the expression 2z + 9 is 2z + 9 > 13.
b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.
c) The inequality for the expression 4 + 2z is 4 + 2z > 8.
d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.
a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:
2z > 2 * 2
2z > 4
Adding 9 to both sides:
2z + 9 > 4 + 9
2z + 9 > 13
Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.
b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:
3z - 3 * 4
3z - 12
Since we are given that z > 2, we can substitute z > 2 into the expression:
3z - 12 > 3 * 2 - 12
3z - 12 > 6 - 12
3z - 12 > -6
Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.
c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:
4 + 2z > 4 + 2 * 2
4 + 2z > 4 + 4
4 + 2z > 8
Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.
d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):
5 * 3z - 5 * 2
15z - 10
Considering the given inequality z > 2, we can substitute z > 2 into the expression:
15z - 10 > 15 * 2 - 10
15z - 10 > 30 - 10
15z - 10 > 20
Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.
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Select the correct answer.
Tom gets $12 off a box of chocolates that had an original price of $48. What percentage is the discount?
A. 12%
B. 25%
C. 50%
D. 60%
5.275 to 2 decimal places
Answer:
5.29
..................................
Los 1600 euros de alquiler de un terreno se reparten entre tres ganaderos que llevan alli a pastar sus ovejas. Como no tienen el mismo número de ovejas, deciden pagar proporcionalmente al número de ovejas de cada uno. Si el primero tiene 120 Ovejas,el segundo 72 y el tercero 68. ¿ Cuánto paga cada uno?
So, each farmer pays the following amounts: The first farmer pays 738.40 euros. The second farmer pays 443.04 euros. The third farmer pays 418.56 euros
What is proportion?Proportion refers to the equality of two ratios. In other words, when two ratios are set equal to each other, they form a proportion. A proportion is typically written in the form of two fractions separated by an equals sign, such as a/b = c/d. Proportions are commonly used in mathematics to solve problems involving ratios and proportions, such as finding missing values or scaling up or down a given quantity.
Here,
To find out how much each farmer pays, we need to determine the proportion of the total rent that each farmer owes based on the number of sheep they have. First, we need to find the total number of sheep:
120 + 72 + 68 = 260
The first farmer has 120 sheep, which is 46.15% of the total number of sheep (120/260). Therefore, the first farmer owes 46.15% of the rent:
0.4615 x 1600 = 738.40 euros
Similarly, the second farmer has 72 sheep, which is 27.69% of the total number of sheep (72/260). Therefore, the second farmer owes 27.69% of the rent:
0.2769 x 1600 = 443.04 euros
The third farmer has 68 sheep, which is 26.15% of the total number of sheep (68/260). Therefore, the third farmer owes 26.15% of the rent:
0.2615 x 1600 = 418.56 euros
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Complete question:
The rent of 1600 euros for a piece of land is divided among three farmers who graze their sheep there. As they do not have the same number of sheep, they decide to pay proportionally according to the number of sheep each has. If the first one has 120 sheep, the second 72, and the third 68. How much does each one pay?
Wendy has 5 and 1 over 3 feet of ribbon. How many 2 over 3 foot pieces can Wendy cut from the 5 and 1 over 3 feet of ribbon? Show your work.
Answer:
Your answer is 8
Step-by-step explanation:
First you have to convert the mixed number into an improper fraction. To do this, multiply the denominator by the whole number. Then add the numerator and put that answer in a fraction over the original. So it would be 3*5=15+1=16/3. So now that the denominators are the same, all you need to do is see how many times 2 goes into 16. 16/2 which is 8. Answer = 8
what is 4 1/8 - 2 2/3 to the nearest whole number
Answer:
1 11/24
Step-by-step explanation:
:))
Write a piecewise function. PLEAE HELP i really need this any help would be very appreciated!!
Answer:
see below
Step-by-step explanation:
Each age bracket defines a domain of the function. The function value is constant for that domain. This function gives admission price (P) as a function of age (a).
\(P(a)=\left\{\begin{array}{ccl}0&\text{for}&a\le5\\3&\text{for}&5<a\le18\\5&\text{for}&18<a<65\\4&\text{for}&a\ge65\end{array}\right.\)
What is the image of point (0,2) after a rotation of 90° counterclockwise about the origin?
Answer:
(-2,0)
Step-by-step explanation:
remember the rule for 90 degree clockwise is (-y,x) opposite y and x
the negative in there DOES NOT mean it will always be negative it means opposite but in this case yes it's negative because the opposite of positive is negative
Hope this helps dude, I'm also learning this in online school lol. ^-^
The image of point (0,2) after a rotation of 90° counterclockwise about the origin is (-2, 0).
The given coordinate point is (0, 2).
What is rotation rule of 90°?Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).
The rule of 90° counterclockwise rotation: (x, y) becomes (-y, x), here
(-2, 0)
Therefore, the image of point (0,2) after a rotation of 90° counterclockwise about the origin is (-2, 0).
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Dequan is training for a marathon. He runs 20 miles every 4 days. What is the unit rate for Dequan?
Answer:
Dequan walks 5 miles per day.
Step-by-step explanation:
So solve this problem, we just need to divide 20 miles by 4 days.
20 ÷ 4 = 5
Therefore, Dequan walks 5 miles per day.
Hope this helps! :D
D is the planar region bounded by y = 0, y = x² and x = 1. Find the value of the integral below.
\(\displaystyle \iint_D x e^y \, dA = \int_0^1 \int_0^{x^2} x e^y \, dy \,dx \\\\ ~~~~~~~~ = \int_0^1 x (e^{x^2} - 1)\, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 e^u \, du - \int_0^1 x \,dx = \boxed{\frac{e - 2}2}\)
Which equation has a slope of –2 and passes through the point (5, 0)?
A. y = 2x + 5
B. y = 2x + 10
C. y = –2x + 5
D. y = –2x + 10
Answer:
D. y = –2x + 10
Step-by-step explanation:
1) First, write the equation of the line in point-slope form with the given information. Use the point-slope formula \(y-y_1 = m (x-x_1)\) and substitute values for \(m\), \(x_1\), and \(y_1\).
Since \(m\) represents the slope, substitute -2 in its place. Since \(x_1\) and \(y_1\) represent the x and y values of a point the line intersects, substitute the x and y values of (5,0) into the formula as well. This gives the following equation:
\(y - 0 = -2(x-5)\\y = -2(x-5)\)
2) Expand the right side of the equation to find the answer:
\(y = -2(x-5)\\y = -2x+10\)
So, option D is correct.
i’m begging someone please help!!
According to the question the height of the tree is 8 ft.
What is height?Height is the distance from the base of a person or object to the top. It is a measure of vertical distance, and is typically measured in centimeters or feet and inches. Height is an important factor in determining one's physical health and well-being. It can also be a factor in determining one's status in the world. Height can impact a person's self-esteem, confidence, and social standing. Height can also be an indicator of overall health, as tall people tend to have better overall health than those who are shorter.
Let x = the height of the tree.
Since the height of the person is 6ft and the distance from the person to the tree is 24 ft, we can write:
6/24 = x/2
Solving for x, we get:
x = 24/3 = 8 ft
Therefore, the height of the tree is 8 ft.
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Given that A={1,2,3,4,5} list the elements of the following sets. i.{x2:x€A} ii.{ :x€A} iii.{2x :x€A} iv.{4x+1:x€A}
Answer:no idea
Step-by-step explanation:
Extensive experience with fans of a certain type used in diesel engines has suggested that the exponential distribution provides a good model for time until failure. Suppose the mean time until failure is 23,100 hours.
(a) What is the probability that a randomly selected fan will last at least 20,000 hours?
What is the probability that a randomly selected fan will last at most 30,000 hours?
What is the probability that a randomly selected fan will last between 20,000 hours and 30,000 hours?
(b) What is the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations?
What is the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations?
Answer:
0.4207149;0.7271136; 0.3063987; 0.04979 ; 0.01832
Step-by-step explanation:
For an exponential distribution:
IF Mean time until failure = 23100
λ = 1/ 23100 = 0.0000432900
What is the probability that a randomly selected fan will last at least 20,000 hours
x ≥ 20000
P(X ≥ 20000) = 1 - P(X ≤ 20000)
1 - P(X ≤ 20000) = [1 - (1 - e^(-λx))]
1 - P(X ≤ 20000) = [1 - (1 - e^(-0.0000432900*20000)
1 - P(X ≤ 20000) = [1 - (1 - 0.4207148)]
1 - P(X ≤ 20000) = 1 - 0.5792851
1 - P(X ≤ 20000) = 0.4207149
11) What is the probability that a randomly selected fan will last at most 30,000 hours?
x ≤ 30000
P(X ≤ 30000) = 1 - e^(-λx)
P(X ≤ 20000) = 1 - e^(-0.0000432900*30000)
= 1 - e^(−1.2987)
= 1 - 0.2728863
= 0.7271136
111) What is the probability that a randomly selected fan will last between 20,000 hours and 30,000 hours?
0.7271136 - 0.4207149 = 0.3063987
B) What is the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations?
More than two standard deviation
X = 23100 + 2(23100) = 23100 + 46200 = 69300
Using the online exponential probability calculator :
P(X > 69300) = 0.04979
C) What is the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations?
X = 23100 + 3(23100) = 23100 + 69300 = 92400
P(X > 92400) = 0.01832
Between which two consecutive integers is \(\sqrt{201}\)
Answer:
14 and 15
Step-by-step explanation:
\(196<201<225 \\ \\ \sqrt{196}<\sqrt{201}<\sqrt{225} \\ \\ 14<\sqrt{201}<15\)
Which number line represents the solution set for the inequality which number line represents the solution set for the inequality 2x-6 is less than or equal to 6(x-2)+8
Answer:
The answer is C
The correct answer is option (C).
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
2x-6 ≥ 6(x-2)+8
Simplify this inequality,
2x-6 ≥ 6x-12 +8
2x-6 ≥ 6x-4
⇒4x≤-2
⇒x≤-0.5
Inequality shows that values less than or equal to -0.5 are the solutions.
Therefore, option C is correct.
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The time between surface finish problems in a galvanizing process is exponentially distributed with a mean of 41 hours. A single plant operates three galvanizing lines that are assumed to operate independently. Round your answers to four decimal places (e.g. 98.7654).
(a) What is the probability that none of the lines experiences a surface finish problem in 41 hours of operation?
(b) What is the probability that all three lines experience a surface finish problem between 24 and 41 hours of operation?
Answer:
a) The probability that none of the lines experiences a surface finish problem in 41 hours of operation is 0.0498.
b)The probability that all three lines experience a surface finish problem between 24 and 41 hours of operation is 0.0346.
Step-by-step explanation:
\(Mean = \frac{1}{\lambda} = 41\\P(X\leq x)= 1-e^{-\lambda x}\)
\(P(X>x)= e^{-\lambda x}\)
a)
\(P(x> 41, y>41, Z>41) = (P(X>41))^{3}\\\\P(X>41)=e^{^{-\frac{41}{41}}}=e^{-1}\)
\(P(x> 41, y>41, Z>41) = \left (e^{-1} \right )^{3}\\\\P(x> 41, y>41, Z>41) = e^{-3} = 0.0498.\)
b)
\(\lambda =\frac{24}{41}\\P(X=1)=e^{-\lambda }\cdot \lambda =\left ( e^{-0.585} \right )\left ( 0.585 \right )\\P(X=1)=0.326\)
For 3 where, P(X=1, Y==1, Z=1)
\(= (0.326)^{3} \\\\= 0.0346\)
As a summer job, Bart is picking strawberries at his uncle's farm. He can pick 6
gallons of strawberries in 9 minutes, and his uncles pays him $5 for 2 bushels. How
much does Bart make per hour picking strawberries?
Given: 8 gallons = 1 bushel & 60 minutes = 1 hour
Answer:
125
Step-by-step explanation:
All the work is in picture attat
Count the best-case number of + operations performed by the following pseudocode segment. Assume that all possible data sets are equally likely. Preconditions: X = {x1, x2, x3, x4, x5} ⊆ {10, 20, 30, 40, 50, 60, 70, 80}, where x1 < x2 < x3 < x4 < x5. t ← 0 i ← 1 while t < 101 do t ← t + xi i ← i + 1
For the best cases there will be 6+operations, The number of operations are best cases 6 and the worst cases are 10.
Given that,
The following pseudocode snippet performs the maximum number of + operations. Assume that the probability of each potential piece of data is equal. Preconditions: X = {x₁, x₂, x₃, x₄, x₅} ⊆ {10, 20, 30, 40, 50, 60, 70, 80}, where x1 < x2 < x3 < x4 < x5. t ← 0 i ← 1 while t < 101 do t ← t + xi i ← i + 1
We know that,
Here,
X = {x₁, x₂, x₃, x₄, x₅} ⊆ {10, 20, 30, 40, 50, 60, 70, 80}
By doing the iteration method
Iteration process till 4th iteration we get 6
Therefore, For the best cases there will be 6+operations, The number of operations are best cases 6 and the worst cases are 10.
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7x^7+10x^4+4x^3-5x^11-10x^6-6x^7
The sum of the terms is x^7+10x^4+4x^3-5x^11-10x^6
How to determine the valueTo determine the value, we need to know that algebraic expressions are described as expressions that are composed of factors, constants, variables, terms and coefficients.
These algebraic expressions are also identified with the presence of arithmetic operations,
These operations are;
AdditionBracketParenthesesSubtractionMultiplicationDivisionFrom the information given, we have that;
7x^7+10x^4+4x^3-5x^11-10x^6-6x^7
collect the like terms
7x^7 - 6x^7+10x^4+4x^3-5x^11-10x^6
add the like terms
x^7+10x^4+4x^3-5x^11-10x^6
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