Evaluate the following integral. - ex-1 dx vx 3
Answers
To evaluate the integral, we can use integration by substitution. Let u = x-1, then du = dx. Substituting these into the integral, we get: ∫e^(u) du / (u+4)^3.
To solve this integral, we can use integration by parts. Let dv = (u+4)^(-3) du, then v = (-1/2)(u+4)^(-2). Using the formula for integration by parts, we get: ∫e^(u) dv = e^(u)v - ∫v du, Plugging in the values for v and u, we get: = -1/2e^(x-1)(x+3)^(-2) - ∫1/2e^(x-1)(x+3)^(-2) dx, This new integral can be solved using integration by substitution again. Let w = x+3, then dw = dx. Substituting these into the integral, we get: = -1/2e^(x-1)(x+3)^(-2) - ∫1/2e^(-2) dw = -1/2e^(x-1)(x+3)^(-2) - 1/4e^(-2) + C
Therefore, the solution to the original integral is: ∫e^(x-1)/(x+3)^3 dx = -1/2e^(x-1)(x+3)^(-2) - 1/4e^(-2) + C.
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Related Questions
Question 1:
Solve for k :
Answers
step by step explanation: divide 108 and -3 and because there is one negative it’d be -36
hope this helps
Answer:
Step-by-step explanation:
Equation:
-3k = 108
We need to separate -3 from k. So we must do the inverse operation.
Divide both sides by -3
k = -36
Hope this helps :)
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How do you know whether a number written in standard form will have a positive or negative exponent when written in scientific notation? The drop down boxes have the words positive and negative.
Answers
Okay, here we have this:
Considering the provided sentence, we are going to identify wich is the correct word, so we obtain the following:
If the number is greater than
Eighty percent of adults drink coffee and seventy percent drink tea. What is the smallest possible percent of adults who drink both coffee and tea?
Answers
Answer:
50%
Step-by-step explanation:
Given that Eighty percent ( 80%) of adults drink coffee and seventy ( 70%) percent drink tea.
Let the percent of the adults that drink coffee and tea be y
The total percentage of adults = 100
80 - y + y + 70 - y = 100
150 - y = 100
- y = 100 - 150
Y = 50.
Therefore, the smallest possible percent of adults who drink both coffee and tea is 50 %
A Simpler Answer:
Add together the probabilities.
80%+70%=150%
Therefore we overcounted 50 percent, so the least amount possible is \(\boxed{50\%}\)
solve each equation -(7-2x)+7=-7
Answers
Answer:
x is -3.5
Step-by-step explanation:
the steps are shown in the picture attached
UL.Z This question is designed to be answered with a calculator. A midpoint approximation of the area under the curve f(x) = 2x(x - 4)(x - 8) over the interval [0, 4) with 4 subintervals is 0 111. 0 120 O 132. O 160.
Answers
The midpoint approximation of the area under the curve f(x) = 2x(x - 4)(x - 8) over the interval [0, 4) with 4 subintervals is 0. To approximate the area under the curve using a midpoint approximation, we divide the interval [0, 4) into four subintervals of equal width.
The width of each subinterval is (4 - 0) / 4 = 1.
Now, we need to evaluate the function at the midpoint of each subinterval and multiply it by the width of the subinterval.
The midpoints of the subintervals are: 0.5, 1.5, 2.5, and 3.5.
Evaluating the function at these midpoints, we get:
f(0.5) = 2 * 0.5 * (0.5 - 4) * (0.5 - 8) = 6
f(1.5) = 2 * 1.5 * (1.5 - 4) * (1.5 - 8) = -54
f(2.5) = 2 * 2.5 * (2.5 - 4) * (2.5 - 8) = 54
f(3.5) = 2 * 3.5 * (3.5 - 4) * (3.5 - 8) = -6
Now, we calculate the sum of these values and multiply it by the width of the subinterval:
Area ≈ (6 + (-54) + 54 + (-6)) * 1 = 0.
Therefore, the midpoint approximation of the area under the curve f(x) = 2x(x - 4)(x - 8) over the interval [0, 4) with 4 subintervals is 0.
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Given the definitions of f(x) and g(x) below, find the value of g (f(5)).
f(x) = x² - 6x + 14
g(x) = x +14
PLEASE HELP!
Answers
g(x)= 23
Explanation:
f(x)=5^2 - 6(5) + 14
25 - 30 + 14
-5 + 14 = 9
g(x) = 9 + 14
g(x) = 23
the world population in 1997 was 5.88billion. the world population in 2017was 7.53billion. assume that the ratio between the population in two consecutive years was constant between 1997 and 2017. which equation can be used to find r,the rate of growth per year of the world population?
Answers
The equation that can be used to find r, the rate of growth per year of the world population, is \(r = (7.53 / 5.88 )^{(1/20)} - 1\).
If we assume that the growth rate of the world population was constant from 1997 to 2017, then we can use the following equation:
Population in 2017 = Population in 1997 × (1 + r)²⁰
where r is the annual growth rate, and the exponent 20 represents the number of years between 1997 and 2017.
We can rewrite this equation to solve for r:
(7.53 ) = (5.88 ) × (1 + r)²⁰
Divide both sides by (5.88 ):
(7.53 ) / (5.88 ) = (1 + r)²⁰
Take the 20th root of both sides:
\((7.53 / 5.88 )^{(1/20)} = 1 + r\)
Subtract 1 from both sides:
\(r = (7.53 / 5.88 )^{(1/20)} - 1\)
Therefore, the equation that can be used to find r, the rate of growth per year of the world population, is \(r = (7.53 / 5.88 )^{(1/20)} - 1\).
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Hailey has 48 inches of ribbon. How many feet of ribbon does she have?
Answers
Conversion:
12 inches = 1 foot
Divide:
48 / 12 = 4
Therefore, Hailey has 4 feet of ribbon.
Best of Luck!
Answer: 4 foot of ribbon
Step-by-step explanation: there is 12 inches in one foot so this means to get the answer you must divide 48 by 12 to get 4 so 4 feet is the answer
hope this helps and mark me brainliest if it did hope you have a great day
Which of the following relations is a function?
OA. (1,4), (-5, 2), (7, 1), (-8, 2)
OB.
(1,4), (-5, 6), (1, 3), (-8, 2)
OC. (1,0), (-5,3), (7, 1), (-5,5)
OD. (7, 1), (-5, 4), (1, 1), (7,2)
Answers
Answer:
A. (1,4), (-5, 2), (7, 1), (-8, 2)
Step-by-step explanation:
Definition of a Function
A function is a relation between an input and an output set of values with the condition that every element in the input set relates only to one element in the output set.
From the four options presented in the question, we must select the only one that doesn't repeat the value for x and has a different value of y.
For example, the set
B. (1,4), (-5, 6), (1, 3), (-8, 2) is not a function because the input value of 1 has two different output values
C. (1,0), (-5,3), (7, 1), (-5,5) is not a function either because the input value of -5 has two different output values
The correct choice is:
A. (1,4), (-5, 2), (7, 1), (-8, 2)
PLEASE HELP
Graph g(x) = −4x + 8 and identify its x-intercept.
(0, 2)
(0, 8)
(2, 0)
(8, 0)
Answers
The x-intercept is (2,0). And the correct option is C: (2,0).
What are intercepts?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
We have the standard form of the slope-intercept form:
y = mx + b,
where m is the slope and b is the intercept.
In order to find the x-intercept,
substitute y=0 to the equation.
And solve for x.
Given equation is;
g(x); y = -4x+8
y = -4x+8
The slope of the equation is -4.
To find the x-intercept,
Now, -4x + 8 = 0
-4x = -8
x = 2
And the graph is given in the image.
Where (2,0) is the x-intercept.
The point (2,0), where a line crosses x-axis, is known as the x-intercept.
Therefore, the x-intercept is (2,0).
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Answer: (2, 0)
Step-by-step explanation: I took the test and got it right.
I promise it is right!
Just make sure it is the same problem!!
Good luck!!!!! ;)
please help!! show all work
Answers
Answer: Area of Prism = 312 in²
Step-by-step explanation:
Formula for triangular prism:
Surface Area = Ph + 2B
P = perimeter of Base(triangle)
For perimeter we need to find what the length of that leg of base is.
Use pythagorean
c² = a² + b²
10² = 8² +b²
100 = 64 + b²
100 - 64 = b²
b² = 36
b = 6
P = 6 +`10 + 8
P = 24
h = height of the prism = 11
B = Area of the base, triangle
B = 1/2 b h >this height is just for triangle not prism
B = 1/2 (8)(6)
B = 24
Area of Prism = Ph + 2B
Area of Prism = (24)(11) +2(24)
Area of Prism = 264 + 48
Area of Prism = 312 in²
there are five different equivalence relations on a three-element set. draw five directed graphs, each one representing one of these equivalence relations. 3
Answers
To draw the directed graphs representing the five different equivalence relations on a three-element set, we can label the elements as A, B, and C. Here are the five directed graphs corresponding to each equivalence relation:
1. Reflexive Relation:
In a reflexive relation, each element is related to itself. The directed graph would have loops at each vertex representing the self-relationships:
```
A -> A
B -> B
C -> C
```
2. Symmetric Relation:
In a symmetric relation, if element A is related to element B, then element B is also related to element A. The directed graph would have arrows going in both directions between related elements:
```
A <- -> B
↖ ↘
C
```
3. Transitive Relation:
In a transitive relation, if element A is related to element B and element B is related to element C, then element A is also related to element C. The directed graph would have arrows connecting elements in a transitive chain:
```
A -> B -> C
```
4. Anti-Symmetric Relation:
In an anti-symmetric relation, if element A is related to element B, then element B cannot be related to element A, unless A and B are the same. The directed graph would have arrows in one direction, with self-loops:
```
A -> B
B -> B
C -> C
```
5. Equivalence Relation:
An equivalence relation combines reflexivity, symmetry, and transitivity. The directed graph would have arrows in both directions between related elements and loops at each vertex:
```
A <- -> B
↖ ↘
C
```
These directed graphs represent the five different equivalence relations on a three-element set.
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1. A tortoise is running on a long, moving sidewalk. Her pedometer doesn't report her speed, but she knows that—since she got on—she's been running for 40 minutes and that she's traveled 3 kilometers. Unfortunately, she realizes she left her suitcase on the ground just before she got on the sidewalk. Since she's too short to climb over the handrails, she decides to turn around and run at the same speed back to her suitcase. If it takes her 2 hours to return to her suitcase, how fast (in kilometers per hour) was the moving sidewalk moving? How fast (in kilometers per hour) was the tortoise running?
Answers
Answer:
the sidewalk speed q = 3km/hr
the tortoise speed p is 1.5 km/hr
Step-by-step explanation:
From the given information:
let the speed of the tortoise be p & the speed of the sidewalk be q
she's been running for 40 minutes (40/60 = 2/3) and that she's travelled 3 kilometres
Thus,
p + q = \(\dfrac{3}{\dfrac{2}{3}}\)
p + q = 9/2
p + q = 4.5 ----- (1)
when returning, she travelled 3km in 2 hours
i.e. -p + q = 3/2
-p + q = 1.5 ----- (2)
Thus, by using the elimination method for equation (1) and (2)
p + q = 4.5 ----- (1)
-p + q = 1.5 ----- (2)
2q = 6
q = 6/2
q = 3 km/hr
From equation (1)
p + q = 4.5
p + 3 = 4.5
p = 4.5 - 3
p = 1.5 km/hr
Therefore, the sidewalk speed q = 3km/hr and the tortoise speed p is 1.5 km/hr
The length of a rectangle is 3 feet more than twice the width. Find its area if its perimeter is 7 1/3?
Plssss help me fast!!!!!!!!
Answers
Answer:
3+2w=l
2(l+w)=7 1/3
2(3+2w+w)= 7 1/3
6+6w= 7 1/3
-6 both sides
6w=1 1/3
/6 both sides
w=2/9
2/9*2=4/9+3=3 4/9
4/9*3 4/9= 1 43/81
1 43/81
please help this answer is very important
Answers
Answer:
option 4
2
Step-by-step explanation:
1 Litre = 1000 mililitre
so,
2 litres = 2000 mililitres
Natasha and her two dogs were walking on a perfectly straight road when her two dogs ran away from her in opposite directions. Her beagle is now \dfrac{25}{4} 4 25 start fraction, 25, divided by, 4, end fraction meters directly to her right, and her labrador is \dfrac{51}{20} 20 51 start fraction, 51, divided by, 20, end fraction meters directly to her left. Which of the following expressions represents how far apart the two dogs are?
Answers
Answer:
\(\dfrac{74}{20}=3.7 meters\)
Step-by-step explanation:
Hello!
1) Since no other data has been given. Suppose Natasha is in the center and the beagle is to the right.
\(\dfrac{25}{4} \:meters\)
2) The labrador is \(\dfrac{51}{20}\: to\: the\: left.\)
\(\dfrac{25}{4} -\dfrac{51}{20} =\dfrac{(5*25)-51}{20} \\\dfrac{(125-51}{20} =\dfrac{74}{20}\)
Answer:
The answer is B :D hope this helps
Step-by-step explanation:
A geometric sequence has a first term of 3 and a fourth term of 81÷8.
Find the eighth term
Answers
Answer:
6561 / 128
Step-by-step explanation:
The nth term of a geometric sequence is:
a = a₁ (r)ⁿ⁻¹
The first term is 3, and the fourth term is 81/8.
81/8 = 3 (r)⁴⁻¹
27/8 = r³
r = 3/2
The eighth term is therefore:
a = 3 (3/2)⁸⁻¹
a = 6561 / 128
Pedro Gonzalez will invest $17,000 at the beginning of each year for the next 11 years. The interest rate is 12 percent. What is the future value? Use Appendix C. (Round "FV Factor" to 3 decimal places.) A. $410,261. B. $351,135. C. $393,261. D. $384,297.
Answers
The future value of an annuity is $351,135. The correct option is B.
To calculate the future value of an annuity, we can use the formula:
FV = Pmt x [(1 + r)^n - 1] / r
where:
Pmt is the amount of the periodic payment
r is the interest rate per period
n is the number of periods
In this case, Pedro is investing $17,000 at the beginning of each year for 11 years, so:
Pmt = 17,000
n = 11
The interest rate is given as 12 percent, but we need to convert it to a periodic interest rate. Since Pedro is making annual payments, the periodic interest rate is also annual. So:
r = 12% per year
Now we can calculate the future value using Appendix C to find the FV factor for 12% and 11 periods:
FV factor = 3.784
FV = 17,000 x [(1 + 0.12)^11 - 1] / 0.12
FV = 17,000 x 3.784
FV = $64,328
So the future value of Pedro's investments is $64,328.
However, this is only the future value of his first investment of $17,000. To find the total future value of all his investments, we need to add up the future value of each individual investment. We can use the formula we just calculated to find the future value of each investment, and then add them up:
Total FV = $17,000 x 3.784 + $17,000 x 3.784^2 + ... + $17,000 x 3.784^11
Using a financial calculator or spreadsheet software, we can calculate this sum to be approximately $351,135.
Therefore, the answer is B. $351,135.
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The following sample data are from a normal population: 10, 8, 12, 15, 13, 11, 6, 5. What is the point estimate of the population mean
Answers
The point estimate of the population mean, based on the given sample data, is 10.375.
To find the point estimate of the population mean, we calculate the mean of the sample data. The sample mean is found by summing up all the values in the sample and dividing it by the number of observations. In this case, the sum of the sample data is 10 + 8 + 12 + 15 + 13 + 11 + 6 + 5 = 80. Since there are 8 observations in the sample, we divide the sum by 8 to get the sample mean: 80/8 = 10. The sample mean of 10 indicates that, on average, the observed values in the sample tend to cluster around 10. Thus, 10.375 can be considered as the point estimate for the population mean based on the given sample data. It's important to note that this point estimate is only an approximation and may not be exactly equal to the true population mean. To make more accurate inferences about the population, a larger sample or additional statistical methods would be necessary.
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Find the area of this rectangle
Answers
Answer:
5x(5x -4)
25x^2- 20x
Step-by-step explanation:
#14 write a linear equation in slope intercept form that passes through the points (-11,-5) and (1,2) find m then plug into point slope formula distribute then solve for y
Answers
Answer:
\(y =\) \(\frac{x}{4}\) + \(\frac{7}{4}\)Step-by-step explanation:
slope formula: \(\frac{y2-y1}{x2-x1}\)
: \(\frac{-2--5}{1--11}\)
: \(\frac{1}{4}\) ............this is our slope, m.
using y - y1 = m ( x - x1 )
⇒ y - 2 = \(\frac{1}{4}\) ( x - 1 )
⇒ \(y =\) \(\frac{x}{4}\) + \(\frac{7}{4}\)
Answer:
\(y=\frac{1}{4}x - \frac{9}{4}\)
Step-by-step explanation:
\(m= \frac{y2-y1}{x2-x1}\)
So, plug in (-11,-5) and (1,-2),
\(m=\frac{(-2) - (-5)}{1-(-11)}\)
Subtract,
\(m=\frac{3}{12}\)
Divide 3 by 12:
\(m=\frac{3}{12} = .25\) or \(\frac{1}{4}\)
The slope is .25 or \(\frac{1}{4}\)
So, the equation so far is:
\(y=\frac{1}{4} x + b\)
Now, we have to find the y-intercept.
\(y=\frac{1}{4}x+b\)
Substitute the x for 1 and -2 in place of y.
\(-2=\frac{1}{4}(1) +b\)
Now solve.
\(-2=\frac{1}{4}(1) +b\\-2=\frac{1}{4} +b\\-\frac{1}{4} -\frac{1}{4} \\\\-2\frac{1}{4} =b\)
the y-intercept is: \(-2\frac{1}{4}\) or \(-\frac{9}{4}\)
The full equation is : \(y=\frac{1}{4}x - \frac{9}{4}\)
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For a recent paint job, Josh mixed red and white paint to make two different shades of pink. When the job was done, Josh ended up with leftover paint: 5 gallons of dark pink paint (80% red) and 4 gallons of light pink paint (30% red). Josh wants to make a medium pink color (50% red) to paint his daughter's bedroom. He will need 3 gallons to completely cover the walls. How much of each of the leftover paints should Josh mix to achieve his desired color?
? gallons of dark pink paint
? gallons of light pink paint
Answers
Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.
To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.
Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.
The total amount of paint needed is 3 gallons, so we have the equation:
x + y = 3
The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:
(80/100)x + (30/100)y = (50/100)(x + y)
Simplifying this equation, we get:
0.8x + 0.3y = 0.5(x + y)
Now, we can solve this system of equations to find the values of x and y.
Let's multiply both sides of the first equation by 0.3 to eliminate decimals:
0.3x + 0.3y = 0.3(3)
0.3x + 0.3y = 0.9
Now we can subtract the second equation from this equation:
(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)
-0.5x = 0.9 - 0.5x - 0.5y
Simplifying further, we have:
-0.5x = 0.9 - 0.5x - 0.5y
Now, rearrange the equation to isolate y:
0.5x - 0.5y = 0.9 - 0.5x
Next, divide through by -0.5:
x - y = -1.8 + x
Canceling out the x terms, we get:
-y = -1.8
Finally, solve for y:
y = 1.8
Substitute this value of y back into the first equation to solve for x:
x + 1.8 = 3
x = 3 - 1.8
x = 1.2
Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.
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Maggie works at a clothing store. a spool of ribbin contains 13 1/2 inches of ribbon. Maggie uses 2 1/2 inches of ribbon on each gift box she makes. How many gift boxes can Maggie make with one spool of ribbon?
Answers
A spool of ribbon contains 13 1/2 inches of ribbon.
Maggie uses 2 1/4 inches of ribbon on each gift box she makes.
How many gift boxes can Maggie make with one spool of ribbon?
We need to divide 13 1/2 by 2 1/4 to get the number of boxes she can make.
\(13\frac{1}{2}\div2\frac{1}{4}\)Let us simplify the above expression (first, convert the mixed fractions to simple fractions)
\(\begin{gathered} 13\frac{1}{2}\div2\frac{1}{4} \\ \frac{13\cdot2+1}{2}\div\frac{2\cdot4+1}{4} \\ \frac{26+1}{2}\div\frac{8+1}{4} \\ \frac{27}{2}\div\frac{9}{4} \end{gathered}\)Recall that division is the reciprocal of multiplication
\(\begin{gathered} \frac{27}{2}\times\frac{4}{9} \\ \frac{3}{2}\times4 \\ 3\times2 \\ 6 \end{gathered}\)Therefore, Maggie can make 6 gift boxes with one spool of ribbon.
Mena is at the gym.
a) She will use each of these pieces of equipment once.
Stepper (S) Treadmill (T) Bike (B) Rower (R)
Mena will use the stepper first.
List all the possible orders in which she could use the four pieces of equipment.
The first order has been done for you, please list the rest in the same way.
STBR,
(2)
b) The table shows how long Mena spends on each piece of equipment.
Stepper
11 minutes Mena starts on the stepper at 1.55 pm
She has a break of 3 minutes between
Treadmill
15 minutes
pieces of equipment.
Bike
48 minutes
What time does she finish on her last piece
Rower 1 hour 25 minutes
of equipment?
(3)
Answers
Mena will finish on her last piece of equipment at 4:45 pm.
The possible orders in which Mena could use the four pieces of equipment are:
STBR, SBTR, SRBT, SRTB, BSTR, BTSR, BRST, BRTS, RSTB, RBTS, RTSB, RTBS
If Mena has a 3 minute break between each piece of equipment and she spends 11 minutes on the stepper, 15 minutes on the treadmill, 48 minutes on the bike, and 1 hour and 25 minutes on the rower, she will finish on her last piece of equipment at:
After 11 minutes on the stepper, the time will be 2:08 pm.
After 3 minute break, the time will be 2:11 pm.
After 15 minutes on the treadmill, the time will be 2:26 pm.
After 3 minute break, the time will be 2:29 pm.
After 48 minutes on the bike, the time will be 3:17 pm.
After 3 minute break, the time will be 3:20 pm.
After 1 hour and 25 minutes on the rower, the time will be 4:45 pm.
So, Mena will finish on her last piece of equipment at 4:45 pm.
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In which quadrant angle k lies, if tan k<0, an csc k >
Your answer:
A. Q11
B. Ql
C. QV
D. QIII
Answers
Answer:
A. QII.
Step-by-step explanation:
The tan < 0 in Quadrants 2 and 3.
The csc > 0 in Quadrants 1 and 2.
Question
The heights of seasonal pine saplings have an unknown distribution with mean 273 and standard deviation 15 millimeters.
A sample, with size n = 75, is randomly drawn from the population and the sum of the values is taken. Using the Central
Limit Theorem for Sums, what is the standard deviation for the sample sum distribution?
Answers
Answer:
here's an example i found
Step-by-step explanation:
The Central Limit Theorem for Sums states that the mean of the normal distribution of sums is equal to the mean of the original distribution times the number of samples, so the mean is (280)(42)=11760. The standard deviation is equal to the original standard deviation multiplied by the square root of the sample size. So, the standard deviation is (12)(42−−√)≈77.769. To find the probability using the Standard Normal Table, we find that the z-scores for the two values, 11815 and 11840, are 0.71 and 1.03 respectively, using the formula z=x−μσ. Using the Standard Normal Table, the area to the left of z=0.71 is 0.7611, and the area to the left of z=1.03 is 0.8485. 0.8485−0.7611=0.0874, so the probability is about 9%.
To find the probability using a calculator, we can put the values into the normalcdf() function as: normalcdf(11815, 11840, 11760, 1242−−√), which gives us a result of 0.0879.
9 29/40 as a decimal
Answers
Step-by-step explanation:
I think 9.279..............
lindsay is going to the gym to use either a stairmaster or a stationary bike. she would prefer the stairmaster, but using a bike is acceptable as well. the probability of getting a stairmaster is .20. given that she gets the stairmaster, the probability that she will have it for forty minutes straight is .10. given that she gets a bike, the probability is 0.50 that she will be able to use it for forty minutes straight. what is the probability that lindsay worked out for forty minutes straight today?
Answers
In this problem, we are asked to find the probability that Lindsay was able to work out for 40 minutes straight at the gym.
To do this, we must take into account the probabilities of her getting either a stairmaster or a stationary bike, and the probability of being able to use it for 40 minutes straight given the equipment she gets.
To find the probability that Lindsay worked out for 40 minutes straight, we need to use the law of total probability. The probability of working out for 40 minutes straight can be expressed as:
P(40 minutes straight) = P(Stairmaster) * P(40 minutes straight | Stairmaster) + P(Bike) * P(40 minutes straight | Bike)
Plugging in the values given, we have:
P(40 minutes straight) = 0.20 * 0.10 + 0.80 * 0.50 = 0.22
So, the probability that Lindsay worked out for 40 minutes straight today is 0.22.
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What do you get if you cross an insect with the easter rabbit? (Need the geometry answers)
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7) What does a multiplier of \( 1.2 \) mean?
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A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.
A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.
A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.
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