Answers
Using integrals, it is found that the cumulative distribution function(cdf) at x = 2.27 is given by:
P(X ≤ 2.27) = 0.897.
How to find the cumulative distribution function of a distribution?The cumulative distribution function of a distribution given by f(x) at a value of x = x* is given by the following integral:
[tex]\int_{-\infty}^{x^{\ast}} f(x) dx[/tex]
For this problem, the distribution is given by:
[tex]f(x) = e^{-x}, x > 0[/tex]
Hence, at x = 2.27, the cdf is given by:
[tex]\int_{0}^{2.27} e^{-x} dx[/tex]
The infinity was replaced by 0 because the lower bound of the definition of the distribution is of 0. Hence:
[tex]\int_{0}^{2.27} e^{-x} dx = -e^{-x}|_{x = 0}^{x = 2.27}[/tex]
Applying the Fundamental Theorem of Calculus:
P(X ≤ 2.27) = -e^(-2.27) + e^0 = -e^(-2.27) + 1 = 0.897.
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Related Questions
Which is a rational number? 1.345 or 6√
Answers
Sqrt 6 is an irrational
Jack is building a wall.
He uses 300 bricks to build part of the wall.
This part of the wall is 5 metres long and 1.5 metres high.
The complete wall will be 8 metres long and 1.5 metres high.
How many more bricks does Jack need to complete the wall?
Answers
The amount of bricks that Jack would need to complete the wall is 180.
How many more bricks does he need?The first step is to determine the total amount of bricks he would need to build the wall. In order to determine this value, ratio analysis would be used.
Total bricks needed = (area of wall x number of blocks already used) / (area of wall already built)
Area of wall = 8 x 1.5 = 12
Area of wall already built = 5 x 1.5 = 7.5
Total bricks needed = (12 x 300) / 7.5 = 400 bricks
Number of bricks needed to complete the wall = 400 - 300 = 180 bricks
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What is the range of the function on the graph?
all the real numbers
all the real numbers greater than or equal to 0
all the real numbers greater than or equal to 2
all the real numbers greater than or equal to -3
Answers
The range of the function on the graph containing all the real numbers greater than or equal to –3 . So the correct option is (d)
What is the range of a function?The collection of all a function's outputs constitutes its range.
The elements of the co-domain that are mapped are known as the images, while the elements of the domain are known as pre-images.
The set of all images of the domain's elements in this case serves as the function's range, as does the set of all of its outputs.
We have to find the function on the graph.
From the given graph, we can see from the graph that the function's maximum y value is -3 and that the graph keeps going up.
Therefore, the range includes all real values that are greater than or equal to -3.
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K
Larry Mitchell invested part of his $19,000 advance at 3% annual simple interest and the rest at 2% annual simple interest. If his total yearly interest from both accounts was $560, find the amount invested at each rate.
Answers
Larry Mitchell invested $7600 at 3% rate of interest and $11400 at 2% rate of interest.
In the field of finance, interest is the payment of a sum over and above the principal amount owed by a lender or depositor to a borrower or deposit-taking financial institution at a set rate.
Rate of an interest in defined as the amount that a lender charges a borrower in interest as a percentage of the principal.
Larry invested part of his $19000 at 3% and the rest at 2%
Let he invested $'x' at 3% interest .
Therefore amount invested at 2%=$(19000-x)
Interest earned annually at 3% on $x = [tex]\frac{3}{100} \times x =0.03x[/tex] .
Interest earned annually at 2% on $(19000-x)=[tex]\frac{2}{100} \times(19000-x)[/tex]
=[tex]380-0.02x[/tex]
Now the combined interest for both the investment is $560 .
Therefore we can form a linear equation to solve for x:
0.03x+380-0.02x=560
or, 0.01x=180
or, x=18000
Therefore Larry invested $18000 at 3% interest.
Money invested at 2%=$(19000-18000)=$1000
Hence Larry invested $18000 at 3% rate of interest and $1000 at 2% rate of interest.
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Find the inverse function
Answers
Answer:
Step-by-step explanation:
at first we must find x according to y :
[tex]y=\frac{8-x}{8}[/tex] 8y= 8-x , x = 8-8y
now we change the place of x and y
y = 8 - 8x
add it
3+8+6+3+3+3+6
Answers
The answer to it would be 32.
Answer:
32
32 is the answer hope this helps
Steve went on holiday.
He recorded the number of photos he took each day.
Steve saves his photos on a memory card.
The memory card has 1000 megabytes of memory space.
Each photo uses 2.4 megabytes of memory space.
Steve has saved 320 photos on the memory card.
Work out how many more photos Steve can save on the memory card.
Answers
Steve can store 96 more photos on the memory card.
Total space in the memory card is = 1000 mega bytes.
Sapec required to store 1 photo = 2.4 mega bytes.
Now, we are given that:
Steve has already saved 320 photos in that memory card.
so, the space required by 320 photos will be calculated by using multiplication.
Space filled = 320 × 2.4 = 768 mega bytes.
Space left in the memory card = 1000 mega bytes - 768 mega bytes = 232 mega bytes.
Photos that can be stored in the space left = 232 / 2.4 = 96.67
which will be = 96
Therefore, Steve can store 96 more photos on the memory card.
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Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?
select all that apply
m - 4 = -7m - 8
-8 - 3m = 4 - m
-3m - 8 = 4 - m
-15m = -4m
-7m - 8 = m - 4
-8 - 7m = -4 + m
Answers
The equations that are equivalent to the given equation are m - 4 = -7m - 8, -7m - 8 = m - 4 and -8 - 7m = m - 4
How to determine the equations that are equivalent to the given equation?The equation is given as
-2m - 5m - 8 = 3 + (-7) + m
Remove the bracket
So, we have
-2m - 5m - 8 = 3 - 7 + m
Evaluate the like terms
So, we have
-7m - 8 = - 4 + m
The above expression can be written as follows
m - 4 = -7m - 8
-7m - 8 = m - 4
-8 - 7m = m - 4
Hence, the equations that are equivalent to the given equation are m - 4 = -7m - 8, -7m - 8 = m - 4 and -8 - 7m = m - 4
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(7a+10)/(3b+6)°
72
what is the values of a and b
Answers
After evaluation we get the values as a = 8 + -0.4285714286b
Given, the expression is (7a ₊ 10)/(3b ₊ 6) = 72
Simplifying
(7a ₊ 10) ₊ (3b ₊ 6) = 72
Reorder the terms:
(10 ₊ 7a) ₊ (3b ₊ 6) = 72
Remove parenthesis around (10 ₊ 7a)
10 ₊ 7a ₊ (3b ₊ 6) = 72
Reorder the terms:
10 + 7a + (6 + 3b) = 72
Remove parenthesis around (6 + 3b)
10 + 7a + 6 + 3b = 72
Reorder the terms:
10 + 6 + 7a + 3b = 72
Combine like terms: 10 + 6 = 16
16 + 7a + 3b = 72
Solving
16 + 7a + 3b = 72
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-16' to each side of the equation.
16 + 7a + -16 + 3b = 72 + -16
Reorder the terms:
16 + -16 + 7a + 3b = 72 + -16
Combine like terms: 16 + -16 = 0
0 + 7a + 3b = 72 + -16
7a + 3b = 72 + -16
Combine like terms: 72 + -16 = 56
7a + 3b = 56
Add '-3b' to each side of the equation.
7a + 3b + -3b = 56 + -3b
Combine like terms: 3b + -3b = 0
7a + 0 = 56 + -3b
7a = 56 + -3b
Divide each side by '7'.
a = 8 + -0.4285714286b
Simplifying
a = 8 + -0.4285714286b
hence we get the solution of the equation.
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3. Find the instantaneous rate of change of f(x) = e^(2x)e^(7x) at x = -1
Answers
Hence , the instantaneous rate of change of f(x) = e^(2x)e^(7x) at x = -1 will be 9e⁻⁹ .
The fast rate of modification is that the modification within the rate at a specific instant, and it's same because the modification within the by-product worth at a selected purpose. For a graph, the fast rate of modification at a selected purpose is that the same because the tangent line slope.Instantaneous rate of modification of a perform is portrayed by the slope of the road, it tells you by what quantity the perform is increasing or decreasing because the x -values modification.We have given a function f(x) = e²ˣ e⁷ˣ.
You can realize the fast rate of modification of a perform at a degree by finding the by-product of that perform and plugging within the x-value of the purpose.
On simplifying , we can write f(x) as e⁹ˣ
Differentiating f(x) with respect to x , we get
f'(x) = d/dx (e⁹ˣ)
f'(x) = e⁹ˣ × 9
Putting x = - 1 in f'(x) , we get
f'(-1) = 9e⁹⁽⁻¹⁾
= 9e⁻⁹
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6.
(x+20)
47"
Solve for x.
Answers
Answer:
So first you do 47 -20=27, So x=27
The answer 27 is X =
a statement with the word per is always a unit rate
Answers
Yes, a statement with the word 'per' is always a unit rate;
When comparing two different kinds of numbers with distinct units, a rate is a ratio that is employed. The unit rate, on the other hand, shows how many units of one quantity are equal to one unit of another. When the rate's denominator is 1, we refer to the rate as a unit rate. In actuality, the amount included in each unit or per unit is referred to as the unit rate. Let's use some instances to help us grasp this:
Unit rate is 20 miles per hour, or 40 miles in two hours.
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12/14 in lowest terms
Answers
Answer:
6/7
Find a number that goes into both numbers ie 2 which goes in 6 and 7 times respectively
12x-3x-10+2x-2 simplified please show steps
Answers
Answer:
11x - 12
Step-by-step explanation:
First, group like terms (numbers with a coefficient (x) together)
12x - 3x + 2x -10 -2
Next, use BODMAS (brackets, of, division, multiplication, addition, subtraction) to know the order to solve.
Addition is before subtraction so we do: -3x + 2x which is -x
12x - x - 10 -2
12x - x = 11x and -10 -2 ÷ -12 so final answer is:
11x -12
Hope I didn't overexplain :)
Pls help me with thisss
Answers
Answer:
A
Step-by-step explanation:
Each hash mark between "School" and "Declan's house" is one-eighth of a mile. Starting at "School" count 5 hash marks to the left to get where Harper lives.
need help with solving this triangle
Answers
Answer:90
Step-by-step explanation:
you add 30 + 60 gives you 90 degrees
PLEASE HELP QUICK WILL GIVE BRAINLIST !!!
How many times larger is 9 x 10^5 than 5 x 10^3?
1.8
18
180
1,800
Answers
Answer:
180.
Step-by-step explanation:
9/5 = 1.8 and 10^5/10^3 = 10^2
so tis 1.8 x 10^2 which is 180
pls give branliest
Answer: 180
Step-by-step explanation:
(9 x 10^5) / (5 x 10^3)=
(9 x 10^(2+3)) / (5 x 10^3)=
(9 x 10^2 x 10^3) / (5 x 10^3)=
(9 x 10^2)/5= ==> Divide each side by 10^3
900/5=180
Which expression is the simplest form of 3x³ – x² + 2 (x³ − 4x²)?
Answers
Answer: [tex]x^{2} (5x-9)[/tex]
Step-by-step explanation:
[tex]3x^3 - x^2 + 2(x^3 - 4x^2)[/tex]
[tex]= 3x^3 - x^2 +2x^3 - 8x^2[/tex]
[tex]=5x^3 -9x^2[/tex]
[tex]=x^2 (5x-9)[/tex]
please help with this
Answers
Using integrals, we have that:
a) The mean is of 1205 and the standard deviation is of 2.87.
b) P(1200 < X < 1202) = 0.2.
What is the probability distribution?The distribution is given by:
f(x) = 0.1, 1200 < x < 1210.
The integral of this function will be used to find the probabilities.
The mean of the distribution is given by:
[tex]\mu = \int_{1200}^{1210} xf(x) dx[/tex]
Hence:
[tex]\mu = \int_{1200}^{1210} 0.1x dx [/tex]
[tex]\mu = 0.05x^2|_{x = 1200}^{x = 1210}[/tex]
Hence the mean is:
0.05(1210² - 1200²) = 1205.
The variance of the distribution is given by:
[tex]\sigma^2 = \int_{1200}^{1210} (x - \mu)^2 f(x) dx[/tex]
Hence:
[tex]\sigma^2 = \int_{1200}^{1210} 0.1(x - 1205)^2 dx[/tex]
[tex]\sigma^2 = 0.033(x - 1205)^3|_{x = 1200}^{x = 1210}[/tex]
[tex]\sigma^2 = 0.033(1210 - 1205)^3 - 0.033(1200 - 1205)^3[/tex]
[tex]\sigma^2 = 8.25[/tex]
The standard deviation is the square root of the variance, hence:
[tex]\sigma = \sqrt{8.25} = 2.87[/tex]
For item b, the probability is given by:
[tex]P(1196 < X < 1202) = \int_{1200}^{1202} 0.1 dx[/tex]
P(1196 < X < 1202) = 0.1x, from x = 1200 to x = 1202.
Applying the Fundamental Theorem of Calculus:
0.1(1202) - 0.1(1200) = 0.2.
The lower bound is of 1200 because the distribution is not defined for values less than 1200.
Hence:
P(1200 < X < 1202) = 0.2.
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A textile artist is asked
to make a wall-hanging that measures at most
3.75 feet wide by 6.5 feet tall. When finished,
the wall hanging measures 3 3/8 feet wide by
6 3/4 feet tall. Does the wall hanging meet the
specifications?
Answers
He wouldn’t be able to meet the specifications as the heigh is greater than the maximum height.
In mathematics, the greater than sign is a basic mathematical notation used to represent an inequality between two values. The symbol used to denote greater inequality is “>”. It is the commonly accepted mathematical notation of two strokes of equal length that meet at an acute right angle. A typical use of the greater than sign is to compare two values, where the first is greater than the second, or one is greater than the other. The greater than sign is an approximation of a closing square bracket.Maximum width of the wall hanging can be 3.75 feet and maximum height can be 6.5 feet.
After completing the work it was found that the width measures 3 3/5 feet and height was 3 3/4 tall.
If the height and width after completing the work is less than or equal to the maximum height and width then he will be able to meet the specifications .
Width
3 3/4
= (12+3)/4
= 15/4
= 3.75
Height
6 3/4
= (24+3)/4
= 27/4
= 6.75
He wouldn’t be able to meet the specifications as the heigh is greater than the maximum height .
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Which is the following in an irrational number?
A. -8.264264264...
B. -5/9
C. 17.47
D. 4.28192489...
*
Answers
Answer:
D
Step-by-step explanation:
Irrational numbers are those which cannot be expressed by the ratio of two integers.
A is rational because it is a recurring decimal. Recurring decimals can be represented by the ratio of two integers (this one can be represented by the fraction -2752/333, which is a ratio of two integers).
B is a fraction with two integers, therefore it is rational. -5/9 is a ratio of two integers.
C can be represented by 1747/100.
D is an infinite decimal but isn't recurring like A, meaning it cannot be represented by the ratio of two integers, and is therefore it is irrational, unless you are shown further digits of the decimal which prove it to be recurring, which is not the case here.
Why is 908-394 equals 514
Answers
Answer:
908 - 394 = 514
Step-by-step explanation:
It's 514 because you took out the 394 from 908. That's why you got 514.
You subtracted the number 394 from 908.
That's why you got 514.
I hope you get it.
step-by-step prime 36
Answers
Answer:
Step-by-step explanation:
36
6*6
3*2*6
3*2*3*2
Gary's is a small publishing company that publishes math books.
the production costs include a one time cost for editing which is $1050 for the book the company is currently working on. once the book is in production, the only cost will be the variable cost, of printing which is $15 per book. the company will market the book at a price of $35.
if you were to plot a graph of the profit generated by the book, what would the slope and y intercept represent?
Answers
The slope of the graph is 20 and the y-intercept is -1050.
The slope of a linear graph is defined as the gradient of the graph .It is also defined by trigonometric properties as the tangent of the angle formed by the line with the positive y-axis.
The y-intercept is the point of intersection of the graph and the y-axis.
The general equation of a straight line in the cartesian plane is given by
y = m x + c where 'm' represents the slope and 'c' represents the y-intercept.
It is given that the one time editing cost is 1050 dollars.
Variable cost of printing each book = 15 dollars
Each book is sold at = 35 dollars
∴profit per book sold = 35 - 15 = 20 dollars
Let Gary sells x number of books . Profit from selling x books = 20 x
Let us consider the net profit of Gary after selling x books be represented by y.
∴ y = profit from x books - establishment cost
or, y = 20 x -1050
Now comparing the above equation with the general equation of a straight line( y = mx + c ) we can infer that:
slope(m) = 20
y-intercept (c) = -1050
Therefore the slope of the graph is 20 and the y-intercept is -1050.
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Find the cost of excavating a space 87 ft long, 48 ft wide, and 9 ft deep at a cost of $39/yd3.
Answers
Answer:
$54288
Step-by-step explanation:
87•48•9=37584÷27=1392•39=54288
the difference of 2 times a number x and 8 is -30
equation =
x =
Answers
Answer:
x = -11
Step-by-step explanation:
2x - 8 = -30
2x = 8 - 30
2x = -22
x = -11
check
2 * (-11) - 8 = -30
-22 - 8 = -30
-30 = -30
the answer is good
For which value of x is line n parallel to line m?
(Click document to see image.)
Answers
Answer: 70
Step-by-step explanation:
Looking at line p, we can form an equation to find the missing angle that would make the line equal to 180* (all straight lines, unless stated otherwise, should be assumed they are a 180* angle). We can use the equation below:
[tex]180 = 80 + 30 + x\\x = 180 - (80 + 30)\\x= 70[/tex]
If lines n and m are parallel, the angles should be equal when looking at an intersecting line.
Hope this helps!
Solve the formula for the variable h v=lwh
Answers
Answer:
[tex] \sf \: h = \frac{v}{lw} [/tex]
Step-by-step explanation:
Let's solve for h.
v=lwh
Step 1: Flip the equation.
hlw=v
Step 2: Divide both sides by lw.
hlw/lw = v/lw
h=v/lw
WILL MARK BRAINIEST AND GIVE POINTS PLS HELP In exercise write a compound inequality that is represented by the graph
Answers
Answer:
-2≤x<3
Step-by-step explanation:
that's the answer
You consider buying a phone from one of two cell phone carriers. The table shows the total costs (in dollars) of the phone and service for different numbers of months at Carrier A . The total cost y (in dollars) of the phone and x months of service at Carrier B is represented by the equation y=55x+300 . Which carrier has the lower initial fee? After how many months of service are the total costs the same?
Answers
Using linear functions, we have that:
Carrier B has the lower initial fee.They will have the same amount after 10 months.What is the missing information?The table for Carrier A is missing and has two points (3,500) and (6,650).
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For Carrier B, the function is:
yB(x) = 55x + 300.
For Carrier A, when in 3 months, the price increases by $150, hence the slope is:
m = 150/3 = 50.
Hence:
yA = 50x + b.
When x = 3, y = 500, hence we use it to find b as follows.
500 = 50(3) + b
b = 350.
Then:
yA = 50x + 350.
Due to the lower intercept, we have that:
Carrier B has the lower initial fee.
They will have the same amount when:
yA = yB.
Hence:
50x + 350 = 55x + 300
5x = 50
x = 10 months.
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