Answer:
(a) less than 1 year =0.751488
(b) more than 2 years but less than 4 years = 0.2458
(c) at least 5 years= 0.760331
Step-by-step explanation:
f(t) = 1 λ e−t/λ, [0, [infinity])
First we calculate the probability for an exponential random variable X with parameter λ
P (X= t) = ∫ 1 λ e−t/λ, dt
P (x=t) = e−t/λ,
λ = 3.5
Now P (X< 1 ) = ∫ 1 λ e−t/λ, dt [the limits are (-∞ to 1)]
= e−1/3.5= 0.751488
P ( 2<X< 4 ) = ∫ 1 λ e−t/λ, dt [ the limits are (2 to 4)]
=e−2/3.5- e−4/3.5
= e-0.57142-e-1.142857
= 0.5647-0.31890
= 0.2458
P (at least 5) = 1- P (x=5)
= 1-∫ 1 λ e−t/λ, dt [ the limits are (∞ to 5)]
= 1- e−5/3.5
= 1 - e-1.4285
= 1-0.239
= 0.760331
cot? 2x + cos2x + sin’ 2x = csc? 2x
Need help with 40
Answer:
[tex]\rule{100mm}{0.1mm}[/tex]
[tex]\cot^2(2x)+\cos^2(2x)+\sin^2(2x)=\csc^2(2x)[/tex]
[tex]\dfrac{\cos^2(2x)}{\sin^2(2x)} +[(\cos^2(2x)+\sin^2(2x)]=\csc^2(2x)[/tex]
[tex]\dfrac{\cos^2(2x)}{\sin^2(2x)} +1=\csc^2(2x)[/tex]
[tex]\dfrac{\cos^2(2x)+\sin^2(2x)}{\sin^2(2x)}=\csc^2(2x)[/tex]
[tex]\dfrac{1}{sin^2(2x)} =\csc^2(2x)[/tex]
[tex]\boxed{\csc^2(2x)=\csc^2(2x)}[/tex] ✔
[tex]\rule{100mm}{0.1mm}[/tex]
Help me out here pleaseeeeeeeeee
Solve the following for y: 9x − 3y = 18 (5 points) y = −3x − 6 y = 3x − 6 y = −3x + 6 y = 3x + 6
Answer:
Y = 3x - 6
Step-by-step explanation:
- 3y = -9x + 18
divide by -3
y = 3x - 6
-5y + 6x = 40
3y - 8x = -46
Answer:
-2y-2x=-6
Step-by-step explanation:
-5y = 3y = -2y
6x - 8x = -2y
40 - 46 = -6
Answer:
Answer:
X=5
Y=-2
Step-by-step explanation:
trust the process
given that 3 feet equal 1 yard, how many yards equals 1 feet ?
Answer:
0.333333
Step-by-step explanation:
Hope this helps and have a great day!
Right triangle FGH has midsegments of 15,36, and 39 centimeters given that area of a triangle is represented by the formula A=1/2bh determine the area of triangle FGH
A.180cm2
B.1080cm2
C.1170cm2
D.2160cm2
Answer:
Step-by-step explanation:
according to the midsegment theorem, a midsegment of a triangle is parallel to a side of a triangle and its length is 1/2 length of the side.
1/2FG= 15, SO FG=30,
1/2 GH=36 SO GH=72
AREA = 1/2(72*30)=1080 CM^2
Answer:
1/2(72*30)=1080 CM^2
Step-by-step explanation:
don't rember how i got it, just remeber having this question on my work.
determine if the 2 triangles are similar or not. if they are similar choose the correct similarity theorem below.
A
B
C
D
A line segment AB has the coordinates A (2,3) AND B ( 8,11) answer the following questions (1) What is the slope of AB? (2) What is the length of AB? (3) What are the coordinates of the mid point of AB?(4) What is the slope of a line perpendicular to AB ?
Answer:
1) The slope of the line segment AB is [tex]\frac{4}{3}[/tex].
2) The length of the line segment AB is 10.
3) The coordinates of the midpoint of the line segment AB is [tex]M(x,y) = (5,7)[/tex].
4) The slope of a line perpendicular to line segment AB is [tex]-\frac{3}{4}[/tex].
Step-by-step explanation:
1) Let [tex]A(x,y) = (2,3)[/tex] and [tex]B(x,y) = (8,11)[/tex]. From Analytical Geometry, we get that slope of AB ([tex]m_{AB}[/tex]), dimensionless, is determined by the following formula:
[tex]m_{AB} = \frac{y_{B}-y_{A}}{x_{B}-x_{A}}[/tex] (1)
If we know that [tex]x_{A} = 2[/tex], [tex]x_{B} = 8[/tex], [tex]y_{A} = 3[/tex] and [tex]y_{B} = 11[/tex], the slope of the line segment is:
[tex]m_{AB} = \frac{11-3}{8-2}[/tex]
[tex]m_{AB} = \frac{4}{3}[/tex]
The slope of the line segment AB is [tex]\frac{4}{3}[/tex].
2) The length of the line segment AB ([tex]l_{AB}[/tex]), dimensionless, can be calculated by the Pythagorean Theorem:
[tex]l_{AB} =\sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}}[/tex] (2)
If we know that [tex]x_{A} = 2[/tex], [tex]x_{B} = 8[/tex], [tex]y_{A} = 3[/tex] and [tex]y_{B} = 11[/tex], the length of the line segment AB is:
[tex]l_{AB} = \sqrt{(8-2)^{2}+(11-3)^{2}}[/tex]
[tex]l_{AB} = 10[/tex]
The length of the line segment AB is 10.
3) The coordinates of the midpoint of the line segment AB are, respectively:
[tex]x_{M} = \frac{x_{A}+x_{B}}{2}[/tex] (3)
[tex]y_{M} = \frac{y_{A}+y_{B}}{2}[/tex] (4)
If we know that [tex]x_{A} = 2[/tex], [tex]x_{B} = 8[/tex], [tex]y_{A} = 3[/tex] and [tex]y_{B} = 11[/tex], the coordinates of the midpoint of the line segment AB are, respectively:
[tex]x_{M} = \frac{2+8}{2}[/tex]
[tex]x_{M} = 5[/tex]
[tex]y_{M} = \frac{3+11}{2}[/tex]
[tex]y_{M} = 7[/tex]
The coordinates of the midpoint of the line segment AB is [tex]M(x,y) = (5,7)[/tex].
4) From Analytical Geometry we can determine the slope of a line perpendicular to line segment AB as a function of the slope of the line segment:
[tex]m_{\perp} = -\frac{1}{m_{AB}}[/tex] (5)
If we know that [tex]m_{AB} = \frac{4}{3}[/tex], then the slope of a line perpendicular to AB is:
[tex]m_{\perp} = - \frac{1}{\frac{4}{3} }[/tex]
[tex]m_{\perp} = -\frac{3}{4}[/tex]
The slope of a line perpendicular to line segment AB is [tex]-\frac{3}{4}[/tex].
A recipe for 45 biscuits uses
5
2
cups of flour. How many biscuits are made from each cup of flour?
Answer:
18
Step-by-step explanation:
Please give brainliest!
Answer:
18
Step-by-step explanation:
What is 39/20 written as decimal ?
Answer:
1.95
Step-by-step explanation:
On a map, the scale is ½ inch to 300 miles. If the trip from Corpus Christi to El Paso is 600 miles, how far apart will those cities appear on the map (in inches)?
Answer:
Step-by-step explanation:
How many miles from El Paso to Corpus Christi?
The total driving distance from El Paso, TX to Corpus Christi, TX is 699 miles or 1 125 kilometers.
Answer:
1 inch
Step-by-step explanation:
1/2 inch = 0.5 inch
0.5/300 = n/600
0.5 * 600 = n * 300
300 = 300n
1 = n or n = 1
Samantha invested $670 in an account paying an interest rate of 5.5% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $1,740?
Answer:
17 years
Step-by-step explanation:
The formula for the value of an account earning compound interest can be used to find the number of years. That formula is ...
A = P(1 +r/n)^(nt)
where P is the principal invested at annual rate r compounded n times per year for t years.
__
Solving for t, we find ...
A/P = (1 +r/n)^(nt) . . . . . . divide by P
log(A/P) = nt·log(1 +r/n) . . . . take logarithms
t = log(A/P)/(n·log(1 +r/n)) . . . . . divide by the coefficient of t
For the given values, the time required is ...
t = log(1740/670)/(365·log(1 +0.055/365)) ≈ 17.353
It would take about 17 years for the account value to reach $1740.
_____
Additional comment
The time-value-of-money (TVM) apps of your calculator or spreadsheet can be used to find the time period of interest. Here, setting P/Y = 1 gives N in years.
How do you rotate triangle A",B",C" 270 degrees around the origin. coordinates A" (-1,1), B"(1,-2) and C"(0,-4)
9514 1404 393
Answer:
rotated vertices are (1, 1), (-2, -1), (-4, 0)
Step-by-step explanation:
When the rotation direction is not specified, it is usually taken to be counterclockwise. Rotation 270° CCW is the same as rotation 90° CW. The transformation of coordinates is ...
(x, y) ⇒ (y, -x)
Then your rotated points become ...
A(-1, 1) ⇒ A'(1, 1)
B(1, -2) ⇒ B'(-2, -1)
C(0, -4) ⇒ C'(-4, 0)
_____
In the attached, the rotated triangle is shown in red. As an example, the arc through which point C is rotated is shown.
A baseball weighs 25.75 ounces less than a bat. Write an equation the represents the relationship between the weight of a baseball and a bat in terms of the weight of the box,w.
Answer:
Step-by-step explanation:
So if a baseball weighs 25.75 ounces less than the bat and it says what is the relationship between the ball and the bat so if the baseball weighs less than the bat then that would be 25.75<B=W I believe
What is the equation for the line in slope-intercept form?
Enter your answer in the box. _____
4
Step-by-step explanation:
so the slope equation is y2-y1 over x2-x1 so by that logic 11-7 =4 and 4-3= 1 therefore it would equal all to 4 over 1 and by dividing that you get 4.
PLZ HELP NOW!!!! PLEASEE
please explain steps
Answer:
122º
Step-by-step explanation:
The interior angles of a heptagon add to 900º. We can write an equation and solve:
(12x-9)º+(9x+14)º+(133)º+(10x+9)º+(10x)º+(136)º+(10x+5)º=900ºCombine like terms, 51xº+288º=900ºSubtract, 51xº=612ºDivide, xº=12ºNow that we know x, we can find the measure of ∠B:
∠B=9(12)+14=108+14=122º8. Given: AD perpendicullar DB, DB perpendicullar BC, AB = CD Prove: AB||DC
Step-by-step explanation:
Angle ADB = Angle CBD = 90° (given)
Side AB = Side DC (given)
Common side DB / BD
By HL congruence, triangles ABD and CDB are congruent.
Therefore Angle ABD = Angle CDB
=> Line AB is parallel to Line DC (Z angles)
Evaluate: 12y+9d if y = 5 and d = 7
Answer:
123
Step-by-step explanation:
Substitute values of y and d into equation.
12y+9d = 12(5) + 9(7)
Evaluate.
12(5) + 9(7) = 60 + 63
Simplify.
60 + 63 = 123
Answer:
123
Step-by-step explanation:
12y + 9d
12(5) + 9(7)
60 + 63
123
Plz help ASAP this is important
Answer:
Option 3
Step-by-step explanation:
10x11=110 +3=113
113/11
Answer:
30/11
Step-by-step explanation:
this answer is 30/11
7x+8y=-23
3x - 16y= 29
Answer:
(-1, -2)
Step-by-step explanation:
Is it A or B or C or D
The answer is A because it makes both triangles congruent
What is the value of the expression shown? 4[4.5 − 2(1.2)]
A bedroom measures 13.62 feet long and 11.5 feet wide. What is the most accurate measure of the area of the bedroom, in square feet?
Answer:
156.63 ft squared
Step-by-step explanation:
The bedroom is a rectangle.
Area of a rectangle- A=length times width
multiply the two numbers and you will get 156.63.
Be sure to add the units (feet).
Evaluate the limit, if it exists. PLEASE SHOW WORK
lim x 5 x^2-3x-10\2x-10
Answer:
-350
Step-by-step explanation:
5×2-3×-10/2×-10
=10-3×-50
=7×-50
=-350
I need your help pls help me I make u big brain\
4 or d object is moving away at an increasing speed
Need urgent help on this! my grade is falling :(
Answer:
the answer is b
Step-by-step explanation:
Seven friends went out to lunch. The meal subtotal was $91.22, including tax. The restaurant has a policy that for parties of six or more, 18% tip is automatically added in. What is the total cost of the meal, including tip?
Answer:
$ 74.80
Step-by-step explanation:
The subtotal cost of the meal was $91.22 including tax.
The 18% tip is added for six or more.
The tip added should reduce the meal subtotal by 18 %
Reduce $91.22 by 18% to get ;
82/100 * 91.22 = $ 74.80
Need help pronto! Will give brainliest!
On Monday, Byron spent $8.00 on lunch to purchase two tacos and one burrito. On Wednesday, he purchased one enchilada, one taco, and one burrito and spent $8.50. On Friday, it cost Byron $10.00 for two enchiladas and two tacos. If t represents the cost of a taco, b represents the cost of a burrito, and e represents the cost of an enchilada, which system of equations can be used to find the cost of each?
Answer:
2t+b=8.00
e+t+b=8.50
2e+2t=10.00
Step-by-step explanation: