The probability the 51st call arriaves within 150hours is 0.0431, the probability the next call arrives within the next 2 hours 0.5488, the probability the sum of these 50 numbers is less than 356 is 0.4165.
Data;
Mean rate = 0.3x = 50standard deviation = ?Poission RuleUsing poission formula,
[tex]P(x=x) = \frac{e^-^\lambda - \lambda^x}{x!}\\\lambda = 0.3 per minute[/tex]
Let's substitute the values into the formula.
For 50 calls in 150 hours
For 150 hours = x = 0.3 * 150 = 45
[tex]p(x=50) = \frac{e^-^4^5 * 45^5^0}{50!} = 0.0431[/tex]
b)
The probability the next call arrives after 2 hours.
[tex]\lambda = 0.3 * 2 = 0.6\\p(x=0) = \frac{e^-^0^.^6 * 0.6^0}{0!} = 0.5488[/tex]
c)
The number of calls recieved each day is recorded for 50 consecutive days.
for 50 days;
[tex]\lambda = 0.3 * 50 * 24 = 360[/tex]
The mean = 360
The standard deviation is given as
[tex]S.D = \sigma =\sqrt{360} = 18.974\\[/tex]
The probability the sum of these 50 number is less than 356 is
[tex]p = (x < 356) = z = \frac{356 - 360}{18.974} = -0.2108\\p(z < -0.2108) = 0.4165[/tex]
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Jack has $1,331 in an account that earns 5% interest compounded annually.
To the nearest cent, how much will he have in 3 years?
Answer:
$1540.80
Step-by-step explanation:
Answer: 1540.80
Step-by-step explanation: i got it right on my ixl
determine how many ways a president, vice president and treasurer can be chosen from a math club that has 7 members.
Answer:
210
Step-by-step explanation:
There are 7 choices for president.
Then there are 6 choices for vice-president.
Finally, there are 5 choices for treasurer.
7 × 6 × 5 = 210
PLEASE HELP. WILL GIVE BRAINLIEST !! Find the cross product <-1, -3, -8> x <7,4, -5>. Is the resulting vector perpendicular to the given vectors?
<47, -61, 71>; yes
<41, -59, 77>; no
<-59, 71, 41>; yes
<41, -61, -59>; no
Answer:
Answer:
The cross product is 47 i - 61 j + 17 k.
Step-by-step explanation:
Given that-
a = < -1, -3, -8 > , b = < 7, 4, -5 >
The cross product is
a × b =\begin{gathered}\left[\begin{array}{ccc}i&j&k\\-1&-3&-8\\7&4&-5\end{array}\right]\end{gathered}⎣⎢⎡i−17j−34k−8−5⎦⎥⎤
= i ( - 3 × -5 - 4 × -8 ) - j ( -1 × -5 - (-8) × 7 ) + k ( -1 × 4 - 7 × -3 )
= i ( 15 + 32 ) -j ×( 5 + 56 ) + k ( -4 + 21 )
= i ( 47) - j (61 ) + k (17)
= 47 i -61 j + 17 k
As we know that if two vectors A & B are perpendicular then
A . B = 0
So here only the given vector b = < 7,4, -5> is perpendicular to the resulting vector .
Step-by-step explanation:
47, -61, 71>; yes
What is the surface area? 34 in 30 in 34 in 32 in 36 in
Answer:
If I am correct to work out the surface area you need to do base times height so the calculation would be...
32(base) × 30(height)
which equals 960 square inches
Please do check with someone else the answer, as I am not that confident and new
In the figure shown, what is the measure of angle x?
Triangle ABC has measure of angle BAC equal to 40 degrees and the measure of angle ABC is equal to 70 degrees. The side BC of the triangle is extended till D. The angle ACD is labeled as x.
100 degrees
110 degrees
120 degrees
140 degrees
➾Firstly, we will find the measure of [tex]\angle[/tex]ACB.
We know that,
Sum of all interior angles of a triangle = 180°.
[tex]\rightarrow[/tex][tex]\angle[/tex]BAC + [tex]\angle[/tex]ABC + [tex]\angle[/tex]ACB = 180°
[tex]\rightarrow[/tex] 40°+70°+[tex]\angle[/tex]ACB = 180°
[tex]\rightarrow[/tex] 110°+[tex]\angle[/tex]ACB = 180°
[tex]\rightarrow[/tex] [tex]\angle[/tex]ACB = 180°-110°
[tex]\rightarrow[/tex][tex]\angle[/tex]ACB = 70°
So, the measure of [tex]\angle[/tex]ACB = 70°.
➾ Side BC of the triangle is extended till D. So, we have to find the measure of [tex]\angle[/tex] ACD.
As we know that,
Sum of any two or more angles that lie on a straight line = 180°.
So, [tex]\sf\angle{ACB}[/tex]+[tex]\sf\angle{ACD}[/tex] = 180°
[tex]\rightarrow[/tex] 70° + [tex]\sf\angle{ACD}[/tex] = 180°
[tex]\rightarrow[/tex][tex]\sf\angle{ACD}[/tex] = 180°-70°
[tex]\rightarrow[/tex][tex]\sf\angle{ACD}[/tex] = 110°.
Therefore, measure of [tex]\sf\angle{ACD}[/tex] = 110°.
____________________________
Hope it helps you:)
Find x to the nearest tenth
Answer:
[tex] {x}^{2} = {8.6}^{2} + {11.5}^{2} \\ {x}^{2} = 73.96 + 132.25 \\ x = \sqrt{206.21} \\ x = 14.185 \\ x = 14.19[/tex]
14.19
3 A packet contains 1.5 kg of oats.
oats
OO
1.5kg
Every day Maria uses 50 g of oats to make porridge.
How many days does the packet of oats last?
Answer:
30 days
Step-by-step explanation:
1.5 Kg = 1500 g
Using 50 g a day
Number of days
= 1500 / 50
= 30 days.
Simplify this exponential expression:
(-49) 2/5
Answer:
I think it is 12 4/5
Step-by-step explanation:
hope this helps if not let me now
[30 PTS!!] Using mathematically precise language, explain in detail how you would multiply the complex number [tex]z_1=r_1(cos[/tex]θ[tex]_1+i sin[/tex]θ[tex]_1)[/tex] with the complex number [tex]z_2=r_2(cos[/tex]θ[tex]_2+isin[/tex]θ[tex]_2)[/tex].
Multiplying z₁ and z₂ involves calculating their products
The product of z₁ and z₂ is r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))
How to multiply the complex numbers?The numbers are given as:
z₁ = r₁(cosΘ₁ + isinΘ₁)
z₂ = r₂(cosΘ₂ + isinΘ₂)
The product is represented as:
z₁ * z₂ = r₁(cosΘ₁ + isinΘ₁) * r₂(cosΘ₂ + isinΘ₂)
This gives
z₁ * z₂ = r₁r₂(cosΘ₁ + isinΘ₁) (cosΘ₂ + isinΘ₂)
Expand
z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂ + i²sinΘ₁sinΘ₂ )
In complex numbers,
i² = -1.
So, we have:
z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂ - sinΘ₁sinΘ₂ )
Rewrite as:
z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂ - sinΘ₁sinΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂ )
Apply sine and cosine ratios
z₁ * z₂ = r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))
Hence, the product of z₁ and z₂ is r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))
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is (1,9) included in the graph p=3m+6
B
An athlete ran uphill at 3 metres per second for x seconds , downhill
at 6 metres per second for y seconds and covered a total distance
of 375 metres . If the athlete took 5 seconds longer to run uphill than
downhill, calculate the values of xandy.
(5)
Step-by-step explanation:
- The distance traveled to get to the top of the hill will be equal to the distance traveled to get to the bottom of the hill. Distance down the hill = Distance up the hill = 187.5 meters.
- Only the speed of going up the hill and down the hill will be different.
Please help with this problem.
Answer:
whats the problem it doesnt say anything
-2x+4y=28
-3x +2y = 6
Solve for x
Answer:
x=4, y=9
Step-by-step explanation:
Solve with substitution.
what expression is equivalent to 1/4 (x+24)
Use the Distributive Property, which states the following:-
[tex]\sf{a(b+c)=ab+ac}[/tex]
Where
we distribute a by multiplying it times b and c
a, b, and c can be either constants (numbers) or variables (letters)
Distribute:-
[tex]\sf{\displaystyle\frac{1}{4}(x+24)}}[/tex]
Multiply the term before the parentheses by the terms inside the parentheses:-
[tex]\sf{\displaystyle\frac{1}{4} x+6}}[/tex]
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
help :(
“two less than a number is less than or equal to thirty three”
- The inequality translated in numerical form
- The solution in set notation
- The solution in interval notation
Answer:
- The inequality translated in numerical form
Step-by-step explanation:
Complete the reasons for the proof.
given:
m 3 = m 4
Prove 1 and 2 are supplementary
Answer:
m3 and m4 are supplementary
Step-by-step explanation:
since m3 and m4 are supplementary, we can state that m3 and m4 are supplementary
see full explanation in the vid below
Mia opens a new savings account with $675 from her birthday last week.
* The bank pays 8% annual simple interest
* She makes no other deposits or withdrawals
What would be her total interest in her account, at the end of 4 years?
Answer:
$891
Step-by-step explanation:
This is Your Answer: $891, Steps below
4/15, 5/27, 7/18 Arrange the fractions in ascending order
Answer:
Take lcm and see
Step-by-step explanation:
5/27 ;4/15 ;7/18
jason is wrapping a gift.The box he is using is a rectangular prism with a length of 20 inches a width 12 inches and a height of 5 inches.Find how many square inches of paper does he need to wrap the intire box?
Answer:
Step-by-step explanation:
Surface area of rectangular prism:
length = l = 20 in
width = w = 12 in
height = h = 5 in
[tex]\boxed{\text{surface area of rectangular prism = 2*[lw + wh + hl]}}[/tex]
= 2* [ 20*12 + 12*5 + 5*20]
= 2* [240 + 60 + 100]
= 2 * 400
= 800 in²
If u = ❬6, –9❭ and v = ❬–24, 36❭ with an angle θ between the vectors, are u and v parallel or orthogonal? Explain.
The vectors are parallel because cos θ = −1.
The vectors are parallel because u • v = 0.
The vectors are orthogonal because u • v = 0.
The vectors are orthogonal because cos θ = −1.
The vectors u = ❬6, –9❭ and v = ❬–24, 36❭ are parallel to each other because the cosine of the angle θ is equal to -1. (Right choice: A)
How to determine the relationship between two vectors
By linear algebra we can use the definition of dot product to determine the relationship between two vectors, whose cases are described below:
Two vectors are orthogonal if and only if cos θ = 0.Two vectors are parallel if and only if cos θ = 1 or cos θ = -1.And the expression for the cosine of the angle between the two vectors is:
[tex]\cos \theta = \frac{\vec u \,\bullet\,\vec v}{\|\vec u\|\cdot \|\vec v\|}[/tex] (1)
Where [tex]\|\vec u\|[/tex] and [tex]\|\vec v\|[/tex] are the norms of the two vectors, which are determined by Pythagorean theorem.
Now we proceed to calculate the angle between the two vectors:
[tex]\cos \theta = \frac{(6)\cdot (-24)+(-9)\cdot (36)}{(3\sqrt{13})\cdot (12\sqrt{13})}[/tex]
cos θ = -1
Thus, the vectors u = ❬6, –9❭ and v = ❬–24, 36❭ are parallel to each other because the cosine of the angle θ is equal to -1. (Right choice: A)
To learn more on vectors, we kindly invite to check this verified question: https://brainly.com/question/13322477
Help me with this assignment please I don’t understand it
rearrange q=w/3-7 to make w the subject
q=w/ 3-7
q(3-7)= w
hope this helps :)
Answer:
w = 3q + 21
Step-by-step explanation:
assuming you mean
q = [tex]\frac{w}{3}[/tex] - 7 ( add 7 to both sides )
q + 7 = [tex]\frac{w}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
3(q + 7) = w , that is
w = 3q + 21
i need help 9th grade math
Answer:
g(x) = 4x + 5
Step-by-step explanation:
f(x) + g(x) = 10x + 7 , then
6x + 2 + g(x) = 10x + 7 ← subtract 6x + 2 from both sides
g(x) = 10x + 7 - 6x - 2 ← collect like terms
g(x) = 4x + 5
Let's find
(f+g)(x)=f(x)+g(x)10x+7=6x+2+g(x)g(x)=10x-6x+7-2g(x)=4x+5Option D
An airplane flies with a constant speed
of 640 km/h. How long will it take to
travel a distance of 640 kilometers?
The time it would take to travel a distance of 640 kilometers is 1 hour
Speed, distance and timeFrom the question, we are to determine how long it would take the airplane to travel a distance of 640 kilometers.
From the give information,
The airplane flies with a constant speed of 640 km/h.
Speed = 640 km/h
Distance to be covered = 640 km
From the formula,
[tex]Speed = \frac{Distance}{Time}[/tex]
We can write that
[tex]Time= \frac{Distance}{Speed}[/tex]
∴ [tex]Time = \frac{640 \ km}{640 \ km/h}[/tex]
Time = 1 hour
Hence, the time it would take to travel a distance of 640 kilometers is 1 hour
Lear more on Speed, distance and time here: https://brainly.com/question/17146782
can someone help me.
Step-by-step explanation:
side of square = 10
area of square = side² = 10² = 100 cm²
P.S : ARE YOU SURE THE OPTIONS ARE CORRECT ???
help , i need to finish this today :)
Use the equation of the curve of best fit to predict what the daily rental price for a two-bedroom condo will be in June and in January.
Type the correct answer in each box.
The daily rental price will be $ _____in June and $ _____ in January.
Hii!
let me answer this for you before i head out!
So, how many days are in 1 week? 7.
To rent daily, we need to find out the price for 1 single month.
1 month is $154
7 times what is 154?
7x22 is 154
Therefore, to rent a room everyday, it would cost 22$ for the first month.
437 divided by 2 is 218
218 divided by 7 is 31
Hope it helps
Sorry if its wrong!
Work out the size of angle x.
Answer:
47
Step-by-step explanation:
because you know that a triangle is 180 degrees and you have the other two degrees, so all you have to do is add 90 (the little box in the corner means 90) +43=133 and subtract by 180 giving you 47 as your answer.
Answer:
Heya! ^^
let's first look at some terms that may help us understand the concept of the question better.
______________________________________
★ Angle sum property of triangle states that the sum of all the angles of a triangle equals 180°
______________________________________
now let's come over what the question says.
we've been given a right angled triangle with measure of one of its angle as 43°.
we've to calculate the measure of the third angle named " x "
therefore ,
[tex]by \: angle \: sum \: property \: of \: triangle \\ \\ 90\degree + 43\degree + x = 180\degree \\ \\ 133\degree + x = 180\degree \\ \\ x = 180\degree - 133\degree \\ \\ x = 47\degree[/tex]
thus the measure of x is 47°.
hope helpful :D
The radius of a circle is 16 cm. Find its area in terms of pi
Which of the following lines is perpendicular to the line with this equation ?
y =4/5X – 12
a. y= -4/5x +9
b. y=5/4x +4
c. y= -5/4x -15
d.y= 4/5x -5
Answer:
soln,
a
y=5/4×-15
Answer:
C: y = -5/4x - 15
Step-by-step explanation:
A perpendicular line is always the negative reciprocal of the slope. In this case, the slope is 4/5. Therefore, the negative reciprocal is -5/4. Only look at the numbers connected to X for the slope, do not look at the constant.
1. Find the surface area of the square pyramid. 13 m 14 m
Answer: [tex]560m^2[/tex]
Step-by-step explanation:
First begin by finding the surface area of the base, which is simply length * width. In this case,
[tex]14*14 = 196 m^2[/tex]
Next, find the surface area of one of the sides of the pyramid. This formula for this is:
[tex]\frac{1}{2}*base*height[/tex]
Since we know the height to be 13 meters and the base to be 14 meters, we can solve for one side.
[tex]\frac{1}{2}*14*13 = 91 m^2[/tex]
We multiply this by 4 to give us all 4 sides of the pyramid:
[tex]91m^2 * 4 = 364m^2[/tex]
Adding together the surface area of the sides and the base gives us:
[tex]196m^2 + 364m^2=560m^2[/tex]
