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]
Learn more on poission formula here;
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need some help I'm stuck on this question in the image
thank you
Help with this please and thank you.
Answer:
the first
Step-by-step explanation:
the first and the second set both multiply out correctly to the original expression, but -2x² is of greater dimension than -2x.
Paulina plays both volleyball and soccer. The probability of her getting injured playing volleyball is 0.10.10, point, 1. The probability of her getting injured playing soccer is \dfrac{1}{10} 10 1 start fraction, 1, divided by, 10, end fraction. Which of these events is more likely? Choose 1 answer: Choose 1 answer:
Answer: Both of these events are more likely.
Step-by-step explanation:
Since we have given that
Probability that she is getting injured playing volleyball = 0.1
Probability that she is getting injured playing soccer is given by
Since we need to compare both the probabilities so, for this we first need to change the second probability in decimal form.
So,
since both the events have same probability.
Hence, Both of these events are more likely.Step-by-step explanation:
Mrs. Galicia is creating a bunny farm. The farm starts with 820 bunnies and is growing at a rate of 20.75% per month. How many months will it take for the farm to triple in size? *Must solve using log/In method*
By using the exponential growth equation, we will see that the population triples after 5.83 months.
How many months will take for the farm to triple in size?We know that the initial population of bunnies is 820, and it grows at a rate of 20.75% per month, then we can write the exponential growth as:
P(t) = 820*(1 + 20.75%/100%)^t
P(t) = 820*(1 + 0.2075)^t
Where t is the time in months.
Then we need to find the value of t such that the population triples, so we actually need to solve:
(1 + 0.2075)^t = 3
If we apply the natural logarithm to both sides, we get:
ln((1 + 0.2075)^t) = ln(3)
t*ln(1.2075) = ln(3)
t = ln(3)/ln(1.2075) = 5.83 months.
So, after 5.84 months, the population of bunnies will triple.
If you want to learn more about exponential functions, you can read:
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014pts)
con
(3x+10)
(2x +20)
CA
B
What does x equal?
What does < ABC equal?
What does
(2pts)
(18+)
(18+)
Show ur work 30 points
Answer:
What does x equal ? 30
What does < ABC equal? 100
What does < DBC equal? 80
Step-by-step explanation:
[tex](3x + 10) + (2x + 20) = 180 \\ 5x + 30 = 180 \\ 5x = 180 - 30 \\ 5x = 150 \\ x = \frac{150}{5} \\ \\ x = 30[/tex]
[tex]3x + 10 = 3(30) + 10 = 90 + 10 = 100[/tex]
[tex]2x + 20 = 2(30) + 20 = 60 + 20 = 80[/tex]
Consider the line y=9x-1.
Find the equation of the line that is perpendicular to this line and passes through the polnt (6, -5).
Find the equation of the line that is parallel to this line and passes through the point (6,-5).
Step-by-step explanation:
Slope=9
i)
[tex]y−y1=m(x−x1)[/tex]
When line is parallel
y+5=9(x-6)
y+5 = 9x - 54
59 = 9x-yWhen line is perpendicular
y+5=-1/9(x-6)
9(y+5)= -1(x-6)
9y + 45 = -x+6
x+9y = -39MARK ME AS BRAINLISTFactor completely 9y+27
Answer: 9(y + 3)
Step-by-step explanation: 9y/9 = y | 27/9 = 3
Please help!! If you aren't going to actually help, please don't even answer.
#1
Change of base formula is given by
[tex]\\ \rm\Rrightarrow log_ab=\dfrac{log_db}{log_da}[/tex]
#2
Two most common bases are
e10As general logarithm has base 10 and natural has base e hence these two are most used
#3
We use e as base
[tex]\\ \rm\Rrightarrow log_23[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{log_e3}{log_e2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{ln3}{ln2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1.0986122886681}{0.6931471805599}[/tex]
[tex]\\ \rm\Rrightarrow 1.6[/tex]
Can anyone help me on this
Answer:
48 ft = r
Step-by-step explanation:
Pythag theorem
r^2 + 55^2 = (25+r)^2
= 625 + 50r + r^2
r = 48
i need help with this one! asap please!
Answer:
D. 60
Step-by-step explanation:
Height = constant / width
30 = c / 2
2* 30 = 60
c = 60
12 = c / 5
12 * 5 = 60
c = 60
10 = c / 6
10 * 6 = 60
c = 60
8, 14.5, 21, 27.5, 34, 40.5 What’s the next number in the sequence
Answer:
47
Step-by-step explanation:
Determine if the sequence is arithmetic or geometric.
The difference between each term in the sequence is constant, so this is an arithmetic sequence.
To calculate the common difference, subtract one term from the next term:
14.5 - 8 = 6.5
21 - 14.5 = 6.5
27. 5 - 21 = 6.5
34 - 27.5 = 6.5
40.5 - 34 = 6.5
So the common difference is 6.5
To find the next term in the sequence, add 6.5 to the last term given:
40.5 + 6.5 = 47
There are 126 students in theater at a school. On a certain day, 94 of the students in choir went on a field trip. What percent of student stayed at school instead of going on the field trip? Round to the nearest whole percent.
Answer:
Step-by-step explanation:
First find the number of students who stayed home.
# students who stayed home = Total number - the choir members.
Total number = 126
Choir members = 94
Stay at homes = 126 - 94 = 32
Formula
Stay at home % = (32 / 126) * 100
Stay at home %= 0.25397 * 100
Stay at home % = 25.397
To the nearest whole %, the answer is 25
Answer:
126/94 = 1.34
1% of the students stayed at school
Step-by-step explanation:
Please help I will give brainliest.
Answer:
the answer is (x-1)^2=4
PLEASE HELP!! I’LL GIVE BRAINLIEST!!
For problems 16-18, classify each triangle by its angles and sides. Mark the congruent sides with tick marks and the congruent angles with arc marks.
16 Angle classification : right angle
Side classificat : isoceles
17. Angle classification : acute angle
Side classification : equilateral
18 angle classification : obtuse angle
Side classification : scalene
16)
Angle classification: right angle
Side classification : isosceles
17)
Angle classification: acute angle
Side classification: equilateral
18)
Angle classification: obtuse angle
Side classification: scalene
What is a triangle?
A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
16)
One angle = 90 degrees
So,
The other two angles' sum must be 90 degrees.
So,
Angle classification: right angle
Side classification : isosceles
17)
We see that all sides are equal.
So,
All angles must be equal and the sum is 180.
So,
Angle classification: acute angle
Side classification: equilateral
18)
One angle is greater than 90.
So,
Angle classification: obtuse angle
Side classification: scalene
Thus,
16)
Angle classification: right angle
Side classification : isosceles
17)
Angle classification: acute angle
Side classification: equilateral
18)
Angle classification: obtuse angle
Side classification: scalene
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#SPJ2
-3y (y⁴ + 2y³ - 5y²- y + 4)
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's expand the given expression ~
[tex]\qquad \sf \dashrightarrow \: - 3y( {y}^{4} + 2 {y}^{3} - 5 {y}^{2} - y + 4)[/tex]
[tex]\qquad \sf \dashrightarrow \: ( - 3y \cdot {y}^{4} ) + ( - 3y \cdot2 {y}^{3} ) + ( - 3y \cdot - 5 {y}^{2} ) + ( - 3y \cdot - y) + ( - 3y \cdot4)[/tex]
[tex]\qquad \sf \dashrightarrow \: - 3{y}^{5} - 6{y}^{4} + 1 5 {y}^{3} + 3{y}^{2} - 12y[/tex]
AABC = AADF, AB = 16,
mZB = 59° m2D = [ ? ]°.
=
Answer:
A+B=C
Step-by-step explanation:
[tex]a + b {15}^{2} [/tex]
Answer:
It's 59
Step-by-step explanation:
There congruent so they would equal the same amount.
what is the perimeter of a 12 inch by 13 inch triangle
Answer:
Perimeter = 30 in
Step-by-step explanation:
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = ab = 12 inc = 13 inSubstitute given values into the formula and solving for a:
⇒ a² + 12² = 13²
⇒ a² + 144 = 169
⇒ a² = 25
⇒ a = 5 in
Therefore, perimeter = a + b + c
= 5 in + 12 in + 13 in
= 30 in
Final Answer:
[tex]\fbox{perimeter \: of \: triangle = 30 \: in.}[/tex]
Step by Step explanation:
Data achieved from diagram:
The given triangle is a right angle triangle
Hypotenuse of triangle = 13 in.
Base of triangle = 12 in.
To find:
Perimeter of triangle = ?
Solution:
We need length of all three sides (Altitude) of triangle,
let's find out the measure of length of Altitude using Pythagoras theorem!
[tex]{Hypotenuse}^2 = {Base}^2 + {Altitude}^2 \\ {13}^{2} = {12}^{2} + {A}^{2} \\ {A}^{2} = 169 - 144 \\ {A}^{2} = 25 \\ {A} = \sqrt{25 } \\ \fbox{A = 5 \: in.}[/tex]
Now we have all three sides of triangle,
[tex]perimeter \: of \: triangle = Hyp. + Base + Alt. \\perimeter \: of \: triangle = 13 + 12 + 5 \\ \fbox{perimeter \: of \: triangle = 30 \: in.}[/tex]
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The length of a rectangle is twice its width, The perimeter of the rectangle is 36ft. what are the length and width of the rectangle?
Answer:
length is 12 feet and the width is 6 feet
Step-by-step explanation:
w=width l=length
l=2w
2l+2w=36ft
4w+2w=36ft
6w=36ft
w=6ft
l=2*6=12ft
WRITE INEQUALITY AND SOLVE Sarah has $325. She spends $10 a week on gas.
If she wants to have at least $150 left, how many
weeks can she buy gas?
17 weeks and she'll have $5 extra.
How many solutions are there to this nonlinear system
Answer:
well its two
Step-by-step explanation:
but A nonlinear system could be representative of two circles that overlap and intersect in two locations, hence two solutions. A nonlinear system could be representative of a parabola and a circle, where the vertex of the parabola meets the circle and the branches also intersect the circle, hence three solutions.
Benjamin’s garden is shaped like a rhombus the area of the garden is 336 ft. The height of the rhombus that represents his garden is 16 feet what is the base of the rhombus
Answer: 21 ft
Step-by-step explanation:
Someone Plss Help!!!! The dot plots compare the number of raffle tickets sold by students for a school fundraiser.
Answer:
That's just the way of the world
Somewhere in the world, they think they're working for themselves
They get up everyday to go to work for someone else
And somebody works for them and, so, they think they got it made
But they're all just working to get paid the very same
And so, they keep on twiddlin' them thumbs.
Someone please
help me I can’t solve this for the life of me!!!!
Answer:
I would think that It is the first one but if it is not trust the other people
Step-by-step explanation:
Padraig is a financial advisor. he earned a salary of $80,000 last year and sold stocks for $5,000. which of the following types of income did padraig have? i earned income ii passive income iii capital gains income a. i and ii b. i and iii c. ii and iii d. iii please select the best answer from the choices provided a b c d
The earned income is $80,000 and the capital income is $5,000. Then the correct option is B.
What is capital gain?A profit in the value of an asset then an investor can make a profit by selling an asset. Then selling price of an asset must be greater than the cost of an asset.
Padraig is a financial advisor.
He earned a salary of $80,000 last year and sold stocks for $5,000.
A salary of $80,000 is known as earned income because of employment bases.
$5,000 is a capital gain because this is obtained from the selling of stocks.
The income gained by the interest income, rental income, or dividend income is known as passive income.
More about the capital income link is given below.
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Distribute to create an equivalent expression with the fewest symbols possible.
6(5x -3) =6 helpppp
Answer:
x=4/5
Step-by-step explanation:
Add 18 to both sides and simplify
Please help fast i I’ll give brainliest
Answer:
The answer is B. 1/4^8
Step-by-step explanation:
Every time the power it to the negative it inverse it.
An example, 2^-2 = 1 / 2^2
So, 4^-8 = 1 / 4^8
A washer and dryer cost a total of $964 . The cost of the washer is three times the cost of the dryer. Find the cost of each item.
Answer:
A washer and dryer cost a total of $964 . The cost of the washer is three times the cost of the dryer. Find the cost of each item.
Answer: 96$
Answer:
The washer costs $723 and the dryer $241.
Step-by-step explanation:
Represent the cost of the washer by w and that of the dryer as d.
Then w = 3d.
Since w + d + $964, we get 3d + d = $964, or 4d = $964, or d = $241.
Three times that is $723.
The washer costs $723 and the dryer $241.
TO ALL AMAZING MATHMATICIANS PLS HELP ASAP, please do not put links in I won't click them and I know they're not the correct answer. Please these are urgent and I know its kind of tedious but i need help. Thank you so much to the kind smart person who ends up answering this.
Answer:
firast divide it by the nearest decimal, then convert your answer into simplest form and you will have your answer.
Step-by-step explanation:
Answer:
can you guys please teach me how to do that
this is hard i need help. Please this is due today.
Answer:
140
Step-by-step explanation: all you have to do is add all the numbers then multiply those by 4 then you will get 140
The smiths were just approved for a 25 year mortgage at an 11% fixed rate. if they had not filed bankruptcy in the past, they could have gotten a rate of 7%. if their loan amount is $128,000, how much more per month will the smiths be paying for their mortgage as a result of their bankruptcy? a. $349.86 b. $125,840.78 c. $904.68 d. $235.09 please select the best answer from the choices provided a b c d
The increase in monthly amortization has result of higher interest rate is $349.86.
We have given ,the smiths were just approved for a 25 year mortgage at an 11% fixed rate. if they had not filed bankruptcy in the past, they could have gotten a rate of 7%.
We have to calculate the mortage value when loan amount is,$128,000,
What is the amortization formula?[tex]A = P \times ((r(1+r)^n)/((1+r)^n-1))[/tex]
A = is the amortization
P = is the principal
r = is the rate
n = is the period
We have to compute for the amortization using the 11% interest rate.
[tex]A = $128000 \times ((0.11(1.11)^{25})/((1.11)^{25}-1))[/tex]
[tex]A = \$1,254.54[/tex]
When we solve manually, the answer should be divided by 12 because it was on a monthly basis.
Next we have to compute for the amortization using the 7% interest rate.
[tex]A = $128000 \times ((0.07(1.07)^25)/((1.07)^25-1))[/tex]
[tex]A = $904.68[/tex]
When solve manually, the answer should be divided by 12 because it was on a monthly basis.
Therefore, the increase in monthly amortization has result of higher interest rate is $349.86.
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