In a call center that stays open all the time, calls arrive as a poisson process with a mean rate of 0.3 complaints per hour.(a) (5 points) after receiving a call (the 1st call), what is the probability that the 51st call arrives within 150 hours?(b) (5 points) after receiving a call, what is the probability that the next call arrives after 2 hours?(c) (5 points) the number of calls received each day is recorded for 50 consecutive days. find the probability that the sum of these 50 numbers is less than 356.
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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I need help please!!!!
Answer:
297 ft squared
Step-by-step explanation:
find the area of the triangle, which is (bh)/2
(22*7)/2=77
find the area of the rectangle (bh)
22*10=220
add
77+220=297
What is the form of the Difference of Squares identity?
A. a^2 + b^2=(a - b)(a - b)
B. a^2- b^2 = (a+b)(a - b)
C. a^2 - b^2 = (a - b)(a - b)
D. a^2- b^2 = (a+b)(a + b)
The answer is B
seeing there are 3 way to put it
(a+b)(a-b)=a 2-b 2
(a+b)(a-b)=a^2-b^2
(a+b)(a-b)=a2-b2
and option B matches with the second way to put it i hope this helps
find variables x, y, and z
Answer:
Step-by-step explanation:
What is the approximate circumference of the circle?
What is the height of the parallelogram?
What would be the approximate length of the parallelogram if the base were completely straight?
What would make the estimation of the circle’s area more precise?
What is the area of the circle used to create the parallelogram-like shape to the nearest tenth of a square unit?
1. 18.8 units
2. 3 units
3. 9.4 units
Breaking the circle into more sectors
4. 28.3 square units1. The circumference of circle is 18.8 units
2. The height of parallelogram is 3 unit.
3. The approximate length of the parallelogram if the base were completely straight is 9.4 unit
4. The estimation is easier by breaking down into sector.
5. Area of Circle is 28. 26 unit²
What is Circumference?The circumference of the circle is 2πr where is the radius of the circle.
1. The circumference of circle
= 2πr
= 2 x 3.14 x 3
= 18.8 units
2. From Figure the height of parallelogram is 3 unit.
3. The approximate length of the parallelogram if the base were completely straight
= 18.8 / 2
= 9.4 unit
4. The estimation is easier by breaking down into sector.
5. Area of Circle
= πr²
= 3.14 x 9
= 28. 26 unit²
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What is the area, in square units, of the shaded part of the rectangle below?
Answer:
10 units²
Step-by-step explanation:
Area = bh/2
b = 4
h = 5
A = (4 x 5)/2 = 10 units²
I hope this helps!
find a polynomial equation of the lowest degree with rational coefficients whose one root is (cbrt 2 + 3*cbrt 4)
Answer:
poly Gon have [tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex][tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex][tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex][tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex][tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex][tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex][tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex][tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex]
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Answer:
240.73 mmStep-by-step explanation:
The hour hand is 20 mm and the minute hand is
200% of 20 mm = 2*20 mm = 40 mm longThe tip of the hour hand travels 1/12 of the circle and the tip of the minute hand travels full circle in one hour.
Find each length and their difference using circumference formula.
C = 2πrHour hand
1/12*(2*3.14*20) = 10.47 mm (rounded)Minute hand
2*3.14*40 = 251.2 mmThe difference between the two above
251.2 - 10.47 = 240.73 mmAnswer:
230.38 mm
Step-by-step explanation:
The distance traveled by the tip of the hands is (part of) the circumference of the circle with radius of the lengths of the hands.
[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]
Radii
Larger circle (minute hand):
r = 200% of 20 mm = 40 mmSmaller circle (hour hand):
r = 20 mmMinute Hand
The minute hand does a full rotation of the circle in one hour.
Therefore, the distance it travels in one hour is the complete circumference of a circle with radius 40 mm:
[tex]\begin{aligned} \implies \textsf{Distance minute hand travels} & = \sf 2 \pi (40)\\ & = \sf 80 \pi \: mm\end{aligned}[/tex]
Hour Hand
There are 12 numbers on a clock.
The hour hand travels from one number to the next in one hour.
Therefore, the distance it travels in one hour is 1/12th of the circumference of the circle:
[tex]\begin{aligned}\implies \sf \textsf{Distance hour hand travels} & =\left(\dfrac{1}{12}\right)2 \pi r\\ & = \sf \left(\dfrac{1}{12}\right)2 \pi (40)\\& = \sf \dfrac{20}{3}\pi \: mm \end{aligned}[/tex]
To find how much farther the tip of the minute hand moves than the tip of the hour hand, subtract the latter from the former:
[tex]\begin{aligned}\implies \textsf{distance} & = \textsf{minute hand distance}-\textsf{hour hand distance}\\& = \sf 80 \pi - \dfrac{20}{3} \pi \\& = \sf \dfrac{220}{3} \pi \\& = \sf 230.38\: mm \:(nearest\:hundredth) \end{aligned}[/tex]
express the following rational algebraic expression to its simple form.show your solution
5. ײ+5×-14/ײ-4
Answer
[tex] \frac{ \times -+7}{×+2} [/tex]
Which type of function best models the data in the table?
A. linear
B. exponential
C. quadratic
D. inverse variation
Answer: Your answer is indeed D. Inverse variation.
Hope this helped!
Answer:
first question:
inverse variation
second question:
for evenly spaced x-values, the ✔ difference of consecutive y-values is not constant.
Step-by-step explanation:
hope this helps!! have an amazing day <3
Which of the x values are solutions to both of the following inequalities
100< X and x<150
From both equations
100<x<150Hence the solution set in interval notation
x[tex]\in[/tex](100,150)Helppp plssssss!!!!!!
I need help please and thank you and show work
Answer:
Ivy is correct
Step-by-step explanation:
the perimeter of a parallelogram can be written as P= 2(a+b), where a and b are the lengths of the sides of the parallelogram.
since the parallelogram has been dilated by a scale factor of 0.6, we multiple the original side lengths by 0.6.
12 × 0.6 = 7.2
16 × 0.6 = 9.6
Plug into the equation
P=2(7.2+9.6)
P=2(16.8)
P= 33.6
You can also solve by plugging in the original values and multiplying the answer by 0.6.
P=2(12+16)(0.6)
P=2(28)(0.6)
P=(56)(0.6)
P=33.6
Wes wants to buy a new truck. There are 3 models to choose from, each has 4 choices of engine, 3 choices of transmission, 8 color choices, 3 interior color choices, and 5 different options packages to choose from. How many different trucks can be built with all of these choices? (Wes can only pick one option package.)
Answer:
1440 different trucks
Step-by-step explanation:
Multiply all of the choices for each part:
3 possible bodies * 4 possible engines * 3 possible transmission types * 8 possible colors * 5 possible options packages
And, you get:
3 * 4 * 3 * 8 * 5
= 1440 different trucks
Answer:
4320 trucks
Step-by-step explanation:
if 7 notebooks $3.85,what is the unit price of the notebooks
Answer:
0.55
Step-by-step explanation:
I think you would just divide the numbers
-3(2x+2)<10 thank you in advance
[tex]-3(2x+2) < 10\\\\\implies -6x -6 < 10\\\\\implies -6x < 10 +6\\\\\implies -6x < 16 \\\\\implies x > -\dfrac{16}6\\\\\implies x > -\dfrac{8}3[/tex]
A boat heading out to sea starts out at Point A, at a horizontal distance of 1465 feet
from a lighthouse/the shore. From that point, the boat's crew measures the angle of
elevation to the lighthouse's beacon-light from that point to be 13º. At some later
time, the crew measures the angle of elevation from point B to be 8°. Find the
distance from point A to point B. Round your answer to the nearest foot if
necessary.
By using what we know about right triangles, we will see that the distance is 1479.4 ft
How to find the distance between point A and point B?We assume that the distance between the points is a hypotenuse of a right triangle whit one of the angles measuring 8°, and the adjacent cathetus measuring 1465 ft.
Then we use the relation:
Cos(a) = (adjacent cath)/(hypotenuse)
cos(8°) = (1465 ft)/(distance)
distance = (1465ft)/cos(8°) = 1479.4 ft
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The length of a rectangular fam is 15 inches, and the width of the frame is 8 inches. What
is the length of a diagonal of this frame in inches?
Record your answer below. Just the number.
Answer: 17 inches
Step-by-step explanation:
The formula for finding the length of a diagonal in a rectangle is [tex]d=\sqrt{w^2+l^2}[/tex]
Where
d is the diagonal
w is the width (8 for this)
l is the length (15 for this)
Sub these values into the equation
[tex]d=\sqrt{w^2+l^2}\\d=\sqrt{(8)^2+(15)^2}[/tex]
Solve
[tex]d=\sqrt{(8)^2+(15)^2}\\d=\sqrt{64+225}\\d=\sqrt{289}\\d=17[/tex]
The quotient of 36 and a whole number increased by 3, is 20 less than four times the number.
Find the number(s).
Answer: [tex]\frac{12}{19}[/tex]
The quotient of 36 and a whole number increased by 3, is 20 less than four times the number. The solution to the algebraic equation here are 6 and -4.
An algebraic equation or polynomial equation is an equation of the form P=0 where P is a polynomial with coefficients in some field, often the field of the rational numbers.
The algebraic equation becomes =
[tex]\frac{36}{x+3}-20 = 4x\\[/tex]
We simplify the equation to find the value of x.
[tex]=\frac{36}{x+3}+20 = 4x\\\\= \frac{36}{x+3} = 4x -20\\\\= \frac{36}{x+3} = 4(x-5)\\\\=36 = 4(x-5)(x+3)\\\\=9 = (x-5)(x+3)\\\\=x^2-5x+3x -15 = 9\\\\= x^2-2x-24=0\\\\=x^2-6x+4x-24=0\\\\=x(x-6)+4(x-6) =0\\\\=(x+4)(x-6) =0\\\\x = -4,6[/tex]
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80 wpm how many words typed while typing 12 hours straight
Answer:
57600 words in 12 hours.
Step-by-step explanation:
80 wpm means 80 words per minute.
We need to know how many minutes are in a 1 hour which is 1 hour is 60 minutes.
We want to know how much words in 12 hours.
Given:
[tex]\frac{80 word}{1 min}, \frac{60 min}{1 hour},\frac{12 hour}{1}[/tex]
[tex]\frac{80 word}{1 min} *\frac{60 min}{1 hour} *\frac{12 hour}{1} =[/tex] 57600 words in 12 hours.
Answer: 57,600
Step-by-step explanation:
80 × 60 = 4800 in 1hr
4800 ×12 = 57, 600 in 12hrs
Find the area of the figure. Use 3.14 as π.
area triangle:
b×h/2
= 11 in×10 in/2
=55 in²
area half-circle:
pi×r² /2
= 3.14×5in² /2
=78.5in² /2
=39.25 in²
Total area: area triangle+ area half-circle
= 55 in²+39.25 in²
=94.25 in²
25/22 as a decimal rounded to the nearest hundreth
Answer:
1.14
Step-by-step explanation:
Long division! Image attached below!
What is the slope of the given line? (Use only whole numbers or fractions to answer)
What is the y-intercept of the given line? (Put your answer as the y-intercept point with no spaces)
Answer:
Slope m= -12/5
Step-by-step explanation:
Slope Solution
m=riserun=ΔyΔx
m=y2−y1x2−x1
m=−9−37−2
m=−125
m=−125
In decimals:
m = -2.4
Point Slope Form
y−y1=m(x−x1)
y−3=−125(x−2)
In decimals:
y−3=−2.4(x−2)
Slope Intercept Form
Find the Equation of the Line:
y=mx+b
by solving for y using the Point Slope Equation.
y−y1=m(x−x1)
y−3=−125(x−2)
y−3=−125x−(−125×2)
y−3=−125x−−245
y−3=−125x+245
y=−125x+245+3
y=−125x+395
m=−125
b=395
In decimals:
y=−2.4x+7.8
Standard Form of a Linear Equation
Ax+By=C
Starting with y = mx + b
y=−125x+395
Multiply through by the common denominator, 5, to eliminate the fractions:
5y=−12x+39
Then rearrange to the Standard Form Equation:
12x+5y=39
A=12
B=5
C=39
y-Intercept, when x = 0
y=mx+b
y=−125x+395
When x = 0
y=−125×0+395
y=395
y-intercept=395
(x,y)=(0,395)
In decimals:
(x,y)=(0,7.8)
x-Intercept, when y = 0
y=mx+b
y=−125x+395
When y = 0
0=−125x+395
125x=395
x=395×512
x=3912
x=134
x-intercept=134
(x,y)=(134,0)
In decimals:
(x,y)=(3.25,0)
65, 46, 78, 3, 87, 12, 99, 38, 71, 38
what is the median?
Answer:
46
Step-by-step explanation:
Just put in least to greatest then you would scratch each number from left to right till you got to the middle number (median)
pls mark brainless
When the 18 French class students randomly line up for a fire drill, what is the probability that Amy is first
and Zach is last in line?
The probability of Amy and Zach to line up at the frond and last in the line will be 11.11%
What is probability?The chances of happening of any random event is called as the probability. Here in the question there are 18 class students we need find that the first and the last position should be occupied by Amy and jach.
Total outcomes =18
favourable outcome=2
So the probability of the Amy and Zach to stand in the front and the last in the line will be
[tex]P=\dfrac{2}{18}=0.11=11\%[/tex]
Hence the probability of Amy and Zach to line up at the frond and last in the line will be 11.11%
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Given m|n, find the value of x.
Rt
(6x+9)
(4x-19)
11
Answer:
x = 19
Step-by-step explanation:
See attched image.
probability pls hurry(13)
Answer:
A (3/16)
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
The spinner is evenly divided and numbered from 1 through 8.
[tex]\sf \implies Probability\:of\:landing\:on\:any\:number= \dfrac18[/tex]
There are 4 even numbers (2, 4, 6 and 8)
[tex]\sf \implies Probability\:of\:landing\:on\:an\:even\:number= \dfrac48=\dfrac12[/tex]
There are 3 numbers less than 4 (1, 2 and 3)
[tex]\sf \implies Probability\:of\:landing\:on\:a\:number\:less\:than\:4=\dfrac38[/tex]
Therefore, the probability of landing of an even number and then on a number of less than 4 is:
[tex]\sf \implies Probability=\dfrac12 \times \dfrac38=\dfrac{3}{16}[/tex]
Find the area of this shape
Answer:
216
Step-by-step explanation:
Split the image into geometric shapes, and then calculate the area of each shape, then add them all up to get your grand total of 216
Hannah is solving a quadratic equation in the form ax^2+ bx + c = 0
She has got to this point in her working out.
x = 3 +/- root 29 / 2
Find the values of a, b and c for the equation Hannah is solving.
A quadratic equation is represented by the form ax^2+ bx + c = 0
The values of a, b and c are 1, -3 and -5, respectively
How to determine the values of a, b and c?The solution is given as:
[tex]x = \frac{3 \pm \sqrt{29}}2[/tex]
The solution to a quadratic equation is represented as:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
By comparing [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex] and [tex]x = \frac{3 \pm \sqrt{29}}2[/tex], we have:
-b = 3
So, b = -3
Also, we have:
2a = 2
So, a = 1
Also, we have:
b² - 4ac = 29
Substitute values for a and b
(-3)² - 4 * 1 * c = 29
This gives
9 - 4c = 29
Subtract 9 from both sides
-4c = 20
Divide by -4
c = -5
Hence, the values of a, b and c are 1, -3 and -5, respectively
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hi , can anyone help me on this question using cross multiplication.
[tex]\textbf{7).}\\\\2g^2 +5g+3\\\\=2g^2 +3g+2g+3\\\\=g(2g+3)+(2g+3)\\\\=(g+1)(2g+3)\\\\\\\textbf{10).}\\\\-6k^2+5k+21\\\\=-(6k^2 -5k-21)\\\\=-(6k^2-14k+9k-21)\\\\=-\textbf{[}2k(3k-7)+3(3k-7) \textbf{]}\\\\=-(2k+3)(3k-7)\\[/tex]
