Answer:
A. 18 calls
B. 0.9
C. 20
Step-by-step explanation:
Number of representatives=2,
Number of extension lines=2,
Average calls each representative can accommodate per hour = 15 calls,
Arrival rate per hour = 30 calls
(a) 90% of the arrival rate = 0.09 × 20 = 18 calls
To handle 18 calls immediately, 18 extension lines should be used
(b) Probability is given by number of possible outcomes ÷ number of total outcomes
Number of possible outcomes = 18, number of total outcomes = 20
Probability (call will receive busy signal) = 18/20 = 0.9
(c) For one extension line, numbers of calls to receive busy signal = 20 - 10 = 10 calls
Number of calls to receive busy signal for the current telephone system with two extension lines = 2 × 10 = 20 calls
Cenntura was having fun playing poker she needed the next two cards out to be heart so she could make a flesh five cards of the same suit there are 10 cards left on the deck and three our hearts what is the probability that two cards doubt to Seterra without replacement will both be hearts answer choices are in percentage for format rounded to the nearest whole number
Answer:
7% probability that the next 2 cards are hearts.
Step-by-step explanation:
Cards are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
10 cards, which means that [tex]N = 10[/tex]
3 are hearts, which means that [tex]k = 3[/tex]
Probability that the next 2 cards are hearts:
This is P(X = 2) when n = 2. So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,10,2,3) = \frac{C_{3,2}*C_{7,0}}{C_{10,2}} = 0.0667[/tex]
0.0667*100% = 6.67%
Rounded to the nearest whole number, 7% probability that the next 2 cards are hearts.
Last week at the business where you work, you sold 120 items. The business paid $1 per item and sold them for $3 each. What profit did the business make from selling the 120 items?
Answer:
240
Step-by-step explanation:
minus how much u sold them and how much it cost to make
3-1=2
times 2 and 120
2(120)
240
If f(x) =4x2 - 8x - 20 and g(x) = 2x + a, find the value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).
Answer:
The possible values are a = -2.5 or a = 4.5.
Step-by-step explanation:
Composite function:
The composite function of f(x) and g(x) is given by:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this case:
[tex]f(x) = 4x^2 - 8x - 20[/tex]
[tex]g(x) = 2x + a[/tex]
So
[tex](f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20[/tex]
Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).
This means that when [tex]x = 0, f(g(x)) = 25[/tex]. So
[tex]4a^2 - 8a - 20 = 25[/tex]
[tex]4a^2 - 8a - 45 = 0[/tex]
Solving a quadratic equation, by Bhaskara:
[tex]\Delta = (-8)^2 - 4(4)(-45) = 784[/tex]
[tex]x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5[/tex]
[tex]x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5[/tex]
The possible values are a = -2.5 or a = 4.5.
A table is on sale for $247, which is 76% of the regular price.
What is the regular price?
Answer:
$325
Step-by-step explanation:
Find the regular price by dividing 247 by 0.76:
247/0.76:
= 325
So, the regular price was $325
15. Mark Twain one observed that the lower Mississippi River is very crooked and that over the years, as the bends and turns straighten out, the river gets shorter and shorter. Using numerical data about the length of the lower part of the river, he noticed that in the year 1700 the river was more than 1200 miles long, yet by the year 1875 it was only 973 miles long. Twain concluded that any person “can see that 742 years from now the lower Mississippi will be only a mile and three-quarters lone.” What is wrong with his inductive reasoning?
Answer:
Step-by-step explanation:
I'm sure he was making a joke at the expense of people who rely on mathematics rather than common sense. It is funny, but then Twain was a remarkably funny author..
The problem is that the comparison is apt using some sort of proportion, but it is absurd to think that the land holding the river would also shrink a proportional amount.
The river reached a minimum (presumably) in 1875 by cutting out all the loops that were there in 1700. The Mississippi was then a straight line from it's beginning to its delta on the gulf of Mexico. It could not get any shorter. Still, Twain managed to get laughs with his whimsical humor.
Thanks for posting. This made my evening.
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 310.
(a) Find an expression for the number of bacteria after
hours.
(b) Find the number of bacteria after 3 hours.
(c) Find the rate of growth after 3 hours.
(d) When will the population reach 10,000?
Answer:
a) The expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].
b) There are 2975 bacteria after 3 hours.
c) The rate of growth after 3 hours is about 3365.3 bacteria per hour.
d) A population of 10,000 will be reached after 4.072 hours.
Step-by-step explanation:
a) The population growth of the bacteria culture is described by this ordinary differential equation:
[tex]\frac{dP}{dt} = k\cdot P[/tex] (1)
Where:
[tex]k[/tex] - Rate of proportionality, in [tex]\frac{1}{h}[/tex].
[tex]P[/tex] - Population of the bacteria culture, no unit.
[tex]t[/tex] - Time, in hours.
The solution of this differential equation is:
[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex] (2)
Where:
[tex]P_{o}[/tex] - Initial population, no unit.
[tex]P(t)[/tex] - Current population, no unit.
If we know that [tex]P_{o} = 100[/tex], [tex]t = 1\,h[/tex] and [tex]P(t) = 310[/tex], then the rate of proportionality is:
[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex]
[tex]\frac{P(t)}{P_{o}} = e^{k\cdot t}[/tex]
[tex]k\cdot t = \ln \frac{P(t)}{P_{o}}[/tex]
[tex]k = \frac{1}{t}\cdot \ln \frac{P(t)}{P_{o}}[/tex]
[tex]k = \frac{1}{1}\cdot \ln \frac{310}{100}[/tex]
[tex]k\approx 1.131\,\frac{1}{h}[/tex]
Hence, the expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].
b) If we know that [tex]t = 3\,h[/tex], then the number of bacteria is:
[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]
[tex]P(3) = 100\cdot e^{1.131\cdot (3)}[/tex]
[tex]P(3) \approx 2975.508[/tex]
There are 2975 bacteria after 3 hours.
c) The rate of growth of the population is represented by (1):
[tex]\frac{dP}{dt} = k\cdot P[/tex]
If we know that [tex]k\approx 1.131\,\frac{1}{h}[/tex] and [tex]P \approx 2975.508[/tex], then the rate of growth after 3 hours:
[tex]\frac{dP}{dt} = \left(1.131\,\frac{1}{h} \right)\cdot (2975.508)[/tex]
[tex]\frac{dP}{dt} = 3365.3\,\frac{1}{h}[/tex]
The rate of growth after 3 hours is about 3365.3 bacteria per hour.
d) If we know that [tex]P(t) = 10000[/tex], then the time associated with the size of the bacteria culture is:
[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]
[tex]10000 = 100\cdot e^{1.131\cdot t}[/tex]
[tex]100 = e^{1.131\cdot t}[/tex]
[tex]\ln 100 = 1.131\cdot t[/tex]
[tex]t = \frac{\ln 100}{1.131}[/tex]
[tex]t \approx 4.072\,h[/tex]
A population of 10,000 will be reached after 4.072 hours.
Help and explain explain !!!!!!!!!!
Answer:
[tex]x=-1\text{ or }x=11[/tex]
Step-by-step explanation:
For [tex]a=|b|[/tex], we have two cases:
[tex]\begin{cases}a=b,\\a=-b\end{cases}[/tex]
Therefore, for [tex]18=|15-3x|[/tex], we have the following cases:
[tex]\begin{cases}18=15-3x,\\18=-(15-3x)\end{cases}[/tex]
Solving, we have:
[tex]\begin{cases}18=15-3x, -3x=3, x=\boxed{-1},\\18=-(15-3x), 18=-15+3x, 33=3x, x=\boxed{11}\end{cases}[/tex].
Therefore,
[tex]\implies \boxed{x=-1\text{ or }x=11}[/tex]
Suppose that a survey was taken and it showed that 18% of online shoppers in the United States would prefer to do business only with large well-known retailers. If 2700 online shoppers were surveyed, how many are willing to do business with any size retailers?
Step-by-step explanation:
You can conclude that 82% of all shoppers will do business with any retailer of any size aslong as they are on the internet.
82% of 2700 = 0.82 * 2700 =2214
which makes the other responder correct.
Uma lâmpada de incandescência traz os seguintes dados inscritos no seu bulbo. U= 220 V e P = 100 W. Conhecendo as relações U = R. i e P = U. i , pode-se afirmar que o valor da resistência R da lâmpada durante o funcionamento é, em omhs:
Answer:
The resistance is 484 ohm.
Step-by-step explanation:
An incandescent lamp has the following data inscribed on its bulb. U= 220 V and P = 100 W. Knowing the relations U = R. i and P = U. i , it can be stated that the value of the resistance R of the lamp during operation is, in omhs:
P = 100 W
V = 220 V
Let the current is I.
P = V I
100 = 220 I
I = 0.45 A
Now,
V = I R
220 = 0.45 x R
R = 484 ohm
The resistance is 484 ohm.
what is the value of -2x²y³ when ×=2 and y=4?
Answer:
1024
Step-by-step explanation:
Given :-
x = 2 y = 4Value of -2x²y³
2x³ y³2 * (2)³ * (4)³2 * 8 * 64 1024Answer:
254
Step-by-step explanation:
^ <- this is the square sign
-2x^y^3
x=2
y=4
put x values in to x place and y value in to y place.
-2(2)^2(4)^3
Find the squares and - it with 2
-2(4)(64)
2-256=254
:. the value of -2x^2y^3 =254
That the answer.
Hope this is what you asked.
Which pair of functions are inverses of each other?
O A. f(x) = f and g(x) = 8x?
O B. f(x) = 4 + 9 and g(x) = 4x - 9
O C. Ax) = 5x – 9 and g(x) = 149
O D. f(x) = 3 - 7 and g(x) = 247
If a woman makes $32,000 a year receives a cost of living increase 2.2% what will her new salary be?
Answer:
$32 704
Step-by-step explanation:
(102.2÷100) × 32 000 = $32 704
1. Find the Perimeter AND Area of the figure
below.
2 ft
5 ft
2 ft
5 ft
Answer:
A = 16 ft^2
P = 20 ft
Step-by-step explanation:
P = perimeter
A = area
STEP 1: divide the shape into rectangles
Rectangle 1: 2ft*3ft
Rectangle 2: 2ft*5ft
STEP 2: Find the area of each rectangle
Equation for area of a rectangle = bh
Rectangle 1: b = 2, h = 3
Rectangle 2: b = 2, h = 5
(2 * 3) + (2 * 5)
6 + 10
16 ft^2
Now, we have to find the perimeter
STEP 1: Find the unknown side lengths.
To find the lengths of the sides not labeled, you have to use the lengths of the sides we already know.
The length of one parallel side is 5, and the length of another parallel side is 2. The length of the unknown side starts at the same place as the top of the side length that is 5, and ends at the top of the side length that is 2. This means that we have to subtract 2 from 5 in order to find the unknown side length.
STEP 2: Add up all the side lengths
P = 2 + 5 + 5 + 2 + 3 + 3
P = 20 ft
Don't forget to label your answers!!
I hope this made sense, it's is a little hard to explain in simple terms without being able to draw, but I hope it helped.
Which complex number does not lie on the line segment plotted on the graph?
Answer:
Notice that for 3 out of the 4 numbers, there is a relationship between the x and the y coordinate of the number; for 3+i, -2i, -2-4i we have that the real part is larger by 2 from the imaginary part. Thus, the points are on the same line in the imaginary plane; they satisfy x=y+2 or Re{z}=Im{z}+2. However, 2-4i does not satisfy this equation since 2 is not equal to -4+2. Hence, this point does not belong to the line that the other 3 points define.
Step-by-step explanation:
If $3000 is invested at 3% interest, find the value of the investment at the end of 7 years if the interest is compounded as follows. (Round your answers to the nearest cent.)
(i) annually
(ii) semiannually
(iii) monthly
(iv) weekly
(v) daily
(vi) continuously
Answer:
annualy=$3689.62
semiannually=$3695.27
monthly=$3700.06
weekly=$3700.81
daily=$3701.00
Continuously=$3701.03
Step-by-step explanation:
Given:
P=3000
r=3%
t=7 years
Formula used:
Where,
A represents Accumulated amount
P represents (or) invested amount
r represents interest rate
t represents time in years
n represents accumulated or compounded number of times per year
Solution:
(i)annually
n=1 time per year
[tex]A=3000[1+\frac{0.03}{1} ]^1^(^7^)\\ =3000(1.03)^7\\ =3689.621596\\[/tex]
On approximating the values,
A=$3689.62
(ii)semiannually
n=2 times per year
[tex]A=3000[1+\frac{0.03}{2}^{2(4)} ]\\ =3000[1+0.815]^14\\ =3695.267192[/tex]
On approximating the values,
A=$3695.27
(iii)monthly
n=12 times per year
[tex]A=3000[1+\frac{0.03}{12}^{12(7)} \\ =3000[1+0.0025]^84\\ =3700.0644[/tex]
On approximating,
A=$3700.06
(iv) weekly
n=52 times per year
[tex]A=3000[1+\frac{0.03}{52}]^3^6 \\ =3000(1.23360336)\\ =3700.81003[/tex]
On approximating,
A=$3700.81
(v) daily
n=365 time per year
[tex]A=3000[1+\frac{0.03}{365}]^{365(7)} \\ =3000[1.000082192]^{2555}\\ =3701.002234[/tex]
On approximating the values,
A=$3701.00
(vi) Continuously
[tex]A=Pe^r^t\\ =3000e^{\frac{0.03}{1}(7) }\\ =3000e^{0.21} \\ =3000(1.23367806)\\ =3701.03418\\[/tex]
On approximating the value,
A=$3701.03
I NEED HELP FAST!!!!!!
Answer:
6.
Step-by-step explanation:
.
Answer:
[tex]C)\:8[/tex]
8 units tiles must be added
--------------------------------------
~HOPE IT HELPS~
~HAVE A GREAT DAY!!~
The greatest common factor of 45a^2b^3 and 18a^4b
Answer:
9a²b
Step-by-step explanation:
Hi there!
We need to find the greatest common factor out of 45a²b³ and 18[tex]a^{4}[/tex]b
We can split apart the monomials to make it easier
45a²b³ is 45*a²b³
18[tex]a^{4}[/tex]b is 18*[tex]a^{4}[/tex]b
First, let's find the GCF out of 45 and 18 (the number coefficients)
we can find all of the multiples of the 2 numbers:
45 is made up of 9 and 5
9 is made up of 3 and 3
so 3*3*5 is 45
18 is made up of 2 and 9
9 is made up of 3 and 3
so 2*3*3 is 18
3*3 is in both 45 and 18, so 9 is the GCF out of 45 and 18
Now let's find the GCF out of a²b³ and [tex]a^{4}[/tex]b
a²b³ made up of a² and b³
so a²b³ is a*a*b*b*b
[tex]a^{4}[/tex]b is made up of [tex]a^{4}[/tex] and b
so [tex]a^{4}[/tex]b is a*a*a*a*b
a*a*b is in both a²b³ and [tex]a^{4}[/tex]b, so the GCF out of a²b³ and [tex]a^{4}[/tex]b is a²b
Now multiply 9 and a²b together, as they are only the GCF of the parts of the monomials
9*a²b=9a²b
there's the greatest common factor of the 2 monomials
Hope this helps!
Which problem has a greater (bigger) answer? Solve both, choose the one that has the bigger answer and explain (1-2 sentences) how you found your
answer.
1) (2 + 3) (5 + 5)
2)2 + 3 x 5 + 5 =
Zero is not a real number True or
False
Select the line segment.
Answer:
i think you need to attach a fine for us to do so?
Step-by-step explanation:
Answer:
I can't tell you without the problem
The ratio of the number of cherry tomatoes in a tossed salad to people served is 7:15. If Waldo wants to serve 105 people, how many cherry tomatoes will Waldo use
Help me please with this maths question thank you
Answer:
Step-by-step explanation:
A)
The opposite sides of a rectangle are equal. The width make this obvious because both of them are x.
B)
The lengths are not so obvious, but it is never the less true. The two sides are obvious and they are therefore true.
4x + 1 = 2x + 12 Subtract 1 from both sides.
- 1 -1
4x = 2x + 11 Subtract 2x from both sides
-2x -2x
2x = 11 Divide by 2
x = 11/2
x = 5.5
C)
P = L + L + w + w
P = 4(5.5) + 1 + 2(5.5) + 12 + 5.5 + 5.5
P = 22 + 1 + 11 + 12 + 11
P = 23 + 23 + 11
P = 57
HELP
Identify the domain of the function shown in the graph.
Answer:
D = [4, 10]
Step-by-step explanation:
Since the line starts when x = 4, the domain begins there. And since the line ends when x=10, the domain ends there.
All I need is number two
HELPPP PLEASEEE! I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please? I am not sure where to start either now. Thank you for your time.
You have some data points labeled by [tex]x[/tex]. They form the set {3, 5, 7}.
The mean, [tex]\bar x[/tex], is the average of these values:
[tex]\bar x = \dfrac{3+5+7}3 = \dfrac{15}3 = 5[/tex]
Then in the column labeled [tex]x-\bar x[/tex], what you're doing is computing the difference between each data point [tex]x[/tex] and the mean [tex]\bar x[/tex]:
[tex]x=3 \implies x-\bar x = 3 - 5 = -2[/tex]
[tex]x=5 \implies x-\bar x = 5-5 = 0[/tex]
[tex]x=7 \implies x-\bar x = 7 - 5 = 2[/tex]
These are sometimes called "residuals".
In the next column, you square these values:
[tex]x=3 \implies (x-\bar x)^2 = (-2)^2 = 4[/tex]
[tex]x=5 \implies (x-\bar x)^2 = 0^2 = 0[/tex]
[tex]x=7 \implies (x-\bar x)^2 = 2^2 = 4[/tex]
and the variance of the data is the sum of these so-called "squared residuals".
Answer correctly and 40 points. Thx. Will report if wrong. ASAP plz! Thx!
Answer:
-7
Step-by-step explanation:
if you multiply by 7 positive it wont work because u cant cancel 7x out and a fraction wont work because theres no fraction involved in this so ur answer is A
What is the GCF of 1683t, 4085, and 68t??
O 4
O 483t
O 8
O 8837
Answer:I’m pretty sure ( not 100% thou ) the awnser would be A) 4
were should i go shopping for fidgets
Answer:
Amazon
Step-by-step explanation:
6. Calculate the area of the octagon in the
figure below.
Answer:
[tex]41\text{ [units squared]}[/tex]
Step-by-step explanation:
The octagon is irregular, meaning not all sides have equal length. However, we can break it up into other shapes to find the area.
The octagon shown in the figure is a composite figure as it's composed of other shapes. In the octagon, let's break it up into:
4 triangles (corners)3 rectangles (one in the middle, two on top after you remove triangles)Formulas:
Area of rectangle with length [tex]l[/tex] and width [tex]w[/tex]: [tex]A=lw[/tex] Area of triangle with base [tex]b[/tex] and height [tex]h[/tex]: [tex]A=\frac{1}{2}bh[/tex]Area of triangles:
All four triangles we broke the octagon into are congruent. Each has a base of 2 and a height of 2.
Thus, the total area of one is [tex]A=\frac{1}{2}\cdot 2\cdot 2=2\text{ square units}[/tex]
The area of all four is then [tex]2\cdot 4=8[/tex] units squared.
Area of rectangles:
The two smaller rectangles are also congruent. Each has a length of 3 and a width of 2. Therefore, each of them have an area of [tex]3\cdot 2=6[/tex] units squared, and the both of them have a total area of [tex]6\cdot 2=12[/tex] units squared.
The last rectangle has a width of 7 and a height of 3 for a total area of [tex]7\cdot 3=21[/tex] units squared.
Therefore, the area of the entire octagon is [tex]8+12+21=\boxed{41\text{ [units squared]}}[/tex]
Step 1: For each circle (A-G) in the table below, use the given information to determine the missing
information. Include supporting work showing and explaining how you found the missing information.
Circle
Center
Radius
Equation
A
(x - 9)2 + (y - 12)2 = 64
B
(-1,-17)
5
С
(-9,13)
9n
D
x2 + (0 - 1)2 = 36
E
x2 + y2 – 26x = -160
F
*2 + y2 + 22x +12y = -93
G
x2 + y2 – 10x+12y = -52
Answer:
I don't really understand the question
Step-by-step explanation:
c
