Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. (Round your answers to four decimal places.)
(a) Compute the probability of receiving two calls in a 5-minute interval of time.
(b) Compute the probability of receiving exactly 10 calls in 15 minutes.
(c) Suppose no calls are currently on hold. If the agent takes 5 minutes to complete the current call.
how many callers do you expect to be waiting by that time?
What is the probability that none will be waiting?
(d) If no calls are currently being processed, what is the probability that the agent can take 2 minutes for personal time without being interrupted by a call?

The equation for each table are:

y = 2x + 6

y = -3x + 1

y = 5x - 24

We have,

The equation can be written in the slope-intercept form as:

y = mx + c

Now,

We will consider the two points in the table in ordered pairs:

(x, y) = (a, b) and (c, d)

Where m = (d - b) / (c - a)

Now,

The equation for each table are:

1.

(1, 8) and (3, 12)

m = (12 - 8) / (3 - 1) = 4/2 = 2

And,

(1, 8) = (x, y)

8 = 2 x 1 + c

c = 8 - 2 = 6

So,

y = 2x + 6

2.

(2 , -5) and (4, -11)

m = (-11 + 5) / (4 - 2) = -6 / 2 = -3

(2, -5) = (x, y)

-5 = -3 x 2 + c

-5 = -6 + c

c = -5 + 6

c = 1

So,

y = -3x + 1

3.

(-2, -14) and (-4, -24)
m = (-24 + 14) / (-4 + 2) = -10 / -2 = 5

(-2 , -14) = (x, y)

-14 = 5 x -2 + c

-14 = 10 + c

c = -14 - 10

c = -24

So,

y = 5x - 24

Thus,

The equation for each table are:

y = 2x + 6

y = -3x + 1

y = 5x - 24

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In trigonometry, cos B represents the ratio of the adjacent side to the hypotenuse of a right-angled triangle where angle B is one of the acute angles.

The formula for cos B is given as:cos B = adjacent/hypotenuse Now, let's say we have a right-angled triangle ABC where angle B is the acute angle. The side opposite angle B is BC, the side adjacent to angle B is AB and the hypotenuse is AC. To find the value of cos B, we need to know the values of AB and AC. Once we have these values, we can substitute them in the formula for cos B and calculate the value.

To calculate the value of cos B in degrees, we use a calculator or a trigonometric table. If we have the value of cos B in decimal form, we can use the inverse cos function to find the value of B in degrees. For example, if cos B = 0.6, then B = cos-1 (0.6) = 53.13 degrees.To summarize, to find the value of cos B, we need to know the adjacent and hypotenuse sides of a right-angled triangle where angle B is one of the acute angles.

We can then substitute these values in the formula for cos B and calculate the value. If we have the value of cos B in decimal form, we can use a calculator or the inverse cos function to find the value of B in degrees.

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We need to find the two equations that represents the total amount of coins Carl has that makes $26.00 and the number of quarters and dimes.

Carl has 35 dimes and 90 quarters. The equations are \(0.1x+0.25y=26\) and \(x+y=125\).

Let the number of dimes be \(x\)

Let the number of quarters be \(y\)

The total number of coins is \(125\)

So, the first equation will be

\(x+y=125\)

The value of the coins is $26. So,

\(0.1x+0.25y=26\)

Let us solve the equations

\(x=125-y\)

\(0.1\times (125-y)+0.25y=26\\\Rightarrow 12.5-0.1y+0.25y=26\\\Rightarrow 0.15y=13.5\\\Rightarrow y=\dfrac{13.5}{0.15}\\\Rightarrow y=90\)

\(x+y=125\\\Rightarrow x=125-90\\\Rightarrow x=35\)

The number of dimes is 35 and the number of quarters is 90.

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To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

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●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

Let's solve your equation step-by-step.

\(2x-3x+5=18\)

Step 1: Simplify both sides of the equation.

\(2x-3x+5=18\\2x + -3x + 5 = 18\)

\(( 2x + -3x ) + ( 5) = 18\) (Combine Like Terms)

\(-x + 5 = 18\\-x + 5 = 18\)

Step 2: Subtract 5 from both sides.

\(-x + 5 - 5 = 18 - 5 \\-x = 13\)

Step 3: Divide both sides by -1.

\(\frac{-x}{-1} = \frac{13}{-1} \\x = -13\)

Answer : \(\boxed {x = -13}\)

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

Answer:

Step-by-step explanation:

\( \mathsf{2x - 3x + 5 = 18}\)

Collect like terms

\( \mathsf{ - x + 5 = 18}\)

Move constant to R.H.S and change it's sign

\( \mathsf{ - x = 18 - 5} \)

Calculate the difference

\( - x = 13\)

Change the signs on both sides of the equation

\( \mathsf{x = - 13}\)

---------------------------------------------------------------

\( \blue{ \mathsf{verification}}\)

\( \mathsf{LHS \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: RHS}\)

\( \mathsf{2x - 3x + 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 18}\)

\( \mathsf{ = 2 \times ( - 13) - 3 \times ( - 13) + 5}\)

\( \mathsf{ - 26 + 39 + 5}\)

\( \mathsf{ = 13 + 5}\)

\( = 18\)

Thus, LHS = RHS

hope I helped!

Best regards!

Answer:

168

Step-by-step explanation:

LxWxH

L=6

W=4

H=7

6x4=24

24x7=168

Answer:

63,168 square inches

Step-by-step explanation:

A=2(wl+hl+hw)

A= 2{(4*6)+(7*6)+(7*4)}

A= 188

188 square inches for each candle

188 square inches times 336 candles= 63,168 square inches in total.

Hope this helped <3 Brainliest? :)

Answer

252

Step-by-step explanation:

12*12=144

18*6= 108

108+144=252

Geometry

Cut the figure into a rectangle and a triangle.

12x12=144cm^2

18x6=108cm^2

Add the areas to find the total area.

Total Area = 252cm^2

To find the domain of an expression, we need to identify all the values of the variable that make the expression undefined.

1. The expression 1/x is undefined when x = 0 because division by zero is undefined. Therefore, the domain of 1/x is all real numbers except x = 0. In interval notation, we can write the domain as (-∞, 0) U (0, ∞).

2. The expression 1/(x+5) is undefined when x+5 = 0, which means x = -5. Therefore, the domain of 1/(x+5) is all real numbers except x = -5. In interval notation, we can write the domain as (-∞, -5) U (-5, ∞).

3. The expression (x+5)/(x+5) is undefined when x+5 = 0, which means x = -5. Therefore, the domain of (x+5)/(x+5) is all real numbers except x = -5. In interval notation, we can write the domain as (-∞, -5) U (-5, ∞).

4. The expression x*x/x is equivalent to x, except when x = 0, where division by zero is undefined. Therefore, the domain of x*x/x is all real numbers except x = 0. In interval notation, we can write the domain as (-∞, 0) U (0, ∞).

5. The expression 7/(x-2) is undefined when x-2 = 0, which means x = 2. Therefore, the domain of 7/(x-2) is all real numbers except x = 2. In interval notation, we can write the domain as (-∞, 2) U (2, ∞).

Therefore, the domain of each expression is:

1. 1/x: (-∞, 0) U (0, ∞)

2. 1/(x+5): (-∞, -5) U (-5, ∞)

3. (x+5)/(x+5): (-∞, -5) U (-5, ∞)

4. x*x/x: (-∞, 0) U (0, ∞)

5. 7/(x-2): (-∞, 2) U (2, ∞)

The required results are:

1. The domain of 1/x is R - {0}, where R represents the set of all real numbers excluding 0.

2. The domain of 1/(x + 5) is R - {-5}.

3. The domain of (x + 5)/(x + 5) is R - {-5}.

4. The domain of x*x/x is R (the set of all real numbers).

5. The domain of 7/(x - 2) is R - {2}.

Given that the expressions are:

1. 1/x

2. 1/x+5

3. x+5/x+5

4. x*x/x

5. 7/x-2

To find the domain of each expression, we need to identify any values of x that would result in division by zero or undefined expressions. Let's examine each expression step by step:

1. For the expression 1/x, the domain consists of all real numbers except x = 0. Division by zero is undefined, so x cannot be 0.

2. In the expression 1/(x + 5), the domain includes all real numbers except x = -5. Similar to the previous case, division by zero occurs if x is equal to -5.

3. For the expression (x + 5)/(x + 5), the domain includes all real numbers except x = -5. Here, we have a common factor of (x + 5) in both the numerator and denominator. As before, division by zero happens if x is -5.

4. The expression x*x/x simplifies to just x. Thus, the domain of this expression is all real numbers. There are no restrictions or values that would result in division by zero.

5. In the expression 7/(x - 2), the domain consists of all real numbers except x = 2. Division by zero occurs when x equals 2, so it is not included in the domain.

Hence, the required results are:

1. The domain of 1/x is R - {0}, where R represents the set of all real numbers excluding 0.

2. The domain of 1/(x + 5) is R - {-5}.

3. The domain of (x + 5)/(x + 5) is R - {-5}.

4. The domain of x*x/x is R (the set of all real numbers).

5. The domain of 7/(x - 2) is R - {2}.

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Answer:

Since she needs 10 cones:

10 * 116.52 sq. ft = 1,165.2 sq ft.

She will need 1,165.2 sq ft of material.

Step-by-step explanation:

Answer:

A. =

B. >

C. >

Step-by-step explanation:

0.30 and 0.3 same

8.3 and 8.09 the " 9 " is in the hundreths place while the " 3 " is in the tenths place

8.34 and 3.88 well 8 is bigger than 3 soo yea

Answer:

See attached graph

Step-by-step explanation:

The equation that has a slope of 10 and intersects (0,0) is:

y = 10x

The slope-intercept form of a straight line equation is y=mx+b, where m is the slope and b the y-intercept (the value of y when x = 0).  

In this case:

m = 10

b is 0 since the value of y when x = 0 is 0 (0,0).

See attached graph.

\(\huge\fbox{Hi\:there!}\)

We are given the slope of the line and a point that it passes through, so we can use the Point-Slope formula:

\(\rm{y-y1=m(x-x1)\)

Where

y1 is the y-coordinate of the point, m is the slope and x1 is the x-coordinate.

In this case:

y1=0

m=10

x1=0

Plug in the values:

\(\bf{y-0=10(x-0)\)

Solve:

\(\bf{y-0=10x\)

\(\bf{y=10x}\)

Now, how to graph the line?

Let's look at its equation.

First of all, it has a y-intercept of 0, which means the line touches the y-axis at (0,0)

Now, what about the slope? The slope is 10.

Thus

We move "up 10, over 1, up 10, over 1" and so on, until we have a line.

Then all we have to do is take a ruler and connect the points.

Hope it helps!

~Just a determined gal

#HaveAGreatDay

\(\bf{-MistySparkles^**^*\)

The length of arc FH is approximately 9.42 units when rounded to the nearest hundredth.

To find the length of arc FH in circle G, we need to use the formula:

Arc Length = (Central Angle / 360°) \(\times\) Circumference

First, let's calculate the central angle m/FGH in degrees:

m/FGH = 60°

Next, we need to find the circumference of the circle. We know that the radius of the circle is equal to half the length of FG:

Radius = FG/2 = 18/2 = 9 units

Circumference = 2 \(\times\) π \(\times\) Radius = 2 \(\times\) π \(\times\) 9

Now, let's substitute the values into the formula to calculate the arc length:

Arc Length = (60/360) \(\\\times\) (2 \(\times\) π \(\times\) 9)

Simplifying this expression:

Arc Length = (1/6) \(\times\) (18π) = 3π units

To round the answer to the nearest hundredth, we can substitute the value of π as approximately 3.14:

Arc Length ≈ 3 \(\times\) 3.14 ≈ 9.42 units

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The attached graph represents the line plot of the dataset

The frequency table is given as:

Amount        3   3.5    4  4.5  5

Frequency   1      2     3   3    1

To create the line plot, we represent the frequency by dots.

Take for instance:

See attachment for the line plot

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The range of the function is :

The correct option is (B) {-8, -3, 5, 7}.

We are given to find the range of the function shown in the figure.

We know that the range of a function is the set of all the elements of the co-domain which are associated to at least one of the elements of the domain.

From the given figure, we note that

Domain, D = {6, 8, 10, 12},

Co-domain , C= {-8, -3, 5, 7].

Also, the set of elements that are associated to some elements of the domain is given by

R = {-8, -3, 5, 7}.

Thus, the required range of the given function is {-8, -3, 5, 7}.

Option (B) is CORRECT.

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Answer:

The height of the pile is increasing at a rate of 16.72 feet per minute. To solve this problem, we need to use the volume formula for a right circular cone: V=pi/3 r²h. We know that the volume is 20 cubic feet per minute, the height is 14 feet and the radius of the base is 14 feet. So we can calculate the rate of change of the height by rearranging the formula to give v/(pi/3r²). So for our example, v/(pi/3*14²)=20/(pi/3*14²)=20/(3.14*196)=20/613.44=16.72 feet per minute.

Answer:

Car 1

Step-by-step explanation:

Answer: Car 1

Step-by-step explanation:

Notice that the speed of each car is the slope of the line that represents its average speed.

Since the graph of the speed of Car 1 passes through (0,0) and (4,256), we get that its slope is:

256/4 = 64

Therefore the average speed of Car 1 is 64 mi/h.

 Now, since the equation that represents the average speed of Car 2 is in slope-intercept form, we get that its slope is 55.

Therefore the average speed of Car 2 is 55 mi/h.

Answer: Car 1.

Answer:

top left

Step-by-step explanation:

Answer:

Step-by-step explanation:

x represents the numbers of months and y represents the insect

population.

We are told that:

  1) we start with 125 insects, and

 2) the rascals double each month

Lets use m for months they double from the start of 125 insects.).

We can form an equation that will predict the insect population as a function of the numbers of months, m, from the start (125 insects).

Month 0 is 125

Month 1 would be 125*(1+1) or 125*2

 We can rewrite this as 125*2^1

Month 2                 125*2^2  [It dounbes again]

Month 3                  125^3     [It dounbes yet again]

Month 4                  125^4     [And again]

Month 5                  125^5     [And so on to Infinity and Beyond]

The pattern is 125*(2)^m. where m is months since the starting month of 0.

Insect Population(m) = 125*(2)^m

See the attached graph.

Answer:

i think the first number is 20 and the second is 69

Step-by-step explanation:

Answer:

I think the answer is 53

Step-by-step explanation:

9x4=36

And ask what would give you 89 from 36

89-36=53

Answer:

1700/7

Step-by-step explanation:

The value of x in 1 1/8=2 1/4x by using inverse operation is 1 / 2.

Addition and subtraction, multiplication, and division are examples of inverse operations, which are pairs of mathematical operations where one operation reverses the effects of the other.

Given:

1 1/8=2 1/4x

Solve the above equation by using the inverse operation.

Solve the mixed fraction into improper fractions as shown below,

9 / 8 = 9 / 4 x

x = 9 / 8 × 4 / 9

x = 1 / 2

Therefore, the value of x in 1 1/8=2 1/4x by using inverse operation is 1 / 2.

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Step-by-step explanation:

Refer to pic............

Answer:

y= -4x+-3 = y=-4x-3

The rest are wrong.

Hi there! :)

We are given the slope of the line and its y-intercept.

So, we write the equation in slope-intercept form (y=mx+b)

m is the slope of the line, and b is the y-intercept.

y=mx+b

y=-4x-3

Hence, that's the equation (Option A)

Hope it helps. Use the comment section to clarify your doubts.

Answered by

~A cheerful gal who helps others and smiles

Good luck.

The statement "x ∈ {x}" is true. The statement "{x} ⊆ {x}" is true. The statement "{x} ∈ {x}" is false. The statement "{x} ∈ {{x}}" is true.

a) The statement is true because an element x can be a member of a set that contains only itself. In this case, the set {x} contains the element x.

b) The statement is true because every element in {x} is also in {x}. Since both sets are identical, {x} is a subset of itself.

c) The statement is false because a set cannot be an element of itself. In this case, {x} is a set, and it cannot be an element of the same set.

d) The statement is true because the set {{x}} contains the set {x} as its only element. Therefore, {x} is an element of the set {{x}}.

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The type of contact force that is not included in the given options is the electrostatic force. The other three options—air resistance, spring compression, and friction force—are examples of contact forces.

Contact forces arise when two objects physically interact with each other. They can be categorized into various types based on the nature of the interaction. In this case, the given options include air resistance, spring compression, and friction force, which are all examples of contact forces.

Air resistance, also known as drag, occurs when an object moves through a fluid medium, such as air or water. It opposes the motion of the object and is directly proportional to the object's velocity.

Spring compression is a contact force that occurs when an external force compresses or stretches a spring. The spring exerts an equal and opposite force in response to maintain its equilibrium position.

Friction force is another type of contact force that opposes the relative motion or tendency of motion between two surfaces in contact. It can either be static friction, which prevents initial motion, or kinetic friction, which opposes motion that is already occurring.

Unlike the other three options, which involve physical contact between objects, electrostatic force is the interaction between electrically charged particles without direct contact. It is a non-contact force that can attract or repel charged objects based on their charges.

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if f(1) = 10 and 2 ≤ f ′ (x) ≤ 5 for all x, The smallest possible value of f(4) is 16.

Using the Mean Value Theorem, we can find a lower bound for f(4) based on the given information. By the Mean Value Theorem, there exists some c between 1 and 4 such that:

f'(c) = (f(4) - f(1))/(4 - 1) = (f(4) - 10)/3

Since 2 ≤ f ′ (x) ≤ 5 for all x, we have:

2 ≤ f'(c) ≤ 5

Substituting the expression we obtained for f'(c), we get:

2 ≤ (f(4) - 10)/3 ≤ 5

Multiplying through by 3, we get:

6 ≤ f(4) - 10 ≤ 15

Adding 10 to each term, we get:

16 ≤ f(4) ≤ 25

Therefore, the smallest possible value of f(4) is 16.

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Answer:

4n - 4

Step-by-step explanation:

3n-4 = the amount of tickets Evie has

n = the amount of tickets Mark has

3n - 4 + n = 4n - 4

The total number of laps would be \("x + (x + 6)"\). We cannot determine the specific number of laps Manny swam on either day or the total number of laps without this information.

To find out how many laps Manny swam on Tuesday, we need to know the number of laps he swam on Monday.

Let's assume he swam "x" laps on Monday.

On Tuesday, Manny swam 6 laps more than what he swam on Monday.

Therefore, the number of laps he swam on Tuesday would be \("x + 6".\)

To find out how many laps Manny swam on both days combined, we simply add the number of laps he swam on Monday and Tuesday.

So the total number of laps would be\("x + (x + 6)".\)
Please note that the exact value of "x" is not provided in the question, so we cannot determine the specific number of laps Manny swam on either day or the total number of laps without this information.

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On Monday, Manny swam x laps at the pool. On Tuesday, he swam 6 laps more than what he swam on Monday. Manny swam 2x + 6 laps on both Monday and Tuesday combined.


To find out how many laps Manny swam on Tuesday, we need to add 6 to the number of laps he swam on Monday.

Therefore, the number of laps Manny swam on Tuesday can be expressed as (x + 6).

To determine how many laps Manny swam on both days combined, we add the number of laps he swam on Monday to the number of laps he swam on Tuesday.

Thus, the total number of laps Manny swam on both days combined is (x + x + 6).

To simplify this expression, we can combine the like terms:

2x + 6

Therefore, Manny swam 2x + 6 laps on both Monday and Tuesday combined.

In summary, Manny swam (x + 6) laps on Tuesday and 2x + 6 laps on both days combined.

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Answer:

8 hours

Step-by-step explanation:

are you doing the rsm principal test too?