In a hardware store you must first go to server 1 to get your goods and then go to a server 2 to pay for them. Suppose that the times for the two activities are exponentially distributed with means six and three minutes. Compute the average amount of time it takes Bob to get his goods and pay if when he comes in there is one customer named Al with server 1 and no one at server 2.

Answer: 2 complete games

Step-by-step explanation:

add shoes and game charge

$10.00 + 2.75 = 12.75 <— that’s 1 complete game

subtract it from $30.00

$30.00 - 12.75 = 17.25.

A complete game costs 12.75. so, Kim had enough money for one more game.

17.25 - 12.75 = $4.50 remaining after 2 complete games

Answer: 7 games

Step-by-step explanation: if it charges 10 for shoes, then you already subtract 10 from 30. 30-10=20. then, to find out how many games she can play, divide 2.75 from 20. 20/2.75=7.272727.... Since you can't pay for half of a game, it would be 7 games.

There are 21 days for there to be 150 frogs in the pond.

There are 37 days for there to be 1400 frogs in the pond.

What is exponential growth?

Quantity increases over time through a process called exponential growth. When a quantity's instantaneous rate of change with respect to time is proportional to the quantity itself, it happens.

Given:

There are currently 25 frogs in a (large) pond. The frog population grows exponentially, tripling every 10 days.

The exponential equation for the given problem is,

[tex]A(t) = Ar^t^/^1^0[/tex]

To find the number of days for there to be 150 frogs in the pond.

Here,

A(t) = 250, A = 25, r = 3

⇒

[tex]250 = 25(3)^t^/^1^0\\10 = 3^t^/^1^0\\t = 20.97[/tex]

t ≈ 21

Hence, there are 21 days for there to be 150 frogs in the pond.

Now to find how long for there to be 1400 frogs in the pond, we solve:

[tex]1400 = 25(3)^t^/^1^0\\56 = (3)^t^/^1^0\\t = 36.64[/tex]

t ≈ 37

Hence, there are 37 days for there to be 1400 frogs in the pond.

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Inverse of the equation y = [tex]2x^2-8[/tex] is [tex]y = \pm \sqrt{\frac{x+8}{2} }[/tex]

What do you mean by inverse function?

Let f and g be two functions. If

f(g(x)) = x and g(f(x)) = x,

g is the reciprocal of f, and f is the reciprocal of g.

Some functions don't have inverses Let f be a function.

If the horizontal line crosses the graph of f more than once, then f has no inverse.

If no horizontal line crosses the graph of f more than once, then f is the inverse.

Given equation:

y = [tex]2x^2-8[/tex]

To find the inverse of the function find the value of the x in terms of y

[tex]2x^2-8=y[/tex]

[tex]2x^2=y+8[/tex]

[tex]x^{2} =\frac{y+8}{2}[/tex]

x = [tex]\pm \sqrt{\frac{y+8}{2} }[/tex]

Therefore, inverse of the equation y = [tex]2x^2-8[/tex] is [tex]y = \pm \sqrt{\frac{x+8}{2} }[/tex]

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The number of square feet each lot measure is 54, 450 square feet.

Five acres of land were divided into 4 lots of equal size. The number of square feet each lot measure can be calculated as follows:

1 acre = 43,560 square ft

5 acres = ?

cross multiply

number of acres = 5 × 43,560

number of acres = 217800 square feet.

Therefore, the lots is divide into 4 equal lots.

Hence,

measure of each lot =  217800 / 4

measure of each lot = 54, 450 square feet.

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The function f(x) = 3[tex]x^{4}[/tex] - 5[tex]x^{3}[/tex] + 3 [tex]\sqrt{x^{2} +4}[/tex] is continuous at x = 2.

Given that,

We need to follow the following steps:

The function is:

f(x) = 3x^4 − 5x + ^3√(x^2 + 4)

The function is continuous at point x=2 if:

The function f(x) exists at x=2.

The limit on both sides of 2 exists.

The value of the function at x=2 is the same as the value of the limit of the function at x = 2.

Therefore:

The value of the function at x = 2 is:

f(x) = 3[tex]x^{4}[/tex] - 5[tex]x^{3}[/tex] + 3 [tex]\sqrt{x^{2} +4}[/tex]

f(2) = 3[tex](2^{4} )[/tex] - 5[tex](2^{3} )[/tex] + 3[tex]\sqrt{2^{2} +4}[/tex]

f(2) = 3*16 - 5*8 + 3 [tex]\sqrt{8}[/tex]

f(2) = 48 - 40 + 3*2.82

f(2) = 8 + 8.46

f(2) = 16.46

The limit of the f(x) is the same at both sides of x=2, that is, the evaluation of the limit for values coming below x = 2, or 1,0.5  is the same that the limit for values coming above x = 2, or 3 , 4 , 5 etc.

For this case:

[tex]lim_{x -2} f(x)[/tex] = 3[tex]x^{4}[/tex] - 5[tex]x^{3}[/tex] + 3 [tex]\sqrt{x^{2} +4}[/tex]

[tex]lim_{x -2} f(x)[/tex] = 16.46

Since

f(2) = 16.46

And

[tex]lim_{x -2} f(x)[/tex] = 16.46

Therefore,

The function f(x) = 3[tex]x^{4}[/tex] - 5[tex]x^{3}[/tex] + 3 [tex]\sqrt{x^{2} +4}[/tex] is continuous at x = 2.

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Answer:

A. 110°

Step-by-step explanation:

according to the theorems,

m∠1=m∠6=m∠9=m∠14=110°;

m∠2=m∠5=m∠10=m∠13=70°;

m∠3=m∠8=m∠11=m∠16=70°;

m∠4=m∠7=m∠12=m∠15=110°.

all the details are in the attachment.

The probability of selecting a white rabbit on the second draw, given that the first rabbit selected was a black rabbit is 3/5.

P(B∩W) = 1/4  getting a black and a white rabbit

P(B) = 5/12  getting a black rabbit

 P(W/B)

= P(B∩W) / P(B)

= (1/4) / (5/12)

= 12/20

= 3/5

Therefore, the conditional probability is 3/5.

Conditional probability is the chance of an event A occurring when another event B in relation to A has previously occurred. P(A|B) represents it. As seen in the picture above, S represents sample space, and A and B represent events.

The potential of an event or outcome occurring based on the existence of a preceding event or outcome is known as conditional probability. It is computed by multiplying the preceding event's probability by the renewed probability of the next, or conditional, occurrence.

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Answer:

  (c)  x = -1/11(y -3)²

Step-by-step explanation:

You want an equation of the parabola with directrix x = 11/4 and vertex (0, 3).

The directrix is a vertical line to the right of the vertex. This means the parabola opens to the left.

The vertex form of the equation is ...

  x = 1/(4p)(y -k)² +h . . . . . . . . where (h, k) is the vertex, and p is the distance from the directrix to the vertex (also, the distance from the vertex to the focus)

Here, we have ...

  p = 0 -11/4 = -11/4 . . . . negative because the vertex is left of the directrix

and

  (h, k) = (0, 3)

so the equation is ...

  x = 1/(4(-11/4))(y -3)² +0

  x = -1/11(y -3)²

Answer:

The two locker numbers are 80 and 69.

Hope it helps!

The correct statements regarding the transformations to the volumes are given as follows:

1. A cone's radius increases x 3: -> The cone's volume will increase x 9.

2. A cone's height increases x 3: -> The cone's volume will increase x 3

3. A sphere's radius increases x 3 -> The sphere's volume will increase x 27.

4. A cylinder's radius increases x 6 -> The cylinders volume will increase x 36.

The volume of a cone of radius r and height h is given as follows:

V = πr²h/3.

Then the scale factors are considered as follows:

The volume of an sphere of radius r is given as follows:

V = 4πr³/3.

Then when the radius is multiplied by 3, the volume is multiplied by 27, as 3³ = 27, and the radius is cubed in the equation.

The volume of a cylinder of radius r and height h is given as follows:

V = πr²h.

Then if the radius is multiplied by 6, the volume is multiplied by 36, as the variable r is squared in the equation for the volume.

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After 81 minutes of driving the distance to destination is 32.8 miles.

Th function that has two variables with first order term is called linear function.  While plotting on the XY coordinate system we get a straight line.

Why do we use linear equation in this problem?

as per question, distance to destination is a linear function of total driving time so we use the equation of straight-line having slope m and y intercept b for determining unknown values.

given, distance to destination in miles is a linear function of total driving time in minutes.

y=mx+b

in the equation, y denotes the distance to destination in miles

                 x is the total driving time in minutes

         m is the slope of linear equation

      b is the y intercept

Milan has 68 miles to his destination after 37 minutes of driving

68 = mx37+b

he has 45.6 miles to destination after 65 minutes of driving

45.6=mX65+b

solving the two equations by addition method

slope, m= -0.8

from the above two equation

we get b=97.6

now, after 81 minutes of driving the distance to destination, y=mx+b

                                               y= -0.8x81+97.6

                               distance = 32.8 miles

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x(7 - x) > 8

First solve x(7 - x)  = 8

x^2 - 7x + 8 = 0

x = 5.56, 1.44

If we plug in these values into the original equation we can see that solution is

1.44 < x < 5.56

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Answer:

Step-by-step explanation:

Given a total of 244 sodas and hot dogs sold, with sodas numbering 42 more than hot dogs, you want to know the number of each that were sold.

Let s represent the number of sodas sold. Then s-42 is the number of hot dogs sold, and the total sold is ...

  s +(s -42) = 244

Add 42 and simplify

  2s = 286

  s = 143 . . . . . divide by 2

  hot dogs = 143 -42 = 101 . . . . . figure the number of hot dogs

143 sodas and 101 hot dogs were sold.

Using the two column proof, we have been able to prove that;

ΔPQR ≅ ΔTSR by AAS Congruency Postulate

A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.

Thus, the two column proof required is as follows;

Statement 1: PR ≅ TR

Reason 1: Given

Statement 2: ∠PQR ≅ ∠TSR

Reason 2: Given

Statement 3: ∠PRQ ≅ ∠TRS

Reason 3: Opposite angles

Statement 4: ΔPQR ≅ ΔTSR

Reason 4: AAS Congruency postulate

AAS congruency postulate is one of the 5 major triangle congruency postulates that is defined as Angle-Angle-Side. This tells us that two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

We can also say that Opposite angles are defined as the angles that are directly opposite each other where two lines cross. The intersection point in this regards is called the vertex, which is the point where the lines connect to form the angle. Opposite angles are also referred to as vertical angles

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Answer:

4/15 cups of soda per hour

Step-by-step explanation:

1 1/4 = 5/4 and if 5/4 hours yielded 1/3 cups, you would have to multiply 1/3 by the reciprocal to find the hourly rate

1         4             4

-   *     -      =      --

3        5             15

Answer: x = 70

Step-by-step explanation:

You can simply solve for x by simplifying both sides of the equation, then isolating the variable

Solve, x/7 - 2 = 8, for x.

x/7 = 10, added the value of 2 to both sides of the equation.

x=70, multiplied the value of 7 to both sides of the equation.

Thus the value of x is equal to 70.

Answer: 12

Step-by-step explanation:

Since we are given what v and w are, we can directly plug them in to solve the expression.

w²+1v        [plug in v and w]

(3)²+1(3)     [exponent]

9+1(3)        [multiply]

9+3            [add]

12

The expression is equal to 12.

Given that x is a normal variable with mean = 47 and standard deviation = 6.4, find the following probabilities.

Generally, To solve these problems, we can use the standard normal distribution table or a computer program to find the desired probabilities.

First, we need to standardize the given values of x by subtracting the mean and dividing by the standard deviation. This gives us a standard normal random variable, denoted by Z, with a mean of 0 and a standard deviation of 1.

(a) P(x ≤ 60) = P(Z ≤ (60 - 47)/6.4) = P(Z ≤ 1.5625). From the standard normal distribution table or a computer program, we find that P(Z ≤ 1.5625) = 0.9356.

(b) P(x ≥ 50) = P(Z ≥ (50 - 47)/6.4) = P(Z ≥ 0.46875). From the standard normal distribution table or a computer program, we find that P(Z ≥ 0.46875) = 0.6744.

(c) P(50 ≤ x ≤ 60) = P(0.46875 ≤ Z ≤ 1.5625) = P(Z ≤ 1.5625) - P(Z ≤ 0.46875) = 0.9356 - 0.6744 = 0.2612.

Therefore, the probabilities are as follows:

(a) P(x ≤ 60) = 0.9356 (b) P(x ≥ 50) = 0.6744 (c) P(50 ≤ x ≤ 60) = 0.2612

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Answer:

Below

Step-by-step explanation:

2^9 possibilities =512

9 possibles with only ONE tails  (9 C 1)

36 possibles with TWO tails     ( 9 C 2)

45 out of 512       45/512 = .088  

44 seconds will pass before the planes are at the same altitude.

What do you mean by algebraic expression?

An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.

There are three main types of algebraic expressions:

Monomial Expression

Binomial Expression

Polynomial Expression

An algebraic expression with only one term is called a monomial.

It is given that plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second.

Let x seconds will pass before the planes are at the same altitude.

Plane A, 3500 + 45.5x

Plane B, 2609 + 65.75x

x is number of seconds of time

When altitudes equal

3500 + 45.5x = 2609 + 65.75x

3500 - 2609 = 65.75x - 45.5x

891 = 20.25x

891/20.25 = x

44 = x

Therefore, 44 seconds will pass before the planes are at the same altitude.

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The value of the expression is 3st² - s² is 315.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Given expression is 3st² - s².

For s = 3 and t = 6, find the value of the expression 3st² - s².

To find the value of the expression, replace s by 3 and t by 6:

3st² - s²

= 3×3×6² - 3²

= (9 × 36) - 9

= 324 - 9

= 315

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Answer:m

Step-by-step explanation:

The required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.

A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

The equation of the line's general form is:

y = MX + c

Where, m = slope, c = y-intercept and slope = ( y₂ - y₁ ) / ( x₂ - x₁ ).

Determine the line's slope:

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -2-2) / (2+7 )

Slope= -4/9

The y-intercept is determined as follows:

y = MX + c

2 = -4/9x 2+c

c = -8/9

The lines' equation:

y = MX + c

y = -4/9x - 8/9

Therefore, the required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.

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The domain and range of the provided function are (-infinite, 3/4) and (5, infinite) respectively.

A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output. A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

The domain of a function is the set of values that may be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the collection of values that the function returns when we enter an x value. To acquire the domain and range, just solve the equation y = f(x) to discover the values of the independent variable x. To compute the function's range, just define x as x=g(y) and then discover the domain of g. (y).

Here,

f(x)=3/4x+5

Domain=(-infinite, 3/4)

Range=(5, infinite)

The domain for given function is (-infinite, 3/4) and range is (5, infinite).

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There is no property named 'left' for the circle. So the answer is 'c'.

Circle is a two dimensional figure which has a round shape. It is formed by joining all the points which are at an equal distance from a fixed point called the center of the circle.

The line formed by joining the center to any point on the boundary of the circle is called radius. Diameter is double of the radius.

Rotate angle is the term defining the angle of rotation of the circle. Angle of rotation of a complete circle is 2π.

Width is another term for diameter of the circle, although it is not commonly used.

Left is the only term which does not have any role in the properties of circles.

Hence, the term 'left' is not a valid property of circles.

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Answer:

[tex]\frac{7}{10}[/tex]

Step-by-step explanation:

The number of djembe drums you sold is 8

From the question, we have the following parameters that can be used in our computation:

Total = 12 sets of maracas, 6 sets of claves, and x djembe drums.

Earning = $326

Also, we have:

The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.

So, we have

12 * 14 + 6 * 5 + x * 16 = 326

Evaluate the products

198 + 16x = 326

Evaluate the iike terms

16x = 128

So, we have

x = 8

Hence, the number of djembe drums is 8

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Complete question

You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of claves, and x djembe drums.

The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.

Find the number of djembe drums you sold.

The expression equivalent to "20 divided by 1 plus 4" is 20 ÷ 1 + 4.

The rules of PEDMAS can be understood by the full form of the name. B stands for bracket, O for of, D for division, M for multiplication, A for addition and S stands for subtraction. For a mathematical expression involving the combination of any of these operators the priority will be given to the letter that comes first.

The given statement for the problem is, " 20 divided by 1 plus 4".

It can be written in the form of expression as follows,

The sign of plus is given as '+'.

And, for divide it is '÷'.

Now, 20 divided by 1 plus 4 can be written as,

20 ÷ 1 + 4

Which is evaluated  by BODMAS to give,

20 + 4 = 24.

Hence, the expression for the given case is 20 ÷ 1 + 4 which is equal to 24.

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After the markup in the price, the new cost of goldfish will be equal to $4.45.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Cost of goldfish = $3.45

Markup = 29%

So, the price increase will be,

(3.45 × 29)/100

= 100.05/100

= 1.0005

So, the new price is,

$3.45 + $1.0005

= $4.4505 ≈ $4.45

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