write a verbal expression for each algebraic expression
9a2

Answer: 6234 × 32 = 199488.

Step by step:

To calculate 6234 × 32 without using a calculator, you can use the traditional multiplication method as follows:

   6234

x    32

-------

  12468   (2 x 6234)

+ 62340   (3 x 6234 with a zero added)

--------

 199488

Answer:  Participant A

Step-by-step explanation:

if you divide 120 by 10 you would get 12 jumping jacks per minute and if you divide 140 by 14 you would get 10 jumping jacks per minute

If d is not a prime number and n^2 is divisible by d, it does not necessarily mean that n is also divisible by d, example is d = 6 and n = 3, where n^2 = 9 is divisible by 6, but n = 3 is not divisible by 6.

A prime number is a positive integer greater than 1 that has exactly two distinct factors: 1 and itself. For example, 2, 3, 5, 7, 11, 13, and 17 are all prime numbers.

If a number d is not prime, then it has at least one factor other than 1 and itself. Let's assume that d is not prime, and let p be a factor of d such that p is not equal to 1 or d. Then, by definition, p divides d evenly with no remainder.

Consider the case where d = 6 and n = 3.

Here, d is not a prime number, and n^2 = 9, which is divisible by d since 9 is a multiple of 6. However, n = 3 is not divisible by d = 6, as 6 does not divide 3 evenly.

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Answer:

C

Step-by-step explanation:

i assume its
C.

The probability of selecting a blue marble on the first draw and a green marble on the second draw is 0.09.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

There are 12 marbles in total in the bag, so the probability of selecting a blue marble on the first draw is 4/12.

After the first marble is drawn, there are 11 marbles left in the bag, so the probability of selecting a green marble on the second draw, given that the first marble was blue and has already been removed, is 3/11.

To determine the probability of both events occurring together, we multiply the probabilities. Therefore, the probability of selecting a blue marble on the first draw and a green marble on the second draw is:

(4/12) * (3/11) = 0.0909

Rounding to the hundredth place, the probability is approximately 0.09.

Therefore, the probability of selecting a blue marble on the first draw and a green marble on the second draw is 0.09.

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Answer: x = 2, y = 0

Step-by-step explanation:

Assuming you need help solving for x or y, and the capital Y is y, we have the system of equations:

3x + y = 6

y + 2 = x

Substituting x for y + 2 gives us

3(y + 2) + y = 6

3y + 6 + y = 6

4y = 0

y = 0

Plugging y = 0 in for the second equation gives us

x = 0 + 2, or x = 2

Students were asked to simplify the expression using trigonometric identities:

 A.  student A is correct; student B was confused by the division

 B.  3: cos²(θ)/(sin(θ)csc(θ)); 4: cos²(θ)

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names.

Each student correctly made use of the trigonometric identities

cosec(θ) = 1/sin(θ)

1 -sin²(θ) = cos²(θ)

A.

Student A's work is correct.

Student B apparently got confused by the two denominators in Step 2, and incorrectly replaced them with their quotient instead of their product.

The transition from Step 2 can look like:

[tex]\frac{(\frac{1-sin^2\theta}{sin\theta} )}{cosec\theta} =\frac{1-sin^2\theta}{sin\theta} .\frac{1}{cosec\theta} =\frac{cos^2\theta}{(sin\theta)(cosec\theta)}[/tex]

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Complete question:

Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given. (In image below)

Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)

Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)

Answer:

The probability that Sara whassell four extended warranties tomorrow is 0.1046

Step-by-step explanation:

Please hit brainliest if this helped! If you have any questions, please comment.

We can use the Poisson probability formula to calculate the probability of selling 4 extended warranties tomorrow:

P(X = k) = (e^(-λ) * λ^k) / k!

where λ is the average number of extended warranties sold per day and k is the number of extended warranties sold.

In this case, λ = 2.7 and k = 4. So, plugging in the values, we get:

P(X = 4) = (e^(-2.7) * 2.7^4) / 4!

P(X = 4) ≈ 0.1046

Therefore, the probability that Sara will sell four extended warranties tomorrow is approximately 0.1046, rounded to four decimal places.

The CH3-CIOI-CNI molecule contains three carbon atoms with different electron geometries and bond angles. The CH3 and CIOI carbon atoms have tetrahedral geometry with a bond angle of approximately 109.5 degrees, while the CNI carbon atom has a trigonal planar geometry with a bond angle of approximately 120 degrees.

Using this Lewis structure, we can determine the electron geometry and bond angle for each carbon atom in the molecule as follows.

The carbon atom in the CH3 group has four electron domains (three bonding pairs and one non-bonding pair). The electron geometry around this carbon atom is tetrahedral, and the bond angle is approximately 109.5 degrees.

The carbon atom in the CIOI group has four electron domains (two bonding pairs and two non-bonding pairs). The electron geometry around this carbon atom is also tetrahedral, and the bond angle is approximately 109.5 degrees.

The carbon atom in the CNI group has three electron domains (one bonding pair and two non-bonding pairs). The electron geometry around this carbon atom is trigonal planar, and the bond angle is approximately 120 degrees.

Therefore, the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI are:

CH3 carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees

CIOI carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees

CNI carbon atom trigonal planar geometry, bond angle of approximately 120 degrees

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_____The given question is incomplete, the complete question is given below:

Determine the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI

Step-by-step explanation:

So first of all u have to convert the metres into centimetres. After the conversation draw the map of both in centimetres and your map is done. The question is answered

Answer:

Determine the dimensions of the room: Measure the length and width of the room you want to draw a floor plan for using a tape measure. Record these measurements in meters.

Choose a scale: Since you want to use a scale of 1cm to 0.5m, you need to convert your measurements from meters to centimeters. For example, if your room measures 6 meters by 4 meters, you need to multiply each measurement by 100 to get 600cm by 400cm. Then, divide each measurement by 2 to get your scale measurement. In this case, your floor plan will be 300cm by 200cm.

Draw a rough sketch: Using a pencil and graph paper, draw a rough sketch of the room's shape based on the dimensions you have recorded.

Add doors and windows: Using the same scale, add doors and windows to your floor plan. Doors are typically represented by a straight line with an arc on top, while windows are represented by a straight line with a horizontal line through the middle.

Add fixtures and appliances: Add any fixtures and appliances that are permanent to the room, such as sinks, cabinets, and appliances. You can use symbols to represent these items, such as a rectangle for a refrigerator or a triangle for a sink.

Label everything: Finally, label everything on your floor plan using a legible font. This includes the dimensions of the room, the location of doors and windows, and the names of fixtures and appliances.

Step-by-step explanation:

The length of h in the attached composite figure where all the angles are right angles is equal to 4m.

In the attached diagram of composite figure,

All are right angles.

Composite figure consist two rectangles,

Upper and lower rectangles.

length of the upper rectangle is equal to 5m

Width of the upper rectangle is equal to 'h' m

Width of the lower rectangle is equal to 2m

Length of each dash '-' mark  is equals to 1m.

length of 'h'm  is equals

= 2 m + 2 dash marks

= 2m + 2m

= 4m

Therefore, the length of the h in the composite figure ( attached diagram ) is equals to 4m.

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The above question is incomplete, the complete question is:

What is the length of h in the following composite figure? All angles are right angles.

5 m

4 m

3 m

2 m

Diagram is attached.

Answer:

4 m is ur answer

Step-by-step explanation:

hope this helps

Since we can't find an ordered pair (x, y) that satisfies all the conditions, there is no solution to this problem.

An equation is a mathematical statement that asserts the equality of two expressions. It typically contains variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true. Equations can be used to model relationships between variables, solve real-world problems, and make predictions.

Here,

Let's start by defining the variables:

x: number of hot dogs

y: number of peanuts

We need to find an ordered pair (x, y) that satisfies the following conditions:

x and y are both integers

x is greater than or equal to 0

y is greater than or equal to 0

2x + y ≤ 7 (total cost of snacks can't exceed $7)

x ≥ 4 (at least 4 snacks)

We can use trial and error to find a suitable ordered pair. Let's start with x = 4 and see if we can find a corresponding y value that satisfies the conditions:

If x = 4, then the total cost of hot dogs is 4 * $2 = $8.

We need to spend no more than $7, so we have $7 - $8 = -$1 left for peanuts.

Since we can't spend a negative amount of money, there is no solution for x = 4.

Let's try x = 5:

If x = 5, then the total cost of hot dogs is 5 * $2 = $10.

We have $7 - $10 = -$3 left for peanuts, so there is no solution for x = 5 either.

Finally, let's try x = 6:

If x = 6, then the total cost of hot dogs is 6 * $2 = $12.

We have $7 - $12 = -$5 left for peanuts, so there is no solution for x = 6 either.

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Complete question:

Cody has $7 dollars. he wants to buy at least 4 snacks. Hot dogs (x) and $2 each. Peanuts (y) are $1 each. Find the solution for this question of equation?

True. The p-value is a probability value that measures the power of evidence in against to the null hypothesis in a statistical test.

Mainly, it represents the possibility of staring at a test statistic as a minimum as extreme as the one computed, assuming that the null hypothesis is genuine.

If the p-value is small, commonly less than a chosen significance stage (e.g., 0.05), it shows that the determined data is unlikely to have took place by danger alone and provides proof against the null hypothesis. alternatively, a large p-value suggests that the determined information is consistent with the null speculation, and the evidence isn't sturdy enough to reject it.

Consequently, the p-value is an critical tool in statistical inference, permitting researchers to draw conclusions about the population based totally on pattern information and degree the extent of uncertainty in their outcomes.

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The value of R500 decrease to ratio 9:8 is x = 400.

By using the cross multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa. Using the mathematical rule of three, we may determine the answer based on proportions. The best illustration is cross multiplication, where we may write in a percentage to determine the values of unknown variables.

Given that, decrease R450 in the ratio 9:8.

Let 9 = 450

Then 8 will have the value = x.

That is,

9 = 450

8 = x

Using cross multiplication we have:

9x = 450(8)

x = 50(8)

x = 400

Hence, the value of R500 decrease to ratio 9:8 is x = 400.

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x = 4.9

Solution:

We can use the intersecting chords formula:

[tex]7\times7 = 10x[/tex]

[tex]49 = 10x[/tex]

[tex]49\div10=10x\div10[/tex]

[tex]4.9 = x[/tex]

Therefore, x = 4.9.

Answer:

(2, -3)

Step-by-step explanation:

You must choose from the 3 ways to solve the system of equations:

1. Substitution

2. Elimination

3. Graphing (least recommended)

My example is going to be substitution, as folllows:

2x - y = 7

(Add y to both sides)

2x = y + 7

(Subtract 7 from both sides)

y = 2x - 7

Now, we are able to use substitution in the next equation with the other equation!

3x + 4y = -6

(Replace y with what y equals -- other equation)

3x + 4(2x -7) = -6

(Simplify the parantheses)

3x + 8x - 28 = -6

(Add 28 to both sides)

3x + 8x = -6 +28

3x + 8x = 22

(CLT - Combine like terms)

11x = 22

(Divide 11 from both sides)

x = 2

Now, we will find what y is by plugging x into the other equation.

y = 2x - 7

x = 2

y = 2(2) - 7

y = 4 - 7

y = -3

y = -3

x = 2

Since we found both of the variables' values, we found our coordinate pairs to solve this equation!

Answer: (2, -3)

The Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts tο make a 35 pοund mixture that sells fοr $5.31 per pοund.

Assume the Nutty Prοfessοr makes a 35-pοund mixture with x pοunds οf cashews and (35 - x) pοunds οf Brazil nuts.

The cashews cοst $6.80 per pοund, sο the tοtal cοst οf x pοunds οf cashews is $6.8x dοllars.

Similarly, Brazil nuts cοst $4.20 per pοund, sο (35 - x) pοunds οf Brazil nuts cοst 4.2(35 - x) dοllars.

The tοtal cοst οf the mixture equals the sum οf the cashew and Brazil nut cοsts, which is:

6.8x + 4.2(35 - x) (35 - x)

When we simplify, we get:

6.8x + 147 - 4.2x

2.6x + 147

The mixture sells fοr $5.31 per pοund, sο the tοtal revenue frοm selling 35 pοunds οf the mixture is:

35(5.31) = 185.85

When we divide the tοtal cοst οf the mixture by the tοtal revenue, we get:

2.6x + 147 = 185.85

Subtractiοn οf 147 frοm bοth sides yields:

2.6x = 38.85

When we divide by 2.6, we get:

x ≈ 14.94

Tο make a 35-pοund mixture that sells fοr $5.31 per pοund, the Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts.

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Answer: Area = 113.14 ft sq. Perimeter =

Step-by-step explanation:

break down the figure and solve area and perimeter for each

triangle = A = 1/2bh

A = 1/2 (8) (6)

A = 24 ft sq.

square = A = LW

A = (8) (8)

A = 64 ft sq

semi circle = A = 1/2 TT r^2

A = 1/2 (3.14) (4)^2

A = 1/2 (3.14) (16)

A = approximately 25.14 ft sq

rounded to hundredths

total AREA = 24 + 64 + 25.14 = 113.14

now we can find perimeter by breaking down the figures again

triangle

we know one leg is 6 ft and the other is 8 ft

we need to find the hypoteneuse using Pythagorean theorem.

a^2 + b^2 = c^2

6^2 = 8^2 = c^2

36 + 64 = c^2

100 = c^2

√100 = √c^2

10 ft = c

square

given two sides are 8ft and 8ft

semi circle - P is the same as circumference

P = ( 1/2 ) 2 π r

P = (1/2) (2) (3.14) (4)

P = 12.56

total PERIMETER = 12.56 + 8 + 8 + 6 + 10 = 44.56 ft

i attached a print screen showing my breakdowns

To remove the y-term in  the given linear equation in two Variable multiply the equation by 4 then add these two equations.

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable. As a result, this equation has a single solution, x = 5/2. Yet, there are two solutions to a linear equation with two variables.

According to given question;

5X+8y=5   ……..eqn 1.

3x-2y=3    ………eqn 2.

Multiply by 4 in the eqn 2.

We get

12x-8y=12 ……..eqn 3 .

When we add eqn 1 and eqn 3 we get ;

17x =17

X =1

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After eliminating the y-term in the given equations i.e 5x+8y=5 and

3x-2y=3, The solution to the system of equations is x = 1, y = 0.

The elimination method is the technique used to solve systems of linear equations. It involves adding or subtracting equations in a system to eliminate one variable and find the value of the other variable.

To eliminate the y-term in these equations, you can multiply the second equation by 4, which will give you:

12x - 8y = 12

Now, you can add this equation to the first equation:

5x + 12x + 0y = 5 + 12

Simplifying the left side gives you 17x, and simplifying the right side gives you 17. So, you have the equation:

17x = 17

Solving for x gives you x = 1.

Now that you have found the value of x, you can substitute it into one of the original equations to solve for y. Using the first equation, you get:

5(1) + 8y = 5

Simplifying this equation gives you:

8y = 0

Solving for y gives you y = 0.

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The three Pythagorean trigonometric identities, which I’m sure one can find in any Algebra-Trigonometry textbook, are as follows:

sin² θ + cos² θ = 1

tan² θ + 1 = sec² θ

1 + cot² θ = csc² θ

where angle θ is any angle in standard position in the xy-plane.

Consistent with the definition of an identity, the above identities are true for all values of the variable, in this case angle θ, for which the functions involved are defined.

The Pythagorean Identities are so named because they are ultimately derived from a utilization of the Pythagorean Theorem, i.e., c² = a² + b², where c is the length of the hypotenuse of a right triangle and a and b are the lengths of the other two sides.

This derivation can be easily seen when considering the special case of the unit circle (r = 1). For any angle θ in standard position in the xy-plane and whose terminal side intersects the unit circle at the point (x, y), that is a distance r = 1 from the origin, we can construct a right triangle with hypotenuse c = r, with height a = y and with base b = x so that:

c² = a² + b² becomes:

r² = y² + x² = 1²

y² + x² = 1

We also know from our study of the unit circle that x = r(cos θ) = (1)(cos θ) = cos θ and y = r(sin θ) = (1)(sin θ) = sin θ; therefore, substituting, we get:

(sin θ)² + (cos θ)² = 1

1.) sin² θ + cos² θ = 1 which is the first Pythagorean Identity.

Now, if we divide through equation 1.) by cos² θ, we get the second Pythagorean Identity as follows:

(sin² θ + cos² θ)/cos² θ = 1/cos² θ

(sin² θ/cos² θ) + (cos² θ/cos² θ) = 1/cos² θ

(sin θ/cos θ)² + 1 = (1/cos θ)²

(tan θ)² + 1 = (sec θ)²

2.) tan² θ + 1 = sec² θ

Now, if we divide through equation 1.) by sin² θ, we get the third Pythagorean Identity as follows:

(sin² θ + cos² θ)/sin² θ = 1/sin² θ

(sin² θ/sin² θ) + (cos² θ/sin² θ) = 1/sin² θ

1 + (cos θ/sin θ)² = (1/sin θ)²

1 + (cot θ)² = (csc θ)²

3.) 1 + cot² θ = csc² θ

Answer:

Step-by-step explanation:

[tex](3x+5)+(x-25)=180 \text{ \ (angles on a straight line are supplementary)}[/tex]

                 [tex]4x-20=180[/tex]

                         [tex]4x=200[/tex]         (+20 both sides)

                           [tex]x=50[/tex]           (÷4 both sides)

Answer: -1/6

Step-by-step explanation:

Put the equation into y = mx + b (slope) form.

3x + 18y = -486

18y = -3x - 486

y = -1/6x - 27

If the line is parallel to this line, the slope must be the same.

Answer:    

The radius of the circle is 3.

The center of the circle is (-2, 1).

Step-by-step explanation:

   Rewrite the equation in standard form:

   We need to rewrite the given equation in standard form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. To do this, we complete the square for both the x and y terms.

x² + 4x + y²-2y = 20

(x² + 4x + 4) + (y² - 2y + 1) = 20 + 4 + 1

(x + 2)² + (y - 1)² = 25

   Identify the center and radius:

   Now that we have the equation in standard form, we can identify the center and radius of the circle.

The center is the point (-2, 1), which we can read directly from the equation.

The radius is the square root of the number on the right side of the equation, which is 5. Therefore, the radius is sqrt(5) or approximately 2.236.

Alternatively, we can also use the Desmos graphing calculator to plot the equation and visually determine the center and radius. When we plot the equation, we see that it forms a circle with center (-2, 1) and radius 3.

The required value of the function  (f + g)(x) for given f(x) and g(x) as ( 3 / √x )  - ( 2 / x³ ) and √(5x - 7) is equals to ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7).

Function f(x) is equals to,

( 3 / √x )  - ( 2 / x³ ) for all x > 0

Function g(x) is equals to,

g(x) = √(5x - 7)

To get the value of (f + g)(x),

Substitute the value of f(x) and g(x) and  add the functions f(x) and g(x) together,

Sum of f(x) and g(x) is equals to,

(f + g)(x)

= f(x) + g(x)

= ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7)

Therefore, value of the function (f + g)(x) is equals to ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7).

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The above question is incomplete, the complete question is:

The function f is defined by f of x is equal to 3 divided by the square root of x minus 2 divided by x cubed for x > 0, g as a function of x is equal to the square root of quantity 5 x minus 7 Find (f + g)(x).

Therefore , the solution of the given problem of unitary method comes out to be common shares of Zeil Inc. is 2.23%.

This common convenience, already-existing variables, or all important elements from the original Diocesan adaptable study that followed a particular methodology can all be used to achieve the goal. Both of the crucial elements of a term affirmation outcome will surely be missed if it doesn't happen, but if it does, there will be another chance to get in touch with the entity.

Here,

Earnings per Share are calculated as (Net Income – Preferred Dividends) / the average number of outstanding Common Shares.

=>  Market price per share / earnings per share is the Price-Earnings Ratio.

=> Dividends per Share are calculated as follows: Common Stock Dividends / Average Common Shares Outstanding

=>  Dividend Yield is the product of dividends per share and the share price.

=>  (Beginning Common Shares plus Ending Common Shares) / 2 equals the average number of Common Shares Outstanding.

=>  Starting common shares equals ending common shares, which is

=>  $3,500,000 / $25, or 140,000.

(a) The earnings per share are ($424,000 - $0) / 140,000, which equals $3.03.

The ordinary stock price of Zeil Inc.

(b) The price-earnings ratio for Zeil Inc.'s common shares is 11.20 divided by 3.03, or 3.69.

(c) Dividends per Share: $35,000./140,000. = $0.25

Therefore, $0.25 in dividends are paid per unit of Zeil Inc. common stock.

(d) Dividend Yield: $0.25 divided by $11.20 equals 0.0223, or 2.23%.

The common shares of Zeil Inc. is 2.23%.

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Using SSS theorem of congruency in triangles, we can prove that in all the cases, each triangle is congruent to the other.

Whether two or more triangles are congruent depends on the size of the sides and angles. A triangle's size and shape are consequently determined by its three sides and three angles. If the pairings of the respective sides and accompanying angles are equal, two triangles are said to be congruent. Both of these are the exact same size and shape. Triangles may satisfy a number of distinct congruence requirements.

The SSS criterion is also known as the Side-Side-Side criterion. This standard states that two triangles are congruent if the sum of the three sides of each triangle is the same.

Here in the question,

It is given that the two sides of each triangle are equal to the corresponding sides of the other triangle.

Now as two sides of a triangle is equal to the two sides of another triangle, it is obvious that he third side will be equal to the corresponding sides of the other triangle.

Now as per the SSS criteria, as all the sides are equal to the corresponding sides of the other triangle, the triangle are congruent.

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a. In this exercise, we are given that Mystery Pizza has an average οf 4.2 teIephοne orders per hour between 11 P.M. and midnight on Thursday night. Nοw using these given vaIues, we wiII caIcuIate the probabiIity that at Ieast 30 minutes wiII eIapse before having the next teIephone οrder.

Accοrding to probabiIity theory and statistics, the exponentiaI distributiοn is the probabiIity distribution of time between occurrences in the Poissοn distribution. It is a distribution of probabiIities that frequentIy correIates to the amount of time before a specific event takes pIace. It is a prοcess in which events take pIace continuousIy, independentIy, and at an average pace that remains constant throughout the process.

In caIcuIating the area under the curve of its graph (CDF), we wiII have to use the fοIIowing formuIa for the mean and the standard deviation,

Mean and Standard Deviatiοn:

[tex]$\begin{array}{r}{\mu={\frac{1}{\lambda}};}\\ {\sigma={\frac{1}{\lambda}}\,.}\end{array}$[/tex]

where,

First, let us calculate the mean and standard deviation using the given Pοisson mean [tex]$\lambda=4.2.$[/tex] Using the fοrmula, we have,

[tex]$\begin{aligned}\rm{\mu=\sigma={\frac{1}{\lambda}}}\\ {={\frac{1}{4.2}\\{=0.2381}\end{aligned}$[/tex]

Sο we have the mean and the standard deviation of 0.2381 hours.

Nοw, we wiII caIcuIate the probabiIity that at Ieast 30 minutes or 0.50 hοurs wiII eIapse before the next teIephone order. Keep in mind that we are caIcuIating the probabiIity for "more than" the x so we wiII use the right-taiIed formuIa for this which is given by,

Right-tailed area(Mοre than x) :

[tex]$P(X\gt x)=e^{-\lambda x};$[/tex]

where,

Using the fοrmula, we have:

[tex]$\begin{array}{r l}{P(X\gt 0.50)=e^{-\lambda x}}\\ {=e^{-42(0.50)}}\\ {=0.1225\,.}\end{array}$[/tex]

Therefοre, we can concIude that there is a 12.25% chance that at Ieast 30 minutes or 0.5 hours wiII eIapse before another teIephone order.

b. Next, we wiII caIcuIate the probabiIity that Iess than 15 minutes wiII eIapse befοre the next teIephone order. Remember that we are caIcuIating the probabiIity of Iess than x. This means that we wiII be using the fοrmuIa for the Ieft-taiIed area which is given by,

Left-tailed area(Less than οr equal to x):

[tex]$P(X\leq x)=1-e^{-\lambda x}$[/tex]

where,

Using the fοrmula, we have:

[tex]$\begin{array}{r l}{P(X\leq0.25)=1-e^{-\lambda x}}\\ {=1-e^{-42(0.25)}}\\ {=1-0.3499}\\ {=0.6501\,.}\end{array}$[/tex]

Therefοre, there is a 65.01% that Iess than 15 minutes wiII eIapse before the next teIephοne caII.

c. In this part, we wiII caIcuIate the probabiity that between 15− 30 minutes wiII eIapse befοre the next teIephone order. MathematicaIIy, we have,

[tex]$P(0.25\lt X\lt 0.5)=P(X\lt 0.50)-P(X\lt 0.25)$[/tex]

Frοm part a, we have the value for P(X>0.50) which is 0.1225. Now using the cοmplement rule, we can get P(X<50}

[tex]$\begin{array}{c}{{P(X\lt 50)=1-P(X\gt 50)}}\\ {{=1-0.1225=0.8775\,.}}\end{array}$[/tex]

We have nοw the value of P(X<0.50) which is 0.8775.

We can nοw get the P(0.25<X<0.50)  by subtracting P(X<0.50) by P(X<0.25) frοm part b.. So we have,

[tex]$\begin{array}{r}{P(0.25\lt X\lt 0.50)=P(X\lt 0.50)-P(X\lt 0.25)}\\ {=0.8775-0.6501}\\ {=0.2274\,.}\end{array}$[/tex]

Sο we have P(0.25<X<0.50)=0.2274. Therefore, we can concIude that there is a 22.74% chance that between 15 and 30 minutes wiII eIapse before having a teIephone order.

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Answer:

60 - 10 = 50

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