On the average, 6.7 cars arrive at the drive-up window of a bank every hour. Define the random variable x to be the number of cars arriving in any hour. What is the distribution that most likely describes the outcome of the random variable x a. uniform b. Poisson c. hypergeometric d. binomial

Answer:

Below

Step-by-step explanation:

You need the RADIUS to calculate area.....since diameter is 8, radius is 4 inches

Area = pi r^2

Cost per square inch =  price / area = $12.56 / ( 3.14 *4^2) =  $ 0.25 per in^2

The approximate cost per square inch of the cookie cake is $0.25

To know the total cost to cover an area, multiply the area with the cost per unit of area.

Given that, a circular cookie cake costs $12.56, the diameter of the cookie cake is 8 inches,

We need to determine that, what is the approximate cost per square inch of the cookie cake,

So, the area of the cake = π × radius² [diameter = 2 radius]

= 3.14 × 4²

= 50.24 in²

Since, the cost for the 50.24 in² of the cookie cake is $12.56,

So, the 1 in² of the cookie cake = $12.56 / 50.24 in²

= $0.25

Hence, the approximate cost per square inch of the cookie cake is $0.25

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False. The null hypothesis does not inherently represent a presumed default state of nature but rather serves as a reference point for hypothesis testing.

The null hypothesis does not necessarily correspond to a presumed default state of nature. In hypothesis testing, the null hypothesis represents the assumption of no effect, no difference, or no relationship between variables. It is often formulated to reflect the status quo or a commonly accepted belief.

The alternative hypothesis, on the other hand, represents the researcher's claim or the possibility of an effect, difference, or relationship between variables. The null hypothesis is tested against the alternative hypothesis to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

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The simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is 729x^6 - V^2.

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

To simplify the expression using the given values, we substitute \(U = 3x^3\)and V = y + 1 into the original expression:

\(81x^6 - (y + 1)^2\)

Replacing U and V:

\(81(3x^3)^2 - (V)^2\)

Simplifying:

\(81 \times 9x^6 - V^2\)

\(729x^6 - V^2\)

Therefore, the simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is\(729x^6 - V^2.\)

In this way, we can represent the original expression in a simplified form using the assigned values for U and V.

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Consider the expression: \(81x^6 - (y + 1)^2\)

If\(U = 3x^3\) and V = y + 1, what is the simplified form of the expression in terms of U and V?

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

Answer:

a)57,600 b)12.5% increase

Step-by-step explanation:

Answer:

Step-by-step explanation:

The value of y is 74°

The measure of an arc is the measure of its central angle.

Therefore to calculate the value of x

Since the diameter divides the circle into 2

The measure of the arc of the segment is 180°

Therefore;

represent the arc of the segment by z

The relationship between x y and the arc of the segment is

1/2 (z-y)= 53

= 1/2 ( 180-y) = 53

180-y = 106

-y = 106-180

-y = -74

y = 74°

therefore the value of y is 74°

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The trigonometric relations from the triangles are

a) tan A = 5/12

b) sin C = 3/5

c) cos X = 3/5

d) sin Z = 4/5

e) tan Z = 4/3

f) tan X = 12/5

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

a)

The triangle is ΔABC

tan A = opposite side / adjacent side

Substituting the values in the equation , we get

tan A = 10/24

tan A = 5/12

b)

The triangle is ΔABC

sin C = opposite side / hypotenuse

Substituting the values in the equation , we get

sin C = 24/40

sin C = 3/5

c)

The triangle is ΔXYZ

cos X = adjacent side / hypotenuse

Substituting the values in the equation , we get

cos X =21/35

cos X = 3/5

d)

The triangle is ΔXYZ

sin Z = opposite side / hypotenuse

Substituting the values in the equation , we get

sin Z = 32/40

sin Z = 4/5

e)

The triangle is ΔXYZ

tan Z = opposite side / adjacent side

Substituting the values in the equation , we get

tan Z = 28/21

tan Z = 4/3

f)

The triangle is ΔXYZ

tan X = opposite side / adjacent side

Substituting the values in the equation , we get

tan X = 12/5

Hence , the trigonometric relations are solved from the triangles

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Answer:

in 3.04 years the will give required intrest

Answer:

63

Step-by-step explanation:

using the ratio

\( \frac{4}{1} = \frac{252}{x} \)

cross multiply

\(4x = 252\)

divide both sides by (4)

\( \frac{4x}{4} = \frac{252}{4} \)

x = 63

i hope this helps

The correct answer is x = 63

\(\boxed{\frac{4}{1}=\frac{252}{x}4x=252\frac{4x}{4} =\frac{252}{4}x=63 }\\\huge\boxed{\underline_ So, \frac{4}{1}=\frac{252}{\bold{63}} }\)

Therefore, the correct answer is x = 63

Step-by-step explanation:

Magnitude = sqrt ( (-12)^2 + (-4)^2 ) = sqrt 160 = 12.649

Angle = arctan(-4/-12) = 198 degrees

The Magnitude: 12.649 and Direction: 18° (option c).

To find the magnitude and direction of the vector v = (-12, -4), we can use the following formulas:

Magnitude (or magnitude) of v = |v| = √(vₓ² + \(v_y\)²)

Direction (or angle) of v = θ = arctan(\(v_y\) / vₓ)

where vₓ is the x-component of the vector and \(v_y\) is the y-component of the vector.

Let's calculate:

Magnitude of v = √((-12)² + (-4)²) = √(144 + 16) = √160 ≈ 12.649 (rounded to the thousandths place)

Direction of v = arctan((-4) / (-12)) = arctan(1/3) ≈ 18.435°

Since we need to round the direction to the nearest degree, the direction is approximately 18°.

So, the correct answer is:

Magnitude: 12.649 (rounded to the thousandths place)

Direction: 18° (rounded to the nearest degree)

The correct option is: 12.649; 18°

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Answer:

£8934.34

Step-by-step explanation:

\(8000 * 1.028^4 = 8934.34\)

rounding to 2dp

if trunctuated at 2dp however, 8934.33

the number is multiplied by 1.028 to the power of four as you go through the equation four times, so it would be the same as

x * n * n * n * n, where it would simplify to x * n^4

1.  For the spring, the sugar-water mixture is in the ratio of 3:2 that is for 2 cups of water, 3 cups of sugar are required. For the fall, for every cup of water, 2 cups of sugar are required, giving a ratio of 2:1.

2. To get the ratio for the mixtures, order the pairs (e.g. (6, 4), (15, 10), and check the proportion of each variable in the other variable, using the least common divisor.

A ratio is the proportion of each variable in the other.

Ratios are expressed using the ratio sign (:) or in fractions, decimals, or percentages.

Spring Sugar-Water Mixture
Cups of Sugar   Cups of Water

          6                         4

        15                        10

        18                        12

       27                        18

The ratio of the spring sugar-water mixture is 3:2.  For instance, 27:18 can be reduced to 3:2 by divisor 9.

Fall Sugar-Water Mixture

Cups of Sugar   Cups of Water

          4                         2

        10                         5

        14                         7

       30                        15

The ratio of the fall sugar-water mixture is 2:1.

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Answer:

The first one is 12

The second one is -12

Just multiply, and remember the negative signs.

Answer:

1st Question- Positive Twelve

Second Question- Negative Twelve

Step-by-step explanation:

Systematic random sampling is sometimes used in place of simple random sampling due to its efficiency, representativeness, ease of implementation, and cost-effectiveness.

Systematic random sampling is sometimes used in place of simple random sampling for several reasons, including:
Efficiency:

Systematic random sampling can be more efficient than simple random sampling, as it involves selecting elements at regular intervals from the population.

This often reduces the time and effort needed to collect data compared to simple random sampling.
Representativeness:

Systematic random sampling may provide a more representative sample of the population.

By selecting elements at regular intervals, it ensures that different segments of the population are included, reducing the potential for sampling bias.
Ease of implementation:

Systematic random sampling is relatively easy to implement, as it involves fewer random selections compared to simple random sampling.

This makes it more practical for large populations or when a sampling frame is not readily available.
Cost-effectiveness:

Systematic random sampling can be more cost-effective than simple random sampling.

Since the process is more efficient, it may require fewer resources, such as time and personnel, to collect data.

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The Sales taxes in Pennsylvania are implemented in order to fund the state and local government's efforts to run the government.

Please note that this question is incomplete so I will instead give a general overview of sales taxes.

Sales taxes are taxes that are charged on the goods and services provided in the market.

They go to state and local governments who then use them to fund governmental activities such as building and maintaining schools and constructing infrastructure. This is the purpose of Pennsylvania's sales taxes.

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The equation of the given line is:

Slope intercept form is: y = -x + 6

Point slope form is: (y - 6) = -1(x - 0)

Standard form is: x + y = 6

The formula for the linear equation between two coordinates is:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

The two coordinates are:

(0, 6) and (1, 5)

Thus:

(y - 6)/(x - 0) = (5 - 6)/(1 - 0)

This can be simplified as:

(y - 6) = -1(x - 0)

It can be further written as:

y - 6 = -x - 0

y = -x + 6

The formula for linear equation in standard form is:

Ax + By = C

Thus, we have: x + y = 6

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Answer:

It's the 3rd picture. -3 1/4 + 4 3/4 = 1 1/2

Step-by-step explanation:

The linear functions of the scenario are y = 12x and y = 24/2x

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

(1, 12) and (2,24)

From the question, we understand that the function is a linear function

A linear function is represented as

y = mx + c

Using the above as a guide, we have the following equations

m + c = 12

2m + c = 24

Subtract the equations

m = 12

Substitute 12 for m in m + c = 12

12 + c = 12

Evaluate

c =0

So, the equation is y = 12x

An equivalent equation is y = 24x/2

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Answer:

\( x\approx 18.0\)

Step-by-step explanation:

Here, a = 30, b = 16, C = x

By law of cosines

\( {c}^{2} = {a}^{2} + {b}^{2} - 2ab \cos C \\ \\ {x}^{2} = {30}^{2} + {16}^{2} - 2 \times 30 \times 16 \: cos 30 \degree \\ \\ {x}^{2} = 900 + 256 - 960 \times \frac{ \sqrt{3} }{2} \\ \\ {x}^{2} = 1156 - 480 \times \sqrt{3} \\ \\ {x}^{2} = 324.615612 \\ \\ x = \sqrt{324.615612} \\ \\ x = 18.0170922 \\ \\ x \approx \: 18.0\)

Answer:

SAS, because vertical angles are congruent.

Answer:

Step-by-step explanation:

Area of a rectangle = Length * Width

Given the dimension

Length = 4x2 + 3x + 12

Width = 4x – 2

A) Area =  (4x^2 + 3x + 12)(4x – 2)

Open the parenthesis

= 16x^3-8x^2+12x^2-6x+48x-24

Area of land in Mathville = 16x^3+4x^2+42x-24

For the land in Algebratown

Area =  (5x^2 + x – 4)(2x + 1)

Area = 10x^3+5x^2+2x^2+x-8x-4

Area  = 10x^3+7x^2-7x-4

B) difference between the area of Mathville and the area of Algebratown

= 16x^3+4x^2+42x-24 -(10x^3+7x^2-7x-4)

= 16x^3+4x^2+42x-24 -10x^3-7x^2+7x+4

collect like terms

= 16x^3-10x^3+4x^2-7x^2+42x+7x-24+4

= 6x^3-3x^2+49x-20

C) The difference if x = 9

Substitute x = 9 into the resulting function

A(x) = 6x^3-3x^2+49x-20

A(9) = 6(9)^3-3(9)^2+49(9)-20

A(9) = 2187-243+441-20

A(9) = 2,365

Hence the difference of the areas if x = 9 is 2,365

Answer:

D.

Step-by-step explanation:

sin 67 = b / 2.4

b = 2.4 sin 67

= 2.2

cos 67 = a / 2.4

a = 2.4 cos 67

= 0.9

M < A = 90-67 = 23 degrees.

Answer:

The answer is 7,540 to the nearest tenth. If I'm wrong put it in the comments olease

The radius of the toy ball is 24.5 millimeter (to nearest tenth)

Let, r be the radius of the sphere.

Then the surface area of the sphere = \(4\pi r^{2}\) sq. unit

The structure of the toy ball is sphere.

Given, Surface area of the toy ball = 7543 square millimeter

Let, the radius be r millimeter

∴  \(4\pi r^{2}\) = 7543

⇒ \(r^{2}\) = \(\frac{7543}{4*3.14}\)  , where \(\pi\) = 3.14

⇒  \(r^{2}\) = \(\frac{7543}{12.56}\)

⇒  \(r^{2}\) = 600.56

⇒ r = \(\sqrt{600.56}\)

⇒ r = 24.5 (approx)

Radius = 24.5 millimeter (to nearest tenth)

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The steps to help him calculate his gross pay are:

1) Determine the actual number of working hours.

2) Multiply the hours worked by the hourly rate.

3) If there is overtime work, it is calculated by multiplying the overtime hours worked by the overtime wage rate.

4) Add the regular wage and the overtime wage to calculate the total wage for this wage period. 

Gross pay wages are the total amount an employee earns for the hours they work. This includes full wages before taxes and deductions. Gross wages include regular hourly wages and salaries, as well as overtime, bonuses, or reimbursements from employers.

To find the total wage, multiply the number of hours worked by the wage rate. Consider additional income, such as overtime. 1) The following steps show how gross wages are calculated for hourly wages.

1) Determine the actual number of working hours.

2) Multiply the hours worked by the hourly rate.

3) If there is overtime work, it is calculated by multiplying the overtime hours worked by the overtime wage rate.

4) Add the regular wage and the overtime wage to calculate the total wage for this wage period. 

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Answer:

mostly to measure interest rates

The correct option H0: µD ≥ 0,HA: µD < 0, is used to determine whether the first population's mean is lower than the second population's mean, a set of hypotheses.

Paired testing, commonly referred to as auditing, is a practical and easy technique to determine whether and how discrimination is present.

Thus, µD ≥ 0,HA: µD < 0, is used to determine whether the first population's mean is lower than the second population's mean, a set of hypotheses.

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Organizational culture is defined as the common beliefs, values, attitudes, customs, behaviors, and traditions that characterize a specific organization and determine the manner in which it functions. Organizational culture is set by the manager.

In a corporate or business environment, organizational culture can influence the daily operations of employees. It is the responsibility of managers to create a positive culture that emphasizes teamwork, respect, integrity, and accountability. The manager is an essential individual responsible for establishing and maintaining the organization's culture, which will ultimately define the employee's attitudes, behaviors, and productivity levels. He or she sets the tone for the workplace by creating an environment that fosters collaboration, innovation, and success. Employees need to feel connected to their workplace and colleagues to be motivated to do their best work. If a manager promotes a culture of fear, competition, or dishonesty, employees may become unmotivated or unproductive. An effective manager understands the importance of creating a positive workplace culture and works hard to establish and maintain it. Managers can establish a positive culture by encouraging open communication, providing regular feedback and recognition, fostering a sense of teamwork, creating opportunities for professional development, and setting high standards for performance. Managers must lead by example and demonstrate the behaviors and attitudes that they expect from their employees. They must hold themselves and others accountable for their actions, communicate expectations clearly, and provide support when needed. A positive organizational culture will enable an organization to attract and retain top talent, increase employee engagement, and promote collaboration and innovation.

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The given system of equations is:

5d + 20e - 10% = -85 …………………..(1)

-20d + 394e = 223 ………………...(2)

4d + 13e = -106 …………………….(3)

We can solve this system of equations using the Gaussian elimination method. In this method, we convert the system of equations into an equivalent system of equations that is easy to solve by eliminating one variable at a time.The elimination process starts by multiplying the equations so that one variable cancels out. We can do this by multiplying both sides of an equation with a constant or by adding or subtracting two equations.

Here, the first equation has a percentage sign which we need to remove.

We can do this by dividing both sides of equation (1) by

10.5d/10 + 20e/10 - 1 = -85/10

⇒ 0.5d + 2e - 1 = -8.5

⇒ 0.5d + 2e = -7.5 ……………………..(4)

Now, we can use equations (2) and (4) to eliminate d.

Multiplying equation (2) by 2 and adding it to equation (4), we get,

2(-20d + 394e = 223) + (0.5d + 2e = -7.5)

⇒ -40d + 788e + 0.5d + 2e = -7.5 + 446

⇒ -39.5d + 790e = 438 ……………………...(5)

Multiplying equation (2) by 5 and adding it to equation (3), we get,

5(-20d + 394e = 223) + (4d + 13e = -106)

⇒ -100d + 1970e + 4d + 13e = -106 + 1105

⇒ -96d + 1983e = 999 ……………………(6)

Now, we can use equations (5) and (6) to eliminate d.

Multiplying equation (5) by 2 and adding it to equation (6), we get,

2(-39.5d + 790e = 438) + (-96d + 1983e = 999)

⇒ -79d + 1563e + (-96d + 1983e) = 876 + 1998

⇒ -175d + 3546e = 2874 …………………..(7)

We can simplify equation (7) by dividing both sides by 7,-25d + 506e = 410 ……………………..(8)

Now, we can use equations (4) and (8) to solve for e.

Multiplying equation (4) by 506/4 and adding it to equation (8), we get,

506/4 × (0.5d + 2e = -7.5) + (-25d + 506e = 410)

⇒ 253d + 506e - 1895 - 25d + 506e = 410

⇒ 228d + 1012e = 2305 ……………………(9)

We can simplify equation (9) by dividing both sides by

4,57d + 253e = 576 ……………………(10)

Now, we can use equations (4) and (10) to solve for d.

Multiplying equation (4) by 57/2 and adding it to equation (10), we get,

57/2 × (0.5d + 2e = -7.5) + (57d + 253e = 576)

⇒ 28.5d + 114e - 214.125 + 57d + 253e = 576

⇒ 85.5d + 367e = 790.125 …………………….(11)

We can simplify equation (11) by dividing both sides by 17,5d + 23e = 46.4166667 …………………….(12)

Now, we can use equations (4) and (12) to solve for e.

Multiplying equation (4) by 23/2 and adding it to equation (12), we get,

23/2 × (0.5d + 2e = -7.5) + (5d + 23e = 46.4166667)

⇒ 11.5d + 46e - 86.625 + 5d + 23e = 46.4166667

⇒ 16.5d + 69e = 133.0416667 ……………………..(13)

We can simplify equation (13) by dividing both sides by 3,5.5d + 23e = 44.3472222 ……………………..(14)

Now, we can use equations (4) and (14) to solve for e.

Multiplying equation (4) by 23 and subtracting it from equation (14), we get,

23 × (0.5d + 2e = -7.5) - (5.5d + 23e = 44.3472222)

⇒ 11.5d - 48.5e = -212.0972222 ……………………..(15)

We can simplify equation (15) by dividing both sides by 1.5,7.6666667d - 32.3333333e = -141.3981481 ……………………..(16)

Now, we can use equations (4) and (16) to solve for e.

Multiplying equation (4) by 32 and adding it to equation (16), we get,

32 × (0.5d + 2e = -7.5) + (7.6666667d - 32.3333333e = -141.3981481)

⇒ 16d + 64e - 240 + 7.6666667d - 32.3333333e = -141.3981481

⇒ 23.6666667d + 31.6666667e = 98.60185185 …………………..(17)

We can simplify equation (17) by dividing both sides by 1.6666667,

14.2d + 19e = 59.1611111 ……………………..(18)

Now, we can use equations (4) and (18) to solve for e.

Multiplying equation (4) by 19 and subtracting it from equation (18), we get,

19 × (0.5d + 2e = -7.5) - (14.2d + 19e = 59.1611111)

⇒ 9.5d - 41e = -186.3111111 ……………………..(19)

We can simplify equation (19) by dividing both sides by 1.9,

5d - 21.57894737e = -98.05789474 ……………………..(20)

Now, we can use equations (4) and (20) to solve for e.

Multiplying equation (4) by 21.57894737 and adding it to equation (20), we get,

21.57894737 × (0.5d + 2e = -7.5) + (5d - 21.57894737e = -98.05789474)

⇒ 43.15789474d + 0e = -252.5263158

⇒ 43.15789474d = -252.5263158

⇒ d = -5.85416667

Substituting the value of d in equation (4), we get,

0.5d + 2e = -7.5

⇒ 0.5(-5.85416667) + 2e = -7.5

⇒ e = -6.5

Now, we have the values of d and e, and we can substitute them in any equation to get the value of the remaining variable.

We can use equation (2),

-20d + 394e = 223

⇒ -20(-5.85416667) + 394(-6.5) = 223

⇒ 117.0833334 + (-2561) = 223

⇒ -2443.916667 = 223

This is not true, which means there is no solution to this system of equations. Hence, the system is inconsistent.

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Answer:

14.28%

Step-by-step explanation:

I'm not sure if it's right but this is how I worked it out,

the box's contents are 4.2 pounds in total,

therefore in a fraction it would be 6/42

you turn a fraction into a percentage you do the numerator divided by the denominator

6÷42=0.142857(decimal form)

now you just turn it into a percentage

14.28%

please correct me if I'm wrong