14. The average time between phone calls to a company switchboard is 1 min. a) Simulate this situation by generating random arrival times for an 8-h business day. Group the waiting times in intervals

Answer:

1.4 meters

Step-by-step explanation:

A building is 52 meters tall. The building next to it is 50.36 meters tall. The difference between the heights of the buildings is 2.36 meters.

The difference is defined as the maximum value minus the minimum value.

A building is 52 meters tall. The building next to it is 50.36 meters tall.

The tallest building = 52

The next building = 50.36

The difference

= 52 - 50.36

= 2.36

Therefore, the difference between the heights of the buildings is 2.36 meters.

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The solution of the system of equations using Cramer's rule is x = 37/39 and y = 9/39.

The solution of the system of equations using Cramer's rule is calculated as follows;

The given equations are as follows;

9x - 2y = -9

-3x - 8y = 1

The determinant of the coefficient matrix is calculated as;

D = [9      -2]

      [-3     -8]

D = -8(9) - (-3 x - 2)

D = -72 - 6 = -78

The x coefficient is calculated as;

Dx = [-2      -9]

       [ -8       1]

Dx = -2(1) - (-8 x -9)

Dx = -2 - 72 = -74

The y coefficient is calculated as;

Dy = [9      -9]

       [ -3       1]

Dy = 9(1) - (-3 x -9)

Dy = 9 - 27 = -18

The x and y values is calculated as;

x = Dx/D  = -74/-78 = 74/78 = 37/39

y = Dy/D = -18/-78 = 18/78 = 9/39

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The measurement of responses that span from 1 to seven is an example of ratio scale or measure so, the statement is True.

A ratio scale is a form of measurement that records the intervals between a series of measurements. The measurements starts from a true zero and proceeds to quantities with equal measurements.

The description of a ratio scale is as described in the researcher's results where respondents can give responses between 0 and 7 days. So, the statement above is true.

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Answer:

x = 2.5

Step-by-step explanation:

4(x + 7) = 38

4x+28 = 38

4x = 10

x = 2.5

Opportunity cost is the price of giving up an option. An opportunity cost is the price you pay for selecting a particular option over another. Opportunity cost is the benefits you lose by choosing one alternative over another one.”

The value of the next-highest-valued alternative use of a resource is what economists mean when they talk about its "opportunity cost." You cannot, for instance, read a book at home during the time you would have spent seeing a movie and spend the money you would have spent on something else.

Opportunity cost is frequently referred to as the second-best option. The loss of benefit that would have been realized if a different option had been taken is sometimes referred to as the alternative cost. The loss of advantage as a result of a change in decision is another way to explain it.

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Answer:

Step-by-step explanation:

a). 3 ...... 8

3 × 8 = 24

3 + 8 = 11

b). n + 1.5 = 6.5 ⇒ n = 5 (across from OR to the left from 1.5)

5 × 1.5 = 7.5 (under the X sign)

Answer:

B

Step-by-step explanation:

50+55+48+50+52=255

255/5=51

Anwser 51

Answer:

x = 10.8

Step-by-step explanation:

9 ÷ x = x ÷ (9 + 4)

9 × (9 + 4) = x × x

9 × 13 = x²

117 = x²

x = 10.81665383

Solution:

The volume of a cylinder is expressed as

Given the cylindrical water tank below:

where

By substitution, we have

Hence, the volume of the cylindrical water tank, to the nearest whole number, is

Answer:

10/8 or 5/4

Step-by-step explanation:

It is pretty easy. If you look at the problem it says "1/8 of a gram of honey to make 1/10 of a cake" That means that we should multiply 1/8 by 10 so it will become a whole cake.

1/8 * 10 = 10/8

If you want we can simplify it.

5/4

And that's your answer!

Answer:

252

Step-by-step explanation:

He earns 2522 for 18 hours of work.

\( \longrightarrow f( \rm x) = (x - 4)(x + 4)\)

\( \\ \\ \)

\( \longrightarrow f( \rm x) = {(x)}^{2} - {(4)}^{2} \)

\( \\ \\ \)

\( \longrightarrow f( \rm x) = {x}^{2} - 16\)

Formula used = (a + b) (a - b) = a² - b²

The parametric representation for the surface is x = -sqrt(1 - 2t^2 - 3s^2), y = sqrt(1 - 2t^2 - 3s^2)/sqrt(2), z = s, where t and s range over appropriate intervals.

To find the parametric representation for the surface, we can use the parameterization method. Since we want the part of the ellipsoid that lies to the left of the xz plane, we can set the x-coordinate as negative. We can parameterize the surface using two parameters, t and s.

Start with the equation of the ellipsoid: x^2 + 2y^2 + 3z^2 = 1.

Since we want the part of the ellipsoid to the left of the xz plane, we set x as negative. Thus, x = -sqrt(1 - 2t^2 - 3s^2).

To determine the values of y and z, we need to rearrange the equation of the ellipsoid and solve for y and z in terms of t and s.

Rearranging, we have 2y^2 + 3z^2 = 1 - x^2.

Substitute the value of x from step 2 into the equation above:

2y^2 + 3z^2 = 1 - (-sqrt(1 - 2t^2 - 3s^2))^2.

Simplifying, we get 2y^2 + 3z^2 = 1 - (1 - 2t^2 - 3s^2).

This simplifies to 2y^2 + 3z^2 = 2t^2 + 3s^2.

Divide both sides of the equation by 2 to get y^2 + (3/2)z^2 = t^2 + (3/2)s^2.

We can rewrite this as y^2 = t^2 + (3/2)s^2 - (3/2)z^2.

Taking the square root of both sides, we have y = sqrt(t^2 + (3/2)s^2 - (3/2)z^2).

Since we want the positive part of the ellipsoid, we can simplify this to y = sqrt(1 - 2t^2 - 3s^2)/sqrt(2).

Finally, the parametric representation for the surface is:

x = -sqrt(1 - 2t^2 - 3s^2),

y = sqrt(1 - 2t^2 - 3s^2)/sqrt(2),

z = s,

where t and s range over appropriate intervals.

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The electric field at point P due to the charges q and -q is zero. Option (iv) None of the above is the correct answer.

The electric field a distance y above the midpoint between two equal and opposite charges, q and −q, that are a distance d apart as shown in Fig. 1 above can be found as follows:

Since, the distance between the charges is d, the distance from the midpoint to either of the charges would be d/2. According to the principle of superposition, the electric field due to the two charges would be the vector sum of the electric fields due to the charges q and -q at point P. Let's consider the electric field due to the charge q at point P and the electric field due to the charge -q at point P.

Electric field due to the charge q: Using Coulomb's law, we can write the electric field due to the charge q at point P as:

E1 = kq/r1²,

where k is Coulomb's constant, q is the charge, and r1 is the distance between the charge q and point P.

The distance r1 can be calculated as:

r1 = [(d/2)² + y²]^1/2

Since the electric field is a vector quantity, we can represent it in terms of unit vector i as follows:

E1 ˉ= kq/[(d/2)² + y²]^1/2 iˉ

Electric field due to the charge -q:

Similarly, the electric field due to the charge -q at point P can be written as:

E2 ˉ= - kq/[(d/2)² + y²]^1/2 iˉ (because the charge is negative)

Therefore, the net electric field at point P can be obtained by taking the vector sum of the electric fields due to the two charges:

E ˉ= E1 ˉ + E2 ˉ= [kq/[(d/2)² + y²]^1/2 - kq/[(d/2)² + y²]^1/2] iˉ= 0

Thus, the electric field at point P due to the charges q and -q is zero. Option (iv) None of the above is the correct answer.

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Answer:

1/28

Step-by-step explanation:

1/4 divided by 7 is 1/28

4x7 is 1/28

Answer:

4 children per counselor

Step-by-step explanation:

Since the question is asking children per counselor, divide the children/counselor. Check all of the rows by dividing the children by counselor to make sure the constant of proportionality is correct. If you divide correctly, the constant of proportionality you get is 4.

Hope it helps!

Answer:

there is 4 students per conceler.

Step-by-step explanation:

please mark as brainllist.

Answer:

4021.2386 cm ^3

Step-by-step explanation:

V = πr2h = π·82·20 = 4021.2386 cm ^3

Answer:

$151

Step-by-step explanation:

225 = 74 + m

- subtract 74 from both sides

225-74 = 74-74 +m

1. 151 = 74 - 74 + m

2. 151 = 0 + m

the 0 is irrelevant so you can remove it and you get

151 = m

the correct way to write it would be:

m = 151

Answer:

150 ________//_/___________///////

Answer:

multiply 0.05 by amount of grid cubes!

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Let us now calculate the cube root of 2197 by using the estimation method in a step-by-step manner.

1. Consider the digit given at the unit’s place of 2197. The unit place 2197 has 7.

2. Look at the cubes table given above. In the cube table, check the cube of which number has digit 7 at the unit’s place.

Clearly, we can see 3³ = 27.

It implies that the unit digit of the cube root of 2197 is 3.

3. Now to calculate the tenth place of the cube root of 2197, we will overlook the last 3 digits of 2197, i.e., 197. Considering 2 as a benchmark figure, we can see that the digit 2 falls between 1³ and 2³, i.e., between 1 and 8. Here, we will consider the lowest numbers closest to 2

which is 1. As 1³ = 1. Hence, the tenth place of the cube root of 2197

is 1. Hence, the cube root of 2197 is 13.

Cube Root of 2197 by Prime Factorization Method

Here, we will discuss about the prime factorization method to determine the prime factors of 2197. After determining the prime

factors of 2197, we will pair the factors in a group of three and write them as cubes. As the cubes of a number neutralise the cube root, we will get the desired value. Now let us learn how to find the cube root of 2197 by the prime factorization method in a step-by-step manner.

1. Calculate the prime factors of 2197.

If we try to divide 2197 by any prime number, we will find

that the smallest prime factor which can divide 2197 is

13. Hence, we get

2197 = 13 * 13 * 13

2. Now pair the factors in a group of 3 and express them in the

form of cubes.

2197 = (13) = 13³ (As we know exponent law: a x × a y =

a x + y )

3. Now apply cube root to both left and right sides of the above

expression.

=

The cube root gets neutralised by the cube of 13.

Hence, the cube root of 2197 is 13.

i prefer FACTORIZATION METHOD

I HOPE THIS HELPED

Answer:

x = 26

Step-by-step explanation:

it is a right angle so

(x+4)3=90

3x+12=90

-12         -12

3x = 90-12

3x = 78

/3       /3

x = 26

400 cupcakes in total

200 would be vanilla

so 100 would be chocolate and the remaining 100 should be funfetti

A: 100

The mean absolute deviation (MAD) and mean absolute percent error (MAPE) are both measures used to assess the accuracy or variability of a dataset. However, they differ in terms of the type of data they analyze and the way they express the deviation.

Mean Absolute Deviation (MAD):

MAD measures the average absolute difference between each data point and the mean of the dataset.

It provides information about the dispersion or spread of the data.

MAD is calculated by taking the absolute value of the differences between each data point and the mean, summing these values, and then dividing by the total number of data points.

MAD is expressed in the same units as the original data.

Mean Absolute Percent Error (MAPE):

MAPE measures the average percentage difference between each data point and its corresponding value in a reference dataset (often a forecast or predicted value).

It provides information about the relative error or accuracy of a model or prediction.

MAPE is calculated by taking the absolute value of the percentage difference between each data point and its corresponding reference value, summing these values, and then dividing by the total number of data points.

MAPE is expressed as a percentage.

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Answer:

44 °

Step-by-step explanation:

In a right triangle such as this

  sin B = opposite leg / hypotenuse

  sin B =   20 / 29

   B = arcsin (20/29) = 44 degrees

The derivative of \( \(e^x \) with respect to \( y \) is 0, and the derivative of \( \tan(y) \) with respect to \( y \) is \( \sec^2(y) \). Therefore, we have:\( f_{xy}(x, y) = 0 \).\\\)
To find the second partial derivatives of the function \(\( f(x, y) = e^x \tan(y) \),\)we need to take the partial derivatives twice with respect to each variable. Let's start with the first partial derivatives:

\(\( f_x(x, y) = \frac{\partial}{\partial x} (e^x \tan(y)) \)\)

Using the product rule, we have:

\(\( f_x(x, y) = \frac{\partial}{\partial x} (e^x) \tan(y) + e^x \frac{\partial}{\partial x} (\tan(y)) \)The derivative of \( e^x \) with respect to \( x \) is simply \( e^x \), and the derivative of \( \tan(y) \) with respect to \( x \) is 0 since \( y \) does not depend on \( x \). Therefore, we have:\)
\(\( f_x(x, y) = e^x \tan(y) \)Now let's find the second partial derivative \( f_{xx}(x, y) \) by taking the derivative of \( f_x(x, y) \) with respect to \( x \):\( f_{xx}(x, y) = \frac{\partial}{\partial x} (e^x \tan(y)) \)Again, the derivative of \( e^x \) with respect to \( x \) is \( e^x \), and the derivative of \( \tan(y) \) with respect to \( x \) is 0. Therefore, we have:\\\)
\(\( f_{xx}(x, y) = e^x \tan(y) \)Now let's find the second partial derivative \( f_{yy}(x, y) \) by taking the derivative of \( f_x(x, y) \) with respect to \( y \):\( f_{yy}(x, y) = \frac{\partial}{\partial y} (e^x \tan(y)) \)\\\)

\(The derivative of \( e^x \) with respect to \( y \) is 0 since \( x \) does not depend on \( y \), and the derivative of \( \tan(y) \) with respect to \( y \) is \( \sec^2(y) \). Therefore, we have:\( f_{yy}(x, y) = e^x \sec^2(y) \)Finally, let's find the mixed partial derivative \( f_{xy}(x, y) \) by taking the derivative of \( f_x(x, y) \) with respect to \( y \):\\\)
\(\( f_{xy}(x, y) = \frac{\partial}{\partial y} (e^x \tan(y)) \)The derivative of \( e^x \) with respect to \( y \) is 0, and the derivative of \( \tan(y) \) with respect to \( y \) is \( \sec^2(y) \). Therefore, we have:\( f_{xy}(x, y) = 0 \)To summarize, the second partial derivatives of \( f(x, y) = e^x \tan(y) \) are:\)

\(\( f_{xx}(x, y) = e^x \tan(y) \)\( f_{yy}(x, y) = e^x \sec^2(y) \)\( f_{xy}(x, y) = 0 \)\\\)
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Answer:

C =62.8 mm

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi *r

C = 2 * 3.14* 10

C =62.8 mm

Using it's concept, the scatter plot that accurately reflects the data given in the problem is scatter plot D.

A scatter plot is a graph that maps each input in the data-set to it's respective output, as points.

Considering this concept, an age of 12(x - axis) should be mapped to a time in minutes of 23(y-axis), and so on, until an age of 71 is mapped to a time of 33 minutes, which happens in option D.

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"The remainder when n is divided by 9 is 45." Let n be the number whose digits add up to 135. For the sum of the digits to be 135.

We need to have a nine in the thousands place (or greater), because a maximum of 8 × 9 = 72 can be made from the other digits. Since n contains the digit 9, its remainder upon division by 9 is the same as the remainder when the sum of its digits is divided by 9.

Because the digits sum to 135, the remainder when n is divided by 9 is the same as the remainder when 135 is divided by 9, which is 0. Thus, the remainder when n is divided by 9 is 0.If the main answer to the problem is x, then, we have x = 135 + 0

= 135. Hence, the remainder when n is divided by 9 is 45.

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