Given a frequency distribution of 10,000 scores, which approximates the normal curve and has a mean of 120 and a standard deviation of 15, what percentage of those tested scored 135 or below

By the demand equation for a certain commodity, the price at which there is unitary elasticity is approximately $78.18 per unit

To find the price at which there is unitary elasticity, we need to determine the price (p) when the elasticity of demand is equal to 1.

The elasticity of demand can be calculated using the formula:

E = (dq/dp) x (p/q)

Given the demand equation: 550p + q = 86,000, we can solve for q in terms of p:

q = 86,000 - 550p

Now, we differentiate q with respect to p to find dq/dp:

dq/dp = -550

Substituting these values into the elasticity formula:

1 = (-550) x (p / (86,000 - 550p))

Simplifying the equation:

p = (86,000 - 550p) / 550

Multiplying both sides by 550 to eliminate the denominator:

550p = 86,000 - 550p

Combining like terms:

1100p = 86,000

Dividing both sides by 1100:

p = 78.18

Therefore, the price at which there is unitary elasticity is approximately $78.18 per unit (rounded to two decimal places).

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8.) The volume of the rectangular prism would be =3,744ft³

9.) The volume of the triangular prism would be = 475.2mm³

For question 8.)

The formula for the volume of a rectangular prism = length×width×height

Where;

length = 39ft

width = 8ft

height = 12 ft

Volume = 39×8×12 = 3,744ft³

For question 9)

The formula for the volume of a triangular prism = 1/2blh

where;

base = 11mm

length = 16mm

height = 5.4 mm

volume = 1/2× 11×16×5.4

= 475.2mm³

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Answer:

C

Step-by-step explanation:

Personal values can have a significant impact on the success of the census. When individuals hold values such as civic duty, privacy, and trust, they are more likely to participate in the census accurately and honestly.

These values contribute to a higher response rate and more reliable data, which is crucial for effective planning, resource allocation, and decision-making.

Conversely, if personal values, such as distrust of the government or concerns about privacy, discourage participation, it can lead to undercounting and incomplete data. Therefore, understanding and addressing individuals' values and concerns are important in ensuring the success and accuracy of the census.

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Answer:Mathematics is the science that deals with the logic of shape, quantity and arrangement. Math is all around us, in everything we do. ... The needs of math arose based on the wants of society. The more complex a society, the more complex the mathematical needs.

Step-by-step explanation:

Answer:

Cheyenne can only buy 4 snacks for 1 week, and Ahmed can buy 14 snacks for 1 week

Step-by-step explanation:

12/3 =4

7/0.50=14

Hope this helped! if not Please tell me! :)

The matching sets for the given orbitals are as follows:

A. 3, 2, -1

C. 5, 1, -1

G. 4, 0, -1

H. 3, 2, 3

In quantum mechanics, each electron in an atom is described by a set of quantum numbers that provide information about its energy level, orbital shape, and orientation. The quantum numbers include the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (ml).

For the given orbitals, we need to match the orbital names with the sets of quantum numbers. Let's go through each option:

A. The quantum numbers 3, 2, -1 correspond to the orbital name 3dxy. The principal quantum number (n) is 3, the azimuthal quantum number (l) is 2, and the magnetic quantum number (ml) is -1. This describes a d orbital in the xy plane.

C. The quantum numbers 5, 1, -1 correspond to the orbital name 5py. The principal quantum number (n) is 5, the azimuthal quantum number (l) is 1, and the magnetic quantum number (ml) is -1. This describes a p orbital oriented along the y-axis.

G. The quantum numbers 4, 0, -1 correspond to the orbital name 4pz. The principal quantum number (n) is 4, the azimuthal quantum number (l) is 0, and the magnetic quantum number (ml) is -1. This describes a p orbital oriented along the z-axis.

H. The quantum numbers 3, 2, 3 correspond to the orbital name 3dxyz. The principal quantum number (n) is 3, the azimuthal quantum number (l) is 2, and the magnetic quantum number (ml) is 3. This describes a d orbital with complex orientation in space.

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Answer:

Ans = (1.50 x 29 movies) + 16

Step-by-step explanation:

y represents total costs

x represents how many movie he rents

$1.50 is the rent of each movie

$16 is the fixed fee

thus

y = 1.50 x + 16

Ans = (1.50 x 29 movies) + 16

Answer:

Step-by-step explanation:  -73.73 D, If its not and its like A,B, or C and one of them is -73.73 its still going to be correct

Answer:

Explanation:

Given the below functions;

a) We're to find f(g(x)).

To do this, we need to substitute x in f(x) with g(x) as shown below;

b) To find g(f(x)), we need to substitute x in g(x) with f(x);

c) Since f(g(x)) = g(f(x)) = x, therefore f and g are inverses of each other.

Yes, f and g are inverses of each other.

So to

Answer:

1 – cos²x = Sin²x

Step-by-step explanation:

Sinx + 1 = cos x

by squaring both sides

(Sinx + 1)² = (cos x )²

Sin²x + 1 = cos²x

1 – cos²x = Sin²x

i hope this helped

The difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

According to the given question.

We have a function

f(x) = -1/(5x -12)

As we know that, the difference quotient is a measure of the average rate of change of the function over and interval.

The difference quotient formula of the function y = f(x) is

[f(x + h) - f(x)]/h

Where,

f(x + h) is obtained by replacing x by x + h in f(x)

f(x) is a actual function.

Therefore, the difference quotient formual for the given function f(x)

= [f(x + h) - f(x)]/h

= \(\frac{\frac{-1}{5(x+h)-12} -\frac{-1}{5x-12} }{h}\)

= \(\frac{\frac{-1}{5x + 5h -12}+\frac{1}{5x-12} }{h}\)

= \(\frac{\frac{-1+5h}{5x + 5h-12} }{h}\)

= \(\frac{-1+5h}{(5x +h-12)(h)}\)

= \(\frac{-1+5h}{5xh + h^{2} -12h}\)

= \(\frac{h(-\frac{1}{h}+5) }{h(5x+h-12)}\)

= \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\)

Hence, the difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

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The equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

To determine the solutions to the equation log₂(x - 1) = x³ - 4x, we can set the two expressions equal to each other:

log₂(x - 1) = x³ - 4x

Since we know that the graphs of the two functions intersect at the points (2, 0) and (1.1187, -3.075), we can substitute these values into the equation to find the solutions.

For the point (2, 0):

log₂(2 - 1) = 2³ - 4(2)

log₂(1) = 8 - 8

0 = 0

The equation holds true for the point (2, 0), so (2, 0) is one solution.

For the point (1.1187, -3.075):

log₂(1.1187 - 1) = (1.1187)³ - 4(1.1187)

log₂(0.1187) = 1.4013 - 4.4748

-3.075 = -3.0735 (approx.)

The equation is not satisfied for the point (1.1187, -3.075), so (1.1187, -3.075) is not a solution.

Therefore, the equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

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Answer:

Step-by-step explanation:

The probability that the florist will sell equal or less than 12 bunches of flowers in an hour is approximately 0.4332.

In probability theory, the number of customers who purchase bunches of flowers in an hour can be modeled using a normal distribution. Given that the population mean is 15 bunches of flowers per hour and the population variance is 4, we can calculate the probability using the z-score.

To find the probability of selling equal or less than 12 bunches, we need to standardize the value using the z-score formula: z = (x - μ) / σ, where x is the given value (12), μ is the mean (15), and σ is the standard deviation (sqrt(variance)).

Calculating the z-score: z = (12 - 15) / sqrt(4) = -1.5

Using a standard normal distribution table or a statistical calculator, we can find the cumulative probability associated with a z-score of -1.5. The probability is approximately 0.0668.

However, since we are interested in the probability of equal or less than 12 bunches, we need to subtract this probability from 0.5 (the total area under the curve). Thus, the probability that the florist will sell equal or less than 12 bunches of flowers in an hour is approximately 0.5 - 0.0668 = 0.4332.

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Answer:

7a^4 - 60a^3 - 8a^2 + 60a + 25

Step-by-step explanation:

(a² - 8a -5) x (7a² - 4a- 5)

= 7a^4 - 4a^3 - 5a^2 - 56a^3 + 32a^2 + 40a - 35a^2 + 20a + 25

= 7a^4 - 60a^3 - 8a^2 + 60a + 25

So, the answer is

7a^4 - 60a^3 - 8a^2 + 60a + 25

The focal distance, f, for the mirror is -10 cm. Option b) is the correct answer.

A concave mirror is a mirror that reflects light and makes an inverted image of the object being reflected. In a concave mirror, the reflecting surface is curved inward, and when light rays fall on it, they converge to a point on the other side of the mirror known as the focal distance or focal point.

The center of curvature (C) is the middle point of a spherical mirror. It's the middle of the imaginary circle that you'd form if you continued the surface of the mirror around until it was a complete circle. The center of curvature is twice the distance from the mirror's surface to the center point of the mirror.

The following formula can be used to calculate the focal distance of a concave mirror:1/f=1/v+1/u where, f is the focal distance v is the image distance u is the object distance. The radius of the mirror is half the distance from the center of curvature.

The radius, in this case, is 20cm. Therefore, C= 2R= 2 x 20 = 40 cm and, f = C / 2f = 40 / 2f = 20 cm. When the image is formed behind the mirror, the value is negative. Therefore, the value is -20 cm. The answer to the question, therefore, is -10 cm.

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The taller of the two boys is Ben if Marcus is 5 7 /24 feet tall and Ben is 5 13/ 16 feet tall.

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

This means that

Marcus = 5 7 /24 feet tall

Ben = 5 13/ 16 feet tall.

Express the heights as decimals

So, we have

Marcus = 5.292 feet tall

Ben = 5.8125 feet tall.

When the above values are compared, we have

5.8125 feet tall > 5.292 feet tall

Hence, the taller of the two boys is Ben

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The net of a triangular prism consists of two triangles and three rectangles.

In the net of a triangular prism, we can observe two types of polygons: triangles and rectangles.

First, let's discuss the triangles.

A triangular prism has two triangular faces, which are congruent to each other.

These triangles are equilateral triangles, meaning they have three equal sides and three equal angles.

Each of these triangles contributes two polygons to the net, one for each face.

Next, we have the rectangles.

A triangular prism has three rectangular faces that connect the corresponding sides of the triangular bases.

These rectangles have opposite sides that are parallel and equal in length.

Each rectangle contributes one polygon to the net, resulting in a total of three rectangles.

To summarize, the net of a triangular prism consists of two equilateral triangles and three rectangles.

The triangles represent the bases of the prism, while the rectangles form the lateral faces connecting the bases.

Altogether, there are five polygons in the net of a triangular prism.

It's important to note that the dimensions of the polygons may vary depending on the specific size and proportions of the triangular prism, but the basic shape and number of polygons remain the same.

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Answer:

You make a table rounding up the times a card was drawn, then find the median. To find the median, find the middle number or the one that appears the most.

Answer:

The square root of 144 will be 12

Answer:

12 is the answer

Step-by-step explanation:

12x12=144

Answer: 5 and 12

Step-by-step explanation:

i did the quiz

Answer:

52 miles per hour

Step-by-step explanation:

I think you're missing some info, so this is all I can help with right now

Answer:

Answer is 21

Step-by-step explanation:

if you multiply 5 x 4=20 and + 1 is 21

The length of the whole field will be 400 while the width will be 200 meters.

Perimeter is the addition of an external measure of sides it will always positive.

Perimeter of square = side + side + side + side

The perimeter of the circle = πd where d is the dia of the circle.

As per the given three equal areas have been drawn,

The perimeter of this area will be as,

2x + 4y = 1600

Area A = xy

A = x(1600 - 2x)/4

A = 400x - 1/2x²

To find the maximum area take the first derivative,

dA/dx = =0

400(1) - (1/2)2x = 0

400 - x = 0

x = 400 meter

And, 4y = 1600 - 2(400)

y = 800/4 = 200 meter

Hence " The length of the whole field will be 400 while the width will be 200 meters".

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Answer:

y ≥ 3x - 1

y < \(-\frac{1}{2}x+2\)

Step-by-step explanation:

Let the equation of the solid line passing through (x', y') given in graph is,

y = mx + b

Here m = slope of the line

b = y-intercept

Slope of the solid line =

                                 m = \(\frac{3}{1}\)

                                 m = 3

y - intercept 'b' = -1

Therefore, equation of the line will be,

y = 3x - 1

Since, shaded (blue) area is above the line, inequality that will represent the solution area will be,

y ≥ 3x - 1

For the dotted line,

Slope of the line (m) = \(\frac{\text{Rise}}{\text{Run}}\)

                                  = \(\frac{-2}{4}\)

                                  = \(-\frac{1}{2}\)

y-intercept (b) = 2

Equation of the dotted line → y = \(-\frac{1}{2}x+2\)

Since, shaded (grey color) area is below the dotted line,

Inequality representing the solution area will be,

y < \(-\frac{1}{2}x+2\)

The mean/standard error of the sampling distribution of the proportion is 0.0111.

Its root-mean The square root of the mean of the squares of all the values in a series calculated from the arithmetic mean is the square deviation, also referred to as the standard deviation and denoted by the symbol.

The standard deviation reveals the degree of data dispersion. It expresses how far away from the mean each observed value is.

Almost 95% of the values in any distribution will be within two standard deviations of the mean. The degree of data dispersion from the mean is described by the term "standard deviation" (or " σ").

The data tend to cluster around the mean when the standard deviation is low; when it is high, the data are more dispersed.

The formula to calculate the standard error of sampling distribution of sample proportion is:

\($ SE(p) =\sqrt{\frac{p(1-p)}{n} }\)

It is given that the bank believes that 8% of people who receive loans will not make payments on time. That is,

Population proportion, p =0.08

Sample size, n= 800

Using the formula defined :

\($ SE(p) =\sqrt{\frac{0.08(1-0.08)}{600} }\)

\($ SE(p) =\sqrt{0.000123}\)

SE(p) = 0.0111

Thus, the mean/standard error of sampling distribution of the proportion is 0.0111.

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The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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Answer:

$6

Step-by-step explanation:

the fixed cost = $13

the variable cost is unknown. It depends on the rounds played. according to the question the additional rounds played is 5 (6 - 1) .Represent the variable cost with x

the next equation can be formed using variables from the question :

$43 = $13 + 5x

collect like terms

$43 - $13 = 5x

$30 = 5x

divide both sides of the equation by 5

x = $6

The probability of drawing 2 green balls simultaneously from a bag containing 2 yellow and 4 green balls can be determined using the following method:

First, calculate the total number of balls in the bag. There are 2 yellow balls and 4 green balls, so the total is 6 balls.

Now, let's find the probability of drawing 2 green balls. To do this, consider the number of green balls (4) and the total number of balls (6). When drawing the first green ball, there are 4 green balls out of 6 total balls. Therefore, the probability of drawing one green ball is 4/6.

Since the balls are drawn simultaneously, there's no change in the number of balls for the second draw. So, the probability of drawing a second green ball remains 4/6.

Now, we can calculate the probability of both events occurring simultaneously by multiplying the probabilities:

(4/6) * (4/6) = 16/36

To simplify the fraction, divide both numerator and denominator by their greatest common divisor (4):

16/36 = 4/9

So, the probability of drawing 2 green balls simultaneously is 4/9.

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