During filming, an IMAX camera uses 65-mm film at a rate
of 5.6 ft/s.

a. At what rate per minute does the camera go through film?

b. How quickly does the camera use a 500-foot roll of 65-mm film? Round to the
nearest second.

The total number of employees is 112.

Explain numbers

Numbers are symbols or representations used to quantify or count objects, quantities, or measurements. They form the basis of mathematical operations, such as addition, subtraction, multiplication, and division, and are used in various fields such as science, finance, and engineering. Numbers can be positive, negative, whole, or fractional, and are essential for communication and calculation in our daily lives.

According to the given information

Let's use x to represent the total number of employees.

According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that out of every 4 + 5 = 9 employee, 4 are union members and 5 are nonunion members.

So, we can set up the following proportion:

4/9 = x/(x - 140)

To solve for x, we can cross-multiply and simplify:

4(x - 140) = 9x

4x - 560 = 9x

560 = 5x

x = 112

Therefore, the total number of employees is 112.

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Answer: 104%

Step-by-step explanation: 26% times 4 years

The correct answer is: Decrease total assets and net income.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

The recognition of uncollectible accounts expense for Year 2 will decrease total assets and net income.

When uncollectible accounts expense is recognized, it is recorded as a debit to the allowance for doubtful accounts and a credit to the uncollectible accounts expense account. This reduces the balance of accounts receivable, which is a current asset, and thus decreases total assets. Additionally, recognizing this expense reduces net income by the same amount.

Therefore, the correct answer is: Decrease total assets and net income.

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Answer:

28°

Step-by-step explanation:

If the angles are supplementary, they add up to 180°.

(3x) + (2x + 40) = 180

5x + 40 = 180

     - 40   - 40

5x = 140

x = 28°

The equation of the function g(x) is g(x) = 1/2x²

If we want to stretch or compress the function f(x) = x^2, we can multiply or divide the input variable x by a constant value a.

Specifically, if we use g(x) = f(ax), then g(x) is a stretched or compressed version of f(x).

To find the value of a that will make g(x) pass through the point (2,2), we can substitute these values into the equation g(x) = f(ax):

[tex]g(2)=f(a*2)=f(2a)=(2a)^2 =4a^2 =2[/tex]

So, we have

a = 1/2

Recall that

g(x) = f(ax)

So, we have

g(x) = f(1/2x)

This means that

g(x) = 1/2x²

Hence. the function is g(x) = 1/2x²

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The log-likelihood function is l(σ) = -n*log(2σ) - sum(|[tex]x_i[/tex]|)/σ.

the moment estimate of σ is σ = 0.

A moment is a quantitative measure of the shape of a probability distribution. Specifically, it is a mathematical calculation that involves taking the product of the distribution's values and certain pre-determined values (such as powers of the variable). Moments are often used to estimate certain parameters of a distribution, such as its mean, variance, or skewness.

Moment estimate of σ:

The kth moment about the origin is defined as E[[tex]X^k[/tex]] = integral from -inf to inf of [tex]x^k[/tex] * f(x) dx.

The first moment about the origin is E[X] = integral from -inf to inf of x * f(x) dx.

E[X] = integral from -inf to inf of x * (1/2σ*[tex]e^{(-|x|/\sigma))[/tex] dx

Let's split the integral into two parts: from -inf to 0 and from 0 to inf.

integral from -inf to 0 of x * (1/2σ[tex]e^{(-|x|/\sigma))[/tex]dx = integral from -inf to 0 of -x * (1/2σ[tex]e^{(-|x|/\sigma))[/tex] dx = 1/2σ * integral from 0 to inf of x * [tex]e^{(-x/\sigma)[/tex] dx

integral from 0 to inf of x * e^(-x/σ) dx is the definition of the gamma function with shape parameter 2 and scale parameter σ, which is Γ(2, σ) = 1 * σ² = σ².

Therefore, E[X] = 1/2σ * σ² = σ/2.

The second moment about the origin is E[X²] = integral from -inf to inf of x² * (1/2σ*[tex]e^{(-|x|/\sigma))[/tex] dx.

E[X²] = 1/2σ * integral from -inf to inf of x² * [tex]e^{(-|x|/\sigma))[/tex] dx

Let's split the integral into two parts: from -inf to 0 and from 0 to inf.

integral from -inf to 0 of x² * (1/2σ [tex]e^{(-|x|/\sigma))[/tex]  dx = integral from -inf to 0 of x² * (1/2σ[tex]e^{(x/\sigma)[/tex]) dx = 1/2σ * integral from 0 to inf of x² * [tex]e^{(-x/\sigma)[/tex] dx

integral from 0 to inf of x² * [tex]e^{(x/\sigma)[/tex]) dx is the definition of the gamma function with shape parameter 3 and scale parameter σ, which is Γ(3, σ) = 2 * σ³.

Therefore, E[X²] = 1/2σ * 2σ³ = σ².

The moment estimate of σ is obtained by solving the equation E[X²] = σ² for σ:

σ² = E[X²] = integral from -inf to inf of x² * (1/2σ*[tex]e^{(-|x|/\sigma)[/tex]) dx

= 1/2σ * integral from -inf to inf of x² * [tex]e^{(-|x|/\sigma)[/tex] dx

= 1/2σ * 2σ³

= σ²

Simplifying the equation, we get:

σ² = σ²/2

Multiplying both sides by 2, we get:

2σ² = σ²

Therefore, the moment estimate of σ is σ = 0.

MLE of σ:

The likelihood function is given by L(σ) = (1/2σ)ⁿ *[tex]e^{(-sum(|x_i|)/\sigma)[/tex], where n is the sample size and [tex]x_i[/tex]are the observed values.

The log-likelihood function is l(σ) = -n*log(2σ) - sum(|[tex]x_i[/tex]|)/σ.

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The equation of the circle is (x - 1/2)^2 + y^2 = 15/4.

The equation of a circle with center (a,b) and radius r is given by the equation:

(x - a)^2 + (y - b)^2 = r^2

Using the given values, the equation of the circle with center (1/2, 0) and radius 2 is:

(x - 1/2)^2 + (y - 0)^2 = 2^2

Expanding and simplifying, we get:

(x - 1/2)^2 + y^2 = 4 - 1/4

Therefore, the equation of the circle is:

(x - 1/2)^2 + y^2 = 15/4

So, the equation of the circle is (x - 1/2)^2 + y^2 = 15/4.

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Angle A equals 41.81°

c:

Using division we know that per pound the loose sweets have a better value which is £0.0089 per pound.

The division is one of the four basic arithmetic operations or the process by which two numbers are added together to produce a new number.

Multiplication, addition, and subtraction make up the remaining operations.

We may examine the quotient and the division's remainder using the division formula Dividend = (Divisor Quotient) + Remainder.

We can multiply our quotient by the divisor to check its accuracy if the remainder is 0.

If the product and dividend are equal, the quotient is correct.

So, the price per gram when pre-packed:

1.49/120 = £0.012

Now, the price per gram when the product is loose:

0.89/100 = £0.0089

Now, we know that per pound the loose sweets are better.

Therefore, using division we know that per pound the loose sweets have a better value which is £0.0089 per pound.

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To respond to the question, we must identify the m-values for which V(m)  equation decreases. The value of the card decreased during the course of the time from January 2020 to July 2020 (about 7 months),

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

We must identify the values of m for which the function V(m) is dropping in order to estimate the time span during which the value of the card was declining.

The function V(m)'s derivative is provided by:

V'(m) = 500m - 3,500

By setting V'(m) = 0 and solving for m, we may determine the crucial point(s):

500m - 3,500 = 0

m = 7

V''(m) = 500

To respond to the question, we must identify the m-values for which V(m) decreases. The value of the card decreased during the course of the time from January 2020 to July 2020 (about 7 months), as we know that V(m) is falling for m 7.

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Answer:

The given expression is:

m/T = 0(9x-17) / (T(4x + 28)S R)

Since the numerator is multiplied by 0, the entire expression becomes 0, regardless of the value of the denominator. Division by 0 is undefined in mathematics, as it is not a valid operation. Therefore, the result of m/T in this case is undefined.

You can double check urself ;D

Answer:

To estimate the difference, we need to round each number to the nearest whole number and then subtract the rounded numbers.

Rounding each number to the nearest whole number, we get:

10 rounded to the nearest whole number is 10

19 rounded to the nearest whole number is 19

19 rounded to the nearest whole number is 19

4 rounded to the nearest whole number is 4

19 rounded to the nearest whole number is 19

-2 rounded to the nearest whole number is -2

Subtracting the rounded numbers, we get:

10 - 19 - 19 - 4 - 19 - (-2) = 10 - 19 - 19 - 4 - 19 + 2 = -49

Therefore, the estimated difference is -49.

The fraction of Earth that is not made up of ocean = 1/4.

The numbers we are familiar with are whole numbers, such as 1, 2, and so on.

Numbers expressed as fractions have a numerator and a denominator, separated by a line known as a vinculum.

In essence, a fraction explains how a portion of a group interacts with the entire group.

Given that-

The fraction of Earth that is not made up of ocean = 1 - fraction of Earth made up of water

The fraction of Earth that is not made up of ocean = 1 - 3/4

The fraction of Earth that is not made up of ocean = (4 - 3)/4

The fraction of Earth that is not made up of ocean = 1/4

Thus, the fraction of Earth that is not made up of ocean = 1/4.

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Complete question:

Approximately 3/4 of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?​

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.

We can use the slope formula to get the slopes of the lines f(x) and g(x):

slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3

slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2

The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

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Answer:

B

Step-by-step explanation:

Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.

A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.

The vertex of the parabola is located at this lowest or highest point.

Vertex form of a quadratic function:

f(x) = a(x – h)² + k, where a, h, and k are constants.

The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).

(h,k) are the vertex of parabola.

From the given graph:

f(b) is the given function:

Vertex (h,k) = (8, 4)

Thus, h= 8 and k = a = 1, x = b.

Put the values in quadratic function:

f(b) = 1(b – 8)² + 4

f(b) = (b – 8)² + 4

Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.

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Is the graph increasing, decreasing, or constant: C. Constant.

In Mathematics and Geometry, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.

By critically observing the graph shown above, we can reasonably infer and logically deduce that the graph is constant because it assumes only one y-value, which is represented by this equation y = 3.

In conclusion, the above is constant, rather than increasing or decreasing.

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Al needs to read 752 more pages to reach his goal of 2,000 pages.

The act of deleting items from a collection is represented by subtraction. Subtraction is denoted by the minus sign.

To find out how many more pages Al needs to read to reach his goal of 2,000 pages, we can subtract the number of pages he has already read from his goal:

Number of pages Al needs to read = Goal - Pages already read

Number of pages Al needs to read = 2,000 - 1,248

Number of pages Al needs to read = 752

Therefore, Al needs to read 752 more pages to reach his goal of 2,000 pages.

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Answer: Total distance of the swimming competition is 55.56 km.

Step-by-step explanation:

Let x be the total distance of the swimming competition.

On the first day, Angie covered 25% of the total distance, which means she swam 0.25x km.

On the second day, she covered one-third of the remaining distance, which is (1 - 0.25)x = 0.75x km.

So, she swam (1/3) * 0.75x = 0.25x km on the second day.

On the third day, she covered 25% of the remaining distance, which is (1 - 0.25 - 1/3)x = 0.42x km.

So, she swam 0.25 * 0.42x = 0.105x km on the third day.

On the final day, she swam half of the remaining distance,

which is (1 - 0.25 - 1/3 - 0.5)x = 0.125x km.

The total distance she swam is the sum of the distances swum on each day:

0.25x + 0.25x + 0.105x + 0.125x = 0.73x

We know that the total distance of the competition is x - 15 km (since she still has 15 km left to swim).

So we can set up the equation:

0.73x = x - 15

Solving for x, we get:

x-0.73x = 15

0.27x = 15

x = 55.56

Therefore, the total distance of the swimming competition is 55.56 km.

x ≤ 4, -2≤ y ≤ 2  are the domain and range of the graph of this function.

What is the domain and domain of the function in the graph?

Another way to identify domains and feature sets is with graphs. Domain refers to the set of possible input values, so a chart's domain consists of all input values ​​displayed on the x-axis.

                                    A range is the set of possible output values ​​plotted on the y-axis. To find the domain and domain of the equation y = f(x), find the value of the independent variable x for which the function is defined. 

y = f(x)

according to the graph value of y

 x ≤ 4,

-2≤ y ≤ 2

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Answer:

Step-by-step explanation:it is 5/5 because it is a whole number and all the others aren’t

Answer:

y = 2x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 3 ← is in slope- intercept form

with slope m = 2

• Parallel lines have equal slopes , then

slope of line AB is m = 2

line AB crosses the y- axis at (0, 4 ) ⇒ c = 4

y = 2x + 4 ← equation of line AB

Answer:

[tex]\frac{?x1}{3}[/tex] is the answer as in ?x1/3 the ?x1/3 is = to ÷3.

so therefore the answer could also be [tex]\frac{?x1}{3}[/tex].

( please note that the [tex]\frac{x}{above}[/tex]  symbolises ×by )

Hope this helps and gets brainliest.

Good luck with studies.

Step-by-step explanation:

the answer is 115 remainder 1

The option that is true about the equations for these two lines iis that they represent the same lines.

The trick to questions like this is to get both equations into the slope-intercept form.  That is done for our first equation (y = 3x + 5).  However, for the second, some rearranging must be done:

5y – 25 = 15x; 5y = 15x + 25; y = 3x + 5

Note: Not only do these equations have the same slope (3), they are totally the same; therefore, they represent the same equation.

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Two lines are described by the equations:

y = 3x + 5 and 5y – 25 = 15x

Which of the following is true about the equations for these two lines?They represent perpendicular lines.

None of the other answers

They represent non-perpendicular, intersecting lines.

They represent the same lines.

They represent parallel lines.

A is riskier than B in terms of pure risk. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio if it has a lower correlation to the market than Stock A.

The profit or loss an investor can anticipate realising from an investment is known as the expected return. Calculating an expected return involves multiplying possible outcomes by their likelihood before adding the results. The expected return is computed by summing the results of multiplying all possible outcomes by the likelihood that each one will occur (as illustrated below).

Expeced return=Sum(probability*return)

Standard Deviation=[tex]\sqrt{sum(probability*(return-expected\ return)^2}[/tex]

Coefficient of Variation=Standard Deviation/Expected Return

1. Expected Returns:

Stock B=0.1*(-38%)+0.2*0%+0.5*21%+0.1*26%+0.1*36%=12.900%

2. Standard Deviation:

Stock A=[tex]\sqrt{(0.1*(-11\%-11.3\%)^2+0.2*(5\%-11.3\% +0.5*(13\%-11.3\%)^2+)^2 0.1*(18\%-11.3\%)^2} \\+0.1*(31\%-11.3\%)^2)[/tex]

= 10.120%

3. Coefficient of Variation:

Stock B=19.892%/12.9%=1.5420

4. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio if it has a lower correlation to the market

than Stock A.

5. Sharpe Ratio:

Stock A=(11.3%-3.5%)/10.120%=0.7708

Stock B=(12.9%-3.5%)/19.892%=0.4726

6. A is riskier than B in terms of pure risk. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio

if it has a lower correlation to the market than Stock A.

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Solving the system of equations using matrices is : = -66, y = 163, and z = 11.

To solve this system of equations using matrices, we can write it in the form AX = B, where:

A = coefficient matrix

X = variable matrix (containing x, y, and z)

B = constant matrix (containing the constants on the right-hand side of each equation)

So, we have:

| 2  -1  3 |   | x |   | 180 |

| -4  2  3 | x | y | = | 225 |

| 3  -4  0 |   | z |   | 270 |

We can solve for X by multiplying both sides of the equation by the inverse of A:

X = A^-1 * B

First, we need to find the inverse of A. We can do this by using the formula:

A^-1 = (1 / det(A)) * adj(A)

where det(A) is the determinant of A and adj(A) is the adjugate (transpose of the cofactor matrix) of A.

| 2  -1  3 |

| -4  2  3 |

| 3  -4  0 |

det(A) = 2(20 - 3(-4)) - (-1)(-40 - 33) + 3(-4*(-1) - 2*3) = 16

| 2  -1  3 |

| -4  2  3 |

| 3  -4  0 |

The cofactor matrix is:

| 2  9  6 |

| 12  0  -2 |

| 13  -9  8 |

Taking the transpose of the cofactor matrix gives us the adjugate of A:

| 2  12  13 |

| 9  0  -9 |

| 6  -2  8 |

So, we have:

A^-1 = (1 / det(A)) * adj(A) = (1 / 16) *

| 2  12  13 |

| 9  0  -9 |

| 6  -2  8 |

Multiplying A^-1 by B gives us:

| x |   | -66 |

| y | = | 163 |

| z |   | 11  |

Therefore, x = -66, y = 163, and z = 11.

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The value of k in the given diagram is 10.

A linear pair refers to two adjacent angles that are created when two lines intersect. The defining characteristic of a linear pair is that the sum of their measures is always equal to 180 degrees, which makes them supplementary angles. Essentially, a linear pair is a type of angle pair where the two angles are not only adjacent to each other, but they also add up to a straight angle. Linear pairs are frequently found in various geometric shapes, including triangles, quadrilaterals, and polygons. They also have real-world applications in areas such as architecture and engineering.

We know that sum of angles of a triangle is 180.

So in tringle XYZ,

Angle ZXY + Angle XYZ + Angle YZX = 180

Given angle values ZXY = 6k+10, YZX = 4K+5 and ZYM = 115

We see that Angle XYZ + Angle ZYM = 180, since they are a linear pair.

This means Angle XYZ = 180 - Angle ZYM = 180 - 115 = 65

Hence, Angle ZXY + Angle XYZ + Angle YZX = 180

6k+10 + 65 + 4K+5 = 180

10k + 80 = 180

10k = 180 - 80 = 100

k = 100/10 = 10

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