What’s the equation for this table?
X : -4, -3, -2, -1
Y: -11, -9, -7, -5

The exercise involves finding the product C = AB, where matrix A is given by [2 9] and matrix B is given by [3 6 1]. We need to perform the matrix multiplication to obtain the resulting matrix C.

Let's calculate the matrix product C = AB step by step:

Matrix A has dimensions 2x1, and matrix B has dimensions 1x3. To perform the multiplication, the number of columns in A must match the number of rows in B.

In this case, both matrices satisfy this condition, so the product C = AB is defined.

Calculating AB:

AB = [23 + 912 26 + 94 21 + 95]

[103 + 612 106 + 64 101 + 65]

Simplifying the calculations:

AB = [6 + 108 12 + 36 2 + 45]

[30 + 72 60 + 24 10 + 30]

AB = [114 48 47]

[102 84 40]

Therefore, the product C = AB is:

C = [114 48 47]

[102 84 40]

In summary, the matrix product C = AB, where A = [2 9] and B = [3 6 1], is given by:

C = [114 48 47]

[102 84 40]

To learn more about matrix visit:

brainly.com/question/29239316

#SPJ11

Answer:

Step-by-step explanation:

-4 (-2x - 8) = -48

-4×(-2x)+4×8=-48

8x+32=-48

8x=-48-32

8x=-80

x=-10

The answer is -10

If you found my answer useful then please mark me brainliest.

Answer:

Step-by-step explanation:

Here you go mate

Use PEMDAS

Parenthesis,Exponent,Multiplication,Division,Addition,Subtraction

Step 1

-4(-2x-8)=-48  Equation/Question

Step 2

-4(-2x-8)=-48  Remove parenthesis

8x+32=-48

Step 3

8x+32=-48  Subtract 32

8x=-80

Step 4

8x=-80  Divide by 8

:answer

x=-10

Hope this helps

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

Answer:

72

Step-by-step explanation:

h = -16t² + 24t+72

initial height means t=0

so h = 72

If $100 is spent on advertising, sales are expected increase by option (2) $189,200.

The equation given is:

Y = 22.9 + 189.2X

Here, Y represents sales in thousands of dollars, and X represents advertising expenditure in hundreds of dollars.

The coefficient of X is 189.2, which means that for every one unit increase in advertising expenditure (i.e., for every $100 increase in advertising expenditure), sales are expected to increase by $189.2 thousand.

So if we spend $100 on advertising (i.e., one unit increase in X), we can expect sales to increase by:

$189.2 x 1 = $189.2 thousand

However, the question is asking for the increase in sales in dollars, not thousands of dollars. So we need to convert the answer to dollars by multiplying it by 1000, since there are 1000 dollars in one thousand dollars. Therefore, the increase in sales in dollars would be:

$189.2 thousand x 1000 = $189,200

Therefore, the correct answer is option (2) $189,200.

Learn more about equation here

brainly.com/question/14603452

#SPJ4

The MP curve initially rises to its maximum value because of the specialized nature of the fixed capital, where each additional worker's productivity rises due to the marginal product of the fixed capital.

Production Function: q = f(L,K) = 20L + 25K + 5KL - 0.03L² - 0.02K²

Given, K = 5, i.e., capital is fixed. Therefore, the total product of labor, average product of labor, and marginal product of labor are:

TPL = f(L, K = 5) = 20L + 25 × 5 + 5L × 5 - 0.03L² - 0.02(5)²

= 20L + 125 + 25L - 0.03L² - 5

= -0.03L² + 45L + 120

APL = TPL / L, or APL = 20 + 125/L + 5K - 0.03L - 0.02K² / L

= 20 + 25 + 5 × 5 - 0.03L - 0.02(5)² / L

= 50 - 0.03L - 0.5 / L

= 49.5 - 0.03L / L

MP = ∂TPL / ∂L

= 20 + 25 - 0.06L - 0.02K²

= 45 - 0.06L

The following diagram illustrates the TP, MP, and AP curves:

Figure: Total Product (TP), Marginal Product (MP), and Average Product (AP) curves

The production function demonstrates increasing marginal returns due to specialization when L is low enough, i.e., when L ≤ 750. The marginal product curve initially increases and reaches a maximum value of 45 units of output when L = 416.67 units. When L > 416.67, MP decreases, and when L = 750 units, MP becomes zero.

The MP curve's initial increase demonstrates that the production function displays increasing marginal returns due to specialization when L is low enough. This is because when the capital is fixed, an additional unit of labor will benefit from the fixed capital and will increase production more than the previous one.

In other words, Because of the specialised nature of the fixed capital, the MP curve first climbs to its maximum value, where each additional worker's productivity rises due to the marginal product of the fixed capital.

The APL curve initially rises due to the MP curve's increase and then decreases when MP falls because of the diminishing marginal returns.

Learn more about average product

https://brainly.com/question/13128888

#SPJ11

It should be noted that QU is not congruent to RV.

It should be noted that congruence simply means that the sides are the same.

From the information,

QU + UR = QR = 4cm

QU = UR

QU = 2cm

RV + VS = RS = 2vm

RV = VS

RV = 2/2 = 1 cm

Therefore, QU is not equal to RV

Therefore, it should be noted that QU is not congruent to RV.

Learn more about congruence on:

brainly.com/question/12054594

#SPJ1

Answer:

∠C = 36.87°

Step-by-step explanation:

tan C = 3/4 = 0.75

∠C = 36.87°

the exact formula for X(n) is given by the sum of i from 1 to 4n + 1. The closed-form formula for X(n) is (4n + 1)(4n + 2)/2, expressed as a polynomial function. The asymptotic value of X(n) is approximately 4n^2, representing the growth rate as n approaches infinity.

(i) The exact formula for X(n) can be determined by analyzing the procedure PrintXs(n) and counting the number of times the letter "X" is printed. In this case, the outer loop runs for 4n + 1 iterations, and for each iteration, the inner loop runs i times. Thus, the total number of "X" letters printed is given by the sum of i from 1 to 4n + 1.

(ii) To express X(n) as a closed-form polynomial function, we can simplify the sum mentioned above. By using the formula for the sum of an arithmetic series, the closed-form formula for X(n) can be written as X(n) = (4n + 1)(4n + 2)/2.

(iii) The asymptotic value of X(n) can be expressed using the e-notation, which represents an estimate of the growth rate. In this case, as n approaches infinity, the dominant term in the expression (4n + 1)(4n + 2)/2 is 4n^2. Therefore, we can express the asymptotic value of X(n) as X(n) ~ 4n^2.

know more about polynomial function  :brainly.com/question/11298461

#SPJ11

Answer:

66

Step-by-step explanation:

Find the area of the rectangle, then add up the area of the triangle.

The area of the rectangle

= 5 × 12

= 60 cm²

The base of the triangle

= 12 - 9

= 3 cm

The height of the triangle

= 9 - 5

= 4 cm

The area of the triangle

= (3 × 4) ÷ 2

= 6 cm²

The total area of the figure

= 60 + 6

= 66 cm²

Answer:

I just finished taking the test and the answer is 15s + 25c ≤ 1500

Answer:

\(\frac{27}{x} =\frac{36}{28} \\\\x =\frac{27*28}{36} = \frac{3*28}{4} =3*7 =21\)

Answer:

x = 21

Step-by-step explanation:

The parallel lines divide the transversals proportionally, that is

\(\frac{27}{x}\) = \(\frac{36}{28}\) ( cross- multiply )

36x = 756 ( divide both sides by 36 )

x = 21

Answer:

B .coz the sign is telling us the way it moves

Answer:

2y=9-x

y=9-x/2

9/2-x/2=mx+c

c=9/2

m=-1/2

Answer:

the answer of this question is

2y=-x+9

Age at natural death is an example of a real-world variable with a left-skewed distribution (heart disease, cancer, etc.). Most of these deaths occur in older people and a minority in younger people.

Salary is an example of a real-world variable with a right-skewed distribution. If there are a few outliers (CEOs, professional athletes, etc.), most individuals have incomes in the low/mid range, with a wide range of higher numbers (a long "tail"). A long left tail indicates that the distribution is skewed to the left. A negatively skewed distribution is similar to a left skewed distribution. This is because the number line has a long tail in the negative direction. The average is also to the left of the peak. The left side of a left-skewed distribution is longer than the right side. That is, a left-skewed distribution has a long tail on the left.

For more information on skewed distributions, see:

Brainly.com/question/12320081

#SPJ4  

The number of  boys and girls in a class of 150 students is 90 and 60 respectively.

RATIO:

Comparing two quantities of the same units and determining the ratio tells us how much of one quantity is in the other.

i.e., it shows how many times a number contains another.

Total number of students = 150

ratio of boys to girls = 3 : 2

B:G = 3 : 2

now

3x + 2x = 150

5x = 150

x = 30

the number of boys = 3x = 3 X 30 = 90 boys.

the number of girls = 2x = 2 X 30 = 60 girls.

The number of  boys and girls in a class of 150 students is 90 and 60 respectively.

To know more about Ratio

https://brainly.com/question/13419413

#SPJ1

Step-by-step explanation:

hope this can help you, if there is any mistakes, you can comment below

Answer:

The slope is 1/3

Step-by-step explanation:

To find the slope of a line, we can use two points and the slope formula

m = ( y2-y1)/(x2-x1)

Picking two points on the line ( 0,2) and ( 3,3)

m = ( 3-2)/(3-0)

    = 1/3

The slope is 1/3

The relation that is a function is the graph (d)

From the question, we have the graphs to represent the given parameters that can be used in our computation

We are to find out which of them represents a function

For a graph to represent a function, the graph must pass the vertical line test

This means that a line drawn from the x-axis must touch the graph at most once

So, we draw these lines  and attach the graphs (see attachment)

The graph that pass the vertical line test is graph d

Read more about relation and function at

brainly.com/question/10283950

#SPJ1

Answer

3.7 or approximately 4 gallons

Step-by-step explanation:

7x2=14 total liters.

3.78 liters=1 gallon

14/3.78= 3.7 gallons

Answer:

26 and 32 are the two numbers, the product is 832

Step-by-step explanation:

According to the nearest hundredth, the length of the wire in the photograph is 200 cm.

What in mathematics is a semicircle?

By dividing a circle into two halves along a diameter line, a semicircle is created, which is a half-circle.

The wire will be cut into four semicircles, each of which will have a circumference equal to its length.

Therefore, if one semicircle has a diameter of 32 cm, its radius is 32/2 cm, or 16 cm.

Right now, a circle's circumference equals 2*(pi)*(radius).

Since this is a semicircle, its circumference is equal to (pi)*(radius), or one-half of a circle.

The circumference of four semicircles is then equal to four * pi * radius.

Pi has a value of 22/7.

Thus, the length of the wire is 4*(22/7)*16 cm, which, when rounded to the nearest hundredth, is 200 cm.

Visit this link to learn more about Semicircle: brainly.in/question/16713555

#SPJ1

Hence, 201 \(cm^{2}\) long is the wire to the nearest hundredth.

In mathematics, a semicircle is a  one-dimensional locus of points that forms  half of a circle. It is a circular arc that  measures 180°.  It has only one line of symmetry.

In geometry, the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure .

In other words ,The meaning of circumference is the distance around a circle or any curved geometrical shape. It is the one-dimensional linear measurement of the boundary across any two-dimensional circular surface.

According to figure

diameter of  all semi circle (d) = 32 cm.

so radius of  all semi circle r = \(\frac{32}{2}\) = 16 cm.

length of wire = circumference of semicircle =

⇒ total length length of wire = 4 * circumference of semicircle

                                                                                 {∵ no. of semicircle=4

∴ total length length of wire = 4 * \(\pi*r\)      

∴ total length length of wire = 4 *3.14*16              {we know that , \(\pi=3.14\)

∴ total length length of wire =200.96\(cm^{2}\) ≅ 201\(cm^{2}\)

learn more about Cicumference here:

https://brainly.com/question/20489969

#SPJ1.

Answer:

The bead will fit.

Step-by-step explanation:

First, we have to convert 0.6 to a fraction, which is 6/10.

Now the question is: is 6/10 less than or equal to 5/8? If it is, then the bead will fit, if it is greater, the bead won't fit.

There are a couple of ways to figure out which is greater:

1. Find a common denominator, whichever one has a greater numerator is bigger.

2. Calculate 6 divided by 10 and 5 divided by 8, and whichever one is a higher number is greater.

I will do number 2:

6/10 = 0.6

5/8 = 0.625

Therefore, since 5/8 is greater than 6/10, the bead will fit.

Since each triangle is a right triangle we can apply trigonometric functions:

Sin a = opposite side / hypotenuse

Where;

a = angle = 60° ( we are looking at the bottom left one)

Opposite side = 30 cm

Hypotenuse = AB

Replace:

Sin60 = 30 / AB

Solve for AB

AB = 30 / sin 60

AB = 34.64 cm

The expected number of matchings goes to infinity as N › [infinity].

Matching in Graph Theory:A matching in Graph Theory is a set of edges of a graph where no two edges share a common vertex. In other words, a matching is a set of independent edges of a graph. A perfect matching in a Graph Theory is a matching of size equal to half the number of vertices in a graph.The expected number of matchings goes to 0 as N › [infinity]:The expected number of matchings goes to zero as N › [infinity] when |E| = 3/N. It is because 3/N is a relatively dense number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very small in comparison to the total number of matchings possible as N › [infinity].The expected number of matchings goes to infinity as N › [infinity]:The expected number of matchings goes to infinity as N › [infinity] when |E| = 4.V. It is because 4.V is a relatively large number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very large in comparison to the total number of matchings possible as N › [infinity]. Hence the expected number of matchings goes to infinity as N › [infinity].

Learn more about graph theory here,

https://brainly.com/question/29538026

#SPJ11

Answer: A line that splits an angle into two equal angles.

Step-by-step explanation:  ("Bisect" means to divide into two equal parts.)

Bisecting angles: A line that splits an angle into two equal angles.

\(-2x+10+4x=70\)

subtract ten from both sides

\(-2x+4x=60\)

simplify

\(2x=60\)

divide

\(x=30\)

The approximate cost of producing the 11th roll of film can be calculated using the given marginal cost function and  total cost of producing one roll ($1,000) to obtain the approximate cost of the 11th roll of film.

The marginal cost function provided is 5 + 2a(1/x), where 'x' represents the roll number. The total cost to produce one roll is given as $1,000. To find the approximate cost of producing the 11th roll, we can substitute 'x' with 11 in the marginal cost function.

For the 11th roll, the marginal cost becomes 5 + 2a(1/11). Since the value of 'a' is not provided, we cannot determine the exact cost. However, we can still evaluate the expression by considering 'a' as a constant.

By substituting the value of 'a' as a constant in the expression, we can find the approximate cost of producing the 11th roll. The calculation of the expression would yield a numerical value that can be added to the total cost of producing one roll ($1,000) to obtain the approximate cost of the 11th roll of film.

Please note that without the value of 'a', we can only provide an approximate cost for the 11th roll of film.

Learn more about marginal here:

https://brainly.com/question/31397351

#SPJ11

The reliability of a two-component product if the components are in parallel is 0.99.

In this question,

The probability of failure-free operation of a system with several parallel elements is always higher than that of the best element in the system. Reliability can be increased if the same function is done by two or more elements arranged in parallel.

A system contains two components that are arranged in parallel, they are 0.95 and 0.80.

Therefore the system reliability can be calculated as follows

⇒ 1 - ( 1 - 0.95 ) × ( 1 - 0.80 )

⇒ 1 - (0.05 × 0.20)

⇒ 1 - 0.01

⇒ 0.99

Hence we can conclude that the reliability of a two-component product if the components are in parallel is 0.99.

Learn more about reliability of components here

https://brainly.com/question/20314118

#SPJ4

A rational number is a number that can be written in the form of p/q where q is not equal to zero.

The rational numbers are -100, -14.5, -2, -2/3, 0,10, 15, 20 1/6.are rational.

A rational number is a number that can be written in the form of p/q where q is not equal to zero.

We have,

-100, -14.5, -2, -2/3, 0, 19, 15, 20, 1/6

-100 = -100/1

It is in the form of p/q.

It is a rational number.

-14.5 = -145/10

It is in the form of p/q.

It is a rational number.

-2 = -2/1

It is in the form of p/q.

It is a rational number.

-2/3 = -2/3

It is in the form of p/q.

It is a rational number.

0 = 0/1

It is in the form of p/q.

It is a rational number.

19 = 19/1

It is in the form of p/q.

It is a rational number.

15 = 15/1

It is in the form of p/q.

It is a rational number.

20 = 20/1

It is in the form of p/q.

It is a rational number.

1/6

It is in the form of p/q.

It is a rational number.

We see that all the numbers given are rational numbers.

Thus,

The rational numbers are -100, -14.5, -2, -2/3, 0, 10, 15, 20 1/6.

To learn more about  rational number refer to:

https://brainly.com/question/12088221

#SPJ1