infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is

The common ratios of the sequence are 4 and 1/4

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

Sequence 1

1, 2, 4, 8, 16,...

The common ratio is the quotient of a term and the previous term

Using the first term and the second term, we have

Common ratio = Second term/First term

Substitute the known values in the above equation, so, we have the following representation

Common ratio = 2/1

Evaluate

Common ratio = 2

Sequence 2

Here, we have

48, 12, 4, 2,...

The common ratio is the quotient of a term and the previous term

Using the first term and the second term, we have

Common ratio = Second term/First term

Substitute the known values in the above equation, so, we have the following representation

Common ratio = 12/48

Evaluate

Common ratio = 1/4

Hence, the common ratio is 1/4

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The value of the missing angle x in the given triangle is; x = 55°

From the image attached, we are told that the line at the top is parallel to the line at the base of the triangle.

Now, alternate angles are defined as angles that occur on opposite sides of the transversal line and have the same size.

This means that the angle formed to the right of 50 degrees will be an alternate angle to 75° and as such they are congruent.

Now, we know that sum of angles on a straight line is equal to 180°. Thus;

x + 50 + 75 = 180

x + 125 = 180

x = 180 - 125

x = 55°

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Answer: y = 3x - 8

Step-by-step explanation:

      We will write a point-slope equation to help us write a slope-intercept equation.

y - 16 = 3(x - 8)

y = 3(x - 8) + 16

y = 3x - 8

      The slope-intercept form equation that represents this line is;

                        y = 3x - 8

Answer: I think its

x>-10/3

Step-by-step explanation:

Answer: Hugo should buy car A

Step-by-step explanation:

Car A

Take 702 divided by 12 = 58.5 miles per gallon of gas

Car B

Take 873 divided by 15 = 58.2 miles per gallon of gas.

So Hugo should buy car A

The total time taken to finish building the transmission if Jose and Luis worked together is 4.44 hours

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total time required to finish building the transmission if Jose and Luis works together be = A

Now , the equation will be

The time required by Jose to build a transmission = 10 hours

The time required by Luis to build a transmission = 8 hours

If it takes one person 10 hours to build a transmission and another person 8 hours to build the same transmission , working together they could build the transmission even quicker

So ,

If Jose builds the transmission is 10 hours , he builds 1/10th of the transmission in one hour

If Luis builds the transmission in 8 hours , he builds 1/8th of the transmission in one hour

And ,

Together they build the transmission in

1/A = 1/10 + 1/8

where A is the total time required to finish building the transmission if Jose and Luis works together

So , the equation is

1/A = 1/10 + 1/8

1/A = 18/80

Taking reciprocals on both sides of the equation , we get

A = 80/18

A = 40/9

On simplifying the equation , we get

A = 4.44 hours

Therefore , the value of A is 4.44 hours

Hence , The total time taken to finish building the transmission if Jose and Luis worked together is 4.44 hours

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Answer:Antonio drove 24 miles west

Step-by-step explanation: 50-26=24

Answer:

Step-by-step explanation:

12.1

Answer:

8 [tex]\frac{1}{10}[/tex]

Step-by-step explanation:

[tex]\frac{17}{20}[/tex] = [tex]\frac{34}{40}[/tex] Multiplied the numerator and denominator by 2

[tex]\frac{1}{2}[/tex] = [tex]\frac{20}{40}[/tex]  Multiplied the numerator and denominator by 20

[tex]\frac{3}{4}[/tex] = [tex]\frac{30}{40}[/tex]  Multiplied the numerator and denominator by 10

2 + 3 + 1 [tex]\frac{34}{40}[/tex] + [tex]\frac{20}{40}[/tex] + [tex]\frac{30}{40}[/tex]

6 [tex]\frac{84}{40}[/tex]  This can be written

6 + [tex]\frac{40}{40}[/tex] + [tex]\frac{40}{40}[/tex] + [tex]\frac{4}{40}[/tex]  another name for [tex]\frac{40}{40}[/tex] is 1

6 + 1 + 1 +[tex]\frac{4}{40}[/tex]

8[tex]\frac{4}{40}[/tex]  Divide the numerator and denominator by 4 to simplify

8 [tex]\frac{1}{10}[/tex]

Answer:

B. [tex]\triangle UVZ \cong \triangle VYX[/tex], SSS

The congruent statement and the reason why the triangles are congruent is (b) ΔUVZ ≅ ΔVYX, SSS

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

Triangles = UVZ and VYX

There are several theorems that make any two triangles to be congruent

One of these theorems is the SSS congruent theorem

The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent

From the question, we can see that the following corresponding sides on the triangles UVZ and VYX have the same mark

UV and VY

UZ and VX

VZ and YX

This implies that these sides are congruent sides

Hence, the congruent statement on the congruency of the triangles is (b) ΔUVZ ≅ ΔVYX and the reason is by SSS

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Answer:Bisect an angle :)

Step-by-step explanation:

The probability of the product of the numbers present on the top faces of all the four six sided dice is equal to 1/108.

As given in the question,

Number of six sided dice to be rolled = 4

Number of outcomes on one dice = 6

Total number of outcomes of 4 dice = 6⁴

                                                            = 1296

Conditions for the product of the numbers of top faces all four dice is prime:

Favourable outcomes are : ( 1, 1, 1,2), (1,1,2,1), (1,2,1,1), (2,1,1,1),

( 1, 1, 1,3), (1,1,3,1), (1,3,1,1), (3,1,1,1),( 1, 1, 1,5), (1,1,5,1), (1,5,1,1), (5,1,1,1)

Total number of favourable outcomes = 12

Required Probability = 12 / 1296

                                  = 1 / 108

Therefore, the probability of the product of all the four numbers on the top faces of the dice is equal to 1/108.

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To calculate the number of votes that Mr. Dyer received, we need to multiply the ratio with the total votes. Mr. Dyer received 1,080 votes.

Ratio of votes = 4:3:2

Total votes = 4 + 3 + 2 = 9

Total votes cast = 2,700

Mr. Dyer's votes = (4/9) x 2,700 = 1,080 votes

The ratio of votes cast for Mr. Dyer, Ms. Frau and Mr. Borak was 4:3:2 respectively. This means that for every 9 votes cast, 4 votes were for Mr. Dyer, 3 votes were for Ms. Frau and 2 votes were for Mr. Borak. Since none of the 2,700 voters cast more than one vote, the total votes cast for each candidate would be 2,700. To calculate the number of votes that Mr. Dyer received, we need to multiply the ratio with the total votes. Therefore, Mr. Dyer received 1,080 votes (4/9 x 2,700).

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The time that it will take for the shadow to travel 1150 miles is; 30 minutes

Let y represent the distance in miles    

Let x represent the time in minutes

The shadow travels 2300 miles in 1 hour or 60 minutes and in the first 20 minutes the shadow traveled 766 ²/₃ miles or 2300/3 miles

Thus, the coordinates are;

(60, 2300) and (20,  2300/3)

The slope is;

m = (2300 - 2300/3)/(60 - 20)

m = 115/3 mi/min

Thus, the linear equation in point slope form is;

y - 2300 = (115/3)(x - 60)

This gives;

y = (115/3)x

When y = 1150 miles, we have;

1150 = (115/3)x

x = 30 minutes

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Answer: M=1

Step-by-step explanation:

hope this help!

The number of different sets of officers possible is 1716 sets.

The number of sets of officers possible is the number of ways people can be chosen for the given posts.

Since there are 13 people available for the post of president,

The choice can be made in

13 ways.

For the post of the Vice-President, there are 12 likely candidates. Hence, the choice can be made in

12 ways

Similarly for the post of treasurer, there are 11 likely candidates available. Hence, the choice can be made in 11 different ways.

Hence, the total number of sets of officers possible are

13 X 12 X 11

= 1716 sets.

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Answer:

6,561

Step-by-step explanation:

((3*3)²)²

((9)²)²

(81)²

6,561

Answer:

Step-by-step explanation

answer:6561

3 times 3 = 9

9^2=81

81^2=6561

Answer:

Tom will pay a total of $58,064 in interest over the 30 year loan.

Step-by-step explanation:

The purchase price of the home is $144,000, and Tom will make a down payment of 10%, or $144,000 * 10/100 = $14,400.

Therefore, Tom borrows $144,000 - $14,400 = $129,600.

Next, we need to calculate the total number of payments he will make over the 30 year loan. Since the loan is for 30 years and the payments are made monthly, there will be 30 years * 12 months/year = <<30*12=360>>360 payments.

Finally, we can use the mortgage formula to calculate the total amount of interest Tom will pay over the loan:

I = P * r * t

Where:

I is the total interest

P is the principal (the amount borrowed)

r is the annual interest rate (in decimal form)

t is the number of payments

Plugging in the values, we get:

I = $129,600 * 0.045 * 360 payments

= $58,064

a) The marginal cost MC at  x=9 units is $154.70.

b) The cost of producing 1 additional unit is $154.70.

c) The cost of producing 2 additional units is $309.40.

The Marginal Cost quantifies the incremental cost incurred from the production of each additional unit of a good or service. The marginal cost of production captures the additional cost of producing one more unit of a good/service.

The analysis of the marginal cost helps determine the “optimal” production quantity, where the cost of producing an additional unit is at its lowest point. The marginal cost of production must be lower than the price per unit for a company to be profitable – thus, the marginal cost pinpoints the output volume and pricing where incremental costs are reduced.

a) Marginal Cost = (Change in Costs) ÷ (Change in Quantity)

C(x) = 1/90[tex]x^{3}[/tex] + 8[tex]x^{2}[/tex] + 8[tex]x[/tex] +18

MC = dC/dx

MC = d( 1/90[tex]x^{3}[/tex] + 8[tex]x^{2}[/tex] + 8[tex]x[/tex] +18) / dx

      = 1/90 (3x²) + 8 (2x) + 8

      = 1/30x² + 16x + 8

At x = 9 units, we get

MC(x=9) = 1/30 (9²) + 16 (9) + 8

              = 154.7

Rounding off to two decimal places, we get 154.70.

Thus, the marginal cost MC at  x=9 units is $154.70.

b) Marginal Cost = (Change in Costs) ÷ (Change in Quantity)

154.70 = Change in costs/ 1

Change in costs = 154.70

So, the cost of producing 1 additional unit is $154.70.

c) Marginal Cost = (Change in Costs) ÷ (Change in Quantity)

154.70 = Change in costs/ 2

Change is costs = 309.40

So, the cost of producing 2 additional units is $309.40.

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The Unit Normal to the Surface cos(x. y) = e. z - 2 at (1,π,0) is -2 ≤ z ≤ 2.

Let F(x, y, z) = cos(x.y) − e.z + 2 .

A given surface is the same as the set of planes F(x, y, z) = 0.

Since the gradient vector ∇F( 1 , π, 0) is normal to this surface at (1, π, 0) , find this vector and normalize it to get the unit vector normal to this surface.

Differentiate:

∇F(x, y, z) = (−y sin(x y), −x sin(x y), e(z)

or

∇F(1, π, 0) = (0 , 0 , 1).

This vector is already of length 1, so this is sufficient. Alternatively, you can use the vector opposite. Therefore, the two vectors that satisfy the problem are ±k.  At problem point, the surface is flat horizontally.

We may want to see what this interface looks like. This is a computer-generated sketch corresponding to:

                      −4 ≤ x ≤ 4, −4 ≤ y ≤ 4, −2 ≤ z ≤ 2.

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The answer to the provided question is No, because the graph of the line connecting the ordered pairs does not pass through the origin.

When two numbers or variables are linearly connected in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable declines in proportion to the other when it falls below 1/100th of its former value.

The relationship has the following form when two linear variables are directly proportional.

=> y = mx

where the constant ratio of change between the variables is denoted by m.

The graph of the direct proportion is a straight line that goes through the origin, which is one of its key characteristics.

You can see in the example image, though, that the line generated by those points won't cross the coordinate system's origin.

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The possible temperatures for the north will be 4 degrees and 6 degrees. The correct option is D and E.

Mathematical statements with at least two terms connected by an operator and containing either numbers, variables, or both are referred to as expressions.

The direction that heat energy will spontaneously flow depends on temperature. Temperature is the degree to which a body is hot or cold. because it was mentioned that the north can occasionally experience temperatures below 3 degrees. D and E are the appropriate choices

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Answer:
The light globe is 1.6 meters above the ground.

Explanation:

height of light globe = height of boy x distance from light globe to base of electric pole / distance from boy to base of electric pole

Plugging in the values given in the problem, we get:

height of light globe = 1.6 m x 8.1 m / 8.1 m

This simplifies to:

height of light globe = 1.6 m

Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.

An alternative name for a combo is a choice. A combination is a choice made from a predetermined group of options. I won't organize anything here. They will be my choice. The number of distinct r selections or combinations from a set of n objects is indicated by the symbol [tex]^nC_{r}[/tex].

There are eight participants in the focus group, including three software engineers, two nurses, one doctor, and two technicians.

So the 3 software engineers =3! ways, 2 nurses =2! ways,

doctor =1! way , 2 technicians =2! ways.

We must determine how many different configurations are possible so that no two pieces of software may coexist.

In order to prevent two software engineers from being seated next to each other, we first arrange five persons in a row with a space between them.

[tex]We get that in 6 places they can sit in ^6C_{3} ways\\ xi.e ^6C_3 = 20 (by formula of combination)\\ Therefore total ways are,6 X 2 X 1 X2 X 20 = 480.[/tex]

Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.

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Answer:

18 tiles

Step-by-step explanation:

There are 20 tiles in total.  Red is 6 of the 20, or 6/20.  That is 3/10 or 30%

Each draw has a 30% chance of being red.  30% or 20 tiles is 1.8 tiles.  Over 30 draws, that would mean a total of 600 tiles are drawn,  The overall chance of red is still 30%, so after 30 draws, the number of red tiles would be predicted to be 30% of 600:

 (0.30)*(600) = 18 tiles will be red.

Answer: 16

Step-by-step explanation:

32% of 50 = 16

The probability that all 3 will be vowels will be .01 to the nearest hundredth

Probability is the study of the odds of an outcome occurring, which are determined by the ratio of favorable examples to probable cases.

There are 26 English alphabets, each with five vowels and twenty-one consonants. As a result, the likelihood of selecting a consonant's alphabet is 21/26.

First of all, we need to know the number of vowels in the 26 letters.

There are 5 vowels among the 26 letters,

probability (3 vowels of 3)

= (5/26)*(5/26)(5/26)    multiplication of probability of each letters

=0.1923*0.1923*0.1923

≈0.0071

≈0.71%

or .01 to the nearest hundredth

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The value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.

Time t = 11 sec

Initial velocity u = 25 kmph

u = (25 × 1000)/(60 × 60) = 6.9 m/s

final velocity v = 75 kmph

v = (75 × 1000)/(60 × 60) = 20.83 m/s

From the first equation of motion;

v = u + at

Put the values;

20.83 = 6.9 + 11a

20.83 - 6.9 = 13a

11a = 13.93

a = 13.93 / 11

a = 1.26 m/s²

Thus, the value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.

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Part (a)

Part (b)

Yes, the triangles are congruent by RHS.