Which equations represent linear functions?

The next number in sequence is 185.

What is arithmetic progression?

A sequence within which each term is made by adding or subtracting an explicit variety to the preceding variety is an arithmetic sequence.

Main body:

Step 1:

Find the pattern and write the recursive formula: \(\left \{ {{a_{n+1} =a_{n} +12} \atop {a_{n+1} =a_{n} +13}} \right.\)

as the sequence is 123,135,148,160,173..

so 1st term 12 is added in 2nd term 13 is added

so after 173 , 12 will be added ,

173+12 = 185

hence, the next number in sequence is 185.

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A

Step-by-step explanation:

Answer:−

-10x to the power 2 −17x+10

Step-by-step explanation:

Easy

Answer:

C

Step-by-step explanation: no

Answer:

-38x - 14y

Step-by-step explanation:

2[x+2y - 24x - 12y + 4x + 3y]

2 [ -19x -7y]

- 38x - 14y

The fitted model log( ) = 1.6 - 0.2c is equivalent to the models y = 21.6 - 0.25(1+\(e^(1.6-0.2c)\)), y = 1.6 - 0.22/(1+\(e^(1.6+0.2)\)), and y = 1.6 - 0.22.

The fitted model log( ) = 1.6 - 0.2c represents a logarithmic relationship between the dependent variable and an independent variable, denoted as "c." To identify equivalent models, we need to examine the given options.

Option 1: y = 21.6 - 0.25(1+\(e^(1.6-0.2c)\))

This model is equivalent to the fitted model log( ) = 1.6 - 0.2c because the right side of the equation contains the term 1+\(e^(1.6-0.2c)\), which corresponds to the exponential function e^(1.6-0.2c). The coefficient -0.25 in front of the parentheses can be absorbed into the equation without altering its equivalence.

Option 2: y = 1.6 - 0.22/(1+\(e^(1.6+0.2)\))

This model is also equivalent to the fitted model because it contains the term 1+e^(1.6+0.2) in the denominator. The coefficient -0.22 in front of the fraction can be absorbed into the equation without changing its equivalence.

Option 3: y = 1.6 - 0.22

This model is a simplified version of the fitted model. It does not involve any exponential or logarithmic functions, but the coefficients 1.6 and -0.22 remain the same as in the original equation.

Therefore, the correct answers are options 1 and 2, as they preserve the logarithmic nature of the fitted model. Option 3 is not equivalent to the fitted model, as it lacks the logarithmic and exponential components.

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The events A and B are not independent.

Given that,

                  P(A|B) = 0.4

                  P(A) = 0.5

                  P(B) = 0.8

Two events A and B are said to be independent, if P(A∩B) = P(A) P(B)

We have, P(A|B) = P(A∩B)/P(B)

Therefore, P(A∩B) = P(A|B) P(B) = 0.4 x 0.8 = 0.32

Now P(A) P(B) = 0.5 x 0.8 = 0.4

So P(A∩B) ≠ P(A)P(B)

Therefore, the events A and B are not independent.

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The equation representing the hanger is 3x - 2y = 0 and when x = 6, y = 9

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, the weight of the square is y

And, the weight of the triangle is x

Now, the equation according to the diagram is;

x + 3y = 4x + y

4x - x + 3y - y = 0

3x - 2y = 0

Now, when, x  = 6

So, y =

3x - 2y = 0

3x = 2y

3(6) = 2y

18 = 2y

y = 9

Hence, the equation representing the hanger is 3x - 2y = 0 and when x = 6, y = 9

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System developers can initiate a formal project as early as the preliminary investigation stage, or later on, as analysis, design, and implementation activities occur. True.

System developers can initiate a formal project as early as the preliminary investigation stage or at any point in the analysis, design, and implementation activities.

The decision to initiate a formal project depends on various factors, including the scope of the project, the availability of resources, the complexity of the system, and the stakeholders' needs and requirements. A formal project may involve a team of developers, analysts, and other experts who work collaboratively to design and implement a system that meets the stakeholders' requirements and objectives.

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True. System developers can initiate a formal project as early as the preliminary investigation stage or later on as

analysis, design, and implementation activities occur.

The initiation stage is when the need for a new system is identified, and preliminary investigations are conducted to

determine the feasibility of the project.

If the project is deemed feasible, the formal project can be initiated at this stage.

However, if the project is initiated later on, the analysis, design, and implementation activities will have already begun.

System developers can initiate a formal project as early as the preliminary investigation stage or later on as

analysis, design, and implementation activities occur. therefore, the given statement is true.

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The number of groups that can be chosen from the team of 17 depends on the given conditions of the selection.

The correct responses are;

(a) The number of ways of choosing groups of 9 from the 17 members are 24,310 ways.

(b) (i) The number of groups of 9 containing 5 women and 4 men are 8,820 groups.

(ii) The number of groups of 9 that contain at least one man is 24,309 groups.

(iii) The number of groups of 9 that contain at most 3 women are 2,649 groups.

(c) If two team members refuse to work together on projects, the number of groups of 9 that can be chosen are 17,875 groups.

(d) If two team members must work together or not at all the number of groups of 9 that can be chosen are 1,430 groups.

Given,

The combination of n objects taking r at a time is given as follows

ₙCr = (ⁿr)

(a) The number of ways of choosing groups of 9 from the 17 members is given as follows;

Number of ways of choosing groups of 9 = (17, 9)  = 24,310 ways.

(b) (i) Number of women = 9

Number of men = 8

Number of groups of 9 containing 5 women and 4 men = (9, 5) x (8, 4)

(9, 5) x (8, 4) = 126 x 70 = 8820

Number of groups of 9 containing 5 women and 4 men = 8,820 groups.

(ii) The number of groups that contain at least one man is (17, 9) - (9, 9)

(17, 9) - (9, 9) = 24,310 - 1 = 24,309

The number of groups that contain at least one man are 24,309 groups.

(iii) The number of groups of 9 that contain at most 3 women if given as follows;

(8, 8) × (9, 1) + (8, 7) × (9, 2) + (8, 6) × (9, 3) = 2649

The number of groups of 9 that contain at most 3 women are 2,649 groups.

(c) Given that two team members refuse to work together on projects, the number of groups of 9 that can be chosen are (15, 9) + 2 × (15, 8)

(15, 9) + 2 × (15, 8) = 5,005 + 2 × 6,435 = 17,875

(d) Two team members must work together or not at all is (15, 7) - (15, 9)

(15, 7) - (15, 9) = 6,435 - 5,005 = 1,430

The number of groups of 9 that can be chosen two team members must work together or not at all are 1,430 groups.

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Answer:you use divition

Step-by-step explanation:

algerbra

The clusters will become denser and more closely spaced due to the addition of the 199 equally spaced data points between 5 and 7.

Adding 199 equally spaced data points between 5 and 7 will increase the density of the data in that range. Previously, the data set had fewer points in that range, resulting in larger gaps between the data points.

However, with the addition of equally spaced points, the clusters will become denser and more closely spaced. This means that the gaps between adjacent data points will decrease, and the overall distribution will appear more uniform and continuous.

The addition of these points helps fill in the gaps and provides a more complete representation of the data within the specified range.

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Torrence needs to buy 468 square feet of flooring for his remodeling project.

To calculate the total square feet of flooring needed, we first need to find the area of the living space and the kitchen. The dimensions given for the living space are 24x10, while the kitchen dimensions are 12x13.

1: Calculate the area of the living space.
Area = Length x Width
Area = 24 x 10
Area = 240 square feet

2: Calculate the area of the kitchen.
Area = Length x Width
Area = 12 x 13
Area = 156 square feet

3: Add the areas of the living space and kitchen to find the total square footage.
Total Area = Living Space Area + Kitchen Area
Total Area = 240 + 156
Total Area = 468 square feet

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Answer:

Answer: $457,835

Step-by-step explanation:

I just took the test :)

Answer:

Slope = 1

Step-by-step explanation:

(5,7) (-4,-2) Answer:1

Step-by-step explanation:

Let x be the amount invested at 6% so that 18000-x is the amount invested at 7.5% both in dollars.

The total interest in 3 years is $3330 so we can write: 0.06x(3)+0.075(18000-x)(3)=3330

Solve for x:

0.06x(3)+0.075(18000−x)(3)=3330

Step 1: Simplify both sides of the equation.

0.06x(3)+0.075(18000−x)(3)=3330

0.06x(3)+−0.225x+4050=3330(Distribute)

0.18x+−0.225x+4050=3330

(0.18x+−0.225x)+(4050)=3330(Combine Like Terms)

−0.045x+4050=3330

−0.045x+4050=3330

Step 2: Subtract 4050 from both sides.

−0.045x+4050−4050=3330−4050

−0.045x=−720

Step 3: Divide both sides by -0.045.

−0.045x/−0.045=−720/−0.045

x=16000

x=16000

So, the amounts borrowed are:

Bank at 6% = 16000

Bank at 7.5% = 2000

The amount of concrete required to make 80 pots is 0.24192 cubic meters after adding 5% of the required concrete.

Given that:External dimensions of the prism, a = 18 cmHeight of the prism, h = 16 cm Thickness of the walls, t = 3 cmNumber of pots, n = 80Wastage is 5% of the required concreteLet the side of the inner square be 'a1'. Then,a = a1 + 2t⇒ a1 = a - 2t = 18 - 2×3 = 12 cmVolume of the pot = volume of the outer prism - volume of the inner prismVolume of the outer prismVolume of the outer prism = a²hVolume of the outer prism = 18²×16 = 5184 cm³Volume of the inner prismVolume of the inner prism = a1²hVolume of the inner prism = 12²×16 = 2304 cm³Volume of the potVolume of the pot = 5184 - 2304 = 2880 cm³In m³, Volume of the pot = 2880/1000000 m³Volume of 80 such potsVolume of 80 pots = 80 × 2880/1000000 m³= 0.2304 m³Concrete required for the potsConcrete required = volume of 80 pots × (100 + 5)/100Concrete required = 0.2304 × 105/100 m³Concrete required = 0.24192 m³

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The magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = −1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0) is 6.21 N.

The value of the net electrostatic force on the 5.0-nC

charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0),

charge Q2 = −1.0 nC is at (0, 0.10 m), and

charge Q3 = 5.0 nC is at (0, 0) can be calculated as follows:

Given data,Charge Q1 = 6.0 nC is at (0.30 m, 0),

Charge Q2 = -1.0 nC is at (0, 0.10 m),

Charge Q3 = 5.0 nC is at (0, 0)

The formula to find out the force on the third charge Q3 is:

                      F = k * |Q1 * Q3| / r1^2 + k * |Q2 * Q3| / r2^2

Here, k = 8.99 × 10^9 N·m^2/C^2, Q1 = 6.0 nC, Q2 = -1.0 nC, Q3 = 5.0 nC

For the third charge Q3, the distance from Q1 is:

                                r1 = √(0.3^2 + 0^2) = 0.3 m

And the distance from Q2 is: r2 = √(0^2 + 0.1^2) = 0.1 m

Substituting all the given values in the formula:

                               F = 8.99 × 10^9 * [ (6.0 × 10^-9 * 5.0 × 10^-9) / 0.3^2 ] + 8.99 × 10^9 * [ (-1.0 × 10^-9 * 5.0 × 10^-9) / 0.1^2 ]F = 6.21 N

Therefore, the magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = −1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0) is 6.21 N.

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Answer:

11.25

Step-by-step explanation:

Multiply 4.5 by the reciprocal of 2/5, which is 5/2. You will then get 11.25. Hope this helped :)

Total number of cups of water needed to prepare 5 cups of rice are 11.25.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

When rice is prepared, the amount of rice varies directly as the amount of water required.

And, 2 cups of rice requires 4.5 cups of water.

Now,

Since, 2 cups of rice requires 4.5 cups of water.

Hence, For 1 cup of rice, number of cups of water = 4.5 / 2

                                                                             = 2.25

So, For 5 cups of rice, number of cups of water = 5 x 2.25

                                                                          = 11.25

Thus, Total number of cups of water needed to prepare 5 cups of rice are 11.25.

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Answer:

y = 2x - 7

Step-by-step explanation:

(1,-5) (2,-3)

y2 - y1 / x2 - x1        -3 - (-5) / 2 - 1     2/1       = 2

y = 2x + b

-3 = 2(2) + b

-3 = 4 + b

-7 = b

Answer:

0.892

Step-by-step explanation:

The probability that it is raining and the flight is delayed is 0.008.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Given that, the probability that it will rain is 0.14 and the probability that the flight will be delayed is 0.06.

Let P(A)=0.14 and P(B)=0.06

Here, P(A and B)=P(A)×P(B)

=  0.14 ×0.06

= 0.0084

= 0.008

Therefore, the probability that it is raining and the flight is delayed is 0.008.

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Answer:

- 7/1 is the simplified fraction for 14/2.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

do 14/2 in a calculator! (dividing)

Answer:

The mass of the Afghan Hound is exactly what is predicted by the line of best fit.

Answer:

no clue i came to recieve answers

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

Is x an exponent?

\( y = 3^x \)

\( 27 = 3^x \)

\( 3^3 = 3^x \)

\( x = 3 \)

Answer:

The answer is

Step-by-step explanation:

x² + 12x - 64

To factorize the expression write 12x as a difference

That's

x² + 16x - 4x - 64

Factor out x from the expression

That's

x( x + 16) - 4x - 64

Factor out - 4 from the expression

That's

x( x + 16) - 4 ( x + 16)

Factor out (x + 16) from the expression

We have the final answer as

Hope this helps you

The equation becomes y = 5(2^-(x-2))+5 if the equation for the graph that has been reflected in the y-axis, given a vertical stretch by a factor of 5, translated 2 units right and 5 units down.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have equation:

\(\rm y = 2^x\)

Plug x → -x to reflected in the y-axis.

The function becomes:

\(\rm y = 2^-^x\)

For vertical stretch, multiply the function by 5.

The function becomes:

\(\rm y\ =\ 5\left(2^{-x}\right)\)

For translate 2 units, right plug x → (x-2)

\(\rm y\ =\ 5\left(2^{-(x-2)}\right)\)

For translate 5 units, up add 5 to the function.

The function becomes:

\(\rm y\ =\ 5\left(2^{-(x-2)}\right)+5\)

Thus, the equation becomes y = 5(2^-(x-2))+5 if the equation for the graph that has been reflected in the y-axis, given a vertical stretch by a factor of 5, translated 2 units right and 5 units down.

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