What is the independent variable in a linear function?; How do the independent and dependent values change in linear functions?; Which function has a constant additive rate of change of?; Which must be true of the data set if a linear function can be used to represent the data?

Therefore the result of adding the system of equations  2x + y = 4  ,

6=3x-y is 5x =10

Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. The relationship between the expressions printed on the left and right sides is shown to be equal in this way. In all mathematical equations, LHS = RHS  is used. You can solve equations to find the value of an unknown variable that stands in for an unknown quantity. If a sentence lacks a "equal to" sign, it is not considered an equation. It will be considered to be a phrase.

Here,

Given:

we have to solve the system of equations given. .Each equation is added together to remove the variable Y.

2x + y = 4  

+

3x - y = 6

________

=> 5x =10

Therefore the result of adding the system of equations  2x + y = 4  ,

6=3x-y is 5x =10

The value of x :

x =10 / 5 = 2

⇒ x=2

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Answer:

(4,2) may be the answer

I guess!!

The probability that the sum of the numbers rolled is either even or a multiple of 5 is 61.11%.

Probability helps us to know the chances of an event occurring. The sum of all the probabilities of an event is always equal to 1. The formula for probability is given as,

Probability = Number of outcomes / Total number of outcomes

The total number of outcomes = 36

The number of outcomes whose sum is either even or a multiple of 5 = 22

The number of outcomes whose sum is either a multiple of 3 or 4 = 20

Now, the probability that the sum of the numbers rolled is either even or a multiple of 5 is,

Probability

= number of outcomes whose sum is either even or a multiple of 5 / total number of outcomes

= 22 / 36

= 11 / 18

= 0.61111

= 61.11%

Further, the probability that the sum of the numbers rolled is either a multiple of 3 or 4 is,

Probability

= number of outcomes whose sum of the numbers rolled is either a multiple of 3 or 4 / total number of outcomes

= 20 / 36

= 5/9

= 0.5555

= 55.55%

Hence, The probability that the sum of the numbers rolled is either a multiple of 3 or 4 is 55.55%.

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Answer:

Yes

Step-by-step explanation:

g(x) = 1/4 x

g(x) = x/4

f(x) = 4x

If you plugin f(x) in g(x) and g(x) into f(x), you should get x:

f(g(x))=

4(g(x)= => plugin g(x) for x in f(x)

4(x/4)=

4*x/4=x √

g(f(x))=

f(x)/4= ==> plugin f(x) for x in g(x)

4x/4 = x√

Hence, f(x) and g(x) are inverse of each other.

Bruce can be advised to correct his reasoning as the number divisible by six will also remain divisible to 3.

The factor of a number is any number that divides it completely.

In order to find the factors of a number keep dividing it with the known factors.

Given that,

A number is product of 6.

Then, 6 is the factor of that number.

But the factors of 6 are 2 and 3 which implies that 3 is also a factor of that number.

It implies that Bruce has not applied the correct reasoning to reach the conclusion.

Hence, a number which is a product of 6 can also be a product of 3.

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Answer:

=5x2-(20-5)x-20

=5x2-20x+5x-20

=5x(x-4)+5(x-4)

=(x-4)(5x+5)

Answer:-5(2+3x)

Step-by-step explanation:

Answer:

Hi, are you missing part of this question?

The temperature on the second day is 11°.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Let the temperature on the second day be x.

Based on the information, temperature cooled by 4° on the first day of the year together on the 1st 2 days of the year the temperature heated up.

-4 + x = 7

Collect the like terms

x = 7 + 4..

x = 11

The temperature is 11°

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The temperature cooled by 4° on the first day of the year together on the 1st 2 days of the year the temperature heated up 7°. What is the Temperature on tue second day?

Answer:

y=5x

Step-by-step explanation:

The rate at which water is draining when the water is  8 feet deep is calculated to be 2.54 ft³/ h

The vertex angle of the conical-shaped reservoir can be given as follows;

tan θ = R/H

Here R represents the radius and H illustrates the depth

so here we can say that the vertex angle will remain constant; therefore;

r/y = R/H

r/8 = 10/20

r = (10/20) × 8

r = 4

now for the volume, we can say;

V=1/3πr^2h

also, we can say;

r = y/2

Therefore here we will have;

V = 1/3π(y/2)^2y = 1/12 πy³

now for volume flow rate, we can determine as follows;

Q = dV/dt = 3/12πy²(dy/dt)

Q = 1/4 πy²v

Substituting the values as follows;

Q = 1/4 π(8)²(1/2)ft³/h

Q = 2.54 ft³/ h

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The Z-value posted in part(c) for a confidence level of 74% is 1.150

The Confidence level in statistics denotes the likelihood that an estimate of the location of a statistical parameter (such as an arithmetic mean) in a sample survey will also hold true for the population.

Confidence levels must be determined before conducting a survey since they affect the poll's margin of error and necessary coverage. 90, 95, and 99% confidence intervals are widely employed in surveys.

A calculated statistic that was based on a sample would also be true for the entire population, within the established confidence level, with a 95% likelihood, if the confidence level were set at 95%.

Every confidence level has different z-value

In the question, We have to write the Z-value of 74% which is 1.15

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Alberto chooses the probability threshold needed for statistical significance and then use inferential statistics. This level layer is described known as the test's significance level.

The significance level refers to the threshold at which one may agree that an event was statistically significant.

To evaluate statistical significance, researchers utilize a measurement called the p-value: whereas if the p-value was lower than the significance level, the result is considered statistically significant. The implies as well as standard deviations of both the data samples determine the p-value.

The confidence level would be the inverse of the significance level and is computed as 1 minus the significance level.

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The number of hours to operate the mines to minimize cost are Mine 1 hour = 30 hours and Mine 2 hour = 10 hours

The given parameters can be represented using the following table of values

                             Mine 1 (x)              Mine 2 (y)   Available

Regular grade          5                            20             350

Low grade               17                             10              610

Operating cost      7000                     29000

Time                        54                              27

From the table, we understand that we are to minimize cost

This means that:

Objective function: C = 7000x + 29000y

Subject to:

5x + 20y ≥ 350

17x + 10y ≥ 610

Next, we plot the constraints on a graph (see attachment)

From the graph, we have

(x, y) = (30, 10)

This means that

Mine 1 hour = 30 hours

Mine 2 hour = 10 hours

Hence, the number of hours are 30 and 10 hours

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The equivalent expression for the given expression is -2i(-8+4i).

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 8 +16i.

The given expression can be written as 8(1+2i)

-2i(-8+4i)

= -2i×(-8)-(-2i)×4i

= 16i-8i²

= 16i-8(-1)

= 8+16i

Therefore, the equivalent expression is -2i(-8+4i).

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The null hypothesis is  H0: μ ≤ 68,800 for the  given  case of The owner of a football team claiming that the average attendance for games is 67,800.

Since we know that a null hypothesis (H0) shows that no significant variation exists between variables in other words it can be said that a single variable is much not different than its mean.  since from the above case we were given the information that The owner of a football team claims that the average attendance for games is 67,800. So, the null hypothesis the that the average attendance at games is less than or equal to 68,800.

H0: μ ≤ 68,800

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Answer:

m = [tex]\frac{rise}{run}[/tex]

Step-by-step explanation:

1. take any two points on the line

2. figure out the vertical change between both points, known as the rise

3. figure out the horizontal change between both points, known as the run

4. slope is defined as the variable m and is the [tex]\frac{rise}{run}[/tex]

Answer:

10mph

keeping it short so you can ace your quiz :D

if this helps you, it would help me a lot if you could mark this as brainliest :)

Answer:

y=-4/3x+13

Step-by-step explanation:

formula:y=mx+b

you need to add 9 on both sides of the equation

so it's look like this:y-9=-4/3x+5

                                  +9          +9

so combine the like terms

y=-4/3x+13

The linear speed of a person on this Ferris wheel is about 628.2 ft/min.

As a body travels a circular path, it has both a linear speed and an angular speed. The rate it travels on that path is the linear speed, and the rate it turns around the center of that path is the angular speed. The linear speed (v) and angular speed (ω) are related by the radius (r) or v = rω .

Given that ;

Radius = r = 50 ft

Frequency = f = 2 rev/min

The angular speed is the product of the angular displacement for one complete turn, namely 2π radians per revolution, and the frequency (f). That is, the angular speed is equal to ω = 2πf. Substituting this into the formula for linear speed (v), we get:

                                v = r (2πf)

                                    = (50 ft) ( 2π / rev) ( 2 rev/min)

                                    = 200π ft/min

                                    ≈ 628.2 ft/min

The linear speed of a person on this Ferris wheel is about 628.2 ft/min.

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.

The solution of the logarithm equation are as follows:

a. l = 100000

b. l = 1000000

Any equation in the variable x that contains a logarithm is called a logarithmic equation.

Let's solve the logarithm equation as follows:

a.

50  = 10 log₁₀ l

Using logarithm law,

50  = 10 log₁₀ l

50  = log₁₀ l¹⁰

10⁵⁰ = l¹⁰

multiply both sides of the exponents by 1 / 10

Hence,

l = 10⁵

Hence, the value of  l = 100000

b.

60 = 10 log₁₀ I

Using logarithm rule,

60 = 10 log₁₀ I

60 = log₁₀ l¹⁰

10⁶⁰ = l¹⁰

multiply both sides of the exponents by 1 / 10

l = 10⁶

Hence, the value of  l = 1000000

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Answer: 6,845.9, or to whole number 6,846

Step-by-step explanation:

The probability of having a boy when a couple has six ​children is 63 / 64.

The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.

Given:

A couple has six ​children, n = 6

The wanted event, p = 1 / 2

Calculate the probability of having a boy given by the following formula,

[tex]P(X) = nC_x px (1-p)n-x[/tex]

Here, [tex]X[/tex] = number of boys,

So,

P(X >= x) = 1 - P(X = 0)

P (X) = 1 - 6C₀ × (1 / 2) 0 × (1/2) 6

P (X) = 63 / 64

Therefore, the probability of having a boy when a couple has six ​children is 63 / 64.

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The option which describes a situation in which reduction occurs Cl2 becoming Cl–. (Option B)

Reduction refers to the type of chemical reactions in which the number of electrons in an atom, or a group of atoms increases. The electrons taken up by the substance reduced are supplied by another substance, which is thereby oxidized. Hence, oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or a decrease in the oxidation state. In the given situation, Cl2 becoming Cl- represents reduction as the oxidation state is decreased from 0 to -1.

Note: The question is incomplete. The complete question probably is: Which option describes a situation in which reduction occurs? A) S2– becoming S. B) Cl2 becoming Cl–. C) Al becoming Al3+. D) Xe2+ becoming Xe6+.

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The vector are quantity that has both magnitude and direction. they are normally visualized in graph.

A vector - values function F : R² ---> R² can be visualized as a vector field. At a point (x,y) , we plot a value of F(x,y) as a vector with the tail anchored as (x,y)

If we visualize the vector field it will look like an explosion emanating from the origin.

At each point (x,y) , the vector F(x,y) points precisely away from the origin.

If you drew the arrows to scale they would be as long as the distance to the origin but again the drawn arrows are shorter than the actual values of the vector field

The graph of a vector field is created by pointing arrows one at a time of substituting points into the plane to determine what error to draw at the point

The question is incomplete so, I have answered in general

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Answer:

Step-by-step explanation:het

In the binomial expression (x + y)^10, the term that will appear in the expansion of expression is ax^3y^7.

Binomial expression refers to the algebraic expression which contains two terms. These expressions are expanded using binomial theorem. According to the theorem, it is possible to expand the binomial (x + y)^n into a sum involving terms of the form ax^by^c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b. Hence, for the given expression, the term which will appear in the expansion of binomial would have variables whose sum of power would be equal to the power of the expression i.e., the sum of the power would be 10. Hence, ax3y7 would appear in the expansion as the sum 3+7=10.

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Answer: Translation T = (x + 8, y + 4)

Step-by-step explanation:

The x coordinate moved to the right by 8 and the y coordinate moved up by 4.

Answer:    If the algae in Lake Skinner doubles every day, then on the 15th day (halfway between the 1st and 30th) the lake will be covered halfway.

   If the algae doubles every day, then on January 26 it would have only doubled six times, meaning it would only cover 1/64 of the lake's surface. This is why your friend may be skeptical that the lake will be completely covered soon.

   The cleanup crew's efforts on January 29 were able to remove most of the algae, but by February 1 only 1% of the lake's surface was still covered. This means that while the problem has been greatly reduced, it is not completely solved and there may still be some risks to the fish in the lake. Continued monitoring and efforts to prevent future algae blooms may be necessary to fully protect Lake Skinner.

Step-by-step explanation:

As per the given question the median size of a new house and the values of different parts of the question will be as follows:

(a) We must locate the period when the rate of change is the smallest in order to establish the period during which the median house size increased the least quickly. Finding the derivative of the following equation will provide us with the rate of change of the house size with respect to time, which we can utilize to do this.

derivative of the function H(x) = 0.359x3 - 15.198x2 + 221.738x + 862.514 given by the equation for the rate of change of the house size with respect to time as

H'(x) = 3 (0.359) x2 - 2 (15.198) x + 221.738

(b) By setting the derivative to 0 and figuring out x, we may determine the moment at which the rate of change is the least. We have x = 3.904 as a result. The time where the rate of change is the smallest is 3.904 years after 1980, or 1984.904, because x denotes the number of years after 1980. This roughly corresponds to 1984, making 1984 the year in which the median house size increased at the slowest rate.

We may enter the value of x into the previous equation to obtain H(1984) = 0.359 x [tex](1984)^{3}[/tex] - 15.198 x [tex](1984)^{2}[/tex] + 221.738 ( 984) + 862.514

= 2,532,358 sq ft. as the comparable house size at this time. In 1984, this was the size of the typical home.

We may enter the value of x into the derivative equation to obtain H'(1984) = 3 (0.359) x [tex](1984)^{2}[/tex] - 2 (15.198 x 1984 + 221.738) = 606.696 sq ft per year, which corresponds to the rate of growth in house size. This represents the median house size's rate of change during the slowest period of growth.

(c) The biggest rate of change must be found in order to pinpoint the period in which the median house size increased most quickly. Finding the derivative equation's greatest value will help us do this. To accomplish this, one can solve for x while setting the derivative equal to 0, then determine the values of x that are either more or less than the answers we obtained. The derivative equation can then be used to solve for the maximum value using these x values.

Using the quadratic formula to solve for x. The quadratic formula is given by x =  [tex]\frac{(-b ± √(b^2 - 4ac))}{2a}[/tex], where a, b, and c are the coefficients of the quadratic equation. Here, a = 3 (0.359) = 1.077, b = -2 (15.198) = -30.396, and c = 221.738. Putting these values into the quadratic formula gives us x = [tex]\frac{(30.396 ± √(30.396^2 - 4 (1.077 X 221.738))}{2 (1.077)}[/tex]

=  [tex]\frac{(30.396 ± √(928.822 - 948.512))}{2.154}[/tex]

=  [tex]\frac{(30.396 ± √(-19.690))}{2.154}[/tex]

=  [tex]\frac{15.198}{2.154}[/tex]

= 7.096.

The derivative equation will have a maximum or lowest value at the value of x that we just discovered because it is a quadratic. We can enter this value of x into the derivative equation to obtain H'(7.096) = 3 x 0 and use this result to determine the derivative equation's maximum value.

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