Find the slope of the line represented by the data below

Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

The solution to the system of linear equations is (x, y) = (- 8 / 5, 6 / 5).

In this problem we need to build and solve a system of two linear equations with two variables. Linear equations are expression of the form:

y = m · x + b

Where:

And the slope is calculated by following formula:

m = Δy / Δx

First, determine the linear equations associated with each table:

First line - Slope

m = (- 2 - 0) / [- 1 - (- 2)]

m = - 2 / 1

m = - 2

First line - Intercept

b = y - m · x

b = 0 - (- 2) · (- 1)

b = - 2

y = - 2 · x - 2

Second line - Slope

m = (3 - 1) / [2 - (- 2)]

m = 2 / 4

m = 1 / 2

Second line - Intercept

b = y - m · x

b = 3 - (1 / 2) · 2

b = 3 - 1

b = 2

y = (1 / 2) · x + 2

Second, find solution the system of linear equations:

Find x:

(1 / 2) · x + 2 = - 2 · x - 2

(5 / 2) · x = - 4

5 · x = - 8

x = - 8 / 5

Find y:

y = (1 / 2) · (- 8 / 5) + 2

y = 6 / 5

The system of linear equations has the following solution: (x, y) = (- 8 / 5, 6 / 5)

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The explicit formula for the given sequence is -

a{n} = 8(2)ⁿ ⁻ ¹

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio.

Given is the sequence as -

8, 4, 2, ....

The given sequence is a geometric sequence with common ratio of -

{r} = 8/4 = 4/2 = 2

{r} = 2

We can write the explicit term as -

a{n} = 8(2)ⁿ⁻¹

Therefore, the explicit formula for the given sequence is -

a{n} = 8(2)ⁿ ⁻ ¹

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The number of zeros/roots it will have is 3

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

P(x) = x^3 - 5x^2 − 2x + 24

The degree of the polynomial is 3

So, the number of roots is 3

Using a graphical calculator, we have the roots to be

Roots = -2, 3 and 4

To do this, we set x = 0

So, we have

P(0) = 0^3 - 5(0)^2 − 2(0) + 24

This gives

P(0) = 24

The end behaviour of the function is:

as x approaches negative and positive infinity, the function is positive

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(p + 90)/6 is the expression equivalent to p/6+ ( 7+ 8)

An expression is combination of variables, numbers and operators.

The given expression is p/6+ ( 7+ 8)

p by six plus seven plus eight.

In the given expression Combine the like terms

p/6 + (7 + 8)

p/6 + 15

LCM 1, 6 is 6

(p + 90)/6

Hence, (p + 90)/6 is the expression equivalent to p/6+ ( 7+ 8)

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The appropriate values to be used on the x and y axis are; w will represent the input values which will be on the x-axis while y will represent the output values which will be on the y-axis.

Usually, linear equation graphs are made up of the y-axis and x-axis values.

In this type of graph, the y-axis values are referred to as the range or output of the function while the x-axis values are referred to as the domain or input of the function.

Now, in the given question, we see that w is clearly the input function and as such will be represented on the x-axis while the output value will be represented on the y-axis.

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Answer:

x [tex]\geq[/tex] 64

Step-by-step explanation:

x is the number

x - 14 [tex]\geq[/tex] 50

Now isolate x to solve. So add 14 to both sides

x [tex]\geq[/tex] 64

Hope this helped :)

The true mean of the population (the true mean of all high school students spending an average of how many hours each week doing sports) is between 22.6 and 29.0 hours.

The 95% Confidence Interval for the mean of the sample of 8 high school students spending an average of 25.8 hours each week doing sports is calculated by using the formula:

CI95 = (X ± (2*Standard Error))

Where X is the sample mean (25.8 hours) and the Standard Error is calculated as the standard deviation (3.2 hours) divided by the square root of the sample size (8).

Therefore, the 95% Confidence Interval is calculated as:

CI95 = (25.8 ± (2*(3.2/√8)))

CI95 = (25.8 ± 3.2)

CI95 = (22.6, 29.0)

This means that we are 95% confident that the true mean of the population (the true mean of all high school students spending an average of how many hours each week doing sports) is between 22.6 and 29.0 hours.

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The value of x in this equation (x/2) - (2/x+1) = 1 is -2 and 3.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. Since we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

Given the equation is

(x/2) - (2/x+1) = 1

thaking LCM of left side of equation we get,

[x(x+1) - 2*2]/ 2(x+1) = 1

⇒ (x² + x - 4) / (2x +2) = 1

multiply both side by (2x +2) we get,

⇒ (x² + x - 4) = (2x +2)

subtract both side by (2x +2) we get,

⇒ (x² + x - 4) - (2x +2) = 0

⇒ x² - x - 6 = 0

to get the value of x we factorize this equation

⇒ x² - (3-2)x - 6 = 0

⇒ x² - 3x +2x - 6 = 0

⇒ x (x - 3) + 2 (x - 3) = 0

⇒ (x - 3) (x +2) = 0

from x+2 = 0, we get the value of x = -2

and from x-3 = 0, we get the value of x = 3,

So that the value of x in this equation (x/2) - (2/x+1) = 1 is -2 and 3.

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This problem can be solved by setting up two equations to represent the number of enchilada and taco meals being served. Let x be the number of enchilada meals and y be the number of taco meals. Then we have:

x + y = 250 (representing the total number of meals)

5x + 7y = 1500 (representing the total cost of the food)

Solving these equations using methods such as substitution or elimination will give you the values of x and y, i.e. the number of enchilada and taco meals being served at the party.

Answer:

x + y = 250 (representing the total number of meals)

5x + 7y = 1500 (representing the total cost of the food)

Step-by-step explanation:

If the store sells 80 feet of rope, it makes a profit of $6.4.

The money made from selling a product, which should be higher than its cost price, is referred to as the profit. It is the gain from any type of commercial activity. In other words, a gain or profit is judged to have occurred when the selling price (SP) of a product exceeds its cost price (CP).

Given the amount a hardware store pays for buying nylon rope is represented by the equation,

y = 0.12x

the cost price of rope is y = 0.12x

and the amount the hardware store charges when selling the rope is represented by the graph,

from graph,

we find the coordinates (1, 0.20) (2, 0.40)

the equation of a line is y = mx + c

since the graph passes from the origin (0, 0) so the equation of the graph will be,

y = mx

and  m = (.40 - 0.20)/(2 - 1)

m = 0.20

selling price of rope = y = 0.20x

where x is the length of rope in feet and y is the amount,

If the store sells 80 feet of rope,

the cost price of  80 feet of rope is

y = 0.12x

y = 0.12(80)

y = $9.6

and the selling price of 80 feet of rope is

y = 0.20x

y = 0.20(80)

y = $16

and profit = selling price - cost price

profit = 16 - 9.6

profit = $6.4

Hence profit is $6.4.

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Answer:

[tex]f(x) = x {}^{2} [/tex]

4 inches he should show for the distance on his floor plan.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure.

Given:

Scale: 1 inch = 2 feet

For 8 foot length of tree house he draw x inch(say)

So, 1 inch/ 2 feet = x/8

8 = 2x

x= 8/2

x= 4 inches

Hence, the distance is 4 inches.

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The required general solution of the differential equation in implicit form y = [tex][(3/2) * (15x + C) * x^{-3}]^{-3/2}[/tex].

The differential equation is a nonlinear equation and cannot be solved exactly by standard methods. One way to approach a solution is to try to find a substitution that transforms the equation into a separable form, where the variables can be separated and integrated separately. A common approach is to make the substitution y = v^(-2/3), which transforms the equation into:

3x^2 * (2/3) * v^(-5/3) * v' + 6x * v^(-2/3) = 15 * v^(-5/3)

Dividing both sides by v^(-5/3), we get:

3x^2 * (2/3) * v' + 6x * 3 * (2/3) * v^(1/3) = 15

This is now a separable differential equation, and we can integrate both sides to find the general solution:

∫(3x^2 * (2/3) * v' dx) = ∫(15 dx) + C

(2/3) * x^3 * v = 15x + C

v = (3/2) * (15x + C) * x^(-3)

Finally, substituting back for y = v^(-2/3), we get the general solution:

y = [tex][(3/2) * (15x + C) * x^{-3}]^{-3/2}[/tex]

This is the general solution of the differential equation in implicit form. To find an explicit form, one could solve for C using initial or boundary conditions.

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Answer:

<+3.5

as I think,.....

Step-by-step explanation:

The correct response is B. Because respondents were self-selected, the findings cannot be extrapolated to the general population.

All citizens of a country, whether they live there permanently or are only passing through, are considered to be part of the "population." Regularly, this indicator shows the local population in a specific location. Growth rates are the yearly changes in population brought on by births, deaths, and net migration. The complete student body at a school is an illustration of a population. At the time of data collection, it would include every student enrolled in that institution. Each of these pupils' data is gathered, depending on the issue statement. Whether they are a part of a nation or a group of people who share a given quality, all of the individuals in a group are considered to be a population.

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Based on the information, she can infer that the children meet at 7:00 pm EST to play video games. Additionally, the best flight ticket for Morgan is Sunset airline since it is $12 cheaper than Autumn airline.

According to the information, Joey is in Ohio and Grayson is in Oregon. These two states have different time zones, in the case of Ohio it is (-5) and in the case of Oregon it is (-8). Therefore, they connect to play at 7:00 pm EST because when Grayson arrives at his house at 4:00 pm, in Ohio it is 7:00 pm. However, Joey is already connected since 4:20 pm that he arrived at his house.

To identify which is the best ticket for Morgan, we must add all the services that she wants to include in her plane trip and then find the difference between the value of the two tickets.

Sunset airline:

$219 + $80 + $30 = $329

Autumn airlines:

$261 + $40 + $40 = $341

$341 - $329 = $12

According to the above, Sunset airlines ticket is cheaper.

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The player would make or miss 10 shots.

The basketball player with a 50 percent shooting average would make or miss 10 baskets out of 21 shots taken. The pattern of makes and misses would be random, meaning there is no particular pattern for the player to follow. For example, we could see the following sequence of makes and misses: make, miss, make, make, miss, miss, make, miss, make, make, miss, make, make, miss, make, miss, make, miss, make, make, miss. We can calculate the expected outcomes of each shot by dividing the total number of shots (21) by the shooting average (50 percent). This gives us an expected outcome of 10.5, which is rounded to 10. Therefore, the player would make or miss 10 shots.

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The number of bracelets and earrings sold is 10 and 16.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

Bracelets = x

Earings = y

Cost of bracelets = $5.00

Cost of the earrings =  $3.00

Now,

One day she sold 6 more earrings than bracelets and her sales totaled $98.

We can make two equations as,

y = x + 6 _____(1)

5x + 3y = 98 ______(2)

Substituting (1) in (2)

5x + 3(x + 6) = 98

5x + 3x + 18 = 98

8x = 98 - 18

8x = 80

x = 10

And,

y = 10 + 6

y = 16

Thus,

Bracelets = 10

Earings = 16

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Answer:

24

Step-by-step explanation:

16/12 is 1.333333333

20/15 is 1.333333333

18x1.333333333 is 24

Volume of the cone is 178 ft³.

Volume is defined as the space occupied within the boundaries of any three-dimensional shape.

Its SI unit is meter³.

Given,

Radius and height of cylinder and cone are same

Volume of cylinder = 534 ft²

Let radius be r and height be h

Volume of cylinder = πr²h

Volume of cone = 1/3πr²h

⇒ Volume of cone = 1/3 (Volume of cylinder)

⇒ Volume of cone = 1/3 × 534

⇒ Volume of cone = 178 ft³

Hence, 178 ft³ is the volume of cone.

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The height that will minimize the amount of tin that will be required to construct is 4 inches.

Given that,

It is necessary to build a cylindrical, open-top container with a 167 cubic inch volume.

To find : What height will result in the least amount of tin being used to make the can? ?

V = πr^2h. Eq1. And. A =2πr^2 +2πrh. Eq2

From Eq1 h = V/πr2. Eq3

Sub Eq3 into Eq2

Then A = 2πr^2 + 2πr ×(V/πr^2). And V =16π

So A = 2πr^2 + 32π/r

dA / d r = 4πr - 32π/r^2 = 0 at max/ min

r^3 -8 =0

r^3 =8

r= 2. sub into Eq3

h = 16π/ π×2^2

h=4 inches

Therefore, 4 inches is the height that will require the least amount of tin to build.

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The number of people they use at least two facilities is 37

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

n( of people that use gym and pool only) = 15-1 = 14

n( of people that use pool and track only) = 14-1 = 13

n( of people that use gym and track only) = 10-1 = 9

therefore total number of people that use atleast two facilities = 14+13+9+1 = 37

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A histogram is a graphical representation of data that uses bars of different heights to represent the frequency of a given variable.

It is used to display the distribution of a categorical variable by showing the number of data points that fall into each of several categories.

To calculate the heights of the bars in a histogram, you first need to determine the number of data points in each category. This is done by counting the number of data points that fall into each category, and then dividing by the total number of data points. This gives us the histogram of each category, which can then be used to calculate the height of the bar. The formula for this is:

Bar Height = Frequency of Category / Total Number of Data Points

For example, say there are 10 data points in the category “A” and 20 data points in the category “B”. The frequency of “A” is 0.5 (10/20), and the frequency of “B” is 0.5 (20/20). The height of the bar for “A” would be 0.5, and the height of the bar for “B” would be 0.5.

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Answer:1 rose bush costs $11.50

             1 geranium costs $9.50

Step-by-step explanation:

4 rose bushes 3 geraniums = $74.50

7 rose bushes 2 geraniums = $99.50

8 rose bushes 6 geraniums = $149

21 rose bushes 6 geraniums = $298.50

13 rose bushes = $149.50

1 rose bush = $11.50

3 geraniums =$74.50-($11.50x4) = $28.50

1 geranium = $9.50

There is no way to accurately answer this question as there are too many variables to consider, such as the population size and crime rate of the state.

There is no way to accurately answer this question as there are too many variables to consider. The population size of the state would be an important factor in calculating the number of murders per 100,000 residents. The population size of the state would determine how many people are in the state with an automatic weapon and therefore how many potential murders could occur. Additionally, the crime rate of the state would be an important factor in determining the number of murders per 100,000 residents as it would indicate whether or not there would be a higher propensity for crime in the state. Additionally, the availability of other weapons, such as handguns or knives, would also be a factor as it could reduce or increase the number of murders with automatic weapons. All of these factors, as well as others, make it impossible to accurately determine the number of murders per 100,000 residents in a state with 1 thousand automatic weapons.

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Answer:

The answer is $99

Step-by-step explanation:

The total money Lincoln has to pay for his family to see a movie and share 4 snacks is $59. When Lincoln buys x snacks to share, the total cost would be $39 plus $5x.

The costs that Lincoln has to pay consists of two parts: the cost for the tickets and the cost for snacks. Lincoln himself and his two kids makes for 3 people in total. A ticket for each person costs $13, so the cost for tickets is 3 multiplied by $13, which equals $39.

If Lincoln buys 4 snacks for everybody to share, each at a price of $5, these snacks would cost 4 multiplied by $5, which is $20 in total. So, the total cost would be $39 (for tickets) plus $20 (for snacks), resulting in a total of $59.

For the case when Lincoln buys x snacks for everybody to share, just replace the number 4 with x in our snacks calculation. That would be $5x for the snacks cost. The total cost Lincoln would have to pay is then, still $39 for tickets, plus $5x for snacks.

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