what is the importance of knowing the history of the earth​

The equation that relates F and s for the spring on the jumper will be F=4x.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, Todd increases the weights by 8 and observes a 2 cm spring extension. According to Hook's Law, the force exerted on a spring by the weights directly affects how much it is stretched, or s.

The equation that relates F and s for the spring on the jumper is obtained as,

F=ks

8=k×2

k=8/2

F=4 x

Thus, the equation that relates F and s for the spring on the jumper will be F=4x.

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Answer:

A (0, -3) translated to the right 4 units.

Step-by-step explanation:

If you go right 4, you get (4, -3)

The average rate of change of the function at the interval x = 5 to x = 9 is 1.25

The interval is given as

x = 5 to x = 9

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

x = 5 and y = 15

x = 9 and y = 20

This means that

f(5) = 15 and f(9) = 20

The average rate of change is then calculated as

Average rate of change = [f(9) - f(5)]/[9 - 5]

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

Average rate of change = [20 - 15]/[9 - 5]

Evaluate

Average rate of change = 1.25

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Answer:A

Step-by-step explanation: 5 to the power of 3 is 5x5x5 which is 25x5 which then equals 125

The distance the pear will be in the air if his Dad sees him and catches if at 6 feet above the ground is 19/30 meters.

The term distance can be defined as a numerical qualitative measurement of how far apart  points are from each other.

Distance is defined by the formula

d=v*t

The given parameters are:

v=30

s=6

height=25

Applying these parameters into the formula

d=30*t

d=30t

If the Dad stands 6 feet above the ground, we have

[tex]\frac{25-6}{30}[/tex]

=[tex]\frac{19}{30}[/tex]

Therefore the pear will be 19/30 feet in the air if the Dad sees him and catches  it at 6 feet above the ground.

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Answer:

Below

Step-by-step explanation:

In three years the interest will be

50 000 *  .1  * 3  = 15 000

He pays this and 25 000   so his remaining loan is 25 000

  we want to know how long will it be before this remaining loan

      incurs 5 000 interest ( for a total of 20 000)

25000 * . 1 * n = 5000     shows n = 2 years   more

              ( 5 years from original loan date)

Answer: 6000

Step-by-step explanation:

The formula for the first [tex]n[/tex] terms of an arithmetic sequence with first term [tex]a[/tex] and common difference [tex]d[/tex] is [tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex].

In this question, [tex]a=-27, d=6, n=50[/tex].

So, [tex]S_{50}=\frac{50}{2}[2(-27)+(50-1)(6)]=6000[/tex].

The expression -16x^(-3/2) represents a term that has a coefficient of -16 and a variable x raised to the power of -3/2.

Generally, The expression -16x^(-3/2) represents a term that consists of a coefficient of -16 and the variable x raised to the power of -3/2.

In general, the exponentiation operator (^) represents the idea of raising a number (called the base) to a certain power (called the exponent). For example, x^2 means "x raised to the power of 2" and can be calculated as x * x = x^2.

Similarly, x^3 means "x raised to the power of 3" and can be calculated as x * x * x = x^3.

The exponent -3/2 means that the base (in this case, x) is raised to the power of -3/2. This can be simplified as follows:

x^(-3/2) = 1 / x^(3/2) = 1 / (x^(3/2))

The expression -16x^(-3/2) can then be simplified as follows:

-16x^(-3/2) = -16 * 1 / x^(3/2) = -16 / x^(3/2)

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The complete Question was not found

The leading team has scored 0.13 points per game for the season that the second place player.

What is PPG Statistics?

First, consider the PPG of the current leader of the season from among the two basketball players.

The total number of points obtained by the current leader is equal to 2112.

The total number of games played by the current leader is equal to 77.

The points per game obtained by the current leader can be calculated as follows,

PPG = Total Points Obtained / Total Number of Games

[tex]\implies PPG=\frac{2112}{77}\\\implies PPG=27.42[/tex]

Now, consider the PPG of the second place player for the season.

The total number of points obtained by the second place player is equal to 2020.

The total number of games played by the second place player is equal to 74.

The points per game obtained by the second place player can be calculated as follows,

PPG = Total Points Obtained / Total Number of Games

[tex]\implies PPG=\frac{2020}{74}\\\implies PPG=27.29[/tex]

Subtracting the points per game of both players, we get

[tex]27.42-27.29=0.13[/tex]

Hence, the leading team has scored 0.13 points per game (PPG) for the season compared to the second place player.

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Answer:As you can see, this line is vertical! It goes directly up. We know that because the equation says that X is equal to -3. It is telling us that no matter what the Y value is, X will be -3.

Step-by-step explanation:

The equation to find slope is to take two points

(A,B) and (C,D) and to do the following equation: D−B

                                                                               ______

                                                                                  C−A

So, let's take two points. Let's say that Y is equal to 3 and 2. In that case, since X is always -3, our points would be (−3,2) and (−3,3).

Now, let's substitute into our formula.

3−2                       1         1

------ =                  ----- =   ---

3 (−3) (subtract)  -3 + 3   0

As you can see, the final slope is 1/0

. If you put that into your calculator, it will come out as undefined, because any number divided by zero is undefined. And so your slope for any vertical line is undefined.

If you bought 90 packs of trading cards then Rare trading cards are 6

The number of favorable events to all the events in an experiment is the ratio that makes up the probability formula. Theoretical probability, Experimental probability, and Axiomatic probability are the three categories into which probability can be divided.

If the conditions are met, Y = 1/15 * X = 90 , then Y = 1/15 x 90 Y = 6.

A deck of cards has 52 cards. Therefore, 52 outcomes overall.

The number of positive results is 4 (as there are 4 kings in a deck)

Hence, there is a chance that this will happen.

P(E) = 4/52 = 1/13.

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The range of u(x) = {-15, -5,1,3,1, -5, -15} and range of v(x)= {-3,-2, -1,0,1,2,3} for the domain of x = { -3,-2,-1,0,1,2,3}

The domain of a function is defined by the set of the values of independent variables and the ranges are the set of values of dependent variables.

The domains act as an input of function where ranges act as an output.

We select domain randomly as domain are the set of independent variables. But how will be the ranges must depend on the function given us.

we are given 2 function u(x) = -2x²+3 and v(x)

for the 1st function the set of domain and ranges are different, but the domain and ranges have the same values for the 2nd function.

we select domain x= {-3, -2, -1, 0, 1, 2, 3}

the ranges for u(x) ={ -15, -5, 1, 3, 1, -5 , -15}

because, u(-3) = -2(-3)²+3 = -15

                u(-2) = -2(-2)²+3 =-5

               u(0) = 3

similarly, for the same set of x value, v(-3) = -3

                                                         v(-2) = -2

                                                         v(0) =0

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Answer:

1 < x < 8

Step-by-step explanation:

x² - 9x + 8 < 0

(x-8)(x-1) = 0

x = 8

x = 1

these are the points where the parabola intercepts the x axis. We have to find when it is under x axis

1 < x < 8

Where the voice rises and falls. But inflection also describes a departure from a normal or straight course.

Inflection points for the given equation x^2e^{-2x} are

f'(x) =[tex]2x2xe^{(-2x)}-2{(x2)} e^{(-2x)}[/tex]

f'(x) =[tex]-2(x-1)xe {(^-2x)}[/tex]

x= -b±√(b^2 - 4ac)/2a

x=4±√(16+16)4

x=4±4√2/4

x=[tex]\sqrt{2+2/2}[/tex]

x=[tex]\sqrt{2-2/2}[/tex]

We get,

x=[tex]\sqrt{(2+2)/2^{2}*\sqrt{2+2}[/tex]

so, inflection points are,

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Answer:

1.  y=2x−5

2.  y=-x-4

3. y=-1/2x+1

Step-by-step explanation:

First Question:

We are given (3, 1) and (1, -3)

The slope is the difference of y-values over x-values. From this we get:

(1−−3)/(3−1)=4/2=2

Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b

Plugging in (3, 1) gives us         1=3∗2+b    ⇒    b=1−6 = −5

We have our slope and y-intercept now, so the equation is y=2x−5.

Second Question:

We are given (-4, 0) and (1, -5)

The slope is

(-5-0)/(1--4)=-5/5=-1

Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b

Plugging in (-4, 0) gives us         0 = -1∗-4+b    ⇒    b = -4

We have our slope and y-intercept now, so the equation is y=-x-4.

Third Question:

We are given (-6, 4) and (-2, 2)

The slope is

(4-2)/(-6--2)=2/48=-1/2

Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b

Plugging in (-2, 2) gives us         2 = -1/2∗-2+b    ⇒    b = 2-1 = 1

We have our slope and y-intercept now, so the equation is y=-1/2x+1

1 hot dog cost is $1.20 .

What is costs?

A cost is the value of money that has been expended to produce something or provide a service and is therefore no longer available for use in production, research, retail, and accounting. In the case of an acquisition cost, the money spent on the acquisition is considered the cost.

Let's say that each drink costs $x and each hot dog costs $y.

Using the provided information, 3 drinks and 2 hot dogs cost $4.80. In equation form, it reads as follows:

3 x+2 y=4.80

1 drink and 1 hot dog costs $2.00. In equation form, we can write it as:

x+y=2

x=2-y

Using this value of x in first equation, we get:

3(2-y)+2 y=4.80

6-3 y+2 y=4.80

6-y=4.80

y=6-4.80

y=1.20

Thus the cost of one hot dog is  1.20$

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There are 3 extreme points does the function g(x) = (2 - x) x².

A relation between a set of inputs having one output each is called a function.

Given that;

The function is,

⇒ g ' (x) = (2 - x) x²

Now,

Since, The function is,

⇒ g ' (x) = (2 - x) x²

We know that;

The extreme points are find as;

⇒ g ' (x) = 0

So, We get;

⇒ g ' (x) = 0

⇒ (x - 2) x² = 0

This gives two values as;

⇒ (x - 2) = 0

⇒ x = 2

And, x² = 0

⇒ x = 0, 0

Thus, The extremes values are;

⇒ x = 2 , 0, 0

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An inequality that represents the height h, in inches, of a person allowed to ride rollar coaster is h ≥  48

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

Let h represent for the height of any member allowed to ride rollar coaster

From the question we know that everyone's height must be greater that 48 inches.

It means the inequalities would be

h ≥  48 tall inches

Thus, an inequality that represents the height h is h ≥  48

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Answer:

Below

Step-by-step explanation:

Deleted

Answer:

Step-by-step explanation:

To pull values from another worksheet, we need to follow these steps:

Select cell C3 and click on it.

Insert the formula: =VLOOKUP(B3,'Sheet 2'!$ B$3:$C$7,2,0)

Press enter.

Drag the formula down to the other cells in the column by clicking and dragging the little “+” icon at the bottom-right of the cell.

How do I add a LOOKUP field in Excel?

Open Design View on the table. Click a cell in the Field Name column in the first available empty row, and then type a field name for the lookup field. Select Lookup Wizard from the drop-down list by clicking the arrow after clicking in the Data Type column for that row.

To compute values in several columns, the VLOOKUP function may be used in conjunction with other functions like the Sum, Max, or Average. Since this is an array formula, all we need to do to make it function is hit CTRL+SHIFT+ENTER at the conclusion of the formula.

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x[tex]x\geq 6[/tex].

[tex]\frac{1}{2}x \geq 3[/tex]

[tex]\frac{\frac{1}{2}}{\frac{1}{2} } x\geq \frac{3}{\frac{1}{2} }[/tex]

Dividing by a fraction of the same as multiplying by its multiplicative inverse. Since the multiplicative inverse of 1/2 is 2/1, we may rewrite as:

[tex]\frac{2}{1} *\frac{1}{2} x\geq \frac{2}{1} *3[/tex]

[tex](1)x\geq(6)\\ \\x\geq6[/tex]

[tex]\frac{1}{2}(6) \geq 3\\ \\3\geq 3[/tex]

Correct!

x[tex]x\geq 6[/tex].

Answer:

f(x) = -2x +7

Step-by-step explanation:

The 2-point form of the equation for a line is suitable for this. For points (x1, y1) and (x2, y2), the equation is ...

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

For the given points (0, 7) and (3, 1), the equation is ...

y = (1 -7)/(3 -0)(x -0) +7

y = -6/3x +7 . . . . . . . . simplify.

We can use f(x) for y to get ...

f(x) = -2x +7

The system of inequalities shown by the graph are

There are some points that help in interpreting inequality graphs.

The first part is to arrange the equation in the form so that y is the subject of the formula and to the left

Then watch out for dashed lines or solid lines

Another part is the shaded portion

Equipped with tis information, it is clear that the two lines of the graph are both dashed and shaded above the line,

Hence we look out for equations having no equality sign in the inequality and due to the shading must be greater than.

This makes the first option the best choice

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The probability that the small bowl contains more cereal than the large​ one is 0.0228.

Given :

The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl.

we know that,

z = x - μ / σ

here

x = 0

μ = 1

σ = 0.5

= 0 - 1 / 0.5

= -1/0.5

= -1 / 05 / 10

= -1 * 10 / 5

=  -10 / 5

= -2

if z = -2 then p value = 0.0228

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Full question :

The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl.

If the difference follows the Normal​ model, what's the probability that the small bowl contains more cereal than the large​ one?

By using the concept of probability, it can be calculated that-

1)   P(Ace [tex]\cup[/tex] 5) = [tex]\frac{8}{52}[/tex]

2)  P(Ace [tex]\cap[/tex] 5) = 0

3)  P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]

4)   P(Even [tex]\cup[/tex] Black) = [tex]\frac{36}{52}[/tex]

5)   P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]

What is probability?

Probability gives us the information about how likely an event is going to occur.

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

1) Number of ace card = 4

  Number of '5' card = 4

  P(Ace [tex]\cup[/tex] 5) = [tex]\frac{4}{52} + \frac{4}{52}[/tex]

                    = [tex]\frac{8}{52}[/tex]

2) P(Ace [tex]\cap[/tex] 5) = 0

3) Number of odd numbered cards = [tex]5 \times 4[/tex] = 20 (Assuming the ace is odd)

 Probability of getting an odd numbered card = [tex]\frac{20}{52}[/tex]

  P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]

4) Number of black coloured even numbered card = 10

   Number of even numbered card = 20

   Number of card of black colour = 26

  P(Even [tex]\cup[/tex] Black) = [tex]\frac{20}{52} + \frac{26}{52} - \frac{10}{52}[/tex]

                              = [tex]\frac{36}{52}[/tex]

5) Number of face cards of diamond = 3

   P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]

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Answer:

182 feet

Step-by-step explanation:

Taking the fact that 112/40 = 2.8, you would need to multiply the miles per hour by 2.8 to get the feet needed.

Why is that, well I cant really explain...its just math and it works out /: