Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.(3,-5) , (4,5)

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Explanation:

The event space is the set of outcomes we want to happen.

The event space is {5, 6, 7, 8, 9, 10, 11} which consists of getting a value greater than 4. There are 7 items in this event space. Let A = 7.

The sample space consists of all possible outcomes. The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} and there are 11 items in the sample space. Let B = 11.

Divide the values of A and B to get the answer we're after

A/B = 7/11

This is the probability of selecting a value greater than 4.

Answer:

Dont really see a question

Step-by-step explanation:

its 21

21x2 is 42+6 is 48 which is 2 less than 50

Complete the square in the denominator.

\(s^2 - 4s + 8 = (s^2 - 4s + 4) + 4 = (s-2)^2 + 4\)

Rewrite the given transform as

\(\dfrac{3s-14}{s^2-4s+8} = \dfrac{3(s-2) - 8}{(s-2)^2+4} = 3\times\dfrac{s-2}{(s-2)^2+2^2} - 4\times\dfrac{2}{(s-2)^2+2^2}\)

Now take the inverse transform:

\(L^{-1}_t\left\{3\times\dfrac{s-2}{(s-2)^2+2^2} - 4\times\dfrac{2}{(s-2)^2+2^2}\right\} \\\\ 3L^{-1}_t\left\{\dfrac{s-2}{(s-2)^2+2^2}\right\} - 4L^{-1}_t\left\{\dfrac{2}{(s-2)^2+2^2}\right\} \\\\ 3e^{2t} L^{-1}_t\left\{\dfrac s{s^2+2^2}\right\} - 4e^{2t} L^{-1}_t\left\{\dfrac{2}{s^2+2^2}\right\} \\\\ \boxed{3e^{2t} \cos(2t) - 4e^{2t} \sin(2t)}\)

Regression equation correctly models the data is: y = -43.98x + 1,279.93

To determine the regression equation that correctly models the data, we can use the method of linear regression. The regression equation for a straight line is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.

Using the given table, we can calculate the necessary values to determine the regression equation. Let's denote the sigma notation as Σ.

The slope (m) can be calculated using the formula:

\(m = (Σxy - (Σx)(Σy) / n(Σx^2) - (Σx)^2)\)

Plugging in the values from the table:

m =\((776,600 - (299)(12,400) / 6(18,109) - (299)^2)\)

m = (776,600 - 3,708,800 / 6(18,109) - 89,401)

m = (-2,932,200 / 66,654)

m ≈ -43.98

The y-intercept (b) can be calculated using the formula:

b = (Σy - m(Σx)) / n

Plugging in the values from the table:

b = (12,400 - (-43.98)(299)) / 6

b ≈ 1,279.93

The correct regression equation that models the data is:

y = -43.98x + 1,279.93

Out of the given options, the correct regression equation is:

y = -43.98x + 1,279.93

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Answer:

this list

Step-by-step explanation:

1×12000=12000

2×6000=12000

3×4000=12000

4×3000=12000

5×2400=12000

6×2000=12000

8×1500=12000

10 ×1200=12000

12 ×1000=12000

The answer should be A. :)

The correct rational function of the graph is,

⇒ f (x) = 1 /(x + 5)²

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The graph is shown in fgigure.

Now, By graph of function,

The graph is not defined at x = - 5.

Hence, From equation (i);

⇒ f (x) = 1 /(x + 5)²

Clearly, Function is noy defined at x = - 5.

Hence, The correct rational function of the graph is,

⇒ f (x) = 1 /(x + 5)²

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Answer:

22 feet

Step-by-step explanation:

As the given measurements are not all in the same units, convert all measurements to inches using the conversion 1 ft = 12 inches:

Therefore:

Draw a diagram using the given information (see attachment).

From the diagram, we can see that the flagpole and the person are parallel.  Therefore, the two triangles are similar.

In similar triangles, corresponding sides are always in the same ratio.

Therefore, set up a ratio of height to shadow length and solve for h:

\(\implies \sf Flagpole\;height:Flagpole:shadow=Person\;height:Person\;shadow\)

\(\implies \sf h:168=66:42\)

\(\implies \sf \dfrac{h}{168}=\dfrac{66}{42}\)

\(\implies \sf h=\dfrac{66}{42} \cdot 168\)

\(\implies \sf h=\dfrac{11088}{42}\)

\(\implies \sf h=264\;inches\)

Convert the height into feet by dividing by 12:

\(\implies \sf h=\dfrac{264}{12}=22\;feet\)

Therefore, the height of the flagpole is 22 feet.

The given statement 53 + x = x - 4 is not a valid equation and 53 = -4 it means that there is no solution.

The expression on the left-hand side of the equals sign is usually referred to as the "left-hand side" or "LHS" of the equation, and the expression on the right-hand side of the equals sign is usually referred to as the "right-hand side" or "RHS" of the equation.

Let's call the unknown number "x".

According to the problem, the sum of 53 and x is 4 less than x. This can be expressed as:

53 + x = x - 4

We must place x on one side of the equation alone in order to solve for it. By removing x from both sides of the equation, we can do this:

53 = -4

This is not a valid equation, and it means that there is no solution.

For example, the equation 2x + 3 = 7 is a simple equation with one variable (x). In this equation, 2x + 3 is the left-hand side and 7 is the right-hand side. To solve this equation, we need to find the value of x that makes both sides equal. We can do this by subtracting 3 from both sides of the equation, and then dividing both sides by 2. This gives us:

2x + 3 - 3 = 7 - 3

2x = 4

x = 2

So the solution to this equation is x = 2.

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The sum of 53 and a number is 4 less than the number. Find the numbers?

Answer:

\(\pi\)

Step-by-step explanation:

Area = \(\pi x^{2}\)  For a full circle.  This is 1/4 of a circle

A= \(\frac{\pi 2^{2} }{4}\) = \(\frac{\pi 4}{4}\) = \(\pi\)

Answer : The area of the shape is, 111.02 units 2

Answer:

Step-by-step explanation:

order is not important so

25 ways to fill the first spot

24 ways to fill the second

23 ways to fill the third

...

19  ways to fill the 7th

25•24•23•22•21•20•19 = 2,422,728,000

which also equals 25! / (25 - 7)!

The constant of proportionality is estimated as 116.67.

Division is a mathematical operation, in which we distribute the number in equal parts, the number on the numerator is the total quantity and the number on the dinominator is equal parts of numbers which have to be distributed.

We denote division by '÷' this symbol.

It is given that the weight of 3 eggs is 350 g.

The constant of proportionality is a constant ratio, which shows that two variables are is in proportional relation.

y = kx

where, x and y are two variables and k is the constant ratio.

the required result is  constant of proportionality in grams per egg.

We have one variable  'number of eggs' and second variable 'weight of eggs'.

3 eggs = 350 g

1 egg =  g

1 egg = 116.67 g

Since the weight of egg increase 116.67 g per egg.

Hence, The constant of proportionality is 116.67.

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Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Answer:

150 yd^2

Step-by-step explanation:

3*5=15

2*5=10

15*10=150 yd^2

Answer:

150 yards

Step-by-step explanation:

2 ft = 10 yards

3 ft = 15 yards

10 * 15 = 150 yards^2

Answer:

7x+10

Step-by-step explanation:

2x(3x)+1x(x+10)

6x+1x+10

7x+10

Answer:

1.5 or 12

Step-by-step explanation:

Answer:

102m-51

Step-by-step explanation:

2(51m-52)+53

= 102m - 104+53

102m-51

Factorize the expression:

\(2(51m-52)+53\)

\(102m-104 +53\)

\(102m-51\)

\(51(2m-51)\)

      ⬆️

Simplify the expression:        

\(2(51m-52)+53\)

\(2*51m-2*52+53\)

\(102m-2*52+53\)

\(102m-104+53\)

\(102m(-104+53)\)

\(102m-51\)

     ⬆️

The value of q is 0.35.

The value of p is 0.16.

The value of r is 0.27.

The value of P(A given NOT B) is approximately 0.4211.

To calculate the values of p, q, and r, we can use the information provided in the Venn diagram and the probabilities of events A and B.

Given:

P(A) = 0.43

P(B) = 0.62

P(A∩B) = 0.27

Calculating the value of p:

The value of p represents the probability of event A occurring without event B. In the Venn diagram, p corresponds to the region inside A but outside B.

We can calculate p by subtracting the probability of the intersection of A and B from the probability of A:

p = P(A) - P(A∩B)

= 0.43 - 0.27

= 0.16

Therefore, the value of p is 0.16.

Calculating the value of q:

The value of q represents the probability of event B occurring without event A. In the Venn diagram, q corresponds to the region inside B but outside A.

We can calculate q by subtracting the probability of the intersection of A and B from the probability of B:

q = P(B) - P(A∩B)

= 0.62 - 0.27

= 0.35

Therefore, the value of q is 0.35.

Calculating the value of r:

The value of r represents the probability of both event A and event B occurring. In the Venn diagram, r corresponds to the intersection of A and B.

We are given that P(A∩B) = 0.27, so the value of r is 0.27.

Therefore, the value of r is 0.27.

Finding the value of P(A given NOT B):

P(A given NOT B) represents the probability of event A occurring given that event B does not occur. In other words, it represents the probability of A happening when B is not happening.

To calculate this, we need to find the probability of A without B and divide it by the probability of NOT B.

P(A given NOT B) = P(A∩(NOT B)) / P(NOT B)

We can calculate the value of P(A given NOT B) using the provided probabilities:

P(A given NOT B) = P(A) - P(A∩B) / (1 - P(B))

= 0.43 - 0.27 / (1 - 0.62)

= 0.16 / 0.38

≈ 0.4211

Therefore, the value of P(A given NOT B) is approximately 0.4211.

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Answer:

The central angle is 5/3 radians or approximately 95.4930°.

Step-by-step explanation:

Recall that arc-length is given by the formula:

\(\displaystyle s = r\theta\)

Where s is the arc-length, r is the radius of the circle, and θ is the measure of the central angle, in radians.

Since the intercepted arc-length is 10 meters and the radius is 6 meters:

\(\displaystyle (10) = (6)\theta\)

Solve for θ:

\(\displaystyle \theta = \frac{5}{3}\text{ rad}\)

The central angle measures 5/3 radians.

Recall that to convert from radians to degrees, we can multiply by 180°/π. Hence:

\(\displaystyle \frac{5\text{ rad}}{3} \cdot \frac{180^\circ}{\pi \text{ rad}} = \frac{300}{\pi}^\circ\approx 95.4930^\circ\)

So, the central angle is approximately 95.4930°

Answer:

1. 40/8 = 45/9

2. 42/14 = 15/5

3. 14/2 = 56/8

4. 8/4 = 26/13

Step-by-step explanation:

Answer: y = -0.5x +1

Step-by-step explanation:

The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.

1. The given function is f(x) = \(-2(x+4)^2\) + 1.

2. To find the maximum of the function, we need to determine the vertex of the parabola.

3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.

4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.

5. The x-coordinate of the vertex is given by h = -4.

6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.

7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.

8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).

9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.

10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.

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Answer:

1. rapid development

2. 2007-2010

Step-by-step explanation:

Answer:

in the picture

Step-by-step explanation:

Answer:

42-9×9+64

=42-81+64

= 106-81

=25

Answer:

Step-by-step explanation:

Answer:8 days and 12 hours

Step-by-step explanation:30$ is each day

Answer:

800 miles

Step-by-step explanation:

Its 800 miles

Step-by-step explanation:

3/4=9/12 CORRECT

2/3=6/12 FALSE

Step-by-step explanation:

What is done to top of the fraction must be done to the bottom as well in order for the renaming to be true.

3*3 = 9

4*3 = 12

Therefore proven to be true

However,

2*3 = 6

but 3*3 = 9

The second fractions is renamed incorrectly and should be either 2/4=6/12 or 2/3=2/9

Hope this helps!

Answer:

The answer is y=-1 (answer is C).

If the water snake is initially 30 meters below the ground level and then climbs 20 meters upward, it will be 30 - 20 = 10 meters below the ground level. However, if it then slips down 10 meters, it will be 10 + 10 = 20 meters below the ground level.