The scatter plot shows the number of pumpkins that have been picked on the farm during the month of October:

A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Pumpkins and the x axis is labeled Days in October

Part A: Using computer software, a correlation coefficient of r = 0.51 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)

Part B: Instead of comparing the number of pumpkins picked and the day in October, write a scenario that would be a causal relationship for pumpkins picked on the farm. (5 points)



Question 4 (Essay Worth 10 points)
(05.07 HC)

A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table shows the data:


Number of hours of sunlight
(x) 0 1 2 3 4 5 6 7 8 9
Height of plant in cm
(y) 4 7 10 13 16 19 22 25 28 31


Part A: Is there any correlation between the number of hours of sunlight that a plant receives and the height to which it grows? Justify your answer. (4 points)

Part B: Write a function that best fits the data. (3 points)

Part C: What does the slope and y-intercept of the plot indicate about the plant? (3 points)


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FDK121.12

Based on the scale, the actual length of the Golden Gate Bridge is  68,600 inches.

A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The scale drawing is usually reduced at a constant dimension. An example of a scale drawing is a map.

The scale of a drawing is usually written in this format -  length in the drawing, a colon (:), then the matching length on the original image. An example of a scale is 1 : 19,600. This scale means that 1 inch of the postcard represents 19.600 of the original Golden Gate Bridge.

Actual length of the Bridge = scale x length of the bridge in the postcard

19,600 x 3.5 = 68,600 inches

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Answer:

[tex]\Large\boxed{a)~4\sqrt{3} }[/tex]

[tex]\Large\boxed{b)~10\sqrt{10} }[/tex]

Step-by-step explanation:

Given term

[tex]\sqrt{48}[/tex]

Factorize 48 inside the radical sign

[tex]\sqrt{2\times2\times2\times2\times3}[/tex]

Combine terms to form squares

[tex]\sqrt{2^2\times2^2\times3}[/tex]

Simplify the radical sign

[tex](2\times2)\sqrt{3}[/tex]

[tex]\Large\boxed{4\sqrt{3} }[/tex]

Given term

[tex]\sqrt{1000}[/tex]

Factorize 1000 inside the radical sign

[tex]\sqrt{2\times2\times2\times5\times5\times5}[/tex]

Combine terms to form squares

[tex]\sqrt{2^2\times5^2\times2\times5 }[/tex]

Simplify the radical sign

[tex](2\times5)\sqrt{2\times5}[/tex]

[tex]\Large\boxed{10\sqrt{10} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The probability that at least one of them will get scholarship is 0.93

The given parameters are:

P(Boy) = 0.75

P(Girl) = 0.72

The probability that at least one of them will get scholarship is calculated using

P = P(Boy only) or P(Girl only) or P(Both)

This is then calculated as:

P = 0.75 * (1 - 0.72) + 0.72 * (1 - 0.75) + 0.72 * 0.75

Evaluate the products

P = 0.21 + 0.18 + 0.54

Evaluate the sum

P = 0.93

Hence, the probability that at least one of them will get scholarship is 0.93

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The question requires that we have to state the hypothesis:

null hypothesis;H0: u1 < u2, the alternate hypothesis;H1: u1 > u2. The one tail test is what is to be used.

H0: u1 < u2

H1: u1 > u2

The one tail test statistic is what is to be used here

[tex]\sqrt{\frac{30.8}{17} +\frac{6.1}{15} }[/tex]

= 1.49

The df = 17 + 15 - 2

= 30

test statistic = 18.9 - 17.4 / 1.49

= 1.007

We have the critical value on excel as T.INV(0.9,30)

=  1.310

E. At 0.1, we can conclude that  t-value (1.007) does not lies in the rejection area. We fail to reject the null hypothesis. Hence we conclude that the mean vacation with the unlimited plan is greater.

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Answer:

B

Step-by-step explanation:

5x - 625[tex]x^{4}[/tex] ← factor out 5x from each term

= 5x(1 - 125x³) ← this factor is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

1 - 125x³

= 1³ - (5x)³

= (1 - 5x) (1² + 5x(1) + (5x)² )

= (1 - 5x) (1 + 5x + 25x²)

Then

5x - 625[tex]x^{4}[/tex] = 5x(1 + 5x + 25x²)

Answer: 18

Step-by-step explanation: 18=1+8=9

its complicated but when you check something like

23= 2+3 =5

 10 = 1+0=1

the individual digits of 18 are 1 and 8

Sum = 1+8=9

multiply 9 by 2 we get 18

18 is also a multiple of 9.

I hope this helps

He worked 43 hours to earn Rs. 23250

His basic pay is Rs. 18000 for a basic 36 hours a week. His salary is

Rs. 23250. This proves that he has worked extra time. So the amount earned in the extra hours equals Rs. 23250 - Rs. 18000 = Rs.5250.

Amount per hour earned in basic pay = 18000/36 = Rs.500 a hour.

∴ Amount per hour earned in extra hours = 1.5 x 500 = 750  per hour.

So number of hours he worked in extra time =  Rs.5250/750 = 7 hours.

Thus total number of hours = 36 + 7 = 43 hours.

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Answer:

1. (2,2)

2. (-20, -1)

3. (4,3)

Step-by-step explanation:

See attached images

Answer:

The solutions to the sets of equations may be found by either a substitution process or by graphing and looking for the point that the two lines formed by the quations intersect.  Both approaches are described.

The "solution" to these sets of equations is the point at which the two lines intersect each other.

Step-by-step explanation:

1. 3x-y=4 and x+2y=6

x+2y=6

6x-2y=8     We can simply add these two equations since y will            disappear, leaving just x.

7x = 14  [result of addition]

x = 2    [Solve]

Since x = 2,  [Then use the solution for x to find y]

x+2y=6

(2)+2y=6

2y = 4

y = 2

(2,2) is the solution (where the lines intersect).  See attached graph.

2. 2x-y= -39 and x+y= -21

2x-y= -39

x+y= -21               Add the two equations (since the y will be eliminated)

3x = -60

x = -20

Find y:  

x+y= -21

(-20)+y= -21

y = -1

Solution is (-20,-1)

3. 2x+y =11 and 6x-5y =9

2x+y =11

-6x+-3y = -33    [Multiply by -3 and then add to other equation.  This allows us to eliminate x]

6x - 5y =   9

 -8y = - 24

y = 3

2x+y =11

2x+(3) =11

2x = 8

x = 4

Solution is (4,3)

==================

See attached graph for all the graphed solutions.

==================

The substitution process also works if we isolate one of the 2 variables in one equation and then use the resulting value in the second eqaution.  For example, in problem 1:

3x-y=4

x+2y=6

Pick either equation and isolate the x or y.  I'll pick the second equation and isolate for x:

x = 6-2y

Now use this value of x (6-2y) in the other equation:

3x-y=4

3(6-2y)-y=4

18 - 6y - y = 4

-7y = -14

y = 2

Then use y=2 to fiond x, using either equation:

x+2y=6

x+2(2)=6

x = 2

The solution is (2,2).

This same approach can be used on all these problems.  It avoids trying to visualize what can be done to an entire equation to eliminate one of the variables, but it takes a bit more paper.

All solutions are graphed in the attachment.

Answer:

x = 10.7

Step-by-step explanation:

2461,8

hope this helps!! just use the formulas and substitute

[tex]f(x) = y \: \: \ \: \: \: \: \: \: \: \: \: {normal \: function} \\ f(x) = y - 1 \: \: \: \: \: \: \: func\: shifted \: down[/tex]

[tex]f(x) = \frac{ - 1}{3} x {}^{2} \\ f(x) = \frac{ - 1}{3} x {}^{2} - 1[/tex]

Answer: F(x)= -1/3x2-1

Step-by-step explanation:

The steps to solve the inverse variation will be:

The example will be y varies inversely with x and y = 2 when x = 5. Find y when x = 30

Step 1: Write the variation equation: y = k/x or k = xy:

k = xy

Step 2: Substitute in for the given values of x and y:

k = (2)(5) = 10

Step 3: Rewrite the variation equation: y = k/x with the known value of k (10):

y = 10/x

Step 4: Substitute the remaining values and find the unknown:

y = 10/30

y = 1/3

Therefore, y is 1/3 when x is 30.

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Answer: If your opponent is winning 3:1 then they are probably better then you if they are winning more then you are. (or you are just having a bad day)

Posterior probability of scenario A: P(A|data) ≈ (0.0625 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.134

Posterior probability of scenario B: P(B|data) ≈ (0.216 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.466

Posterior probability of scenario C: P(C|data) ≈ (0.05184 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.400

Let's denote the three possibilities as follows:

A: Equally talented, each player has a 0.5 probability of winning a game.

B: You are slightly better, with a 0.6 probability of winning a game.

C: Your opponent is slightly better, with a 0.6 probability of winning a game.

Given that you won the second game but lost the first, third, and fourth games, we want to find the probability of scenario C given this outcome. Let P(C) represent the prior probability of scenario C being true.

According to the given information, each of the three scenarios (A, B, and C) is equally likely, so P(A) = P(B) = P(C) = 1/3.

Now, let's update the probabilities based on the outcome of the match:

In scenario A:

The probability of winning the second game is 0.5, and the probability of losing the first, third, and fourth games is 0.5 each. Therefore, the overall probability of the observed outcome in scenario A is (0.5 * 0.5 * 0.5 * 0.5) = 0.0625.

In scenario B:

The probability of winning all three games (assuming you are slightly better) is (0.6 * 0.6 * 0.6) = 0.216.

In scenario C:

The probability of winning the second game (assuming your opponent is slightly better) is 0.4, and the probability of losing the first, third, and fourth games is 0.6 each. Therefore, the overall probability of the observed outcome in scenario C is (0.4 * 0.6 * 0.6 * 0.6) = 0.05184.

Now, we can update the probabilities based on Bayes' theorem:

Posterior probability of scenario A: P(A|data) = (P(data|A) * P(A)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))

Posterior probability of scenario B: P(B|data) = (P(data|B) * P(B)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))

Posterior probability of scenario C: P(C|data) = (P(data|C) * P(C)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))

P(data|A) = 0.0625

P(data|B) = 0.216

P(data|C) = 0.05184

Plugging in the values, we get:

Posterior probability of scenario A: P(A|data) ≈ (0.0625 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.134

Posterior probability of scenario B: P(B|data) ≈ (0.216 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.466

Posterior probability of scenario C: P(C|data) ≈ (0.05184 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.400

So, after the match, the posterior probability that your opponent is slightly better than you is approximately 0.400 or 40%.

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Answer:

y does not depend on x - it is not a function

That leaves (2) or (4)

Since one does not need y in the equation (4) is eliminated

(2) is the only possible result

For example:        x = 5

Answer:

range is 10

Step-by-step explanation:

highest number is 49

loweest number is 39

49 - 39 = 10

Answer:

10

Step-by-step explanation:

The range is found by taking the largest number and subtracting the smallest number

The largest number is 49

The smallest number is 39

The range is 49-39 = 10

If Connie spent $26 on 8 books, The number of hard covers she buy is 5 hard cover.

Let h represent hard cover

Let p represent paperbacks

Formulate an equation

h + p= 8.......(1)

4h + 2p= 26......(2)

Multiply equation (1) by -2

-2h + -2p = -16

4h  +  2p   = 26

2h  +   0p =10

2h = 10

Divide both side by 2h

h=10/2

h =5 hard covers

Paper backs

P=5-2

P=3 paper backs

Therefore If Connie spent $26 on 8 books, The number of hard covers she buy is 5 hard cover.

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Given

[tex]7 - px - x^2 = 16 - (q + x)^2[/tex]

expanding the right side gives

[tex]7 - px - x^2 = 16 - (q^2 + 2qx + x^2)[/tex]

[tex]7 - px - x^2 = 16 - q^2 - 2qx - x^2[/tex]

Two polynomials of equal degree are the same if their coefficients are identical. This means

[tex]\begin{cases}16 - q^2 = 7 \\ -2q = -p\end{cases}[/tex]

[tex]16 - q^2 = 7 \implies q^2 = 9 \implies q=\pm3[/tex]

[tex]-2q = -p \implies p = 2q = \pm6[/tex]

Both [tex]p[/tex] and [tex]q[/tex] are positive, so [tex]\boxed{p=6}[/tex] and [tex]\boxed{q=3}[/tex].

Answer: D

Step-by-step explanation:

If the leading coefficient is negative, then as [tex]x \to \infty[/tex], [tex]f(x) \to -\infty[/tex].

If the leading coefficient is negative, then as [tex]x \to -\infty[/tex], [tex]f(x) \to \infty[/tex].

This leaves D as the correct answer.

The slope-intercept form of given equation is y = 1/2x + 5/2.

According to the statement

we have given that the equation y-3 = 1/2(x-1) and the passing points are (–9, –2) and (1, 3).

And we have to find the slope-intercept form of the equation

slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

So, According to this

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

convert this into y = mx +b form then

y-3 = 1/2x -1/2

here m is 1/2 and b is -1/2.

Then

y-3 = 1/2x -1/2

Add three on both sides then

y = 1/2x + 5/2

So, The slope-intercept form of given equation is y = 1/2x + 5/2.

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Answer:

its cccccccc

Step-by-step explanation:

Answer:

3 sqrt 5

Step-by-step explanation:

diameter talks about the center of the circle..and the middle of the circle lies between 3 and 5

Answer:

Number = 12

Step-by-step explanation:

2n-7=n+5 (+7 to both sides)

2n=n+12 (-n to both sides)

n=12

Answer:

a = 3.14

b = 6.28

Step-by-step explanation:

The interval where the function is decreasing is where increasing x values result in decreasing y values. The y values peak at the point (3.14, 2) and decrease until the point (6.28, 0) where the function starts increasing again.

The correct unscrambling of whyrot is worthy.

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Using the fundamental theorem of calculas the derivative of function g(x)=[tex]xt^{3}+t^{5}[/tex] at x=0 is [tex]t^{3}[/tex].

Given a function g(x)=[tex]xt^{3}+t^{5}[/tex].

We are required to find the derivative of the function g(x) at x=0.

Function is relationship between two or more variables expressed in equal to form. The values entered in a function are part of domain and the values which we get from the function after entering of values are part of codomain of function. Differentiation is the sensitivity to change of the function value with respect to a change in its variables.

g(x)=[tex]xt^{3}+t^{5}[/tex]

Differentiating with respect to x.

d g(x)/dx=[tex]t^{3}[/tex]+0  [Differentiation of x is 1 and differentiation of constant is 0]

=[tex]t^{3}[/tex]

Hence using the fundamental theorem of calculas the derivative of function g(x)= [tex]xt^{3}+t^{5}[/tex] at x=0 is [tex]t^{3}[/tex].

The function given in the question is incomplete. The right function will be g(x)=[tex]xt^{3}+t^{5}[/tex].

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.

The correct option is: (b)

                                =432.

By employing multiple processes, simplification refers to reducing the expression to a simpler form. Approximation is the process of making something less complicated and hence easier to accomplish or understand, or the object that arises from this process. The mathematical formula is simplified to its nearest value but is not exactly correct.

Therefore, we must follow the order listed above when simplifying expressions. In the example before, we divide 8 by 4 and then add the result to 12 because, according to BODMAS, division (D) comes before multiples (M).

[tex]$3 \cdot 2^{3} \cdot 2 \cdot 3^{2}Calculate exponents $2^{3}: 8$$$=3 \cdot 8 \cdot 2 \cdot 3^{2}$$Calculate exponents $3^{2}: 9$$$=3 \cdot 8 \cdot 2 \cdot 9$$ $3 \cdot 8 \cdot 2 \cdot 9= 432$$$=432$$[/tex]

So. the value will be = 432

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I understand that the question you are looking for is :

Simplify the expression to a single numerical value.

3*2^3*2*3^2

(a)144

(b)432

(c)900

(d)5,184

Compounded continuously the balance grows at a continuous rate of 1.7%.

What is compound interest ?

The model used for continuous compounding is

 f(t) = Pe^(rt)

where P is the principal amount, and r is the interest rate being compounded. Assuming a typo in your given equation, you have

 f(t) = 1000·e^(0.017t)

Matching the various parts of the equation, we see that P = 1000 and r = 0.017 = 1.7%.

Therefore, the balance grows at a continuous rate of 1.7%.

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Answer:

  32.4 inches

Step-by-step explanation:

Sam wants the increase to be 8% of 30 inches.

The amount of increase Sam wants in his waist size is ...

  8% × 30 in = 0.08×30 in = 2.4 in

Adding the wanted increase to his present size would make Sam's waist size be ...

  30 in + 2.4 in = 32.4 in

Sam wants his waist size to be 32.4 inches.

__

Additional comment

The larger size can also be computed from ...

  30 +8%×30 = (1 +8%)×30 = 1.08×30 = 32.4 . . . inches

Considering the piecewise function, it is found that f(5) is given by:

f(5) = -1.

A piecewise function is a function that has different definitions, depending on the input.

To find the value of f(5) looking at the graph, we have to find y when x = 5. Researching this graph on the internet, we have that, when x = 5:

The definition is at the closed circle, hence f(5) is given by:

f(5) = -1.

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