The diagonal of a TV is 28 inches long. Assuming that this diagonal forms a pair of 30-60-90 right triangles, what are the exact

Answer:

The null hypothesis states that 48% of the healthcare provider's members received their flu shot.

The alternative hypothesis claims that the proportion of members who received their flu shot differs from 48%.

Step-by-step explanation:

A null hypothesis is a proposed statement regarding a population parameter that is tested for acceptance or rejection.

An alternative hypothesis presents a contradicting statement to the null hypothesis and is accepted when evidence disproves the null hypothesis.

Answer:

1. 3.767

2. 0.145

Step-by-step explanation:

Define X as the exam scores and Y as the number of drinks.

X     Y   X-Xbar    Y-Ybar   (X-Xbar)(Y-Ybar)    (X-Xbar)²       (Y-Ybar)²    

75    5    -2.3          2.3          -5.29                      5.29              5.29

92    3     14.7         0.3           4.41                       216.09           0.09

84    2     6.7         -0.7           -4.69                     44.89             0.49

64    4     -13.3        1.3           -17.29                     176.89           1.69

64    2     -13.3       -0.7           9.31                       176.89           0.49

86    7     8.7           4.3           37.41                     75.69            18.49

81     3     3.7           0.3           1.11                         13.69             0.09

61     0    -16.3        -2.7           44.01                     265.69          7.29

73    1      -4.3         -1.7            7.31                        18.49             2.89

93    0    15.7         -2.7           -42.39                    246.49          7.29

sumx=773, sumy=27, sum(x-xbar)(y-ybar)= 33.9, sum(X-Xbar)²= 1240.1,sum(Y-Ybar)²= 44.1

Xbar=sumx/n=773/10=77.3

Ybar=sumy/n=27/10=2.7

1.

Cov(x,y)=33.9/9

Cov(x,y)=3.76667

Thus, the sample covariance of exam scores and energy drink consumption is 3.767

2.

Cor(x,y)=r=33.9/233.85553

Cor(x,y)=r=0.14496

The sample correlation coefficient for the relationship between exam scores and energy drink consumption is 0.145.

Response: 8n

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Clarification:

The two sides, 4n+5 and 5n+6, comprise terms 4n and 5n which total to 9n. We require 8n to add to this to achieve 17n. In simpler terms, 4n + 5n + 8n = 9n + 8n = 17n

That is the reason why the outcome is 8n. There are no additional terms because the "+5" and "+6" in the two given expressions (4n+5 and 5n+6) sum to 5+6 = 11, matching what we aim for in the perimeter expression 17n + 11

Side 1 = 4n + 5

Side 2 = 5n + 6

Side 3 = 8n

Perimeter = (side1) + (side2) + (side3)

Perimeter = (4n + 5) + (5n + 6) + (8n)

Perimeter = 4n + 5 + 5n + 6 + 8n

Perimeter = (4n + 5n + 8n) + (5 + 6)

Perimeter = 17n + 11

So this confirms we possess the correct expression for the third side that is missing.

Conclusion:

Please refer to the explanation provided.

Detailed explanation:

Starting with these facts:

Total revenue = $250

Fee charged = $70 per car

Tips received = $50

Equation 1 representing the above:

(Fee per car × number of cars) + tips = total revenue

Let the number of cars be c.

Thus, we have:

$70c + $50 = $250

Part B:

Total revenue = $250

Fee charged = $75 per car

Tips received = $35

Supplies cost per car washed = $5

Equation 2:

(Fee per car × number of cars) + tips - (supplies cost × number of cars) = total revenue

$75c + $35 - $5c = $250

$70c + $35 = $250

Part C:

Equation 1 does not factor in costs associated with washing the car, while equation 2 does incorporate costs, which are deducted from the amount charged per car. Additionally, tips in equation 1 total $50 compared to a $35 fee in equation 2.

Answer:

60

Step-by-step explanation:

The function provided is:

The average rate of change of h(t) as time goes from t=a to t=b is expressed as:

This function can be reformulated as:

The rocket's peak height is 231, which occurs at t=3.75 seconds.

The initial launch happens at: t=0

and

The average rate of change from launch to max height is