A 4-foot tall person standing with her back to the sun casts an 6-foot long shadow.

To the nearest degree, what angle does the sun make with the ground?

A) The event is "tossing a number cube once"

The sample space of this event is {1,2,3,4,5,6}.

The expected value of this event is  

[tex]1\times \frac{1}{6}+2\times \frac{1}{6}+3\times \frac{1}{6}+4\times \frac{1}{6}+5\times \frac{1}{6}+6\times \frac{1}{6}\\ \\ =\frac{1}{6}+\frac{1}{3}+\frac{1}{2}+\frac{2}{3}+\frac{5}{6}+1\\ \\ =\frac{7}{2} = 3.5[/tex]

Since 3.5 is not in the sample space of the event. Therefore, option (A) is not correct.

(B) The event is "Flipping a coin"

Sample space of this event is {HH,TT,HT,TH}

Since sample space of this event is not numbers, therefore, this cannot be the correct option either.

(C) The event is, "Randomly picking a number between 1 and 9, inclusive."

The sample space of this event is {1,2,3,4,5,6,7,8,9}.

Expected value of this event is [tex]\frac{1}{9}(1+2+3+4+5+6+7+8+9) = \frac{1}{9}(45) = 5[/tex]

Since 5 is the expected value and it is present in the sample space for this event. Therefore, option (C) is a correct choice.

(D) The sample is "Randomly picking a number between one and ten, inclusive".

The sample space of this event is {1,2,3,4,5,6,7,8,9,10}.

Therefore, expected value of the event is [tex]\frac{1}{10}(1+2+3+4+5+6+7+8+9+10) = \frac{1}{10}(55)=5.5[/tex]

Since 5.5 is not present in the sample space of this event. Therefore, option (D) is not correct either.

Hence, the correct choice is option (C).

The formula for the area of a cylinder is [tex]\pi[/tex][tex]r^{2}[/tex]×h

First, we do not have to worry about pi because we are leaving our answer in terms of it so we can move on to the radius squared.

The radius is halfway across a circle so our radius would be 4 and we have to square that and we will get a product of 16.

Lastly, we have to multiply 16 by 8 because 8 is the height of the cylinder

16 × 8 = 128

Therefore, the volume of the cylinder would be 128[tex]\pi[/tex] in.³

Answer:

V = 36 π cubic inches

Step-by-step explanation:

Test

Answer:

Its a 12

Step-by-step explanation:

The answer to the above question can be explained as under -

Here, we need to convert large units into smaller units of same class i.e. to convert liters into milliliters.

We know that,

1 liter = 1000 milliliters

So, 2 liter of soda will have -

2 X 1 liter = 2 X 1000 milliliters

2 liters of Soda = 2,000 milliliters

Thus, the correct option will be = D) 2,000 ml

25

Let w represent the weight of the animal in pounds, and d the age in days. The problem statement tells us ...

... w = 75 +2d

We want to find d when w > 125.

... 75 +2d > 125 . . . . . substitute the above expression for w

... 2d > 50 . . . . . . . . . subtract 75

... d > 25 . . . . . . . . . . . divide by 2

The animal will weigh more than 125 pounds when it is more than 25 days old.

Answer:

1 x 8

Step-by-step explanation:

7/8 rounded up equals 1 whole. 8 1/10 rounded makes 8.

In the simple linear regression model, y[tex]_i[/tex] represents the observed value of the response variable for the [tex]i_{th}[/tex] observation. Therefore, the correct answer is option c.

The simple linear regression model is expressed as y[tex]_i[/tex] = β₀ + β₁x[tex]_i[/tex] + ε[tex]_i[/tex]. In this equation, y[tex]_i[/tex] stands for the observed value of the response variable  for the i[tex]_{th}[/tex] observation in the population.

The equation y[tex]_i[/tex] = β₀ + β₁x[tex]_i[/tex] + ε[tex]_i[/tex] is used to model the relationship between a single explanatory variable and the response variable.

In this equation, y[tex]_i[/tex] denotes the observed value of the response variable.

The key components include β0 (y-intercept), β1 (slope), xi (explanatory variable), and εi (error term).

So, option c. it is the observed value of the response variable for the i[tex]_{th}[/tex] observation in the population, is the correct answer.

The probabilities are 0.25 and 0.454.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Given

A bucket contains 3 red balls, 4 yellow balls, and 5 purple balls.

The probability that the first ball is red and the second ball is purple.

We know the formula

[tex]\rm Probability = \dfrac{favorable\ events}{total\ events}[/tex]

For the first ball is red, then

Total event = 12

Favorable event = 3

[tex]\rm Probability = \dfrac{favorable\ events}{total\ events}\\\\\rm Probability = \dfrac{3}{12}\\\\\rm Probability = 0.25[/tex]

For the second ball is purple, then

one ball is taken from the bucket and is not replaced

Total event = 11

Favorable event = 5

[tex]\rm Probability = \dfrac{favorable\ events}{total\ events}\\\\\rm Probability = \dfrac{5}{11}\\\\\rm Probability = 0.454[/tex]

Thus the probabilities are 0.25 and 0.454.

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The probability that the first ball drawn is red and the second ball drawn is purple, in a situation where the drawn ball is not replaced, is 5/44.

In this probability question, we are dealing with a situation where sampling occurs without replacement, meaning, the first ball drawn is not put back into the bucket before the second ball is drawn. This impacts the probability of the outcomes.

There are 3 red balls, 4 yellow balls, and 5 purple balls in the bucket, making a total of 12 balls. The probability of drawing a red ball first is the number of red balls divided by the total number of balls, so P(Red1) = 3/12 = 1/4.

After taking out a red ball, there are now 11 balls left. The probability of drawing a purple ball next is the number of purple balls divided by the new total number of balls. So, P(Purple2 | Red1) = 5/11.

The question asks for the probability that the first ball is red and the second ball is purple. In probability theory, the probability of two independent events happening is computed by multiplying the probability of the first event by the probability of the second event given that the first one has occurred. So, the answer is P(Red1 and Purple2) = P(Red1) * P(Purple2 | Red1) = 1/4 * 5/11 = 5/44.

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a) It will reach the maximum in 1 second;

b) the maximum height is 22 feet.

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We find the maximum by finding the vertex.  

We first find the axis of symmetry, whose equation is,

x = -b/2a

x = -32/2(-16)

x = -32/-32

x = 1

This gives us that it reaches the maximum in 1 second.

And, To find the y-coordinate, the maximum height, we substitute this into the equation:

h(1) = -16(1²)+32(1)+6

h(1) = -16+32+6 = 22

Hence, It reaches a height of 22 feet.

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Heather made $32.27 per hour at her part-time job.

To find out how much Heather made per hour at her part-time job, we need to divide her total earnings by the number of hours she worked. Heather made a total of $451.78 and worked 14 hours, so we can calculate her hourly rate by dividing $451.78 by 14.

$451.78 / 14 = $32.27 per hour

Therefore, Heather made $32.27 per hour at her part-time job.

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The answer is to this is B. 0

Answer:

The correct option is D.

Step-by-step explanation:

The correlation coefficient represent the relationship between two variables. It is denoted by r and the value of r lies from -1 to 1.

If r=-1 and close to -1, then it represents strong negative correlation.

If -1<r<0 and close to -0.5, then it represents weak negative correlation.

If r=0 and close to 0, then it represents no correlation.

If 0<r<1 and close to 0.5, then it represents weak positive correlation.

If r=1 and close to 1, then it represents strong positive correlation.

From the given graph it is clear than the data represents the strong positive correlation because the data set lie close to the positive strait line. So, the value of r is near to 1.

Option 1, 2 represent the negative correlation and option 3 represents weak positive correlation.

Since 0.95 close to 1, therefore it represents strong positive correlation.

Hence option D is correct.

To calculate the holding-period return, add the dividend, selling price, and initial investment, then divide by the initial investment. In this case, the holding-period return is 12.5%.

Holding-Period Return Calculation:

Initial investment: $30

Dividend received: $1.50

Selling price: $32.25

Holding-Period Return = (Dividends + Selling Price - Initial Investment) / Initial Investment

Substitute the values: ($1.50 + $32.25 - $30) / $30 = $3.75 / $30 = 0.125 or 12.5%

The theoretical probability of rolling each number ([tex]1[/tex] through [tex]6[/tex]) on a six-sided number cube is [tex]\(\frac{1}{6}\)[/tex]. The probability of rolling an even number ([tex]2, 4,[/tex] or [tex]6[/tex]) is [tex]\(\frac{3}{6}\)[/tex] or [tex]\(\frac{1}{2}\).[/tex]

Since there are six possible outcomes when rolling a six-sided number cube and each outcome is equally likely, the probability of rolling any specific number is calculated by dividing the number of favorable outcomes (which is 1 for each specific number) by the total number of possible outcomes (which is [tex]6[/tex]). Therefore, the theoretical probability [tex]\(P\)[/tex] for each roll is:

[tex]\[ P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{6} \][/tex]

To find the probability of rolling an even number, we consider the number of even outcomes ([tex]2, 4[/tex], and [tex]6[/tex]) and divide by the total number of possible outcomes:

[tex]\[ P(\text{even}) = P(2) + P(4) + P(6) = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2} \][/tex]

The experimental probability is calculated based on the results of the [tex]25[/tex]rolls. For each number, the experimental probability is the number of times that number was rolled divided by the total number of rolls ([tex]25[/tex]). For example, if the number [tex]1[/tex] was rolled [tex]4[/tex] times, the experimental probability of rolling a [tex]1[/tex] would be [tex]\(\frac{4}{25}\).[/tex]

The probability of rolling an even number based on observed frequencies would be the sum of the experimental probabilities of rolling a [tex]2, 4[/tex], or [tex]6[/tex]. If the number of rolls for each even number was [tex]\(x\), \(y\),[/tex] and [tex]\(z\)[/tex]respectively, then the experimental probability of rolling an even number would be [tex]\(\frac{x + y + z}{25}\).[/tex]

The experimental probability may differ from the theoretical probability due to random variation and the finite number of trials. In a small number of trials, the observed frequencies may not match the theoretical probabilities exactly. However, as the number of trials increases, the experimental probabilities should converge to the theoretical probabilities. This is due to the law of large numbers, which states that the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.