An object is traveling at a steady speed of 8 2/3 miles per hour. How long will it take the object to travel to 5 1/5 miles

The equation of a parabola with a focus at (0,-5) and a directrix at y=-3 is derived by equating the distances of any point (x, y) in the parabola from the focus and the directrix respectively. Simplifying these expressions leads to the equation y = (1/8)x² - 1.

The equation for a parabola can be derived from its definition. A parabola is defined as the set of all points (x, y) in a plane which are equidistant from a fixed point, the focus (given here as (0,-5)) and a fixed line, the directrix (given as y=-3).

Let's calculate the distance between the focus (0, -5) and any point in the parabola (x, y). We get the equation:
√[(x-0)² + (y-(-5))²].

And the distance between the point (x, y) and the directrix (y=-3) is |y - (-3)| = y + 3.

Since we know that the two distances are equal, we can equate the two expressions:
√[(x-0)² + (y-(-5))²] = y + 3.

Solving it further, squaring both sides, and simplifying, we get:
y = (1/8)x² - 1.

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The function f(x) = 3x^2 - 11x - 4 is a quadratic equation; the negative x-intercept is at (-1/3,0) and the positive x-intercept is at (4,0)

The x-intercept of  a function is the point where the function crosses the x-axis

Check below on how to determine the x-intercept

The function is given as:

f(x) = 3x^2 - 11x - 4

Next, we plot the graph of the function

From the attached graph, the function crosses the axis at:

(-1/3,0) and (4,0)

Hence, the negative x-intercept is at (-1/3,0) and the positive x-intercept is at (4,0)

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Final answer:

The surface area of the cylinder forming the sides of a microvillus rod with a diameter of 0.1 µm and a height of 1.0 µm is 0.314 µm².

Explanation:

To calculate the surface area of the cylinder that forms the "sides" of the microvillus rod, we will use the formula for the surface area of a cylinder without the top or bottom, which is circumference multiplied by height

(A = 2πrh).

Since the diameter (d) of the microvillus is given as 0.1 µm, we first find the radius (r) by dividing the diameter by 2.

Therefore, r = 0.1 µm / 2 = 0.05 µm.

The height (h) is given as 1.0 µm.

Inserting these values into our formula, we get:

A = 2 × 3.14 × 0.05 µm × 1.0 µm = 0.314 µm².

Hence, the surface area of the sides of the microvillus rod is 0.314 µm².

Answer:

EG, DH, CG, FH

Step-by-step explanation:

The last choice, segments EG, DH, CG and FH, do not cross AB, nor are they parallel to AB. So, they are all skew.

In the first choice, GH is parallel to AB, so it would not be skew. So, this is not the answer.

In the second choice CD is parallel to AB, so it would not be skew. So, this is not the answer.

In the third choice, AC and AB cross, so it would not be skew. So, this is not the answer.

Skew lines do not cross and are not parallel.

The correlation between two angles in a random triangle is negative. This means that as one angle increases, the other angle decreases, and vice versa.

In a random triangle, the angles are not independent of each other; they are constrained by the fact that the sum of the angles in any triangle must be 180 degrees (or π radians). Let's consider two of the angles, say A and B, in the triangle.

Since the sum of all three angles is a constant (180 degrees or π radians), if one of the angles (let's say A) increases, it implies that the other angle (B) must decrease in order to maintain the sum as a constant. Conversely, if A decreases, B must increase. This negative relationship between the two angles implies that they are negatively correlated.

Therefore, the correlation between two angles in a random triangle is negative. This means that as one angle increases, the other angle decreases, and vice versa.

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Final answer:

The probability that a randomly selected student is male, given that the student is a nursing major, is 0.027. The probability that a randomly selected student is a nursing major, given that the student is male, is undefined.

Explanation:

To find the probability that a randomly selected student is male, given that the student is a nursing major, we can use conditional probability. Let's assume that P(M) represents the probability of selecting a male student, and P(N) represents the probability of selecting a nursing major. The given information states that P(M|N) = 0.027, which means the probability of selecting a male student, given that the student is a nursing major, is 0.027.

To find the probability that a randomly selected student is a nursing major, given that the student is male, we can use conditional probability once again. The given information states that P(N|M) = nothing. This implies that there is no information given about the probability of selecting a nursing major, given that the student is male. Therefore, the probability is undefined and we cannot determine an answer.

Final answer:

The random variable X is defined as the number of days Pete catches fish. The probability that Pete will catch fish on exactly one day is 0.096.

Explanation:

The random variable X is defined as the number of days Pete catches fish when he goes fishing.

To find the probability that Pete will catch fish on exactly one day, we can use the binomial probability formula. The formula is:

P(x) = (n C x) * p^x * (1-p)^(n-x)

where n is the number of trials (in this case, 3 days), x is the number of successes (in this case, 1 day), and p is the probability of success (in this case, 0.8).

Plugging in the values, we get:

P(x = 1) = (3 C 1) * 0.8^1 * (1-0.8)^(3-1) = 3 * 0.8 * 0.2^2 = 0.096

The median of the numbers 81, 87, 93, 89, 61, 81 is 84.

To find the median of the set of numbers 81, 87, 93, 89, 61, 81, you first need to arrange them in numerical order. The sorted list is 61, 81, 81, 87, 89, 93. Since there is an even number of data points, the median will be the average of the two middle numbers.

The two middle numbers in this ordered list are 81 and 87. We can calculate the median by finding the average of these two numbers:

(81 + 87) / 2 = 168 / 2

168 / 2 = 84

Therefore, the median of this data set is 84.

To find the percentage of Norman's original $100 that he has left after buying the game, subtract the cost of the game from $100 and then calculate the percentage. Norman has 65% of his original $100 left after buying the game.

To find the percentage of Norman's original $100 that he has left after buying the game, we need to subtract the cost of the game from $100 and then calculate the percentage.

Therefore, Norman has 65% of his original $100 left after buying the game.

zero would be where the slanted line crosses the x axis, in tis picture that would be -6

 so answer is A

It is found 3+0.7+0.04 in standard form as; 3.74

Suppose the considered polynomial is of only one variable.

Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.

We have to write 3+0.7+0.04 in standard form.

First Place them accordingly, the decimal point will always stay between the 3 and the 7.

3.00 + 0.70 + 0.04 the numbers fall right in place.

So, it would come out as 3.74

Therefore, It is found 3+0.7+0.04 in standard form as; 3.74

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The equation 4y = x represents a direct variation. This type of relationship between variables implies that the ratio between x and y is constant. In this specific example, the constant of variation is 0.25.

Yes, the given equation 4y = x is a representation of direct variation. Direct variation in mathematics refers to a situation where the ratio of two variables is constant. In a direct variation equation the form is y = kx, where k is the constant of variation. Here, you can rewrite 4y = x as y = x/4 or y = 0.25x, so the constant of variation is 0.25. It's important to note that a direct variation has no y-intercept, it always passes through the origin (0,0) which is the case in this equation.

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Answer:

[tex]m<CED=m\°[/tex]  

Step-by-step explanation:

we know that

Triangles ABC and CDE are similar triangles, because the corresponding angles are congruent

[tex]m<BCA=m<DCE[/tex] ------> by vertical angles

[tex]m<ABC=m<CDE[/tex] ----> given problem

[tex]m<BAC=m<CED[/tex] ----> The sum of the internal angles of the triangle must be equal to [tex]180[/tex] degrees

we have

[tex]m<BAC=m\°[/tex]

so

[tex]m<CED=m\°[/tex]

To find the unit rate divide total miles by total hours:

501.9 / 21 = 23.9 miles per hour