Which expression represents the distance between 4.7 and −11.2 on the number line? Drag and drop the correct expression into the box.

Answer:

The rate of change of the volume of the cylinder when the radius is 10 ft is

[tex]\frac{dV}{dt}=400\pi \:{\frac{ft^3}{min} }[/tex]

Step-by-step explanation:

This is a related rates problem. A related rates problem is a problem in which we know the rate of change of one of the quantities (the height of a grain) and want to find the rate of change of the other quantity (the volume of grain in the cylinder).

The volume of a cylinder is given by

[tex]V=\pi r^2 h[/tex]

V and h both vary with time so you can differentiate both sides with respect to time, t, to get

[tex]\frac{dV}{dt}=\pi r^2 \frac{dh}{dt}[/tex]

Now use the fact that [tex]\frac{dh}{dt} = 4 \:{\frac{ft}{min} }[/tex] and [tex]r = 10 \:ft[/tex]

[tex]\frac{dV}{dt}=\pi (10)^2 \cdot 4\\\\\frac{dV}{dt}=100\cdot \:4\pi \\\\\frac{dV}{dt}=400\pi[/tex]

Answer with explanation:

The Given Quadratic Polynomial which can be Broken into integer factors:

 [tex]\rightarrow 6 x^2 + 37 x - 60\\\\ \text{Splitting the Middle term}}\\\\ \rightarrow 6 x^2 + 37 x - 60\\\\\rightarrow 6 x^2 + 45 x-8 x - 60\\\\ \rightarrow 3x \times (2 x+15)-4 (2 x +15)\\\\\rightarrow (3 x -4)(2 x+15)[/tex]

Factors of the above Expression are:

     = (3 x -4)(2 x+15)  

dive distance traveled by time

 90 feet / 15 seconds = 6

 since the diver is below the surface they are changing position at -6 feet per second

The unit rate at which Belmond cuts bricks is 28 bricks per hour, which is calculated by dividing the total number of bricks (84) by the total hours worked (3).

To find the unit rate of bricks cut per hour by Belmond, we simply divide the total number of bricks by the total time in hours. Belmond cuts 84 bricks in 3 hours, so the unit rate is:

Unit rate = Total bricks \/ Total time in hours
Unit rate = 84 bricks \/ 3 hours = 28 bricks per hour

This means that Belmond cuts 28 bricks every hour. When you need to find a unit rate, it is a matter of dividing the total quantity by the time it takes to accomplish that quantity, thus yielding the rate per single time unit (in this case, per hour).

A binomial experiment has a fixed number of trials, all are independent and conducted under identical conditions. Only two results—success or failure—are possible with each trial, each having the same probability, fitting a binomial probability distribution.

For a random experiment to be binomial, it must meet certain conditions. Firstly, there should be a fixed number of trials, denoted as 'n'. The results of these trials don't influence each other, meaning that the trials are independent. This signifies that the outcome of a trial, for example, the first one, does not affect the outcomes of the subsequent trials. Moreover, all these trials should be conducted under identical conditions.

In a binomial experiment, there are only two possible results, often referred to as 'success' and 'failure'. Each trial has the same probability of success, denoted as 'p'. The outcomes of a binomial experiment fit a binomial probability distribution. The random variable 'X' stands for the number of successful trials. The mean 'µ' is given by 'np', and the standard deviation 'o' by √npq. The probability of exactly 'x' successes in 'n' trials is P(X = x).

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The odds against selecting a person who commutes by bicycle from a town where 10% of people commute that way would be 9 to 1. This is based on the percentage of people who do not commute by bicycle versus those who do.

In statistical terms, the question is asking us to calculate the odds against selecting someone who commutes by bicycle. With 10% of people in this town commuting by bicycle, it means that 90% of them do not. Therefore, the odds against selecting someone who commutes by bicycle are 90 to 10 or 9 to 1.

This is calculated by dividing the number of unsuccessful outcomes (people not commuting by bicycle - 90%) by the number of successful outcomes (people commuting by bicycle - 10%). This gives us the odds against selecting someone who commutes by bicycle.

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The point slope form of the line has the following form:

y – y1 = m (x – x1)

The slope m can be calculated using the formula:

m = (y2 – y1) / (x2 – x1)

m = (1 - -3) / (4 – 0) = 1

So the whole equation is:

y – -3 = 1 (x – 0)

y + 3 = x

The unknown number A, when rounded to the nearest thousand and hundred, is determined to be within the range from 20500 to 20549. A can be any number within this range.

In mathematics, when you're given that a number A, when rounded to the nearest thousand, ends up being 21000 or that when rounded to the nearest hundred, it ends up being 20500, you can infer that the unknown number A lies somewhere between two specific values. Since A rounds to 21000 when we round to the nearest thousand, this implies that A is between 20500 and 21499.

However, we also know that, when rounded to the nearest hundred, A is 20500. This implies that A is between 20450 and 20549. Comparing these two ranges, the unknown number A must lie within the common range, which is from 20500 to 20549. Therefore, the number A can be any number within this range.

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Answer:

Option A - 4

Step-by-step explanation:

Given : Inequality [tex]30 - x^2 < 3x + 7[/tex]

To find : Choose the value of x that makes the open sentence true  ?

Solution :

We substitute the value of x from options to check which is true,

A) x=4

[tex]30 - 4^2 < 3(4) + 7[/tex]

[tex]30-16 < 12+ 7[/tex]

[tex]14< 19[/tex]

It is true.

B) x=3

[tex]30 - 3^2 < 3(3) + 7[/tex]

[tex]30-9< 9+ 7[/tex]

[tex]21< 16[/tex]

It is false.

C) x=2

[tex]30 - 2^2 < 3(2) + 7[/tex]

[tex]30-4<6+ 7[/tex]

[tex]26< 13[/tex]

It is false.

D) x=1

[tex]30 - 1^2 < 3(1) + 7[/tex]

[tex]30-1<3+ 7[/tex]

[tex]29< 10[/tex]

It is false.

Therefore, Option A is correct.

To find the absolute minimum and absolute maximum values of the function f(x) = x - ln 8x on the interval [1/2, 2], we find the critical points and evaluate the function at the endpoints and critical points. The absolute minimum value is f(1/2) = 1/2 - ln 4 and the absolute maximum value is f(2) = 2 - ln 16.

To find the absolute minimum and absolute maximum values of the function f(x) = x - ln 8x on the given interval [1/2, 2], we need to find the critical points and the endpoints of the interval. First, we find the derivative of the function: f'(x) = 1 - 1/x. Then, we solve the equation f'(x) = 1 - 1/x = 0 to find the critical points. The critical point is x = 1. Next, we evaluate the function at the critical point and the endpoints of the interval to determine the absolute minimum and absolute maximum values.

1. Evaluating the function at the critical point: f(1) = 1 - ln 8
2. Evaluating the function at the endpoint x = 1/2: f(1/2) = 1/2 - ln 4
3. Evaluating the function at the endpoint x = 2: f(2) = 2 - ln 16

The absolute minimum and absolute maximum values of the function on the given interval are:

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The line of linear function h(x) = –6 + x is not going to enter in the second quadrant so option second will be correct.

The link between lines and points is described by a graph, which is a diagrammatic representation of a network.

A graph is made up of some points and the distance between two. It doesn't matter how much time the lines are or where the points are located. A node is a name for each constituent in a graph.

Given equation is h(x) = –6 + x

at x = 0 , h(x) = -6 so ( 0 , -6 ) is first point.

at x =1 , h(x) = -5 so ( 1 , -5 ) is second point.

If we draw a line by the two-point which I have attached then you can see it not going to the second quarter.

For more details about the graph

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We know that there is no universal acceptance meaning of a percentile. When someone told you that you are in the 80th percentile, the meaning of that is you have achieved the lowest score that is greater than 80 percent of the score. It is calculated by using the formula     R = P/100 x (N + 1)

Final answer:

The 80th percentile represents the score below which 80% of the scores fall.

Explanation:

The 80th percentile represents the score below which 80% of the scores fall. It is calculated by finding the value at which 80% of the data is below and 20% is above. For example, if you scored in the 80th percentile on a 60-point assignment, it means that 80% of students scored equal to or below 49 points and 20% scored above.

A binary search in a set of 64 sorted items will, in the worst-case scenario, require 6 comparisons. This is calculated as log2(64) = 6. The binary search method works by repeatedly halving the search interval until it finds the desired item.

In order to find out how many comparisons are needed for a binary search in a set of 64 elements, we need to understand how a binary search works. It's an efficient algorithm that finds an item from a sorted list by repeatedly dividing the search interval in half. Every time it analyzes the middle element, it either discards the half that it is sure does not contain the desired item, or determines that the middle element is the desired item.

With a set of 64 elements, a binary search would perform log2(64) or 6 comparisons, as the base-2 logarithm of 64 is 6. Therefore, the maximum number of comparisons necessary using a binary search to locate a particular item in a set of 64 elements is 6 comparisons.

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In a binary search of a 64 element set, the worst-case scenario requires 6 comparisons. This is determined by the base 2 logarithm of the number of elements.

The number of comparisons in a binary search is governed by the logarithm base 2 of the number of elements in the set. With a set of 64 elements, the worst case scenario for the number of comparisons needed would be log2(64) which equals 6. This is because a binary search works by repeatedly dividing the searchable set in two until it finds the desired element, making it a very efficient search algorithm.

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Answer:

slope of the line will be [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

We have to find the slope of a given line whose equation is 4y - 3x + 6 = 0

If a line is in the form of y = mx + c

Then m represents slope of the line

4y - 3x + 6 = 0     [ Given equation ]

4y = 3x - 6

y = [tex]\frac{1}{4}[/tex] ( 3x-6 )

y = [tex]\frac{3}{4}x[/tex] - [tex]\frac{3}{2}[/tex]

Therefore, slope of the line will be [tex]\frac{3}{4}[/tex]

To find the diameter of the circular hot tub, divide the circumference by π.

To find the diameter of the circular hot tub, we need to use the formula for the circumference of a circle. The formula is C = πd, where C represents the circumference and d represents the diameter.

In this case, the circumference is given as 56.5 yards. So we can plug that value into the formula and solve for d: 56.5 = πd.

To isolate the variable d, we divide both sides of the equation by π. This gives us: d = 56.5/π.

Using a calculator, we can find the approximate value of d to be 18 yards.

The diameter of the hot tub is approximately 18 yards, calculated using the formula [tex]\(D = \frac{56.5}{\pi}\)[/tex] from the given circumference.

The circumference of a circle is given by the formula [tex]\(C = \pi \times D\)[/tex], where C is the circumference and D is the diameter. In this case, the circumference of the hot tub is given as 56.5 yards. So, the formula can be rearranged to solve for the diameter:

[tex]\[ C = \pi \times D \][/tex]

[tex]\[ 56.5 = \pi \times D \][/tex]

To find D, divide both sides of the equation by [tex]\(\pi\)[/tex]:

[tex]\[ D = \frac{56.5}{\pi} \][/tex]

Using the value of  [tex]\(\pi \approx 3.14159\)[/tex], the diameter D is approximately:

[tex]\[ D \approx \frac{56.5}{3.14159} \approx 18 \][/tex]

Therefore, the diameter of the hot tub is approximately 18 yards.

Answer:

The correct answer is 151.

Step-by-step explanation:

Given,

In triangle ABC,

BC = a = 9 unit,

AB = c = 5 unit,

m∠B = 120°,

We have to find : b² or AC²,

By the cosine law,

[tex]b^2=a^2+c^2-2ac cosB[/tex]

[tex]=9^2+5^2-2\times 9\times 5\times cos 120^{\circ}[/tex]

[tex]=81+25-90\times -0.5[/tex]

[tex]=81+25+45[/tex]

[tex]=151[/tex]

Hence, the value of [tex]b^2[/tex] is 151.

Answer:

Option D) [tex]b^2 = 151[/tex]  

Step-by-step explanation:

We are given the following information in the question:

[tex]\triangle ABC\\\text{Side } a = 9\text{ units}\\\text{Side } c = 5\text{ units}\\\angle ABC = 120^{\circ}[/tex]

We have to find [tex]b^2[/tex]

The law of cosines state that if a, b and c are the sides of triangle and b is the side opposite to angle B, then,

[tex]b^2 = a^2 + c^2 - 2ac~\cos(B)[/tex]

Putting the values, we have,

[tex]b^2 = (9)^2 + (5)^2 - 2(9)(5)~\cos(120)\\\\b^2 = 81 + 25 - 90(-0.5)\\\\b^2 = 151[/tex]

Option D) [tex]b^2 = 151[/tex]