There were 45 runners to start a race. In the first half of the race, 1/3 of them dropped out. In the second half of the race, 2/3 of the remaining runners dropped out. How many runners finished the race? ​

Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

This occurs when the number of $5 price increases is approximately 10.82 or 15.32.

The function given is P(x) = −6x2 + 156x + 1,000, where x is the number of $5 price increases for each solar panel. We are to identify the approximate value of the x-intercept and explain what the x-intercept means in terms of the problem scenario.

The x-intercept is a point where the graph of the function crosses the x-axis. At this point, the value of the function is zero.

We can find the x-intercept by setting P(x) = 0 and solving for x.0 = −6x2 + 156x + 1,0006x2 - 156x - 1000 = 0Dividing by 6, we get:x2 - 26x - 166.67 = 0Solving using the quadratic formula,

we get:x ≈ 10.82 or x ≈ 15.32So, the x-intercepts are approximately 10.82 and 15.32. In terms of the problem scenario, the x-intercept represents the point at which the company breaks even, i.e., the point at which the daily profit is zero.

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Answer:

240 ft

Step-by-step explanation:

When she stops, her velocity is 0.  The first time that happens is at t = 3 minutes.  Her position at that time is equal to the area under the curve.

You can use area of a trapezoid, or you can split the shape into two triangles and a rectangle.  Watch your units!  Speed is given in ft/s, and time is given in minutes.

Using trapezoid area:

A = ½ (1 min + 3 min) (2 ft/s)

A = ½ (60 s + 180 s) (2 ft/s)

A = 240 ft

The interval of the graph at which Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

Given data ,

Susan is running a 5k race. The graph of distance vs. time is shown

So , the slope of the first line is m₁

And , the slope of the second line is m₂

where the points are A ( 0 , 0 ) , B ( 10 , 3 ) , C ( 20 , 4 )

Now , slope of AB is

m₁ = ( 3/10 ) = 0.3

And , m₁ = 0.3 kilometers per minute

And , slope of BC is

m₂ = ( 4 - 3 ) / ( 20 - 10 )

m₂ = 1/10

m₂ = 0.1 kilometers per minute

Therefore , the interval is fastest at second line from B ( 10 , 3 ) , C ( 20 , 4 )

Hence , Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

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A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

In this case, it would be a function

Based on the given quantities, the quantity that is directly proportional is B) speed and time if the distance traveled is 110 miles.

Two quantities are said to be proportional if the increase or decrease between the two quantities is constant. For instance, if a single unit in one will always lead to the same increase in the other quantity.

When people are travelling at a constant 77 mph then it means that for every hour(time) that passes, the distance would increase by 77 miles. The distance and time here are therefore proportional.

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Answer:

It's definitely not parallel... I think it's neither...

Step-by-step explanation:

Tip: if it is parallel, the slope is the same. The formula for finding slope is y two minus y one divided by x two minus x one.

\(2n=10\)

Divide both sides by 2:

\(\dfrac{2n}{2} =\dfrac{10}{2}\)

\(\fbox{n = 5}\)

Answer:

a) ending inventory:     11,850,000

  cost of goods sold: 25,200,000

 gross profit               25,200,000

b)

ending inventory:     1,800,000

cost of goods sold:  23,100,000

gross profit  50,400,000 - 23,100,000 =  27,300,000

5,200 at $600

4,100 at $700

6,200 at $800

purchase 29,000 at $900

-sold 28,000 grills

As we use LIFO we sale from the last purchase thus, 29,000 - 28,000 = 1,000 of this units are added as another layer for the inventory account

ending inventory

5,200 at $  600

4,100 at $   700

6,200 at $  800

1,000  at $  900

Total    $ 11,850,000

cost of good sold:

28,000 x $900 = $25,200,000

sales revenue

28,000 x 900 x 200% = $50,400,000

gross profit sales revenue less COGS

b) 5,200 at $600

4,100 at $700

6,200 at $800

purchase 15,500 at $900

-sold 28,000 grills

we check how many layer deep we go:

28,000 - 15,500 at 900= 12,500

12,500  -  6,200  at 800=  6,300

6,300 - 4,100 at 700      =  2,200  at 600

Ending Inventory

3,000 at $600 = $ 1,800,000

COGS:

15,500 x 900 + 6,200 x 800 + 4,100 x 700 + 2,200 x 600 = 23,100,000

Step-by-step explanation:

Answer:

$82.5

Step-by-step explanation:

$16.50 * 5 = $82.5

Answer:

27.50

Step-by-step explanation:

The given limit is 0.

To solve the given limit, we can recognize the sum as a Riemann sum and convert it into an integral.

The given sum can be rewritten as:

\(\lim_{n \to \infty} \sum_{i=1}^{n} \frac{3}{n} \sqrt{1+\frac{3i}{n}}\)

Let's rewrite it in terms of integration:

\(\lim_{n \to \infty} \frac{3}{n} \sum_{i=1}^{n} \sqrt{1+\frac{3i}{n}}\)

Since we are taking the limit as n approaches infinity, we can approximate the sum as an integral.

The integral that corresponds to the given sum is:

\(\lim_{n \to \infty} \frac{3}{n} \sum_{i=1}^{n} \sqrt{1+\frac{3i}{n}} \approx \lim_{n \to \infty} \frac{3}{n} \int_{0}^{1} \sqrt{1+3x} ,dx\)

To solve this integral, we can use a change of variables.

Let u = 1 + 3x, then du = 3dx.

The integral becomes:

\(\lim_{n \to \infty} \frac{3}{n} \int_{0}^{1} \sqrt{1+3x} ,dx = \lim_{n \to \infty} \frac{1}{n} \int_{1}^{4} \sqrt{u} ,du\)

Integrating \(\sqrt{u}\), we get,

\(\lim_{n \to \infty} \frac{1}{n} \int_{1}^{4} \sqrt{u} ,du = \lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} u^{3/2}\right]_{1}^{4}\)

Substituting the limits, we have:

\(\lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} (4)^{3/2} - \frac{2}{3} (1)^{3/2}\right]\)

Simplifying further:

\(\lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} (8 - 2)\right] = \lim_{n \to \infty} \frac{1}{n} \left[\frac{12}{3}\right] = \lim_{n \to \infty} \frac{4}{n} = 0\)

Therefore, the given limit is 0.

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To solve for X in this equation, you would subtract both sides by 14 because our goal is to get X on its own. If we write it out, we see that

X + 14 - 14 = 56 - 14

X=42

Because we have a positive 14, a negative 14 will average out to be 0, but what you do to one side, you must do to the other.

If you have any more questions, feel free to ask!

The coordinates of the y-intercept are (0, 3.5) and the coordinates of the x-intercepts are (-17.5, 0). Using these coordinates, the graph of the equation is shown below.

From the question, we are to graph the given linear equation.

To graph the equation,

We will determine the coordinates of the x-intercepts and y-intercepts.

When x = 0

y = 1/5x + 3.5

y = 1/5(0) + 3.5

y = 3.5

(0, 3.5)

When y = 0

y = 1/5x + 3.5

0 = 1/5x + 3.5

Multiply through by 5

0 = x + 17.5

x = -17.5

(-17.5, 0)

Using the coordinates of the x-axis and y-axis, the graph of the equation is shown below.

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EXPLANATION

Let's consider the facts:

Success rate= 9% = 0.09 (in decimal form)

Number of advertised people = 500

So, n=500, p=0.09 and 1-p=0.91

By definition, we know that:

Mean = np = 500*0.09 = 45

Now, we need to find the standard deviation:

So the Probability of getting fewer than 38 sales is given by the following relationship:

P(X<38):

Look up z= -1.0939 on a z-table.

The obtained value is z= 0.13786 or %13.786

This means that there is a %13.78 of fewer than 38 sales.

Answer:

The commission rate is of 12%.

Step-by-step explanation:

Commission rate:

The commission rate is given by the commission value multiplied by 100% and divided by the value of merchandise sold.

In this question:

$252 in commission for selling $2100 in merchandise. So

252*100%/2100 = 12%

The commission rate is of 12%.

Answer:

2 > x or x < 2

Step-by-step explanation:

-1 + 6(-1 - 3x) > -39 - 2x

-1 - 6 - 18x > -39 - 2x

-7 - 18x > -39 - 2x

32 > 16x

2 > x or x < 2

the reason that x < 2 is because of the negative sign. I solved it so that x stays positive but if you solve the equation with x on the other side like -16x > -32 then when you divide by -16 it changes to x < 2

PLEASE RATE!!! I hope this helps!!

(I have verified my answer on an online calculator)

2 represent (d) the rate at which the population is growing every day.

The given expression is 100(2) x.

According to the ideal exponential expression f(x) = a(b)x.

‘a' is the function's beginning or starting value.

‘b’ is the growth multiplier or growth factor per unit x.

In our question,

f(x) = a(b)x = 100(2)x.

So, a = 100 = initial value

     b = 2 = growth factor.

Hence, 2 in the expression 100(2)x represents the growth factor or growth multiplier or rate at which the population is growing.  

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Answer:

8:24

Step-by-step explanation:

Just multiply 4*2 and 12*2

Hope it helps

Answer:

8:24, 24: 72, 16:48

Step-by-step explanation:

There's a lot just multiply them by the same number

Answer:

if you're solving for M then your answer is

m = -19/17

Answer: $4,998

Step-by-step explanation:

34000*1.147

38998-34000=4998

True statement for Protecting classified data is classified material must be appropriately marked.

Classified information being transmitted from one commission office to another shall be protected with a classified document cover sheet and hand delivered by an appropriately cleared person to another appropriately cleared person.

Classified information is material that a government body deems to be sensitive information that must be protected. Access is restricted by law or regulation to particular groups of people with the necessary security clearance and need to know, and mishandling of the material can incur criminal penalties.

Data classification is broadly defined as the process of organizing data by relevant categories so that it may be used and protected more efficiently. Data classification involves tagging data to make it easily searchable and trackable.  

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The required function y = 7 cos (2π * 0.1 * x) and period of the function is 10 seconds, which is the time it takes for one complete cycle of the wave.

he cosine function can be used to model periodic motion, and its general form is:

y = A cos (Bx + C) + D

where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.

In this case, we know that a 14 in. wave occurs every 10 s, so we can use this information to find the frequency, which is the reciprocal of the period. The period is the time it takes for one complete cycle of the wave, which in this case is 10 s.

Therefore, the frequency is:

\(f = \frac{1}{T}=\frac{1}{10} = 0.1 Hz\)

We can also see that the amplitude of the wave is 7 inches, since the wave has a height of 14 inches from its highest point to its lowest point.

Now we can write the function that models the height of the particle in inches y as it moves in seconds x:

y = 7 cos (2π * 0.1 * x)

Here, the frequency is expressed in radians per second (2π * 0.1 = 0.2π), since the cosine function takes radians as its argument. The phase shift and vertical shift are both zero in this case, since the wave starts at its highest point and has no vertical shift.

Therefore, the period of the function is 10 seconds, which is the time it takes for one complete cycle of the wave.

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The equation for the g(x) is g(x) = -3f(x) after applying the transformation.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a graph of a function shown in the picture.

From the graph:

When, x=0, y=3

The graph f(x) is reflected over the x-axis and stretched upward.

The transformation can be applied:

g(x) = -3f(x)

Thus, the equation for the g(x) is g(x) = -3f(x) after applying the transformation.

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The length of a 45° arc with a radius of 4 miles is approximately 3.14 miles, calculated using the formula for arc length.

To determine the length of a 45° arc given a radius of 4 miles, we can use the formula: Arc length = (angle measure / 360°) x 2πr, where r is the radius of the circle and π is a constant equal to approximately 3.14.

Substituting the given values into the formula, we get: Arc length = (45° / 360°) x 2π(4 mi)Arc length = (1/8) x 2π(4 mi)Arc length = (1/8) x 8π Arc length = π

The length of the 45° arc is approximately 3.14 miles.

Summary: To find the length of a 45° arc of a circle, we use the formula: Arc length = (angle measure / 360°) x 2πr. Given a radius of 4 miles, we can substitute the values into the formula to get the length of the 45° arc, which is approximately 3.14 miles.

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Answer:

-4d

Step-by-step explanation:

L.c.m=15

15×2/5(d-10)-2/3×15(d+6)

3×2(d-10)-2×5(d+6)

6(d-10)-10(d+6)

6d-60-10d-60

6d-10d-60-60

-4d-0

-4d

Step-by-step explanation:

3 is the answer

-7x+12x-6=9

when -6 goes to other side it becomes +6

-7x+12x=9+6

5x=15

when 5x which means 5 multiplied to x . When 5 goes other side it becomes division

x=15÷5=3

x=3

The height of the tree is 186 inches if Shadow of tree is 523 inch shadow of human is 180 inch height of human is 64 inch.

Cross multiplication occurs when the numerator of the first fraction is multiplied by the denominator of the second fraction, and the numerator of the second fraction is multiplied by the denominator of the first fraction.

We have given information that

Shadow of tree = 523 inch

Shadow of human = 180 inch

Height of human = 64 inch

height of tree = x

Lets solve this with cross multiplication

⇒ \(\frac{64}{180} = \frac{x}{523}\)

⇒ 180 × x = 64 × 523

⇒ x = (64 × 523)/180

⇒ x = 185.95

       = 186 approx.

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