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2 years ago

Identify the explicit function for the sequence in the table.

Mathematics

1 answer:

lubasha [3.4K]2 years ago

4 0

Answer:

Step-by-step explanation:

The sequence is as follows:

7,19,31,43,55

Here:

a_1=7

d= 12

The standard formula for arithmetic sequence is:

$a_n=a_1+(n-1)d\\a_n=7+(n-1)12$

By looking at the options we can see that

option B is correct ..

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Which of the following values for m proves that 2m + 2m is not equivalent to 4m2?

Mashutka [201]

M=0 i am not sure it is right

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2 years ago

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To make a profit, a company’s revenue must be greater than its operating costs. The company’s revenue is modeled by the expressi

myrzilka [38]

Revenue = 7.5x - 100
Operation Costs = 5.8x + 79.86

To break even, operation cost = Revenue
⇒ 7.5x - 100 = 5.8x + 79.86
7.5x = 5.8x + 179.86 (Add 100 to both sides)

7.5x - 5.8x = 179.86
1.7x = 179.86
x = 105.8

This implies that the company will need to sell at least 106 items to make a profit.

The inequality that will determine the number of items at need to be sold to make a profit is x ≥ 106

The solution to the inequality is as follows

Revenue = 7.5x - 100
if x =106
Revenue = 7.5(106) - 100
Revenue = 695

Operational Cost = 5.8x + 79.86
if x = 106
Operational Cost = 5.8(106) + 79.86
Operational Cost = 694.66

Profit ≥ (695 - 694.66)
Profit ≥ 0.34

The company must sell at least 106 items to make a profit.

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2 years ago

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Write and solve a quadratic equation for the situation below. Choose the answer that has both an equation that correctly models

Andreas93 [3]

Acceleration is:

a=g

Velocity is the integral of the above

v=gt+v0

And position is the integral of the above

h=gt^2/2+v0t+h0

You are given that v0=15ft/s and h0=0ft and let g≈-32 so

h(t)=-16t^2+15t

It will hit the ground when h(t)=0 so:

0=-16t^2+15t which is equal to

16t^2-15t=0 factor

t(16t-15)=0, since we are looking for the time other than zero...

t=15/16 of a second :)

So they obviously just rounded to one whole second. So C.) was the correct answer. (Although I would say they are all wrong because they didn't SAY to round the answer :P) Haha, not trying to confuse you, the answer is most likely C. because they had the correct equation.

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2 years ago

Each day, X arrives at point A between 8:00 and 9:00 a.m., his times of arrival being uniformly distributed. Y arrives independe

astraxan [27]

Answer:

Y will arrive earlier than X one fourth of times.

Step-by-step explanation:

To solve this, we might notice that given that both events are independent of each other, the joint probability density function is the product of X and Y's probability density functions. For an uniformly distributed density function, we have that:

$f_X(x) = \frac{1}{L}$

Where L stands for the length of the interval over which the variable is distributed.

Now, as X is distributed over a 1 hour interval, and Y is distributed over a 0.5 hour interval, we have:

$f_X(x) = 1\\\\f_Y(y)=2$ .

Now, the probability of an event is equal to the integral of the density probability function:

$\iint_A f_{X,Y} (x,y) dx\, dy$

Where A is the in which the event happens, in this case, the region in which Y<X (Y arrives before X)

It's useful to draw a diagram here, I have attached one in which you can see the integration region.

You can see there a box, that represents all possible outcomes for Y and X. There's a diagonal coming from the box's upper right corner, that diagonal represents the cases in which both X and Y arrive at the same time, under that line we have that Y arrives before X, that is our integration region.

Let's set up the integration:

$\iint_A f_{X,Y} (x,y) dx\, dy\\\\\iint_A f_{X} (x) \, f_{Y} (y) dx\, dy\\\\2 \iint_A dx\, dy$

We have used here both the independence of the events and the uniformity of distributions, we take the 2 out because it's just a constant and now we just need to integrate. But the function we are integrating is just a 1! So we can take the integral as just the area of the integration region. From the diagram we can see that the region is a triangle of height 0.5 and base 0.5. thus the integral becomes:

$2 \iint_A dx\, dy= 2 \times \frac{0.5 \times 0.5 }{2} \\\\2 \iint_A dx\, dy= \frac{1}{4}$

That means that one in four times Y will arrive earlier than X. This result can also be seen clearly on the diagram, where we can see that the triangle is a fourth of the rectangle.

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2 years ago

A round table top has a diameter of 2.6 meters.What is its surface area

sergij07 [2.7K]

Hello!

To find the area of a circle you use the equation

$\pi r^{2}$

r is radius which is half the diameter

r = 2.6 / 2

r = 1.3

Put in the values you know

$\pi 1.3^{2}$

Square the number

$1.69 \pi = 5.31$

The answer is $1.69 \pi$ or ≈5.31

Hope this helps!

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2 years ago

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