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3 years ago

1A research firm finds that the average number of customers that are in Somerset Mall on a

Mathematics

1 answer:

SpyIntel [72]3 years ago

8 0

Answer: C(t) = -475.5*cos(t*pi/6) + 475.5

Step-by-step explanation:

We know that we have a sinusoidal relation, with a minimum at 9:00 am and at 9:00 pm.

If we define the 9:00 am as our t = 0, we have that the maximum, at 3:00pm, is at t = 6 hours.

and the other minimum, at 9:00pm, is at t = 12 hours.

Then we need to find a trigonometric function that has the minimum at t = 0, we can do this as:

-Cos(c*t)

when t = 0

-cos(0) = - 1

then we have a function:

C(t) = -A*cos(c*t) + B

where A, c and B are constants.

We know that at t = 0 we have 0 customers, and that at t = 6h we have 875 customers, that is the maximum.

then:

C(0) = 0 = -A + B

this means that A = B, then our function is:

C(0) = -A*cos(c*t) + A.

now, at t = 6h we have a maximum, this means that -A*cos(c*6h) = A

then:

C(6h) = A + A = 875

2A = 875

A = 875/2 = 437.5

and we also have that, if -cos(c*6) = 1

then cos(c*6) = -1

and we know that cos(pi) = -1

then c*6 = pi

c = pi/6

Then our function is

C(t) = -475.5*cos(t*pi/6) + 475.5

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Using either the critical value rule or the p-value rule, if a one-sided null hypothesis is rejected at a given significance lev

sergeinik [125]

Answer:

Step-by-step explanation:

In hypothesis testing if p value < alpha i.e. our significance level we reject null hypothesis

Consider for example, 95% confidence level is taken, and p value one tailed is 0.026. Since p <0.05, We reject null hypothesis

p value two tailed is twice p value for one tailed. Hence p value two tailed =0.052.

Since p value >0.05 our alpha. So in this case, null hypothesis will be accepted

Hence sometimes it would be rejected and sometimes it would be accepted

Using either the critical value rule or the p-value rule, if a one-sided null hypothesis is rejected at a given significance level, then the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) need not ______________ be rejected at the same significance level.

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3 years ago

A sequence consists of 20102010 terms. Each term after the first is 11 larger than the previous term. The sum of the 20102010 te

Nataliya [291]

You're considering a sequence of in which consecutive terms differ by 1, meaning

a(n) = a (n - 1) + 1

so a(n) is an arithmetic sequence. (I'm guessing 20102010 should actually be 2010, and 53075307 should be 5307, so 11 should probably be just 1.)

The sum of the first 2010 terms is 5307, or

$\displaystyle\sum_{n=1}^{2010}a(n)=5307$

Find the value of the first term in the sequence, a(1).

We can write a(n) in terms of a(1) by iterative substitution:

a(n) = a(n - 1) + 1

a(n) = (a(n - 2) + 1) + 1 = a(n - 2) + 2

a(n) = (a(n - 3) + 1) + 2 = a(n - 3) + 3

and so on, down to

a(n) = a(1) + n - 1

So the sum of the first 2010 terms is

$\displaystyle\sum_{n=1}^{2010}a(n)=\sum_{n=1}^{2010}\left(a(1)+n-1\right)=(a(1)-1)\sum_{n=1}^{2010}1+\sum_{n=1}^{2010}n=5307$

Recall that

$\displaystyle\sum_{n=1}^N1=\underbrace{1+1+\cdots+1}_{N\text{ times}}=N$

and

$\displaystyle\sum_{n=1}^Nn=1+2+\cdots+N=\dfrac{N(N+1)}2$

So we have

$\displaystyle\sum_{n=1}^{2010}a(n)=2010(a(1)-1)+\frac{2010\cdot2011}2=5307$

Solve for a(1) :

2010 (a(1) - 1) + 2,021,055 = 5307

2010 (a(1) - 1) = -2,015,748

a(1) - 1 = - 335,958/335

a(1) = - 335,623/335

Now, every second term, starting with a(1), differs by 2, so they form another arithmetic sequence b(n) given by

b(n) = b(n - 1) + 2

or, using the same method as before,

b(n) = b(1) + 2 (n - 1) = a(1) + 2n - 2

The sum of the 1005 terms in this sequence is

$\displaystyle\sum_{n=1}^{1005}b(n)=(a(1)-2)\sum_{n=1}^{1005}1+2\sum_{n=1}^{1005}n$

= (- 335,623/335 - 2)•1005 + 2•1005•1006/2

= 1146

6 0

3 years ago

The equation of a circle centered at the orgin is x^2 + y^2 = 16. What is the radius of the circle

Yuri [45]

Given:

The equation of the circle is:

$x^2+y^2=16$

To find:

The radius of the circle.

Solution:

The standard form of a circle is:

$(x-h)^2+(y-k)^2=r^2$ ...(i)

Where, (h,k) is the center and r is the radius.

We have,

$x^2+y^2=16$

In can be written as:

$x^2+y^2=4^2$ ...(ii)

On comparing (i) and (ii), we get

$h=0$

$k=0$

$r=4$

Here, the center of the circle is the origin and the radius is equal to 4 units.

Therefore, the radius of the given circle is 4 units.

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3 years ago

What type of polynomial is 3x+x to the second power +4

mina [271]

The answer is quadratic.

A quadratic equation takes this form:

ax^2+ bx + c

The "a,""b,"and "c" represent numerical coefficients.

This is how your equation looks:

3x + x^2 + 4

Now it is standard that we organize the polynomial in descending order so it will look like this:

x^ 2 + 3x + 4

(commutative property of addition says that the arrangement will not affect the result)

It matches the quadratic polynomial form.

* You might be thinking, x to the second power has no number next to it though, well actually it does. The numerical coefficient of x to the power of two in this case is actually 1. It's just that in math, it is not necessary to put the one anymore. It is already assumed.

6 0

3 years ago

30 points. Precalculus HELP.

Reika [66]

lim x→ 0+ f(x)

you will find the limit is inf

lim x→ 0- f(x)

you will find the limit is - inf

because

lim x→0+ f(x) no equal to lim x→0- f(x)

thus lim x→0 f(x) does not exist

form the graph

lim x→2- f(x) = 6

lim x→2+ f(x)= -2

because

lim x→2- f(x) not equal tolim x→2+ f(x)

thus lim x→2 f(x) does not exist

hope this would help you.

6 0

3 years ago