You bought a new television that has a 92 in. 76 in. screen. It has a feature that splits the screen to allow you to watch 4 channels at once. What is the scale factor and size for each channel when this feature is turned on?

Answer: Option B.

Step-by-step explanation:

Given the polynomial:

[tex]16x^2-36x+9[/tex]

 Observe that [tex]16x^2[/tex] and [tex]9[/tex] are perfect squares. Then, you can rewrite the polynomial in this form:

[tex](4x)^2-36x+(3)^2[/tex]

You can identify that:

[tex]A=4\\B=3[/tex]

Then, we can check if [tex]2AB=36[/tex]

 [tex]2(4x)(3)=36x\\\\24x\neq 36x\\\\2AB\neq36x[/tex]

Since [tex]2AB\neq36x[/tex], the polynomial [tex]16x^2-36x+9[/tex] IS NOT a perfect square trinomial of the form [tex]A^2 - 2AB + B^2[/tex]

Answer: B

Step-by-step explanation:

Answer:

positive

Step-by-step explanation:

Find the sign of (2-2x+y) for any point (x,y) in quadrant 2.

In quadrant 2, the x's are negative and the y's are positive.

So choose a negative value for x and a positive value for y and evaluate:

2-2x+y

Let's try (-4,5):

2-2(-4)+5

2+8+5

15 (positive)

Let's try(-1/2 , 10):

2-2(-1/2)+10

2+1+10

3+10

13 (positive)

Let's try in general Let (x,y)=(-a,b) where a and b are positive:

2-2(-a)+b

2+2a+b

Since a and b are positive, then 2+2a+b is positive because you are adding three different positive numbers.

Answer:

5

Step-by-step explanation:

Since this is a rectangle, opposite sides are congruent.

That is, the perimeter in terms of w is:

(2w-1)+(2w-1)+(w)+(w)

or

2(2w-1)+2(w)

We can simplify this.

Distribute:

4w-2+2w

Combine like terms:

6w-2

We are given that the perimeter, 6w-2, is 28.

So we can write an equation for this:

6w-2=28

Add 2 on both sides:

6w   =30

Divide both sides by 6:

w   =30/6

Simplify:

w   =5

w is 5

Check if w=5, then 2w-1=2(5)-1=10-1=9.

Does 5+5+9+9 equal 28? Yep it does 10+18=28.

Answer:

w=5

Step-by-step explanation:

To find the perimeter of the rectangle

P = 2(l+w)

where w is the width and l is the length

Our dimensions are w and 2w-1 and the perimeter is 28

Substituting into the equation

28 = 2(2w-1 +w)

Combining like terms

28 = 2(3w-1)

Divide each side by 2

28/2 = 2(3w-1)/2

14 = 3w-1

Add 1 to each side

14+1 = 3w-1+1

15 = 3w

Divide each side by 3

15/3 =3w/3

5 =w

Answer:

  $46,141.71

Step-by-step explanation:

This looks about right, based on weekly deposits for the duration. However, I cannot vouch for it entirely, as the number of weekly deposits in 15 years will actually be 782.

_____

Computing this by hand doing the initial balance separately from the weekly deposits, I get a total of $46,252.10 using 782 weekly deposits. For that purpose, I tried to figure an equivalent weekly interest rate given monthly compounding and the fact there are 52 5/28 weeks in a year on average.

I suspect the only way to get this to the cent would be to build a spreadsheet with payment dates and interest computation/payment dates. Some months, there would be 5 deposits between interest computations; some years there would be 53 deposits.

Answer:

Bonnie needs [tex]67.8\ in[/tex] of ribbon

Step-by-step explanation:

we know that

A Kite is a quadrilateral that has two pairs of equal sides

so

To find out how much ribbon Bonnie needs calculate the perimeter of the kite

[tex]P=2(L1+L2)[/tex]

where

L1 is the length of one side

L2 is the length of the other side

[tex]P=2(13.2+20.7)=67.8\ in[/tex]

Answer:

one large box is 40 pounds

one small box is 30 pounds

Step-by-step explanation:

let large be l and small be s ,

l + s = 70 ------- equation1

70l + 55s. = 4450 ------- equation 2

equation 1 multiply by 55,

55l + 55s = 3850 ------ equation 3

equation 3 - equation 2 ,

(70l + 55s) - (55l +55s) = 4450 - 3850

70l + 55s - 55l - 55s = 4450 - 3850

15l = 600

l = 40

sub l = 40 into equation 1

40 + s = 70

s = 70 - 40

s = 30

Answer:

  sin(2x) = 120/169

Step-by-step explanation:

A suitable calculator can figure this for you. (See below)

__

You can make use of some trig identities:

Then your function value can be written as ...

  sin(2x) = 2sin(x)cos(x) = 2(sin(x)/cos(x))cos(x)² = 2tan(x)/sec(x)²

  = 2tan(x)/(tan(x)² +1)

Filling in the given value for tan(x), this is ...

  sin(2x) = 2(12/5)/((12/5)² +1) = (24/5)/(144/25 +1) = (120/25)/((144+25)/25)

  sin(2x) = 120/169

The probability that no more than [tex]25[/tex] were victims of e-mail fraud is [tex]\fbox{0.00169}[/tex].

Further explanation:

Given:

The probability of a user experience e-mail fraud [tex]p[/tex] is [tex]0.7[/tex].

The number of individuals [tex]n[/tex] are [tex]50[/tex].

Calculation:

The [tex]\bar{X}[/tex] follow the Binomial distribution can be expressed as,

[tex]\bar{X}\sim \text{Binomial}(n,p)[/tex]

Use the normal approximation for [tex]\bar{X}[/tex] as

[tex]\bar{X}\sim \text{Normal}(np,np(1-p))[/tex]

The mean [tex]\mu[/tex] is [tex]\fbox{np}[/tex]

The standard deviation [tex]\sigma[/tex] is [tex]\fbox{\begin{minispace}\\ \sqrt{np(1-p)}\end{minispace}}[/tex]

The value of [tex]\mu[/tex] can  be calculated as,

[tex]\mu=np\\ \mu= 50 \times0.7\\ \mu=35[/tex]

The value of [tex]\sigma[/tex] can be calculated as,

[tex]\sigma=\sqrt{50\times0.7\times(1-0.7)} \\\sigma=\sqrt{50\times0.7\times0.3}\\\sigma=\sqrt{10.5}[/tex]

By Normal approximation \bar{X} also follow Normal distribution as,

[tex]\bar{X}\sim \text{Normal}(\mu,\sigma^{2} )[/tex]

Substitute 35 for [tex]\mu[/tex] and 10.5 for [tex]\sigma^{2}[/tex]

[tex]\bar{X}\sim\text {Normal}(35,10.5)[/tex]

The probability that not more than [tex]25[/tex] were victims of e-mail fraud can  be calculated as,

[tex]\text{Probability}=P(\bar{X}<25)}\\\text{Probability}=P(\frac{{\bar{X}-\mu}}{\sigma}<\frac{{(25+0.5)-35}}{\sqrt{10.5} })\\\text{Probability}=P(Z}<\frac{{25.5-35}}{\sqrt{10.5} })\\\text{Probability}=P(Z}<-2.93})\\[/tex]

The Normal distribution is symmetric.

[tex]P(Z>-2.93})=1-P(Z<2.93)\\P(Z>-2.93})=1-0.99831\\P(Z>-2.93})=0.00169[/tex]

Hence, the probability that no more than [tex]25[/tex] were victims of e-mail fraud is [tex]\fbox{0.00169}[/tex].

Learn More:

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Answer Details:

Grade: College Statistics

Subject: Mathematics

Chapter: Probability and Statistics

Keywords:

Probability, Statistics, E-mail fraud, internet, Binomial distribution, Normal distribution, Normal approximation, Central Limit Theorem, Z-table, Mean, Standard deviation, Symmetric.

Answer:

The correct option is D) How many visitors came to the museum each month last year?

Step-by-step explanation:

First, understand that what is the statistical question.

Statistical questions are those question which involves the collection of data. Which can be represented with the help of a chart or tables.

Now consider the provided options:

Options A, B and C are not a statistical question, because these questions do not require or involve the collection of data.

But the option D involves the collection of data because to find the number of visitors came to the museum each month, we need to collect the data.

Therefore the correct option is D.

Answer:

D.) How many visitors came to the museum each month last year?

i am taking the test rn :)

Answer:

The answer is 3093.

3093 (if that series you posted actually does stop at 1875; there were no dots after, right?)

Step-by-step explanation:

We have a finite series.

We know the first term is 48.

We know the last term is 1875.

What are the terms in between?

Since the terms of the series form a geometric sequence, all you have to do to get from one term to another is multiply by the common ratio.

The common ratio be found by choosing a term and dividing that term by it's previous term.

So 120/48=5/2 or 2.5.

The first term of the sequence is 48.

The second term of the sequence is 48(2.5)=120.

The third term of the sequence is 48(2.5)(2.5)=300.

The fourth term of the sequence is 48(2.5)(2.5)(2.5)=750.

The fifth term of the sequence is 48(2.5)(2.5)(2.5)(2.5)=1875.

So we are done because 1875 was the last term.

This just becomes a simple addition problem of:

48+120+300+750+1875

168      +   1050  +1875

          1218          +1875

                         3093

The greatest common factor (or GCF) is, as the name says, the greatest factor a set of numbers have in common. We can find this by listing out all the possible factors (multiples) of each number:

For 28:

1, 2, 4, 7, 14, 28

For 42

1, 2, 3, 6, 7, 21, 42

(note you don't need to list out all the factors, I just did it for visual purposes)

As you can see, 28 and 42 have 3 factors in common, with 7 being the greatest.

Therefore, the answer would be C: the GCF is 7.

Hope this helps! :)

Answer:

it is 14... have a blessed and amazing day

Step-by-step explanation:

Answer:

[tex]12x^8+15x^7-8x^6-10x^5[/tex]

Step-by-step explanation:

Start by using the FOIL method on your second and third terms.

[tex](3x^2-2)(4x^2+5x)\\12x^4+15x^3-8x^2-10x[/tex]

Next, multiply the first term ([tex]x^4[/tex]) against your result.

[tex]x^4(12x^4+15x^3-8x^2-10x)\\12x^8+15x^7-8x^6-10x^5[/tex]

For this case we must find the product of the following expression:[tex](x ^ 4) (3x ^ 2-2) (4x ^ 2 5x) =[/tex]

We must bear in mind that to multiply powers of the same base, the same base is placed and the exponents are added:

Multiplying the terms of the first two parentheses, applying distributive property we have:

[tex](x ^ 4 * 3x ^ 2-x ^ 4 * 2) (4x ^ 2 5x) =\\(3x ^ 6-2x ^ 4) (4x ^ 2 5x) =\\3x ^ 6 * 4x ^ 2 3x ^ 6 * 5x-2x ^ 4 * 4x ^ 2-2x ^ 4 * 5x =\\12x ^ 8 15x ^ 7-8x ^ 6-10x ^ 5[/tex]

Answer:

The product is: [tex]12x ^ 8 15x ^ 7-8x ^ 6-10x ^ 5[/tex]

Answer:

The y-intercept is (0,-407/5).

Step-by-step explanation:

The y-intercept can be found by setting x to 0 and solving for y.

10x-5y=407

10(0)-5y=407

   0-5y=407

     -5y=407

Divide both sides by -5:

       y=(407/-5)

       y=-407/5

The y-intercept is (0,-407/5).

Answer:

50 degrees

Step-by-step explanation:

The measure of an inscribed angle of a circle is half the degree measure of the intercepted arc.

m<Q = (1/2)m(arc)RS

m<Q = (1/2)(100 degrees)

m<Q = 50 degrees

Answer:

∠Q = 50°

Step-by-step explanation:

An inscribed angle whose vertex lies on a circle and whose sides are two chords of the circle is one half the measure of its intercepted arc.

arc RS is the intercepted arc, hence

∠Q = 0.5 × 100° = 50°

Answer:

a) The population proportion is 0.625

b) The confidence interval is (0.578 , 0.672)

Step-by-step explanation:

* Lets explain how to solve the problem

- The Fox TV network is considering replacing one of its prime-time

  crime investigation shows with a new family-oriented comedy show

- There are 400 viewers

∴ The sample size is 400

- 250 of them indicated they would watch the new show and

  suggested it replace the crime investigation show

∴ The number of success is 250

∵ The population proportion P' = number of success/sample size

∴ P' = 250/400 = 0.625

a) The population proportion is 0.625

* Lets solve part b

- Develop a 95 percent confidence interval for the population

  proportion

∵ The confidence interval (CI) = [tex]P'(+/-)z*(\sqrt{\frac{P'(1-P')}{n}}[/tex],

  where P' is the sample proportion, n is the sample size, and z*

  is the value from the standard normal distribution for the desired

  confidence level

∵ 95% z is 1.96

∴ z* = 1.96

∵ P' = 0.625

∵ n = 400

∵ [tex]\sqrt{\frac{P'(1-P')}{n}}=\sqrt{\frac{0.625(1-0.625)}{400}}=0.0242[/tex]

∴ CI = 0.625 ± (1.96)(0.0242)

∴ CI = (0.625 - 0.047 , 0.625 + 0.047)

∴ CI = (0.578 , 0.672)

b) The confidence interval is (0.578 , 0.672)

Answer:

320 bags

Step-by-step explanation:

Let's first assign some literals, to simplify the problem. The goal is to set everything up, in order to only use one symbol.

[tex]p [/tex]: number of bags with only peanuts.

[tex] a [/tex]: number of bags with only almonds.

[tex] r [/tex]: number of bags with only raisins.

[tex] x [/tex]: number of bags with only raisins and peanuts.

Now, the problem establish 3 useful equations. We can find equations equivalences for the next sentences.

"The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts"  is equivalent to [tex] r = 10p[/tex].

"The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts" is equivalent to [tex] a= 20x[/tex].

"The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds" is equivalent to [tex] p = \frac{1}{5} a [/tex].

We already know that [tex] a = 20x[/tex].  And because of that, we also know that

[tex]p = \frac{1}{5}a = \frac{1}{5}(20x) = 4x[/tex]

and to conclude this stage of the problem, we also know that [tex]r = 10p =10(4x) = 40x[/tex]

As there are only 3 items, it is possible to use a Venn diagram. As we can see in the diagram, the entire quantity of bags is going to be

[tex]210 + 4x + x + 40x = 210 + 45x[/tex]

But, we also know that there are 435 bags, then we only have to solve the equation:

[tex]210 + 45x = 435[/tex]

[tex]45x = 435 - 210[/tex]

[tex]45x = 225[/tex]

[tex]x = 225/45 [/tex]

[tex]x = 5 [/tex]

Substituting [tex]x = 5[/tex] we get

[tex]a = 20 x = 20(5) = 100[/tex]

[tex]p = 4 x = 4(5) = 20[/tex]

[tex]r = 40 x = 40(5) = 200[/tex]

Finally [tex] ans = 100 + 20 + 200 = 320 [/tex]

Answer:

a. 226 pounds

b. 8 weeks

Step-by-step explanation:

To solve this problem, simply plug in the numbers for the variables it told you they correspond to. 12 is the number of weeks, and t represents the number of weeks, so we can plug 12 in for t.

[tex]W=-2(12)+250[/tex]

Simplify and you'll have your answer.

[tex]W=-24+250\\W=226[/tex]

For part B, 234 is the amount of pounds, and W represents the weight in pounds, so we can plug 234 in for W.

[tex]234=-2t+250\\-16=-2t\\8=t[/tex]

Answer:

  0.196 lbs

Step-by-step explanation:

The area of the cross section is the difference of the areas of circles with the different diameters. The volume of the pipe material is the product of its cross section area and its length:

  V = π(D² -d²)L/4 = π(0.82² -0.75²)36/4 ≈ 3.107 . . . in³

Then the weight of the material is this volume multiplied by the density.

  W = V·δ = (3.107 in³)(0.063 lb/in³) ≈ 0.196 lb

Finding the weight of the PVC pipe involves calculating the volumes of the outer and inner cylinders then finding the difference, which is multiplied by the weight per cubic inch of PVC.

The weight of a 36 inch piece of PVC pipe can be calculated using the formula for the volume of a cylinder and the given weight per cubic inch of PVC material. Firstly, calculate the volume of the outer cylinder, which we know the diameter and length (or height). The formula for the volume of a cylinder is πr²h, where r is the radius and h is the height. We need to halve the diameter to get the radius, which gives us 0.82/2 = 0.41 inches.

Secondly, we calculate the volume of the inner cylinder in the same way, except we use the inner diameter, which is 0.75 inches, halved gives us a radius of 0.375 inches. The volume of material used is then the volume of the outer cylinder minus the volume of the inner cylinder. Lastly, multiply the volume of material by the weight per cubic inch to get the total weight.

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Answer:

  (4, -3)

Step-by-step explanation:

-2u +v = -2(-1, 5) +(2, 7) = (-2(-1)+2, -2(5)+7)

  = (4, -3)

Answer:

150%

Step-by-step explanation:

Best Tire : 50,000 miles

Better Tire : 20,000 miles

Difference : 50,000 - 20,000 = 30,000

The difference expressed as a percentage of the less expensive tire

= (30,000 / 20,000) x 100%

=150%

Final answer:

The domain for the base price of a car that Leonard can initially afford is [24,000, 30,000]. After buying car insurance worth $2,200, the domain changes to [24,000, 28,000], reflecting the reduced budget available for the car purchase.

Explanation:

Initially, Leonard can afford a car with a base price up to his budget of $33,000. Since car accessories cost one-tenth of the base price, we calculate the maximum base price he can afford as follows: Let x be the base price of the car. The total cost of the car, including accessories, would be x + (1/10)x = (1 + 1/10)x = (11/10)x. So, to stay within budget, (11/10)x ≤ $33,000. Solving for x gives us x ≤ $33,000 / (11/10) = $30,000.

Therefore, the domain representing the base price Leonard can afford is [24,000, 30,000].

After buying car insurance for $2,200, Leonard's budget for the car decreases. The new budget for the car including accessories is $33,000 - $2,200 = $30,800. Solving (11/10)x ≤ $30,800, we get x ≤ $30,800 / (11/10) = $28,000.

Now, the domain for the base price that Leonard can afford after the insurance payment is [24,000, 28,000].

Answer:

1st problem: b) [tex]A=2500(1.01)^{12t}[/tex]

2nd problem:  c) [tex]A=2500e^{.12t}[/tex]

Step-by-step explanation:

1st problem:

The formula/equation you want to use is:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where

t=number of years

A=amount he will owe in t years

P=principal (initial amount)

r=rate

n=number of times the interest is compounded per year t.

We are given:

P=2500

r=12%=.12

n=12 (since there are 12 months in a year and the interest is being compounded per month)

[tex]A=2500(1+\frac{.12}{12})^{12t}[/tex]

Time to clean up the inside of the ( ).

[tex]A=2500(1+.01)^{12t}[/tex]

[tex]A=2500(1.01)^{12t}[/tex]

----------------------------------------------------

2nd Problem:

Compounded continuously problems use base as e.

[tex]A=Pe^{rt}[/tex]

P is still the principal

r is still the rate

t is still the number of years

A is still the amount.

You are given:

P=2500

r=12%=.12

Let's plug that information in:

[tex]A=2500e^{.12t}[/tex].

Answer:use a VPN and also write down your passwords, never keep them saved on your computer in case of a leak/breach of privacy and information

Step-by-step explanation:

Other than that all you got a do is download a VPN and also write your passwords and then proceed to be careful by not sharing any private/key info to identify who you are

Given that [tex]P(Q)=\dfrac{3}{5},P(R)=\dfrac{1}{3}[/tex]

Also,

[tex]P(Q\wedge R)=P(Q)\cdot P(R)=\dfrac{3}{5}\cdot\dfrac{1}{3}=\dfrac{1}{5}[/tex]

We can conclude that,

[tex]P(Q\vee R)=P(Q)+P(R)=\dfrac{3}{5}+\dfrac{1}{3}=\boxed{\dfrac{14}{15}}[/tex]

The answer is B.

Hope this helps.

r3t40

Answer:

There are 15 partitions of 7.

Step-by-step explanation:

We are given that a partition of a positive integer $n$ is any way of writing $n$ as a sum of one or more positive integers, in which we don't care about the numbers in the sum .

We have to find the partition of 7

We are given an example

Partition of 4

4=4

4=3+1

4=2+2

4=1+2+1

4=1+1+1+1

There are five partition of 4

In similar way  we are finding  partition of 7

7=7

7=6+1

7=5+2

7=5+1+1

7=3+3+1

7=3+4

7=4+2+1

7=3+2+2

7=4+1+1+1

7=3+1+1+1+1

7=2+2+2+1

7=3+2+1+1

7=2+2+1+1+1

7=2+1+1+1+1+1

7=1+1+1+1+1+1+1

Hence, there are 15 partitions of 7.

Answer:

Step-by-step explanation:

When a quantity changes exponentially by a fraction r in some time period t, the quantity is multiplied by 1+r in each period. That is the quantity (y) as a function of t can be described by ...

  y = y0·(1+r)^t

where y0 is the initial quantity (at t=0).

Here, the problem statement gives us two quantities and their respective rates of change.

Treatment A

  y0 < 300, r = -0.04, so the remaining amount is described by ...

  y < 300·0.96^t

__

Treatment B

  y0 ≤ 400, r = -0.062, so the remaining amount is described by ...

  y ≤ 400·0.938^t

__

When we graph these, we realize these inequalities allow the quantity of each substance to be less than zero. Mathematically, those quantities will approach zero, but not equal zero, so we can put 0 as a lower bound on the value of y in each case:

_____

Comment on these inequalities

We suspect your answer choices will not be concerned with the lower bound on y.

Answer:

y (arrow left) 300e-0.04t

y (arrow left underlined) 400e-0.062t

Step-by-step explanation:

The answer is 40 shirts.

Explanation

Equation: y= ((616-(14*12))/16)+12

First, multiply the 12*14 because we know that 12 shirts were $14. You'll get $168. Next, subtract that from 616, the total number of dollars, to get the 12 shirts out of the way. Your answer will be $448. Then, divide by 16 because that's the remaining money that was spent on the $16 shirts. You'll get 28 shirts. However, we can't forget about the dozen $14 shirts, so add 12 to your answer and you get 40 shirts.

Answer:

  f(x) = 4^x -3

Step-by-step explanation:

All of the listed functions are linear functions with a constant slope of 4. None of them goes through the point (0, -2).

__

So, we assume that there is a missing exponentiation operator, and that these are supposed to be exponential functions. If the horizontal asymptote is -3, then there is only one answer choice that makes any sense:

  f(x) = 4^x -3

_____

The minimum value of 4^z for any z will be near zero. In order to make it be near -3, 3 must be subtracted from the exponential term.

Answer:

193.04

Step-by-step explanation:

If one inch equals 2.54 centimeters, a 76-inch tall man is 193.04 centimeters.

1 inch = 2.54 centimeters

76 inches

2.54 x 76 = 193.04

Answer:

193.04 cm

Step-by-step explanation:

So let's line up our corresponding information.

1 inch=2.54 cm

76 in =x       cm

This is already setup for you to write a proportion:

[tex]\frac{1}{76}=\frac{2.54}{x}[/tex]

Cross multiply:

[tex]1(x)=76(2.54)[/tex]

Multiply:

[tex]x=193.04[/tex]

Answer:

The tip of the man shadow moves at the rate of [tex]\frac{20}{3} ft.sec[/tex]

Step-by-step explanation:

Let's draw a figure that describes the given situation.

Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.

Here it forms two similar triangles.

Let's find the distance "y" using proportion.

From the figure, we can form a proportion.

[tex]\frac{y - x}{y} = \frac{6}{15}[/tex]

Cross multiplying, we get

15(y -x) = 6y

15y - 15x = 6y

15y - 6y = 15x

9y = 15x

y = [tex]\frac{15x}{9\\} y = \frac{5x}{3}[/tex]

We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).

[tex]\frac{dy}{t} = \frac{5}{3} \frac{dx}{dt}[/tex] ----(1)

We are given [tex]\frac{dx}{dt} = 4 ft/sec[/tex]. Plug in the equation (1), we get

[tex]\frac{dy}{dt} = \frac{5}{3} *4 ft/sect\\= \frac{20}{3} ft/sec[/tex]

Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.

To find the speed at which the tip of the man's shadow is moving, we need to solve a proportional relationship between the length of the shadow and the distance of the man from the pole. Using similar triangles and setting up a ratio, we can find the length of the shadow and then find its rate of change with respect to time. The tip of the shadow is not moving when the man is 45 ft from the pole.

To solve this problem, we need to use similar triangles. Let's call the length of the shadow x. The height of the pole is 15 ft and the height of the man is 6 ft. So, we can set up the following ratio:

15 / x = 6 / (x + 45)

To find x, we can cross-multiply:

(15)(x + 45) = 6x

Now, we can simplify and solve for x:

15x + 675 = 6x

9x = 675

x = 75 ft

To find the rate of change of the shadow's tip, we can take the derivative of x with respect to time:

dx/dt = 0

So, the tip of the shadow is not moving when the man is 45 ft from the pole.

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