home security service. This private home security service guarantees to either dispatch one of their own five guards immediately if one of their customers sends in an alarm or, in the case that all five guards are responding to other calls, direct the alarm to the local police. The company receives 12 calls per hour, evenly distributed over the course of the day. The local police charges the home security company $500 for every call that the police responds to. It takes a guard, on average, 90 minutes to respond to an alarm. a. What fraction of the time are incoming alarms directed to the police? b. How much does the home security company have to pay the local police every month?

Answer:

[tex]3x^5+6x^4+12x^3[/tex]

Step-by-step explanation:

Given that,

[tex]f(x) = 3x^3+ 6x^2+ 12x[/tex]

and

[tex]g(x)=x^2[/tex]

We need to find the product of f(x) and g(x). SO,

[tex]f(x)\times g(x)=(3x^3+ 6x^2+ 12x)\times (x^2)\\\\=3x^3\times x^2+6x^2\times x^2+12x\times x^2\\\\=3x^5+6x^4+12x^3[/tex]

Hence, the correct option is (d).

Answer:

4(3) - 7 = 4(3 - 1) - 3

12 - 7 = 4(2) - 3

5 = 8 - 3

= 5

They are equivalent because when they are both simplified they have the same answer 5

Answer:

120 and 40

Step-by-step explanation:

Because when we subtract 80 and 40 is equal 40 or 160 and 40 is 120.

Answer:

if t=60, then 6(60)/9-23. (360-198)/9

=18

Answer:

Angle 3 is = to angle 2 because:

Angle 3 & angle 7 are corresponding angles, meaning they have the same measure.

Angle 7 & angle 2 are vertical angles, meaning they also have the same measure.

Therefore, if angle 7 is equal to angle 3, then angle 2 must also be equal to angle 3.

Hope this helps! Have a great day!

Answer:

im guessing .30, .3, and 30/100

Step-by-step explanation:

im not sure how to explain it but fractions. yes.

Answer:

What do you want us to find?

Step-by-step explanation:

Answer:

Step-by-step explanation:

If you add the lengths of two sides, 12 and 14, you will get 28. Using the above theorem, the third side cannot be greater than or equal to 28. Therefore, the greatest possible whole-number length of the unknown side is 27.

Answer:

Step-by-step explanation:

7 or C

Answer:

Josh won all the prizes for the contest

Step-by-step explanation:

Answer:

Perimeter = 12.246 units

Area = 11.314 units²

Step-by-step explanation:

A=2√2r²=11.314

P=2(8)(√2-√2)=12.246

Answer:

1 6 3b 0ny 5i bhk

Step-by-step explanation:

Answer: 14.967

Step-by-step explanation:

Use Pythagorean Theorem to find the missing length.  

a² + b² = c²        

x² + 10² = 18²      

x² + 100 = 324         [Subtract 100 from both side]  

          x²= 224        

      √x² = √224     [solve the square root from both sides]

        x   ≈  14.967

Answer:

-6

Step-by-step explanation:

The equation is y = -7x - 6.

The initial value is found when x = 0.

y = -7(0) - 6

y = 0 - 6

y = -6

Answer:

The developer bought 4.9 acres of land, increasing its property to 29.4 acres.

Step-by-step explanation:

Given that a developer has 24.5 acres of land, and she buys an adjacent plot of land and increases the total acreage she owns by 20%, to determine the amount of acres she bought and the total acres she now owns, the following calculations must be done:

24.5 x 1.2 = 29.4

24.5 x 0.2 = 4.9

Thus, the developer bought 4.9 acres of land, increasing its property to 29.4 acres.

Answer:

it is 3 inches

3 x 4 = 12

Answer:

2

Step-by-step explanation:

Answer:

91m + 13n + 52

Step-by-step explanation:

13(n + 4 + 7m)

= (13) (n+4+7m)

= (13) (n) + (13) (4) + (13) (7m)

= 13n + 52 + 91m

= 91m + 13n + 52

hope this helps and is right :)

p.s. i really need brainliest

Answer:

13n + 52 +91m

Step-by-step explanation:

As far as I can tell, all you are doing is distributing the 13 into the numbers. You multiply 13* 1n, 13*4, and 13*7m to give you 13n +52+91m.

Answer:

4

Step-by-step explanation:

1) Simplify 2⁴ to 16.

[tex]20 - 16[/tex]

2) Simplify.

[tex]4[/tex]

Therefor, the answer is 4.

Answer:

20 - 2^4 =4

Step-by-step explanation:

Answer:

The slope of the line would be 3/6 or 1/2

Step-by-step explanation:

To get from point (1,2) to point (7,5) you have to rise 3 places and run (move to the right) 6 times. Rise/run=3/6

hope this helps. ; )

Answer:

-3

Step-by-step explanation:

-11(-3)+7=40

33+7=40

If the 0's are indeed zeroes, then it would appear that you're using degrees, so that the equation

r(θ) = 2 sin(0°) + 3 sin(90°)

describes a circle r = 3 (since sin(0°) = 0 and sin(90°) = 1). In this case, the area would simply be π r ² = 9π.

But I suspect you meant to use θ, so the curve has the far more interesting equation,

r(θ) = 2 sin(θ) + 3 sin(9θ)

Since sin(9θ) has a period of 2π/9 and sin(θ) has a period of 2π, their sum has a period of 2π. (That is, 2π times the LCM of 1 and 1/9, which is 1.) But we observe r(θ) is odd, since

r(-θ) = 2 sin(-θ) + 3 sin(-9θ)

… = -2 sin(θ) - 3 sin(9θ)

… = - r(θ)

which tells us that the curve closes itself over a half-period. So the area bounded by the curve is given by the integral,

[tex]\displaystyle\int_0^\pi\int_0^{r(\theta)}r\,\mathrm dr\,\mathrm d\theta[/tex]

If you're not familiar with double integrals yet, all you need to know is that this reduces to the area formula you may/should be familiar with,

[tex]\displaystyle\frac12\int_0^\pi r(\theta)^2\,\mathrm d\theta[/tex]

Compute the integral:

[tex]=\displaystyle\frac12\int_0^\pi(2\sin(\theta)+3\sin(9\theta))^2\,\mathrm d\theta[/tex]

[tex]=\displaystyle\frac12\int_0^\pi(4\sin^2(\theta)+12\sin(\theta)\sin(9\theta)+9\sin^2(9\theta))\,\mathrm d\theta[/tex]

Apply some identities:

sin²(θ) = (1 - cos(2θ)) / 2

sin(θ) sin(9θ) = (cos(9θ - θ) - cos(9θ + θ)) / 2 = (cos(8θ) - cos(10θ)) / 2

sin²(9θ) = (1 - cos(18θ)) / 2

[tex]=\displaystyle\frac14\int_0^\pi(4(1-\cos(2\theta))+12(\cos(8\theta)-\cos(10\theta))+9(1-\cos(18\theta))\,\mathrm d\theta[/tex]

[tex]=\displaystyle\frac14\int_0^\pi(13 - 4\cos(2\theta) + 12\cos(8\theta) - 12\cos(10\theta) - 9\cos(18\theta))\,\mathrm d\theta[/tex]

[tex]=\dfrac14 \left(13\theta-2\sin(2\theta)+\dfrac32\sin(8\theta)-\dfrac65\sin(10\theta)-\dfrac12\sin(18\theta)\right)\bigg|_0^\pi[/tex]

[tex]=\dfrac1{40} \left(130\theta-20\sin(2\theta)+15\sin(8\theta)-12\sin(10\theta)-5\sin(18\theta)\right)\bigg|_0^\pi[/tex]

[tex]=\dfrac{130\pi-20\sin(2\pi)+15\sin(8\pi)-12\sin(10\pi)-5\sin(18\pi)}{40}[/tex]

= 13π/4

Answer:soultion

Step-by-step explanation:      solution

Answer:

r < 4

Step-by-step explanation:

r+6<10

r < 4

Answer:

5 Probability

5.1 Probabilities

Probabilities are used to describe how likely or unlikely it is that something will happen.

Weather forecasters often talk about how likely it is to rain, or perhaps snow, in particular

parts of the country.

Worked Example 1

(a) When you roll a dice, which number are you most likely to get?

(b) If you rolled a dice 600 times how my sixes would you expect to get?

(c) Would you expect to get the same number of ones?

Solution

(a) You are equally likely to get any of the six numbers.

(b) You would expect to get a six in about 1

6

of the throws, so 100 sixes.

(c) Yes, in fact you would expect to get about 100 of each number.

Worked Example 2

Use one of the following to describe each one of the statements (a) to (d).

Certain

Very likely

Likely

Unlikely

Very unlikely

Impossible

(a) It will snow tomorrow.

(b) It will rain tomorrow.

(c) You win a car in a competition tomorrow.

(d) You are late for school tomorrow.

Solution

(a) Very unlikely for most places in Britain, especially in summer.

(b) Likely or Very likely in Britain in winter.

(c) Very unlikely if you have entered the competition. Impossible if you have not

entered the competition.

(d) Very unlikely, unless the school bus breaks down.

Answer:

x = 29

angles are 90 degrees, 56 degrees, and 34 degrees

Step-by-step explanation:

90 + (2X-2) + (X+5) = 180

3X + 93 = 180

3X = 87

X = 29

Answer:

B

Step-by-step explanation:

Answer:

Its E

Step-by-step explanation: