The university police department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 7.5. Find the probability that fewer than six tickets

The value of x, considering the volume of the triangular prism, is given as follows:

x = 3.67.

The volume of a triangular prism is calculated as the multiplication of the base area by the height, as follows:

Volume = Base Area x Height

The base is a right triangle with sides 8 and 9, hence it's area is given as follows:

Base area = 0.5 x 8 x 9

Base area = 36 units squared.

x represents the height, hence the value of x is obtained considering the volume of 132 units³ as follows:

36x = 132

x = 132/36

x = 3.67.

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145 = 100 + 40 + 5

237 = 200 + 30 + 7

Adding both

145 + 237 = 300 + 70 + 12

12 = 10 + 2

Hence 145 + 237

= 300 + 70 + 10 + 2

= 382

Answer:

a. \(\tt \frac{1}{9}\)

b. \(\frac{1}{16}\)

c. 4

Step-by-step explanation:

\(\tt a. \:3^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\) So, we have:

\(\tt 3^{-2} = \frac{1}{3^2} = \frac{1}{9}\)

\(\hrulefill\)

\(\tt b.\: -2^{-4}\)

We can use the rule that \(\boxed{\tt -a^{-n} = (-1)^n \cdot a^n}.\) So, we have:

\(\tt -2^{-4} = (-1)^4 \cdot 2^{-4} = 1 \cdot \frac{1}{2^4} = \frac{1}{16}\)

\(\hrulefill\)

\(\tt c. \:(\frac{1}{2})^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\). So, we have:

\(\tt (\frac{1}{2})^{-2} = \frac{1}{(\frac{1}{2})^2} = \frac{1}{\frac{1}{4}} = 4\)

Answer:

Step-by-step explanation:

(a) 3^-2 = 1/9

(b) (-2)^-4 = 1/(-2)^4 = 1/16

(c) (1/2)^-2 = 1/(1/2)^2=1 / 1/4 = 4

60 x 5 + 45 = 345 Seconds

Answer: 3.

Step-by-step explanation:

\(\left \{ {{4x-3y=3 \ |[*(-4)]} \atop {5x-4y=3} \ |[*3]} \right. \ = > \ \left \{ {{-16x+12y=-12} \atop {15x-12y=9}} \right. \ = > \ \left \{ {{y=3} \atop {x=3}} \right.\)

The volume of cylinder is 191 cubic centimeters.

What is volume?

The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.

Here cylinder with height 6 cm ,

Volume = 128 cubic centimeters.

Now using volume of cylinder formula then,

=> Volume V =

=> 128 = 3.14**6

=>  =  = 6.79406

=> r = 2.6 cm.

Now volume of cylinder with height 9 cm is ,

=> Volume V = 3.14**9 = 191 cubic centimeters.

Hence the volume of cylinder is 191 cubic centimeters.

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Answer:

no it's not

Step-by-step explanation:

3% of 45,500 is 1455 which is less then 2,500 which also means 1.5% is not more then 2,500

Answer

1-right

2-not a triangle

3-acute

4-obtuse

5-right

6-obtuse

7-acute

Step-by-step explanation:

The proportion that represents the down payment is 20% or 0.2 of the condominium's value.

2. The down payment is $25,000.

The down payment is the proportion required to secure a purchase transaction.

The down payment is an upfront cost that the purchaser settles in cash before being granted a long-term credit (loan or mortgage).

The purpose of a down payment is to reassure the lender of the borrower's ability to repay the loan.

To compute the down payment, apply the down payment percentage or proportion to the value of the asset.

The cost of the condominium = $125,000

Down payment = 20%

20% = $25,000 ($125,000 x 20%)

Mortgage loan = $100,000 ($125,000 - $25,000)

Thus, in this situation, the down payment is 20% of the cost of the property.

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Answer:

2 5/12

Step-by-step explanation:

deduct the sum of 2 1/4 and 3 2/6 from 8

i prefer to change them to improper fractions

9/4 + 20/6 = 27/12 + 40/12 = 67/12

8 can be change to 96/12

96/12 - 67/12 = 29/12 or 2 5/12

The surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

To find the increase in surface area, we first need to calculate the initial surface area of the box and then calculate the surface area after increasing the height.

The formula for the surface area of a rectangular prism is given by:

Surface Area = 2*(length width + length height + width*height)

Initial Surface Area:

Length (L) = 13 cm

Width (W) = 8.7 cm

Height (H) = 28 cm

Initial Surface Area = 2*(138.7 + 1328 + 8.7*28)

Next, we calculate the new surface area after increasing the height by 0.2 cm. The new height is:

New Height = Initial Height + Increase in Height = 28 cm + 0.2 cm

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2))

To find the increase in surface area, we subtract the initial surface area from the new surface area:

Increase in Surface Area = New Surface Area - Initial Surface Area

Let's calculate the values:

Initial Surface Area = 2*(138.7 + 1328 + 8.728) = 2(113.1 + 364 + 243.6) = 2*(720.7) = 1441.4 cm²

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2)) = 2*(113.1 + 377.2 + 244.1) = 2*(734.4) = 1468.8 cm²

Increase in Surface Area = New Surface Area - Initial Surface Area = 1468.8 cm² - 1441.4 cm² = 27.4 cm²

Therefore, the surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

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To find the common roots between two functions, we need to find the roots (or solutions) of each function individually and then identify the shared solutions.

For the function f(x) = x^2 + x - 6, we can find the roots by setting the function equal to zero and solving for x:

x^2 + x - 6 = 0

To factorize this quadratic equation, we need to find two numbers that multiply to -6 and add up to 1 (the coefficient of x). The numbers that satisfy these conditions are 3 and -2:

(x + 3)(x - 2) = 0

Setting each factor equal to zero:

x + 3 = 0 or x - 2 = 0

Solving for x in each equation:

x = -3 or x = 2

Therefore, the function f(x) = x^2 + x - 6 has two roots: x = -3 and x = 2.

To find the common roots between this function and another function, we would need to know the second function. If you provide the second function, I can help determine if there are any shared roots.

Answer:

50

Step-by-step explanation:

if we sad the son is 10 years old so 40*10=40 this the mark age then and 10 his son age =50

Answer:

27

Step-by-step explanation:

Answer:

Step-by-step explanation:

u take the equation apart and start with what is inside the parenthesis so (12+2) which equals 14 so then you subtract 14 from 55 which gives us 41

Answer:

  192.7 cm³

Step-by-step explanation:

You want the volume of a regular pentagonal prism with a base side length of 4 cm and a height of 7 cm.

The area of a regular n-gon is given by the formula ...

  A = n·s²/(4·tan(180°/n))

For n=5 and s=4 cm, the area of the prism base is ...

  A = 5·(4 cm)²/(4·tan(36°)) = 20/tan(36°) cm² ≈ 27.528 cm²

The volume of a prism is ...

  V = Bh

where B is the base area, and h is the height. Here, we have h=7 cm, so the volume is ...

  V = (27.528 cm²)(7 cm) ≈ 192.7 cm³

The volume of the interior of the box is about 192.7 cm³.

Answer:

Here ya go!

Step-by-step explanation:

The unknown angles in the cyclic quadrilateral is as follows:

∠BGX = 74° (sum of angles in a triangle)

∠BGF = 180° (opposite angles of cyclic quadrilateral are supplementary)

∠BCF = 100°(sum of angles in a triangle)

∠BCG  = 26°

∠BFG = 22°

A cyclic quadrilateral has all its angles equal to 360 degrees. The sum of angles in a cyclic quadrilateral is equals to 360 degrees.

Let's find the missing angles as follows:

∠BGX = 180 - 48 - 58 = 74° (sum of angles in a triangle)

∠BGF = 180 - 100 = 80° (opposite angles of cyclic quadrilateral are supplementary)

∠BCF = 180 - 22 - 58 = 100°(sum of angles in a triangle)

∠BCG = 100 - 74 = 26°

∠BFG ≅ CBF = 22°(alternate angles)

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Answer:

No.

Step-by-step explanation:

Sweet Potatoes= 0.79 Per pound including tax.

So 0.79 · 8 = $6.32

And Stuart only have $5.00.

Therefore He don't have enough money for 8 pound of sweet potatoes.

Answer:

give me points plzzz

Step-by-step explanation:

Answer:

Vc = (π/3)✓17 ≈ 4.12 ft³

Step-by-step explanation:

h = ✓(4²+1²)

h = ✓17

V = πr²h/3

V = π(1)²✓17/3

V = (π/3)✓17 ≈ 4.12

Answer:

8

Step-by-step explanation:

(-11/2x +3) -2(-11/4x -5/2)

(-11/2x +3) +22/4x +10/2

-11/2x +3 +11/2x +5

8

Answer:

14 and 10

Step-by-step explanation:

We have the equation x(x-4)=140. We can distribute the x to everything in the parenthesis so it's easier to work with.

x(x-4)=140

\(x^2-4x=140\)

Let's move 140 to the left side, so we can solve this equation better by finding the zeros of the equation.

\(x^2-4x-140=0\)

To find the zero, we have to find TWO values that multiply to -140 but add to -4.

(x-14)(x-10)=0

To find the zeros. make both of those parenthesis equal to zero.

x=14, 10

Answer:

300-20w=?

150+10w=?

Step-by-step explanation:

Answer:

Step-by-step explanation:

320

There are 20 possible routes that a man could take to go between cities and then take a different route back.

In mathematics, a permutation of a set is, broadly speaking, the rearranging of its elements if the set is already sorted, or the arrangement of its members into a sequence or linear order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context.

Let the number of roads between the cities A and B = 5.

The rules of permutation must be used in this situation.

A permutation is an arrangement of all or a portion of a collection of items that takes into account the arrangement's order.

The man uses five different routes to get from A to B because there are five different routes accessible.

He can get back by 4 (5 1) methods because he needs to take a different route.

Therefore, there are 20 possible routes that a man could take to go between cities and then take a different route back.

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Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70

Answer:

x = 10/243

Step-by-step explanation:

3^5x = 10

243x = 10

Divide 243 on both sides

10/243

Answer:

Function, function

Step-by-step explanation:

Each input corresponds to one output. Thus, by the definition of a function, both graphs represent functions

Answer:

m=7

Step-by-step explanation: