On average, indoor cats live to 16 years old with a standard deviation of 2.5 years. Suppose that the distribution is normal. Let X = the age at death of a randomly selected indoor cat. Round answers to 4 decimal places where possible.


a. What is the distribution of X? X ~ N([],[])


b. Find the probability that an indoor cat dies when it is between 17.2 and 19.6 years old.[]



c. The middle 20% of indoor cats' age of death lies between what two numbers?

Low: [] years

High: [] years

Answers

Answer 1

Answer:

(a) N (16, 2.5²)

(b) 0.241

(c) Low: 15.4 years

    High: 16.6 years

Step-by-step explanation:

The random variable X is defined as the age at death of a randomly selected indoor cat.

(a)

The distribution of X is:

[tex]X\sim N(\mu = 16, \sigma^{2}=2.5^{2})[/tex]

(b)

Compute the probability that an indoor cat dies when it is between 17.2 and 19.6 years old as follows:

[tex]P(17.2<X<19.6)=P(\frac{17.2-16}{2.5}<\frac{X-\mu}{\sigma}<\frac{19.6-16}{2.5})[/tex]

                            [tex]=P(0.48<Z<1.44)\\=P(Z<1.44)-P(Z<0.48)\\=0.92507-0.68439\\=0.24068\\\approx 0.241[/tex]

Thus, the probability that an indoor cat dies when it is between 17.2 and 19.6 years old is 0.241.

(c)

Compute the two numbers within which 20% of indoor cats' age of death lies as follows:

[tex]P(x_{1}<X<x_{2})=0.20\\\\\Rightarrow P(-z<Z<z)=0.20\\\\P(Z<z)-P(Z<-z)=0.20\\\\P(Z<z)-[1-P(Z<z)]=0.20\\\\2P(Z<z)-1=0.20\\\\2P(Z<z)=1.20\\\\P(Z<z)=0.60[/tex]

The corresponding value of z is, 0.25.

Compute the value of x₁ and x₂ as follows:

[tex]z=\frac{x_{1}-\mu}{\sigma}\\\\0.25=\frac{x_{1}-16}{2.5}\\\\x_{1}=16+(0.25\times 2.5}\\\\x_{1}=16.625\\\\x_{1}\approx 16.6[/tex]                [tex]z=\frac{x_{1}-\mu}{\sigma}\\\\-0.25=\frac{x_{2}-16}{2.5}\\\\x_{2}=16-(0.25\times 2.5}\\\\x_{2}=15.375\\\\x_{2}\approx 15.4[/tex]

Low: 15.4 years

High: 16.6 years


Related Questions

Help please I’lol really appreciate it

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Answer:

j+z+12

Step-by-step explanation:

your brother is 1/2 your age.your sister is 5 years older than your brother . your sister is 15 years old write and solve an equation to find your age x

pls help me I will mark brainleyest​

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You would be 20 years old.

Question 5 of 10 If f(x) = 4x - 12, what is f(2)? h O A. -20 O B. 8 O c. -4 O D. 4 SUE​

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Answer:

-4

Step-by-step explanation:

What must 111,111,102 be divided by to get 9 as the quotient and 0 as the remainder?

Answers

ANSWER: 12,345,678

EXPLANATION:
we can work backwards by figuring out what 9(the answer) is multiplied by to get 111,111,102 (the starting number) we can do this by dividing by 9:

111,111,102/9 = 12,345,678

so: 9 * 12,345,678 = 111,111,102
which also means

111,111,102/12,345,678 = 9 (with 0 as a remainder)

HELP ASAP DUE TOMORROW!!!
On a family outing, Tyler bought 5 cups of hot cocoa (x)
and 4 pretzels (y) for $18.40. Some of his family members
would like a second serving, so he went back to the same
food stand and bought another 2 cups of hot cocoa (x) and
4 pretzels (y) for $11.20.

Answers

Answers:

x = 2.40

y = 1.60

This means 1 hot cocoa costs $2.40 and 1 pretzel costs $1.60

=======================================

Work Shown:

x = cost of 1 cup of hot cocoa

y = cost of 1 pretzel

5x = cost of 5 cocoas

4y = cost of 4 pretzels

5x+4y = cost of 5 cocoas+4 pretzels

5x+4y = 18.40

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

2x = cost of 2 cocoas

4y = cost of 4 pretzels

2x+4y = cost of 2 cocoas+4 pretzels

2x+4y = 11.20

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

The system of equations we have is

[tex]\begin{cases}5x+4y = 18.40\\2x+4y = 11.20\end{cases}[/tex]

Note how 4y shows up twice. This is handy to be able to get rid of the y terms completely.

How? By subtracting the equations straight down

The x terms subtract to 5x-2x = 3x

The y terms subtract to 4y-4y = 0y = 0 and they go away

The right hand sides subtract to 18.40 - 11.20 = 7.20

After those three separate subtractions, we have this new equation:

3x = 7.20

Divide both sides by 3 to isolate x

3x/3 = 7.20/3

x = 2.40

Each hot cocoa costs $2.40

Now use this x value to find y. You can pick any equation you want as long as it has x,y in it. I'll pick the first equation

5x+4y = 18.40

5(2.40)+4y = 18.40

12+4y = 18.40

4y = 18.40-12

4y = 6.40

y = 6.40/4

y = 1.60

Each pretzel costs $1.60

If we picked on the second equation, we should get the same y value

Let's find out

2x+4y = 11.20

2(2.40)+4y = 11.20

4.80+4y = 11.20

4y = 11.20-4.80

4y = 6.40

y = 6.40/4

y = 1.60

We get the same result as before.

To check the answers, you need to plug those values back into the two original equations and simplify. You should get the same thing on both sides.

What is 7/8 x 4/5 divided by 7/20

Answers

Answer: 2

Step-by-step explanation: First, multiply 7/8 by 4/5 which equals to 7/10. Then, divide 7/10 by 7/20. Finally, you should end up with a result of 2.

4/10 would be your answer to your question

The right triangle ABC, shown below is reflected over the line y = -x. Where will the point C' be located?

Answers

Answer:

(4, -3)

Step-by-step explanation:

It says my answers need to be at least 20 characters long so I had to write this.

Carlos buys a box of frozen flavored ice sticks. 2/5 of the ice sticks are blue raspberry. Of the remaining ice sticks, 1/3 are grape, and the rest are cherry. If there are 48 blue raspberry and cherry flavored ice sticks altogether, how many ice sticks total are in the box?

Answers

Given:

[tex]\dfrac{2}{5}[/tex] of the ice sticks are blue raspberry.

Of the remaining ice sticks, [tex]\dfrac{1}{3}[/tex] are grape, and the rest are cherry.

There are 48 blue raspberry and cherry flavored ice sticks altogether.

To find:

The total number of ice sticks.

Solution:

Let x be the total number of ice sticks.

[tex]\dfrac{2}{5}[/tex] of the ice sticks are blue raspberry.

Blue raspberry [tex]=\dfrac{2}{5}x[/tex]

Remaining raspberry [tex]=x-\dfrac{2}{5}x[/tex]

                                   [tex]=\dfrac{3}{5}x[/tex]

Of the remaining ice sticks, [tex]\dfrac{1}{3}[/tex] are grape, and the rest are cherry.

Grape [tex]=\dfrac{1}{3}\times \dfrac{3}{5}x[/tex]

          [tex]=\dfrac{1}{5}x[/tex]

Cherry [tex]=\dfrac{3}{5}x-\dfrac{1}{5}x[/tex]

           [tex]=\dfrac{2}{5}x[/tex]

There are 48 blue raspberry and cherry flavored ice sticks altogether.

[tex]\dfrac{2}{5}x+\dfrac{2}{5}x=48[/tex]

[tex]\dfrac{4}{5}x=48[/tex]

[tex]x=48\times \dfrac{5}{4}[/tex]

[tex]x=60[/tex]

Therefore, the total number of ice sticks is 60.

The height of a stack of DVD cases is in a proportional relationship to the number of cases in the stack. A stack of 8 cases and its height are shown. Find the constant of proportionality. Then use the constant of proportionality to find the height of a stack of 13 cases.

Answers

Answer:

a. The equation is y = 19 x

b. The height of 13 DVD cases is 247 mm

Step-by-step explanation:

- A proportional relationship is about two quantities vary directly with

each other

- Ex: If y proportion to x, then y is varies directly with x

 That means y ∝ x ⇒ y = k x, where k is the constant of variation

- The height of a stack of DVD case is proportional to the number of

 case in the stack

- That means the height of DVD cases varies with the number of cases

- The height of 6 DVD case is 114 mm

a.

∵ The number of cases = x

∵ The height of the cases = y

∴ y ∝ x

∴ y = k x

- To find k lets use the first information above

∵ y = 114 mm when x = 6

- Substitute these values in the equation above to find k

∵ 114 = 6 k

- Divide both sides by 6

∴ k = 19

- Substitute the value of k in the equation above

∴ y = 19 x

* The equation is y = 19 x

b.

- We need to find the height of 13 DVD cases

∵ y = 19 x

∵ x = 13

- Substitute the value of x in the equation

∴ y = 19 × 13

∴ y = 247 mm

* The height of 13 DVD cases is 247 mm

The height will be 143 mm for a stack of 13 DVD cases.

What is the constant of proportionality?

The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.

The overall height of the 8 cases stacked on top of each other is 88 mm.

Because you need to know the height of each individual DVD case, divide the height (88 mm) by the number of DVD cases (8):

⇒ 88/ 8 = 13

⇒ 88 ÷ 8 = 13

Then it asks for the height of a stack of 13 cases, so multiply the 11 (the height of each DVD case) by 13:

11 × 13= 143

Therefore, 13 DVD cases stacked on top of each other have a height of 143 mm.

To learn more about the constant of proportionality here:

https://brainly.com/question/17302514

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The question seems to be incomplete the correct question would be:

The height of a stack of DVD cases is in proportional relationship to the number of cases in the stack. A stack of 8 cases and its height is shown. Find the constant of proportionality. Then use the constant of proportionality to find the height of a stack of 13 cases.

The height of the 8 cases stacked on top of each other is 88 mm.



A car travels 30.5 miles in of an hour. What is the average speed, în miles per hour
of the car?

Answers

Answer:

rounded to the nearest hundredth its 46.21

Step-by-step explanation:

trust im smart

A map is drawn using a scale of 1 centimeter to 25 kilometers.

What actual distance is represented by a map length of 3.2 centimeters?

Answers

Answer:

80 kilometers

The radius of the red circle is 7 units and the distance between the two circles is 3 units.
What is the diameter of the red circle?
A 8 units
B 12 units
C 14 units
D 20 units

Answers

Answer:

14

Step-by-step explanation:

The diameter is always the same as 2*the radius, so if the radius is 7, the diameter is 14.  Most of the information presented is unrelated.

Which is equivalent to

Answers

Answer:

-12

Step-by-step explanation:

-36 divided by 3 = -12

A recycling truck begins its weekly route at the recycling plant at point A, as pictured on the coordinate plane below. It travels from point A to point B, then points C, D, and E, respectively, before returning to the recycling plant at point A at the end of the day. The truck’s route is illustrated on the coordinate plane below. If each unit on the coordinate plane represents one mile, what is the total distance the truck travels on its route?

Answers

Answer:

78

Step-by-step explanation:

Answer:

i need a photo

Step-by-step explanation:

Four out of nine dogs weigh less than 20 pounds.
What is the decimal equivalent for the number of dogs weighing less than 20 pounds

Answers

Answer:

.44 repeating would be your decimal of dogs that weigh under 20 pounds.

Step-by-step explanation:

Answer:

.44

Step-by-step explanation:

Please Help Me :(((((( I Really Dont Know How TO Do This :(((((((
which explicit formula describes the sequence −9, −3, 3, 9, 15, …?
Group of answer choices

an = 9n + 6

an = 6n + 15

an = 6n - 15

an = 9n – 6

Answers

Answer:  an = 6n - 15   (Choice C)

======================================================

Explanation:

This sequence is arithmetic

The first term is a = -9

The common difference is d = 6 since we're adding 6 to each term to get the next one (eg: -3+6 = 3 or 3+6 = 9 or 9+6 = 15)

Plug those values into the arithmetic nth term formula below

an = a + d*(n-1)

an = -9 + 6*(n-1)

an = -9 + 6n-6

an = 6n - 15

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

As a check, let's plug in something like n = 1

an = 6n - 15

a1 = 6*1 - 15

a1 = 6 - 15

a1 = -9

We see that the 1st term is -9, which matches the sequence given

Now let's plug in n = 2

an = 6n - 15

a2 = 6*2 - 15

a2 = 12 - 15

a2 = -3

The 2nd term is -3. This also matches.

I'll let you check the other values of n to confirm the answer.

Solve.
5
2x+
1
2x=5
1
2+
7
2x
The value of x is

Answers

Answer:

-64

Step-by-step explanation:

The volume of a rectangular prism is 504 cubic centimeters. If the length of a rectangular prism is 9 centimeters and the width is 8 centimeters, what is the height?

Answers

Answer:

7 cm

Step-by-step explanation:

Given:

Volume of a rectangular prism ( V ) = 504 [tex]\sf{ cm^{3} }[/tex]

Length of a rectangular prism ( l ) = 9 cm

Width of a rectangular prism ( w ) = 8 cm

To find:

Height of a rectangular prism ( h ) = ?

Volume of a rectangle = lwh

[tex]\dashrightarrow[/tex] 504 = 9 * 8 * h

[tex]\dashrightarrow[/tex] 504 = 72 h

[tex]\dashrightarrow[/tex] 72h = 504

[tex]\dashrightarrow[/tex] h = [tex]\frac{504}{72}[/tex]

[tex]\dashrightarrow[/tex] h = 7 cm

The height of a rectangular prism is 7 cm.

Hope I helped!

Best regards!

~TheAnimeGirl

The height is 7 cm of the rectangular prism whose volume is 504 cm³.

What is a rectangular prism?

A rectangular prism is a solid three-dimensional structure with six faces and rectangular bases. A rectangular prism is also a cuboid. A cuboid and a rectangular prism have the same cross-section.

Given, The volume of a rectangular prism is 504 cubic centimeters. If the length of a rectangular prism is 9 centimeters and the width is 8 centimeters.

From the general formula of the rectangular prism

Volume  = length *width *height

Substituting the data given above

504 = 9 * 8 * height

Height = 7 cm

Therefore, the Height of the rectangular prism is 7 cm.

Learn more about rectangular prism here:

https://brainly.com/question/29753475

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a mercury thermometer records a temperature of 8 degrees fahrenheit at 10 a.m. if the temperature drops by 3 degrees fahrenheit every hour what will be the temperature by 2 p.m. of the same day ​

Answers

Answer:

-4 Degrees Fahrenheit

Step-by-step explanation:

Given

[tex]Initial\ Temperature = 8[/tex] ---- at 10am

[tex]Difference = -3[/tex]

Required

Determine the final temperature at 2pm

First, we need to determine the hour from 10am to 2pm (Both inclusive)

[tex]Interval = 2pm - 10am + 1hr[/tex]

[tex]Interval = 4hr + 1hr[/tex]

[tex]Interval = 5hr[/tex]

To solve further, we make use of the following Arithmetic Progression formula:

[tex]T_n = a + (n - 1)d[/tex]

Where

[tex]a = 8[/tex] --- Initial

[tex]d = -3[/tex] --- difference

[tex]n = 5[/tex] -- 5th term

[tex]T_n[/tex] --- Final temperature at 2pm

So: we have:

[tex]T_n = 8 + (5 - 1) * -3[/tex]

[tex]T_n = 8 + (4) * -3[/tex]

[tex]T_n = 8 + 4 * -3[/tex]

[tex]T_n = 8 -12[/tex]

[tex]T_n = -4[/tex]

Hence:

The temperature is -4 Degrees Fahrenheit

Six students are working to simplify the expression shown 4y+13x-5+6y-x

Answers

Answer:12x+10y-5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Chloe was given a box of assorted chocolates for her birthday. Each night, Chloe treated herself to some chocolates. There were originally 30 chocolates in the box and after 2 nights, there were 24 chocolates remaining in the box. Write an equation for C, in terms of t, representing the number of chocolates remaining in the box t days after Chloe's birthday.​

Answers

Answer:

C=-3t+30

Step-by-step explanation:

Given the perimeter of a rectangle and either the length or​ width, find the unknown measurement using the appropriate formula.
The perimeter is 70ft . and the width is 16ft .

Answers

Answer:

Step-by-step explanation:

Givens

P = 2*L + 2*W

P = 70

w = 16

Solution

70 = 2L + 2*16

70 = 2L + 32

70-32 = 2L

38 = 2L

38/2 = 2L/2

L = 19

HELPP ME PLEASEEE
ill give brainiest to whoever answers first

Answers

Answer:

the answer is d

Step-by-step explanation:

it would be 9.7 x 10^3

how many times 92 go in too 100​

Answers

Answer:

5

Step-by-step explanation:

Answer:

1 time

Step-by-step explanation:

what is 2 to the power of 8 minus 10 minus 15 divided by 3

Answers

Answer:

241

Step-by-step explanation:

241

Answer:

241

Step-by-step explanation:

2^8 - 10 -15 / 3

256 - 10 - 15 / 3

256 - 10 - 5

246 - 5

241

Hope this helps!

HELP URGENT!!!!!!!!!!!!!!!!!!!
NEEDED IN 10 MINUTES

Answers

Answer:

1.  124 degrees                       2.141 degrees

3.         b then a                4.b then b

Step-by-step explanation:

is 7.66 a rational number

Answers

Answer:

yes

Step-by-step explanation:

Yes it is a rational number

A parking garage charges an initial fee to enter, as well as an hourly rate to park. The equation, T = 6 + 2.50h, relates hours parked, h, and
the total charges in dollars, T.
What is the initial fee to enter the garage?
O A $2.50
OB. $3.50
OC. $6.00
OD. $8.50
S RESET
Anala Ramon, ID#******63
Growth: Algebra 1 CCSS 2010
Question # 36

Answers

Answer:

The answer is $6.00.

Step-by-step explanation:

They said that there was an initial fee along with an hourly fee. They also said that the hourly fee depended on the number of hours put in. Which would be h. So the initial fee stays the same and is just added to the hourly fee. As you can see the fee added on to the hourly fee is $6.oo.

The initial fee to enter the garage is option (C) $6.00.

What is the linear equation?

The linear equation is the algebraic form of equation whose variables has the exponent of one. It is the combination of two variables and a constant value present in them.

For the given situation,

The equations is, T = 6 + 2.50 h

where, h is the parking hours and

T is the total charges in dollars.

The initial fee to enter the garage means there will be no fee for parking,

⇒ [tex]h=0[/tex]

Then the equation becomes,

⇒ [tex]T=6[/tex]

Hence we can conclude that the initial fee to enter the garage is option (C) $6.00.

Learn more about linear equation here

https://brainly.com/question/19549073

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A high school class wants to make atleast $1500 by hosting a dance. The class knows that hey will make $500 in refreshments.
If the class sells tickets for $5 what’s the inequality to determine the number of tickets the class would need to sell to make at least $1500.
And determine the number of ticket the class would need to sell to make $1500

Answers

Answer:

1000=5x

Step-by-step explanation:

200 tickets

200*5 is 1000. 1000+500 is 1500

Solve for r.
19.72 = 4r

Answers

Answer: R = 4.93

Step-by-step explanation:

19.72/4 = 4.93

Hope the answer helps!!!
:)
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