What is the difference of the polynomials? (–2x3y2 + 4x2y3 – 3xy4) – (6x4y – 5x2y3 – y5)

Answer:

Step-by-step explanation:

Let X denote the life span of a car battery and it follows and exponential distribution with average of 6 years.

Thus , the parameter of the exponential distribution is calculated as,

μ = 6

[tex]\frac{1}{\lambda} =6[/tex]

[tex]\lambda = \frac{1}{6}[/tex]

a) The required probability is

[tex]P(X>4)=1-P(X\leq 4)\\\\=1-F(4)\\\\1-(1-e^{- \lambda x})\\\\=e^{-\frac{4}{6}[/tex]

= 0.513

Hence, the probability that a randomly selected car battery will last more than four years is 0.513

b) The variance of the battery span is calculated as

[tex]\sigma ^2=\frac{1}{(\frac{1}{\lambda})^2 }\\\\\sigma ^2=\frac{1}{(\frac{1}{6})^2 } \\\\=6^2=36[/tex]

The 95% percentile [tex]x_{a=0.05}[/tex] (α = 5%) of the battery span is calculated

[tex]x_{0.05}=-\frac{log(\alpha) }{\lambda} \\\\=-\frac{log(0.05)}{1/6} \\\\=-6log(0.05)\\\\=17.97 \ years[/tex]

c)  

Let [tex]X_r[/tex] denote the remaining life time of a car battery

i)the probability the battery will last an additional five years is calculated below

[tex]P(X_r>5)=e^{-5\lambda}\\\\=e^{-\frac{5}{6} }\\\\=0.4346[/tex]

ii) The average time that the battery is expected to last is calculated

[tex]E(X_r)=\frac{1}{\lambda} \\\\=6[/tex]

Answer:

your number should be 8

Step-by-step explanation:

5x+(-3)=37

5x-3=37

+3       +3

5x=40

÷5  ÷5

x=8

hope this helps

Answer:

The answer is 8.

5x-3=37

5x=37+3

5x=40

x=40/5

x=8

HOPE IT HELPS!!

Answer:

D: 17 times

Step-by-step explanation:

Volume of tank = 36×13×24

= 11,232 cubic inches

Now

Bucket = 693 cubic inches

Number of time Valeria will use the bucket = 11232/693

= 16.2

≈ 17

Answer:

D

Step-by-step explanation:

(eˣ − e⁻ˣ) / (eˣ + e⁻ˣ) = t

Multiply by eˣ/eˣ.

(e²ˣ − 1) / (e²ˣ + 1) = t

Solve for e²ˣ.

e²ˣ − 1 = (e²ˣ + 1) t

e²ˣ − 1 = e²ˣ t + t

e²ˣ = 1 + e²ˣ t + t

e²ˣ − e²ˣ t = 1 + t

e²ˣ (1 − t) = 1 + t

e²ˣ = (1 + t) / (1 − t)

Solve for x.

2x = ln[(1 + t) / (1 − t)]

x = ½ ln[(1 + t) / (1 − t)]

Use log rule.

x = ln(√[(1 + t) / (1 − t)])

Answer:

P(2c - h, 2n - s )

Step-by-step explanation:

If there are two points (x1,y1) and (x2,y2) on the coordinate plane

then midpoint is given by (x1+x2)/2 , (y1+y2)/2

_________________________________________________

in the problem midpoint is m(c,n)

one point is Q(h,s)

let other point be P(x,y)

By using midpoint formula given above

for point P(x,y) and Q(h,s)

midpoint = (x+h)/2, (y+s)/2

also midpoint is m(c,n)

comparing m(c,n) with (x+h)/2, (y+s)/2

c = x+h/2

=> 2c = x+h

=> 2c - h = x

n = (y+s)/2

=> 2n = y+s

=> 2n - s = y

Thus, second endpoint is P(x,y) = P(2c - h, 2n - s )

Answer:

x=-21

Step-by-step explanation:

x+12=-9

minus twelve on both sides

-9-12 equals -21

x=-21

Answer:

96

Step-by-step explanation:

Rectangle area:

(8)(10)=80

Triangle area:

(1/2)(4)(8)=16

Total area:

16+80=96

Answer:

[tex]96 {ft}^{2} [/tex]

Step-by-step explanation:

[tex]area = \frac{1}{2} (a + b)h \\ = \frac{1}{2} \times (10 + 14) \times 8 \\ = \frac{1}{2} \times 24 \times 8 \\ = 96 {ft}^{2} [/tex]

Answer:

[tex]\frac{a^3 b^2}{\frac{1}{a} \frac{1}{b^3}}[/tex]

And simplifying we got:

[tex] a^3 b^2 a b^3[/tex]

[tex] a^3 a b^2 b^3 = a^{3+1} b^{2+3} = a^4 b^5[/tex]

Step-by-step explanation:

We want to simplify the following expression:

[tex] \frac{a^3 b^2}{a^{-1} b^{-3}}[/tex]

And we can rewrite this expression using this property for any number a:

[tex] a^{-1}= \frac{1}{a}[/tex]

And using this property we have:

[tex]\frac{a^3 b^2}{\frac{1}{a} \frac{1}{b^3}}[/tex]

And simplifying we got:

[tex] a^3 b^2 a b^3[/tex]

[tex] a^3 a b^2 b^3 = a^{3+1} b^{2+3} = a^4 b^5[/tex]

Answer:

  [tex]f^{-1}(x)=4x+48[/tex]

Step-by-step explanation:

To find the inverse, solve for y:

  x = f(y)

  x = (1/4)y -12

  x +12 = (1/4)y . . . . add 12

  4(x +12) = y . . . . . multiply by 4

  y = 4x +48 . . . . . . simplify

The inverse function is ...

  [tex]\boxed{f^{-1}(x)=4x+48}[/tex]

Answer:

C. can have more than one factor, each with several treatment groups.

Step-by-step explanation:

A completely randomized design can be used in experimental research of a primary factor or multiple factors. The factors could have several treatment groups which are assigned in a random manner. For example, a researcher, could want to determine the effect of a drug against a disease on a class of people. To do this, he designs a treatment group with different concentrations of the drug and a placebo group. He then gets an equal number of subjects, randomly assigning them to each of the groups. The effect of both treatments are compared to know if the drug is indeed effective against the disease the researcher is experimenting on.

Completely randomized design has found application in agricultural and environmental researches.

Answer:

FALSE

Step-by-step explanation:

Answer:

-3/5

Step-by-step explanation:

3x+5y=0

Subtract 3x from each side

3x+5y-3x=0-3x

5y = -3x

Divide each side by 5

5y/5 = -3x/5

y = -3/5 x

A direct variation is y = kx

y = -3/5 x

The constant of variation is -3/5

Answer:

  24

Step-by-step explanation:

Let t represent the volume of the tank in gallons. Then we have ...

  (1/8)t + 15 = (3/4)t . . . . . . . . . . . adding 15 gallons fills the tank to 3/4

  15 = (6/8 -1/8)t = (5/8)t . . . . . . . subtract 1/8t

  15(8/5) = (8/5)(5/8)t . . . . . . . . . multiply by 8/5 (the inverse of 5/8)

  24 = t

The tank holds 24 gallons.

Answer:

8.20 am

Step-by-step explanation:

First, we have that Bus A will be back after 20 minutes, then after 40, then 60, 80, 100, 120, 140, 160 minutes, etc.

Then, we have that Bus B will be back after 35 minutes, then 70, then 105, then 140, 175....

From the list above we see that the first time they are both back at the station is after 140 minutes. (it's the MCM).

If we express this in terms of minutes, since one hour has 60 minutes, 2 hours have 120 minutes and thus, 140 minutes is 2 hours and 20 minutes.

Therefore, they will be both back at the station 2 hours and 20 minutes after they first departed at 6 am, so they will be back at the depot at 8.20 am

Answer:

I think it is -2

Step-by-step explanation:

I think but I do not know

Answer:

a. $840

b. $1,260

Step-by-step explanation:

a. 2/5 x 2100 = 840

b. 2100 - 840 = 1,260

Answer:

[tex]P(X<3) =[/tex] [tex]0.9619[/tex]

Step-by-step explanation:

From the given information;

the probability of getting returned p = 0.1

If eight rings are sold today, what is the probability that fewer than three will be returned;

According to binomial distribution

Binomial distribution is the probability of success or failure of an outcome of an experiment under observation which is usually repeated several trials. Binomial experiments are random experiment with fixed number of repeated experiment. If we cannot predict before head, the outcome of an experiment , the experiment is called a random experiment.

So , using binomial distribution to determine the probability that fewer than three will be returned;

i.e

[tex]P(X<3) =[/tex] [tex]\sum_{x=0}^{2}\binom{8}{x}(0.1)^{x}(1-0.1)^{8-x}[/tex]

[tex]P(X<3) =[/tex] [tex]0.9619[/tex]

Answer: 880 oz

Step-by-step explanation:

We want to write it in the same units, let's use oz as our common unit.

1 gal = 128 oz

then 5 gal = 5*128 oz = 640 oz

1 qt = 32 oz

then 6 qt = 6*32 oz = 192 oz

Then we have:

640 oz + 192 oz + 48 oz = 880 oz

The value of standard notation is,

⇒ 880 oz

We have to given that,

Measures are,

⇒ 5 gal 6qt 48 oz

We have to change it into standard notation as,

We want to write it in the same units, let's use oz as our common unit.

1 gal = 128 oz

then 5 gal = 5 x 128 oz = 640 oz

1 qt = 32 oz

then 6 qt = 6 x 32 oz = 192 oz

Then we have:

⇒ 5 gal 6qt 48 oz

⇒ 640 oz + 192 oz + 48 oz

⇒ 880 oz

Learn more about the measurement unit visit:

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Answer:

B.

Step-by-step explanation:

In the attached file

Answer:

Yes

Step-by-step explanation:

the function that gives the alcohol level is:

[tex]A ( x ) = - 0.015 x^3 + 1.05 x[/tex]

where x is the number of hours.

we need to know if after 4 hours an average person is legally drunk, thus:

[tex]x=4[/tex]

and we substitute this in the function:

[tex]A ( 4 ) = - 0.015 (4)^ 3 + 1.05(4)[/tex]

solving these operations we obtain:

[tex]A(4)=-0.015(64)+4.2\\A(4)=-0.96+4.2[/tex]

[tex]A(4)=3.24[/tex]

the alcohol level after 4 hours is 3.24.

Since a person is considered to be legally drunk if the level exceeds 1.5, and we obtained 3.24 which is greater than 1.5, a person who has been drinking for 4 hours under the conditions indicated by the problem would be considered legally drunk.

Answer:

x = -6

Step-by-step explanation:

-2/3x + 9 = 4/3x - 3

First we need to simplify to where we have x on one side and a constant (number not connected to a variable) on the other side.

Subtract 4/3x from both sides:

-2/3x + 9 - 4/3x = -3

-6/3x + 9 = -3

Now subtract 9 from both sides:

-6/3x + 9 - 9 = -3 - 9

-6/3x = -12

Now turn -6/3 into a whole number to make things more simple:

-6/3 = -2

-2x = -12

Now divide both sides by -2 to get x by itself

-2x/-2 = -12/-2

x = -6

Answer:

19.2

Step-by-step explanation:

It's right on Acellus.

The required value of x nearest to tenth is 19.17

The longest side of the right angled triangle is called hypotenuse

By the Pythagoras theorem in the right angled triangle

h^2 = b^2 + p^2

where h = hypotenuse, b = base, p = perpendicular

Here we have given perpendicular p = 9

and an angle = 28°

Using sin for the given angle we have

sin 28° = [tex]\frac{perpendicular}{hypotenuse}[/tex]

0.46947 = [tex]\frac{9}{x}[/tex]

x = [tex]\frac{9}{0.46947}[/tex]

x =  19.17

Hence the required length of the side hypotenuse = x = 19.17

This is the conclusion to the answer.

Learn more about hypotenuse here-

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As the x values go up, the y values go down which means the line is higher on the left side than it is on the right side.

The 4th graph would be the correct one

The slope is zero. Slope formula is Y=mx+b and since B is 1.5 and it is a straight line, Y=mx+1.5. What plus 1.5 is 1.5? 0. Hope this helps.

Answer: The answer is 19

Step-by-step explanation:

Question Correction

A group of neighbors are constructing a community garden that is 80 meters wide and 40 meters long. The top two vertices are plotted below at (10, 70) and (90, 70). What are the coordinates for the bottom two vertices of the garden?

Answer:

(10,30) and (90,30)

Step-by-step explanation:

The community garden is 80 m wide and 40 m long.

The top two vertex are plotted at: (10, 70) and (90, 70).

Horizontal Distance =90-10=80

This serves as the Width of the garden.

Since the length is 40m, the bottom two vertex can be derived by the transformation: (x,y-40).

(x,y-40)-->(10, 70)=(10,30); and

(x,y-40)-->(90, 70)=(90,30)

The coordinates for the two bottom vertices are (10,30) and (90,30).

Answer:

Option (2).

Step-by-step explanation:

From the figure attached,

EFGH is a quadrilateral and FH is line which divides the quadrilateral into two right triangles, ΔFEH and ΔHGF.

In ΔFEH and ΔHGF,

Sides EH ≅ FG [Given]

FH ≅ FH [reflexive property]

ΔFEH ≅ ΔHGF [HL (Hypotenuse - length) postulate of congruence]

Option (2) will be the answer.

Answer:

the Swiss Chalet had higher occupancy than its competitive set in 2019

Step-by-step explanation:

Answer:

The percentage of the employee will experience a lost-time accident in both years is 0.0%

Step-by-step explanation:

Let A denote events that employees suffered lost-time accidents during the last year

Let B denote events that employees suffered lost-time accidents during the current year

P(A) = 5% = 0.05

P(B) = 4% = 0.04

P(B | A) = 15% = 0.15

(a) P (A ∩ B) = P(B | A) × P(A)

= 0.15 × 0.05

= 0.0075

= 0.0 (1 decimal place)

The probability that an employee will experience a lost- time accident in both years is 0.0