How to find the surface area of a cuboid

Answer:

t = 13.56915448 hrs.

Step-by-step explanation:

500 = 300 [tex]e^{2k}[/tex]

5/3 = [tex]e^{2k}[/tex]

ln(5/3) = 2k ln(e)

k = ln(5/3)/2

k= 0.255412812

~~~~~~~~~~~~

9600 = 300 [tex]e^{0.255412812 t}[/tex]

32= [tex]e^{0.255412812 t}[/tex]

ln(32) = [tex]0.255412812 t[/tex] ln(e)

t = ln(32)/0.255412812

t = 13.56915448 hrs.

Answer:

9 hours

Step-by-step explanation:

Let

x = number of hours it would take Seth to work by himself

He would paint 1/x in 1 hour

x + 2 = number of hours it would take Ted to work by himself

He would paint 1/(x + 2) in 1 hour

Seth and Ted = 5 hours

They would paint 1/5 in 1 hour

The equation is this:

1/x + 1/(x + 2) = 1/5

(x + 2)+x/x(x+2) = 1/5

x+2+x / x(x+2) = 1/5

2x + 2 / x(x+2) = 1/5

2x + 2 = x(x + 2)1/5

2x + 2 = (x² + 2x)1/5

5(2x + 2) = x² + 2x

10x + 10 = x² + 2x

x² + 2x - 10x - 10 = 0

x² - 8x - 10 = 0

x = -b ± √b² - 4ac/2a

= -(-8) ± √(-8)² - 4(1)(-10) / 2(1)

= 8 ± √64 - (-40) / 2

= 8 ± √64 + 40) / 2

= 8 ± √104 / 2

= 8 ± 2√26 / 2

= 8/2 ± 2√26/2

= 4 ± √26

= 4 ± 5.0990195135927

= 4 + 5.0990195135927 or 4 - 5.0990195135927

= 9.0990195135927 or -1.Answer:

Step-by-step explanation:

Let

x = number of hours it would take Seth to work by himself

He would paint 1/x in 1 hour

x + 2 = number of hours it would take Ted to work by himself

He would paint 1/(x + 2) in 1 hour

Seth and Ted = 5 hours

They would paint 1/5 in 1 hour

The equation is this:

1/x + 1/(x + 2) = 1/5

(x + 2)+x / x(x+2) = 1/5

x+2+x / x(x+2) = 1/5

2x + 2 / x(x+2) = 1/5

Cross product

2x + 2 = x(x + 2)1/5

2x + 2 = (x² + 2x)1/5

Cross product

5(2x + 2) = x² + 2x

10x + 10 = x² + 2x

x² + 2x - 10x - 10 = 0

x² - 8x - 10 = 0

x = -b ± √b² - 4ac/2a

= -(-8) ± √(-8)² - 4(1)(-10) / 2(1)

= 8 ± √64 - (-40) / 2

= 8 ± √64 + 40) / 2

= 8 ± √104 / 2

= 8 ± 2√26 / 2

= 8/2 ± 2√26/2

= 4 ± √26

= 4 ± 5.0990195135927

= 4 + 5.0990195135927 or 4 - 5.0990195135927

= 9.0990195135927 or -1.0990195135927

Approximately,

x = 9 hours or -1 hour

It can't take Seth negative hours to work

Therefore,

x = number of hours it would take Seth to work by himself = 9 hours

Answer:

x = 960.4

Step-by-step explanation:

980 = 1000[tex]e^{kt}[/tex]

.98 = [tex]e^{10 k}[/tex]

ln(.98) = 10k ln(e)

k = ln(.98)/10

k=-0.00202

~~~~~~~~~~~~~~

x = 1000[tex]e^{20 *-.00202}[/tex]

x = 960.4

The amount of the material right after 20 years will be x = 960.4.

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."

Given that radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 1000 grams of the material 10 years ago. There are 980 grams right now.

The amount of the material will be calculated as,

980 = 1000

[tex]0.98 = e^{10k}[/tex]

ln(.98) = 10k ln(e)

k = ln(.98)/10

k=-0.00202

The value after 20 years will be,

[tex]x = 1000e^{20\times 0.00202}[/tex]

x = 960.4

Therefore, the amount of the material right after 20 years will be x = 960.4.

To know more about an exponential expression follow

https://brainly.com/question/2456547

#SPJ5

Answer:

(a) A = 20(1.6)^t

(b) 210 rabbits

Step-by-step explanation:

Initial number of rabbits = 20

rate of growth, R = 60 % annually

(A) The general equation is  

[tex]A = P \left ( 1+\frac{R}{100} \right )^t\\\\A = 20\left ( 1+\frac{60}{100} \right )^t\\\\A = 20 (1.6)^t[/tex]

(B) Let the time, t = 5 years

So, the population after 5 years is

[tex]A = 20 (1.6)^5\\\\A = 209.7 = 210 rabbits[/tex]

Answer:

it's H. 1/2 in.=1,000 ft

[tex]{hope 8 helps}}[/tex]

Answer:

x = 3 , y = 4

Step-by-step explanation:

5x + y = 19 --------- ( 1 )

=> y = 19 - 5x

7x - 2y = 13 ------------ ( 2 )

Substitute y in ( 2 ) :

                        7x - 2( 19 - 5x ) = 13

                        7x - 38 + 10x = 13

                        17x = 13 + 38

                        17x = 51

                           x = 3

Substitute x in ( 1 ) :

                           5x + y = 19

                           5( 3 ) + y = 19

                            15 + y = 19

                              y = 19 - 15

                               y = 4

Answer:

a) The mean number of radioactive atoms that decay per day is 81.485.

b) 0% probability that on a given day, 50 radioactive atoms decayed.

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\lambda[/tex] is the mean in the given interval.

a. Find the mean number of radioactive atoms that decayed in a day.

29,742 atoms decayed during 365 days, which means that:

[tex]\lambda = \frac{29742}{365} = 81.485[/tex]

The mean number of radioactive atoms that decay per day is 81.485.

b. Find the probability that on a given day, 50 radioactive atoms decayed.

This is P(X = 50). So

[tex]P(X = 50) = \frac{e^{-81.485}*(81.485)^{50}}{(50)!} = 0[/tex]

0% probability that on a given day, 50 radioactive atoms decayed.

Answer:

When most people have a smartphone, that is, the variable starts getting closer to its capacity, the demand will start to have a slight decrease, until it stabilizes, so yes, Nikola is correct.

Step-by-step explanation:

Exponential model:

The variable keeps growing consistently, at a fixed rate.

Logistic model:

The variable starts growing, but as it approaches a limit, for example, the carry capacity of an environment, the growth rate starts to decrease, until the variable stabilizes at a fixed value.

Growth of smartphones shipped from manufacturers to stores around the world.

When most people have a smartphone, that is, the variable starts getting closer to its capacity, the demand will start to have a slight decrease, until it stabilizes, so yes, Nikola is correct.

Answer:

24

Step-by-step explanation:

To find the range, you must subtract the lowest value from the highest value in the data set. If you organize the set from least to greatest, 72 is the lowest, and 96 is the highest.

So, 96 - 72 = 24, which is the range.

Step-by-step explanation:

Let's say the rectangle's width is equal to y. We know that the length is three times the width, so the length = 3 * y. We also know that the area for a rectangle is equal to length * width, so the area, z, is equal to

(3*y) * y = z

3 * y² = z

Now, let's increase the width of the rectangle by 1. We can replace y with y+1 (as y+1 is 1 greater than y), and 3 * y with 3 * (y+1) to get

3*(y+1) * (y+1) = new area

(3y+3)*(y+1) = new area

3y²+3y +3 y + 3 = new area

3y² + 6y + 3 = new area

The difference in area is equal to the new area subtracted by the old area, or

3y²+6y+3 - 3y² = 6y +3. The variable for x is not given, so if x = (2y+1), the answer would be the second choice. However, solely using the information given, it is impossible to determine a solution outside of saying that it is not option 4, as 6y + 3 ≠ 3

Answer:

Parameter

Step-by-step explanation:

Required

Parameter of Statistic

From the question, we understand that the teacher is to calculate the class average.

To calculate the class average, the teacher will use the mean function/formula, which is calculated as:

[tex]Mean = \frac{\sum x}{n}[/tex]

Generally, mean is an example of a parameter.

So, we can conclude that the teacher will use parameer

the e-function stuff can be confusing sometimes, but notices that g(x) / the blue line, is just somewhat lower, rest is the same.

how much lower? look at the y-intercepts

f(0)= "about 5"

g(0)= "about -3"

with this y-intercept only option c can work

Answer:

let inverse f(x) be m:

[tex]m = \frac{1}{2x + 1} \\ 2x + 1 = \frac{1}{m} \\ 2x = \frac{1 - m}{m} \\ x = \frac{1 - m}{2m} [/tex]

substitute x in place of m:

[tex]{ \bf{ {f}^{ - 1}(x) = \frac{1 - x}{2x } }}[/tex]

Answer:

2. 2200 m²

3. 703 m²

Step-by-step explanation:

2. Given,

Base (b) = 45m

Top (a) = 35m

Height (h) = 55m

Area = (a+b)*h/2

= (45+35)*55/2

= 85*55/2 = 2200 m²

3. Given,

Base (b) = 19m

Height (h) = 37m

Area = b*h

= 19*37

= 703 m²

(The * sign represents the multiplication sign)

Answered by GAUTHMATH

Answer:

2. area = 2200 m²

3. area = 703 m²

Step-by-step explanation:

2. Find the area of a trapezium shaped field with a base of 45m, top is 35m and with a height of 55m applying the

formula for trapezium = 0.5 * (b+a) * h

Given:

Base= 45 m

Top (a) = 35 m

Height = 55 m

area = 0.5 * (b+a) * h

area = 0.5 * (45 m + 35 m) * 55 m

area = 2200 m²

3. Find the area of a Parallelogram shaped field where the base measures 19m and with a h of 37m.

Applying the formula for parallelogram = b * h

Given:

Base= 19 m

Height= 37 m

area = b * h

area = 19 m * 37 m

area = 703 m²

9514 1404 393

Answer:

  y = 2

Step-by-step explanation:

Subtracting the second equation from the third gives ...

  (2z +3x) -(2z -2x) = (-6) -(-6)

  5x = 0

  x = 0

Using this in the third equation, we have ...

  2z +0 = -6

  z = -3

And substituting these values into the first equation, we have ...

  5y -3(0) -4(-3) = 22

  5y = 10 . . . . . subtract 12

  y = 2

__

The solution to the system is (x, y, z) = (0, 2, -3).

Answer:

6 and 2

Step-by-step explanation:

6+2= 8, so they can combine to equal 8. First box checked. Then, they can also be subtracted to get 4, half of 8. 8/2= 4 and 6-2=4. Second box checked.

Hope this helped :D

Step-by-step explanation:

Let's take the numbers as m and n and classify the info

m+n=8

m-n=4

So solving the sums Simultaneously you can get

2n=4

n=2

Substituting this value gives

2+m=8

m=6

Inorder to check if your answers are valid add them to the equations

6+2=8✅

6-2=4✅

Therefore the answers are valid

Answer:

angle C= 65 degree

Step-by-step explanation:

60+55+x= 180

115+x= 180

x= 180-115

x= 65

angle C= 65 degree

Please mark me as brainliest.

Answer:

[tex]\begin{array}{cc}{Class}& {Frequency} & 138 - 202 & 14 & 203 - 267 & 5 & 268 - 332 & 3 & 333 - 397 & 1 & 398 - 462 & 3 \ \end{array}[/tex]

The class with the greatest is 138- 202 and the class with the least relative frequency is 333 - 397

Step-by-step explanation:

Solving (a): The frequency distribution

Given that:

[tex]Lowest = 138[/tex] --- i.e. the lowest class value

[tex]Class = 5[/tex] --- Number of classes

From the given dataset is:

[tex]Highest = 459[/tex]

So, the range is:

[tex]Range = Highest - Lowest[/tex]

[tex]Range = 459 - 138[/tex]

[tex]Range = 321[/tex]

Divide by the number of class (5) to get the class width

[tex]Width = 321 \div 5[/tex]

[tex]Width = 64.2[/tex]

Approximate

[tex]Width = 64[/tex]

So, we have a class width of 64 in each class;

The frequency table is as follows:

[tex]\begin{array}{cc}{Class}& {Frequency} & 138 - 202 & 14 & 203 - 267 & 5 & 268 - 332 & 3 & 333 - 397 & 1 & 398 - 462 & 3 \ \end{array}[/tex]

Solving (b) The relative frequency histogram

First, we calculate the relative frequency by dividing the frequency of each class by the total frequency

So, we have:

[tex]\begin{array}{ccc}{Class}& {Frequency} & {Relative\ Frequency} & 138 - 202 & 14 & 0.53 & 203 - 267 & 5 & 0.19 & 268 - 332 & 3 & 0.12 & 333 - 397 & 1 & 0.04 & 398 - 462 & 3 & 0.12 \ \end{array}[/tex]

See attachment for histogram

The class with the greatest is 138- 202 and the class with the least relative frequency is 333 - 397

Answer:

answer is 1 2 3 and 4 respectively of given match the following

Answer: (8x8x9)/3=192

Answer:

altitude = 30 cm

lateral surface area = 301 cm² (approximately)

Step-by-step explanation:

let the altitude be x,

240=6*4*x/3

or, x=30 cm

Lateral surface area,

=l×√(w/2)²+h²]+w×√[(l/2)²+h²]

=6×√[(4/2)²+30²]+4×√[(6/2)²+30²]

≈300.99806

≈ 301 cm²

Answered by GAUTHMATH

Answer:

0.15866

Step-by-step explanation:

6-7/1

=-1

p(x>-1)=1-p(x<1)

=0.15866

Answer:

Step-by-step explanation:

i think if its -10 degrees i think the fahrenheit would be 50 degrees

Answer:

a) r ⋀~p

b)(r⋀p)⟶q

c) ~r ⟶ ~q

d) (~p ⋀r) ⟶q

Step-by-step explanation:

To solve this question we will make use of logic symbols in truth table.

We are told that;

p means "The user enters

a valid password,”

q means “Access is granted,”

r means “The user has paid the

subscription fee”

A) The user has paid the subscription fee, but does not enter a valid

password.”

Fist part of the statement is correct and so it will be "r". Second part of the statement is a negation and will be denoted by ~p. Since both statements are joined together in conjunction, we will use the conjuction symbol in between them which is "⋀" Thus, we have; r ⋀~p

B) Still using logic symbols, we have;

(r⋀p)⟶q

⟶ means q is true when r and p are true.

C) correct symbol is ~r ⟶ ~q

Since both statements are negation of the question. And also, if ~r is true then ~q is also true.

D) Similar to answer A to C above, applying similar conditions, we have (~p ⋀r) ⟶q

Answer:

A. x=2 y=7

Step-by-step explanation:

-12x -3 = 3y

6x + 3y = 33

sooo you add them up...

so its

-6x = -12

x=2

and then you plug in the x value into one of the equations

6x + 3y = 33

6(2) + 3y = 33

12 + 3y = 33

3y = 33 - 12

3y = 21

21/3=7

y=7

Answer:

[tex]P(\frac{A}{B'})[/tex]=0.111

Step-by-step explanation:

Given:

The probability of winning the first game is 10.1

The first game is won

The probability of winning the second game is 15

If the first is lost, the probability of winning the second game is 25

Solution:

[tex]P(B)=P(A)P(\frac{B}{A})+P(A')P(\frac{B}{A'})\\ =0.1(0.15)+(0.3)*0.25)\\P(B)=0.24 ------(1)\\P(\frac{A}{B})=\frac{P(\frac{B}{A})P(A) }{P(B)}\\ =\frac{0.15(0.1)}{0.24}\\ =0.0625 ------(2)\\P(B')=1-P(B)=0.76 ------(3)\\P(A)=P(B)P(\frac{A}{B})+P(B')P(\frac{A}{B'})\\0.1=0.24(0.0625)+0.76(p(\frac{A}{B'} ))\\P(\frac{A}{B'})=0.111[/tex]

Answer:

[tex]P(W_1/W_2')=0.1110[/tex]

Step-by-step explanation:

Probability of winning the first game be considering the given factors be, [tex]W_1=0.1[/tex]

Probability of winning the second game be considering the given factors be, [tex]W_2[/tex]= probability of winning the second game when the first game is won + probability of winning the second game when the first game is lost:

[tex]P(W_2)=P(W_1).P(W_2/W_1)+P(W_1').P(W_2/W_1')[/tex]

[tex]P(W_2)=0.1\times 0.15+0.9\times 0.25[/tex]

[tex]P(W_2)=0.24[/tex]

Hence the probability of losing the second game:

[tex]P(W_2')=1-P(W_2)[/tex]

[tex]P(W_2')=0.76[/tex]

Probability of winning the first game when the second game is won:

[tex]P(W_1/W_2)=\frac{P(W_2/W_1).P(W_1)}{P(W_2)}[/tex]

[tex]P(W_1/W_2)=\frac{0.15\times 0.1}{0.24}[/tex]

[tex]P(W_1/W_2)=0.0625[/tex]

Probability of winning the first game be considering the given factors, [tex]W_1[/tex]= probability of winning the first game when the second game is won + probability of winning the first game when the second game is lost:

[tex]P(W_1)=P(W_2).P(W_1/W_2)+P(W_2').P(W_1/W_2')[/tex]

[tex]0.1=0.24\times0.0625+0.76\times P(W_1/W_2')[/tex]

[tex]P(W_1/W_2')=0.1110[/tex]

Solution :

Given :

[tex]f(x) = \left\{\begin{matrix}\frac{1}{450}(x^2-x) & \text{if } 6 < x < 12 \\ 0 & \text{otherwise}\end{matrix}\right.[/tex]

1. Cumulative distribution function

[tex]$P(X \leq x) = \int_{- \infty}^x f(x) \ dx$[/tex]

              [tex]$=\int_{- \infty}^6 f(x) dx + \int_{6}^x f(x) dx $[/tex]

             [tex]$=0+\int_6^x \frac{1}{450}(x^2-x) \ dx$[/tex]

             [tex]$=\frac{1}{450} \int_6^x (x^2-x) \ dx$[/tex]

             [tex]$=\frac{1}{450}\left[\frac{x^3}{3}-\frac{x^2}{2}\right]_6^x$[/tex]

             [tex]$=\frac{1}{450}\left[ \left( \frac{x^3}{3} - \frac{x^2}{2}\left) - \left( \frac{6^3}{3} - \frac{6^2}{2} \right) \right] $[/tex]

            [tex]$=\frac{1}{450}\left[\frac{x^3}{3} - \frac{x^2}{2} - 54 \right]$[/tex]

2.  Mean [tex]$E(x) = \int_{- \infty}^{\infty} \ x \ f(x) \ dx$[/tex]

                       [tex]$=\int_{6}^{12}x . \left( \frac{1}{450} \ (x^2-x)\right)\ dx$[/tex]

                     [tex]$=\frac{1}{450} \int_6^{12} \ (x^3 - x^2) \ dx$[/tex]

                     [tex]$=\frac{1}{450} \left[\frac{x^4}{4} - \frac{x^3}{3} \right]_6^{12} \ dx$[/tex]

                     [tex]$=\frac{1}{450} \left[ \left(\frac{(12)^4}{4} - \frac{(12)^3}{3} \right) - \left(\frac{(6)^4}{4} - \frac{(6)^3}{3} \right) $[/tex]

                     [tex]$=\frac{1}{450} [4608 - 252]$[/tex]

                    = 17.2857

Answer:

18

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

b = 3

y = -3

5b - y

Step 2: Evaluate

Answer:

A. (1, -5), (2, -1), (-1, 7)

Step-by-step explanation:

Reflecting a function over the x-axis:

When a function is reflected over the x-axis, the x-value stays the same, while y changes the signal, so the transformation rule is:

[tex](x,y) \rightarrow (x,-y)[/tex]

To find the range:

We apply the transformation to the points in the domain. Thus:

[tex](1,5) \rightarrow (1,-5)[/tex]

[tex](2,1) \rightarrow (2,-1)[/tex]

[tex](-1,-7) \rightarrow (-1,-(-7)) = (-1, 7)[/tex]

Thus the correct answer is given by option a.

Answer:

It is letter A and please give me brainliest

Step-by-step explanation: