Solve the simultaneous equations y=x-2 and y=3x+5

Answer:

[tex](f/g)x = \frac{x-1}{5x - 2}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x - 1[/tex]

[tex]g(x) = 5x - 2[/tex]

Required

(f/g)x

In functions:

[tex](f/g)x = \frac{f(x)}{g(x)}\ \ \ g(x)\ne 0[/tex]

So:

[tex](f/g)x = \frac{x - 1}{5x - 2}[/tex]

Answer:

0.207 = 20.7% probability that the wait time will be more than an additional 41 minutes

Step-by-step explanation:

To solve this question, we should understand the exponential distribution and conditional probability.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

The average waiting time for this distribution is 38 minutes.

This means that [tex]m = 38, \mu = \frac{1}{38} = 0.0263[/tex]

Given that it has already taken 37 minutes, what is the probability that the wait time will be more than an additional 41 minutes?

Event A: Taking more than 37 minutes.

Event B: More than 37 + 41 = 78 minutes.

Probability of taking more than 37 minutes:

[tex]P(A) = P(X \leq 37) = 1 - e^{-0.0263*37} = 0.6221[/tex]

More than 37 minutes and more than 78 minutes:

The intersection is more than 78 minutes, so:

[tex]P(A \cap B) = P(X > 78) = e^{-0.0263*78} = 0.1286[/tex]

The probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1286}{0.6221} = 0.207[/tex]

0.207 = 20.7% probability that the wait time will be more than an additional 41 minutes

Answer:

8

Step-by-step explanation:

i dont know set by step but m brother give me the answer he is in high school

24 divided by 12 equals 2,083

The division of 25 by 12  gives the quotient 2 and remainder is 1.

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.

Given:

We have to divide 25 by 12.

The division is as follow:

                            12| 25 | 2

                                  24

                              ______

                                   1

Thus the Quotient is 2 and remainder is 1.

Learn more about Division here:

brainly.com/question/21416852

#SPJ5

Answer:

try to do this formula

XYZ

= X times Y times Z

The principal was $600.

Explanation:

Find principal by using the formula , where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.

In this example I = $72, i = 4% and t = 3 years, so

Answer: 173,200

Step-by-step explanation:

This is very simple and I can help with this!!

Interest= Principal x Rate x Time

Interest = ($400)($72)(6)= 172,800+400= 173,200

Answer:

i•8xy^2yz

Step-by-step explanation:

Remove unnecessary parentheses

Answer:

i) 8x^2 yz=2×2×2×x×x×y×z

Answer

x=29

Step-by-step explanation:

Okay we know that the sum of all angles in a triangle is 180, so all we have to do is add them up first

(x+17)+(2x+5)=3x+22

(3x+22)+(3x-16)=6x+6

okay so we now know that 6x+6=180

subtract 6 on both sides 6x=174

then divide by 6 to get x=29

hope this helps!

Answer:

There are total 30 books in the 5 feet high stack of books.

Step-by-step explanation:

The complete question is

Given, Each note book is 2 inches thick, How many notebooks do you think it would take to make a stack that is 5 feet high

Solution

Thickness of each book [tex]= \frac{2}{12} = \frac{1}{6}[/tex]

The total height of the book stack is [tex]5[/tex] feet.

The number of books in the stack is equal to total height of the stack divided by the thickness of one book

Number of books in five feet high stack is

[tex]\frac{5}{\frac{1}{6} } \\5 * \frac{6}{1} \\30[/tex]

Hence, there are total 30 books in the 5 feet high stack of books.

Answer:

for every rise of 1 the run would be 25

Answer:

x < 3

Step-by-step explanation:

Answer:

x < 3

Step-by-step explanation:

treat the sign as if it was an equal sign

then you would solve for x

2x < 6

x < 3

however, there are some cases where the sign would switch directions, you can search up "inequalities algebra" to see more examples

Answer:

dy/dx = x(1+2lnx)

Step-by-step explanation:

Given y = x² In(x).

dy/dx = Udv/dx + Vdu/dx

Let U = x², V = lnx

du/dx = 2x

dv/dx = 1/x

Substitute into the formula;

dy/dx = x²(1/x) + lnx(2x)

dy/dx = x + 2xlnx

dy/dx = x(1+2lnx)

Answer:

94697330

Ur welcome

Step-by-step explanation:

Answer:

94,697,330

Explanation:

[tex]1235 x 76678 = 94697330[/tex]

1.A gain of five meters:5

Because gain＝+

Answer:

hereeeeeeeeeeee

Answer:

163.5625 or 163.56

Step-by-step explanation:

Answer:

163.5625

Step-by-step explanation:

Answer:

The 32th term is 127.

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same. The general equation for an arithmetic sequence is given by:

[tex]a_n = a_1 + (n-1)d[/tex]

In which d is the common difference.

It can also be written as:

[tex]a_n = a_m + (n - m)d[/tex]

75th term is equal to 342, and the 4th term, 24, is equal to - 13.

This means that [tex]a_4 = -13, a_75 = 342[/tex]. We use this to find d. So

[tex]a_{75} = a_4 + (75 - 4)d[/tex]

[tex]342 = -13 + 71d[/tex]

[tex]71d = 355[/tex]

[tex]d = \frac{355}{71}[/tex]

[tex]d = 5[/tex]

Find the value of the 32th term:

[tex]a_n = a_m + (n - m)d[/tex]

[tex]a_{32} = a_{4} + (32 - 4)d[/tex]

[tex]a_{32} = -13 + 28(5) = -13 + 140 = 127[/tex]

The 32th term is 127.

Answer:

It is by contract the same amount every month.

Step-by-step explanation:

Given:

The equation of parallel line is [tex]y=6[/tex].

The line contains the point (-1,1).

To find:

The equation of the line.

Solution:

The slope intercept form of a line is:

[tex]y=mx+b[/tex]

Where, m is the slope and b is the y-intercept.

The equation of parallel line is

[tex]y=6[/tex]

It can be written as

[tex]y=(0)x+6[/tex]

The slope of this line is 0.

The slopes of two parallel lines are always equal. So, the slope of the required line is also 0. It passes through the point (-1,1) so the equation of the line is:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-1=0(x-(-1))[/tex]

[tex]y-1=0[/tex]

[tex]y=1[/tex]

Therefore, the equation of the required line is 1.

Answer:

24+24=48

Step-by-step

24+24=48

Answer: first pic: true. second pic: is D. third pic: false. forth pic: C.

Step-by-step explanation:

Answer:

29 x 56 = 1,624

Step-by-step explanation:

Answer: 1/48

Step-by-step explanation: equation: 1/8x1/6

you have to multiply both numerators together (1x1)=1  then you multiply the denominators together (8x6)=48. you can't simplify it so your answer is 1/48

Answer:

D

Step-by-step explanation:

Answer:

Perimeter=100  area=688.19

Step-by-step explanation:

There's a big formula for area of pentagon and I pretty tired, so unless you want me to show my work I wont

Answer:

$11468.52

Step-by-step explanation:

Given data

Principal= $6,082

Rate= 5%

time= 13 years

The expression for compound interest is

A= P(1+r)^t

substitute

A=6082(1+0.05)^13

A=6082(1.05)^13

A=6082*1.885649

A=11468.52

Hence the Amount is $11468.52

Answer:

0

Step-by-step explanation:

Answer:

y =  ( x − 2 ) ^ 2 + 3

y =   x^2 − 4x + 7

Step-by-step explanation:

y = a ( x − h ) ^ 2 + k

where vertex is (h,k) = (4,-1)

h=4, k=-1

y = a ( x − 4 ) ^ 2 - 1

sub ( 2,3 )

3 = a (2 - 4)^2 - 1

a=1

y = 1 ( x − 2 ) ^ 2 + 3

y =  ( x^2 − 4x + 4 )  + 3

y =   x^2 − 4x + 7

Complete question :

Wright et al. [A-2] used the 1999-2000 National Health and Nutrition Examination Survey NHANES) to estimate dietary intake of 10 key nutrients. One of those nutrients was calcium in all adults 60 years or older a mean daily calcium intake of 721 mg with a standard deviation of 454. Usin these values for the mean and standard deviation for the U.S. population, find the probability that a randonm sample of size 50 will have a mean: (mg). They found a) Greater than 800 mg b) Less than 700 mg. c) Between 700 and 850 mg.

Answer:

0.10935

0.3718

0.9778

0.606

Step-by-step explanation:

μ = 721 ; σ = 454 ; n = 50

P(x > 800)

Zscore = (x - μ) / σ/sqrt(n)

P(x > 800) = (800 - 721) ÷ 454/sqrt(50)

P(x > 800) = 79 / 64.205295

P(x > 800) = 1.23

P(Z > 1.23) = 0.10935

2.)

Less than 700

P(x < 700) = (700 - 721) ÷ 454/sqrt(50)

P(x < 700) = - 21/ 64.205295

P(x < 700) = - 0.327

P(Z < - 0.327) = 0.3718

Between 700 and 850

P(x < 850) = (850 - 721) ÷ 454/sqrt(50)

P(x < 850) = 129/ 64.205295

P(x < 700) = 2.01

P(Z < 2.01) = 0.9778

P(x < 850) - P(x < 700) =

P(Z < 2.01) - P(Z < - 0.327)

0.9778 - 0.3718

= 0.606