Find the distance between the two points rounding to the nearest tenth (if
necessary).
(8, -3) and (4, 6)

Answer:

5

Step-by-step explanation:

The given fraction (x^2-25)/(x^2-x-20) expressed in simplest form is (x+5)/(x+4). (Option C)

A fraction is in simplest form if the numerator and denominator have no common factors other than 1. In order to solve the given fraction, the numerator and denominator must be factorized, and the common factor will be canceled out.

Factoring x^2 – 25 using the difference of squares formula that states that a^2 – b^2 = (a + b)(a - b)

x^2 – 25 = x^2 – 5^2 = (x + 5)(x – 5)

Factoring x^2 – x – 20,

x^2 – x – 20 = x^2 + 4x – 5x – 20 = x(x + 4) -5(x + 4) = (x + 4)(x – 5)

Hence, factor (x – 5) is there in both numerator and denominator, it is canceled out. Hence the fraction in the simplest form is:

(x + 5)(x – 5)/ (x + 4)(x – 5) = (x + 5)/(x + 4)

Note: The question is incomplete.  The complete question probably is:  What fraction represents(x^2-25)/(x^2-x-20) expressed in simplest form. A) 5/4 B) (x-5)/(x-4) C) (x+5)/(x+4) D)25/(x+20)

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280 dogs in all of the city's animal shelters are puppies. The solution has been obtained by using ratios.

What is ratio?

The ratio between two amounts of the same unit can be used to determine how much of one quantity is included in the other.

We are given that different animal shelters in a city shows that 10 of the 70 dogs are puppies and the city's animal shelters collectively house 1,960 dogs each year.

So, from this we get the ratio as

⇒ \(\frac{10}{70}\) = \(\frac{x}{1960}\)

Now, by cross multiplying, we get

⇒ 19,600 = 70x

⇒ x = 280

Hence, 280 dogs in all of the city's animal shelters are puppies.

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a)The probability of female and no opinion is: 0.375

b) The probability of student approves of the proposed change is: 0.5

c) The probability of student is male, given the student does not approve of the proposed change is: 0.398

d)  The probability of student is male and approves of the proposed change is : 0.2

The formula for probability states that the possibility of an event happening, or P(E), equals the ratio of the number of favorable outcomes to the number of total outcomes. Mathematically, it looks like this:

P(E) = favorable outcomes/total outcomes.

They are  70 mathematics majors were asked whether they approved of the proposed change.

The table are as follows:

                Approved(A)    No opinion(No)      Did not approve(DA)

Female      21                   6                           12

Male          14                    10                           7

a) To find the probability that the student is female, given no opinion:

So, The probability of Female and no opinion :

We have to apply the probability formula:

P(F | No) = P(F∩No)/ P(No) = \(\frac{6}{70}/\frac{16}{70}\) = \(\frac{6}{16}\) = 0.375

b) The probability of student approves of the proposed change:

P(A) = \(\frac{21+14}{70}\)= 35/70 = 1/2 = 0.5

c) The probability of student is male, given the student does not approve of the proposed change:

P(M|DA) = P(M∩DA)/P(DA) = \(\frac{\frac{7}{70} }{\frac{19}{70} }\) = 7/19 = 0.398

d) The probability of student is male and approves of the proposed change.

P(M∩A) = 14/70 = 0.2

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A linear function is one that begins with f{x} followed by the rest of the equation that respects the slope intercept form of an equation

The general solution of the given differential equation expressed explicitly as a function of the independent variable, is:

w(x) = (1/16) * \(((3x + 2)^2 + 4Cx - 4x^2)^2\)

To obtain the solution, we can rewrite the given differential equation by separating the variables and integrating. First, we can divide both sides by √w and rearrange the terms:

√w dw = (3x + 2)/\(x^2\) dx

Then, with regard to the relevant variables, we integrate both sides. The integral of √w with respect to w can be computed using the power rule, while the integral of (3x + 2)/\(x^{2}\) with respect to x can be found using partial fractions. After integrating and simplifying, we obtain the general solution as:

w(x) = (1/16) * \(((3x + 2)^2 + 4Cx - 4x^2)^2\)

Here, C is the arbitrary constant that can take any real value.

This general solution represents a family of functions that satisfy the given differential equation. By choosing different values for the constant C, we can obtain specific solutions corresponding to different initial conditions or constraints imposed on the problem.

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The complete question is:

Find the general solution of the following equation. Express the solution explicitly as a function of the independent variable.

\(x^2\)(dw/dx) = √(w)(3x+2)

Anwser: 41°

Okay so every triangle is 180° degrees in total.

We need to find the angle of x in the triangle BDC.

We know that the angle of x is 180 - ( x + 15)

We also have another triangle named BAD

Which angles are 90 + 56 + x

the angle of D in the triangle BDC is 180 -58 = 124

So 124 + 15 = 139

180 - 139 = 41

Answer:

2, 3, 6

Step-by-step explanation:

Answer:

C, E, F,

Step-by-step explanation:

They all equal 4x^2+16x+16

we have two points (x, y): (0,1) and (1,3)

We can use the point-slope form

(y - y1) = m (x -x1)

The slope = m= (y2-y1)/ (x2-x1)

or

The slope-intercept form.

y = mx + b

m= (y2-y1)/ (x2-x1)

y-intercept is (0, b)

__________________________

Using The slope-intercept form,

y = mx + b

b = 1

point (0,1)

Replacing

y = mx + 1

finding the slope

point 1 (0, 1), x1= 0; y1= 1

point 2 (1, 3); x2= 1; y2= 3

m= (y2-y1)/ (x2-x1)

Replacing

m= ( 3- 2)/ (1 - 0) = 2/1 = 2

___________________

Replacing the slope

y = 2x + 1

__________________

Answer

y = 2x + 1

Answer:

your answer would be 339

Step-by-step explanation:

i used a circle calculator

you would multiply 2.25 and 24

which gives you 54

and you wanna find the circumference i dont knowhow to do that but it would be 339

Answer:

5n

Step-by-step explanation:

:)

Answer:5n

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

The negative would just cancel the positives out. Therefore, since they are both adding together the same things the negatives would make the outcome 0.

Answer:

\( \sf \large( \frac{2}{5} ) {}^{14} \)

Step-by-step explanation:

=((2/5)^4(2/5)^3)^2

=((2/5^4+3))^2

=((2/5^7))^2)

=(2/5)^14

Answer:

 (c + 2d) • (9d - 2c)

Step-by-step:

Step  1  :

Equation at the end of step  1  :

 ((c + 2d)2) -  (c + 2d) • (3c - 7d)

Step  2  :

Pulling out like terms :

2.1      Pull out     c+2d

After pulling out, we are left with :

     (c+2d) • ( (c+2d) +( (-1)  *  (3c-7d) ))

Answer:

(c+2d)(9d - 2c) = \(5dc - 2c^{2} + 18d^{2}\)

Step-by-step explanation:

\((c+2d)^{2} - (c+2d)(3c-7d)\)

\((c+2d)(c+2d) - (c+2d)(3c-7d)\)

Both sides have (c+2d) so pull out (c+2d)

(c+2d) [(c+2d) - (3c-7d)]

(c+2d) [c+2d - 3c +7d]

(c+2d) [-2c + 9d] = (c+2d)(9d - 2c)

(c+2d)(9d - 2c) = \(9dc - 2c^{2} + 18d^{2} -4dc\) = \(5dc - 2c^{2} + 18d^{2}\)

Hope this helps ^-^

Answer:

8000 in^3

Step-by-step explanation:

V = s^3

  = 20^3 = 8000 in^3

The answer is that the expected waiting time until the next service completion is 7.44 minutes.



To calculate the expected waiting time, we need to first find the expected remaining service time for each server. Since the service times are exponentially distributed, the expected remaining service time for each server is equal to the reciprocal of its service rate. The service rate is the inverse of the expected service time.

Thus, the expected remaining service time for the first server is 1/λ1 = 1/0.2 = 5 minutes, where λ1 is the arrival rate for the first server. Similarly, the expected remaining service time for the second and third servers are 1/λ2 = 1/0.0333 = 30 minutes and 1/λ3 = 1/0.1 = 10 minutes, respectively.

Since each server has been busy for 5 minutes with a current customer, the expected remaining service time for each server is reduced by 5 minutes. Thus, the expected remaining service times are 0 minutes, 25 minutes, and 5 minutes, respectively.

The expected waiting time until the next service completion is equal to the sum of the expected remaining service times weighted by the probability that a customer arrives at each server while it is busy. The probability of a customer arriving at each server while it is busy can be calculated using the Erlang C formula.

Using the Erlang C formula, we can calculate that the probability of a customer arriving at the first server while it is busy is 0.016, the probability of a customer arriving at the second server while it is busy is 0.524, and the probability of a customer arriving at the third server while it is busy is 0.091.

Thus, the expected waiting time until the next service completion is (0 minutes)*(0.016) + (25 minutes)*(0.524) + (5 minutes)*(0.091) = 7.44 minutes.

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Answer:

Step-by-step explanation:

0.7 cubic kilometers

V= lwh

V=(.5)(2)(.7)

The point that the graphs of f and g have in common are (1,0)

The given functions are:

f(x) = log₂x

and

g(x) = log₁₀x

We know that logarithm of 1 is always zero.

This means that irrespective of the base, the y-values of both functions will be equal to 0 at x=1

Therefore the point the graphs of f and g have in common is (1,0).

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Answer:

−18f+6g

Step-by-step explanation:

Answer:

-24

Step-by-step explanation:

-6 · f(3) – 6 • g(-1) =

= −6⋅f(3)−6⋅g(−1)=−6(−2)−6(6)

= 12 - 36

= -24

Have a good day :p

There are approximately 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

Anna has 2 dozen Rollo bars, which is equivalent to 2 x 12 = 24 Rollo bars.

She also has 1 dozen apples, which is equivalent to 1 x 12 = 12 apples.

So, Anna has a total of 24 + 12 = 36 treats to hand out.

Now, she needs to hand out 1 treat to each of the 36 children who come to her door.

This can be thought of as selecting 1 treat from the total of 36 treats for each child, without replacement, as each child can only receive 1 treat.

The number of ways to do this is given by the concept of permutations, denoted by "nPr", which is calculated as;

nPr = n! / (n - r)!

where n is the total number of items (treats) to choose from, and r is the number of items (treats) to choose.

In this case, n = 36 (total number of treats) and r = 36 (number of children).

Plugging in the values, we get;

36P36 = 36! / (36 - 36)! = 36! / 0! = 36!

Since 0! (0 factorial) is equal to 1, we can simplify further:

36! / 1 = 36!

36! ≈ 3.72 x 10⁴¹

So, there are 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

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Answer:

6ft

Step-by-step explanation:

we went over this in class

If 8 men and 8 women collaborate, the task can be finished in 36 days for the former and 45 days for the latter.

Using the following formula, we can determine the total quantity of work that needs to be done.

Total work equals (people) ×(time spent).

The first scenario is as follows:

Total work is equal to (288 man-days)= (12 men x 24 days)

Total work is calculated as (15 women) x (24 days) = (360 woman-days).

Using the same approach, we can now determine how many days it would take eight people—either eight men or eight women—to do the same amount of work:

Eight men:

Total labor: (8 men)× (time required)

288 man-days = (8 men) × (time taken)

time taken = 36 days

Eight women:

total work = (8 women) × (time taken)

360 woman-days = (8 women) × (time taken)

time taken = 45 days

Thus, if 8 males collaborate, they can finish the job in 36 days, and if 8 women collaborate, they can finish the job in 45 days.

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Answer:

23

Step-by-step explanation:

12+24=36

36-13=23

He gave 23 away.

Answer:

Is that a prolem and only real ones get the refance lol

Step-by-step explanation:

To solve the integral of 1/sqrt(x^2 - a^2) dx, we can use the substitution method. Let u = x^2 - a^2, then du/dx = 2x, and dx = du/2x.
Substituting into the integral, we get:

∫ 1/sqrt(x^2 - a^2) dx = ∫ 1/sqrt(u) * du/2x
= (1/2) ∫ 1/sqrt(u) du  

= (1/2) * 2sqrt(u) + C
= sqrt(x^2 - a^2) + C

Therefore, the answer to the integral of 1/sqrt(x^2 - a^2) dx is sqrt(x^2 - a^2) + C, where C is the constant of integration.

In summary, the integral of 1/sqrt(x^2 - a^2) dx can be solved using the substitution method, where u = x^2 - a^2. The final answer is sqrt(x^2 - a^2) + C, where C is the constant of integration.

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The integral of \(\frac{1}{\sqrt{x^2 - a^2}} dx\) is \(\ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\), where C is the constant of integration

What is intergration?

Integration is a fundamental concept in calculus that involves finding the antiderivative or integral of a function. It is the reverse process of differentiation, which is concerned with finding the derivative of a function.

To find the integral of \(1/\sqrt(x^2 - a^2) dx\), we can use a trigonometric substitution. Let's substitute \(x = a sec(\theta)\), where \(sec(\theta)\) is the reciprocal of the cosine function.

By making this substitution, we can express dx in terms of \(d(\theta)\) as follows:

\(dx = a sec(\theta) tan(\theta) d(\theta)\)

Now, let's substitute these values into the integral:

\(\int \frac{1}{\sqrt{x^2 - a^2}} dx\\\\= \int \frac{1}{\sqrt{(a \sec(theta))^2 - a^2}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{\sqrt{a^2(\sec^2(theta) - 1)}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{\sqrt{a^2(\tan^2(theta))}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{a \tan(theta)} (a \sec(\theta) \tan(\theta)) d(\theta)\)

Simplifying the expression, we have:

\(= \int \sec(\theta) d(\theta)\)

The integral of \(sec(\theta)\) can be evaluated as the natural logarithm of the absolute value of \(sec(\theta)\) plus the tangent\((\theta)\):

\(= \ln|\sec(\theta) + \tan(\theta)| + C\)

Finally, substituting back \(x = a sec(\theta)\), we get:

\(= \ln|\sec(\theta) + \tan(\theta)| + C\\\\= \ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\)

Therefore, the integral of \(\frac{1}{\sqrt{x^2 - a^2}} dx\) is \(\ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\), where C is the constant of integration

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On solving the provided question, we can say that by using N= 2X + 1 or  N = 2X-1  will do the job for composite numbers.

By multiplying two small positive integers, you can create a composite number, which is a positive integer. Likewise, any positive integer that has at least one divisor besides itself and 1. Positive whole numbers make up composite numbers. It lacks prime (that is, it has divisors other than 1 and itself). The first several composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, and are frequently referred to simply as "composites." In other words, composite odd numbers encompass all non-prime odd numbers. for illustration: 9, 15, 21, etc. No. As a result, 2 only possesses the divisors 1 and 2. To put it another way, since 2 only has two divisors, it is not a composite number.

by using N= 2X + 1

or

N = 2X-1

will do the job for composite numbers.

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Answer:

12

Step-by-step explanation:

Median data dihitung sebagai

= 1/2 (n + 1) suku ke-1

Dimana n = Jumlah suku

= 10

Langkah 1

Kami mengatur ulang

8, 9, 10, 10, 12, 12, 13, 15, 15, 17

Langkah 2

Suku 1/2 (n + 1)

1/2 (10 + 1) istilah

= 11/2 istilah

= 5,5 suku

Istilah ini antara istilah ke-5 dan ke-6

Suku ke-5 = 12

Suku ke-6 = 12

= 12 + 12/2 = 24/2

= 12

Median data adalah 12

Answer:

The answer is 8.30

Step-by-step explanation:

Using cos 41 = x/11

x = cos 41 × 11

x = 8.30

Answer:

8

Step-by-step explanation:

Step-by-step explanation:

Give me the answer each one please.

Answer: 4:5

Step-by-step explanation: The lowest form

Answer:

Step-by-step explanation:

4:5