Find a mathematical model for the below statement. (Use k for the constant of proportionality.) The gravitational attraction F between two objects of masses m1 and m2 is jointly proportional to the masses and inversely proportional to the square of the distance r between the objects.

Answer:

-3

Step-by-step explanation:

in these equations the slope is multiplied by x which is -3 in this one.

Answer:

[tex]-3[/tex]

Step-by-step explanation:

The equation of a line is [tex]y=mx+b[/tex], and m is the gradient which is the slope. Hence, the number with x is the slope, which is [tex]-3[/tex].

Hope that helped.

Answer:

It is A (5, -7)

Step-by-step explanation:

Answer:

A 5,-7

Step-by-step explanation:

Answer:

x = 32

exterior = 104

Step-by-step explanation:

The exterior angle is equal to the sum of the  opposite interior angles

40 + 2x = x+72

Subtract x from each side

40+2x-x = x+72-x

x+40 = 72

Subtract 40 from each side

x+40-40 =72-40

x = 32

The exterior angle

x+72 = 32+72 = 104

Answer:

in a relationship that maps elements from one set (the inputs) into elements from another set (the outputs), the usual notation for the ordered pairs is:

(x, y), where x is the input and y is the output.

In this case, the point where the arrow starts is the input, and where the arrow ends is the output.

a)

The ordered pairs are:

(28, 93)

(17, 126)

(52, 187)

(34, 108)

(34, 187)

b) The domain is the set of the inputs, in this case the domain is the set where all the arrows start, then the domain is:

{17, 28, 34, 52}

And the range is the set of the outputs, in this case the range is:

{93, 108, 126, 187}

c) A function is a relationship where the elements from the domain, the inputs, can be mapped into only one element from the range.

In this case, we can see that the input {34} is being mapped into two different outputs, then this is not a function.

d) We can remove one of the two ordered pairs where the input is {34},

So for example, we could remove:

(34, 108)

And then the relation would be a function.

Answer:

a) The probability of sampling at random a fish that is smaller in size than the value you would obtain by subtracting half the standard deviation from the average is 0.3085.

b) The probability of sampling at random a fish that is greater in size than the value you would obtain by adding half the standard deviation from the average is 0.3085.

c) The probability of sampling at random a fish that has a size between the two values is 0.383.

d) The 25th and 75 percentiles of fish size for the population using the normal distribution table is 5.69 and 5.87 respectively.

e) The probability that the average calculated will be less than the value is 0.3707.

Step-by-step explanation:

For the given data set mean [tex](\mu) = 5.75913[/tex]

Standard deviation [tex](\sigma) = 0.172229[/tex]

Variance [tex](\sigma2) = 0.0296[/tex]

Here we get is

a)

[tex]P(x < \mu - \sigma/2) = p(x < 5.673) \\\\ = 0.3085[/tex]

b)

[tex]P(x < \mu + \sigma/2) = p(x < 5.845) \\\\= 0.3085[/tex]

c)

[tex]P(\mu - \sigma/2 < x < \mu + \sigma/2) = p(5.673 < x < 5.845) \\\\= 0.383[/tex]

d)

25th percentile:-

[tex]= 25*[(n+1)/100]th term \\\\= 5.69[/tex]

75the percentile:-

[tex]= 75*[(n+1)/100]th term\\\\ = 5.87[/tex]

e)  

[tex]p(x < \mu - \sigma/3) = p(x < 5.7017) \\\\= 0.3707[/tex]

Answer:

Ok ☺️✌️✌️✌️Ok ok ok ok

Answer:

a÷(b+c)≠(a÷b)+(a ÷c)

Step-by-step explanation:

To verify that a÷(b+c)=(a÷b)+(a ÷c)

Using the values ;

a=10 , b=5 , 6=2​

plugging the values into a÷(b+c) should give the same result as (a÷b)+(a ÷c) ;

That is, right hand side = left hand side

a÷(b+c) = 10 ÷ (5+ 2)

a÷(b+c) = 10 / 7

Also;

(a÷b)+(a ÷c) = (10/5) + (10/2) = 2 + 5 = 7

Given the result, it can be seen that ;

RHS ≠ LHS

10/7 ≠ 7

Answer:

ITS C. (0, 3)

Step-by-step explanation:

I JUST ASKED THE TEACHER ;)

Answer:

5x+3y=6

Step-by-step explanation:

Use the slope intercept form then rearrange

Answer:

Step-by-step explanation:

A = [tex]pe^{rt}[/tex]

A = 100[tex]e^{.08 *15}[/tex]

A=. $332.01

The value of the investment after 15 years is $332.01.

Option A is the correct  answer.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

The continuous compounding formula is given by:

[tex]A = Pe^{rt}[/tex]

Where:

A = the ending amount

P = the principal (initial investment)

e = the mathematical constant (approximately equal to 2.71828)

r = the interest rate (as a decimal)

t = the time period (in years)

Using this formula, we can find the value of the investment after 15 years:

A = 100 \times e^{0.08 \times 15} ≈ $332.01

Therefore,

The value of the investment after 15 years is $332.01.

Learn more about compound interest here:

https://brainly.com/question/13155407

#SPJ7

Answer:

Simpson's Paradox

Step-by-step explanation:

Answer:

Simpson's Paradox

Step-by-step explanation:

Got it right on the test.

Answer:

a

Step-by-step explanation:

Answer:

Question... is the commission given 10 times or 3?

If the commission is 10 then

5*(48,000 * .075) + 3*(48,000 * .05) +2*(48,000 * .035)

5*(3600) + 3*(2400) +2*(1680)

= 28560

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

If the commission is 3 then (once for first five years, once for the next three,

and once for the last two

(48,000 * .075) + (48,000 * .05) +(48,000 * .035)

=7680

Step-by-step explanation:

Answer:

It's answer is - 9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4......

[tex]\huge\bold{Given:}[/tex]

Length of the base = 8

Length of the hypotenuse = 17

[tex]\huge\bold{To\:find:}[/tex]

The length of the third side ''[tex]x[/tex]".

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

[tex]\longrightarrow{\purple{x\:=\: 15}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

Using Pythagoras theorem, we have

(Perpendicular)² + (Base)² = (Hypotenuse)²

[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] + (8)² = (17)²

[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] + 64 = 289

[tex]\longrightarrow{\blue{}}[/tex]  [tex]{x}^{2}[/tex] = 289 - 64

[tex]\longrightarrow{\blue{}}[/tex]  [tex]{x}^{2}[/tex] = 225

[tex]\longrightarrow{\blue{}}[/tex]  [tex]x[/tex] = [tex]\sqrt{225}[/tex]

[tex]\longrightarrow{\blue{}}[/tex]  [tex]x[/tex] = [tex]15[/tex]

Therefore, the length of the missing side [tex]x[/tex] is [tex]15[/tex].

[tex]\huge\bold{To\:verify :}[/tex]

[tex]\longrightarrow{\green{}}[/tex] (15)² + (8)² = (17)²

[tex]\longrightarrow{\green{}}[/tex] 225 + 64 = 289

[tex]\longrightarrow{\green{}}[/tex] 289 = 289

[tex]\longrightarrow{\green{}}[/tex] L.H.S. = R. H. S.

Hence verified.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]

Answer:please write in english

Step-by-step explanation:

Answer:

It will take him 5.85 seconds.

Step-by-step explanation:

12.5 (0.2t - 1) + 21t = 150

Use Distributive Property:

2.5t - 12.5 + 21t = 150

Combine like terms:

23.5t - 12.5 = 150

Subtract 12.5 from both sides:

23.5t = 137.5

Divide both sides by 23.5 to isolate variable t:

5.851063.....

Round to two decimal places (hundredths place):

5.85

Step-by-step explanation:

The perimeter of a rectangle is the length of all its 4 sides. Formula to calculate the perimeter of a rectangle is:

Perimeter of Rectangle = 2 × Length + 2 × Breadth

The perimeter can be represented using a model as below.

Perimeter = Length + Breadth + Length + Breadth

= 2 × Length + 2 × Breadth

Length + Breadth = Perimeter ÷ 2

Answer:

- At 95% confidence interval, the true mean is ( 13.5245 < μ < 15.0755 )

- the time allowed will be  0.50 hours or 30 minutes

Step-by-step explanation:

Given the data in the question;

sample size; n = 28

mean; x" = 14.3 miles

standard deviation; S = 2 miles.

degree of freedom DF = n - 1 = 28 - 1 = 27

confidence interval = 95%

level of significance = 1 - 95% = 1 - 0.95 = 0.05

so

[tex]t_{\alpha /2, df[/tex] = [tex]t_{0.025, df=27[/tex] = 2.0518

Hence, we have;

x" + [tex]t_{\alpha /2, df[/tex]( S/√n ) = 14.3 + 2.0518( 2/√28 )

= 14.3 + 0.7755

= 15.0755     { Upper Limit }

Also,

x" - [tex]t_{\alpha /2, df[/tex]( S/√n ) = 14.3 - 2.0518( 2/√28 )

= 14.3 - 0.7755

= 13.5245    { Lower Limit }

Therefore, at 95% confidence interval, the true mean is ( 13.5245 < μ < 15.0755 )

b)

If a manager wants to be sure that the employees are not late, then he/she should consider the upper bound of the confidence interval as the permissible distance range.

Now given that the average speed were 30 miles per hour

suggested time will be;

t = Upper limit / speed

t = 15.0755 / 30

t = 0.50 hours or 30 minutes

Therefore, the time allowed will be  0.50 hours or 30 minutes

Answer:

Step-by-step explanation:

72/8 = 9 acres per day

Answer:

250

Step-by-step explanation:

Density = mass / volume

density = 0.5 g / mL

mass = 125 g

0.5 = 125 / V                 Multiply both sides by V

0.5 * V = 125                 Divide by 0.5

0.5V 0.5 = 125/0.5

V = 250

When doing these kinds of ratios make sure that you get the numbers all on one side before you actually do the division or multiplication. That way you won't get confused.

Answer:

16%

Step-by-step explanation:

To find what percent of the regular cost is saved by renting a movie on a Tuesday, we must do 0.49/3.00. This helps us find the decimal point to convert into a percentage. 0.49/3.00 is equal to 0.163333333333 . And 0.163333333333  converted into a percentage is approximately 16%.

Hope this helps and if it does, don't be afraid to rate my answer as well as maybe give it a "Thanks"? (Or even better a "Brainliest")

Solution :

a). P(X = x)

     =   [tex]$p(1-p)^x$[/tex]  for x = 0, 1, 2, ....

   P(x ≤ 3) = 0.837

b). Expectation = [tex]$\frac{(1-p)}{p}$[/tex]

                        = 1.7397

  Variance = [tex]$\frac{(1-p)}{p^2}$[/tex]

                 = 4.7663726

  Standard deviation = 2.1832

 Therefore, mean + standard deviation

                  = 1.7397 + 2.1832

                  = 3.9229

[tex]$P(x > 3.9229) = 0.1626$[/tex]

So the required P = 2 x 0.1626

                             = 0.325

Answer:

to get x you need to divide

210/42= 5

x=5

210 = 42x

210/42=5

42*5=210

so remove the x it'd be 210 = 42(5)

x = 5

Answer:

52

Step-by-step explanation:

4 1/2 x + 2x

Let x = 8

4 1/2 (8) + 2(8)

Change to an improper fraction

9/2(8) +2(8)

36+16

52

si 8888888888888888888888888888

Answer:

382.925 feets

Step-by-step explanation:

The solution diagram is attached below :

Converting radian measurement to degree :

radian angle * 180/π = degree angle

1.2 * 180/π = 68.755°

0.9 * 180/π = 51.566°

Height of dam is h:

Using trigonometry :

Tan θ = opposite / Adjacent

Tan 68.755° = h / x

h = x Tan 68.755° - - - (1)

Tan 51.566° = h / (155+x)

h = (155+x) tan 51.566° - - - (2)

Equate (1) and (2)

x Tan 68.755 = (155+x) Tan 51.566

x Tan 68.755 = 155tan 51.566 + x tan 51.566

x Tan 68.755 = 195.32311 + x Tan 51.566

x Tan 68.755 - x Tan 51.566 = 195.32311

x(tan 68.755 - tan 51.566) = 195.32311

x * 1.3120110 = 195.32311

1.3120110x = 195.32311

x = 195.32311 / 1.3120110

x = 148.87307

Using :

h = x Tan 68.755

h = 148.87307 * tan(68.755)

h = 382.92539

h = 382.925 feets

Answer:

$20

Step-by-step explanation:

500 x .04 = 20