ASAP!!! NEED HELP!!!! Max is stacking logs at his campground for firewood. After his first load of logs, he has 8 logs on the stack. After his seventh load of logs, he has 62 logs on the stack. Use sequence notation to represent the arithmetic function. ANSWER CHOICES: A. an = 8 + 6(n − 1) B. an = 62 + 6(n − 1) C. an = 8 + 9(n − 1) D. an = 62 + 9(n − 1)

Answer:

y+2 = 4(x-6)

Step-by-step explanation:

The point slope equation of a line is

y-y1 = m(x-x1)  where m is the slope and ( x1,y1) is a point on the line

y - -2 = 4( x-6)

y+2 = 4(x-6)

Answer:

Answer:

y = 1.8

Step-by-step explanation:

Question 39).

Let the operation which defines the relation between a and b is O.

Relation between a and b has been given as,

a O b = [tex]\frac{(a+b)}{(a-b)}[/tex]

Following the same operation, relation between 3 and y will be,

3 O y = [tex]\frac{3+y}{3-y}[/tex]

Since 3 O y = 4,

[tex]\frac{3+y}{3-y}=4[/tex]

3 + y = 12 - 4y

3 + y + 4y = 12 - 4y + 4y

3 + 5y = 12

3 + 5y - 3 = 12 - 3

5y = 9

[tex]\frac{5y}{5}=\frac{9}{5}[/tex]

y = 1.8

Therefore, y = 1.8 will be the answer.

Answer:

[tex] -3n - 7 [/tex]

Step-by-step explanation:

Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.

Using the slope-intercept formula, y = mx + b, let's find the equation.

Where,

m = the increase in output ÷ increase in input = [tex] \frac{-13 - (-10)}{2 - 1} [/tex]

[tex] m = \frac{-13 + 10}{1} [/tex]

[tex] m = \frac{-3}{1} [/tex]

[tex] m = -3 [/tex]

Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept

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

[tex] -10 = -3(1) + b [/tex]

[tex] -10 = -3 + b [/tex]

Add 3 to both sides:

[tex] -10 + 3 = -3 + b + 3 [/tex]

[tex] -7 = b [/tex]

[tex] b = -7 [/tex]

The equation of the given linear function can be written as:

[tex] y = -3x - 7 [/tex]

Or

[tex] f(x) = -3x - 7 [/tex]

Therefore, if the input is n, the output would be:

[tex] f(n) = -3n - 7 [/tex]

Answer:

Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].

Step-by-step explanation:

The general equation in rectangular form for a 3-dimension plane is represented by:

[tex]a\cdot x + b\cdot y + c\cdot z = d[/tex]

Where:

[tex]x[/tex], [tex]y[/tex], [tex]z[/tex] - Orthogonal inputs.

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex], [tex]d[/tex] - Plane constants.

The plane presented in the figure contains the following three points: (2, 0, 0),  (0, 2, 0), (0, 0, 3)

For the determination of the resultant equation, three equations of line in three distinct planes orthogonal to each other. That is, expressions for the xy, yz and xz-planes with the resource of the general equation of the line:

xy-plane (2, 0, 0) and (0, 2, 0)

[tex]y = m\cdot x + b[/tex]

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Where:

[tex]m[/tex] - Slope, dimensionless.

[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.

[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.

[tex]b[/tex] - x-Intercept, dimensionless.

If [tex]x_{1} = 2[/tex], [tex]y_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]y_{2} = 2[/tex], then:

Slope

[tex]m = \frac{2-0}{0-2}[/tex]

[tex]m = -1[/tex]

x-Intercept

[tex]b = y_{1} - m\cdot x_{1}[/tex]

[tex]b = 0 -(-1)\cdot (2)[/tex]

[tex]b = 2[/tex]

The equation of the line in the xy-plane is [tex]y = -x+2[/tex] or [tex]x + y = 2[/tex], which is equivalent to [tex]3\cdot x + 3\cdot y = 6[/tex].

yz-plane (0, 2, 0) and (0, 0, 3)

[tex]z = m\cdot y + b[/tex]

[tex]m = \frac{z_{2}-z_{1}}{y_{2}-y_{1}}[/tex]

Where:

[tex]m[/tex] - Slope, dimensionless.

[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the independent variable, dimensionless.

[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.

[tex]b[/tex] - y-Intercept, dimensionless.

If [tex]y_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]y_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:

Slope

[tex]m = \frac{3-0}{0-2}[/tex]

[tex]m = -\frac{3}{2}[/tex]

y-Intercept

[tex]b = z_{1} - m\cdot y_{1}[/tex]

[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]

[tex]b = 3[/tex]

The equation of the line in the yz-plane is [tex]z = -\frac{3}{2}\cdot y+3[/tex] or [tex]3\cdot y + 2\cdot z = 6[/tex].

xz-plane (2, 0, 0) and (0, 0, 3)

[tex]z = m\cdot x + b[/tex]

[tex]m = \frac{z_{2}-z_{1}}{x_{2}-x_{1}}[/tex]

Where:

[tex]m[/tex] - Slope, dimensionless.

[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.

[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.

[tex]b[/tex] - z-Intercept, dimensionless.

If [tex]x_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:

Slope

[tex]m = \frac{3-0}{0-2}[/tex]

[tex]m = -\frac{3}{2}[/tex]

x-Intercept

[tex]b = z_{1} - m\cdot x_{1}[/tex]

[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]

[tex]b = 3[/tex]

The equation of the line in the xz-plane is [tex]z = -\frac{3}{2}\cdot x+3[/tex] or [tex]3\cdot x + 2\cdot z = 6[/tex]

After comparing each equation of the line to the definition of the equation of the plane, the following coefficients are obtained:

[tex]a = 3[/tex], [tex]b = 3[/tex], [tex]c = 2[/tex], [tex]d = 6[/tex]

Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].

Answer:

It is A    3x+3y+2z=6

Step-by-step explanation:

Answer:

3+x

Step-by-step explanation:

sum= addition

a number= a number

Answer:

3+x  

eplanation                                  

Answer:  A, B, and D

Step-by-step explanation:

Input the coordinates into the inequality to see which makes a true statement:

                             5x - 2y < 8

A) x = -1, y = 1       5(-1) - 2(1) < 8

                              -5  -  2   < 8

                                    -7     < 8       TRUE!

B) x = -3, y = 4       5(-3) - 2(4) < 8

                              -15  -  8   < 8

                                    -23    < 8     TRUE!

C) x = 4, y = 0       5(4) - 2(0) < 8

                              20  -  0   < 8

                                    20     < 8    False

D) x = -2, y = 3       5(-2) - 2(3) < 8

                              -10  -  6   < 8

                                    -16     < 8   TRUE!

Answer:

I believe 45.50

Step-by-step explanation: The locksmith is 18.3 miles W from furniture, the hotel is 27.2 E from furniture store  so 18.3+27.2=45.50

Answer:

7.24 hrs

Step-by-step explanation:

Janet can do the order in 14 hours.

In 1 hour, she can do 1/14 of the order.

Jim can do the order in 15 hours.

In 1 hour, he can do 1/15 of the order.

Let the total amount of time they take to do the job working together be x hours.

[tex]\frac{1}{14} x+\frac{1}{15}x =1[/tex]

[tex]\frac{29}{210} x=1[/tex]

[tex]\frac{210}{29}* \frac{29}{210} x=1*\frac{210}{29}[/tex]

[tex]x= 7.241379...[/tex]

This question is incomplete

Complete Question

The function s(V) = ∛V describes the side length, in units, of a cube with a volume of V cubic units.

Jason wants to build a cube with a minimum of 64 cubic centimeters.

What is a reasonable range for s, the side length, in centimeters, of Jason’s cube?

a) s > 0

b) s ≥ 4

c) s ≥ 8

d) s ≥ 16

Answer:

b) s ≥ 4

Step-by-step explanation:

From the above question, we are given Volume of the cube = 64cm³

We are given the function

s(V) = ∛V

Hence,

The range for the side length s =

s(V) ≥ ∛V

s(V) ≥ ∛64 cm³

s(v) ≥ 4 cm

Therefore, the reasonable range for s, the side length, in centimeters, of Jason’s cube

Option b) s ≥ 4

Answer:

s≥ 4

Step-by-step explanation:

Answer:

D. -0.98

Step-by-step explanation:

Well it is a negative correlation and it is really strong but it is impossible to go pasit -1.

Thus,

the answer is D. -0.98

Hope this helps :)

Answer:

D. -0.98

Step-by-step explanation:

The correlation is a negative if the Y value decreases as the x value increases. It is not -1.43 because it is not decraeseing that fast.

Answer:

The bass fish was the better catch

Step-by-step explanation:

From the question we are told that

     The  population mean for trout is  [tex]\mu_1 = 12 \ in[/tex]

     The  standard deviation is  [tex]\sigma_1 = 2.75 \ in[/tex]

      The  population mean for  base  is  [tex]\mu _2 = 4 \ lb[/tex]

      The standard deviation is  [tex]\sigma_2 = 0.8 \ lb[/tex]

      The number of  trout caught   [tex]x_1 = 18[/tex]

     The number of  bass caught  [tex]x_2 = 6[/tex]

Generally z-value(standardized value ) for the of number  trout caught  is mathematically represented as

        [tex]z_1 = \frac{x_1 - \mu_1}{\sigma_1 }[/tex]

substituting value

       [tex]z_1 = \frac{18 - 12}{2.75 }[/tex]

       [tex]z_1 = 2.18[/tex]

Generally z-value(standardized value ) for the of number  bass caught  is mathematically represented as

        [tex]z_2 = \frac{x_2 - \mu_2}{\sigma_2 }[/tex]

substituting value

       [tex]z_2 = \frac{6 - 4}{0.8 }[/tex]

       [tex]z_2 = 2.5[/tex]

From our calculation we see that  [tex]z_2 > z_1[/tex]

The  fish that was the better catch is the bass fish

Answer:

the percentage of people who have an IQ between 115 and 140 is 16.79%

Step-by-step explanation:

From the information given:

We are to  determine the percentage of people who have an IQ between 115 and 140.

i.e

P(115 < X < 140) = P( X  ≤ 140) - P( X  ≤ 115)

[tex]P(115 < X < 140) = P( \dfrac{X-100}{\sigma}\leq \dfrac{140-100}{16})-P( \dfrac{X-100}{\sigma}\leq \dfrac{115-100}{16})[/tex]

[tex]P(115 < X < 140) = P( Z\leq \dfrac{140-100}{16})-P( Z\leq \dfrac{115-100}{16})[/tex]

[tex]P(115 < X < 140) = P( Z\leq \dfrac{40}{16})-P( Z\leq \dfrac{15}{16})[/tex]

[tex]P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.9375)[/tex]

[tex]P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.938)[/tex]

From Z tables :

[tex]P(115 < X < 140) = 0.9938-0.8259[/tex]

[tex]P(115 < X < 140) = 0.1679[/tex]

Thus; we can conclude that the percentage of people who have an IQ between 115 and 140 is 16.79%

Using the normal distribution, it is found that 82.02% of people who have an IQ between 115 and 140.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

The proportion of people who have an IQ between 115 and 140 is the p-value of Z when X = 140 subtracted by the p-value of Z when X = 115, hence:

X = 140:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{140 - 100}{16}[/tex]

[tex]Z = 2.5[/tex]

[tex]Z = 2.5[/tex] has a p-value of 0.9938.

X = 115:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{115 - 100}{16}[/tex]

[tex]Z = -0.94[/tex]

[tex]Z = -0.94[/tex] has a p-value of 0.1736.

0.9938 - 0.1736 = 0.8202.

0.8202 = 82.02% of people who have an IQ between 115 and 140.

More can be learned about the normal distribution at https://brainly.com/question/24663213

Answer:

96 square units

Step-by-step explanation:

The surface area of the prism can be calculated using its net.

The net consists of 3 rectangles and 2 triangles.

The surface area = area of the 3 rectangles + area of the 2 triangles

Area of 3 rectangles:

Area of 2 rectangles having the same dimension = 2(L*B) = 2(7*3) = 2(21) = 42 squared units

Area of the middle triangle = L*B = 7*6 = 42 square units.

Area of the 3 triangles = 42 + 42 = 84 square units.

Area of the 2 triangles:

Area = 2(½*b*h) = 2(½*6*2) = 6*2

Area of the 2 triangles = 12 square units

Surface area of the triangular prism = 84 + 12 = 96 square units.

Answer:

It's 96 unit2

Step-by-step explanation:

I just do it in khan and it's correct

Answer:

C. If 75% of Americans still favor mandatory testing this year, then there is a 3% chance that poll results will show 72% or fewer with this opinion.

Step-by-step explanation:

Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis. In this question the sample of 1000 Americans is under test. It is the result of the poll that 75% still favor mandatory testing.

Answer:

Option (C)

Step-by-step explanation:

Let the red cases sold = r

and the number of white cases sold = w

Total number of cases sold by the winery = 81

r + w = 81 -------(1)

If number of red cases sold is twice of white cases sold,

r = 2w ------- (2)

By substituting the value of r from equation (2) to equation (1),

2w + w = 81

3w = 81

w = 27 cases

From equation (1),

r + 27 = 81

r = 54 cases

Therefore, number of white cases sold are 27 cases

Option (C) is he answer.

Greetings from Brasil...

In a linear function, the rate of change is given by M (see below).

M = rate of change

N = linear coefficient

The Function 2 has M = 4, cause

F(X) = 4X + 1

(M = 4 and N = 1)

For Function 1 we have a rate of change equal to zero, becaus it is a constant function... let's see:

M = ΔY/ΔX

M = (3 - 3)/(4 - 0)

M = 0/4 = 0

So, the Function 2 has 4 times more rate of change than the first

Your answer is two!!

Answer:

(4, 4)

Step-by-step explanation:

All you really need to do is multiply C's original coordinates with the scale factor. So (2, 2), becomes (4, 4).

Answer:

( 4 , 4 )

Step-by-step explanation:

original C coordinates : ( 2 , 2 )

since the problem is telling us to dilate by the factor of 2 we multiply both 2's by 2.

( 2 ‧ 2 ) ( 2 ‧ 2 )

= ( 4 , 4 )

Answer:

see attachment

Step-by-step explanation:

We differentiate implicitly with respect to x taking y as a constant and we differentiate implicitly with respect to y taking x as a constant.

[tex]\rm \dfrac{\partial z}{\partial x} = - \dfrac{(x^5 + 3yz)}{z^5 + x} \ \ and \ \ \dfrac{\partial z}{\partial y} &= - \dfrac{(y^5 + 3xz)}{z^5 + y}[/tex]

When in a function the dependent variable is not explicitly isolated on either side of the equation then the function becomes an implicit function.

The equation is given as [tex]\rm x^6 + y^6 + z^6 + 18xyz = 1.[/tex]

Differentiate partially the function with respect to x treating y as a constant.

[tex]\begin{aligned} \dfrac{\partial}{\partial x} x^6 + y^6 + z^6 + 18xyz &= 0\\\\6x^5 + 0 + 6z^5 \dfrac{\partial z }{\partial x} + 18y(z + x\dfrac{\partial z}{\partial x}) &= 0\\\\x^5 + z^5 \dfrac{\partial z }{\partial x} + 3y(z + x\dfrac{\partial z}{\partial x}) &= 0\\\\\dfrac{\partial z}{\partial x} &= - \dfrac{(x^5 + 3yz)}{z^5 + x} \end{aligned}[/tex]

Similarly, differentiate partially the function with respect to y treating x as a constant.

[tex]\begin{aligned} \dfrac{\partial}{\partial y} x^6 + y^6 + z^6 + 18xyz &= 0\\\\ 0 + 6y^5+ 6z^5 \dfrac{\partial z }{\partial y} + 18x(z + y\dfrac{\partial z}{\partial y}) &= 0\\\\y^5 + z^5 \dfrac{\partial z }{\partial y} + 3x(z + y\dfrac{\partial z}{\partial y}) &= 0\\\\\dfrac{\partial z}{\partial y} &= - \dfrac{(y^5 + 3xz)}{z^5 + y} \end{aligned}[/tex]

More about the implicit function link is given below.

https://brainly.com/question/6472622

Answer:

p-value = 0.1213  (to 4-decimal places)

Step-by-step explanation:

Given:

N = 240

mean  = 7.5

s = 1.0

Solution

With N=240 and using the central limit theorem, distribution can be approximated as normal.

Let

Null hypothesis H0, mu = 7.6

Alternate hypothesis, mu not equal to 7.6  (two-tail test)

for

Alpha = 0.1 (two sided)

Z = sqrt(N)(mean – mu)/s = sqrt(240)(7.5-7.6)/1.0 = -1.54919

p-value  

= P(|Z|>1.54919)  

= 2P(Z>1.54919)

= 2(1-P(Z<1.54919)

=2(1-0.9393)     (using normal distribution table)

=0.12134

Since alpha = 0.1 < p-value (0.1213), H0 that mean = 7.6 is not rejected.

Answer:

Option A is the correct option.

Step-by-step explanation:

[tex] \frac{3}{x } = \frac{6}{x - 4} [/tex]

Apply cross product property:

[tex]3(x - 4) = 6 \times x[/tex]

[tex]3(x - 4) = 6x[/tex]

Hope this helps...

Best regards!!

Answer:

3 * (x - 4) = 6 * x.

Step-by-step explanation:

3 / x = 6 / (x - 4)

3 * (x - 4) = 6 * x

3x - 12 = 6x

6x = 3x - 12

6x - 3x = -12

3x = -12

x = -4.

Hope this helps!

Answer:

x=3

Step-by-step explanation:

To solve this problem, we should check the x coordinate of the point where both graphs intersect. Based on both graphs, they intersect at the point (3,-1). So, the input value for which both graphs have the same value is x=3.

Answer:

its x=-2

Step-by-step explanation:

cause i got it wrong and it said the answer was x=-2

Answer:

x + 1 - ( 4 / x³ + 3x² + 8 )

Step-by-step explanation:

If the volume of this rectangular prism ⇒ ( x⁴ + 4x³ + 3x² + 8x + 4 ), and the base area ⇒ ( x³ + 3x² + 8 ), we can determine the height through division of each. The general volume formula is the base area [tex]*[/tex] the height, but some figures have exceptions as they are " portions " of others. In this case the formula is the base area  [tex]*[/tex] height, and hence we can solve for the height by dividing the volume by the base area.

Height = ( x⁴ + 4x³ + 3x² + 8x + 4 ) / ( x³ + 3x² + 8 ) = [tex]\frac{x^4+4x^3+3x^2+8x+4}{x^3+3x^2+8}[/tex] = [tex]x+\frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex] = [tex]x+1+\frac{-4}{x^3+3x^2+8}[/tex] = [tex]x+1-\frac{4}{x^3+3x^2+8}[/tex] - and this is our solution.

Answer:

[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]

Step-by-step explanation:

[tex]volume=base \: area \times height[/tex]

[tex]height=\frac{volume}{base \: area}[/tex]

[tex]\mathrm{Solve \: by \: long \: division.}[/tex]

[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]

[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]

[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]

Answer:

Below

Step-by-step explanation:

The average speed is given by the following formula:

● V = d/t

● d is the distance covered

● t is the time spent to cover the distance d

■■■■■■■■■■■■■■■■■■■■■■■

Ava takes 8 minutes to go from mile marker 0 to mile marker6.

● the distance Ava traveled is 6 miles

● the time Ava spent to reach mile marker 6 is 8 minutes

So the average speed of Ava is:

● V = 6/ 8 = 3/4 = 0.75 mile per min

●●●●●●●●●●●●●●●●●●●●●●●●

Let's The equation of the line that links the number of milemarkers (n) and the time (t).

Ava went from mile marker 0 to mile marker 6.

At t=0 Ava just started travelling from mile marker 0 to 1.

Afrer 8 minutes,she was at mile marker 6.

So 8 min => 6 mile markers (igonring mile marker 0 since the distance there was 0 mile)

6/8= 0.75

Then n/t = 0.75

● n = 0.75 * t

Let's check

● n= 0.75*4 = 3

That's true since after 4 minutes Ava was at mile marker 3.

Answer:

√41

Step-by-step explanation:

Considering the sides with lengths 48 and 52 units, we would use Pythagoras theorem to find the third side. Let that side be t

52² = 48² + t²

t² = 52² - 48²

= 2704 - 2304

= 400

t = √400

= 20

Considering the next triangle with sides t (20 units) and 12 units, again using the theorem

20² = 12² + y²

where y is the third side

400 = 144 + y²

y² = 400 - 144

= 256

y = √256

= 16 units

Considering the triangle with two sides given as 5 and 13 units, the third side (which is part of the 16 units calculated earlier)

13² = 5² + u²

where u is the 3rd side

169 = 25 + u²

u² = 169 - 25

u² = 144

u = √144

u = 12

The other part of the side of that triangle

= 16 - 12

= 4

Considering the smallest triangle whose sides are x, 5 and 4,

x² = 5² + 4²

= 25 + 16

= 41

x = √41

Answer:

a = 9h + bn

Step-by-step explanation:

total = $9 an hour + (bonus x number of items repaired)

Answer: 0.271

Step-by-step explanation:

Probability of complement of an even is 1 decreased by the probability of the event

P(At least one) =1 - P(none)

The probability that of testing negative is 0.9 because the probability of testing positive is 0.1

P( at least one) = 1 - P(none) = 1 - (0.93^3) = 0.271

Answer:

A. $22,223

B. $20,000

C. $20,000

Explanation:

The annual return of the retired couple's investment is called the yield in percentage.

A. If they go for Treasury bills which has a yield of 9%, to attain a return of at least $2,000 their investment must exceed $20,000. 9% of 22,223 = $2,000.07

B. . If they go for Corporate bonds option which has a yield of 11%, to attain a return of at least $2,000; 11% of 20,000 = $2,200

C. . If they go for Junk bonds option which has a yield of 13%, to attain annual return of at least $2,000; 13% of $20,000= $2,600

Answer:

John is 9, Brian is 6.

Step-by-step explanation:

I)

Let [tex]J[/tex] represent John's age and [tex]B[/tex] represent Brian's age.

John is three years older than Brian. In other words:

[tex]J=B+3[/tex]

The product of their ages is 54. Or:

[tex]JB=54[/tex]

II)

Write this as a quadratic by substituting:

[tex]JB=54\\(B+3)B=54\\B^2+3B-54=0[/tex]

III)

Solve the quadratic:

[tex]B^2+3B-54=0\\B^2-6B+9B-54=0\\B(B-6)+9(B-6)=0\\(B+9)(B-6)=0\\B=-9, 6[/tex]

Since age cannot be negative, Brian must be 6 years old right now.

John is three year older, so John is 9.

Answer:

[tex]\large\boxed{\sf \ \ \ 404,699 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

At the beginning the population is 240,000

After 1 year the population will be

   240,000*(1+7.75%)=240,000*1.0775

After n years the population will be

   [tex]240,000\cdot1.0775^n[/tex]

So after 7 years the population will be

   [tex]240,000\cdot1.0775^7=404699.058...[/tex]

So rounded to the nearest whole number gives 404,699

Hope this helps