Solve the system by substitution.
2.5x-3y=-13
3.25x-y=-14

Answer:

80% People Decreased after 3 Stops.

Step-by-step explanation:

Given:

Total Number of People on the bus =60

Number of people decreased = 48

We need to find the the percent of decrease in the number of people on the bus.

The percent of decrease in the number of people on the bus can be calculated by dividing Number of people decreased on the bus with Total Number of people on the bus and then multiplied with 100.

Framing in equation form we get;

percent of decrease in the number of people on the bus = [tex]\frac{\textrm{Number of people decreased on the bus}}{\textrm{Total Number of people on the bus}}\times100[/tex]

Substituting the values we get;

percent of decrease in the number of people on the bus = [tex]\frac{48}{60}\times100 = 80\%[/tex]

Hence 80% People Decreased after 3 Stops.

Answer:

Maximum 3 socks (minimum 2) to be taken out to have a pair of same color.

Step-by-step explanation:

Well, it can be assumed that for example there are 4n black and 5n brown socks in a drawer (which satisfies ratio of 4/5). If first sock is taken out the probability of this sock being black is 4/9 (4n/(4n+5n)) or being brown is 5/9 (5n/(4n+5n)). If the first sock is black, the probability of second attempt being black is (4n-1)/(9n-1), but being brown is (5n)/(9n-1). f the first sock is brown, the probability of second attempt being brown is (5n-1)/(9n-1), but being black is (4n)/(9n-1). In either case, there is a probability of taking out different colors of socks in two attempts (taking black first then brown or vice-versa). So maximum 3 (minimum 2) attempts required to make sure you have a pair of the same color of socks.

To ensure you have a pair of the same color socks, you must take out a minimum of 5 socks from the drawer containing a mix of black and brown socks in a ratio of 4 to 5.

If you have black socks and brown socks in your drawer, mixed in a ratio of 4 to 5, you need to consider the worst-case scenario to ensure you have a pair of the same color. If you take out 4 black socks, one by one, you may still not have a matching pair if they are all black—so you need to take out another sock. If this fifth sock is brown, you now have one pair of brown socks. If it's black, then you already had a pair from the four black socks. Thus, you must take out a minimum of 5 socks to guarantee a matching pair.

Answer:

Step-by-step explanation:

Shane spends $2,000 each week for supplies and labor to run his car detailing business. This means that his total cost of running his car detailing business is $2000

Let x represent the number of cars that he would need. If he charges $30 for each car, the total amount charged for x cars would be 30×x = $30x

Let y represent the number of trucks that he would need. If he charges $45 for each car, the total amount charged for y trucks would be 45×y = $45y

In order to make profit, the inequality would be

30x + 45y greater than 2000

Final answer:

Shane can use the inequality 30c + 45t > 2000 to calculate the combination of cars (c) and trucks (t) he needs to detail in order to make a profit, where the costs are $2,000 weekly and charges are $30 and $45 respectively.

Explanation:

To calculate the number of cars (c) and trucks (t) Shane needs to detail in order to make a profit, we can set up an inequality based on his weekly costs and his charges for detailing cars and trucks.

With $2,000 for supplies and labor as his weekly expenses and charging $30 for each car and $45 for each truck, Shane's profit inequality would look like:

30c + 45t > 2000

This inequality states that the total revenue from detailing c cars and t trucks must be greater than his weekly expenses of $2,000 to make a profit.

Answer:

The parents who didn't answer with either naughty and nice are 6.

Step-by-step explanation:

Given:

150 parents were surveyed. 26% said that the kids were naughty and 70% said their kids were nice.

Now, to find parents who didn't answer with either naughty and nice.

So, as given in question:

70% said that their kids are naughty.

26% said that their kids are nice.

So, to get the percentage of parents who didn't answer we subtract.

Thus, the percentage of  parents who didn't answer with either naughty and nice:

100% - (70% + 26%)

100% - 96% = 4%.

Hence, 4% of parents didn't answer.

Now, to get how many  parents didn't answer we calculate the percentage of the total who didn't answer:

Total parents surveyed = 150.

Parents who didn't answer =  4% of the total parents surveyed.

[tex]Parents\ who\ didn't\ answer = 4\% of 150.[/tex]

[tex]Parents\ who\ didn't\ answer = \frac{4}{100}\times 150.[/tex]

[tex]Parents\ who\ didn't\ answer = \frac{600}{100}.[/tex]

[tex]Parents\ who\ didn't\ answer = 6.[/tex]

Therefore, the parents who didn't answer with either naughty and nice are 6.

In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct  random sampling and random group assignment

Explanation:

The terms Random sampling and Random group assignment are greatly different in process of the sample selection.  The study related to the determination of how sample participants can be drawn from the population refers to the process of Random sampling. The sample participants are subjected to a treatment by the usage of a random procedure comprises the Random group assignment.

When a researcher wants validate externally then random selection can be used. When a researcher wants to determine the effects of treatment within that group which is known as determination of internal validity then he can opt for Random group assignment.

Answer:

In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling/random group assignment.

Explanation:

Random selection is a representation of the sample of people for your research from a community. Random assignment is the assigning of the sample that describes various groups or operations in the study.

Reasons:

Thus we can say in order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling/random group assignment.

To learn more about random sampling/random group assignment, refer:

Answer:

The description of the company's is marketing mix.

Step-by-step explanation:

Consider the provided information.

Jakubowski Farms Gourmet Bread Base is the brand name for a mix designed for use in bread making machines which is the product.

We have given that the price is $14.99 plus shipping.

The promotion is word of mouth and public demonstrations.

The place is mail.

The marketing mix is defined as the set of actions or tactics that a company uses to market its brand or product. The 4Ps constitute a standard marketing mix-price, product, promotion and venue.

These four elements are the marketing mix—product, price, promotion, and place.

Hence, the description of the company's is marketing mix.

No options given in the question are equivalent to the original system of equations because none of them retain the same solutions as the original system.

The equivalent system for the given system of equations can be found by manipulating the original system of equations. The original system of equations is:

2x + 3y = 7

4x − 2y = 4.

Equations are equivalent if one is a multiple of the other. We can see that if the second equation is multiplied by 2, it will become:

8x - 4y = 8,

which is not an option given in your question. Therefore, none of the presented options (A-D) are equivalent to the initial system of equations. Always remember that an equivalent system retains the same solutions as the original system.

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Answer:

3n+2

Step-by-step explanation:

[where, a and b are some constants and x is a variable ( input values)]

so, a+b=5

so,2a+b=8

subtract the first equation from second:

2a+b-a-b=8-5

a=3.

by substituting the value of a in one of the above equations,

you will get b as 2

so, when the input is n, output will be : 3n+2

Yes. Micheal and Ashley bought same amount of turkey which is 6 pounds.

Step-by-step explanation:

The question requires to you to form simultaneous equations and solve them.

Take the number of pounds for turkey to be x and that for ham to be y

For store A where michael spent $18

turkey cost $3 per pound ---- 3x

ham cost $4 per pound------4x

The equation for cost will be ; 3x+4y =18

For store B where Ashley spent $27

turkey cost $4.5 per pound

ham cost $6 per pound

The equation for cost is : 4.5x +6y=27

The two equations are;

3x+4y=18

4.5x+6y=27

Solving the equations by graph you get ;

x=6 and y=4.5 for both linear graphs. This means both equations produce similar amounts of turkey and ham . Micheal and Ashley bought same amount of turkey which is 6 pounds.

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Answer:

t = 1

Step-by-step explanation:

3 (8 - 3t) = 5 (2 + t)

24 - 9t = 10 + 5t

- 9t - 5t = 10 - 24

- 14t = - 14

- t = - 14/14

- t = - 1

t = 1

Answer:

  "closed"

Step-by-step explanation:

A set is closed with respect to an operation if the operation on members of the set produces a member of the set.

Answer: D. [tex]\dfrac{qd}{(q+2)}[/tex]

Step-by-step explanation:

Given : q workers can paint a house in d days.

Let [tex]d_1[/tex] be the number of days taken by q+2 workers to paint the same house.

Since there is inverse relationship between the number of workers and the number of days to do same work ( condition - all workers paints at the same rate), as the number of workers increases the number of days to complete it decreases.

Equation of inverse variation between x and y  : [tex]x_1y_1=x_2y_2[/tex]

Substitute , [tex]x_1=q ,\ y_1=d[/tex] and  [tex]x_2=q+2 ,\ y_2=d_2[/tex] , we get

[tex]qd=(q+2)d_2\\\\\Rightarrow\ d_2=\dfrac{qd}{(q+2)}[/tex]

Therefore , the number of days it will take  q+2 workers to paint the same house = [tex]\dfrac{qd}{(q+2)}[/tex]

Hence, the correct answer is : D. [tex]\dfrac{qd}{(q+2)}[/tex]

Answer:

Measure of arc ZWX is 230°.

Step-by-step explanation:

Given:

arc WX = 50°

Now

The diameter divide a circle into two equal parts

so

[tex]arc\ ZWX=arc\ ZRW+arc\ WX[/tex]

Since WZ is diameter of the circle.

[tex]arc\ ZRW=180\°[/tex]

substituting in above equation we get

[tex]arc\ ZWX=180\°+50\°=230\°[/tex]

Hence Measure of arc ZWX is 230°.

Answer:

B. 230

Step-by-step explanation:

Just took the test

Answer:

Approximately 4,000 times

Step-by-step explanation:

If you're flipping a coin to get 4 heads out of 10 and you times it by 10,000 then you would have a probable win rate of 4,000.

Answer:

31.0 grams.

Step-by-step explanation:

According to the given information

Half-life of a substance = 37 years

Initial amount = 202 gram

The exponential function for half-life of a substance is

[tex]A(t)=A_0(0.5)^{\frac{t}{h}}[/tex]

where, A₀ is initial amount, t is time and h is half life.

Substitute A₀=202 and h=37 in the above function.

[tex]A(t)=202(0.5)^{\frac{t}{37}}[/tex]

We need to find the amount of the substance remaining after 100 years.

Substitute t=100 in the above function.

[tex]A(100)=202(0.5)^{\frac{100}{37}}[/tex]

[tex]A(100)=31.0282146[/tex]

Round the answer to the nearest tenth.

[tex]A(100)\approx 31.0[/tex]

Therefore, the amount of the substance remaining after 100 years is 31.0 grams.

Answer:

D i guess

Step-by-step explanation:

quarterly means 1/4

so 1.35*1/4

=0.3375

this number is changed to decimal from percentage so change it to percentage which is 33.75%

Answer:

The number of hamburger does the cook make is 73 hamburger .

Step-by-step explanation:

Given as :

The quantity of beef use by cook to make hamburger= [tex]\dfrac{2}{3}[/tex] pound

The total quantity of beef does the cook have = 48 [tex]\dfrac{2}{3}[/tex] pound

I.e The total quantity of beef does the cook have = [tex]\dfrac{146}{3}[/tex] pound

Let The number of hamburger does the cook make = n hamburger

Now, According to question

The number of hamburger does the cook make = [tex]\dfrac{\textrm total quantity of beef does cook have}{\textrm total quantity of beef required for hamburger}[/tex]

Or, n = [tex]\frac{\frac{146}{3}}{\frac{2}{3}}[/tex]

Or, n = [tex]\frac{146\times 3}{2\times 3}[/tex]

∴   n = 73

So,The number of hamburger does the cook make = n = 73 hamburger

Hence,The number of hamburger does the cook make is 73 hamburger . Answer

Answer:

y = -5/3 + 5/3x

Step-by-step explanation:

Solve for y. View image.

Answer:

Option 3)

[tex]x^3-9^3 = (x-9)(x^2 + 9x + 81)[/tex]

Step-by-step explanation:

We use the identities:

[tex]a^3 + b^3 = (a+b)(a^2-ab+b^2)\\a^3-b^3 = (a-b)(a^2+ab+b^2)[/tex]

1.

[tex](x + 7)(x^2 -7x + 14)[/tex]

It is not a sum or difference of cubes because it does not satisfies the identity.

2.

[tex](x + 8)(x^2 + 8x + 64)[/tex]

It is not a sum or difference of cubes because it does not satisfies the identity.

3.

[tex](x - 9)(x^2 + 9x + 81)\\\text{Comparing with the identity:} \\a^3-b^3 = (a-b)(a^2+ab+b^2)\\\text{We get}\\a = x\\b = 9\\x^3-9^3 = (x-9)(x^2 + 9x + 81)[/tex]

Thus, it can be expressed as a difference of cubes.

4.

[tex](x - 10)(x^2 - 10x + 100)[/tex]

It is not a sum or difference of cubes because it does not satisfies the identity.

Answer:

C

Step-by-step explanation:

Answer:Area is 50 cm^2

Step-by-step explanation:

Let L represent the length of the rectangle.

Let W represent the width of the rectangle.

The formula for determining the area of a rectangle is expressed as

Area = LW

The length of a rectangle Is twice the width of the rectangle. This means that

L = 2W

The length of a diagonal of the rectangle is 25cm. This is the hypotenuse of the right angle triangle that is formed. Applying Pythagoras theorem,

25^2 = L^2 + W^2 - - - - - - - 1

Substituting L = 2W into equation 1, it becomes

25^2 = (2W)^2 + W^2

25^2 = 4W^2 + W^2 = 5W^2

Taking square of both sides,

W = √25 = 5

L = 2W = 3×5 = 10

Area = LW = 10×5 = 50 cm^2

The length of a rectangle is twice the width. Using the Pythagorean Theorem, we can find the dimensions of the rectangle and calculate its area. Hence the final answer is 248 cm².

To find the area of a rectangle, we need to know both the length and the width of the rectangle.

Let's assume the width of the rectangle is 'w'.

According to the question, the length of the rectangle is twice the width, so the length of the rectangle is '2w'.

We can use the Pythagorean Theorem to find the length of the diagonal:

Using the formula a^2 + b^2 = c^2, where 'a' and 'b' are the length and width of the rectangle, and 'c' is the length of the diagonal, we can set up the equation:

w^2 + (2w)^2 = 25^2.

Simplifying the equation, we get: 5w^2 = 625

Dividing both sides of the equation by 5, we get: w^2 = 125

Taking the square root of both sides, we get: w = 11.18

The area of the rectangle is length times width, so the area is: 2w * w = 2 * 11.18 * 11.18 = 248.27

Rounding to the nearest integer, the area of the rectangle is approximately 248 cm².

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The limit of the given expression as x approaches negative infinity is 1. This is computed by simplifying and rationalizing the expression, then applying the limit, which leads to a result of 1.

To solve the given limit problem, we will first rationalize the expression. Given the expression as: (1-x⁴) / (x²+4x), we can simplify this by factoring out an x² from both the numerator and the denominator. The expression then becomes: (1/x²- 1) / (1+ 4/x). Taking the limit as x approaches negative infinity, we will have: lim (1/x² - 1)⁵/ (1+4/x)⁵. Factoring out x² from the numerator and x from the denominator, we have: lim (1 - 1/x^2)⁵/ (1+ 4/x)⁵ As x approaches negative infinity, the terms 1/x²and 4/x approaches 0, hence the limit becomes (1⁵)/(1⁵) = 1.

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The limit as x approaches -∞ of [(1 - x^4) / (x^2 + 4x)]^5 is -1. This is calculated by dividing each term in the fraction by x^2, and observing the resulting behaviours of the terms as x approaches -∞.

Finding the limit of a function as x approaches -∞ is a fundamental concept in Calculus. In order to find the limit of (1 - x^4) / (x^2 + 4x) all raised to the power of 5 as x approaches -∞, divide each term in the fraction by x^2. This results in Limit x → -∞ (1/x^2 - 1)((1 + 4/x)^-5). We then can observe that as x approaches -∞, the expression 1/x^2 and 4/x will become zero.

Consequently, the limit of the fraction is (-1)^5, which equals -1. As a result, the limit as x approaches -∞ of [(1 - x^4) / (x^2 + 4x)]^5 is -1. This limit-finding process works because of the application of laws of limits and the behaviour of polynomials, particularly their asymptotic behaviours as demonstrated in concepts like infinite limit and powers.

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Answer:

894.19 mi/hr

Step-by-step explanation:

Total distance of the trip = 3990 mi

Let the speed of the sound be 'x' miles per hour

Now,

Total distance = Speed × Time

Therefore,

According to the question

3,990 mi = [ ( x - 120 ) × 0.1 ] + [ ( x + 410 ) × 3.0 ]

or

3,990 mi = 0.1x - 12 + 3x + 1230

or

0.1x + 3x = 2772

or

3.1x = 2772

or

x = 894.19 mi/hr

Answer:

293 feet

Step-by-step explanation:

The distance the wire is attached in the tower is 200 feet

the angle between the wire and the tower is 47 degrees

The length of the wire (x) is the hypotenuse of the triangles formed

The formed triangle is a right angle triangle

For 47 degree angle the adjacent side is 200 feet and hypotenuse is x

[tex]cos(theta)=\frac{adjacent}{hypotenuse}[/tex]

[tex]cos(47)=\frac{200}{x}[/tex]

Cross multiply it

[tex]xcos(47)= 200[/tex]

divide by cos on both sides

[tex]x=\frac{200}{cos(47)}[/tex]

x=293.25 feet

Answer:

Step-by-step explanation:

1.

A

2.

A

3.

A

4.

Let the number=x

double=2x

add 6

2x+6

divide by 2

(2x+6)/2=x+3

subtract 3

x+3-3=x

which is the original number

(2x+6)/2-3=x+3-3=x

Answer:

The Amount after 18 years is $66,942,391.5

Step-by-step explanation:

Given as :

The principal invested in saving bond = p = $150

The Time period for the bond = t = 18 years

The rate of interest applied on bond = 106%

Let The Amount after 18 years = $A

Now, From compound interest

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or, A = $150 × [tex](1+\dfrac{\textrm 106}{100})^{\textrm 18}[/tex]

Or, A = $150 × [tex](2.06)^{\textrm 18}[/tex]

Or, A = $150 × 446,282.61

∴ A = $66,942,391.5

So,The Amount after 18 years = A = $66,942,391.5

Hence,The Amount after 18 years is $66,942,391.5 Answer

Answer:

A. 2.8 minutes

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Solution to the problem

Let X the random variable that represent the length of time it takes a college student to find a parking spot in the library parking of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(3.5,1)[/tex]  

Where [tex]\mu=3.5[/tex] and [tex]\sigma=1[/tex]

And we need to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.758[/tex]   (a)

[tex]P(X<a)=0.242[/tex]   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.242 of the area on the left and 0.758 of the area on the right it's z=-0.700. On this case P(Z<-0.700)=0.242 and P(z>-0.700)=0.758

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.242[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.242[/tex]

But we know which value of z satisfy the previous equation so then we can do this:

[tex]z=-0.700<\frac{a-3.5}{1}[/tex]

And if we solve for a we got

[tex]a=3.5 -0.700*1=2.8[/tex]

So the value of height that separates the bottom 24.2% of data from the top 75.8% is 2.8 minutes.  

The point in time where 75.8% of students exceed when finding a parking spot is calculated using Z-scores in a normal distribution. The time is approximately 2.8 minutes.

The process to find the point in the distribution where 75.8% of the students exceed the required time to find a parking spot in the library parking lot is essentially to calculate the Z-score corresponding to a given cumulative probability (or area) in the standard normal curve.  If the area to the left of the Z-score is 75.8%, then the area to the right of the Z-score is 100%-75.8% = 24.2%.

We then find the Z-score corresponding to 24.2% in the Z-tables. In this case, the corresponding Z-score is approximately -0.7 (since the tables usually give the area to the left, and we are dealing with the area to the right of the Z-score, we consider the negative of the found Z-score).

To convert this back to the time it takes to find a parking spot, we use the formula for converting Z-scores back to raw scores: X = μ + Zσ, where X is the raw score (time to find a parking spot), μ is the mean time to find a parking spot, Z is the Z-score, and σ is the standard deviation of the time to find a parking spot.

Substituting the given values, we get X = 3.5 + (-0.7)*1 = 2.8.

Thus, the time at which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot is 2.8 minutes (option A).

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the reason that these are inverses is because if you switch x with z

and g(f(x))=x, then (x-9)/(x+5) is (z-9)/(z+5)=x. which implies that:

(z+5) - 14/(z+5)=1-(14/(z-5))=x.

(1/(1 - x) * 14) + 5 = z = g(x) maybe i messed up?

Step-by-step explanation:

f(x) = (x − 9) / (x + 5)

g(x) = (-5x − 9) / (x − 1)

To find f(g(x)), substitute g(x) into f(x).

f(g(x)) = [(-5x − 9) / (x − 1) − 9] / [(-5x − 9) / (x − 1) + 5]

Multiply top and bottom by x − 1.

f(g(x)) = [(-5x − 9) − 9(x − 1)] / [(-5x − 9) + 5(x − 1)]

Simplify.

f(g(x)) = (-5x − 9 − 9x + 9) / (-5x − 9 + 5x − 5)

f(g(x)) = (-14x) / (-14)

f(g(x)) = x

To find g(f(x)), substitute f(x) into g(x).

g(f(x) = [-5(x − 9) / (x + 5) − 9] / [(x − 9) / (x + 5) − 1]

Multiply top and bottom by x + 5.

g(f(x) = [-5(x − 9) − 9(x + 5)] / [(x − 9) − (x + 5)]

Simplify.

g(f(x) = (-5x + 45 − 9x − 45) / (x − 9 − x − 5)

g(f(x) = (-14x) / (-14)

g(f(x) = x

The coordinates provided represent vertices of a triangle on a 2-dimensional grid like a city map. Visualizing the points and connecting them creates a right triangle. Vectors can express the sides of this triangle in terms of magnitude and direction.

This is a problem pertaining to geometry and the use of coordinate systems. In the question, we're given vertices of a triangle on a coordinate grid. The coordinates, (1, 1), (1, 4), and (-3, 4), denote specific points on this two-dimensional grid system. Just as in a city map, these coordinates help define the exact location of the points in a well-defined and universally understood manner.

To visualize the triangle formed by these coordinates on a city map, we can consider (1, 1) as a starting point. From this point, move 3 units north to reach (1, 4), then move 4 units to the left to reach (-3, 4), and finally move back 3 units south to reach the starting point (1, 1). This forms a right triangle, with (1, 4) as the right-angle vertex.

Similar to the concept of directional travel mentioned in the supplementary text, vectors can also be utilized in such coordinate systems to describe movement or distance between different points on the map. In our triangle example, each side of the triangle can be represented by a vector, with its magnitude (length) and direction.

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To find the area of the triangle park, we can calculate the lengths of the sides using the distance formula and then use Heron's formula to find the area. The area of the triangle park is 6 square units.

The given question is about a city planner mapping out a triangle park on a grid paper using coordinates. The vertices of the park are given as (1, 1), (1, 4), and (-3, 4). The subject of this question is Mathematics, and the grade level is High School.

To find the area of the triangle park, we can use the formula for the area of a triangle. We connect the vertices with line segments and calculate the lengths of the sides. Then, using the Heron's formula, we can calculate the area.

First, we calculate the lengths of the sides using the distance formula. The length of AB is sqrt((1-1)^2 + (4-1)^2) = sqrt(9) = √9 = 3. The length of BC is sqrt((1-(-3))^2 + (4-4)^2) = sqrt(16) = √16 = 4. The length of AC is sqrt((1-(-3))^2 + (4-1)^2) = sqrt(25) = √25 = 5.

Next, we use Heron's formula to calculate the area. Heron's formula states that the area of a triangle with side lengths a, b, and c is given by: Area = sqrt(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (s = (a+b+c)/2).

In this case, a = 3, b = 4, and c = 5. Therefore, s = (3+4+5)/2 = 12/2 = 6. Plugging in the values, the area of the triangle is given by: Area = sqrt(6(6-3)(6-4)(6-5)) = sqrt(6*3*2*1) = sqrt(36) = √36 = 6.

Therefore, the area of the triangle park is 6 square units.

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Final answer:

The common multiple of the heights of the two stacks is 72 inches which will also be the same height of stack

Explanation:

The boxes that are being stacked have different heights - 18 inches and 24 inches. To find the shortest height at which the two stacks will be the same height, we need to determine the common multiple of 18 and 24.

18 and 24 have a common multiple of 72. Therefore, the two stacks will be the same height when they reach 72 inches.

Answer: The shortest height at which the two stacks will be the same height is 72 inches.

Answer:

Step-by-step explanation:

A geometric sequence is a sequence in which the successive terms increase or decrease by a common ratio. The formula for the nth term of a geometric sequence is expressed as follows

Tn = ar^(n - 1)

Where

Tn represents the value of the nth term of the sequence

a represents the first term of the sequence.

n represents the number of terms.

From the information given,

r = 1/3

T3 = - 81

n = 3

Therefore,

- 81 = a× 1/3^(3 - 1)

-81 = a × (1/3)^2

-81 = a/9

a = -81 × 9 = - 729

The exponential equation for this sequence is written as

Tn = - 729 * (1/3)^(n-1)

Answer:

[tex]t(n)=-729(\frac{1}{3}) ^{n-1}[/tex]

Step-by-step explanation:

Given:

A geometric sequence with third term = -81

Common ratio = [tex]\frac{1}{3}[/tex]

General term of a geometric sequence is given by the formula:

[tex]t(n)=ar^{n-1}[/tex]

where :

t(n) is nth term

a is the first term

r is the common ratio

n=1,2,3,4...

Here r=1/3 and t(3)=-81

[tex]ar^{2}=-81\\a\times\frac{1}{3}^{2}=-81\\a=-729[/tex]

General equation becomes:

[tex]t(n)=-729(\frac{1}{3}) ^{n-1}[/tex]