Georgina was given that the length of the rectangle was 2.5 inches longer than its width, and that the perimeter of the rectangle was 75.4 inches. Algebraically, find the length and width of the rectangle.

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

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:

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:

Option A) (x, y) = (4, -3)

Step-by-step explanation:

we know that

A function is a relation from a set of inputs (independent variable) to a set of possible outputs (dependent variable) where each input is related to exactly one output

we know that

The set of the function is { (-4, 2), (3, 6), (4, 3), (x, y) }

The ordered pair (x, y) = (4, -3)

could not be included, because for the input value of x=4, the function would have two output values (y=-3,y=3) and remember that each input is related to exactly one output

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:

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.

At t = 4, the distance traveled is 68 miles. This means that after the break, Joanna traveled 48 miles.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The linear function is given below.

d(t) = 12t + 20

The distance traveled when t = 4 is calculated as,

d(4) = 12 x 4 + 20

d(4) = 48 + 20

d(4) = 68 miles

So, at t = 4, the distance traveled is 68 miles. This means that after the break, Joanna traveled 48 miles.

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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]

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

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:

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 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.

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: the low temperature on Tuesday is 0 degree Fahrenheit

Step-by-step explanation:

The low temperature on Monday was 6 degrees warmer than Sunday's low of -9°F. This means that the temperature on Monday would be

- 9 + 6 = - 3 degrees Fahrenheit

The low temperature on Tuesday was 3 degrees warmer than Monday's low temperature. This means that the low temperature on Tuesday would be

- 3 + 3 = 0 degree Fahrenheit

Final answer:

By sequentially adding the temperature differences to each day's low, we find that Sunday's low was -9°F, Monday's was -3°F, and Tuesday's was 0°F.  So the low temperature on Tuesday was 0°F.

Explanation:

The student's question involves calculating temperature changes over consecutive days. Here's the step-by-step explanation:

The low temperature on Sunday was -9°F.

Monday's low was 6 degrees warmer than Sunday's, so we add 6 to -9°F, resulting in -3°F for Monday's low.

Tuesday's low was 3 degrees warmer than Monday's, so we add 3 to -3°F, which is 0°F.

Therefore, the low temperature on Tuesday was 0°F.

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:

  see attached

Step-by-step explanation:

For the figure A, the figure is symmetrical about a vertical line through its center. It has line symmetry.

__

For the figure O, it is symmetrical about both vertical and horizontal lines, as well as being symmetrical about its center point. It has line and point symmetry.

Answer: the number is 3

Step-by-step explanation:

Let the number be represented by x.

If 4 more than 4 times a certain number is the same as 4 more than the product of 3 and 4, it means that

4x + 4 = 4 + 3×4

4x + 4 = 4 + 12

4x + 4 = 16

Subtracting 4 from the left hand side and the right hand side of the equation, it becomes

4x + 4 - 4 = 16 - 4

4x = 12

Dividing the left hand side and the right hand side of the equation by 4, it becomes

x = 12/4 = 3

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:

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.

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: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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Answer:

y = -5/3 + 5/3x

Step-by-step explanation:

Solve for y. View image.

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.

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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.

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: x = 28/33, y = 25/23

( 28/23, 25/23)

Step-by-step explanation:

3x + 4y = 8 ----------------------(1)

-2x + 5y = 3 ---------------------(2)

Using elimination method

Consider the coefficient of y in equation 1 and 2

Therefore multiply as follows

(1) x 5 -------- 15x + 20y = 40.

(2) x 4 -------- -8x + 20y = 12

Therefore carry out subtraction on the two equations

23x + 0y = 28

23x = 28

x = 28/23.

Now substitute for x in any of the equations above to get y

3(28/23) +4y = 8

84/23 +4y = 8

Multiply through by 23 to have s simple linear equation

84 + 92y = 184

Collect like terms

92y = 184 - 84

92y = 100

y = 100/92

Reduce to lowest term by dividing by 4

y = 25/33.

(28/23, 25/23)------ solution

Check

Substitute for x and y values in any equations above.

3(28/23) + 4(25/23)

84/23 + 100/23

Resolved into fraction with 23 as the common LCM

184/23

= 8

Answer:

Solar Eclipse will required 30 mins to travel Distance of 1150 miles.

Step-by-step explanation:

Given:

Total Distance = 2300 miles

Time required = 1 hr

we will convert hour in minutes.

1 hr = 60 mins

hence Time = 60 mins

We need to find the time required to travel 1150 miles.

We will first find the speed at which solar eclipse travels.

Speed can be calculated by dividing Distance with time.

Speed = [tex]\frac{Distance}{time}[/tex]

Substituting the values we get;

Speed = [tex]\frac{2300}{60}=38.33\ mi/hr[/tex]

Now to find Time required to travel 1150 miles we will divide 1150 miles with Speed.

Time required to travel 1150 miles = [tex]\frac{1150}{38.33}= 30\ mins[/tex]

Hence Solar Eclipse will required 30 mins to travel Distance of 1150 miles.

Answer:

$1,828,669

Step-by-step explanation:

For the original lump sum of $28,000 is our principal, P, the annual interest rate r, compounded monthly for n=12 months throughout  a period of 35 years (t) will have a final Accrued Amount of investment A given by the formula:

A= (Principal + Interest)  = P(1 + r/n)^nt  =28000(1+0.12/12)^35*12

=28000(1.01)^420=

28000*65.3096= $1828669

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:

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