Tell whether it shows growth or decay and graph by using a table of values

The working equation when dealing with problems regarding compounded interest is

where A is the future value, P is the principal value, r is the annual rate, and n is the number of compounding periods.

The problem compounds quarterly, hence, we have n = 4.

We derive the working equation to solve for t, as follows:

Substitute the values of A, P, n, and r on the derived equation above and solve for t, we get

Therefore, the $4000 investment grows to $5780 in 9.25 years.

The percentage increase when the price of an item increased is 30%.

From the information, the price of an item yesterday was $130 and today, the price rose to $169.

The increase in the price will be:

= $169 - $130

= $39

Therefore, the percentage increase will be:

= Increase in price / Original price × 100

= 39 / 130 × 100

= 30%

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Answer:

Multiplying a quantity by a conversion factor changes the units that measure a quantity but does not change the original amount of the quantity.

Step-by-step explanation:

There is no explanation

His lifetime earnings when he retires at the age of 68 is $2,817,385.1728.

The total number of years Demarcus will work is 68 - 24 = 44 years.

Now, there are about 52.1429 weeks per year; therefore, the number of weeks in 44 years will be:

44 years × 52.1429 weeks/year = 2294.2876 weeks

We are also told that Demarcus gets paid once every two weeks; this means the number of payments made in 44 years will be:

2294.2876 / 2 = 1147.1438 payments

Since each payment is worth $2,456.00, the total amount earned from 1147.146 payments will be:

1147.146 payments × 2456 per payment = $2,817,385.1728

Hence, Demarcus' lifetime earnings if he retires at the age of 68 will be $2,817,385.1728.

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among all rectangles that have a perimeter of 48 Then the  dimensions of the one whose area is largest is 12 by 12

The formula for calculating the perimeter of a rectangle is expressed as:

P = 2(L + W)

L is the length of the rectangle

W is the width

Given that the perimeter is 156, hence;

2(L + W) = 48

2L + 2W = 48

L + W = 24

W = 24 - L

The area of the rectangle is expressed as:

A = LW

A = L(24-L)

A = 24L - L^2

To get the dimensions of the one whose area is largest, dA/dL = 0

dA/dL = 24 - 2L

0 = 24 - 2L

2L = 24

L = 24/2

L = 12

Recall that 2(L+W) = 48

2(12 + W) = 48

12 + W = 24

W = 24 - 12

W = 12

Hence the dimensions of the one whose area is largest is 12 by 12

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Answer:

p=1

Step-by-step explanation:

p(6+1.5n)=18+4.5n

6p+1.5np = 18+4.5n

18p+4.5np=18+4.5n

p=1

:]

Answer:

i think y=1/2x+1 or y+3=1/2 times (x+8)

Step-by-step explanation:

The values of the inequality -d ≥ 7 are  -12, -8 and -7.1

The inequality is

-d ≥ 7

The inequality is the equation that shows the relationship between the numbers or algebraic expression. The relationship maybe greater than, greater than or equal, less than, less than or equal. In inequality there is no equal relationship.

The given inequality is

-d ≥ 7

Divide both sides of the given inequality  by -1

-d/-1 ≥ 7/-1

d ≤ -7

Therefore the value of d is less than -7

So the values are -12, -8 and -7.1

Hence, the values of the inequality -d ≥ 7 are  -12, -8 and -7.1

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[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{ - 8 - 5}{ - 8 - ( - 2)} \\ m = \frac{ - 13}{ - 8 + 2} \\ m \frac{ - 13}{ - 6} \\ m = \frac{13}{6} [/tex]

ATTACHED IS THE SOLUTION.

I also provided you with the formula to calculate the slope between the points.

formula to calculate the slope between the points.GOODLUCK

After finding the probability we find that 0.04 students are left-handed from the 209 students randomly selected from the campus.

11 % of the population is left-handed so here we have to find the probability of left-handed students if 209 random students are selected from 5225 students on campus here Favorable outcome is 209 and the total outcome is 5225, so the favorable outcome upon the total number of the outcome.

According to the probability formula :

Probability = [tex]\frac{favorable outcome}{Total number of outcome}[/tex]

Probability = 209 / 5225

After diving the above equation we find that 0.04 students are left-handed from the 209 students randomly selected from the campus.

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1. The cheapest meat is Ms barker free Ronge whole chicken in $6 per kilo.

2. The cost of 200 grams of honey leg ham is $3.4.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The cost of all meat is shown in figure.

Now,

By the figure, we get;

The cheapest meat is Ms barker free Ronge whole chicken which is in

$6 per kilo.

And, The cost of honey leg ham = $17 per kilo

Since, 1 kilograms = 1,000 grams

The cost of 1 gram of honey leg ham = $17/1000

So, The cost of 200 grams of honey leg ham = 200 × 17 / 1000

                                                                      = $3.4

Thus,

1. The cheapest meat is Ms barker free Ronge whole chicken in $6 per kilo.

2. The cost of 200 grams of honey leg ham is $3.4.

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The equation for Kilberly's running or walking will be R+4w ≤ 6.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that For Kimberly's P.E final she must either walk or run at least 5 miles this week. She knows it would take her 15 minutes to run a mile and 40 minutes to walk a mile, Kimberly only has 6 hours in which she must accomplish this final.

Let the running is represented by 'R' and walking by 'w". The equation will be written as below:-

R + 4W ≤ 6

Put the running and walking times in the equation above.

15 + ( 4 x 40 ) ≤ 6

175 minute ≤ 6 x 60

175 minutes ≤ 360 minutes.

Therefore, Kimberly covers the distance in less than 6 hours.

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A) The end behavior of the polynomial graph is that;

as x → -∞, y → -∞, and as x → ∞, y → ∞

B) The given graph polynomial represents an even degree polynomial.

The end behavior of the graph of a polynomial function is the behavior of the graph of as approaches positive infinity or negative infinity.

Now, we see from the graph that as x approaches a larger value, y values are getting increasingly negative. This means that as x approaches negative infinity, the values of y approach negative infinity.

In a similar approach, we can see that as the values of x approach positive infinity, the values of y also approach positive infinity.

Thus, we can say that option  D is correct.

B) Odd-degree polynomial functions, are those that have graphs that extend diagonally across the quadrants while even-degree polynomial functions are those that have graphs that open upwards or downwards.

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Answer:

Step-by-step explanation:

-11+?=15

?=15+11

15+11= 26

So, -11+26=15.

?-(-3)= 5

?+3=5

?=5-3

?=2

So, 2-(-3)=5.

?+(-4)=7

?-4=7

?=7+4

?=11

So, 11+(-4)=7.

?+-8=3

?=3+8

?=11

So, 11+-8=3.

-2+?=1

?=1+2

?=3

So, -2+3=1.

?-12=-4

?=-4+12

?=8

So, 8-12=-4.

The population of rabbits by the year 2023  is 13985.

We have to use the following exponential function. This will be:

y = a b^t

In 2008 means, t=0

So we have 7100 = a b^0

a = 7100

y = 7100b^t

In 2013 means t = 2013-2008 =5

8900 = 7100 b⁵

b⁵ = 89/71

b = 1.046

So the equation will be

y = 7100 (1.046)^t

For 2023, t=2023-2008= 15

y = 7100(1.046)¹⁵

= 13985

The population is 13985.

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Answer: Equation is x+45 = 90

It solves to x = 45

Explanation:

The two angles are complementary, which by definition means they join together to form a right angle. The two pieces x and 45 add to 90 degrees.

To solve the equation x+45 = 90, we subtract 45 from both sides to get x = 45.

As a check x+45 = 45+45 = 90.

The base length of triangle for the store is b ≤ 5in.

Having three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object.

A polygon also includes a triangle.

Triangle's characteristics:

Given:

height of triangle(h)=4in

Area of triangle(A)≤ 10in²

let base length of triangle be b

Area of triangle is given by:

Area = (1/2) × base × height

(1/2) × b × 4 ≤ 10

2b ≤ 10

b ≤ 5 in

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From the scatter plot of sales of Ceiling Fan in relation to Temperature.

(a) We are asked to characterized the money spent on Ceiling Fan to Temperature.

The relationship between the money spent on Ceiling Fan and Temperature is positive correlation.

When the y variable tends to increase as the x variable increases, we say there is a positive correlation. Which we can see in the scatter plot in the question.

(b) using the function y = 20x + 0, we are to find the predicted amount of sales if temperature is 21 degrees Celsius.

With the function:

y = 20x + 0

When Temperature is 21 degrees that means x = 21

So let's input x = 21 into the given function.

y = 20(21) + 0

y = 420 + 0

y = 420

Therefore, the predicted amount of sales when Temperature is 21 degrees Celsius is $420.

(c) What does the number 0 in the function mean in the contest of this situation?

In a linear interpretation which the function represents, the number 0 can be seen as the y intercepts of the function.

The ending balance for a amount of Rs. 341,000 with a interest rate of 4% for the time period of 3 years is Rs. 381920.  

What is interest?

In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principal amount (the amount borrowed).

Information given in the question,

Principle amount = 341,000

Time period = 3 years

Interest rate is 4 % which can be written as 0.04 in decimals.

We can calculate the ending balance using this formula formula for simple interest:

[tex]S.I. = Principle \times Interest \times time[/tex]

Putting the values given in the question

S.I. = (341000)(0.04)(3)

S.I. = 40,920

Interest is 40,920.

The ending balance is the sum of Principle amount and Interest. So,

ending balance = 341000+40920

ending balance = 381920  

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In the given figure,

(7x + 73) + (10x + 22) = 180 ........(Because they are linear pair)

⇒ 7x + 73 + 10x +22 = 180

⇒ 17x + 95 = 180

⇒ 17x = 180-95

⇒ 17x = 85

⇒ x = 85/17

⇒ x = 5

Now, 7x +73 = z ....................(Because they are vertically opposite angles)

⇒ 7 x 5 + 73 = z

⇒ z = 35 + 73

⇒ z = 108°

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Answer:

0 miles driven:$45, 1 miles driven:$47.5, 2 miles driven:$50, 3 miles driven:$52.5

Step-by-step explanation:

Answer: 0.195

Step-by-step explanation:

A t-shirt and a pair of shorts cost $29.75 together. jason paid $228.55 for 12 t-shirts and 5 shorts. Then ted pay for 2 t-shirts and 4 pairs of shorts is $59.4

A t-shirt and a pair of shorts cost $29.75 together.

jason paid $228.55 for 12 t-shirts and 5 shorts.

how much will ted pay for 2 t-shirts and 4 pairs of shorts

let T denote for t shirt and S denote for shorts

then T+ 2S=29.75

       12T+ 5S=228.55

solving these equation

multiply by 12 in 1 , we get

12T+ 24S= 357

12T+ 5S=228.55

substract these two equation we have

19S=128.45

S= 6.76

we can substitute in 1 we get

T + 13.52 =29.75

T=16.23

Hence , 2T + 4S = 32.46+27.04=59.4

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5.25 pounds of mashed potatoes is required to fill the container.

In the question, we were told the container was 4/6 filled and the chef used  3 2/4 pounds which is equal to 14/4 pounds of mashed potatoes.

In doing this, we are calculating the volume of the container.

Let's equate this and find how many pounds will fill the container.

[tex]\frac{4}{6}fill = \frac{14}{4} pounds\\ 1 fill = x pounds[/tex]

Let's cross multiply both sides and solve for x.

[tex]\frac{4}{6}fill = \frac{14}{4} pounds\\1 = x pounds\\x = \frac{1 * \frac{14}{4} }{\frac{4}{6} }\\x = \frac{21}{4} = 5.25 pounds[/tex]

To fill the container, we need 5.25 pounds of mashed potatoes.

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The range of the exponential function f(x) is 1 / 32 ≤ f(x) ≤ 16.

Exponential functions are monotonous functions, that is, functions that are increasing or increasing but never both. Functions are defined by the following three features:

In this problem we find a function with an input variable (x) and an output variable (f(x)). Since exponential functions are monotonous functions we can determine the bounds of the range by the function evaluated at x = - 5 and x = 4. Thus:

f(- 5) = 2⁻⁵

f(- 5) = 1 / 2⁵

f(- 5) = 1 / 32

f(4) = 2⁴

f(4) = 16

The range of the function f(x) = 2ˣ for - 5 ≤ x ≤ 4 is 1 / 32 ≤ f(x) ≤ 16.

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If the area of the rectangular billboard covered by the ribbon was approximately 3360 square feet, and the width of the billboard was approximately 56 feet, the height of the billboard would be 71.25 feet.

The exact measurement that helps to express the size of a region on a plane or curved surface is thus called as area.

Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

In mathematical terminology, area can be defined as the total space that is taken up by a flat (2-D) surface or shape of a present object.

Here the area of the billboard = 3360 sq feet

Width of the billboard = 56 feet

We know that

area of the billboard = Height of the billboard x Width of the billboard

⇒ Height of the billboard = [Area of the billboard] / [Width of the billboard]

⇒ Height of the billboard= 3360/56

⇒ Height of the billboard = 71.25 feet

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The function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.

If g(x) is the inverse of f(x), 2 is the value of f(g(2)).

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.

The function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.

Given

[tex]&x \rightarrow f(x) \\[/tex]

[tex]&-6 \rightarrow 1 \\[/tex]

[tex]&-3 \rightarrow 2[/tex]

[tex]$$g(x)=f^{-1}(x)[/tex] inverse

To find the value of f(g(2)).

For two functions f(x) and g(x) where f(x) and g(x) are inverse; f(g(x))=x

So, by comparison: f(g(2)) = 2.

Therefore, the inverse of the function f(g(2)) = 2.

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If we solve for the value of x using the graph we get the coordinates of X as X( [tex]\frac{21}{4}[/tex] , [tex]\frac{35}{4}[/tex] ).

What is the linear equation with two variables ?

A linear equation with two variables is any equation that can be expressed in form ax + by + c = 0, where a, b, and c are all real values.

The given equation is a form of linear equation with two variables.

The equation is 16x + 28y = 112.

From graph it is clear that coordinates of Y are Y(1 , -1).

So , let's check for the value of x by putting the values of y in given expression.

i.e.,

The resulted equations will be :

16 x + 28 (1) = 112

or

16x + 28(-1) = 112

So ,

16 x + 28 = 112    --- -- -- ----- ----- ---- ---- ---- ---- ---- ---- ---- Equation 1

16x - 28 = 112     --- -- -- ----- ----- ---- ---- ---- ---- ---- ---- ---- Equation 2

The values of x will be :

x = 84 / 16 = 21 / 4

or

x = 140 / 16 = 35 / 4

The coordinates of X will be X([tex]\frac{21}{4}[/tex] , [tex]\frac{35}{4}[/tex] ).

Therefore , solving for the value of x using the graph we get the coordinates of X as X( [tex]\frac{21}{4}[/tex] , [tex]\frac{35}{4}[/tex] ).

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