Clinton is having a coin drive. Each class has a goal of 600 pennies.Layla has already collected 338 pennies. How many more pennies does Layla need to collect to reach their goal. PLEASE SHOW YOUR WORK I WILL MARK YOU BRAINLIEST PLEASE AND EXPLAIN HOW YOU GOT YOUR ANSWER

Answers

Answer 1

Answer:

262 pennies

Step-by-step explanation:

If Layla already has 388 pennies and she needs 600 pennies total, all she needs to do is is take the amount she already has away from 600:


Related Questions

Find the value of y.
148°
y
x
y = [?]°

Answers

Answer:

y=90 degree

Step-by-step explanation:

bcz this triangle is drawn in the semi-circle and the greatest angle of triangle in a semi-circle is always right angle.

Charles has 24 marbles. He has 6
more yellow marbles than blue marbles.
Which equation represents this situation?

Answers

Answer:

6+x=24

Step-by-step explanation:

he has 6 more marbles than the blue

the amount of blue marbles is unknown

so let blue marble be x

we know that the total number of marbles is 24

so 6+x=24

I NEED HELP WITH THIS QUESTION PLEASE ? :(

Answers

Answer:

x=42

Step-by-step explanation:

Please answer this question now

Answers

Answer:

95 degrees

Step-by-step explanation:

Measure of arc AB is 360 - (101+97+69) = 360 - 267 = 93 degrees.

Measure of arc DAB is 97+93 = 190 degrees, so measure of angle C is 190/2 =  95 degrees.

Joey's pizza sells large cheese pizzas for $12.00. Each additional topping costs $0.50. Basketball Boosters bought 12 large pizzas, each with 3 toppings. There are 8 slices per pizza. How much does it cost per slice? Round to the nearest cent.

Answers

Answer:

169 cent

Step-by-step explanation:

Given the following :

Cost of large pizza = $12

Cost of additional topping = $0.5

Number of large pizza purchased = 12

topping per large pizza = 3

Amount paid for each pizza :

(cost of pizza) + (3 * cost of topping)

($12) + (3*$0.5)

($12 + $1.5) = $13.5

Total cost of pizza:

Number of pizzas bought * cost per pizza

12 * $13.5 = $162

Number of slices per pizza = 8

Total slices = 12 * 8 = 96 slices of pizza

Cost per slice :

Total cost / total slices

$162 / 96 = $1.6875

= $1.69 = 169 cent

The common difference of an ap is -2 find its sum of first term is hundred and last term is -10 with full solution

Answers

Answer:

2520

Step-by-step explanation:

The n th term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference.

To find the number of terms given [tex]a_{n}[/tex] = - 10 , d = - 2 and a₁ = 100, then

100 - 2(n - 1) = - 10 ( subtract 100 from both sides )

- 2(n - 1) = - 110 ( divide both sides by - 2 )

n - 1 = 55 ( add 1 to both sides )

n = 56 ← number of terms

Given n, a₁ and a₅₆ , then the sun of the terms is

[tex]S_{56}[/tex] = [tex]\frac{n}{2}[/tex] (a₁ + a₅₆ )

      = [tex]\frac{56}{2}[/tex] (100 - 10) = 28 × 90 = 2520

(x+3)(x-5)=(x+3)(x−5)=

Answers

Answer:

All real numbers are solutions. 0=0

Step-by-step explanation:

(x+3)(x−5)=(x+3)(x−5)

Step 1: Simplify both sides of the equation.

x2−2x−15=x2−2x−15

Step 2: Subtract x^2 from both sides.

x2−2x−15−x2=x2−2x−15−x2

−2x−15=−2x−15

Step 3: Add 2x to both sides.

−2x−15+2x=−2x−15+2x

−15=−15

Step 4: Add 15 to both sides.

−15+15=−15+15

0=0

All real numbers are solutions.

La madre de rosita se ha comprado una mascarilla por un valor de 1 25 dolares al mismo tiempo se ha comprado un paquete de jabones de 2 00 dolares y luego compra un gel de alcohol en 3 00 dolares después de pagar le queda 7 65 dolares que debemos saber que tengo que hacer para obtener el resultaron

Answers

Answer:

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos es de $13.90

Step-by-step explanation:

La información dada son;

El valor de la máscara = $ 1.25

El valor del paquete de jabones = $ 2.00

El valor del gel de alcohol = $ 3.00

La cantidad que le quedaba después de pagar = $ 7.65

Por lo tanto, tenemos;

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = La cantidad que le quedaba después de pagar + El valor del gel de alcohol + El valor del paquete de jabones + El valor de la mascarilla

Por lo tanto;

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = $ 7.65 + $ 3.00 + $ 2.00 + $ 1.25 = $ 13.90.

if the Diameter of a cicle is 28cm calculate the perimeter

Answers

Answer:

Simple. 28pi

// pi is [tex]\pi[/tex].

Which is 88.0 by rounding tenth

Step-by-step explanation:

Please pick me brainliest.

Hope it helps!

Answer:

88 cm

Step-by-step explanation:

Perimeter = πd

= (22/7)× 28

= 88 cm

If a person invests $290 at 6% annual interest, find the approximate value of the investment at the end of 15 years. A. $450 B. $2030 C. $695 D. $707

Answers

Answer:

[tex]\large \boxed{\sf \bf \ \ C. \ \$ 695 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

At the beginning, we have $290.

After 1 year, we get 290 + 6% * 290 = 290 (1+0.06)= 290 * 1.06

After n years, we get [tex]290\cdot 1.06^n[/tex]

So after 15 years, we get.

[tex]290\cdot 1.06^{15}=695.0018...[/tex]

Thank you

The surface area, A, of a cylinder of radius, r, and height, h, can be found with the equation above. Which of the following correctly shows the cylinder's height in terms of its radius and surface area?

Answers

Step-by-step explanation:

If r and h are the radius and height of the cylinder, then its surface area A is given by :

[tex]A=2\pi r^2+2\pi rh[/tex] ....(1)

We need to find the cylinder's height in terms of its radius and surface area. Subtracting [tex]2\pi rh[/tex] on both sides, we get :

[tex]A-2\pi r^2=2\pi rh+2\pi r^2-2\pi r^2\\\\A-2\pi r^2=2\pi rh[/tex]

Dividing both sides by [tex]2\pi r[/tex]. So,

[tex]\dfrac{A-2\pi r^2}{2\pi r}=\dfrac{2\pi rh}{2\pi r}\\\\h=\dfrac{A-2\pi r^2}{2\pi r}[/tex]

Hence, this is the required solution.

24. Three minus four times a number is equal to ten times a number plus ten.
25. Four times the quantity of three times c plus 5 is equal to 8.
26. Six less than two thirds of a number is negative ten. Find the number.
27. Twenty-nine is thirteen added to four times a number. What is the number.

Answers

Answer:

(24) 3 - 4b = 10c + 10

(25) 4(3c+5) = 8

(26) - 6

(27) 4

Step-by-step explanation:

These questions require that words are translated into equations and then may be solved.

(24)  Three minus four times a number is equal to ten times a number plus ten.

let the first number be b.

(a)Three minus four times a number ... can be represented as:

3 - (4 x b) = 3 - 4b

(b) ...ten times a number plus 10

let the other number be c. Therefore we have;

(10 x c) + 10 = 10c + 10

Now, three minus four times a number is equal to ten times a number plus ten means that expressions in (a) and (b) above are equal. i.e

3 - 4b = 10c + 10

(25) Four times the quantity of three times c plus 5 is equal to 8.

(a) four times the quantity of three times c plus 5 can be represented as

4 x (3 x c + 5) = 4(3c + 5)

(b) ... is equal to 8. This means that the expression in (a) is equal to 8.

4(3c + 5) = 8

(26) Six less than two thirds of a number is negative ten. Find the number.

(a) six less than can be represented as:

- 6

(b) two thirds of a number can be represented as

([tex]\frac{2}{3}[/tex])x           [where x is the number]

(c) six less than two thirds of a number can thus be written as;

([tex]\frac{2}{3}[/tex])x - 6

(d) ... is negative 10 means that the expression is (c) above is equal to -10. i.e

([tex]\frac{2}{3}[/tex])x - 6 = -10

(e) Find the number.

The number can be found by solving for x in the expression in (d) above.

([tex]\frac{2}{3}[/tex])x - 6 = -10         [multiply through by 3]

2x - 18 = -30        [collect like terms]

2x = -30 + 18

2x = -12               [divide both sides by 2]

x = - 6

Therefore, the number is -6

(27) Twenty-nine is thirteen added to four times a number. What is the number.

(a) ... thirteen added to four times a number can be written as:

13 + 4b         [where the number is b]

(b) Twenty-nine is thirteen added to four times a number means that the 29 is equal to the expression in (a) above. i.e

29 = 13 + 4b

(c) Find the number.

The number can be found by solving for b in the expression in (b) above. i.e

29 = 13 + 4b        [collect like terms]

4b = 29 - 13

4b = 16                [divide both sides by 4]

b = 4

Therefore, the number is 4.

Which graph represents the solution to the system of equations? {x+2y=4 2x−y=1/2}

Answers

Answer:

Below

Step-by-step explanation:

I graphed the functions here

The graph is shown below:

What is graphing ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

The graph of a linear equation in one variable x forms a vertical line that is parallel to the y-axis and vice-versa, whereas, the graph of a linear equation in two variables x and y forms a straight line

As, per the given equations

x+2y=4 & 2x−y=1/2.

The document attached with the question shows the fourth graph correct.

The intersecting point of both line is (1, 1.5)

Learn more about graph here:

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what is the sum of the interior angles of a regular hexagon ​

Answers

Answer:

see below

Step-by-step explanation:

The sum of the interior angles of any polygon can be found with the formula 180(n - 2) where n = number of sides. In this case, n = 6 so the answer is 180(6 - 2) = 180 * 4 = 720°.

Answer:

The sum of the interior angles of a regular hexagon is 720°

Step-by-step explanation:

As we know that the sum of interior angle is 180(n-2). So the number of sides of hexagon is 6. Now, 180(6-2)=180*4=720°

Can anyone help idk how to do it

Answers

Answer:

Carl can type 450 words in 5 minutes at that rate.

Step-by-step explanation:

Every two minutes, carl can type 180 words. To find out how many words he can type in 1 minute, all we have to to is divide 180 by 2 to get 90wpm (words per minute)

if we multiply 90wpm by 5 Minutes, we get 450 words per minute

Answer: 450 words in 5 minutes

Step by step:
2+2=4
180+180=360
180/2=90
4+1=5
360+90=450

4. A car is priced at $7200. The car dealer allows a customer to
pay a one-third deposit and 12 payments of $420 per month.
How much extra does it cost the customer?

Answers

Answer:

$240 extra

Step-by-step explanation:

1/3(7200) + 12(420) = 2400 + 5040 = 7440

7440 - 7200 = 240

The customer had to pay 1720 extra.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A car is priced at $7200.

If the deposit is one third = 7200/3

                                          = 240

The amount after 12 payments will be

= 240 x 12

= 2880

total cost will be

= 2880 + 2400

= 5280

and, The customer had to pay extra amount

= 7200 - 5280

= 1720

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Find the slope of the line passing through the points (-9, -3) and (7,-7).
DI
DD
Undefined
$
?

Answers

Answer:

-1/4

Step-by-step explanation:

Slope = y/x - y1/x1

=> -7/7 - (-3/-9)

=> -7 +3 / 7+9

=> -4/16

=> -1/4

The slope for the given coordinates of points is -1/4.

What is the slope of straight line?

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference.

The negative slope indicates the rate of decrease while the positive shows the rate of increase.

The given points are (-9, -3) and (7,-7).

The general expression to find the slope for two points (x₁, y₁) and (x₂, y₂) is given as,

m = (y₁ - y₂)/(x₁ - x₂)

Plug (x₁, y₁) = (-9, -3) and (x₂, y₂) = (7, -7) to get,

⇒ m = (-3 + 7)/(-9 - 7)

⇒ -1/4

Hence, the slope is obtained as -1/4.

To know more about slope click on,

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when simplifying the expression y=(2x(x-3)(x-3))/(x-1)(x-3) do all of the x-3 s get cancelled or just one in the numerator and one in the denominator?​

Answers

Answer:

Just one of the ones in the numerator and the one in the denominator

Step-by-step explanation:

determine if the equation is a linear equation -x + 3y^2=18

Answers

Answer:

No

Step-by-step explanation:

Linear equations must have no squares, roots, cubes, or any powers. If the graph has an asymptote or any restrictions, it is not a linear function.

A linear function will only appear in either point-slope form or slope-intercept form. These forms will not have square roots or powers in them.

-x + 3y² = 18

We know here that this is not a linear function. But we can try to write it in slope-intercept form:

3y² = x + 18

y² = x/3 + 6

y = √(x/3 + 6)

We can see from here that our graph is a square root function and has a restricted domain (no negative numbers).

Alternatively, we can graph the equation to see if it is a constant line (linear equation) or not. When we do so, we see that it is definitely not a linear function:

MAKE EXAMPLES WHERE YOU USE THE DISCOUNT AND THE INCREASE OF PERCENTAGES

Answers

Answer:

once upon a time a dude went to a store. there was a dude jacket for 20% off.

Step-by-step explanation:

Now do the opposite. for exapmle, the price increased by 20 %.

Earnings per share, EPS is calculated using the formula \large EPS=\frac{NI-PD}{SO}, where NI is net income, PD is preferred dividence, and SO number of outstanding shares.

What is a company's net income if they have $50,000 in preferred dividends and pay out $0.55 per share on 200,000 shares?

Answers

Answer: $160,000

Step-by-step explanation:

Given the following :

Earning per share (EPS) = $0.55

Number of outstanding shares = 200,000

Preferred dividend = $50,000

EPS = (NET INCOME - PREFERRED DIVIDEND) / NUMBR OF OUTSTANDING SHARES

0.55 = ( NET INCOME - 50000) / 200000

200000 × 0.55 = NET INCOME - 50000

110,000 = NET INCOME - 50000

NET INCOME = 110,000 + 50,000

NET INCOME = $160,000

Autumn runs a farm stand that sells peaches and grapes. Each pound of peaches sells
for $2 and each pound of grapes sells for $4. Autumn sold 35 more pounds of grapes
than pounds of peaches and made $200 altogether. Graphically solve a system of
equations in order to determine the number of pounds of peaches sold, 2, and the
number of pounds of grapes sold, y.

Answers

Answer:

She sold 10 pounds of peaches and 45pounds of grapes

Step-by-step explanation:

X= pounds of peaches

x+35=pounds of grapes

2x+4(x+35)=200

2x+4x+140=200

6x=200-140

6x=60

x=10

She sold 10 pounds of peaches and 45pounds of grapes. (Sorry, can’t help you graph it.)

Mai is putting money into a checking account.Let Y represent the total amount of money in the account (dollars)Let X represent the number of weeks Mai has been adding money suppose that x and y are related by the equation 550+40x =y what is the change per week in the amount of money in the account ?

Answers

Answer:

The answer is $40.

Step-by-step explanation:

According to the equation given in the question, we can assume that 550 is constant and was there when Mai started saving into a checking account.

Then as x gets increased by 1 each week, the amount of change in the account per week is $40.

I hope this answer helps.

A study table of length 2 m and breath 1.25 m in decorted with square design of size 10x 10 find the number of such designs??? ​

Answers

Answer:

250

Step-by-step explanation:

Area of the shape of the table = Length * Breadth (Rectangular in nature)

Area of the study table = 2m * 1.25m

Converting the units to cm

Since 100cm is equivalent to 1m, hence;

Area of the study table = 200cm * 125cm

Area of the study table = 25000cm²

If the study table is decorated with square design of size 10cm x 10cm, then the area of one square of such design will be 100 cm².

The number of square designs = Area of the study table/area of one square design

= 25000/100

= 250

Hence the number of such design on the study table is 250

Please help i need this answered!!

Answers

Everything you answered so far looks good. Nice work.

For question 10, we need to find two numbers that multiply to 3(-1) = -3 and also add to 2. The 3 and -1 are the first coefficient and last term. The 2 is the middle coefficient.

Through trial and error, the two numbers we're after are 3 and -1

3 times -1 = -3

3 plus -1 = 2

We break up the 2x into 3x - 1x and factor like so...

3x^2 + 2x - 1

3x^2 + 3x - 1x - 1 ... replace 2x with 3x-1x

(3x^2+3x) + (-1x-1) ... pair up terms

3x(x+1) - 1(x+1) .... factor each parenthesis group

(3x-1)(x+1) ... pull out the gcf (x+1)

You can use FOIL, the box method, or distribution to go from (3x-1)(x+1) back to 3x^2+2x-1 again.

The answer to problem 10 is  (3x-1)(x+1)

Answer:

Step-by-step explanation:

WILL CHOOSE BRAINLIEST Let Events A & B be described as follows: P(A) = watching a movie P(B) = going out to dinner The probability that a person will watch a movie is 62% and the probability of going out to dinner is 46%. The probability of watching a movie and going out to dinner is 28.52% Are watching a movie and going out to dinner independent events? Group of answer choices No, because the P(A)P(B) ≠ P(A and B). Yes, because the P(A)P(B) = P(A and B). No, because the P(A) + P(B) ≠ P(A and B). Yes, because the P(A) + P(B) is greater than 100%.

Answers

Answer:

Yes, because the P(A)P(B) = P(A and B)

Step-by-step explanation:

Independent Events are events that occurs simultaneously i.e they occur at the same time. This means that the occurrence of one does not affect the other. If A and B are two events, for the to be independent then;

P(A and) = P(A)P(B)

Given: P(A) = watching a movie = 62% = 0.62

P(B) = going out to dinner = 46% = 0.46

The probability of watching a movie and going out to dinner will be

P(A and B)

P(A and B) = 0.62×0.46

P(A and B) = 0.2852

P(A and B) = 28.52%

Since the probability of watching a movie and going out to dinner is 28.52% which tallies with the question, hence it can be concluded that watching a movie and going out to dinner are independent events.

PLEASE HELP
Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square.

Answers

Answer:

perimeter is  4 sqrt(29) + 4pi  cm

area is 40 + 8pi cm^2

Step-by-step explanation:

We have a semicircle and a triangle

First the semicircle with diameter 8

A = 1/2 pi r^2 for a semicircle

r = d/2 = 8/2 =4

A = 1/2 pi ( 4)^2

  =1/2 pi *16

  = 8pi

Now the triangle with base 8 and height 10

A = 1/2 bh

  =1/2 8*10

  = 40

Add the areas together

A = 40 + 8pi cm^2

Now the perimeter

We have 1/2 of the circumference

1/2 C =1/2 pi *d

         = 1/2 pi 8

        = 4pi

Now we need to find the length of the hypotenuse of the right triangles

using the pythagorean theorem

a^2+b^2 = c^2

The base is 4 ( 1/2 of the diameter) and the height is 10

4^2 + 10 ^2 = c^2

16 + 100 = c^2

116 = c^2

sqrt(116) = c

2 sqrt(29) = c

Each hypotenuse is the same so we have

hypotenuse + hypotenuse + 1/2 circumference

2 sqrt(29) + 2 sqrt(29) + 4 pi

4 sqrt(29) + 4pi  cm

Step-by-step explanation:

First we need to deal with the half circle. The radius of this circle is 4, because the diameter is 8. The formula for the circumference of a circle is 2piR.

2pi4 so the perimeter for the half circle would be 8pi/2.

The area of that half circle would be piR^2 so 16pi/2.

Now moving on the triangle part, we need to find the hypotenuse side of AC. We will use the pythagoram theorem. 4^2+10^2=C^2

16+100=C^2

116=C^2

C=sqrt(116)

making the perimeter of this triangle 2×sqrt(116)

The area of this triangle is 8×10=80, than divided by 2 which is equal to 40.

We than just need to add up the perimeters and areas for both the half circle and triangle.

The area would be equal to 8pi+40

The perimeter would be equal to 4pi+4(sqrt(29))

The polygons are regular polygons. Find the area of the shaded region to the nearest tenth.

Answers

The area of the shaded region in the regular polygon is 161.3 cm²

What is a regular polygon?

A regular polygon is a polygon in which all the sides are equal.

From the diagram, the regular polygon is a square which is composed of a small square and a large square. In a square, all the sides are equal.

For the small square, half of the diagonal is 4 cm, therefore the length of the diagonal is 8 cm (2 × 4 cm). Let the length of the side be a cm, using Pythagoras theorem:

a² + a² = 8²

2a² = 64

a² = 32

a = √32 = 5.7 cm

The area of the small square = length × length = 5.7 × 5.7 = 32.5 cm²

For the large square, half of the diagonal is 9 cm, therefore the length of the diagonal is 18 cm (2 × 9 cm). Let the length of the side be b cm, using Pythagoras theorem:

b² + b² = 18²

2b² = 324

b² = 162

b = √162 = 12.7 cm

The area of the large square = length × length = 12.7 × 12.7 = 161.3 cm²

The area of the shaded region = Area of large square - Area of small square = 161.3 cm² - 32.5 cm² = 128.8 cm²

The area of the shaded region in the regular polygon is 161.3 cm²

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Answer:

it’s actually 130 or 130.0

Step-by-step explanation:

If you're good at exact values of trig ratios pea shell me with 13a

Answers

It is an equilateral triangle so its angles are equal 60°. From the definition, we know that:

[tex]\sin60^\circ=\dfrac{h}{4}[/tex]

and

[tex]\sin60^\circ=\dfrac{\sqrt{3}}{2}[/tex]

so

[tex]\dfrac{\sqrt{3}}{2}=\dfrac{h}{4}\quad \Big|\cdot4\\\\\\h=\dfrac{4\cdot\sqrt{3}}{2}\\\\\boxed{h=2\sqrt{3}}\\[/tex]

Answer:

h = √12

Step-by-step explanation:

use the Pythagorean

h² = 4² - 2²

h² = 16 - 4

h = √12

Please Help. Will Mark Brainliest Answer. A container of juice is taken from the refrigerator and poured into a pitcher. The temperature of the juice will warm to room temperature over time. The temperature of the juice can be modeled by the following function: f(t)=72−32(2.718)−0.06t, where t is measured in minutes after the juice is taken out of the refrigerator. Use the drop-down menus to complete the explanation of how the function models the juice warming over time. Dropdown possible answers: When t = 0, the temperature of the juice is -0.06, 0, 2.718, 32, 40, 72 degrees. As time increases, -32(2.718)^-0.06t gets close and closer to -0.06, 0, 2.718, 32, 40, 72. So, f(t) gets close and closer to -0.06, 0, 2.718, 32, 40, 72.

Answers

Answer:

When t= 0

f(t)= 40 degrees

The value of −32(2.718)^−0.06t approach 0 as t increases

If −32(2.718)^−0.06t approach 0 as t increases then f(t)=72−32(2.718)−0.06t approach 72

Step-by-step explanation:

The temperature of the juice can be modeled by the following function: f(t)=72−32(2.718)−0.06t, where t is measured in minutes after the juice is taken out of the refrigerator.

f(t)=72−32(2.718)^−0.06t

When t= 0

f(t)=72−32(2.718)^−0.06(0)

f(t)=72−32(2.718)^(0)

f(t)=72−32(1)

f(t)=72−32

f(t)= 40 degrees

As t increases −32(2.718)^−0.06t

Let t= 1

=−32(2.718)^−0.06(1)

= −32(2.718)^−0.06

= -30.14

Let t = 2

=−32(2.718)^−0.06(2)

=−32(2.718)^−0.12

=−32(0.8869)

= -28.38

The value of −32(2.718)^−0.06t approach 0 as t increases

If −32(2.718)^−0.06t approach 0 as t increases then f(t)=72−32(2.718)−0.06t approach 72

When t = 0, the temperature of the juice is 40°.

                    As time increases, [tex]-32(2.718)^{-0.06\times 0}[/tex] gets closer and closer to 0.

                    So, f(t) gets close to 72°

    Function representing the temperature of of the juice at any time 't' is,

[tex]f(t)=72-32(2.718)^{-0.06t}[/tex]

1). If t = 0,

  [tex]f(0)=72-32(2.718)^{-0.06\times 0}[/tex]

          [tex]=72-32(1)[/tex]

          [tex]=40[/tex] degrees

2). If [tex]t\rightarrow \infty[/tex],

    [tex]-\frac{1}{32(2.718)^{0.06t}} \rightarrow 0[/tex]  

[As denominator of the fraction becomes larger and larger with the increase in the value of t, value of fraction gets smaller and smaller]

3). if [tex]t\rightarrow \infty[/tex], [tex]f(t)\rightarrow 72[/tex]

  Therefore, when t = 0, the temperature of the juice is 40°.

                    As time increases, [tex]-32(2.718)^{-0.06\times 0}[/tex] gets closer and closer to 0.

                    So, f(t) gets close to 72°.

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