A certain element has a half-life of approximately 15 hours. How long would it take
for 500 grams of the element to decay to 299 grams? Leave your answer as an integer
or simplified expression.

Answers

Answer 1

Using an exponential decay equation, we will see that after 11 hours the element will decay to 299 grams.

How long takes to decay?

We know that we have an element with a half-life T, and it has a decay equation that can be written as:

f(t) = A*e^(-t*ln(2)/T)

Where A is the initial amount of the element, and f(t) is the amount of the element t hours after.

In this case the given values are:

A = 500g

T = 15h

Then the exponential decay is:

f(t) = 500g*e^(-t*ln(2)/15h)

And we want to find the value of t such that f(t) = 299g, then we can solve:

299g =  500g*e^(-t*ln(2)/15h)

299/500 = e^(-t*ln(2)/15h)

If we apply the natural logarithm in both sides we get:

ln(299/500) = -t*ln(2)/15h

-ln(299/500)*15h/ln(2) = t

11 h = t

It will take 11 hours to go from 500 grams to 299 grams.

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Related Questions

Periodic Inventory Using FIFO, LIFO, and Weighted Average Cost Methods The units of an item available for sale during the year were as follows: Jan. 1 Inventory 16 units at $31 $496 Aug. 13 Purchase 14 units at $33 462 Nov. 30 Purchase 13 units at $35 455 Available for sale 43 units $1,413 There are 21 units of the item in the physical inventory at December 31. The periodic inventory system is used. Determine the inventory cost using the (a) first-in, first-out (FIFO) method; (b) last-in, first-out (LIFO) method; and (c) weighted average cost method (round per-unit cost to two decimal places and your final answer to the nearest whole dollar). a. First-in, first-out (FIFO) $fill in the blank 1 b. Last-in, first-out (LIFO) $fill in the blank 2 c. Weighted average cost

Answers

The ending inventory cost on December 31 for 21 units, under the three inventory methods, is as follows:

a) first-in, first-out (FIFO) method: $719

b) last-in, first-out (LIFO) method: $661

c) weighted average cost method: $690

What does the ending inventory cost?

The ending inventory cost is the difference between the cost of goods available for sale and the cost of goods sold determined by the various inventory methods.

Some of the inventory methods include:

First-in, First-outLast-in, First-outWeighted AverageSpecific Identification.

Date       Activities         Units     Unit Cost   Total

Jan. 1      Inventory           16            $31       $496

Aug. 13   Purchase           14           $33         462

Nov. 30  Purchase           13           $35         455

Available for sale            43                       $1,413

Average cost = $32.86 ($1,413 ÷ 43)

Ending inventory             21

Units sold =                     22 (43 - 21)

a) FIFO:

Ending inventory = $719 (13 x $35 + 8 x $33)

Cost of goods sold = $694 ($1,413 - $719)

b) LIFO:

Ending inventory = $661 (16 x $31 + 5 x $33)

Cost of goods sold = $752 ($1,413 - $661)

c) Weighted Average:

Ending inventory = $690 (21 x $32.86)

Cost of goods sold = $723 (22 x $32.86)

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select all the expressions equivalent to 4^10​

Answers

The expressions equivalent to 4^10​ are 2^20, 4^4 . 4^6, and  4^4 / 4^-6. Option B, option C, and option E are correct.

Some laws of exponents are:

(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹a⁻¹ = 1 / a

We need to find all the expressions equivalent to 4^10​.

We will use laws of exponents for all the options one by one.

Option A:

2^5 . 2^2 = 2^(5 + 2) = 2^7

This is not equivalent to 4^10​.

Option B:

2^10 = 2^(2 * 10) = (2^2)^10 = 4^10

This is equivalent to 4^10​.

Option C:

4^4 . 4^6 = 4^(4 + 6) = 4^10

This is equivalent to 4^10​.

Option D:

4^7 . 4^-3 = 4^(7 + (-3)) = 4^4

This is not equivalent to 4^10​.

Option E:

4^4 / 4^-6 = 4^(4 - (-6)) = 4^10

This is equivalent to 4^10​.

So, 2^20, 4^4 . 4^6, and  4^4 / 4^-6 are equivalent to 4^10​.

So, option B, option C, and option E are correct.

Thus, the expressions equivalent to 4^10​ are 2^20, 4^4 . 4^6, and  4^4 / 4^-6. Option B, option C, and option E are correct.

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The sum of two numbers is
36. Three times the smaller plus
twice the larger is 87. Find the
two numbers.

Answers

Answer:

2 and 43.5

Step-by-step explanation:

Help. I'll mark as brainlist.

Answers

Answer: 22 square unit

Step-by-step explanation:

As each small square represents one square unit, we can count the squares and get the answer easily.

A book sold 41,900 copies it’s first month of release. Suppose this represents 9.2% of the number of copies sold to date. How many copies have been sold to date? Round your number to the nearest whole number.

Answers

455,435

Do you want the explanation?

Anita works a part time job where she makes 9.45$ per hour Anita’s gross pay for the current period is $238.61 her deductions include $28.63 for federal taxes 14.79 for social security 3.46 for Medicare 10.14 for state taxes . How many hours did Anita work and what was her net pay ? Anita works 31 hours next week what is her gross pay total amount of deductions and net pay assuming the same percentage is taken out for each deductions during the next pay period ?

Answers

For the gross pay of $238.61 and given deduction Anita's net pay is equal to $181.59 at the rate of $9.45 per hour and she works for 25.25 hours.

When Anita works for 31 hours with the given conditions her gross pay and net pay is equal to $292.95 and $235.93 respectively.

As given in the question,

a. Anita get pay per hour = $9.45

Gross pay received by Anita = $238.61

Deductions :

Federal tax = $28.63

Society tax : $14.79

Medicare : $3.46

State tax : $10.14

Total deduction = $ ( 28.63 + 14.79 + 3.46 + 10.14 )

                          = $57.02

Net pay = Gross pay - total deduction

             = $ ( 238.61 - 57.02 )

             = $ 181.59

Let us consider Anita works for 'h' hours at the rate of $9.45,

9.45h = 238.61

⇒ h = 238.61/ 9.45

⇒ h = 25.25 hours

b. When Anita works for 31 hours

Her gross pay = 31 × 9.45

                       = $ 292.95

Deductions are same

Net pay = $ ( 292.95 - 57.02 )

            = $ 235.93

Therefore, for the gross pay of $238.61 and given deduction Anita's net pay is equal to $181.59 at the rate of $9.45 per hour and she works for 25.25 hours.

When Anita works for 31 hours with the given conditions her gross pay and net pay is equal to $292.95 and $235.93 respectively.

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Which set of fractions is ordered from least to greatest?
A) 5/8, 8/12, 3/4
B) 8/12, 5/8, 3/4
C) 3/4, 5/8, 8/12
D) 5/8, 3/4, 8/12

Answers

The arrangement of the fraction from least to greatest is A. 5/8, 8/12, 3/4.

What is a fraction?

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator, as well as the denominator, are both integers

The fraction can be changed to percentage to make it easier.

5/8 = 5/8 × 100 = 62.5%

8/12 = 8/12 × 100 = 66.7%

3/4 = 3/4 × 100 = 75%

The arrangement is 5/8, 8/12, 3/4.

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leo
toring
29
Due Dec 6 by 11:59pm
Question 13
Ch. 9 Quadratics Homework (Copy)
Score: 12/17 12/17 answered

The width or short side is
The length or long side is
Points 20
Submit Question
The length of a rectangle is 6 feet longer than it is wide. If each side is increased 6 feet, then the area is
multiplied by 2. What was the size of the original rectangle?
<
Submitting an external too

Answers

The width or short side is 12 feet

The length or long side is 18 feet

What is Area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Consider your square as being composed of smaller unit squares. The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some common units for measuring area include square cms, square feet, square inches, square meters, etc.

Let Width= x feet

so, as per question Length = x+6 feet

Area = Length x Width = x(x+6) = [tex]x^{2} +6x[/tex]

According to the question each side is increased 6 feet

New Length = x+12 feet

New Width = x+6 feet

New Area = Length x Width[tex]= 2x(x+6)[/tex] <the area is multiplied by 2>

Length x Width=[tex](x+6)(x+12) = 2x(x+6)[/tex]

x+12=2x

x=12 feet

so, original width = 12 feet

original length = 18 feet

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Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value tα/2​, ​(b) find the critical value zα/2​, or​ (c) state that neither the normal distribution nor the t distribution applies. The confidence level is 90 %, σ is not​ known, and the histogram of 52 player salaries​ (in thousands of​ dollars) of football players on a team is as shown.

Answers

The correct statement regarding the critical value of the t-distribution is given as follows:

a) [tex]t_{\frac{\alpha}{2}} = 1.6753[/tex]

Which distribution should be used?

What defines which distribution should be used is whether the population standard deviation is known, as follows:

If the population standard deviation σ is known, then the z-distribution is used.If the population standard deviation σ is not known, then the t-distribution is used.

As stated in the problem, the population standard deviation is not known, hence the t-distribution is used, as the sample standard deviation can be calculated from the histogram.

The critical value is obtained using a t-distribution calculator, considering that:

The confidence level is of 90%.The amount of degrees of freedom, which is one less than the sample size, is of 52 - 1 = 51.

Hence it is given as follows:

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Use the number line below, where RS


I need help with this please help me

Answers

Y=6
Rs=39
St=38
hope this is helpful

Is 3 4/9 greater than 3 4/5?

Answers

No, three and four fifths is greater than 3 and four ninths.

An interest survey was taken at a summer camp to plan leisure activities. The results are given in the tree diagram.

The tree diagram shows campers branching off into two categories, prefer outdoor activities, which is labeled 80%, and prefer indoor activities, which is labeled 20%. Prefer outdoor activities branches off into two sub-categories, prefer hiking, which is labeled 70%, and prefer reading, which is labeled 30%. Prefer indoor activities branches off into two subcategories, prefer hiking, which is labeled 20%, and prefer reading, which is labeled 80%.

What percentage of the campers prefer outdoor activities and reading?

24%
30%
56%
80%

Answers

The percentage of the campers prefer outdoor activities and reading is A. 24%.

What is the percentage?

From the information, the tree diagram shows campers branching off into two categories, prefer outdoor activities is labeled 80%, and those who prefer reading, which is labeled 30%.

Therefore, percentage of the campers prefer outdoor activities and reading will be:

= Percentage for outdoor × Percentage of reading

= 80% × 30%

= 24%

In conclusion, the correct option is A.

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Answer: 56% i did the test

Step-by-step explanation:

for every 4 male birds in a cage there are 6 females what is the ratio of males to females

Answers

The ratio of males to females in the cage is 2:3.

According to the question,

We have the following information:

For every 4 male birds in a cage there are 6 females.

The ratio of males to females = Number of males in the cage: number of females in the cage

Ratio of males to females = 4:6

We can convert this ratio into the simplest form by dividing both the numbers by 2 and this will also be the equivalent ratio of this obtained ratio.

Ratio of males to females = 2:3

Hence, the ratio of males to females in the cage is 2:3.

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For a $250,000 mortgage, with an interest rate of 6% paid over 25 years, the monthly payment is $1,610.75. After one month, what is the balance of the loan?
Round your answer to the nearest dollar.
Do NOT round until you calculate the final answer.

Answers

The balance on the loan after a month is $623389.25.

How to calculate the interest?

The following can be deduced from the information given:

Principal = $250000

Time = 25

Rate = 6%

Interest = (Principal × Rate × Time) / 100

Interest = (250000 × 6 × 25) / 100

Interest = $375000

The total amount will be:

= Principal + Interest

= $250000 + $375000

= $625000

The balance of the loan will be:

= Amount - One month payment

= $625000 - $1,610.75

= $623389.25

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This table gives a few (x, y) pairs of a line in the coordinate plane.
x
Y
-54
-21
-40
-14 -26
- 28
What is the y-intercept of the line?

Answers

The y-intercept of the line is y = 2

What is an intercept?

A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.

Here,

A linear function has the following equation:

y = mx + b

Where m is the slope and b is the y-intercept, which is the value of y when x = 0.

We have given three points:

(-28, -54)

(-21, -40)

(-14, -26)

We use two of them to construct a system, to find values for m and b.

(-28, -54)

This means that when x = - 28 , y = - 54

so, y = mx + b

- 54 = - 28m + b

28m = b + 54

m = (b + 54)/28

Now, we have x = -21, y = -40

so, y = mx + b

- 40 = - 21m + b

we put the value of m here

- 40 = - 21 {(b + 54)/28} + b  we get,

7b - 1134 = - 40 × 28

b = 2

Hence, the y-intercept of the line is y = 2

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Answer:

(0,2)

Step-by-step explanation:

khan academy

How MANY THOUSANDTHS IN 0.1?

Answers

Answer:

100

Step-by-step explanation:

.001*100=.1

Answer:

100 thousandths

Step-by-step explanation:

A food company stores grain in a hopper. The hopper is 12 feet in diameter and holds 2024.5 cubic feet of grain. When turned on, the hopper empties grain at a constant rate of 42 cubic feet per second. About how long does it take for the hopper to empty all the grain?

Answers

The hopper will empty all of the grain in approximately 48.2 seconds .

Total amount of grain in the hopper = 2024.5 cubic feet

Rate at which the grain is emptied = 42 cubic feet /second.

Time taken to empty the grain

= 2024.5 / 42

= 48.202...

≈ 48.2 seconds

The ratio of two related quantities represented in several units is known as a rate. The numerator of something like the ratio expresses the rate of change for the other dependent variable if the denominator of both ratios is expressed as a single unit of each of these quantities and it is assumed that even this quantity can also be changed in a predictable way.

Hence the hopper will empty all the grain in about 48.2 seconds.

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a property map is drawn at a scale of 1:1000. Calculate the corresponding actual distance for each distance between 2 points on the map.
10 cm
= __ cm

Answers

If two points on the map measures 10 cm, with a scale of 1 : 1000 the actual distance is 10 000 cm

How to find the actual distance on a scale of 1 :1000

information gotten from the question

a scale of 1:1000

2 points on the map 10 cm = ?

Scale factors refer to the amount or the factor the image on a map was increased or reduced in comparison with the actual dimension of the image

A map has a scale of 1 : 1000

the scale factor is 1/1000 then 10/?

1/1000 = 10/?

cross multiplying gives

? = 10 000 cm

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5. Chris, Kiona, Seiko, and Dwayne each run 100 meters in a relay
race. Chris runs his part of the race in 12.35 seconds, Kiona takes
13.12 seconds, and Seiko takes 11.91 seconds.
a. The team wants to break the school record of 48.92 seconds. How
fast will Dwayne have to run?

Answers

Dwayne have to complete the race in 11.53 second or the speed of Dwayne  is 11.53 second/ 100 meter.

What is speed of an object?

Speed, expressed in terms of meters per second, is the rate at which an object's location changes. An item moves one meter in one second, for instance, if it starts at the origin and moves three meters in three seconds. The formula for speed is straightforward: time divided by distance.

Given that Chris, Kiona, Seiko, and Dwayne each run 100 meters in a relay

race. Chris runs his part of the race in 12.35 seconds, Kiona takes

13.12 seconds, and Seiko takes 11.91 seconds.

The total time that is taken by Chris, Kiona, and Seiko is (12.35 + 13.12 +  11.91) seconds = 37.38 seconds.

The team wants to break the record of 48.92 seconds.

To break the record, they should complete the race in 48.91 seconds.

Thus Dwayne have to run 100 meters in ( 48.91 - 37.38) = 11.53 seconds.

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Find the scale of a map if 4.2 cm on the map corresponds to an actual distance of 6.2 km.

Answers

Answer:

  21/3100000 ≈ 1/147619

Step-by-step explanation:

You want the scale of a map on which 4.2 cm corresponds to an actual distance of 6.2 km.

Scale

The scale of a drawing is the ratio of drawing distance to actual distance. It can be expressed a couple of ways. We can write the given scale as ...

  4.2 cm : 6.2 km

or, we can reduce it to ...

  2.1 cm : 3.1 km

Often, we like to have a single unit of map distance in this ratio, which would make it be approximately ...

  1 cm : 1.47619 km

Fraction

Another way to write the scale of a map is as a fraction.

  (4.2 cm)/(6.2 km) = (0.042 m)/(6200 m) = 21/3100000

When this is expressed as a unit fraction, the denominator is a repeating decimal with a 6-digit repeat. We can round it to ...

  ≈ 1/147619 . . . . map scale

The scale of the map is ...

  21/3100000 ≈ 1/147619   or   2.1 cm : 3.1 km   or   ≈ 1 cm : 1.47619 km

__

Additional comment

You may need to round the answer to match one of your answer choices.

<95141404393>

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Employee Number Years Worked 1 8 2 13 3 15 4 3 5 13 6 28 7 4 8 12 9 4 10 26 11 29 12 3 13 10 14 3 15 17 16 13 17 15 18 15 19 23 20 13 21 12 22 1 23 14 24 14 25 17 26 16 27 7 28 27 29 18 30 24 The data shows the number of years that 30 employees worked for an insurance company before retirement. is the population mean for the number of years worked, and % of the employees worked for the company for at least 10 years. (Round off your answers to the nearest integer.)

Answers

The population means that the number of years worked is 14, and 73% of employees worked for the company for at least 10 years.

The mean is calculated by dividing the number of employees by the number of years of service. The total number of years of service is 417, hence the average will be

The average years worked = 417/30 = 13.9 ≈ 14 years

The % of workers who have worked there for at least ten years is calculated by calculating the number of employees who have ten or more years of service and dividing that number by the total number of employees.

The final result is presented as a percentage will be:

(10 years or more)/(total number) = 22/30 = 0.73 = 73%

Thus, the population means that the number of years worked is 14, and 73% of employees worked for the company for at least 10 years.

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Sarah ran 7/8 of the distance around the school track. Jacob ran 2/3 of Sarah‘s distance what fraction of the total distance around the tractor Jacob run?

Answers

Jacob run 7/12 of the total distance around the school track.

What is distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.

Given: Sarah ran 7/8 of the distance around the school track.

Jacob ran 2/3 of Sarah‘s distance.

To find what fraction of the total distance around the track Jacob ran, we will find when solving 2/3 of 7/8 or symbolically

[tex](\frac{2}{3})(\frac{7}{8}) = \frac{14}{24} = \frac{7}{12}[/tex]

Hence, Jacob run 7 / 12 of the total distance around the school track.

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NEED HELP PLEASE!!!!!!!!!!!!!!!!!!!

Answers

x=-3.645 and x=1.645 is the solution for the given inequality.

What is quadratic equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

The given inequality is

y<x²+2x-6

a=1, b=2, c=-6

x=-b±√b²-4ac/2a

=-2±√2²-4(1)(-6)/2(1)

=-2±√4+24/2=

=-2±√28/2=

=-2+√28/2

=-2+5.29/2

=1.645

and -2-5.29/2

x=-3.645

Hence x=-3.645 and x=1.645 is the solution for the given inequality.

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A scale drawing of a rectangular bedroom is shown below. Using a scale of 1cm=4 feet, enter the actual area of the bedroom in square feet.

Answers

Answer:

Below

Step-by-step explanation:

Need the drawing but take the two cm measurements and multiply them together then multiply by 4   and then multiply by 4 again to get ft^2

solve for each proportion

Answers

Answer:

r = 20/7

x = 13.5

Step-by-step explanation:

Hello!

7)

Solve for r by cross-multiplying:

[tex]\frac r2 = \frac {10}7[/tex][tex]r*7 = 10 * 2[/tex][tex]7r = 20[/tex][tex]r = \frac{20}7[/tex]

The value of r is 20/7.

8)

Solve for x by cross-multipying:

[tex]\frac 94 = \frac x6[/tex][tex]9*6 = 4*x[/tex][tex]4x = 54[/tex][tex]x = 13 \frac12[/tex]

The value of x is 13.5.

Answer:

7) r = 20/7 8) x = 27/2

Step-by-step explanation:

7) r/2 = 10/7, value of r?

→ r/2 = 10/7

→ r = (10/7) × 2

→ r = (10 × 2)/7

→ [ r = 20/7 ]

Hence, value of r is 20/7.

8) 9/4 = x/6, value of x?

→ 9/4 = x/6

→ x/6 = 9/4

→ x = (9/4) × 6

→ x = (9 × 6)/4

→ x = 54/4

→ [ x = 27/2 ]

Hence, value of x is 27/2.

If 1300 square centimeters of material is available to make a box with a square base and an open top, find the largest possible
volume of the box.(include units)

Answers

4,096 cm^3

it's useful to know that the box with the largest volume - to - surface area ratio is a cube. Your shape will be a cube (with a missing top).

Thus there will be five square faces with a total area of 1300 square centimeters. The area of each side will thus be:

1300/5 = 260

The length of each side will again be an irrational number (√260), because 260 is not a perfect square. This comes out to roughly:

16

The simplest way to do it from here would be to simply take the cube of your side length:

163 = 4096

Your box's volume will be roughly 4096 cm^3


If < 1 and <2 are complementary, and m< 1 = 42°, find m< 2.

Answers

Answer:

m< 2= 48°

Step-by-step explanation:

Complementary angles sum up to 90 degrees

We know that m< 1 = 42°

All we have to do is subtract 90 from 42 to find m< 2:

m< 2= 90 - 42

m< 2= 48°

Hope this answers your question :)

Write (-4x^2ya^3)^2 as a monomial in standard form.

Answers

Answer:

[tex]16a^6x^4y^2[/tex]

Step-by-step explanation:

To simplify this expression, use the exponent rule stating that when an exponent is put to an exponent, the exponent values are multiplied (e.g., [tex](x^2)^2 = x^{2 \cdot 2} = x^4[/tex])

Using that rule, we get:

[tex](-4x^2ya^3)^2 = (-4)^2 \cdot x^{(2 \, \cdot \, 2)} \cdot y^2 \cdot a^{(3 \, \cdot \, 2)}[/tex].

This can be simplified to

[tex]16 \cdot x^4 \cdot y^2 \cdot a^6[/tex],

which can be written as:

[tex]16a^6x^4y^2[/tex]

using the commutative property of multiplication.

The sum of four consecutive numbers is thirty-two. Find the largest number. (show work)

Answers

9.5 is the largest number

Consecutive numbers are the number will follow each other in order.

The difference between every two numbers is one. if n is the number so, the consecutive number will be n+1,n+2 , . . . . . .

Let four consecutive numbers be a , a+1 , a+2 , a+3

where a+3 will be largest number

Given the sum of these is 32

a + a +1 +a + 2 + a +3 = 32

=> 4a + 6 = 32

=>4a = 26

=> a= 26/4

=> a = 6.5

putting the values,

consecutive number will be = 6.5 , 7.5 , 8.5 , and 9.5

9.5 is the largest number

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what is the value of f(2) when given f(x)=4x+12

Answers

f(2) indicates that in order to solve the problem, we are going to plug in 2 in any spot that we see the variable x. we can then use pemdas to solve!
f(2) = 4(2) + 12
f(2) = 8 + 12
f(2) = 20

i hope this helps!
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