A town has a population of 16000 and grows at 2.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 24300?

A) The number of cans of soup in ending inventory is 19.

B) The cost of the ending inventory under LIFO, FIFO, and the weighted average is as follows:

LIFO                                  $17.15

FIFO                                 $25.65

Weighted average          $21.47

The inventory methods include First-in, First-out (FIFO), Last-in, First-out (LIFO), Weighted Average, and Specific Identification.

FIFO assumes that the physical flow of goods during sales follows the chronological sequence of their acquisition.

LIFO assumes that the first goods acquired are the last to be sold.

The Weighted Average uses an average to determine the costs allocated to ending inventory and the cost of goods sold.

Specific Identification identifies the specific goods sold with their costs.

Description                 Units Unit Cost  Total

Beginning inventory     12     $0.85     $10.20

Purchases                      4     $0.95       $3.80

Purchases                      6     $1.05        $6.30

Purchases                      7     $1.35        $9.45

Purchases                     8     $1.50       $12.00

Total                            37                     $41.75

Sales                            18

Ending inventory        19 (37 - 18)

Average cost = $1.13 ($41.75/37)

LIFO:

Ending inventory = $17.15 ($10.20 + $3.80 + 3 x $1.05)

FIFO:

Ending inventory = $25.65 (4 x $1.05 + $9.45 + $12.00)

Weighted Average

Ending inventory = $21.47 (19 x $1.13)

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The derivative of the function f(x) = Sin⁻¹(3x) is f'(x) = 3/√(1-9x²)  , the correct option is (c) .

In the question ,

a function is given as

f(x) = Sin⁻¹(3x) , we need to find the derivative .

we know that the derivative of Sin⁻¹(x) is equal to 1/√(1 - x²) .

So , on differentiating both sides with respect to "x" .

we get

f'(x) = d/dx (Sin⁻¹(3x))

= 1/√1-(3x)² ×  d/dx (3x)

= 1/√(1 - 9x²) × 3

On simplifying further ,

we get

= 3/√(1 - 9x²)

Therefore ,the derivative of the function is 3/√(1-9x²)  , the correct option is (c) .

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Answer:

9600000000

Step-by-step explanation:

9.6 x (10^9)

First, write 10^9 as 1000000000

Multiply by 9.6

= 9600000000.

Answer: $8.55

because 6.65 divided by 7 is 0.95 and 0.95 multiplied by 9 is 8.55

so the answer is $8.55

Answer: Integers less than 4 will make the inequality true.

Step-by-step explanation:

1) subtract both sides by 4 to isolate 2x so we are now left with 8 > 2x.

2) divide both sides by 2 so we are left with just x, leaving us now with 4 > x.

Integers must be less than 4 because if you substitute x as 4, we have 12 > 12, which is not true. But, if we substitute x as 3, we are left with 12 > 10, which makes the inequality true.

The equivalent quotient to -5/8 are; -5/8 and .5/-8.

The correct answer options are options A and C

A quotient is the number resulting from the division of one number by another. For instance, the quotient of 12 divided by 4 is 3.

A divisor number or expression that another is to be divided by. For instance, in "42 ÷ 3" the divisor is the 3.

Dividend is a number or expression that is to be divided by another. For instance, In "42 ÷ 3" the dividend is the 42.

Complete question:

Given options:

A. -5/8

True

B. 5/8

False

C.5/-8

True

D. -(5/-8)

False

E. -5/-8

False

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(3.201 x 10^9) * (4.85 x 10^3) =

15524850000000

in scientifc notation

1.552485 x 10^13

Answer:

20.4 m

Step-by-step explanation:

mean is calculated as

mean = [tex]\frac{total}{count}[/tex]

given mean height of 12 men is 1.70 m , then

[tex]\frac{total}{12}[/tex] = 1.7 ( multiply both sides by 12 to clear the fraction )

total height = 12 × 1.7 = 20.4 m

Answer:

the last one= It takes longer to fall because it experiences greater air resistance.

also the reason is the air resistance provides an upthrust to the parachute which takes longer time to fall

Answer: It takes longer to fall because it experiences greater air resistance.

Answer:

d = -5

Step-by-step explanation:

[tex]\frac{4}{5}d + 3 = -2 -\frac{1}{5}d\\ \\ \frac{4}{5}d + \frac{1}{5} d = -3 -2\\\\\frac{4+1}{5}d = -5\\\\ \frac{5}{5} d = -5\\\\d = -5[/tex]

Check:

[tex](\frac{4}{5} )(-5) + 3 = (-2) - (\frac{1}{5})(-5)\\\\(\frac{-20}{5} ) + 3 = -2 - (\frac{-5}{5} ) \\\\-4 + 3 = -2 + 1\ = -1[/tex]

The probability that the boy will select a palindrome number is 1/900.

A number that reads the same both forward and backward is known as a palindrome.

The 6 digits palindrome numbers can be formed starting from 100 and writing the reverse of 100 before 100 like 100-001, 101-101, 102-201,...,

995-599, 996-699, 997-799, 998-899,999-999.

Therefore, the 6 digits palindrome numbers can be formed using three digits starting from 100 to 999.

Since we are starting from 100, subtract 99 from 999 to get the total number of 6 digits palindrome numbers,

999-99

=900

Therefore, there are 900 six digits palindrome numbers.

The probability of selecting one palindrome number out of a total of 900 numbers is,

1/900

Therefore, the probability that the boy will select a palindrome number is 1/900.

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The steps that Patel could he use to solve the quadratic equation include:

8(x² + 2x) = –3

8(x² + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

It is preferred to solve quadratic equations without the use of the known quadratic formula solver. This can be completing squares and solving for x.

The equation given is:

8x² + 16x + 3 = 0

8(x² + 2x) = -3

Completing squares in the brackets and balancing the equation:

8(x² + 2x + 1) = -3 + 8

Factoring the perfect square will give 8(x + 1)² = 5.

This is illustrated in the options picked for the step.

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Answer:

x>=3 make the inequality false

Step-by-step explanation:

4x-2x<12-6

2x<6

x<3

Answer:

Any number higher than 3

Ex. 4, 5, 6, 7, 8, 9, 10, etc

Step-by-step explanation:

4x + 6 < 2x + 12

-2x        -2x

---------------------

2x + 6 < 12

      -6    -6

------------------

2x < 6

÷2   ÷2

-----------

x < 3

Since x is less than 3, any number higher than 3 will make the inequality false. For Ex. 4

4(4) + 6 < 2(4) + 12

16 + 6 < 8 + 12

22 < 20 (false)

I hope this helps!

The greatest temperature in Africa occur is 367 feet.

The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion.

Given:

The greatest temperature ever recorded in the United States occurred at an elevation of 178 feet below sea level.

Using integers we represent it as (-178) feet.

and, greatest temperature ever recorded in Africa 545 feet greater than in the United States

= -178 + 545

= 367 feet.

Hence, The greatest temperature in Africa occur is 367 feet.

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By using subtraction, it can be calculated that there were 496 round beads more than heart shaped beads

What is subtraction?

Suppose, there are two numbers and it is required to find out how much one number is bigger than  the other. The operation used for this is subtraction.

The larger number is called minuend and the smaller number is called subtrehend.

Here, subtraction will be used

Number of round glass beads = 675

Number of beads in the shape of heart = 179

Number of more round beads there were = 675 - 179

                                                                      = 496

There were 496 round beads more than glass beads

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The solution is

a) The ascending order is 32 % < 2 1/2 < √9 < π

b) The ascending order is -4 < -3.4 < -3 < -2 1/2 < π

c) The ascending order is -5/8 < 0 < 250% < 3.4

What is Ascending Order?

When numbers are arranged in ascending order, they are done so from least to largest. We must first compare the numbers before we may arrange them in any order. Compare first, then order. Numbers arranged in ascending order: Determine how many digits each number has.

Given data ,

A)

32 % , π , 2 1/2 , √9

32 % = 32 / 100

        = 0.32

π = 3.14

2 1/2 = 2.5

√9 = 3

So , arranging the numbers in ascending order we get ,

0.32 < 2.5 < 3 < 3.14

Hence , the ascending order is 32 % < 2 1/2 < √9 < π

B)

-3.4 , -4 , -3 , -2 1/2 , π  

Hence , the ascending order is -4 < -3.4 < -3 < -2 1/2 < π

C)    

250 % , 3.4 , -5/8 , 0

250 % = 2.5

-5/8 = -0.625

So , arranging the numbers in ascending order we get

-0.625 < 0 < 2.5 < 3.4

Hence , the ascending order is -5/8 < 0 < 250% < 3.4

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Answer:  The correct answer in 9/12

Step-by-step explanation:

For 3/4, the numerator is 3 and the denominator is 4

To change the denominator to 12, you must multiply by 3 (12/4=3)

3/4 * 3/3

= (3*3)/(4*3)

= 9/12

a) The null and alternative hypothesis are given as follows:

b) The errors are given as follows:

c) The conclusion of a rejected null hypothesis is: There is enough evidence that most adults would erase their data if they could.

d) The conclusion of a not rejected null hypothesis is: There is not enough evidence that most adults would erase their data if they could.

At the null hypothesis, it is tested if there is not enough evidence that most adults would erase all of their personal data online if they could, that is, if the proportion is not greater than 50%, hence:

[tex]H_0: p \leq 0.5[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that they would erase the information, that is, if the proportion is greater than 50%, hence:

[tex]H_1: p > 0.5[/tex]

A rejected null hypothesis means that the alternative hypothesis is accepted, that is, there is enough evidence that most adults would erase their data if they could.

A not rejected null hypothesis, conversely, means that there is not enough evidence that most adults would erase their data if they could.

Type I errors are when a true null hypothesis is rejected. Hence, the context of this problem, it would mean a sample which gives enough evidence that most people would erase the data, if in reality they wouldn't.

Type II errors are when a false null hypothesis is not rejected. Hence, the context of this problem, it would mean a sample in which the proportion of people that would erase their data isn't significantly above 50%, when in fact it is.

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Answer:

Step-by-step explanation:

the side opposite to greater angle is greater.

72>60>48

AB>AC>BC

A=Afton

B=Badeton

C=Capeton

The experimental probability of choosing a blue golf ball based on Lorena's trials is 0.75.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true

In this case, Lorena chooses a golf ball from the bucket at random 4 times and 3 times, he picked blue balls.

The probability of picking a blue ball will be:

= Number of times a blue ball was picked / Total number of trials

= 3/4

= 0.75

The probability is 0.75.

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Answer:

60%

Step-by-step explanation:

i actually hope this helps!

9/16 must be added to this expression [tex]x^{2} -3x/2[/tex] to make it a perfect square.

According to the question,

We have the following expression:

[tex]x^{2}[/tex] -3x/2

Now, in the given four options, we only have two perfect squares which 9/16 and 16/9.

Now, 9/16 is the square of 3/4.

So, we will first solve it using 9/16:

[tex]x^{2}[/tex]-3x/2+9/16

Now, this formula is of identity [tex](a-b)^{2}[/tex] where we have a = x and b = 3/4.

The formula of the identity [tex](a-b)^{2} = a^{2} + b^{2} -2ab[/tex].

Now, adding 9/16 make it a perfect whole square.

(More to know: we can add or subtract a number or a term from an expression to make it a perfect square or perfect cube.)

Hence, the correct option is C.

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1. The completion of the inventory table is as follows:

2. The Cost of Ending Inventory and the Cost of Goods Sold under LIFO, FIFO, and Weighted-Average, are as follows:

                                      LIFO           FIFO      Weighted-Average

Ending inventory          $425          $691                $573

Cost of goods sold      $492          $226               $344

FIFO (First-in, First-out) lies on the assumption that the physical flow of goods sold depends on the chronological order of acquisition.

LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.

The weighted-average method uses the average cost of goods to determine both the ending inventory and the cost of goods sold.

LIFO:

Ending inventory = $425 ($917 - $492)

Cost of goods sold = $492 (12 x $20 + 12 x $21)

FIFO:

Ending inventory = $691 (9 x $11 + 17 x $20 + 12 x $21)

Cost of goods sold = $226 ($917 - $691)

Weighted Average:

Ending inventory = $573 (40 x $14.33)

Cost of goods sold = $344 (24 x $14.33)

                                    Units  Unit Cost    Total Cost

Jan. 1      Beg. Inventory  20     $8.00           $160

May 10   Purchases          15     $11.00           $165

June 30 Purchases          17    $20.00         $340

Dec. 10  Purchases          12    $21.00          $252

Total                                64                          $917

Units sold                       24

Ending inventory           40 (64 - 24)

Average cost = $14.33 ($917/64)

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2. Calculate the cost of the ending inventory and the cost of goods sold under LIFO, FIFO, and Weighted-Average.

Answer:

Selling price = RS 3150

Loss percent = 10%

Step-by-step explanation:

1 quintal = 100kg

Cost price = 35*100

= RS 3500

Loss = RS 350

Selling price = RS 3500-350

Selling price = RS 3500-350 =RS 3150

Loss percent = Loss *100%

Cost Price

= 0.1 *100

= 10%

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The two combined geometric series is separated and the common ratios are shown

The total of a geometric sequence's finite or infinite terms is known as a geometric series.

The ratios of every two successive terms in the series (sum of terms) are equal. this means that

The common ratio is calculated by dividing the succeeding term (eg 2nd term) by the preceding term (eg 1st term)

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The value of c by using the mean value theorem is c = 6.25.

The mean value theorem in mathematics says that for any given planar arc between two endpoints, there exists at least one point where the tangent to the arc is parallel to the secant between its endpoints. It is one of the most significant findings in the real-world analysis.

Given that the function is f(x) = 5√x and the interval is (4,9).

Calculate the value of 'c' as below,

f(x) = 5√x

f(4) = 5√4 = 10

f(9) = 5√9 = 15

Calculate the value of f'(c) as below,

f'(c) = ( f(b) - f(a) ) / (b - a)

f'(c) = f(9) - f(4) / ( 9 - 4 )

f'(c) = (15 - 10 )  / ( 9 - 4)

f'(c) = 1

Again the value of f'(x) is,

f'(x) = 5/2/√x

f'(c) = 5 / 2 / (√c)

5 / 2 / (√c) = 1

√c = 5 / 2

c = 25 / 4

c = 6.25

Therefore, the value of c by using the mean value theorem is c = 6.25.

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Answer:

y=2x-22

Step-by-step explanation:

lets make the equation into slope intercept form

-2x+y=-8 let's move the -2x to the other side we get

y=2x-8

now let's create our equation with the points given

to create the equation you want to make it point slope form with the point given

y-0=2(x-11) distribute the 2 and we can remove the 0

y=2x-22

The angles that are congruent are as follows:

Vertical angles are angles that are opposite of each other when two lines cross. In other words, vertical angles are formed when two lines meet each other at a point.

Vertically opposite angles are congruent.

Therefore, let's find the angles that are congruent in the diagram.

When lines intersect angle relationship such as vertically opposite angles are formed.

Therefore, the following angles are congruent because they are vertically opposite angles.

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If P= (2, 7) and Q= (2, -3), then for triangle to be isosceles coordinate of R must be 2

Let coordinates

P = (2, 7) and Q = (2, -3)

PR = QR

(X-2)^2 +(Y-7)^2 = (X-2)^2 + {Y-(-3)}^2

(Y-7) = {Y - (-3)}^2. or y - 7 = ±(Y

or Y^2 - 14Y + 49 = Y^2 + 6Y + 9

20Y = 40

Y=2

coordinates of R if triangle PQR is isosceles ;

Hence any point R on the line Y = 2 will make PQR a isosceles triangle

with PR = QR.

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