Grandparents want to make a gift of $100,000 for their grandchild’s 20th birthday. How much would have to be invested on the day of their grandchild’s birth if their investment could earn: (a) 10.5% compounded continuously? (b) 11% compounded continuously? (c) Describe the effect that this slight change in the interest rate makes over the 20 years of this investment

The point after the first one is (2,5). The point after the third one is (4,11) The fifth point is (5,14). The last point is (6,17)

After 5 sec will be the same seconds of the elevator.

The two elevators will reach the same floor at the same time if they are both going at a constant speed. If one elevator is going faster than the other, it will reach the bottom first and vice versa.

Given that, elevator A speed = 27-21/3-1=6/2=3

Elevator B speed = 23-19/3-1=4/2=2

suppose x second After will be the Elevator be at the same height

when at 1 second, Elevator A is 27, Elevator B is 23

so Elevator A start at height (27+3), Elevator B start at 23+2

30-3x=25-2x

-3x+2x=25-30

-x=-5

x=5

Hence, after 5 sec will be the same seconds of the elevator.

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Answer:$12

Step-by-step explanation: 75 -39 and we get $36 remaining. Then we do 36/3 t-shirts which gives us $12 per shirt

75-39=36

36/3=$12 per shirt

Answer:

$12

Step-by-step explanation:

$75-$39 which = 36

36 divided by 3 which =12

each t-shirt is $12

Answer:

Step-by-step explanation:

There are 4 five's in the deck.

Probability of drawing a five is:

Since the card is replaced, it has same probability the second time.

So the probability of drawing a five twice is:

The diameter in standard notation is 250,000 km, so the correct option is C.

we know that the diameter in scientific notation is:

D = 2.5*10^5 km

Now we want to rewrite this in standard notation, to do so you just need to solve the product, we can rewrite:

10^5 = 10*10*10*10*10 = 100,000

Then we can rewrite the diameter as:

D = 2.5*10^5 km = 2.5*100,000 km

D = 250,000 km

The diameter in standard notation is 250,000 km, so the correct option is C.

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Answer: I think 5

Step-by-step explanation: because think about what would equal 9 so 9x1 equals 9 I thought so I did it for the division 5/5 is 1 so 9/1 is 9 so do multiply 5/5 is 1

then 9x1 is 9 so N=5

hope that helps

Answer:

Increasing Speed, Decreasing Speed, and changing direction. Or a change in direction.

Step-by-step explanation:

Answer: 1, 2, 4

Step-by-step explanation:

Step-by-step explanation:

Remember your exponent rules.

[tex] {a}^{ - m} = \frac{1}{a} [/tex]

And

[tex] {(\frac{a}{b} )}^{ - m} = {(\frac{b}{a} )}^{ m}[/tex]

So the first one would be

[tex] \frac{1}{ {4}^{3} } \times 4 = \frac{1}{16} [/tex]

Answer:

To find the inverse interchange the variables and solve for y.

Step-by-step explanation:

f−1(x)=6x−53(1+x)

Step-by-step explanation:

Given that

To find

So, according to the question

we have,

For finding the y coordinate, we have find f(8) from equation,

So now put 8 from x, or in other word x = 8,

So, we will get

f(x) =  -5x²-8x+6

f(8) =  -5(8)²-8(8)+6

       = -5× 64- 8×8 +6

       = -320 -64 +6

       = -384 + 6

       = 378

Answer:

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1. The predetermined overhead rate is $7 per machine hour.

2. The total manufacturing overhead applied to the Work in Process Inventory account during the first month of operations is $49,000.

3. The balance in the Work in Process Inventory account at the end of the first month is $33,200.

4. The gross profit that Tyler Tooling Company reported during the first month of operations before adjusting overapplied overhead is $5,000.

5-a. The balance in the Manufacturing Overhead account at the end of the first month is $4,000.

5-b. The overhead is overapplied.

Estimated total manufacturing overhead = $420,000

Estimated total machine hours = 60,000 hours

Predetermined overhead rate = $7 ($420,000/60,000)

                                            Job 101     Job 102          Job 103         Total

Direct materials used       $ 19,200    $ 14,400       $ 9,600     $ 43,200

Direct labor                      $ 28,800     $ 11,200       $ 9,600     $ 49,600

Applied overhead              $7,000     $28,000      $14,000      $49,000

Total costs                       $55,000     $53,600      $33,200     $141,800

Machine hours             1,000 hours   4,000 hours 2,000 hours 7,000 hrs

Status of Jobs                   Sold             Finished      WIP

Sales revenue (Job 101) = $60,000

Actual overhead costs for the first month = $45,000

Applied overhead for the first month = $49,000 ($7 x 7,000)

Overapplied overhead = $4,000 ($49,000 - $45,000)

Sales revenue       $60,000

Cost of goods sold 55,000

Gross profit            $5,000

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Reginald spent 7/4 hours if his time in writing notes.

As, per the given question;

Total time of Reginald doing research in the library is 2 1/3 hours.

2 1/3 is given in the mixed fraction;

Solving this;

= (2×3 + 1)/3

= (6 + 1)/3

= 7/3

Thus, total hours in library is 7/3 hours.

He spent 3/4 of that time in writing notes;

3/4 of 7/3 will be. simply multiply.

= (3/4)(7/3)

= 7/4

Thus, the total time spent 7/4 hours of his library time in writing his notes.

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Answer:

answer is 2025,,,,, just multiply 2700 with 75/100

Answer:

Step-by-step explanation:

Answer:

X = 11

Step-by-step explanation:

7( x – 4) –3 = 46

7( x– 4 ) = 46 + 3

x – 4 = 49/7

x – 4 = 7

x = 7 + 4

x = 11

Hope This Help :)

Answer:

RS = 41 , ST = 18

Step-by-step explanation:

from the number line

RT = RS + ST ( substitute values )

59 = 9y + 5 + 3y + 6

59 = 12y + 11 ( subtract 11 from both sides )

48 = 12y ( divide both sides by 12 )

4 = y

Then

RS = 9y + 5 = 9(4) + 5 = 36 + 5 = 41

ST = 3y + 6 = 3(4) + 6 = 12 + 6 = 18

Lelah can arrange the four posters in 24 ways.

A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order.

Now it is given that,

Number of poster = 4

Number of walls = 4

Since one poster of each team to put one poster on each of her four walls.

So, number of ways = 4!

⇒ number of ways = 4x3x2x1

⇒ number of ways = 24 ways

Thus,  Lelah can arrange the four posters in 24 ways.

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Answer: x∈(-∞,3]      x∈(-∞,1.5)

Step-by-step explanation:

2(3x+1)≤20

Divide both parts of the equation by 2:

3x+1≤10

3x+1-1≤10-1

3x≤9

Divide both parts of the equation by 3:

x≤3

Thus, x∈(-∞,3]

[tex]\displaystyle\\4(x-1) < 2\\\\Divide\ both\ parts\ of\ the\ equation \ by \ 4:\\\\x-1 < \frac{2}{4} \\\\x-1 < 0.5\\\\x-1+1 < 0.5+1\\\\x < 1.5\\\\Thus,\ x\in(-\infty,1.5)[/tex]

The solution in interval notation, x∈(-∞,3] and x∈(-∞,1.5)

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

An inequality is a mathes that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). Inequalities is used to describe relationships between quantities or to express constraints or conditions.

WE are given that the inequality  as;2(3x+1)≤20

Divide both parts of the equation by 2:

3x+1≤10

3x+1-1≤10-1

3x≤9

Now Divide both parts of the equation by 3:

x≤3

Thus, x∈(-∞,3]

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A swimming pool has a volume of 256 yd³.The amount of water in gallons needed to completely fill the pool is 51705.344 gallons.

Given that,

A swimming pool has a volume of 256 yd³.

We have to find The amount of water in gallons needed to completely fill the pool.

What is the conversion factor defined as?

An amount is used as a conversion factor when multiplying or dividing one set of units by another.

The appropriate conversion factor must be applied when converting to an equivalent value.

For instance, 12 inches equals 1 foot when converting between inches and feet.

Regarding the given problem;

The pool has a volume of 256 yd³.

Convert the yd³ volume to gallons.

201.976 gallons are in 1 yd³.

As a result, multiply both sides by 256 to get the total volume, which is 256 yd³.

201.976 yd³ are equal to 256 gallons.

51705.344 gallons are equal to 256 yd³.

Consequently, 51705.344 gallons of water are needed to completely fill the pool.

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Answer:

The answer to this question is 72x3

The number of lines drawn through the 3 collinear points is 10, so the correct option is option d) 10.

It is said that there are 5 points such that no three points out of them are lying in a straight line. This refers to the points being collinear.

Collinear points are associated with three or more different points that do lie on the same straight line and thus, non-collinear points will be defined as points that do not lie on the same straight line.

This means that the points that are non-collinear cannot be connected together via a single line as they are not lying in the same line.

For non-collinearity, not more than two points should be lying in the same straight line.

This is what is given in the question which says that no 3 points can lie on the same line joined through a straight line.

However it is not necessary that the points that are non-collinear will also not lie on the same plane, that is, exhibit the coplanar property.

So hence, non-collinear points are independent of the coplanarity property which means that points that cannot lie on the same line can lie on the same plane.

This is the case given here as it is said that the 5 points that are non-collinear in nature, however, do lie on the same plane which is a single paper. They are coplanar as they lie on the same plane of the paper.

A solution is required to be derived where the 5 points need to be connected so that the above conditions are to be satisfied.

The points must be placed in such a way that no 3 points are collinear but they all must lie on the same plane.

This means that 1 or 2 points are allowed to lie on the same line. Thus, if a figure can be drawn out of these conditions it will form a star-shaped figure enclosed inside a pentagon. (Figure attached at the end)

The number of lines that can be drawn through them satisfying the condition is to be found out. So all the possible pairs are connected via straight lines drawn.

As it can be seen in the figure below if there are 5 points A, B, C, D, and E such that no three points lie on the same line there are 10 lines that are possible that can be drawn connecting them.

The pairs are however considered distinctly which means that either of the lines AB or BA must be taken for example. Both are not to be taken as they represent the same straight-line pair.

So the number of possible connections in the setup given below (from the figure) is 10 namely AB, BC, AE, CA, CD, DE, CE, DA, DB, and BE.

Thus, the number of lines that can be drawn through the 5 points such that no 3 points are collinear is 10.

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Answer:

3 18/19

Step-by-step explanation:

1. Change to improper fractions.

        (You do this by multiplying the denominator and the whole number, then add the numerator.)

7 1/2 ⇒ 15/2

1 9/10 ⇒ 19/10

So now its:  15/2 ÷ 19/10

2. Keep, change, flip

Keep the first number (15/2), change the division to multiplication, flip the other fraction (From 19/10 to 10/19).

3. Multiply

15/2 × 10/19 = 150/38

Simplified, the answer is 3 18/19

When we want to rationalize the denominator of the number 2✓2/ 3✓11 the numbers that should be used for the multiplication will be 3✓11.

It should be noted that rationalizing the denominator is to ensure that it becomes easy to perform a calculation.

It should be noted that based on the information, we want to rationalize the denominator. This will be 2✓2/ 3✓11 multiplied by 3✓11.

Therefore, the appropriate number is 3✓11.

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Answer:

89m

Step-by-step explanation:

Denote:- L = Length, W = Width

Area of a rectangular = L × W

7031m = L × 79m

7031/79m = L

89 = L

Answer:

length = 89

Step-by-step explanation:

Let A represent area

      L represent length and

      W represent width

A = L.B

7031 = L . 79

7031 = L

79

L = 89

Answer:

67.25

Step-by-step explanation:

Since they can each get 1/2 the jelly beans but need to eat it over 4 days they will be eating 1/2*1/4 jelly beans per day. This is equal to 1/8x where x is the total jelly beans. We know the total so we can plug 538 in for x and divide 538 by 8 to get 67.25

The possible answers for the vertices of triangle A'B'C' are (14, 3), (- 6, 2) and (- 8, 6). (Correct answers: A, E, D)

In this problem we find the locations of the three vertices of a triangle, which is modified by a non-rigid transformation rule, that is, a transformation that does not conserve the original form of the triangle. If we know that A(x, y) = (7, 6), B(x, y) = (- 3, 5) and C(x, y) = (- 4, 9), then the vertices of the image of the triangle are, respectively:

A'(x, y) = (2 · 7, 6 - 3)

A'(x, y) = (14, 3)

B'(x, y) = (2 · (- 3), 5 - 3)

B'(x, y) = (- 6, 2)

C'(x, y) = (2 · (- 4), 9 - 3)

C'(x, y) = (- 8, 6)

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Answer:

2x/3

Step-by-step explanation:

[tex] \frac{16 {x}^{4} }{24 {x}^{3} } = \frac{2x}{3} [/tex]

By evaluating this equation we get , -64.

-10c + 3a + a = -10(6) + 3(-1) + (-1)

=- 60 + (-3) + (-1)

= - 60 -3 -1

= -64

Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression). Let's use the equation 5x + 7 as an example. Thus, 5x + 7 is an illustration of an algebraic expression.

To evaluate an algebraic expression, you must substitute a number for each variable and perform the arithmetic operations.. Since 6 + 6 equals 12, the variable x in the example above is equal to 6.

Hence, the algebraic expression can be expanded and solved as -64.

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The area of the triangle = the area of the rectangle = 6 cm².

The area of a triangle = 1/2(base)(height)

The area of any rectangle = (length)(width)

Area of the triangle:

Base = 4 cm

Height = 3 cm

Area of the triangle = 1/2(4)(3)

Area of the triangle = 6 cm²

Area of the rectangle:

Length = 3 cm

Width = 2 cm

Area of the rectangle = (3)(2) = 6 cm²

Therefore, the area of the triangle = the area of the rectangle = 6 cm².

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