$.
(b) (i) Annie invests $330 at a rate of 1.5% per year compound interest.
Calculate the amount that Annie has after 8 years.
Give your answer correct to the nearest dollar.

The area of the tile in square centimeters is 929cm2

The area in square centimeters is calculated as follows

First, let convert the tile measures 12 inches on each side into centimeters

1 inch = 2.54 centimeters

= 12 x 2.54
= 30.48 centimeters

Next is to find the area of the tile in square centimeters
The area of square = (side) x (side) square units
= 30.48 centimeters x 30.48 centimeters

= 929.0304

= 929 square centimeters (rounded)

So, the area of the tile in square centimeters is 929 square centimeters

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Answer:

The area of the tile in square centimeters is 929cm2

Step-by-step explanation:

I took the exam and got it right

The value of  g(x) = 1/16[tex]x^{2}[/tex] = (1/4[tex]x^{2}[/tex]). The correct option is (C).

Given,

In the question:

f(x) = [tex]x^{2}[/tex]

To find the value of g(x)

To see the graph and analysis

Now, According to the question:

We know that:

g(x) = k f(x) = k[tex]x^{2}[/tex]

In the graph, The value are given as:

Plug (4,1) into g(x):

1 = k. [tex]4^2[/tex]

k = 1/16

=> g(x) = 1/16[tex]x^{2}[/tex] = (1/4[tex]x^{2}[/tex])

Hence, The value of  g(x) = 1/16[tex]x^{2}[/tex] = (1/4[tex]x^{2}[/tex]). The correct option is (C).

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The equation can be given as X+20 = 60

Wyatt needs to save $40 to buy the new game.

What is an equation?

An equation is an expression which has an equality symbol in it.

We are given that, Wyatt is saving up money for a new game. It costs $60,

including tax.

He has already saved $20. At least how much more money, X, does he need to save

Hence the equation can be given as

X + 20 = 60

On solving the equation X = 40

Hence Wyatt needs to save $40 to buy the new game

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The three-unit multipliers are follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.

As per the given,5280ft

It is known that 1 ft = 12 inches.

5280ft = 5280 x 12 inches

It is known that 1 inch = 2.54 cm

5280 x 12 inches = 5280 x 12 x 2.54 cm

It is known that 1 cm = 0.01 meter

5280 x 12 x 2.54 cm = 5280 x 12 x 2.54 x 0.01 meter

⇒  1609.344 meters

Hence "The three-unit multipliers are as follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters".

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Check the picture below.

Answer:

b=98 and a=82

Step-by-step explanation:

b and 98 are corrisponding angles which means that they are both 98

a+b=180 because it is a straight line

a+98=180 subtract 98 from both sides a d you get a=82

The value of the variables in the equation are as follows:

1. x = -4 / 9

2. t = -8

3. x = -54

4. x = -3

5. x = 1 / 6

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Let's find the solution of the equations. The solution of the equation is the value of the variable x. A variable is a number represented by a letter in an equation.

Therefore,

1.

-4  = 9x

divide both sides of the equation by 9

x = - 4 / 9

2.

−32=4t

divide both sides of the equation by 4

t = - 32 / 4

t = - 8

3.

x − 18 = −72

add 18 to both sides of the equation

x - 18 + 18 = -72 + 18

x = -54

4.

−18 = x − 15

add 15 to both sides of the equation

-18 + 15 = x - 15 + 15

-3 = x

x = -3

5.

−24x = −4

divide both sides of the equation by - 24

x = - 4 / -24

x = 1 / 6

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The simple interest earned on a 2,000 principal at 8% interest for 5 years is I = $1,937.50.

Therefore,

I = Prt

First, converting R percent to r a decimal

r = R/100 = 3.875%/100 = 0.03875 per year,

then, solving our equation

I = 10000 × 0.03875 × 5 = 1937.5

I = $ 1,937.50

The simple interest accumulated

on a principal of $ 10,000.00

at a rate of 3.875% per year

for 5 years is $ 1,937.50.

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The dimension of each corral should be 25 feet in width and 33⅓ feet in length so that the enclosed area will be a maximum.

Adjacent rectengular corral has length and width with area formula as below.

A = L × W

Given:

Because the dimension of adjacent rectangular corrals are the same, so:

W = 4x

L = 3y

3y + 4x = 200

[tex]y = \frac{200 - 4x}{3} [/tex]

There are two adjacent rectangular corrals, so:

A = 2×L×W

[tex]A = 2 \times \frac{200 - 4x}{3} \times \: x [/tex]

A = ⅓(400x–8x²)

We can differentiate to get the maximum area:

⅓×(400x–8x²) = 0

400–16x = 0

16x = 400

x = 25 feet

Substitute x value (width) to get y value (length):

y = (200–4(25)) ÷ 3

y = (200–100) ÷ 3

y = 100 ÷ 3

y = 33⅓ feet

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The complete two-column proof that shows that ΔAKZ ≅ ΔAKC by AAS is explained below.

The AAS congruence theorem states that if two angles and one non-included side in one triangle have measures that are equal to the two corresponding angles and a corresponding side of another triangle, the two triangles are therefore congruent to each other.

In the image above, we are given two triangles that share a common side, AK. We are informed that line AK bisects an angle, ZKC, and also angles Z and C are congruent.

Therefore, using the information we are given, the two-column proof that can be written to show that the triangles are congruent by the AAS is explained below.

Statements                             Reasons                                      

1. ∠Z ≅ ∠C                              1. Given

AK bisects ∠ZKC

2. ∠ZKA ≅ ∠CKA                   2. Definition of bisection

3. AK ≅ AK                             3. Reflexive property

4. ΔAKZ ≅ ΔAKC                   4. AAS

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If sara takes two random sweets. The probability that the two sweets will not be the same is :111/190.

Probability of getting two of each sweet:

P( Liquorice) = (12/20)×(11/19)

P (Liquorice) =132/380

P (mints) =(5/20)×(4/19)

P (mints)  =20/380

P (Humbugs) =(3/20)×(2/19)

P (Humbugs) =6/380

Probability that two sweets will be the same

P(same) =132/380+20/380+6/380

P(same) =158/380

Hence,

Probability that two sweets will not be the same

P(not same) = 1- (158/380)

P(not same) =380 -158 /380

P(not same) = 222 /380

P(not same) =111 /190

Therefore the probability is 111/190.

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Answer: x=3

Step-by-step explanation:

5x+2=7x-4
-5x +4    -5x +4
2x=6
divide both sides by 2
x=3

The translation T due to the transformation is (5,3)

Translation can be defined as movement in a straight line

Given the rule: (x,y) → (x + 3, y + 1) as seen in the image. That means  (x,y) translated to (x + 3, y + 1). This is what we use to solve this problem.

From the figure, the value of  (x, y) can be read i.e. (x, y) = (2,2)

Thus the translation will be:

(x,y) → (x + 3, y + 1)

(2,2) → (2 + 3, 2 + 1) = (5, 3)

Therefore, the  translation T of the transformation shown in the graph is (5, 3)

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Answer:

The graph is a function.

Step-by-step explanation:

Considering the figure the unknown angles are

Using the angle in a straight line are supplementary we have

60 + a + 55 = 180

a + 115 = 180

a = 180 - 115

a = 65

applying sum of angles in a triangle equal to 180, b is calculated as follows

a + b + 90 = 180 right angle triangle

substituting for a

65 + b + 90 = 180

b + 155 = 180

b = 180 - 155

b = 25

applying vertical angle theorem

angle c = angle b

angle c = 25

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The width, labelled x in the figure is 162.5 meters

From the question, we have the following parameters that can be used in our computation:

Length = 650 - 2x

Width = x

The area of a rectangle is the product of its dimensions

So, we have

Area = Length x Width

Substitute the known values in the above equation, so, we have the following representation

A = (650 - 2x) * x

Evaluate

A = 650x - 2x²

Differentiate and set to 0

650 - 4x = 0

So, we have

4x = 650

Divide by 4

x = 162.5

Hence, the width is 162.5 meters

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Answer:

Nathan

Step-by-step explanation:

4.76 / 2.5

= (476/100) / (25/10)

= (476/100) * (10/25)

= 238/125

= 1.904

Thus, Nathan is right in saying that the decimal is incorrectly placed in the quotient of the given answer 0.19

Answer: 23%

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A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11.

A sequence's series is the total number of terms in the sequence.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

As per the given sequence, 20 - n²

The 20 - n² represents the nth term of the sequence.

Thus a(n) = 20 - n²

For the third term n = 3

a(3) = 20 - (3)²

a(3) = 20 - 9 = 11

Hence "A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11".

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The unit rate of change , d with respect to t is =  1.6  .

In the question,

it is given that ,  the relationship between d and t is proportional

also given that "  increase of 5 units in t corresponds to increase of 8 units in d ".

which is represented as 5t = 8d

Divide both sides of the equation  5t = 8d by "5" ,

t = 8/5d

t = 1.6d

next we plot the graph of t = 1.6d

we see that the above equation is a proportional linear equation

and A proportional linear equation is represented as

t = md , Where m represents the unit rate .

So , after comparing , we get

m = 1.6

Therefore , The unit rate of change of d with respect to t is 1.6  .

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Answer:

Step-by-step explanation:

first you need to find the nth term

that would be -4n+28

then you just need to substitute 20 into the position of n

-4*20 = -80

-80+28=-52

Answer:

-5 with the exponet of 11

Answer:

-1/5 or -0.2 if you are going by fraction or decimal

Using the concepts of probability, we got that that Stratified sampling is the experiment design which an insurance company which wants to study whether offering incentives for preventative care reduces overall health care costs.

In the question, actually the insurance company intends to study and understand the relationship between the health care cost of the customers and the provision of incentives for the preventative care by two groups, each having one of  two given attributes under study, which are;

a) One group consist of the customers having high health care cost and offered incentives for preventative care

b) The other group consist of the customers having only high health care cost without incentives

Therefore, the insurance company customers are stratified into the groups based on health care cost and again into the groups that have high health care cost and are offered preventative care and those that have only the high heath care cost, which is the process used to implement the stratified sampling technique.

Hence, an insurance company which wants to study whether offering incentives for preventative care reduces overall health care costs, by selecting a random sample of 200200200 of their customers and using a random number generator to select 100100100 customer account numbers to offer the incentive, the experiment design is named as  Stratified sampling.

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Answer: $2.08

Step-by-step explanation: First multiply $52 by 4% as a decimal or 0.04. Then, multiply that by the number of years.
=52(0.04)(1)

=2.08