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Question 2
Geometric sequences are a subset of:

Question 2 options:

Linear Functions


Exponential Functions


Linear and Exponential Functions

The measurement closest to the number of miles between the two towns is 227.5 miles.

A method for finding the answer to linear equations in two variables is cross-multiplication. It turns out to be the quickest way to resolve two linear equations. To cross multiply two fractions, multiply the first fraction's numerator by the second's denominator and the second fraction's numerator by the first fraction's denominator.

Given that, distance between Dallas and Houston is about 364 kilometers.

The measurement of:

8 km = 5 miles

364 km = x miles

Using the method of cross multiplication, we have:

x = 364 (5) / 8

x = 227.5 miles

Hence, the measurement closest to the number of miles between the two towns is 227.5 miles.

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Option a) $213.34 is the correct answer.

Given that, Suppose that you are 34 years old now and that you would like to retire at the age of 75. Furthermore, you would like to have a retirement fund from which you can draw an income of $70,000 annually. You plan to reach this goal by making monthly deposits into an investment plan until you retire. The amount to be deposited each month needs to be calculated. It is assumed that the annual interest rate is 8% and compounded monthly.

The formula for the future value of the annuity is given by, \(FV = C * ((1+i)n -\frac{1}{i} )\)

Where, FV = Future value of annuity

            C = Regular deposit

            n = Number of time periods

            i = Interest rate per time period

In this case, n = (75 – 34) × 12 = 492 time periods and i = 8%/12 = 0.0067 per month.

As FV is unknown, we solve the equation for C.

C = FV * (i / ( (1 + i)n – 1) ) / (1 + i)

To get the value of FV, we use the formula,FV = A × ( (1 + i)n – 1 ) /i

where, A = Annual income after retirement

After substituting the values, we get the amount to be deposited as $213.34.

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Answer:

Step-by-step explanation:

X = shirts

Y = trousers

3x + 2y = 155

Now

y + 10 = x

Make y + 10 = x equal y

-10. -10

y = x - 10

Replace y with this equation in our other equation.

3x + 2(x - 10) = 155

Do the math:

This equals x = 35

Now put x = 35 in the other equation

Y + 10 = 35

Do the math:

y = 25

$35 per shirt

$25 per trousers

Now for the bar model, the total is 155

Make a fraction of 35/155

Make a long bar. Split it into 5 parts.

Label three parts 35 and two 25

Make the 35 parts slightly bigger.

It should look like this

The expression that correctly calculates the perimeter of the shape is given as follows:

P = 2(6s + πr).

In which:

The perimeter of a square of side length s is given as follows:

P = 4s.

Hence, for three squares, the perimeter is given as follows:

P = 3 x 4s

P = 12s.

The perimeter, which is the circumference of a semicircle of radius r, is given by the equation presented as follows:

C = πr.

Hence the perimeter of two semicircles is given as follows:

C = 2πr.

The perimeter of the entire shape is given by the sum of the perimeter of each shape, hence:

P = 12s + 2πr.

P = 2(6s + πr).

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The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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Answer:

C

Step-by-step explanation:

Given y = amount of money spend for the long distance plan per month

and x = minutes used each month

Note these 2 plans are in per month basis.

Plan A: Flat $5 + $0.99 Per min used (variable cost)

transform into an equation:

y = 0.99x + 5

Plan B: Flat $10 + $0.79 per min used (variable cost)

transform into equation:

y = 0.79x + 10

Put these 2 equations together, will give you the answer as C.

The equation of the perpendicular line to x + 6y = 42 is: y = 6x + 1.

The lines that are perpendicular to each other will have slope values that have a product of -1, which means one is a negative reciprocal of the other.

Given the equation, x + 6y = 42, it can rewritten in slope-intercept form as shown below:

6y = -x + 42

6y/6 = -x/6 + 42/6

y = -1/6x + 7

The slope of the line is -1/6. The negative reciprocal of -1/6 is 6. Therefore, the slope of the line that is perpendicular to x + 6y = 42 is 6.

Substitute m = 6 and (x, y) = (1, 7) into y = mx + b to find the y-intercept (b):

7 = 6(1) + b

7 = 6 + b

7 - 6 = b

b = 1

Tp write the equation of the perpendicular line, substitute m = 6 and b = 1 into y = mx + b:

y = 6x + 1

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Answer:

O conjunto B é dado por: B = {4, 5, 6, 7, 8}

Step-by-step explanation:

A U B= { 1,2,3,4,5,6,7,8}

Todos os elementos pertencem a pelo menos um desses conjuntos.

A intersecção B = {4,5}

Os elementos 4 e 5 pertencem a pelo menos um desses conjuntos. Então, tem-se os dois primeiros elementos de B, que são 4 e 5.

A-B = { 1,2,3}

1, 2, 3 são os elementos que pertencem ao conjunto A e não pertencem ao conjunto B.

Como A U B= { 1,2,3,4,5,6,7,8}, tem-se que os elementos 4, 5, 6, 7 e 8 pertencem ao conjunto B.

O conjunto B é dado por: B = {4, 5, 6, 7, 8}

The material remained for the blanket after trimming off by Keith is 2.5 yards.

Simple subtraction and multiplication can provide the result. Beginning will be by the multiplication. Firstly finding the exact amount of material trimmed = 3×1/6

Performing multiplication and division on Right Hand Side of the equation

Trimmed material = 1/2 or 0.5

Now, we need to subtract the trimmed material from overall amount of material

Remaining material = 3 - 0.5

Performing subtraction on Right Hand Side of the equation

Remaining material = 2.5 yards

Hence, 2.5 yards of material remained.

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The type of transformation that is shown in the graph below is reflection.

option C.

A rotation is a form of transformation that turns a figure about a point. We call this point the center of rotation.

A figure and its rotation maintain the same shape and size but will be facing a different direction.

A reflection can be thought of as folding or "flipping" an object over the line of reflection.

So we can conclude that rotation involves rotating a figure around a fixed point, while reflection involves creating a mirror image of a figure across a line.

Rotation changes the orientation of the figure, while reflection changes its position relative to the line of reflection.

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Answer:

6.50

Step-by-step explanation:

Is it

Answer:

x = 7.5

Step-by-step explanation:

This can be solved via cross multiplying.

6x = 5 × 9 | Multiply the denominators by the respective nominators.

6x = 45 | Multiply 5 × 9

x = 7.5 | Divide 45 ÷ 6 (Division Property of Equality)

Answer:

x=7.5

Step-by-step explanation:

for this you would cross-multiply to get x

6x=9(5)

6x=45

x=7.5

We see that since they are congruent triangles, their corresponding sides are also equal.

-> 2x + 1 = x + 3.
-> x + y = 3x - 3y

From the first equation, we can solve for x ;

2x + 1 = x + 3

Minus both sides by 1 :

2x = x + 2

Finally, minus both sides by x :

x = 2.

We substitute the value of x = 2 into the second equation :

2 + y = 6 - 3y

Add both sides by 3y :

2 + 4y = 6

Solve for y : 4y = 4 -> y = 1.

\(n-2=10n+42\\n-10n=42+2\\-9n=44\\\frac{-9n}{-9} =\frac{44}{-9} \\n=-\frac{44}{9}\)

Hope this helps.

Answer:

x=3

Step-by-step explanation:

6 times 3 equals 18. 18+2 equals 20. So X=3

Answer:

\( \sf \: x = 3\)

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 2 + 6x = 20

Then the value of x will be,

→ 2 + 6x = 20

→ 6x = 20 - 2

→ 6x = 18

→ x = 18 ÷ 6

→ [ x = 3 ]

Hence, the value of x is 3.

The nurse should teach the parents to administer 2.5 teaspoons of the acetaminophen liquid suspension per dose.

The prescribed dosage of acetaminophen is 300 mg every 4 hours as needed. The liquid suspension provides 120 mg of acetaminophen per 5 mL (1 teaspoon). To determine the number of teaspoons required for the prescribed dosage, we can set up a proportion:

120 mg / 5 mL = 300 mg / x mL

Cross-multiplying, we get:

120 mg * x mL = 5 mL * 300 mg

Simplifying, we have

120x = 1500

Dividing both sides by 120, we find:

x = 1500 / 120 = 12.5 mL

Since there are 5 mL (1 teaspoon) in each dose, we can convert 12.5 mL to teaspoons:

12.5 mL / 5 mL = 2.5 teaspoons

Therefore, the nurse should teach the parents to administer 2.5 teaspoons of the acetaminophen liquid suspension per dose to ensure the child receives the prescribed dosage of 300 mg.

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Answer:

Sale price:  $722.50

Step-by-step explanation:

Subtract 15% from 100%, obtaining 85%.  The computer is sold for 85% off.

Converting this 85% to a mixed decimal, we get 0.85, and then we multiply the original price ($850) by this 0.85:  0.85($850) = $722.50

According to the question The local sidereal time (LST) at noon on March 21st is approximately 12:00 (option c).

To determine the LST, we need to consider the rotation of the Earth and its relation to the stars. LST is based on the apparent motion of the vernal equinox, which completes a full cycle in approximately 24 hours.

Since noon is halfway through the day, we can estimate that the LST at noon would be approximately half of 24 hours, which is 12:00. This assumes that we are considering a location where the local time is synchronized with the standard time zone and there are no factors like daylight saving time or variations in the location's longitude that can affect the LST calculation.

Therefore, the correct answer is option c) 12:00 local sidereal time.

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Ordered pairs of points that can be plotted to graph are (-1,1),(1,5).

The correct option is (b).

A graph is a structure made up of a collection of things where some object pairs are conceptually "connected." Each pair of connected vertices is known as an edge, and the items are represented by mathematical abstractions called vertices (also known as nodes or points) (also called a link or line). In a diagram, a graph is often represented by a group of dots or circles for the vertices and lines or curves for the edges. Graphs are one of the subjects covered in discrete mathematics. Both directed and undirected edges are possible. The fundamental topic of graph theory is graphs.

Calculation:

We have to find the ordered pair of points that can be plotted to graph of 6x - 3y = -9

By putting x =  -1

⇒ -6 - 3y = -9

⇒ 3 = 3y

⇒ y = 1

By putting x = 0

⇒ -3y = -9

⇒ y = 3

By putting x = 1

⇒ 6 - 3y = -9

⇒ 15 = 3y

⇒ y =  5

So, the ordered pairs obtained are (-1,1),(0,3) and (1,5).

Hence, the correct option is (b)

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The exponential equation is \(y=ab^x\). Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

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The exponential equation is y = \(ab^{x}\) . Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

The formula for exponential regression is y = \(ab^{x}\) . This refers to the process of arriving at the best exponential curve equation for your dataset. This regression is very similar to linear regression and tries to find the best (straight line) line equation for a data set.

Exponential regression refers to the process of obtaining the best exponential curve equation for a data set.

A model that explains the process of doubling growth.

The exponential equation is y = \(ab^{x}\)

Exponential functions are commonly used in life sciences and are used to represent the specific quantity that you want to model. B. Population size modeled over time. Plots of experimental data are usually plotted with time on the x-axis and quantity on the y-axis.

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The ratio of the volume of one of alex's cans to the volume one of felicia's cans is 1:2.

The cylinder three-dimensional shape consists of two parallel circular bases connected by a curved surface.

We have to find the ratio of the volumes of the can, which are in cylinder shape.

We will find the volume first.

Diameter is given, we divide by 2 to get the radius. h is height and  is radius in the formula.

Volume=πr^2h

Volume of alex can V1= π*(6/2)^2*12

                                 =π*3^2*12

                                   =π*9*12

                                   =108π

Volume of felicia can V2= π*(12/2)^2*12

                                 =π*6^2*6

                                   =π*36*6

                                   =216π

V1:V2= 108π:216π

          =1:2

The ratio of volumes are 1:2.

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Complete question

Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are 6 cm in diameter and 12 cm high. Felicia buys cat food in cylindrical cans that are 12 cm in diameter and 6 cm high. What is the ratio of the volume one of Alex's cans to the volume one of Felicia's cans?

Answer:

0, 1/18, and 1/36

Step-by-step explanation:

For i = 2, the probability it lands on 6 is 0, because you cannot sum to 2 with a 6. The same applies to i = 3 thru i = 6.

For the probability that at least one of a pair of fair dice lands on 6 for i = 7, there are only two possible ways, the first roll is a 6 and the second roll is a 7, and the first roll is a 1 and the second roll is a 6. The total amount of ways is 6 * 6 = 36, so the total probability is 1/18. This also applies to i = 8 thru i = 11.

For i = 12, there is only one way to get 12, the first dice lands on 6 and the second dice lands on 6. Assuming the dice are indistinguishable, the probability is 1/36.

The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.

We have,

The complementary probability of "at least one die lands on 6" is "neither of the dice lands on 6."

Therefore, you need to find the probability that neither of the dice lands on 6 for each possible sum i, and then subtract that probability from 1 to get the desired probability.

Let's go through the cases:

i = 2 (only possible sum with two dice):

In this case, both dice must show a 1.

The probability of this happening on a fair 6-sided die is

(1/6) * (1/6) = 1/36.

i = 3: The combinations are (1, 2) and (2, 1).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 4:

The combinations are (1, 3), (2, 2), and (3, 1).

The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.

i = 5:

The combinations are (1, 4), (2, 3), (3, 2), and (4, 1).

The probability of any of these happening is 4 * (1/6) * (1/6) = 1/9.

i = 6:

The combinations are (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1).

The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.

i = 7:

The combinations are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).

The probability of any of these happening is 6 * (1/6) * (1/6) = 1/6.

i = 8:

The combinations are (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2).

The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.

i = 9:

The combinations are (3, 6), (4, 5), and (5, 4).

The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.

i = 10:

The combinations are (4, 6) and (6, 4).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 11:

The combinations are (5, 6) and (6, 5).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 12:

The combination is (6, 6).

The probability of this happening is (1/6) * (1/6) = 1/36.

Now, sum up the probabilities for each case:

(1/36) + (1/18) + (1/12) + (1/9) + (5/36) + (1/6) + (5/36) + (1/12) + (1/18) + (1/18) + (1/36)

This simplifies to:

69/36 = 23/12

Thus,

The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.

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Answer:

3

Step-by-step explanation:

Answer:

its not 3

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

Step 1

Matt is ordering basketball jerseys For his country's league. Last year he ordered 512 jerseys. 64 those jerseys were orange.

The ratio of all Jerseys to Jerseys that are Orange =

512 : 64

8 : 1

Step 2

If he ordered 600 jerseys this year, how many of them will be Orange if the ratio of orange jerseys to all the jerseys remain the same?

Since we are maintaining the ratio in step 1

Let the number of orange jerseys = x

600 : x = 8 : 1

Hence

600/x = 8/1

Cross Multiply

8 × x = 600 × 1

8x = 600

x = 600/8

x = 75

Therefore, this year, the number of orange jerseys = 75

Answer:

0.333

Step-by-step explanation:

The expression (9.6 × 10³) × (6.7 × 10²) can be simplified in scientific notation as  6.432 × 10⁶ , 64.32 × 10⁵ and (9.6 × 6.7) × (10³ × 10²) .

Scientific notation is a means to express values that are either too big or too little to be conveniently stated in decimal form (typically would result in a long string of digits). It is also known as standard form in the UK and scientific form, standard index form, and standard form. Scientists, mathematicians, and engineers frequently utilize this base ten notation because it can make some mathematical operations simpler.

The given expression is : (9.6 × 10³) × (6.7 × 10²)

First we multiply the decimal terms separately.

So  (9.6 × 6.7) = 64.32 and now we multiply the power terms

10³ × 10² = 10²⁺³ = 10⁵ ( By using the properties of exponents)

So in proper scientific notation 64.32 × 10⁵ = 6.432 × 10⁶

Which can also be written as 6.432 × 10⁶ or (9.6 × 6.7) × (10³ × 10²) .

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