At the beginning of the year, Alyssa had $100 in savings and saved an additional $7
each week thereafter. Colton started the year with $55 and saved $10 every week. Let
A represent the amount of money Alyssa has saved t weeks after the beginning of the year and let C represent the amount of money Colton has saved t weeks after the
beginning of the year. Write an equation for each situation, in terms of t, and determine the amount of money Alyssa and Colton have saved in the week that they
have the same amount of money saved.

The equation of the square root function is g(x) = √(x - 1) + 3

A square root function is represented as

f(x) = √x

The transformation rule is given as

Shifted up 3 units and right 1 unit

This can be represented as

(x - 1, y + 3)

So, we have

g(x) = f(x - 1) + 3

This gives

g(x) = √(x - 1) + 3

From the question, we have

It contains the point (5,7).

This means that

g(5) = 7

So, we have

g(5) = √(5 - 1) + 3

Evaluate

g(5) = 7

Hence, the equation of the square root function is g(x) = √(x - 1) + 3

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The height of the building is 1122.528 feet.

Angle of elevation:

Angle of elevation means an angle between the horizontal plane and oblique line from the observer's eye to some object above his eye.

Given,

The angle of elevation to the top of a building in New York is 12° from the ground and 1 mile from the base of the building.

Here we need to find the height of the building.

We know that,

The expression for the height of the building is,

h = tanΘ × x

Where the value of

tan Θ = 12°

x = 1 mile

So, When we apply the value on the formula,

The we get,

h = tan 12° x 1

So, apply the value of tan 12 degree,

h = 0.2126 x 1

h = 0.2126 mile

Simplify the above equation using the information

1 mile = 5280 ft.

That is equal to

h = 1122.528 feet.

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The solution of the of the expression is as follows:

Three less than the quotient of a number and two has a result of thirteen.

Therefore,

let

the number = x

The quotient of the number and two  = x / 2

Therefore,

x  / 2 - 3 = 13

add 3 to both sides

x  / 2 - 3 = 13

x  / 2 - 3 + 3 = 13 + 3

x / 2 = 16

cross multiply

x = 2 × 16

x = 32

Therefore, the solution of the of the expression is as follows:

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The populations of both towns would be​ equal in nine months.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let's assume that both town's populations will be equal in x months.

After x months, the population of the first town is given by

200x - 75x + 57,900  

The population of the second town after x months is  given by

60,600 - 175x

In order for the population of both towns to be equal, we have

200x - 75x + 57,900 = 60,600 - 175x

This is the required equation that represents the given situation.

200x - 75x + 57,900 = 60,600 - 175x

Rearrange the likewise terms and apply arithmetic operation

200x - 75x + 175x = 60,600 - 57,900

300x = 2700

x = 2700/300

x = 9

Therefore, the populations of both towns would be​ equal in nine months.

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A box with a square base and a top is to be constructed from 10 square meters of material. 40 square meters will maximize the volume that the box can hold.

LSD use among secondary school understudies is a specific concern. More Volume is a proportion of consumed three-layered space. It is frequently evaluated mathematically utilizing SI inferred units or by different supreme units. Volume is characterized as the space involved inside the limits of an article in three-layered space. It is otherwise called the limit of article. Volume is a proportion of consumed three-layered space. It is frequently measured mathematically utilizing the SI determined unit, the cubic meter. The volume of a compartment is by and large comprehended to be the limit of the compartment, how much liquid (gas or fluid) that the holder could hold, instead of how much space the actual holder dislodges. Three layered numerical shapes are additionally relegated volumes.

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Answer:

k = 2.25 or  9/4

Step-by-step explanation:

2x^2 - 6x + k = 0

2(x^2 - 3x + 2.25) = 0

x                 -1.5

x                 -1.5

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

(x - 1.5) (x - 1.5) = 0

x = 1.5 or 15/10 = 3/2

one solution

The set of ordered pairs that represents a function is: {(0, 2), (1, 4), (2, 6), (3, 6)}

We know that a function defines a relation between input and output values.

In function for each input there is exactly one output.

We need to find the set of ordered pairs that represents a function.

We need to find the set of ordered pairs such that for each x value (x coordinate) there is unique y value (y coordinate).

1) {(0, 1), (1, 3), (1, 5), (2, 8)}

This set of ordered pairs cannot be a function.

As for x = 1, there are two output values 3 and 5.

2) {(0, 0), (1, 2), (2, 6), (2, 8)}

This set of ordered pairs cannot be a function.

As for x = 2, there are two output values 6 and 8.

3) {(0, 0), (0, 2), (2, 0), (2, 4)}

This set of ordered pairs cannot be a function.

As for x = 0, there are two output values 0 and 2.

and for x = 2, the output values are 0 and 4.

4) {(0, 2), (1, 4), (2, 6), (3, 6)}

This set of ordered pairs represents a function.

Here, for each input value there is unique output value.

Therefore, the set of ordered pairs that represents a function is: {(0, 2), (1, 4), (2, 6), (3, 6)}

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Darren's monthly payment on car loan is $210.83

Given,

Cost of the car Darren purchased = $11000

The simple interest for the car loan = 3%

Time period of loan = 5 years

We have to find the monthly payment amount:

Simple interest = PRT / 100

Where,

P = Principal amount = $11000

R = Rate of interest = 3%

T = Time period = 5 years

Now,

SI = PRT / 100

SI = (11000 × 3 × 5) / 100

SI = 110 × 3 × 5

SI = 1650

Here, the simple interest for 5 years is $1650

Now,

Total amount to be paid after 5 years = Principal amount + Simple interest

A = P + SI

A = 11000 + 1650

A = 12650

The amount to be paid after 5 years is $12650

Next,

The monthly payment amount:

Number of months in 5 years = 12 × 5 = 60 months

So,

Monthly payment amount = Total amount after 5 years / Total months in 5 years

Monthly payment amount = 12650 / 60 = 210.83

That is, the monthly payment amount on car loan is $210.83

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x=±a

1. take the square root of both sides

If two markers are selected at random, one after another, without replacement, the probability that both will be blue = 0.0316

For given question,

there are 20 colored markers in a package – 8 black, 4 blue, 4 red, 4 green.

if two markers are selected at random, one after another, without replacement, we need to find the probability that both will be blue.

The probability that the selecting one blue marker is:

4/20

After selecting one blue marker, there are 19 markers in a package -  8 black, 3 blue, 4 red, 4 green.

The probability of selecting second blue marker would be,

3/19

So, the probability that both will be blue:

4/20 × 3/19

= 0.2 × 0.16

= 0.0316

Therefore, if two markers are selected at random, one after another, without replacement, the probability that both will be blue = 0.0316

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The two equations to set up to solve the equation are 3x - 2 = 19 and 3x - 2 = -19

The equation is given as

|3x - 2| = 19

The above equation is an absolute value equation.

When it is split, the constant would be represented as positive and negative

So, the equivalent equations are

3x - 2 = 19 and 3x - 2 = -19

Hence, the two equations to set up to solve the equation are 3x - 2 = 19 and 3x - 2 = -19

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Answer:

anaaaa

Step-by-step explanation:

Average of 5 courses is 72

• In simple words, average is the number which is the representative of the list of the numbers.

• Average of numbers is calculated by the sum of the numbers divided by total numbers.

We are given that

Number of courses took by Adrianna = 4

Average of her course grade = 90

Number of course took by Roberto = 5

We also know that , Both students have the same sum of course grades

Let the average of Roberto be x

Average = Sum / Total Subjects

Sum = Average * Total Subjects

So,

90 * 4 = x * 5

x = 360/5

x = 72

Therefore, average of Roberto is 72

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Answer: 128

Step-by-step explanation:

a whole supplementary angle adds up to 180 degrees

so 180

   - 52

     128

Answer:

Step-by-step explanation:

(-3, 2)

Horizontal is y = 2

Vertical is x = -3

In the same way (1, 4) is

y = 4

x = 1.

Answer:

Answer is option A.

X cannot be equal to -4

Answer:

hi awaz are u in india server ?

The equation of the line with slope 2/3 and y-intercept at ( 0, - 2) is y = ( 2/3 )x - 2.

The slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible.

We have the slope 2/3 of a line and the y-intercept at ( 0, - 2 ).

Now, we know that

The slope-intercept form of the equation of a line with slope m and y-intercept at the point (0, c) is given by:

y = mx + c

The slope of the line is :

m = 2/3

And, the y-intercept is (0, c) = ( 0, -2)

Hence, the equation of the line in the slope-intercept form will be:

y = mx + c

y = ( 2/3 )x + ( - 2)

y = ( 2/3 )x - 2

Therefore, the slope-intercept form of the equation of the line is y = ( 2/3 )x - 2.

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Given the midpoint, the value of PT will be 10 2/7.

Q is the midpoint of PT,

so PQ = QT.

R is the midpoint of QT,

so QR=RT.

S is the midpoint off RT,

so RS=ST.

Let us say RS = ST = x .

Then, RT= RS + ST= x + x = 2x ,

so RT = QR = 2x

Then, QT = QR+RT = 2x+2x = 4x ,

and PQ = QT = 4x .

Then, PS= PQ+QR+RS=4x+2x+x=7x ,

and PT=PQ+QT=4x+4x=8x

The problem says that PS = 9

Therefore, 7x = 9 and x = 9/

PT = 8x = 8 × 9/7 = 10 2/7.

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P, Q, R, S, and T are on line k such that Q is the midpoint of segment PT, R is the midpoint of segment QT, and S is the midpoint of segment RT. If segment PS = 9, then what is PT?

The meaning of the function notation is the inital amount of money (in dollars) it costs you to be a member at the YMCA

The function is given as

m(x) represents the amount of money (in dollars) it costs you to be a member at the YMCA after x months

The function notation is given as

m(0)

The function notation m(0) implies that

We determine the value of m(x) when x = 0

This represents the x-intercept of the function

The x-intercept of the function is the initial value of the function

Hence, the meaning of the function notation is the inital amount of money (in dollars) it costs you to be a member at the YMCA

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The equation which can be used to determine the number of pounds of peaches and crumbles that Stephen could have purchased is 1.8x+2.5y=19.4 and if Stephen purchased 8 pounds of peaches then he also purchased 2 pounds of crumbles.

Given that the cost of peaches is $1.80 per pound and cost of crumbles is $2.50 per pound and the total expenditure done by Stephen is $19.40.

We are required to find the equation that can be used to determine the number of pounds of peaches and crumbles that Stephen could have purchased and find the number of crumbles that Stephen purchased if he had 8 pounds of peaches.

Suppose the number of pounds of peaches be x and the number of crumbles be y.

The equation will be as under:

x*1.80+y*2.50=19.40

1.80x+2.50y=19.40---------1

Put the value of x=8 to find the number of crumbles.

1.8 *8+2.50y=19.40

14.4+2.50y=19.40

2.50y=19.4-14.4

2.50y=5

y=5/2.5

y=50/25

y=2

Hence the equation which can be used to determine the number of pounds of peaches and crumbles that Stephen could have purchased is 1.8x+2.5y=19.4 and if Stephen purchased 8 pounds of peaches then he also purchased 2 pounds of crumbles.

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Answer:

113.04

Step-by-step explanation:

The probability that i will end up with one card from each suit is 3/32.

Probability:

Probability refer the possibility of the event.

The formula for the probability of the event is,

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Given,

If i choose four cards from a standard 52-card deck, with replacement,

Then we need to find the  probability that i will end up with one card from each suit.

In the first draw, we can take one card, if it is a spade one,

Then for the second draw we have 39 options

For the third draw we have 26 options

For the fourth draw we have 13 options,

So, the probability that i will end up with one card from each suit is

=> 1 x 39/52 x 26/52 x 13/52

=> 1 x 3/4 x 1/2 x 1/4

=> 3/32

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correct answer is random sample

A simple random sample, also known as an SRS, is a subset of people (also known as a sample) picked at random from a larger group of people (also known as a population) with an equal probability. It is a method of choosing a sample at random. Each subset of k people in SRS has the same chance of getting selected for the sample as any other subset of k people. [1] An objective sampling strategy is a straightforward random sample. Simple random sampling is a fundamental kind of sampling that may be used in combination with other, more sophisticated sampling techniques.

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There are 1176 is the minimum whole number of tiles Tomás needs to completely cover the rectangular floor.

Rectangle:

Rectangle means a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles.

Given,

Tomás wants to tile a rectangular floor with square tiles that measure 12 inches on a side. The floor measures 10 feet 6 inches long by 8 feet 6 inches wide.

Here we need to find if he is able to cut the tiles without waste, what is the minimum whole number of tiles Tomás needs to completely cover the floor.

Here we have to convert the feet into inches for easy calculation,

1 feet = 12 inches

So, the length is ,

l = 120 + 6 = 126 inches

w = 96 + 6 = 112 inches

So, the area of the floor is,

=> l x w

=> 126 x 112

=> 14,112

Here we need to use 12inches square tile,

So,

=> 14112 / 12

=> 1176.

Therefore, there are 1176 tiles are need to cover the floor.

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Answer:

Let's call the number of Twix bars "x".

Since there are three times as many Twix bars as Milky Ways, the number of Milky Ways is x / 3.

And, since there are 5 fewer Snickers bars than there are Twix bars, the number of Snickers bars is x - 5.

So, the total number of candy bars can be found by adding the number of each type of candy bar:

x + x / 3 + x - 5 = total number of candy bars

Combining like terms, we get:

5x / 3 - 5 = total number of candy bars

To find the value of x, we can solve this equation for x.

5x / 3 = total number of candy bars + 5

5x / 3 = total number of candy bars + 5

5x = 3(total number of candy bars + 5)

5x = 3(total number of candy bars) + 15

5x = 3(total number of candy bars) + 15

5x - 15 = 3(total number of candy bars)

5x - 15 = 3(total number of candy bars)

(5x - 15) / 3 = total number of candy bars

So, the total number of candy bars can be found by dividing (5x - 15) by 3. The value of x represents the number of Twix bars, and the rest of the candy bars can be found using the relationships described in the problem.

If the equation of the circle is [tex]x^{2} +y^{2}-8x+6=0[/tex] then the center and radius of the circle is (4,0) and [tex]\sqrt{10}[/tex] respectively

Given,

The equation,

[tex]x^{2} +y^{2}-8x+6=0[/tex]

Rearrange the equation

[tex]x^{2} -8x+6+y^{2} =0[/tex]

Add 10 on both sides

[tex]x^{2} -8x+16+y^{2} =10[/tex]

Change to standard form

[tex](x-4)^{2}+(y-0)^{2}=(\sqrt{10})^{2}[/tex]

Standard form of the equation of a circle is

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

Here the r is the radius of the circle and (h,k) is the center

So,

Center = (4,0)

Radius = [tex]\sqrt{10}[/tex]

Hence, if the equation of the circle is [tex]x^{2} +y^{2}-8x+6=0[/tex] then the center and radius of the circle is (4,0) and [tex]\sqrt{10}[/tex] respectively.

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If the number of checks are greater than 25, the Simple Checking plan cost​ less.

We have two checking account plans at Parson's bank.

We have to determine for what number of checks per month will the Simple Checking plan cost​ less.

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Let for x number of checks per month the simple checking plan cost less.

For No frills plan -

Charge per check - $0.25

Therefore, for x checks, it will cost - $0.25x

For Simple Checking plan -

Fixed monthly charges - $5

Charges per check - $0.50

Therefore - for x checks - $5 + $0.50x

Now - for Simple Checking plan to cost​ less than No frills plan -

5 + 0.05x < 0.25x

5 < 0.25x - 0.05x

5 < 0.2x

x > 25

Hence, if the number of checks are greater than 25, the Simple Checking plan cost​ less.

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Answer:

108525975,11111111111111111111111

Answer: 108525975.111

Step-by-step explanation: