Mariah invested her money. The balance in the account for any given year is modeled by the function f(t)=400(1.15)t , where t represents the number of years after she opened the account. Colton invested his money and his balance is modeled by the function represented in the table:

Year 0 1 2 3 4
Balance ($) 500 550 600 650 700
Compare the two functions. Which statements are correct?

Select each correct answer.

Question 1 options:

Colton's account will always have a higher balance than Mariah's for any given year.


Mariah's balance will always be higher than Colton's for any given year.


In the fifth year, Mariah's balance will be higher than Colton's.


Mariah's beginning balance was $400 and Colton's beginning balance was $500.


In the fifth year, Colton's balance will be higher than Mariah's.

Answer:

P=4

Step-by-step explanation:

P(3) =12

This means that P multiplied by 3 would equal 12.

3 x 4 = 12

So, 'P' equals 4.

So,

We're going to find the x and y intercepts of the equation so we could graph it.

Let's find the x-intercept first:

To find the x-intercept, what we do is to make y=0 and then solve the equation for x. This is:

Therefore, the x-intercept is x=5 , y=0. Or (5,0) as well.

To find the y-intercept, we state something similar. We make x=0 and then solve the equation for y. This is:

Therefore, the y-intercept is x=0 y=-9, or (0,-9) as well.

Finally, to graph, we just plot both points and draw a line that passes through them. This is:

Garage B is more cost-effective for any parking duration exceeding 2 hours.

When comparing Garage A and Garage B based on their pricing structure, it's important to consider both the flat fee and the hourly rate to determine which option is more cost-effective.

Garage A charges a flat fee of $5, regardless of the duration of parking, and an additional $2 for every hour parked. This pricing structure benefits those who need to park for shorter durations, as the flat fee is relatively low.

However, for longer parking durations, the hourly charge can accumulate significantly, making it less favorable for extended stays.

On the other hand, Garage B follows a different approach by charging a rate of $4.50 per hour with no flat fee. This pricing structure is more suitable for those who require shorter parking times, as they only pay for the exact duration of their stay. In such cases, Garage B would likely be more cost-effective compared to Garage A.

However, for longer stays, Garage A might offer better value. For example, if someone needs to park for 6 hours, Garage A would charge $17 ($5 flat fee + 6 hours * $2/hour) while Garage B would charge $27 ($4.50/hour * 6 hours). In this scenario, Garage A would be the more affordable option.

Ultimately, the choice between Garage A and Garage B depends on the individual's specific parking needs. If the stay is anticipated to be short, Garage B's hourly rate is preferable.

However, for longer durations, Garage A's combination of a flat fee and hourly rate may result in lower overall costs. It's essential to consider the anticipated length of stay to make an informed decision.

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Answer:

  4

Step-by-step explanation:

You are given a table of function values in which x increases by 2, and you want to know the factor by which f(x) increases when x increases by 1.

Let k represent the factor by which f(x) increases when x increases by 1. This means ...

  f(2) = k·f(1)

  f(3) = k·f(2) = k·(k·f(1)) = k²·f(1)

  64 = k²·4

  k² = 64/4 = 16

  k = √16 = 4

The output value increases by a factor of 4 as the input value increases by 1.

__

Additional comment

The table values would also be obtained if the factor of increase were -4. That is, f(x) = -(-4)^x would give the same table. In that case, f(x) would not be a continuous function.

The expression without absolute value bars is 3.84.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

|√10 - 7 |

= | 3.16 - 7 |

= | -3.84 |

= 3.84

Thus,

The value of the expression is 3.84.

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The Equivalent ratio to 8/2 is 4/1, 24/6, 32/8 and 48/12.

We have,

Cylinder and prism.

Here we have to find the equivalent ratio to 8/2.

First simplifying the given ratio as

8/2

= (4 x 2)/2

= 4 /1

Now, some more ratios equivalent to 8/2.

1. 8/2 x 3/3 = 24/ 6

2. 8/2 x 4/4 = 32/8

3. 8/2 x 6/6= 48/12

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Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

The smallest positive integer n such that t \($\sqrt[4]{56 \cdot n}$\)  is an integer is 686.

We have to find the smallest positive integer n such that \($\sqrt[4]{56 \cdot n}$\) is an integer

To find the smallest positive integer n such that  \($\sqrt[4]{56 \cdot n}$\)   is an integer, we need to determine the factors of 56 and find the smallest value of n that, when multiplied by 56, results in a perfect fourth power.

The prime factorization of 56 is:

56 = 2³ × 7

The prime factors of 56 need to be raised to multiples of 4.

Therefore, we need to determine the smallest value of n that includes additional factors of 2 and 7.

To make the expression a perfect fourth power, we need to raise 2 and 7 to the power of 4, which is 2⁴ × 7⁴

The smallest value of n that satisfies this condition is:

n = 2 × 7³ = 2× 343 = 686

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Answer:

0.36ml

Step-by-step explanation:

Note: micrograms = \(10^{-6} g\)

Given the concentration,

\(500*10^{-6} g = 1ml\\1*10^{-6}g =\frac{1}{500} ml\\180*10^{-6} g=(\frac{1}{500} *180)ml\\180micrograms = 0.36ml\)

Answer:  89 yards

Step-by-step explanation: The perimeter is all the sides added up together. Since the width of the field is 52, the two sides are 52 yards which in total is 104 yards. 282- 104 = 178 yards. The length is 178/2 yards which is 89 yards.

Answer:

75

Step-by-step explanation:

math

Answer:

-7

Step-by-step explanation:

The numerator of a  fraction is 1 more than  twice its denominator.

Let the denominator=x

Therefore, the numerator=2x+1

The fraction is: \(\dfrac{2x+1}{x}\)

If 4  is added to both the  numerator and the denominator, the fraction reduces to 3.

Therefore:

\(\dfrac{2x+1+4}{x+4} =3\)

First, we solve for x

\(\dfrac{2x+5}{x+4} =3\)

Cross multiply

2x+5=3(x+4)

Open the bracket on the right-hand side

2x+5=3x+12

Collect like terms

3x-2x=5-12

x=-7

Therefore, the denominator of the fraction, x=-7

Answer:

25

Step-by-step explanation:

range = largest value - smallest value (123-25)

Answer:

Step-by-step explanation:

6x+12≥48

    -12   -12

6x   ≤   36

6           6

 x≤6

Answer:

x − 43 = 90

Step-by-step explanation:

2x + 43 = 180

2x − 43 = 90

x + 43 = 180

x − 43 = 90

Recall the definition of absolute value:

\(|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}\)

Then we have a few cases to consider:

• If \(4x-5\ge0\) and \(-x+5\ge0\), the equation simplifies to

\(4x-5 = -x+5 \implies 5x=10 \implies \boxed{x=2}\)

• If \(4x-5<0\) and \(-x+5\ge0\), we get

\(-(4x-5) = -x + 5 \implies -3x = 0 \implies \boxed{x=0}\)

• If \(4x-5\ge0\) and \(-x+5<0\), then

\(4x-5 = -(-x+5) \implies 3x=0 \implies x=0\)

but we already have this solution.

• If \(4x-5<0\) and \(-x+5<0\), then

\(-(4x-5) = -(-x+5) \implies -5x = -10 \implies x=2\)

which we also already found.

Answer:

19 of each

Step-by-step explanation:

You have the right one selected.

The answer is 2:1

To find this take each side of ABC and its corresponding side on DEF, then simplify. You can treat ratios just like fractions, so simplify them in the same way.

20:10 becomes 2:1

12:6 becomes 2:1

16:8 becomes 2:1

Answer:

Denise types faster.

Step-by-step explanation:

In order to get to 12 minutes you must times 4 by 3. When you do this you also must time 13 by 3. That number is greater than Nancy's typing rate, so that means Denise is faster.

Answer:

Personally they both type slow but denise

Step-by-step explanation:

because denise is averaging 3 words 1 minute and nancy is averaging 2 words a minute I type an average of 48 Words per miniute

The correct statement is that the theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 16 over 40.

We know that there are 40 students at summer camp who are divided into two groups for either swimming or hiking. Each camper flips a coin, where heads represents swimming and tails represents hiking. The outcome frequency for swimming is 16 and for hiking is 24.
To compare the probabilities, we need to first understand the difference between theoretical probability and experimental probability. Theoretical probability is the expected probability of an event occurring based on mathematical calculations and assumptions, whereas experimental probability is the actual observed probability of an event occurring based on data from experiments or observations.
Option 1 states that the theoretical probability of swimming is one half, but the experimental probability is 24 over 40. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is equal to one half, and the experimental probability of swimming is also 40%, which is equal to 16 over 40. Therefore, this option is false.
Option 2 states that the theoretical probability of swimming is one half, but the experimental probability is 16 over 40. This statement is correct because the theoretical probability of swimming is 50%, which is equal to one half, and the experimental probability of swimming is also 40%, which is equal to 16 over 40. Therefore, this option is true.
Option 3 states that the theoretical probability of swimming is 16 over 24, but the experimental probability is one half. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is not equal to 16 over 24, and the experimental probability of swimming is also 40%, which is not equal to one half. Therefore, this option is false.
Option 4 states that the theoretical probability of swimming is 24 over 40, but the experimental probability is one half. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is not equal to 24 over 40, and the experimental probability of swimming is also 40%, which is not equal to one half. Therefore, this option is false.
In conclusion, the correct statement is that the theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 16 over 40.

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Answer:

x=11.34

Step-by-step explanation:

The next 3 terms of the sequence defined recursively by the formula f(n + 1) = f(n) + 2 are; 1, 3 and 5.

A sequence is defined as an arrangement of numbers in a particular order.

From the question f(n + 1) = f(n) + 2 such that rewriting we have;

f(n) = f(n + 1) - 2

The first is -1, so n = 1 and we derive the next term f(2) as follows;

f(1) = f(1 + 1) - 2 = -1

f(1) = f(2) - 2 = -1

f(2) = 2 - 1 {add 2 to both sides}

f(2) = 1

f(2) = f(2 + 1) - 2 = 1

f(3) = 2 + 1 {add 2 to both sides}

f(3) = 3

f(3) = f(3 + 1) - 2 = 3

f(4) = 3 + 2 {add 2 to both sides}

f(4) = 5

Therefore, we have the next three terms of the sequence to be 1, 3, and 5.

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Answer:

A

Step-by-step explanation:

Answer:

A) I hope I helped you ◉‿◉

The best estimate of how much she will spend on movies and eating out is given as follows:

$162.

The best estimate of how much she will spend on movies and eating out is obtained applying the proportions in the context of the problem.

The percentages associated with movies and eating out are given as follows:

The amount that she has left is given as follows:

$300.

Hence the best estimate of how much she will spend on movies and eating out is obtained as follows:

(0.3 + 0.24) x 300 = 0.54 x 300 = $162.

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The correct statement regarding why f(x) ≠ g(x) is given as follows:

a. f(x) ≠ g(x) because the graphs do not intersect.

Two functions are classified as different when they do not intersect.

The functions in this problem are given as follows:

For them to intersect, it is needed that:

f(x) = g(x).

x² = 2x - 3.

x² - 2x + 3 = 0.

Which is a quadratic function with the coefficients given as follows:

a = 1, b = -2, c = 3.

The number of solutions of the quadratic function depends on the discriminant, given as follows:

Discriminant = b² - 4ac.

Hence the numeric value for the discriminant in this problem is given as follows:

Discriminant = (-2)² - 4 x 1 x 3 = -8.

As the discriminant is negative, the quadratic function has no solutions, meaning that the functions do not intersect and statement a is correct.

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Answer:

its C

Step-by-step explanation:

At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

From given graph we can see that

At x=2, the function in the graph is approaches to infinity.

It means function is not defined at x=2

We know that a rational function is undefined when denominator is equal to zero.

For equation 1:

f(x)= 2(x+2)/(x-2)

Equating the denominator:

x-2=0

x=2

It means function is not defined at x=2

The y-intercept is: y= -2

The function is passing through the point (1,-6).

When we substitute x=1

Hence, option 1 is true.

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The slope of the straight line passing through the two given points is undefined which means the line is parallel to the y-axis.

Let us consider the two points A(x₁,y₁) and B(x₂,y₂) be the two points (7,-6) and (6,-6) on the cartesian coordinates.

Let the slope of the line joining A (7,-6)  and B(6,-6)  be m.

We know that the slope of a line is given by:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Slope of the line

= (6-7) / (-6+6)

= -1 / 0

= undefined

Since the slope is undefined we can say that the straight line is parallel to the y axis.

we know that tan 90° = ∞

So any line parallel to this line will have the same slope as the y axis.

Hence the slope of the given line is undefined or infinity.

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Answer:

-14k+17

Step-by-step explanation:

Answer:

i think the question might be wrong.

Rays: BD, AC, CA, AB. Lines:  AC

A line is a straight path of points that has no beginning or end

A ray is a portion of a line which has one endpoint and extends forever in one direction

Let's put the definitions:

Note: the arrow is an indication no endpoint

So we have ray BD (it starts from the dot at B and the arrow shows it extends forever  in the direction of D)

We have ray AC (it starts from the dot at A and the arrow shows it extends forever  in the direction of C)

We also have ray CA (it starts from the dot at C and the arrow shows it extends forever  in the direction of A)

Then ray AB (it starts from the dot at A and the arrow shows it extends forever  in the direction of B)

Then  line AC (it's bounded by 2 arrows, so it has no endpoint)

Therefore, the rays are BD, AC, CA and AB, and the line is AC. So the 1st option is the answer

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