What does y equal?
5(2y-1)<-15

Answer:

180

Step-by-step explanation:

6 different letters.

we need to pick groups of 4.

no repetitions, but the sequence matters (code words), as e.g. RAGE is different to GEAR, although they contain the same letters.

so, we need basic permutations (instead of combinations) :

P(6, 4) = 6! / (6 - 4)! = 6! / 2! = 6×5×4×3 = 360

that is simply because regularly we would have 6 choices for the first letter, then 5 for the second, 4 for the third, and 2 for the fourth letter.

the second to the last letter is the second letter from the left in a 4-letter word.

so, we have 3 vowels for that second position.

normally, such a restriction would mean

6×3×4×3 = 216 possibilities.

but we have to distinguish the 2 cases that we pick a vowel for the first position - or not.

if not, we have 3 consonants for the first, 3 vowels for the second position as options.

if yes, we have 3 vowels for the first and 2 vowels for the second position.

that means we get

3×3×4×3 + 3×2×4×3 = 108 + 72 = 180

possibilities.

this makes also sense, when we simply say that this restriction eliminates half of our possible permutations (all with a consonant in the second position) : 360/2 = 180.

Answer:

x = 3, y = -2

Step-by-step explanation:

Rotating a point (x, y) 90° clockwise around the origin will result in the point:

(y, -x)

Applying this to point A:

A = (2, 3)

A' = (3, -2)

x = 3, y = -2

The requried initial value and value after 10 years of car are $24500 and $4285

The given exponential function is:

[tex]V(t) = 24500(0.84^t)[/tex]

To find the initial value of the car, we need to evaluate V(0):

V(0) = 24500(0.84⁰)
       = 24500(1)
       = 24500

Therefore, the initial value of the car is $24,500.

To find the value after 10 years, we need to evaluate V(10):

V(10) = 24500(0.84¹⁰)
        ≈ $4285

Therefore, the value of the car after 10 years is approximately $4285.

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The value of x is 4.4, option D is correct.

A geometric figure called an angle is made up of two rays that end at the same point, called the vertex. Radians or degrees are used to measure angles.

Given the value are;  

∠XOZ = 78°, ∠YOZ = 40° and ∠XOY = (5x + 16)°,

See the figure, according to that

∠XOZ = ∠YOZ + ∠XOY

put the values,

78 = 40 + (5x + 16)

78 - 40 - 16 = 5x

22 = 5x

22 / 5 = x

4.4 = x

Therefore, the value of x is 4.4 option D is correct.

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Therefore, the solution to the inequality is: -8 < x ≤ 1 or x = 2. In interval notation, we can write the solution as: (-8, 1] ∪ {2}.

Inequality is a mathematical statement that compares two quantities or expressions and indicates that one is greater than, less than, or not equal to the other. An inequality is typically expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to).

Here,

Since the function f is increasing, we know that if x₁ < x₂, then ƒ(x₁) < ƒ(x₂). To solve the inequality, we need to isolate x on one side of the inequality. We'll start by applying the function ƒ to both sides of the inequality:

ƒ(4x − 3) ≥ ƒ(2 − x²)

Since ƒ is increasing, we can apply it to each side of the inequality without changing the direction of the inequality:

4x − 3 ≥ 2 − x²

Next, we'll simplify the right side of the inequality by expanding the square:

4x − 3 ≥ 2 + x²

Now we'll move all the terms to one side of the inequality:

x² - 4x + 5 ≤ 0

We can factor the quadratic expression to get:

(x - 2)(x - 2 + 1) ≤ 0

Simplifying further:

(x - 2)(x - 1) ≤ 0

Now we need to determine the sign of the expression (x - 2)(x - 1) over the domain D = (-8, 4). We can do this by using a sign chart:

x x - 2 x - 1 (x - 2)(x - 1)

-8 -10 -9 +90

-1 -3 -2 +2

1 -1 0 0

4 2 3 -6

We see that (x - 2)(x - 1) is negative (less than zero) over the interval (-8,1) and positive (greater than zero) over the interval (1,4).

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According to the similarity rule, the required values are:

M = 25.2 units

∠N = 9.0°

∠P = 10.0°

Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.

One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

Triangles are similar if they have two of the same angle type, or AA (Angle-Angle).

Triangles are identical if they have two sets of proportional sides and equal included angles, or SAS (Side-Angle-Side).

So, here we have two similar figures.

First, observe the pattern of the sides of the figure.

Then, we know that:

M = 25.2 units

And in the angles:

∠N = 90/10 = 9.0°

∠P = 100/10 = 10.0°

Therefore, according to the similarity rule, the required values are:

M = 25.2 units

∠N = 9.0°

∠P = 10.0°

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These findings support the histograms in that data set 1 is skewed to the right while data set 3 is skewed to the left.

(a) A histogram for each of the data sets is as follows:Data set (1) is skewed to the right.Data set (2) has a normal distribution.Data set (3) is skewed to the right.(b) For each of the data sets, we will compute the sample mean and sample median.Sample Mean for Data Set 1: [tex]$\frac{19+24+12+19+18+24+8+5+9+20+13+11+1+12+11+10+22+21+7+16+15+15+26+16+1+13+21+21+20+19}{30}$ = 15.4[/tex]

Sample Median for Data Set 1:Arrange data set in order: {1, 1, 5, 7, 8, 9, 10, 11, 11, 12, 12, 13, 13, 15, 15, 16, 16, 18, 19, 19, 19, 20, 20, 21, 21, 21, 21, 22, 24, 24}Median = 18Sample Mean for Data Set 2: $\frac{17+24+21+22+26+22+19+21+23+11+19+14+23+25+26+15+17+26+21+18+19+21+24+18+16+20+21+20+23+33}{30}$ = 21

Sample Median for Data Set 2:Arrange data set in order: {11, 14, 15, 15, 16, 17, 17, 18, 18, 19, 19, 19, 20, 21, 21, 21, 21, 22, 22, 23, 23, 24, 24, 25, 26, 26, 26, 33}Median = 21

Sample Mean for Data Set 3: $\frac{56+52+13+34+33+18+44+41+48+75+24+19+35+27+46+62+71+24+66+94+40+18+15+39+53+23+41+78+15+35}{30}$ = 43.7333

Sample Median for Data Set 3:Arrange data set in order: {13, 15, 15, 18, 18, 19, 23, 24, 24, 27, 33, 34, 35, 35, 39, 40, 41, 41, 44, 46, 48, 52, 53, 56, 62, 66, 71, 75, 78, 94}Median = 41The mean and median of data set 1 and data set 3 are not the same. In data set 1, the mean is less than the median. In data set 3, the mean is greater than the median.

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Answer:

Using the volume formula we know that (B) 27 cubes can be fitted into the right rectangular prism.

What is the right rectangular prism?

The right rectangular prism has four rectangle-shaped side faces and two parallel end faces that are perpendicular to each of the bases.

Parallelograms make up the sides of an oblique prism, a non-right rectangular prism.

A cuboid is yet another name for a right rectangle prism.

So, the volume of the right rectangular prism:

V = wlh

Insert values:

V = wlh

V = 6*8*4.5

V = 216cm³

Now, the volume of the cube:

V = a³

V = 2³

V = 8cm³

Then, the number of cubes that can be fitted in the right rectangular prism:

216/8 = 27

Therefore, using the volume formula we know that (B) 27 cubes can be fitted into the right rectangular prism.

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Correct question:

How many cubes, with side measures of 2 cm, will fit inside a right rectangular prism with dimensions of 6 cm by 8 cm by 4 1/2 cm?

Group of answer choices

a. 24

b. 27

c. 108

d. 54

The final answer is 27

To determine how many cubes will fit inside the right rectangular prism, we need to find the volume of the prism and the volume of the cubes, then divide the volume of the prism by the volume of the cubes.

Volume of a cube (V_cube) = side^3
V_cube = 2 cm * 2 cm * 2 cm = 8 cubic cm

Volume of the right rectangular prism (V_prism) = length * width * height
V_prism = 6 cm * 8 cm * 4.5 cm = 216 cubic cm

Now, divide the volume of the prism by the volume of the cubes:
Number of cubes = V_prism / V_cube = 216 cubic cm / 8 cubic cm = 27 cubes

Therefore, 27 cubes with side measures of 2 cm will fit inside the right rectangular prism.

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The exact value of cscθ / csc(π - θ) is 1.

What is simplest radical form ?

The simplest radical form is the expression of a radical where the radicand (the number under the radical sign) has been simplified as much as possible.

First, we need to determine the hypotenuse of the right triangle formed by the terminal side of angle θ and the x-axis.

Using the Pythagorean theorem, we have:

[tex]h^{2}[/tex] = 16+ 1*1

[tex]h^{2}[/tex] = 16 + 1

[tex]h^{2}[/tex] =17

h = [tex]\sqrt{17}[/tex]

Now, we can find the value of sine and cosine of angle θ:

sinθ = opposite/hypotenuse = 1/ [tex]\sqrt{17}[/tex]

cosθ = adjacent/hypotenuse = -4/[tex]\sqrt{17}[/tex]

Therefore, cscθ = 1/sinθ = [tex]\sqrt{17}[/tex]

Now, we can substitute these values into the expression cscθ / csc(π - θ):

cscθ / csc(π - θ) = [tex]\sqrt{17}[/tex]) / csc(π - θ)

We know that csc(π - θ) = 1/sin(π - θ), and since sin(π - θ) = sinθ, we have:

csc(π - θ) = 1/sinθ = [tex]\sqrt{17}[/tex]

Substituting this back into the expression, we have:

cscθ / csc(π - θ) = [tex]\sqrt{17}[/tex]/ [tex]\sqrt{17}[/tex]  = 1

Therefore, the exact value of cscθ / csc(π - θ) is 1.

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Answer:

[tex]\large\boxed{\tt 18a+42}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to simplify the given expression.}[/tex]

[tex]\textsf{Per similar problems, we should use the \underline{Distributive Property}.}[/tex]

[tex]\large\underline{\textsf{What is the Distributive Property?}}[/tex]

[tex]\boxed{\begin{minipage}{25 em} \\ \underline{\textsf{\large Distributive Property;}} \\ \\ \textsf{Distributive Property is a property that allows us to multiply the term to the left of the parentheses into the terms inside the parentheses.} \\ \\ \underline{\textsf{\large Example;}} \\ \tt a(b+c)=ab+ac \\ \textsf{Per this example, a will multiply with the terms b and c.}\end{minipage}}[/tex]

[tex]\large\underline{\textsf{Simplifying the Expression;}}[/tex]

[tex]\textsf{For our given expression, let's use the Distributive Property.}[/tex]

[tex]\underline{\textsf{Use the Distributive Property;}}[/tex]

[tex]\tt 6 (3a + 7) \rightarrow (6 \times 3a) + (6 \times 7) \rightarrow \large\boxed{\tt 18a+42}[/tex]

Hello and greetings AtticusR9000.

To solve this exercise, we apply the distributive property, which is a mathematical rule that establishes that the multiplication of a number by the addition or subtraction of two or more numbers is equal to the addition or subtraction of the multiplication of that number by each of the numbers. that are being added or subtracted. In other words, if we have three numbers a, b and c, then the distributive property can be written as:

a × (b + c) = (a × b) + (a × c)

or also as:

a × (b - c) = (a × b) - (a × c)

This means that the multiplication of the number "a" can be distributed through the addition or subtraction of the numbers "b" and "c" to obtain the same result as if "a" were multiplied by "b" and "a" by "c" and then add or subtract the results. The distributive property is fundamental in mathematics and is used in numerous algebraic and arithmetic operations.

Now we solve by applying the distributive property:

a × (b + c) = (a × b) + (a × c)

6(3a + 7) = (6 × 3a) + (6 × 7)

18a + 42

Therefore, the solution of exercise 6(3a+7) is 18a+42.

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Angle L is 67.5 degrees. Angles F and L are opposite each other, yet the same angle degree.

Alternate interior angles are a pair of angles that are on opposite sides of a transversal and are located between two lines.

More specifically, alternate interior angles are formed when a transversal intersects two parallel lines. These angles are congruent, which means that they have the same measure or degree of rotation.

In the figure,we can see that ∠F and ∠L are alternate interior angles.

So the angles are ∠F=∠L=67.5

Hence Angle L is 67.5 degrees. Angles F and L are opposite each other, yet the same angle degree.

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Log b b an is defined as [logc c a] / [logc c b] in the base-change formula. A base of a logarithmic may utilize any (same) constant value as it's basis, therefore to change the base, we just divide [log a] by [log b].

Activity logs keep track of the time you and your staff spend on particular tasks. It is a thorough record of a tasks, the date, and the amount of time it took to perform each activity.

Log: The opposite of exponentiation in mathematics is the logarithm function. The logarithm is described as a power in which an integer must be increased in order to obtain another number, or, put another way, as a power.

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If Sara sat down to eat at 6:45 pm, the two numbers to show the time range would be 6 and 7 because 6:45 pm is between 6:00 pm and 7:00 pm.

To determine the two numbers that should be between to show the time Sara sat down to eat, follow these steps:
1. Identify the given time:

Look for the time mentioned in the question or context.

Since the time is not provided, we cannot provide specific numbers.
2. Determine the range:

Find the nearest hour before and after the given time.

These two hours will be the numbers to show the time range.

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the probability that a top-selling red and voss tire wears out before 80,000 miles is about 2.56%.

The student question asks about the probability that a top-selling red and voss tire, rated for 80,000 miles, wears out before reaching 80,000 miles. The tire's lifespan follows a normal distribution with a mean of 94,000 miles and a standard deviation of 7200 miles.
To find the probability, we need to calculate the z-score first. The z-score is a measure of how many standard deviations away from the mean a particular value is. We can use the following formula to calculate the z-score:
z = (X - μ) / σ
where X is the value (in this case, 80,000 miles), μ is the mean (94,000 miles), and σ is the standard deviation (7200 miles).

Calculate the z-score:
z = (80,000 - 94,000) / 7200
z = -14,000 / 7200
z ≈ -1.944
The z-score is approximately -1.944, which means the tire wearing out at 80,000 miles is about 1.944 standard deviations below the mean.
Find the probability:
Now, we can use the z-score to find the probability. We can look up the z-score in a standard normal distribution table or use a calculator with a built-in function for this purpose.
Using a standard normal distribution table or calculator, we find that the probability corresponding to a z-score of -1.944 is approximately 0.0256 or 2.56%.

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Assuming that the "9ft" and "11ft" refer to the dimensions of a right circular cone, we can find the surface area of the cone using the formula:

A = πr² + πrl

where r is the radius of the base of the cone, l is the slant height of the cone, and π is approximately equal to 3.14.

To find the radius and slant height, we can use the Pythagorean theorem.

Let's assume that 9ft is the height of the cone, and 11ft is the slant height.

Then, we have:

r² + 9² = 11²

r² + 81 = 121

r² = 40

r ≈ 6.32 ft

Now that we have the radius and slant height, we can find the surface area of the cone:

A = πr² + πrl

A = π(6.32)² + π(6.32)(11)

A ≈ 199.3 square feet

Therefore, the surface area of the cone is approximately 199.3 square feet.

The Probablity that the exam will be finished in under 74 minutes is 0.9332, or roughly 93.32%. By standardising the provided data to the standard normal distribution, which has a mean of 0 and a standard deviation of 1, we can use the standard normal distribution to address this issue. 

The formula: can be used to accomplish this. z = (x - μ) / σ where x equals the number that is provided (74 minutes), equals the mean (62 minutes), and equals the standard deviation. (8 minutes). z = (74 - 62) / 8 z = 1.5

The chance that a standard normal random variable is less than 1.5 can then be determined using a calculator or a chart of the standard normal distribution. The likelihood is roughly 0.9332.

Therefore, the likelihood that the exam will be finished in under 74 minutes is 0.9332, or roughly 93.32%.

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The hotel owner needs approximately 2,248 square feet of fabric to make a pool covering for the winter for their regular hexagonal pool with a side-to-side length of 30 feet.

To calculate the area of the pool, we first need to find the apothem (the distance from the center of the hexagon to the midpoint of any side). For a regular hexagon, the apothem is equal to the side length times the square root of 3 divided by 2. So, the apothem of this hexagonal pool is:

apothem = 30 × √3/2 = 25.980762

The area of a regular hexagon is given by the formula:

area = 3 × √3/2 × apothem^2

Substituting the value of the apothem, we get:

area = 3 × √3/2 × 25.980762^2 = 2247.72

Rounding this to the nearest square foot, the hotel owner will need approximately 2,248 square feet of fabric to construct the cover for the pool.

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A sample of bacteria is grown in a petri dish. It contains 1,000 bacteria, and the population doubles every half hour. The inequality 1,000(2)^(2t)>50,000, where t is the number of hours, models when the population of the bacteria sample will be greater than 50,000.

Based on the inequality, the population in the sample will be greater than 50,000 after 2 hours. To solve the inequality, we need to isolate the variable t.

First, divide both sides of the inequality by 1,000:2^(2t)>50/1,0002^(2t)>1/20Next, take the logarithm of both sides of the inequality (base 2):2t>log2(1/20)t>log2(1/20)/2t>−4/2t>−2Therefore, the population of the bacteria sample will be greater than 50,000 after 2 hours.

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Thus, the solution of the given inequality is found as: n > 4.86. The graph is plotted.

When two parameters are equal, we use the sign "=," and when they aren't equal, we use the symbol "," meaning refers for "not equal." The first value may be greater than (>), less than (<), greater than equal to (≥), or less than equal to (≤) the second value if the two values are not equal.

Given inequality:

1.9(2.3n + 6) + 10.45 > 43.7

Subtract each side by 10.45

1.9(2.3n + 6) + 10.45 - 10.45 > 43.7 - 10.45

1.9(2.3n + 6) > 33.25

Divide each side by 1.9

1.9(2.3n + 6) / 1.9 > 33.25/1.9

2.3n + 6 > 17.5

Subtract both sides by 6

2.3n + 6 - 6 > 17.5 - 6

2.3n > 11.5

Now, divide each side by 2.3

2.3n/2.3 > 11.5/2.3

n > 4.86

Thus, the solution of the given inequality is found as: n > 4.86.

As, n must be great then 4.86, value of 4.86 is not take for n.

The graph is plotted.

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Correct question:

1. Solve 1.9(2.3n + 6) + 10.45 > 43.7 . Then graph the solution.

Answer:

1. x ≈ 15,73

P = 104,96

.

2. x ≈ 50,51

P = 136,26

.

3.

[tex] \cos( \alpha ) = \frac{ \sqrt{3} }{3} [/tex]

P ≈ 24,88

Step-by-step explanation:

1.

Use trigonometry:

[tex] \cos(70°) = \frac{x}{46} [/tex]

Cross-multiply to find x:

[tex]x = 46 \times \cos(70°) ≈15.73[/tex]

In order to find the perimeter, we have to know all three side lengths of the triangle

Let's find the third one by using the Pythagorean theorem:

[tex] {bc}^{2} = {ab}^{2} - {ac}^{2} [/tex]

[tex] {bc}^{2} = {46}^{2} - ({15 .73})^{2} = 1868.5671[/tex]

[tex]bc > 0[/tex]

[tex]bc = \sqrt{1868.5671} ≈43.23[/tex]

Now, we can find the perimeter (the sum of all side lengths):

P = AB + BC + AC

P = 46 + 43,23 + 15,73 = 104,96

.

2.

[tex] \tan(29°) = \frac{28}{x} [/tex]

[tex]x = \frac{28}{ \tan(29°) } ≈50.51[/tex]

[tex] {ab}^{2} = {ac}^{2} + {cb}^{2} [/tex]

[tex] {ab}^{2} =( {50.51})^{2} + {28}^{2} = 3335.2601[/tex]

[tex]ab > 0[/tex]

[tex]ab = \sqrt{3335.2601} ≈57.75[/tex]

P = 57,75 + 28 + 50,51 = 136,26

.

3.

[tex] \cos( \alpha ) = \frac{ac}{ab} [/tex]

[tex] \cos( \alpha ) = \frac{6}{6 \sqrt{3} } = \frac{ \sqrt{3} }{3} [/tex]

[tex]p = 6 + 6 \sqrt{2} + 6 \sqrt{3} ≈24.88[/tex]

This results in the systematic measurement error as the deviation is consistently in one direction. Hence, this is an

example of systematic measurement error.

In the given scenario, the researcher reviews study data about head circumference in newborns and notes that study

personnel are measuring from the end of the measuring tape and not from the zero point, which is 1 cm from the end.

This is an example of systematic measurement error.

Systematic measurement error refers to a consistent deviation from the true value in a particular direction in a series of

measurements.

This error is also referred to as bias. In the given scenario, the personnel are measuring from the end of the measuring

tape and not from the zero point, which is 1 cm from the end.

This results in the systematic measurement error as the deviation is consistently in one direction. Hence, this is an

example of systematic measurement error.

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Answer: compensation strategy

Step-by-step explanation:

Scatterplot: We can see that there is a linear relationship between length of courtship and length of marriage. The higher the courtship the longer the marriage.

A scatter chart is a graphical or mathematical plot for data that uses Cartesian coordinates to display the results of two variables, usually. An additional difference may occur if the content is encoded. The data is displayed as a collection of points, and at each point the value of one variable increases to determine the position on the horizontal axis, and the value among other variables determines the position of the vertical axis.

Scatter plots can be used when one continuous variable is under the experimenter's control and the other is independent of it, or when both continuous variables are independent. If there are increasing and/or decreasing processes, they are called uncontrolled or independent variables and are usually plotted along the horizontal axis. The index or dependent variable is usually plotted along the vertical axis. If there is no difference, you can plot the two variables on two axes, and the scatter plot shows the relationship (not the reason) between the two variables.

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Answer:

The cheapest flight from Washington, D.C. to Portland was found 87 days before departure, on average. Book at least 2 weeks before departure in order to get a

Step-by-step explanation:

The dοmain οf the relatiοn is the set οf all x-values that appear in the graph, which is {-5, -2, -1, 0, 1, 5}.

In mathematics, the dοmain οf a functiοn is the set οf all pοssible input values fοr which the functiοn is defined.

The dοmain οf the relatiοn is {-5, -2, -1, 0, 1, 5}.

This is because the x-values οf the given pοints are -5, -2, -1, 0, 1, and 5, and there are nο οther x-values indicated in the graph.

Hence, the dοmain οf the relatiοn is the set οf all x-values that appear in the graph, which is {-5, -2, -1, 0, 1, 5}.

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Part A: The formula for the future value of an investment with compound interest is given by:

A = P(1 + r/n)^(nt)

Where: A = the future value of the investment P = the principal investment amount r = the annual interest rate (as a decimal) n = the number of times the interest is compounded per year t = time in years

For this situation, P = $300 r = 2.45% = 0.0245 (since the interest rate is given as an annual rate, we need to divide it by 100 to convert it to a decimal) n = 4 (since interest is compounded quarterly) t = time in years

Therefore, the equation to model this situation is:

A = 300(1 + 0.0245/4)^(4t)

Part B: To find the value of the account after 15 years, we can simply substitute t=15 into the equation:

A = 300(1 + 0.0245/4)^(4*15) = $476.78

Therefore, the amount of money in the account after 15 years is $476.78.

To calculate the actual percentage of interest that is charged when interest is compounded daily, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where: A = the amount of money owed after one year P = the initial amount owed r = the annual interest rate (as a decimal) n = the number of times the interest is compounded per year t = time in years

In this case, Felipe didn't pay his monthly statements, so we can assume that the balance owed increased each day. Therefore, we should use n = 365 (the number of days in a year) in the formula. Also, since r = 24%, we should use r = 0.24 in the formula. Finally, t = 1, since we are looking for the amount owed after one year.

Using the formula, we get:

A = P(1 + r/n)^(nt) = P(1 + 0.24/365)^(365*1) = P(1.0028)^365 ≈ P(1.34)

Therefore, if Felipe doesn't pay his statements for a full year, the actual percentage he gets charged is approximately 34% (or 0.34 as a decimal).

Answer:

if Felipe never pays his statements for a full year, he would end up paying an actual percentage rate of approximately 471.7% per year (4.717 times the initial balance).

Step-by-step explanation:

Part A:

Let P be the principal amount (initial deposit) of $300

Let r be the annual interest rate of 2.45% = 0.0245

Since the interest is compounded quarterly, we need to divide the annual interest rate by 4 to get the quarterly rate:

i = r/4 = 0.0245/4 = 0.006125

Let n be the number of quarters in t years. Since there are 4 quarters in a year, we have:

n = 4t

The formula for compound interest is:

A = P(1 + i)^n

Substituting the given values, we get:

A = 300(1 + 0.006125)^(4t)

Part B:

We want to find the balance in Lucy's savings account after 15 years, so we substitute t = 15 into the equation:

A = 300(1 + 0.006125)^(4t)

A = 300(1 + 0.006125)^(4×15)

A = 300(1.006125)^60

A ≈ $464.25

Therefore, Lucy's savings account will have approximately $464.25 after 15 years.

If Felipe never pays his statements for a full year, the interest would compound daily, so we need to use the formula for daily compounded interest, which is:

A = P(1 + r/n)^(nt)

where:

P is the principal (starting balance) on the credit card

r is the annual interest rate (24%)

n is the number of times the interest is compounded per year (365 for daily compounding)

t is the time in years (1 year)

Substituting the values, we get:

A = P(1 + r/n)^(nt)

A = P(1 + 0.24/365)^(365×1)

A = P(1.0006575)^365

A ≈ 4.717P

Therefore, if Felipe never pays his statements for a full year, he would end up paying an actual percentage rate of approximately 471.7% per year (4.717 times the initial balance).

Answer:

The college will have about 480 students who prefer cookies.

Step-by-step explanation:

We Know

The table shows the preference of 225 students.

Ice Cream, Candy, Cake, Pie, Cookies

81              , 9         , 72    , 36,   27

Which statement is the best prediction about the number of cookies the college will need?

We Take

4000 / 225 ≈ 17.78

Then we take

27 x 17.78 = 480.06 cookies

So, The college will have about 480 students who prefer cookies.