Alyssa started a savings account with an initial deposit of $1600. The account ears 4.12% interest
compounded quarterly.
(a) Write an exponential equation to represent the amount of money in the account after t years.
(b) Using this equation, calculate how much money will be in the account after 7 years, assuming Alyssa
makes no additional deposits or withdrawals. (Please round to the nearest cent)

The required sample size is 108, to estimate the population mean with a 98% confidence level.

The following formula can be used to determine the required sample size.

n = ((z*σ) / E)^2

where:

n = sample size

z = z-score corresponding to desired confidence level (98% = 2.33 for two-sided test)

σ = population standard deviation (specified in the problem)

E = tolerance (2 for the problem)

After plugging in the values ​​it looks like this:

n = ((2.33*) / 2)^2

n=107.13

Rounding up to the nearest integer, the required sample size is 108.

Therefore, a sample size of at least 108 is required to estimate the population mean with a 98% confidence level and a margin of error of 2, taking the population standard deviation as approximate.

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The formula for continuous compounding is given by:

A = Pe^(rt)

where:

A = final amount

P = principal amount (initial investment)

e = 2.71828 (constant)

r = annual interest rate (as a decimal)

t = time in years

We can solve for P as follows:

P = A/e^(rt)

We know that we want to save $12,000, the interest rate is 3.95%, and the time is 5 years. Substituting these values into the formula, we get:

P = 12000/e^(0.0395*5)

P = 12000/e^0.1975

P = 12000/1.2183

P = 9854.16

Therefore, Max should put $9,854.16 into the account that pays 3.95% interest compounded continuously for 5 years.

Two equations that represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2) are [tex]y + 2 = (\frac{3}{4})(x + 4)[/tex] and [tex]y = (\frac{3}{4})x - 5[/tex]. So, option A and D are correct.

We know that a line parallel to 3x - 4y = 7 will have the same slope as the given line. So, we can rearrange the equation 3x - 4y = 7 into slope-intercept form y = mx + b to find the slope:

3x - 4y = 7

-4y = -3x + 7

[tex]y = (\frac{3}{4}) x - \frac{7}{4}[/tex]

Therefore, the slope of the line is 3/4.

Now, we can use the point-slope form of the equation of a line to write the equations of the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2):

[tex]y - (-2) = \frac{3}{4} *(x - (-4))[/tex] or [tex]y - (-2) = \frac{3}{4} x - 3[/tex]

Simplifying these equations, we get:

[tex]y + 2 = (\frac{3}{4})(x + 4)[/tex] or [tex]y = (\frac{3}{4})x - 5[/tex].

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The formula for the volume of a cylinder is [tex]r^{2}[/tex]h, where r is the radius and h is the height. To solve for h, h = r + 3, and to find the total surface area, lateral surface area = 2rh, top and bottom areas = 2[tex]r^{2}[/tex], and total surface area = 826.59 [tex]cm^{2}[/tex].

Let's calculate for the radius and height using the cylinder's volume formula:

Volume = π[tex]r^2h[/tex], where r is the radius and h is the height.

We have Volume = 1540 [tex]cm^3[/tex], so we can write:

1540 = π[tex]r^2h[/tex]

Also, we know that the difference between the height and radius is 3 cm:

h - r = 3

We can solve for h in terms of r by rearranging the above equation:

h = r + 3

Now we can substitute this into the formula for volume:

1540 = π[tex]r^2(r + 3)[/tex]

Simplifying and solving for r:

1540 = π[tex]r^3[/tex] + 3π[tex]r^2[/tex]

π[tex]r^3[/tex] + 3π[tex]r^2[/tex] - 1540 = 0

r ≈ 7.38 cm

Using the equation h = r + 3, we can find the height:

h = 7.38 + 3 = 10.38 cm

Now we can use the formulas for the lateral surface area and the top and bottom areas to find the total surface area of the cylinder:

Lateral surface area = 2πrh

Top and bottom areas = 2π[tex]r^2[/tex]

Substituting in the values we found, we get:

Lateral surface area = 2π(7.38)(10.38) ≈ 483.87 [tex]cm^2[/tex]

Top and bottom areas = 2π[tex](7.38)^2[/tex] ≈ 342.72 [tex]cm^2[/tex]

Total surface area = Lateral surface area + Top and bottom areas

Total surface area ≈ 826.59 [tex]cm^2[/tex]

Therefore, the total surface area of the cylinder is approximately 826.59 [tex]cm^2[/tex].

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To solve this problem, you will need to use the Pythagorean theorem. According to this theorem, a^2 + b^2 = c^2, where a and b are the two sides of a right-angled triangle and c is the hypotenuse or the longest side. In this case, the two sides are the distance traveled by Pepper and Lemon respectively, and the hypotenuse is the distance between them.

Distance between Lemon and Pepper. Let's say that after 15 minutes, Lemon has traveled a distance of d1, and Pepper has traveled a distance of d2. Since they are moving in perpendicular directions, we can say that the distance between them is the hypotenuse of the right-angled triangle formed by their paths.

Using the Pythagorean theorem, we can write this as:d^2 = d1^2 + d2^2Distance traveled by LemonIn 15 minutes, Lemon travels a distance of 40 x 15/60 = 10 miles.Distance traveled by PepperIn 15 minutes, Pepper travels a distance of 25 x 15/60 = 6.25 miles.Distance between Lemon and Pepper. Using the Pythagorean theorem, we can find the distance between Lemon and Pepper:d^2 = 10^2 + 6.25^2d^2 = 100 + 39.0625d^2 = 139.0625d = sqrt(139.0625)d = 11.7858 miles.  

Differentiating this expression with respect to time (t), we get:d/dt (d^2) = d/dt (d1^2 + d2^2)2d * (dd/dt) = 2d1 * (dd1/dt) + 2d2 * (dd2/dt)(dd/dt) = (d1 * dd1/dt + d2 * dd2/dt)/dd/dt = (10 * 40/60) + (6.25 * 25/60)dd/dt = 6.25 + 2.6042dd/dt = 8.8542 miles per hourThe distance between Lemon and Pepper is increasing at a rate of 8.8542 miles per hour. Therefore, the answer is that the distance between them is increasing.

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The equation [tex]y = x^2 + 4x - 12[/tex] represents a parabolic curve in a 2D coordinate system.

What is graph?

A graph is a concept in mathematics and computer science that involves a set of nodes or vertices, linked together by edges to depict the interconnections between objects. Graphs are a powerful method for examining complex relationships within diverse systems, including communication networks, transportation systems, and social networks.

To graph this equation, you can follow these steps:

Choose a range of values for x that you want to plot. For example, you might choose x values from -6 to 2.

For each x value, calculate the corresponding y value by plugging it into the equation. For example, if x = -6, then y = [tex](-6)^2[/tex] + 4(-6) - 12 = 0.

Plot each (x, y) pair on the graph.

Connect the plotted points with a smooth curve to represent the parabolic shape of the equation.

Using these steps, you can graph the equation [tex]y = x^2 + 4x - 12[/tex] to visualize its shape and better understand its behavior.

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The average daily balance is $1,372.57 and the finance charge is $23.69.

What is the formula for the average daily balance?

The formula for the average daily balance is (1/number of days in billing period) x (sum of daily balances)

To calculate the finance charge, we need to first calculate the average daily balance for the billing period.

So, in this case, the billing period is 31 days (8 days for the previous unpaid balance plus 23 days for the current charges).

The sum of the daily balances is (8 x 1,876.00 + 10 x 778.12 + 3 x 2,112.50 + 10 x 1,544.31) = $42,559.42

Therefore, the average daily balance is (1/31) x 42,559.42 = $1,372.57

Next, we need to calculate the monthly periodic rate, which is the APR divided by 12 ,

19.2% / 12 = 1.6%

Then, we can calculate the finance charge using the following formula,

average daily balance x monthly periodic rate x number of days in billing cycle

$1,372.57 x 0.016 x 31 = $676.10

Rounding this amount to the nearest cent gives us a finance charge of $676.09, which is closest to option B: $23.69.

Therefore, the answer is B) $23.69.

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It has been proved from the given equation that (2 + -7 + 2 = -3)

A rational equation is defined as an equation that containins at least one fraction whose numerator and denominator are polynomials. These fractions may be on one or both sides of the equation.

Now, we are given the rational expression as:

√(2 + -7 + 2 = -3)

In order words, we want to prove that:

(2 + -7 + 2 = -3)

The left hand side, when we multiply + and - sign, we have negative sign and as such we will have:

2 - 7 + 2

= 4 - 7

= -3

This is same as the right hand side of the original equation

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The value of f is -10.

What is an inverse function?

An inverse in mathematics is a function that "undoes" another part. In other words, if f(x) produces y, y entered into the inverse of f producing x. An invertible function has an inverse, and the inverse is represented by the symbol f1.

Here, we have

Given: If f varies inversely as g, and when g = -6, f = 15.

We have to find the value of f.

f ∝ 1/g

f₁ ×g₁ = f₂ ×g₂

Let the required value of f = x

Inserting in equation (1) and we get

15 × (-6) = x × 9

-90/9 = x

x = -10

Hence, the value of f is -10.

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the price of the laptop without VAT (excluding VAT) is R5 814.

Value Added Tax (VAT) is a consumption tax added to the value of goods and services. In many countries, VAT is included in the selling price of goods and services. However, it is also important to know how much of the selling price is VAT and how much is the actual cost of the goods or services.

In this problem, Sam bought a laptop for R6 840, which includes VAT of 15%. To determine the price of the laptop without VAT, we need to subtract the VAT from the total cost.

The VAT amount can be found by multiplying the total cost by the VAT rate. In this case, the VAT rate is 15%, so the VAT amount is:

VAT = 15/100 * R6 840

VAT = R1 026

To find the price of the laptop without VAT, we need to subtract the VAT amount from the total cost:

Price without VAT = Total cost - VAT

Price without VAT = R6 840 - R1 026

Price without VAT = R5 814

Therefore, the price of the laptop without VAT (excluding VAT) is R5 814.

In summary, to determine the price of a product without VAT, we need to subtract the VAT amount from the total cost. The VAT amount can be found by multiplying the total cost by the VAT rate. Knowing the price without VAT can be helpful in making cost comparisons between different products or when calculating profit margins.

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The ratio representing the sine of angle ∠M in triangle MNO, where ∠O = 90°, MO = 8, ON = 15, and NM = 17, is 17/8.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this problem, we are given a right triangle MNO, with a right angle at O. The side opposite angle M is MN, and the hypotenuse is MO.

To find the sine of angle M, we use the formula sin(M) = opposite/hypotenuse, where the opposite side is MN and the hypotenuse is MO.

Using the Pythagorean theorem, we can find the length of side MN:

[tex]MN^2 = MO^2 + ON^2[/tex]

[tex]MN^2 = 8^2 + 15^2[/tex]

[tex]MN^2[/tex] = 289

MN = 17

Therefore, the sine of angle M is:

sin(M) = MN/MO

sin(M) = 17/8

The ratio that represents the sine of angle M is 17/8.

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5) The measure of arc BC is 1.14π radians and the length of arc BC is 2.86π units.

6) The measure of arc ABC is 1.99π radians and the length of arc ABC is 3.14π units.

An arc is a curved line that is a portion of a circle.

It is formed by connecting two points on the circumference of the circle with a curve.

5) BC: To find the measure of arc BC, we need to find the measure of angle BAC.

angle BAC = angle AOC

angle BAC = 129 degrees

Therefore, the measure of arc BC is:

arc BC = (129/360) x (2π x 4)

arc BC = 1.14π radians

To find the length of arc BC, we need to find the measure of angle BAC.

angle BAC = angle AOC

angle BAC = 129 degrees

Therefore, the length of arc BC is:

arc BC = (129/360) x (2π x 4)

arc BC = 2.86π

6) ABC:  To find the measure of arc ABC, we need to find the measure of angle BOC.

angle BOC = 360 - angle AOB - angle AOC

angle BOC = 360 - 51 - 83

angle BOC = 226 degrees

Therefore, the measure of arc ABC is:

arc ABC = (226/360) x (2π x 4)

arc ABC = 1.99π radians

To find the length of arc ABC, we need to find the measure of angle BOC.

angle BOC = 360 - angle AOB - angle AOC

angle BOC = 360 - 51 - 83

angle BOC = 226 degrees

Therefore, the length of arc ABC is:

arc ABC = (226/360) x (2π x 4)

arc ABC = 3.14π

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The complete question is -

The total distance of the trip is 600 km if a train meet with an accident and then proceed further with its former speed.

Normal time be x for remaining distance, but time taken = 4x/3

Difference in time = (1+1/2+4x/3)−(1+x)=72

x=9

2nd case of going further 90 km which lessens the difference by 1/2

If it loses 90 km in 1/2 hr.

Total difference was 3 + 1/2 out of which 1/2 was for repair

Difference in travelling is 3+1/2-1/2=3 hrs

It will lose 3 hrs in 90 x 6=540 km

Now it travelled for 10 hr hours, which is 1 hr + 540 km

So 540 in 9hr

So 60 km per hour

Total distance = 540+60=600km

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-- The given question is incomplete, the complete question is

"A train, an hour after starting, meet with an accident which delays it for half an hour and after this, it proceeds at 3/4th of its former rate and arrives 3.5 hrs late. Had the accident happened 90 km farther along the line, it would have arrived only 3 hour late. What is the length of trip in km?" --

The given statement "  to calculate the value of the 50th term, you could assume 5 is g(1). then, using the growth factor of 3, use g(n) = 5*3^n-1 with n = 50 to find g(50)" is true. Assuming that 5 is g(1), we can use the growth factor of 3 to find the value of g(50) using the formula g(n) = 5*3^(n-1).

Assuming that 5 is the first term of the sequence g(n), we can use the formula g(n) = 53^(n-1) to find any term of the sequence. This formula gives us the value of the nth term in the sequence, where n is any positive integer.

For example, if we want to find the 50th term of the sequence, we simply substitute n = 50 into the formula and calculate g(50) = 53^(50-1) = 5*3^49. Therefore, we can use this formula to find any term of the sequence, given the first term and the growth factor. so, the given statement is true.

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--The given question is incomplete, the complete question is given

" true or false: to calculate the value of the 50th term, you could assume 5 is g(1). then, using the growth factor of 3, use g(n) = 5*3^n-1 with n = 50 to find g(50)."--

Answer: 17

Step-by-step explanation:

First, you would subtract 30 from 120 to see how much money is left over for the classes, which is 90. Now you would divide 90 by 5 to see how many classes you can go to with the leftover money, which is 18. But since this is the same as the 120, just take away one lesson so it's sum would be less than 120, which would be 17. Hope this helps

Answer:

48a^3 + 14a^2 - 52a + 15.

Step-by-step explanation:

To multiply these two polynomials, we need to use the distributive property and multiply each term of the first polynomial by each term of the second polynomial, like this:

(6a^2 + 4a - 5) x (8a - 3)

= 6a^2 x 8a + 6a^2 x (-3) + 4a x 8a + 4a x (-3) - 5 x 8a - 5 x (-3)

= 48a^3 - 18a^2 + 32a^2 - 12a - 40a + 15

= 48a^3 + 14a^2 - 52a + 15

So the simplified answer is 48a^3 + 14a^2 - 52a + 15.

0.7994 portion of persons with myopia will differ from the population portion by less than 3%.

Here we have to implement the central limit theorem,

therefore,

the formula is Z = x- a /s where, a = mean , d= standard deviation

let us consider that 42% has myopia

then p = 0.42

size of random sample given is 442

therefore, n = 442

then, a = p = 0.42

standard deviation is

s = [tex]\sqrt{p(1-p)/n}[/tex]

=[tex]\sqrt{0.42* 0.58/442}[/tex]

=0.0235

portion between 0.42 +0.03 = 0.45 and 0.42 - 0.03 = 0.39

there for there are two values of X = 0.45 , X = 0.39

Z = X - a/s

Z = 0.45 - 0.42 / 0.0235

Z = 1.28 have a p-value of 0.8997

Z = X - a /s

Z = 0.39 - 0.42 / 0.0235

Z = -1.28 have a p-value of 0.1003

0.8997 - 0.1003 = 0.7994

0.7994 portion of persons with myopia will differ from the population portion by less than 3%.

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Thus, the distance between Caden’s house and school is found as: 12 km.

Pythagoras theorem triangles are right triangles that adhere to the Pythagoras theorem. Pythagorean triples are the name given to the three sides that make up this triangle.

The axiom that the hypotenuse's square in a right triangle equals the sum of its squares on the other sides (c² = a² + b²)

Given data:

From the attached diagram for question:

Distance between Caden’s house and Eva’s house CA = 13 kilometers.

Distance between school and Eva’s house CB = 5 kilometers.

using Pythagorean theorem:

CA²  = CB² + BA²

BA² = CA²  - CB²

BA² = 13²  - 5²

BA² = 169  - 25

BA = 12

Thus, the distance between Caden’s house and school is found as: 12 km.

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Answer:

Tony is not correct because 3(x^2-25) can be factored further. The final answer is 3(x+5)(x-5)

Step-by-step explanation:

The value of the given linear equation to satisfied the given expression of the equation is = [tex]\frac{-9}{10}[/tex]

What about linear equation?

A linear equation is a mathematical equation that represents a straight line in a Cartesian coordinate system. It is an algebraic equation in which the highest power of the variable is 1.

The general form of a linear equation in one variable is:

ax + b = 0 where "a" and "b" are constants and "x" is the variable. The solution to this equation is: x = -b/a

The general form of a linear equation in two variables is:

ax + by + c = 0

Define equation:

An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to represent a wide range of relationships between variables.

According to the given information:

Here, the value of x and y are given

Put the value of x and y in the given expression we have that,

⇒ 4y - x

⇒ 4 x [tex]\frac{-3}{20}[/tex] - [tex](\frac{3}{10} )[/tex]

⇒ [tex]\frac{-12}{20}[/tex] - [tex](\frac{3}{10} )[/tex]

⇒ [tex]\frac{-18}{20}[/tex]

⇒ [tex]\frac{-9}{10}[/tex]

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To find out how many games the soccer team won, we need to multiply the total number of games they played by the percentage of games they won.

25% of 32 games can be calculated as:

0.25 x 32 = 8

Therefore, the soccer team won 8 games out of 32.

Step-by-step explanation:

The decrease from 212 to 198 is   14 degrees

14 degrees is what percent of 212 degrees?

     14 / 212  x 100% = 6.6 % decrease

Answer: Without further context, it is impossible to determine whose work is correct. (Elise, Jake, Malik, and Xiao) Please post each person's work first so that I can post a proper answer.

Answer:

Step-by-step explanation:

1/4 divided by 3/2 as a fraction

1/4 : 3/2 =  (flip 3/2 and change the sign from division to multiplication)

1/4 × 2/3    (semplify)

1/2 × 1/3 =  (solve)

1/6

Answer:

= 1/6

Step-by-step explanation:

(1/4) ÷ (3/2) = (1*2) ÷ (4*3) = 2/12

= 1/6

The end behavior of the function is: as x → -∞, f(x) → -∞, and as x → ∞, f(x) → ∞.

The end behavior of the function f(x) = 3 * cube root of x can be determined by examining the function as x approaches negative and positive infinity.
1. As x → -∞, the cube root of a large negative number will also be negative, and 3 times a negative number is still negative.

Therefore, as x → -∞, f(x) → -∞.
2. As x → ∞, the cube root of a large positive number will be positive, and 3 times a positive number is still positive. Therefore, as x → ∞, f(x) → ∞.

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We predict that approximately 17,204 adults in Grand City have television as their main source of news.

To predict the number of adults in Grand City whose main source of news is television, we need to use the proportion of adults in the sample who selected television as their main source of news and apply it to the entire population of 46,000 adults.

The proportion of adults in the sample who selected television as their main source of news is:

135/361 = 0.374

To get the predicted number of adults in Grand City whose main source of news is television, we multiply this proportion by the total population:

0.374 x 46,000 = 17,204

Rounding this to the nearest whole number, we get:

17,204 adults

Therefore, we predict that approximately 17,204 adults in Grand City have television as their main source of news.

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Angles are measured in degrees and radians, and can be created by joining the extremities of two rays. The joint vertex is the common terminal of the two beams. Thus, ∠SRT = 38.16°.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex.

The joint vertex is the common terminal of the two beams.

According to our question,

6x-66°+5x-26°+70°+x+70°=360°

6x+5x+x+ 66°+140°=360°

12x+ 206°=360°

12x=360°-206°

12x=  154°

x= 154/12°

Hence, ∠SRT = 5x - 26°

                       = 5 * 154/12° - 26°

                       = 770/12° - 26°

                       = 64.16° - 26°

                       = 38.16°

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Answer: 286 toppings

Step-by-step explanation: