About how much interest is earned on an investment of $646 receiving a simple interest rate of 5% for 10 years

Answer:

greater than

Step-by-step explanation:

positive is higher than negative

Answer:

C. (f - g)(x) = 3ˣ - 2x + 14

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 3ˣ + 10

g(x) = 2x - 4

(f - g)(x) is f(x) - g(x)

Step 2: Find (f - g)(x)

Answer:

hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

Step-by-step explanation:

Answer:

Mhm mhm that's right

Step-by-step explanation:

Hope this helps lolllll

To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

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Answer:

18%

Step-by-step explanation:

if i am right

it would be subtract 492- 600 = -108

make this a positive value so 108

and divide it by the actual made amount

108/600 which would be 0.18 multiply this by 100 and you have 18% !!

this is what i remember doing!  

let me know if it helped

The resulting fraction is 35/12..Converting the fraction back to a mixed number, we find that 35/12 is equal to 2 and 11/12.Comparing this result to 2 and k/12, we can see that k = 11.5 and 2/3 minus 2 and 3/4 equals 2 and 11/12, where k = 11.

To prove that 5 and 2/3 minus 2 and 3/4 is equal to 2 and k/12, we'll perform the necessary operations to determine the value of k.

First, let's convert the mixed numbers into improper fractions:5 and 2/3 can be written as (3*5 + 2)/3 = 17/3.

2 and 3/4 can be written as (4*2 + 3)/4 = 11/4.

Now, subtracting these fractions: (17/3) - (11/4).

To find the common denominator, we multiply the denominators: 3 * 4 = 12.Rewriting the fractions with the common denominator, we have: (68/12) - (33/12).Subtracting the numerators, we get: 68 - 33 = 35.

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Answer:

Mixed martial artist

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

the coefficient of x is 4,, leading the answer to be 4

Answer:

To work this question out you need to split the shape from a complex shape to a simple shapes and finding the areas of those shapes and adding them together to get the area of the complex shape.

Looking at the figure we can make two simple shapes, a rectangle and a triangle.

To find the area of rectangle is calculated by multiplying the length and width. In this case, length is 11 and width is 8. So 11*8 = 88 cm^2.

To find the area of a triangle is by multiplying the base by the height and dividing by 2.

So for a triangle with a base of 11 and a height of 7:

(11 * 7) / 2 = 77 / 2 = 38.5

The area of the triangle is 38.5 cm^2

Therefore the area of the figure is 88 + 38.5 = 126.5cm^2

27 well if you're asking that then

Considering the equations for the length of each segment, the numerical length of line ln is of 17 units.

Line segment ln is divided by the point m, hence the length of the line can be written according to the following equation:

ln = lm + mn.

The measures are given as follows:

Hence, using the equation we can solve for x, as follows:

ln = lm + mn.

4x + 9 = 2x + 7 + 3x

5x + 7 = 4x + 9

x = 2.

Hence the numerical length of line ln is given by:

ln = 4x + 9 = 4(2) + 9 = 8 + 9 = 17 units.

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Answer:

y = 5x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x + 9 ← is in slope- intercept form

with slope m = 5

Parallel lines have equal slopes, thus

y = 5x + c ← is the partial equation

To find c substitute (- 2, - 3) into the partial equation

- 3 = - 10 + c ⇒ c = - 3 + 10 = 7

y = 5x + 7 ← equation of parallel line

a) Total students in campus is 1560

b) Number of students started the rumor are 5

c)  it will take 13 hours approximately for 100 students to have heard the rumor including those who started it .

Given,

The spread of a rumor on a college campus is described by the equation 1560/ 1 + 311\(e^{-234t}\)

a)

If t is taken to be very large, it would mean that all of the students on the campus would have heard the rumor by then. Accordingly

\(\lim_{n \to \infty} N(t) = 1560/1 + 0 = 1560\)

Hence the student on campus will be 1560 .

b)

At t=0, N(t) would be the number of students who have not heard the rumor , but started the rumor.  Accordingly,

N(0) = 1560/ 1 + 311 = 5

c)

If N(t) = 100

then,

100 = \(1560/ 1 + 311e^{0.234t}\)

\(1 + 311e^{0.234t} = 15.60\)

\(311e^{0.234t} = 14.60\)

Take natural log on both sides,

0.234t= ln (311/14.6) =3.058,

t= 3.058/0.234 = 13 hours

Hence it will take 13 hours approximately for 100 students to have heard the rumor including those who started it .

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Answer:

C. I and III

Step-by-step explanation:

3(2x+8) = 6x + 24

Answer:

C

Step-by-step explanation:

Option 2 is 4(2x + 6) which is also equal to:

\(8x + 24\)

Distribute the 4 with the 2x + 6.

Option 3 is 3(2x+8) which is also equal to:

\(6x + 24\)

Distribute the 3 with the 2x + 8.

So, option 3 and option 1 are equivalent to each other.

DH= x+2

HF=2y

GH=4x-3

HE=5y+1

x=6

y=4

Answer:

2750

Step-by-step explanation:

So, the scale is broken up into 3 sections per whole number, so starting a 2, it would be 2.25 then 2.50, then 2.75 which is where the scale is pointing to! Next part is the conversion. The scale is in kilograms and we are supposed to find the weight in grams. There are 1000 grams in one kilogram so the answer is 2750.

Hope it helped!

The equation of the line with given coordinates in slope intercept form is given by y = 6x.

Use the slope-intercept form of the equation of a line,

y = mx + b,

where m is the slope of the line

And b is the y-intercept.

The slope of the line is equals to,

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points on the line.

Using the coordinates (-3, -18) and (3, 18), we get,

⇒m = (18 - (-18)) / (3 - (-3))

⇒m = 36 / 6

⇒m = 6

So the slope of the line is 6.

Now we can use the slope-intercept form of the equation of a line .

Substitute in the slope and one of the points, say (-3, -18) to get the y-intercept,

y = mx + b

⇒ -18 = 6(-3) + b

⇒ -18 = -18 + b

⇒ b = 0

So the y-intercept is 0.

Putting it all together, the equation of the line in slope-intercept form is,

y = 6x + 0

⇒ y = 6x

Therefore, the slope intercept form of the line is equal to y = 6x.

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The probability that the student is a junior is 0.5.

The probability that the selected student takes calculus is given by:

P(C) = probability that the selected student takes calculus= probability of seniors taking calculus + probability of juniors taking calculus= 0.4 x 1/2 + 0.2 x 1/2= 0.2

Now,Let's find the probability that a calculus student selected is a junior.i.e., we need to find P(J|C).We know that,

P(J|C) = probability that the selected student is a junior given that the student takes calculus= P(C|J) × P(J) / P(C)

We already know,P(C) = 0.2

Also,P(C|J) = probability that a junior student takes calculus= 0.2

So,P(J|C) = probability that the selected student is a junior given that the student takes calculus= P(C|J) × P(J) / P(C)= 0.2 × 1/2 / 0.2= 1/2= 0.5

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To maximize profits, the firm should produce a quantity of goods x = 5 and y = 10, based on the cost function and price constraints.

To maximize profits, the firm needs to find the quantities of goods x and y that will yield the highest profit. The profit function can be defined as the revenue minus the cost. Revenue is calculated by multiplying the quantity of each good produced with their respective prices, while the cost function is given as C(x, y) = 10x + xy + 10y.

The firm is committed to delivering a total of 15 units, which can be expressed as x + y = 15. To determine the optimal production quantities, we need to maximize the profit function subject to this constraint.

By substituting the price expressions Ps = 50 - x + y and Py = 50 - x + y into the profit function, we obtain the profit equation. To find the maximum profit, we can take the partial derivatives of the profit equation with respect to x and y, set them equal to zero, and solve the resulting system of equations.

Solving the equations, we find that the optimal production quantities are x = 5 and y = 10, which maximize the firm's profits.

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The strategy used by Dr. Chang for the research study of undergraduate students is c. stratified sampling.

Stratified sampling can be defined as the type of sampling in which a population is divided into subpopulations and then random samples are taken from these subpopulations. These subpopulations or subgroups are also called strata.

The strategy used by Dr. Chang is stratified sampling because she divided all the undergraduate students into subgroups based on grade level and then from these subgroups she randomly selected 50 students.

Contrastingly, in simple random sampling, no subgroups are involved and the subset of individuals are chosen from a single large population randomly. On the other hand, quota sampling and accidental sampling are not a type of random sampling.

In cluster sampling, the subgroups are internally heterogeneous but in this case, the subgroups are internally homogenous as they are made based on grade level.

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Answer: no solutions

\(\left \{ {{y=6x + 1} \atop {y=-2+ 6x}} \right.\\\\<=>\left \{ {{-2+6x=6x+1} \atop {y=-2+6x}} \right.\\\\<=>\left \{ {{6x-6x=1+2} \atop {y=-2+6x}} \right.\\\\<=>\left \{ {{0=3} \atop {y=-2+6x}} \right.\)

but 0 ≠ 3 =>  There are no values ​​for x and y => no solutions

Step-by-step explanation:

E(U) = 4, which is an integer.

What is Linearity of expectation?

Linearity of expectation is a fundamental property of expected value that states that the expected value of a sum or difference of random variables is equal to the sum or difference of their individual expected values.

To find E(U), where U = 2X - Y - 4, we can use the properties of expected value.

First, let's find the expected values of 2X, Y, and 4 separately using the linearity of expectation:

E(2X) = 2E(X) = 2 * 6 = 12

E(Y) = 4 (given)

E(4) = 4

Now, let's calculate the expected value of U:

E(U) = E(2X - Y - 4)

Since expected value is a linear operator, we can rearrange and simplify the expression:

E(U) = E(2X) - E(Y) - E(4)

= 12 - 4 - 4

= 4

Therefore, E(U) = 4, which is an integer.

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Answer:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a right triangle to represent the situation:

        |\

        | \

   h    |  \   9 ft

        |   \

        |    \

        |     \

        -------

        6 ft

Here, h represents the height on the wall where the ladder touches. We want to find the angle of elevation θ.

Using the right triangle, we can write:

sin(θ) = h / 9

cos(θ) = 6 / 9 = 2 / 3

We can solve for h using the Pythagorean theorem:

h^2 + 6^2 = 9^2

h^2 = 9^2 - 6^2

h = √(9^2 - 6^2)

h = √45

h = 3√5

So, sin(θ) = 3√5 / 9 = √5 / 3. We can solve for θ by taking the inverse sine:

θ = sin^-1(√5 / 3)

θ ≈ 37.5 degrees

Therefore, to the nearest tenth of a degree, the angle of elevation the ladder makes with the ground is 37.5 degrees.

Answer:

Step-by-step explanation:

How many questions are on the exam?  Represent this by n.

Then 40% of n comes out to 12 questions, or more symbolically,

               0.40n = 12, after which we get n = 12/0.40 = 30

Answers:

(1)  0.40n = 12 is the desired equation.

(2) n = 30 is the number of questions on the exam.

(3) See above for explanations.

Alright, let's take this step by step.

First, let's understand what an ordinary annuity is. An ordinary annuity is a series of equal payments made at the end of consecutive periods over a fixed length of time. For example, if you save $100 every year for 5 years, that’s an ordinary annuity.

Now, let’s understand the formula to calculate the future value (FV) of an ordinary annuity:

FV = P x ((1 + r)^n - 1) / r

Where:

- FV is the future value of the annuity.

- P is the payment per period (how much you save each time).

- r is the interest rate per period (in decimal form).

- n is the number of periods (how many times you save).

Let’s solve each part:

a) $500 per year for 6 years at 8%.

P = 500, r = 8% = 0.08, n = 6

FV = 500 x ((1 + 0.08)^6 - 1) / 0.08

  ≈ 500 x (1.59385 - 1) / 0.08

  ≈ 500 x (0.59385) / 0.08

  ≈ 500 x 7.4231

  ≈ 3701.55

So, the future value of $500 per year for 6 years at 8% is about $3,701.55.

b) $250 per year for 3 years at 4%.

P = 250, r = 4% = 0.04, n = 3

FV = 250 x ((1 + 0.04)^3 - 1) / 0.04

  ≈ 250 x (1.12486 - 1) / 0.04

  ≈ 250 x (0.12486) / 0.04

  ≈ 250 x 3.1215

  ≈ 780.38

So, the future value of $250 per year for 3 years at 4% is about $780.38.

c) $1,000 per year for 2 years at 0%.

P = 1000, r = 0% = 0.00, n = 2

FV = 1000 x ((1 + 0.00)^2 - 1) / 0.00

  = 1000 x (1 - 1) / 0.00

  = 1000 x 0

  = 0

Wait, something went wrong, because we know that if we save $1000 for 2 years with no interest, we should have $2000. This is a special case, where we just sum the contributions because there's no interest:

FV = 1000 x 2

   = 2000

So, the future value of $1,000 per year for 2 years at 0% is $2,000.

An annuity due is similar to an ordinary annuity, but the payments are made at the beginning of each period instead of the end. To convert the future value of an ordinary annuity to an annuity due, you can use the following formula:

FV of Annuity Due = FV of Ordinary Annuity x (1 + r)

a) Reworked

FV of Annuity Due = 3701.55 x (1 + 0.08)

                 ≈ 3701

.55 x 1.08

                 ≈ 3997.67

b) Reworked

FV of Annuity Due = 780.38 x (1 + 0.04)

                 ≈ 780.38 x 1.04

                 ≈ 810.80

c) Reworked

FV of Annuity Due = 2000 x (1 + 0.00)

                 = 2000 x 1

                 = 2000 (This doesn't change because there's no interest).

And there you have it! The future values for both ordinary annuities and annuities due!

Answer:

C

Step-by-step explanation:

1/18 x³y + 7/18 xy²

1/18 xy (x² + 7y)

Answer:

C. (5x√2)² = 50x²

Step-by-step explanation:

Area of parallelogram = QR²

QR = √((5x)² + (5x)²) ---› pythagorean theorem

QR = √(25x² + 25x²) =

QR = √(50x²)

QR = √(25*2*x²)

QR = 5x√2

✔️Area of parallelogram = QR²

= (5x√2)² = 25x² × 2 = 50x²

The probability that a student's score is less than 81 points on the reading ability test is 0.9772. We would expect approximately 489 students to earn a score less than 81 points if 500 students took the reading ability test. The probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

To find the probability that a student's score is less than 81 points, we need to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the student's score, μ is the mean score, and σ is the standard deviation. Plugging in the values, we get:

z = (81 - 65) / 8 = 2.00

Using a standard normal distribution table or calculator, we can find the probability of a z-score less than 2.00 to be approximately 0.9772. Therefore, the probability that a student's score is less than 81 points is 0.9772.

Since the distribution is normal, we can use the normal distribution to estimate the number of students who would earn a score less than 81. We can standardize the score of 81 using the z-score formula as above and use the standardized score to find the area under the normal distribution curve. Specifically, the area under the curve to the left of the standardized score represents the proportion of students who scored less than 81. We can then multiply this proportion by the total number of students (500) to estimate the number of students who would score less than 81.

z = (81 - 65) / 8 = 2.00

P(z < 2.00) = 0.9772

Number of students with score < 81 = 0.9772 x 500 = 489

Therefore, we would expect approximately 489 students to earn a score less than 81 points.

The distribution of the sample mean reading ability test scores is also normal with mean μ = 65 and standard deviation σ / sqrt(n) = 8 / sqrt(35) ≈ 1.35, where n is the sample size (number of students in the sample). To find the probability that the sample mean score is between 66 and 68, we can standardize using the z-score formula:

z1 = (66 - 65) / (8 / sqrt(35)) ≈ 0.70

z2 = (68 - 65) / (8 / sqrt(35)) ≈ 2.08

Using a standard normal distribution table or calculator, we can find the probability that a z-score is between 0.70 and 2.08 to be approximately 0.2190. Therefore, the probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

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The statement ''f. if a is an m n matrix whose columns do not span rm, then the equation ax d b is inconsistent for some b in rm '' is TRUE.

Let us assume that a is an m x n matrix that doesn't span rm. It means that the columns of a matrix don't contain all the vectors in the m-dimensional vector space that a is associated with. Therefore, it is not possible to find the linear combination of the columns of a that produces some vectors in rm.

We can also say that a matrix is inconsistent when there is no solution possible for the given linear equation. A system of linear equations is inconsistent when it has no solution.To prove the statement f, we need to prove that if a matrix doesn't span rm, then the given equation ax = b is inconsistent for some b in rm.

Here is a proof:

Let's assume that the columns of the matrix a don't span rm. It means that some vector in rm is not in the column space of a matrix.

Let's assume that vector is v.

Now, let's consider the linear equation ax = v. Since v is not in the column space of matrix a, there is no solution to this equation. It means that the equation ax = v is inconsistent.

Hence, we can say that the statement f. if a is an m n matrix whose columns do not span rm, then the equation ax d b is inconsistent for some b in rm is true

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