The Serenity and the Mystic are sail boats. The Serenity and the Mystic start at the same point and travel away from each other in opposite directions. The Serenity travels at 14 mph and the Mystic travels at 21 mph. How far apart will they be in 3 hours?

Answer: The amount borrowed or deposited

Step-by-step explanation:

there isn't really an explanation, I just know the answer because I took a test with the exact same question and answer

Option C is correct, The difference between the future value and the amount of interest earned is the present value of money

percentage, a relative value indicating hundredth parts of any quantity.

The present value of money refers to the value of a future amount of money in today's dollars, based on a certain interest rate or discount rate.

It is the amount of money that would need to be invested today, at a given rate, to equal the future amount.

To calculate the present value of a future amount of money, we need to discount the future amount based on the interest rate or discount rate, which accounts for the time value of money

The difference between the future value and the amount of interest earned.

Hence, option C is correct, the difference between the future value and the amount of interest earned is the present value of money

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The graph to the inequality is added as an attachment

From the question, we have the following parameters that can be used in our computation:

2y+8x<4

5x+20 is greater than or equal to -10y

Express properly

2y+8x<4

5x+20 > -10y

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, the shaded area has a coordinate of (1.143, -2.571)

Hence, the solution is (1.143, -2.571)

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The measure of side AB of the triangle is given by equation AB = 3.5 cm

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔACE

Let the second triangle be represented as ΔBCD

The measure of side AC = 14 cm

The measure of side EC = 84 cm

The measure of side ED = 21 cm

Now , ΔACE is similar to ΔBCD

So , corresponding sides of similar triangles are in the same ratio

Substituting the values in the equation , we get

AB / AC = ED / EC

AB / 14 = 21 / 84

Multiply by 14 on both sides of the equation , we get

AB = ( 1/4 ) 14

AB = 3.5 cm

Therefore , the value of AB is 3.5 cm

Hence , the measure of side AB of triangle is 3.5 cm

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Using an equation, the bride-to-be and her maid of honor will each have made 25 favors in 5 minutes.

An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.

Equations are depicted using the equal symbol (=), while mathematical expressions, which combine variables, constants, and values only use mathematical operands.

The total number of wedding favors assembled by the bride-to-be = 15

The bride's assembling rate per minute = 2 favors

The maid of honor's assembling rate per minute = 5 favors

Let x = the number of minutes used

Let the number of favors assembled by the bride = 15 + 2x

Let the total number of favors assembled by the maid of honor = 5x

For the two to assemble the same number of favors, 15 + 2x = 5x

15 = 3x

5 = x

Thus, in 5 minutes the bride-to-be and her maid of honor will have assembled 25 favors each.

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Answer:

6x-3 - (x-1) is the expression.

You want to make sure to bring the - over both the "x" and the "-1". You end up with the expression 5x-2. I need more info to "evaluate the expression", it is not possible to evaluate it currently because of limited information on what the expression would equal.

According to the information, the value of the missing angle would be 206°, in a quadrilateral.

To calculate the value of the missing angle we must take into account that the angles of a quadrilateral must add up to 360°. On the other hand, the angles of a triangle must sum to 180°.

According to the previous information, if it is a triangle, then we must add the angles that we know and then subtract it from 180°.

On the other hand, if it is a quadrilateral we must add the angles and subtract them from 360°.

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The missing angle is approximately 108.5 degrees.

Law of sines is a trigonometric formula that relates the sides and angles of any triangle. Specifically, the law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in the triangle.

Using the law of sines:

sin(128°)/15 = sin(x)/12

Multiplying both sides by 12:

sin(x) = 12sin(128°)/15

Taking the inverse sine of both sides:

x = sin^-1(12sin(128°)/15)

x ≈ 108.5°

Therefore, the missing angle is approximately 108.5 degrees.

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Area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

To find the area of a parallelogram, we use this equation:

Now that we have this equation, we can apply it to each parallelogram.

Now, we can figure out which has the greatest area.

Therefore, the parallelogram that has the greatest area is 3, or III.

Answer:

III

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

I

A = 3 × 5 = 15 units²

II

A = 5 × 3 = 15 units²

III

A = 4 × 4 = 16 units²

IV

A = 4 × 3 = 12 units²

parallelogram III has the greatest area

In a case whereby three numbers are in the ratio 2:3:5 and the sum of their cube is 34560 then the numbers are  12, 18, and 30.

The given Ratio of three numbers can be expressed as 2:3:5

Then we can represent the three numbers  as: 2x, 3x, and 5x.

We were given the Sum of their cubes as  34560

Thern we can cube them as 2x^3 + 3x^3 + 5x^3 =34560

The we will have 8x^3 + 27x^3 + 125x^3 =34560

Then we have 160x^3 = 34560

x^3 =34560/160

x= 6.

then we can find the values of the ratio as :

2x =( 2×6)

= 12

3x = (3×6 )

= 18

5x = (5×6 )

= 30

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If he want to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually, then the multiplicative rate will be 0.98

The initial investment = $10000

decreasing percentage = 2%

Therefore, the second term will be the 98% of the first term

The first term = 10000

The second term = 10000 × 98/100

= 10000 × 0.98

= 9800

The common ratio is the ratio of the second term to the first term

The common ratio = second term / first term

= 9800 / 10000

= 0.98

Therefore, the multiplicative rate of change should Hal use in his function is 0.98

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The solution to the system of linear equations associated with the reduced row-echelon form matrix is (0, 0). This indicates that both variables, x and y, have a value of zero.

The reduced row-echelon form of a matrix is the simplest way to represent the solution to a system of linear equations. In the case of a matrix with two rows and two columns, a solution is produced when the matrix is in its reduced row-echelon form. Specifically, for the given matrix, 0 0, the solution to the corresponding system of linear equations is (0, 0). This indicates that both variables, x and y, have a value of zero. This is because the reduced row-echelon form is the simplest way to represent the solution to a system of linear equations. In this form, all the leading entries are ones and all the other entries are zero. Since the matrix is 0 0, this indicates that the solution is (0, 0). This solution can be seen as an ordered pair, where the first value represents the solution for the x variable, and the second value represents the solution for the y variable. In this case, both values are zero, which means that the solution to the system of linear equations is (0, 0).

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The complete question is

The matrix 1 −1 ]5 0 0 ]0 is in reduced row-echelon form. Determine the solution of the corresponding system of linear equations. Write the solution as an ordered pair. For parametric solutions use either x = t or y = t as the parameter form matrix(0,0).

The correct option is "the standard error is the standard deviation of the sampling distribution." Correct option is A.

The standard error is a measure of the variability of a sampling distribution, which is the distribution of sample statistics (e.g., mean, proportion) that would be obtained from multiple random samples of the same size from the same population.

The standard error represents the standard deviation of the sampling distribution, and it provides a measure of the precision of the sample statistic in estimating the population parameter.

The standard error is not the same as the standard deviation of the sample, which is a measure of the variability of the individual observations in the sample.

The standard deviation of the sample is typically used to estimate the standard deviation of the population, while the standard error is used to estimate the variability of the sample statistic and to construct confidence intervals or perform hypothesis tests.

While the other options are related to the concept of the standard error, they are not equivalent or fully accurate descriptions of what the standard error represents.

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Complete question is:

What is the standard error?

group of answer choices

A. the standard error is the standard deviation of the sampling distribution

B. the standard error is a measure of how representative a sample statistic is likely to be of the population parameter.

C. the standard error is calculated using the standard deviation of the sample all of the options describe the standard error.

Robert's box-and-whisker plot should look like the following: C. box-and-whisker plot C.

In Mathematics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Next, we would sort the observations (data set) from the least to greatest as follows:

14, 18, 21, 27, 32, 38, 46}.

Based on the information provided above, the five-number summary for the given data set include the following:

Minimum = 14

First quartile = 18.

Median = 27.

Third quartile = 38.

Maximum = 46.

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If the functions be f(x) = 4x + 13 and g(x) = 10x − 2 then the expression (f + g)(x) be 4x + 11.

A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the function's codomain. Initially, functions were just an idealized representation of the relationship between two changing quantities.

Given f(x) = 4x + 13 and g(x) = 10x − 2

We must add both functions to reflect the amount of time it takes to travel east and west in order to calculate the round-trip time.

Let the equation be (f + g)(x) = f(x) + g(x)

substitute the values in the above equation, we get

= (4x + 13) + (10x − 2)

simplifying the above equation, we get

= 4x + 13 + 10x − 2

= 4x + 10x − 2 + 13

= 4x + 11

Therefore, the expression (f + g)(x) be 4x + 11.

The completed question is:

The function f(x) represents the time it takes an airplane to travel east. The function g(x) represents the time it takes an airplane to travel west. Given f(x) = 4x + 13 and g(x) = 10x − 2, solve for (f + g)(x) to determine the total roundtrip time.

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Answer:

im him

Step-by-step explanation:

To buy down the quoted interest rate from 4.75% to 4.5% will cost Trystan and Kendall $4,800 after the down payment.

The down payment refers to the initial cash payment for the purchase of an item on mortgage.

The down payment is required by the financier to evaluate the buyer's financial readiness.

The cost of the new home = $300,000

Down payment = 20% or $60,000 ($300,000 x 20%)

Mortgage loan required = $240,000 ($300,000 - $60,000)

Bank quoted interest rate = 4.75%

Desired interest rate = 4.5%

Difference in interest rate = 0.25% (4.75% - 4.5%)

Rate of buy down of the quoted interest per point = 0.125%

The number of points to buy down the interest rate = 2 (0.25/0.125)

The cost of each point = 1% of $240,000 = $2,400

The total cost of 2 points = $4,800 ($2,400 x 2)

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The solution of the system of linear equations y = 9x + 14 and y = 6x + 35 will be (7, 77).

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

The system of linear equations is given below.

y = 9x + 14                ....1

y = 6x + 35              ....2

From equations 1 and 2, then we have

9x + 14 = 6x + 35

3x = 21

x = 7

The value of 'y' is given as,

y = 6 (7) + 35

y = 42 + 35

y = 77

The solution of the system of linear equations y = 9x + 14 and y = 6x + 35 will be (7, 77).

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Answer: the correct answer is 51

Step-by-step explanation: i solved this on my quiz

i hope this helps!

Sidney will use 54 cups of soda for 17 cups of ice cream, So the answer is 54 cups.

What is the ratio?

A ratio is a relationship between two things when it is expressed in numbers or amounts. For example, if there are ten boys and thirty girls in a room, the ratio of boys to girls is 1:3, or one to three.

We can start by noticing that the ratio of cups of ice cream to cups of soda used to make the floats is always 1:3.

To find out how much soda Sidney will use for 17 cups of ice cream, we can set up a proportion:

3.5/10.5 = 8/24 = 12.5/37.5 = 17/x

Solving for x, we can cross-multiply:

3.5x = 10.5 * 17

x = 54

Therefore, Sidney will use 54 cups of soda for 17 cups of ice cream, So the answer is 54 cups.

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Answer:

Step-by-step explanation: 22/7 is a rational number because it can be expressed as a ratio or fraction of two integers. The numerator (22) and denominator (7) are both integers, and the denominator is not equal to zero, so 22/7 is a well-defined fraction. Since every fraction represents a rational number, 22/7 is also a rational number

The number that can each terms of the equation be multiplied by to eliminate the decimals before solving is 100

The equation is

5.6j + 0.12 = 4 + 1.1j

The equation is defined as the mathematical expression that shows the relationship between one expression and another expression with equal sign. The equation consist of mathematical operator like addition, subtraction, division and multiplication

The equation is

5.6j + 0.12 = 4 + 1.1j

Here three term has fractional part.

In 0.12 there are two digits after the decimal point to eliminate the decimal number we have to multiply the number with 100 .

Then the equation will become

560j + 12 = 400 + 110j

Therefore, the number is 100

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The given question is incomplete, the complete question is

Which number can each term of the equation be multiplied by to eliminate the decimals before solving?

5.6j + 0.12 = 4 + 1.1j

Answer:

20(4+3)

Step-by-step explanation:

GCF of 80 and 60 = 20

20*4=80

20*3=60

20(4+3)

hope this helps! :)

Answer:

Step-by-step explanation:

y = 2x:

This is an equation for a straight line in which "y" is proportional to "x" with a coefficient of 2. If you plot this line on a coordinate plane, it will have a slope of 2 and y-intercept of 0.

12 x 12:

This is a mathematical expression for finding the product of 12 and 12. The result is 144. In mathematical writing, it's usually written as "12 * 12 = 144".

Answer:

It is a function. You can identify when something is a function by finding whether plugging in any x value will result in one y value.

Answer:

-7

Step-by-step explanation:

Answer: -7

Step-by-step explanation: I hope this helped you out!!!! Please mark me as brainiest.

The required we can save $13.86 annually by buying all your turkey at the discount store.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let's call the price of turkey per pound at the supermarket "x". Then the price of turkey per pound at the discount store would be x - $0.99.

Since we consume 14 pounds of turkey annually, the cost of the turkey at the supermarket would be 14 × x dollars.

And the cost of the turkey at the discount store would be 14 × (x - $0.99) dollars.

Therefore, the amount you would save annually by buying all your turkey at the discount store is,

= 14 × x - 14 × (x - $0.99) = 14 × $0.99
= $13.86

So, we would save $13.86 annually by buying all your turkey at the discount store.

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Answer:

4x * -16

Step-by-step explanation:

You use the distributive property and multiply 4 by everything in the parentheses. The 16 is negative because you keep the minus sign with the number behind it.

a) Periodic Deposit = (A - P×(1 + r/n)ⁿᵗ) × (n / ((1 + r/n)ⁿᵗ - 1))

b) The amount of the financial goal that comes from deposits is $60305.24 and the amount that comes from interest is = $149694.76.

Compound interest is a method of calculating interest on a principal amount that includes not only the initial principal but also the accumulated interest from previous periods.

a. The formula for periodic deposits, assuming a fixed interest rate and the same amount of deposit made at the end of each period, is:

Periodic Deposit = (A - P×(1 + r/n)ⁿᵗ) × (n / ((1 + r/n)ⁿᵗ - 1))

Where:

A = Financial goal

P = Initial deposit (assumed to be 0 in this case)

r = Annual interest rate (as a decimal)

n = Number of compounding periods per year

t = Time (in years)

Substituting the given values, we have:

Periodic Deposit = (210000 - 0*(1 + 0.035/12[tex])^{(12\times 13)}[/tex] * (12 / ((1 + 0.035/12[tex])^{(12\times 13)}[/tex] - 1))

= $543.15 (rounded to the nearest cent)

Therefore, the periodic deposit needed to reach the financial goal of $210000, with a 3.5% annual interest rate compounded monthly over 13 years, is $543.15 at the end of each month.

b. To determine how much of the financial goal comes from deposits and how much comes from interest, we can use the following formula for the future value of an annuity:

FV = P * ((1 + r/n)ⁿᵗ - 1) / (r/n) + A * (1 + r/n)ⁿᵗ

Where:

FV = Future value of the annuity (i.e., the financial goal)

P = Initial deposit

A = Periodic deposit

r, n, t = Same as before

Substituting the given values and solving for P, we have:

P = (210000 - 543.15 * (1 + 0.035/12[tex])^{(12\times 13)}[/tex] ) * (0.035/12) / ((1 + 0.035/12[tex])^{(12\times 13)}[/tex] - 1)

= $60305.24 (rounded to the nearest cent)

Therefore, the amount of the financial goal that comes from deposits is $60305.24, and the amount that comes from interest is $210000 - $60305.24 = $149694.76.

Hence,

a) Periodic Deposit = (A - P*(1 + r/n)ⁿᵗ) * (n / ((1 + r/n)ⁿᵗ - 1))

b) The amount of the financial goal that comes from deposits is $60305.24 and the amount that comes from interest is = $149694.76.

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Answer: AB and BC form a right angle at point B, so BC is perpendicular to AB. To find the equation of BC, we can use the slope-point formula, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

The slope of a line perpendicular to AB can be found by finding the negative reciprocal of the slope of AB. To find the slope of AB, we need to find the difference in the y-coordinates and divide it by the difference in the x-coordinates:

m_AB = (y2 - y1) / (x2 - x1)

= (4 - (-1)) / (4 - (-3))

= 5 / 7

The slope of a line perpendicular to AB is the negative reciprocal of m_AB:

m_BC = -1 / m_AB = -1 / (5/7) = -7/5

Now that we have the slope of BC, we can use the slope-point formula to find the equation of BC. We'll use the point B = (4, 4) as (x1, y1):

y - 4 = -7/5 (x - 4)

y = -7/5 x + 4(7/5) + 4

y = -7/5 x + 36/5

So the equation of BC is y = -7/5 x + 36/5.

Step-by-step explanation:

The correct quadratic equation that can be used to determine the thickness of the frame, x, is: 2x² + 10x - 7 = 0, Therefore Option B is the right answer

Here's how we can get this equation:

We are given that the mirror and frame together have an area of 7 square feet. The mirror itself has an area of 2 x 3 = 6 square feet. So, the area of the frame is 7 - 6 = 1 square foot.

Let's assume that the width of the frame is x feet. Then the overall width of the mirror and frame becomes 2 + 2x, and the overall length becomes 3 + 2x. The area of the mirror and frame can be expressed as:

(2 + 2x)(3 + 2x) = 6 + x(10 + 4x)

We know that this expression equals 7, so we can set it equal to 7 and obtain the quadratic equation:

2x² + 10x - 7 = 0

Therefore, the correct quadratic equation is 2x² + 10x - 7 = 0.

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Answer: 240 Grams.

Step-by-step explanation: First I need to find how many grams each bat eats, then multiply the 48 bats by each gram the bats eat. And you would get 240!