For Exercises 16-18, use the following information. Brian invests $200 in an
account that pays 5% annual interest compounded continuously.
16. Write a function that models the amount y in the account after x years.
17. Write the domain and range using inequalities. Explain their meaning in this context.
18. How much will Brian have in the account after 8 years?

The amount of each quarterly payment, rounded, for a $30,000 loan with a 6% annual interest rate to be paid off in 10 equal quarterly payments is $2,803 (option B).


To calculate the amount of each quarterly payment, we need to use the formula for calculating the equal payments on an installment loan. In this case, the loan amount is $30,000, the annual interest rate is 6%, and the loan term is 10 quarters.

Using the formula, we can determine that the amount of each quarterly payment is approximately $2,803. This amount is rounded to the nearest whole number, as specified in the question. Therefore, option B, $2,803, is the correct answer. The other options (A, C, and D) are not applicable to the calculation based on the given information.

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Answer:

6x^3+16x^2 I think that is correct

Step-by-step explanation:

The height of bridge in the square is 15 units. This is determined by using the ratio of sides in a 30-60-90 triangle and multiplying the hypotenuse by the corresponding ratio for the shorter leg, which is 1.

Let's calculate the height of the bridge step by step using the given information

In a 30-60-90 triangle, the ratio of the sides is 1:√3:2.

Given:

Hypotenuse = 15

Step 1: Determine the length of the shorter leg (height of the bridge)

Since the ratio is 1:√3:2, the length of the shorter leg can be found by multiplying the hypotenuse by the ratio corresponding to the shorter leg, which is 1.

Length of the shorter leg = 15 * 1 = 15

Step 2: Simplify the expression for the shorter leg

Since the hypotenuse of the 30-60-90 triangle is given as 15, the length of the shorter leg is also 15.

Height of the bridge = 15

Therefore, the height of the bridge is 15 units.

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Step-by-step explanation:

The distance BC is given as follows:

BC = 12.5.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

For the right triangle in this problem, we have that:

Hence the length BC is obtained as follows:

x² + 4.3² = 13.2².

x = sqrt(13.2² - 4.3²)

x = 12.5.

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The "rise" direction represents the Recession Velocity, indicating the motion of galaxies away from us, while the "run" direction represents the X axis, representing the independent variable used to measure distance or time in the Hubble Constant equation.

The "rise" direction in the context of the slope of the Hubble Constant represents the Recession Velocity (RV). It signifies the rate at which galaxies are moving away from us in the expanding universe.

On the other hand, the "run" direction represents the X axis. It refers to the distance or time, depending on the specific interpretation, along the X axis used to measure the independent variable in the Hubble Constant equation.

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Things that were not included in the class demo of Excel graph: Setting the axes to log scale , Drawing a trend line from data ,Filling down a column of formulae and Finding the slope of a line

The class demo of Excel graph showed how to create a basic graph, but it did not cover all of the features that are available. Here are some of the features that were not included:

Setting the axes to log scale: This allows you to plot data that has a logarithmic relationship. For example, you could plot the Richter scale of earthquakes, which is logarithmic.

Drawing a trend line from data: This allows you to add a line to your graph that represents the trend of the data. This can be helpful for seeing the overall direction of the data.

Filling down a column of formulae: This allows you to copy a formula down a column of cells, so that the formula is applied to each cell in the column. This can be helpful for saving time and making sure that all of the cells in the column have the same formula.

Finding the slope of a line: This allows you to calculate the slope of a line on your graph. The slope of a line is a measure of how steep the line is.

These are just a few of the features that were not included in the class demo of Excel graph. If you are interested in learning more about these features, you can find tutorials online or in the Excel help documentation.

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Answer: 45 in.

Step-by-step explanation:

Step 1:

Length × Width = Area           How to find Area

Step 2:

5 in. × 9 in.       Equation

Answer:

45 in.       Multiply

Answer:

ratio of a is 44:56, ratio of b is 97:3

fraction of a is 44/100, fraction of b is 97/100

decimal of a is 0.44, decimal of b is 0.97

percent of a is 97%, and percent of b is 97%

if this is wrong im so sorry :()()()()(

step-by-step explanation:

Answer:

y = -5/3x - 6/5

Step-by-step explanation:

Brainliest pls

Answer:

A) 96 cm

Step-by-step explanation:

Split into three parallelograms

Shape 1: 6 by 7     6×7=42

Shape 2: 3 by 4    3×4=12

Shape 3: 6 by 7    6×7=42

42+12+42=96

Answer:

96 cm

Step-by-step explanation:

Breaking the shape up into 3 smaller rectangles then finding the area of each gives us the total area

\(6*7=42*2=84\)

\(3*4=12\)

\(84+12=96\)

The probability of the random item chosen that it is less than 16.4 inches long is 2.7%

Probability means ?

The likelihood of an event happening is calculated using the probability formula. To review, probability is the probability that an event will occur. What is the likelihood that a specific event will occur when a random experiment is considered? is one of the first queries that pops into our heads. A prediction's chance is expressed as a probability. If we suppose that, for example, x represents the probability that an event will occur, then (1-x) is the probability that the event will not occur.

Variance of sample mean =1.3^2/1= 1.69

S D of sample mean =1.69^(1/2)= 1.3

Z score for length of 16.4 is( 16.4-15.4)/1.3= 0.7692307

The p value for -1.67 in standard normal table is 0.04746

The required probability =0.02764

Only 2.7% of the time will the sample mean be shorter than 16.4 inches.

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The solution to the given differential equation is: x⁷ cos y = y + C

where C is the constant of integration

To solve the given differential equation:

\(\[7x^6\cos y dx - dy = 0\]\)

We can separate the variables and integrate both sides.

Separating variables, we can write the equation as:

\(\[7x^6\cos y dx = dy\]\)

Now, we can integrate both sides with respect to their respective variables:

\(\[\int 7x^6\cos y dx = \int dy\]\)

Integrating the left side:

\(\[\int 7x^6\cos y dx = 7 \int x^6 \cos y dx\]\)

To integrate \(\(x^6 \cos y\)\)with respect to x, we can use integration by parts.

Let's take u = x⁶ and \(\(dv = \cos y dx\)\).

Differentiating u with respect to \(\(x\) gives \(du = 6x^5 dx\).\)

Integrating dv with respect to x gives \(\(v = \int \cos y dx = \cos y \cdot x\).\)

Applying the integration by parts formula:

\(\[\int x^6 \cos y dx = u \cdot v - \int v \cdot du\]\)

Substituting the values:

\(\[\int x^6 \cos y dx = x^6 \cdot \cos y \cdot x - \int (\cos y \cdot x) \cdot (6x^5 dx)\]\)

Simplifying:

\(\[\int x^6 \cos y dx = x^7 \cos y - 6 \int x^6 \cos y dx\]\)

Moving the integral term to the left side:

\(\[7 \int x^6 \cos y dx = x^7 \cos y\]\)

Dividing both sides by 7:

\(\[\int x^6 \cos y dx = \frac{x^7 \cos y}{7}\]\)

Now, substituting this result back into our original equation:

\(\[7 \int x^6 \cos y dx = dy\]\)

\(\[\frac{7x^7 \cos y}{7} = dy\)

Simplifying:

x⁷ cos y = dy

Finally, the solution to the given differential equation is:

x⁷ cos y = y + C

where C is the constant of integration.

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The two exponential functions f(x) = a bx and f(x) = a ekx are equivalent when their bases are equal.

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Answer:

6x×9y×15

Step-by-step explanation:

that's the answear I got because you didn't add any math signs so assuming its all multiplication you take 3 and multiply it with each of the numbers with there variables

When multiplying integers, the rules for determining the sign of the product are as follows:

1. If both integers have the same sign (either both positive or both negative), the product will be positive.

2. If one integer is positive and the other is negative, the product will be negative.

3. When multiplying zero by any integer, the product is always zero.

Remember to always multiply the absolute values of the integers and then determine the sign of the product based on the rules above.

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Transformation involves changing the form of a function.

The equation that represents g(x) is (c) \(g(x) =-\sqrt[3]{x+1}\)

Function f(x) is given as:

\(f(x) =\sqrt[3]{x}\)

The rule of this transformation (i.e. reflection) is:

\((x,y) \to (x,-y)\)

So, we have:

\(f'(x) = -f(x)\)

This gives

\(f'(x) =-\sqrt[3]{x}\)

The rule of this transformation (i.e. translation) is:

\((x,y) \to (x+1,y)\)

So, we have:

\(g(x) = f'(x+1)\)

This gives

\(g(x) =-\sqrt[3]{x+1}\)

Hence, the equation that represents g(x) is (c)

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Answer:

Its D

Step-by-step explanation:

just did the quiz

according to question the final equation is:

(y - k)^2/(9/4) - (x - h)^2/16 = 1

The equation of a hyperbola centered at the origin with a vertical transverse axis of length 2a and a conjugate axis of length 2b is:

y^2/a^2 - x^2/b^2 = 1

Since the center is not at the origin, we need to use a slightly modified equation. If the center of the hyperbola is at (h, k), then the equation becomes:

(y - k)^2/a^2 - (x - h)^2/b^2 = 1

In this case, the center is not given, so we cannot write the full equation. However, we can write the equation of the hyperbola if we assume that the center is at the origin (0,0) and then shift it later.

Given that the length of the vertical transverse axis is 3, we know that 2a = 3, so a = 3/2. Similarly, since the length of the conjugate axis is 8, we know that 2b = 8, so b = 4.

Therefore, assuming that the center of the hyperbola is at the origin, the equation of the hyperbola is:

y^2/(9/4) - x^2/16 = 1

To shift the center of the hyperbola to a different point (h,k), we replace x with (x - h) and y with (y - k),

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The value of X = 25.

Solution:

The two equations are

(i) the first condition is difference of x and y is 14

x - y = 14 ---------equation 1

(ii) the second condition of the given data is value of x is 3 times more than two times of y value.

x - 2y = 3 --------equation 2

From equation 2, we have to separate two variables x and y,

x = 3 + 2y  --------equation 3

We have to Substitute equation 3 in equation 1

3 + 2y - y = 14

3 + y = 14

y = 14 - 3

y = 11

Substitute y = 11 in equation 1........

x - 11 = 14

x = 14 + 11

x = 25

So, the value of x is 25 and y is 11.

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Answer:

Step-by-step explanation:

Given the difference of x and y is 14, and the difference of x and 2y is 3, you want two equations, their graph, and the value of x.

The difference of 'a' and 'b' is (a -b). Here, the two differences are expressed as the equations ...

The attachment shows a graph of these equations. Their point of intersection is (25, 11), meaning the value of x is 25.

The graph of the first equation is easily drawn by recognizing the x- and y-intercepts are 14 and -14, respectively.

The graph of the second equation will go through the x-intercept point of (3, 0) and the y-intercept point of (0, -3/2). It is probably easier to graph this by hand by considering the x-intercept point and the slope of 1/2.

Since we're only interested in the value of x, it is convenient to eliminate the variable y. We can to that by subtracting the second equation from twice the first:

  2(x -y) -(x -2y) = 2(14) -(3)

  x = 25 . . . . . . . . . simplify

Answer:

Third option is the correct answer

Step-by-step explanation:

Given end points are: \( (x_1, \:y_1) \:\&\: (x_2, \:y_2)\)

\( \huge\purple {\therefore Midpoint =\bigg(\frac{x_1+x_2}{2},\: \frac{y_1+y_2}{2}\bigg)} \)

Answer:

Step-by-step explanation:

Since the hexagon is regular, all of its sides have the same length. Therefore, each side has a length of 57 inches / 6 = 9.5 inches.

To find the area of the hexagon, we can use the formula:

Area = (3√3 / 2) × s^2

where s is the length of a side.

Substituting s = 9.5 inches, we get:

Area = (3√3 / 2) × (9.5 inches)^2

Area ≈ 244.3 square inches

Rounding to the nearest tenth, the area of the hexagon is 244.3 square inches.

For a regular pentagon, the apothem is the distance from the center of the pentagon to the midpoint of one of its sides. We can use the formula for the area of a regular pentagon to find the apothem:

Area = (5/4) × apothem × side length

Substituting the given values, we get:

118.25 square meters = (5/4) × apothem × (4.3 meters)

apothem = 118.25 square meters / (5/4) / (4.3 meters)

apothem ≈ 8.4 meters

Therefore, the length of the apothem is approximately 8.4 meters.

Since the hexagon is regular, all of its sides have the same length. Therefore, each side has a length of 90 feet / 6 = 15 feet.

To find the area of the hexagon, we can use the same formula as in the first problem:

Area = (3√3 / 2) × s^2

Substituting s = 15 feet, we get:

Area = (3√3 / 2) × (15 feet)^2

Area ≈ 1161.4 square feet

Rounding to the nearest tenth, the area of the hexagon is 1161.4 square feet.

Answer:The area A of a rectangle is represented by the formula A=lw where l is the length and w is the width. The length of the rectangle is 5.

Write an equation that makes it easy to find the width of the rectangle if we know the area and the length.

Step-by-step explanation:

The value of the expression is -65.

It should be noted that the function given is illustrated as:

-2 - 5x -7 - 9x

In this case, you've to put the value of x as 4.

This will be:

= -2 - 5x -7 - 9x

= -2 - 5(4) - 7 - 9(4)

= -2 - 20 - 7 - 36

= -65

Therefore, the value of the expression is -65.

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Answer:

55 and 68

Step-by-step explanation:

The list that shows the numbers |-0.12|, 1/8, 1/9 in order from smallest to largest is:

1/9, |-0.12|, 1/8.

The absolute value of a number is the distance of the number to the origin, hence it is represented by the number without the signal.

In the context of this problem, the absolute value of -0.12 is:

|-0.12| = 0.12.

To convert a fraction to decimal, we divide the top term of the fraction, called numerator, by the bottom term of the fraction, called the denominator.

Hence, in the context of this problem, the decimal representation of the fractions is given as follows:

To order the three numbers, both have integer part 0, hence we look at which one has the greater decimal part, hence they are ordered as 1/9, |-0.12|, 1/8, from least to greatest.

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Women make up 64% of the sample and are typically the household's main investment.

There is a correlation between American women and being the main provider in their home.

Descriptive statistics, also known as brief informative coefficients, are used to summarize a specific data collection, which may be a sample of a population or a representation of the entire population. Descriptive statistics include measures of variability and central tendency (spread). Measures of central tendency include the mean, median, and mode, whereas measures of variability include the standard deviation, variance, minimum and maximum variables, kurtosis, and skewness.

For instance, the sum of the following data set is 20: (2, 3, 4, 5, 6). A 4 (20/5) is the mean. A data set's mode is the number that appears most frequently, while its median is the value that is in the middle of the range of values. It is the value that separates a data set's higher values from lower values. There are many less common ways to use descriptive statistics, but they are nevertheless essential.

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The correct question is - Suppose a survey of 580 women in the United States found that more than 64​% are the primary investor in their household. Which part of the survey represents the descriptive branch of​ statistics? Make an inference based on the results of the survey.

Answer:

900,000 That's Your Answer UwU

Step-by-step explanation:

Answer:

Step-by-step explanation:

that is incorrect.

if it were to be equal, one side should equal each other when multiplied to make the ratio equal.

20-5x=40-10x (when multiplied by 2 on each side)

It CANNOT equal 50, if it were there would not be -10x

20-5x=100-25x

DIVIDE BY 2 to get 50 WOULD GIVE:

20-5x=50-17.5x

Answer:

Yes

Step-by-step explanation:

solve the equation for x , then evaluate and compare both sides

20 - 5x = 50 - 10x ( add 10x to both sides )

20 + 5x = 50 ( subtract 20 from both sides )

5x = 30 ( divide both sides by 5 )

x = 6

then

left side = 20 - 5x = 20 - 5(6) = 20 - 30 = - 10

right side = 50 - 10x = 50 - 10(6) = 50 - 60 = - 10

since both sides are equal then

20 - 5x = 50 - 10x is true

Answer:

3

Step-by-step explanation:

-21/-7 = 3

negative times negative or negative divided by negative is always positive

The thing to tell Irene to convince her that these cards don’t match is that the addition of the variables will not give 4x + 2.

An expression can be used to illustrate the relationship between the variables that are given in the data.

The addition of the variables will be illustrated thus:

x + 2 + x + 2 + x + 2 + x + 2 = 28

4x + 8 = 28

In the question, it was written as 4x + 2 = 28. This shows that it won't match.

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