How many years will it take $6,000 invested at 8% interest to earn $1,680?

Answer: 46 ft by 92 ft

Step-by-step explanation:

The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.

The equation of the function g(x) is g(x) = 1/2x²

If we want to stretch or compress the function f(x) = x^2, we can multiply or divide the input variable x by a constant value a.

Specifically, if we use g(x) = f(ax), then g(x) is a stretched or compressed version of f(x).

To find the value of a that will make g(x) pass through the point (2,2), we can substitute these values into the equation g(x) = f(ax):

[tex]g(2)=f(a*2)=f(2a)=(2a)^2 =4a^2 =2[/tex]

So, we have

a = 1/2

Recall that

g(x) = f(ax)

So, we have

g(x) = f(1/2x)

This means that

g(x) = 1/2x²

Hence. the function is g(x) = 1/2x²

Read more about trasnformation at

https://brainly.com/question/1548871

#SPJ1

Answer:

5x (x + 7)

Step-by-step explanation:

5x² + 35x

First, we find the GCF! In this case, the GCF is 5x

Factor out 5x

5x (x + 7)

So, the answer is 5x (x + 7)

Answer:

90 cubic feet

Step-by-step explanation:

3 feet × 5 feet × 6 feet = 90 cubic feet

Answer: 104%

Step-by-step explanation: 26% times 4 years

The probability of drawing a marble that is green or even-numbered is  28/35

The total number of marbles in the jar is 35, of which 10 are blue, 12 are green, and 13 are red.

We need to find the probability of drawing a marble that is green or an even number.

First, let's find the number of even-numbered marbles.

Out of 35 marbles, 17 of them are even-numbered (2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34).

There are 12 green marbles, and 17 even-numbered marbles,

Therefore, there are 12 + 17 - 1 = 28 marbles that are either green or even-numbered.

The probability of drawing a marble that is green or even-numbered is

28/35

So the probability of drawing a marble that is green or even-numbered is  28/35

Read more about probability at

https://brainly.com/question/251701

#SPJ1

The total number of employees is 112.

Explain numbers

Numbers are symbols or representations used to quantify or count objects, quantities, or measurements. They form the basis of mathematical operations, such as addition, subtraction, multiplication, and division, and are used in various fields such as science, finance, and engineering. Numbers can be positive, negative, whole, or fractional, and are essential for communication and calculation in our daily lives.

According to the given information

Let's use x to represent the total number of employees.

According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that out of every 4 + 5 = 9 employee, 4 are union members and 5 are nonunion members.

So, we can set up the following proportion:

4/9 = x/(x - 140)

To solve for x, we can cross-multiply and simplify:

4(x - 140) = 9x

4x - 560 = 9x

560 = 5x

x = 112

Therefore, the total number of employees is 112.

To know more about numbers visit

brainly.com/question/17429689

#SPJ1

Is the graph increasing, decreasing, or constant: C. Constant.

In Mathematics and Geometry, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.

By critically observing the graph shown above, we can reasonably infer and logically deduce that the graph is constant because it assumes only one y-value, which is represented by this equation y = 3.

In conclusion, the above is constant, rather than increasing or decreasing.

Read more on a graph here: brainly.com/question/4546414

#SPJ1

A 90% confidence interval for µ is (8.92, 9.28).

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

The formula for a confidence interval for the population mean is:

CI = x ± z * (σ / sqrt(n))

where x is the sample mean, σ is the population standard deviation, n is the sample size, z is the z-score associated with the desired confidence level, and CI is the confidence interval.

Given the values provided:

c = 0.90

x = 9.1

σ = 0.6

n = 45

First, we need to find the z-score associated with a 90% confidence level. We can use a standard normal distribution table or a calculator to find that z = 1.645.

Then, we can plug in the values and calculate the confidence interval:

CI = 9.1 ± 1.645 * (0.6 / sqrt(45))

= 9.1 ± 0.176

= (8.92, 9.28)

Therefore, a 90% confidence interval for µ is (8.92, 9.28).

To learn more about statistics from the given link:

https://brainly.com/question/28053564

#SPJ1

The answers to each question are:

(a)  0.351.

(b)  0.317.

(c)  20.24 years.

(d)  16.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

(a) What is the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years?

To answer this question, we need to standardize the values of 18 and 20 using the mean and standard deviation provided. Let X be the age at which growth plates fuse for males. Then,

Z = (X - mean) / standard deviation

Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53

Z for X = 20 is (20 - 18.8) / (15.1/12) = 0.53

Using a standard normal distribution table or a calculator, we can find the probability of Z being between -0.53 and 0.53, which is approximately 0.351.

Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years is 0.351.

(b) What is the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years?

We need to standardize the values of 16 and 18 using the mean and standard deviation provided.

Z for X = 16 is (16 - 18.8) / (15.1/12) = -2.03

Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53

Using a standard normal distribution table or a calculator, we can find the probability of Z being between -2.03 and -0.53, which is approximately 0.317.

Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years is 0.317.

(c) What is the age at which growth plates fuse for the top 5% of males?

We need to find the age X such that the probability of a male having growth plates fuse at an age less than X is 0.95 (since 5% is the complement of 95%).

Using a standard normal distribution table or a calculator, we can find the Z-score corresponding to the 95th percentile, which is approximately 1.645.

Then, we can solve for X using the formula:

Z = (X - mean) / standard deviation

1.645 = (X - 18.8) / (15.1/12)

Simplifying the equation, we get:

X = 18.8 + (1.645)(15.1/12) = 20.24

Therefore, the age at which growth plates fuse for the top 5% of males is approximately 20.24 years.

(d) What percentage of males have growth plates that fuse before the age of 16?

We need to find the probability of a male having growth plates fuse before the age of 16, which is equivalent to finding the probability of Z being less than -2.03 (calculated in part (b)).

Using a standard normal distribution table or a calculator, we can find the probability of Z being less than -2.03, which is approximately 0.0228.

Therefore, approximately 2.28% of males have growth plates that fuse before the age of 16.

hence, the answers to each question are:

(a)  0.351.

(b)  0.317.

(c)  20.24 years.

(d)  16.

To learn more about the mean and standard deviation visit:

brainly.com/question/475676

#SPJ1

The fraction of Earth that is not made up of ocean = 1/4.

The numbers we are familiar with are whole numbers, such as 1, 2, and so on.

Numbers expressed as fractions have a numerator and a denominator, separated by a line known as a vinculum.

In essence, a fraction explains how a portion of a group interacts with the entire group.

Given that-

The fraction of Earth that is not made up of ocean = 1 - fraction of Earth made up of water

The fraction of Earth that is not made up of ocean = 1 - 3/4

The fraction of Earth that is not made up of ocean = (4 - 3)/4

The fraction of Earth that is not made up of ocean = 1/4

Thus, the fraction of Earth that is not made up of ocean = 1/4.

Know more about the fraction:

https://brainly.com/question/78672

#SPJ1

Complete question:

Approximately 3/4 of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?​

The correct answer is: Decrease total assets and net income.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

The recognition of uncollectible accounts expense for Year 2 will decrease total assets and net income.

When uncollectible accounts expense is recognized, it is recorded as a debit to the allowance for doubtful accounts and a credit to the uncollectible accounts expense account. This reduces the balance of accounts receivable, which is a current asset, and thus decreases total assets. Additionally, recognizing this expense reduces net income by the same amount.

Therefore, the correct answer is: Decrease total assets and net income.

To learn more about statistics from the given link:

https://brainly.com/question/28053564

#SPJ1

Answer:

[tex]25.5h = 153[/tex]

[tex]h = 6[/tex]

The height is 6 feet, so A is correct.

Answer: 76 pages

Step-by-step explanation:

700 photo spaces = 100%

-The total

168 photo spaces = 24%

-The number of empty spaces in the album.

- Find 24% of 700:

70(10%) x 2 = 140

7(1%) x 4 = 28

140 + 28 = 168

532 photo spaces = 76%

- The number of photos in the album

700 - 168 = 532

Finding the number of pages.

-As we know 1 page holds 7 photos, if we had 532 photos we'd have to divide it by 7 to see how many pages all the photos would be held in.

532 ÷ 7 = 76.

The value or measure of following are :-

x = 17.18°

∠JK = 143.78°

∠MJ = 116.48°

∠LMK = 47.17°

A segment of a circle called an arc is made up of two endpoints on the circle and the curve that connects them.

Since the two lines JL and MK intersect at the center of the circle at point N, the angles formed by them are inscribed angles of the circle. Moreover, the angles formed by an inscribed angle and its corresponding arc are equal. Therefore, we can write:

∠JNK = ½ arc JNK = ½(5x+23)° = 2.5x + 11.5°

∠KNL = ½ arc KNL = ½(17x-41)° = 8.5x - 20.5°

We are also given that arc MNJ and LNK are similar, so their corresponding angles are equal. Similarly, arc MNL and JNK are similar, so their corresponding angles are equal. Let's use these facts to find x:

∠MNJ = ∠LNK

The arc MNJ is equal to the sum of arcs MNL and LNK. Therefore, we have:

½(5x+23)° + ½(17x-41)° = ∠MNJ + ∠LNK

2.5x + 11.5° + 8.5x - 20.5° = 2∠MNJ

11x - 9° = 2∠MNJ

∠MNL = ∠JNK

The arc MNL is equal to the sum of arcs MNJ and JNK. Therefore, we have:

½(5x+23)° + ½(8.5x-20.5°) = ∠MNL + ∠JNK

2.75x + 1.5° = 2∠JNK

1.375x + 0.75° = ∠JNK

Since ∠MNJ = ∠LNK and ∠MNL = ∠JNK, we can write:

2∠MNJ + 2∠JNK = 360°

Substituting the expressions we found for ∠MNJ and ∠JNK, we get:

22x - 18° = 360°

22x = 378°

x = 17.18° (rounded to two decimal places)

Now that we know x, we can find the values of the other angles of arc-

∠JNK = 1.375x + 0.75° = 24.43°

∠KNL = 8.5x - 20.5° = 119.35°

∠MNJ = (11x - 9°)/2 = 92.05°

∠LNK = ∠MNJ = 92.05°

∠MNL = 360° - ∠MNJ - ∠JNK = 243.52°

∠JK = ∠JNK + ∠KNL = 143.78°

∠MJ = ∠MNJ + ∠JNK = 116.48°

∠LMK = 360° - ∠MNJ - ∠JNK - ∠KNL = 47.17°

To know more about angles of arc visit:

https://brainly.com/question/29886231

#SPJ1

A timeline that spans 541 centimeters would be equivalent to a length of 5.41 meters or approximately 17.75 feet.

What is the unit conversion?

Unit conversion is the process of converting a quantity expressed in one unit of measurement to another unit of measurement that is equivalent in value. The need for unit conversion arises because different units are used to measure the same physical quantity in different countries or regions, or in different fields of study.

Making a model of the geologic time scale with a scale of 1 centimeter equals 1 million years means that each centimeter on the timeline represents 1 million years of geologic time.

To create the model, we can start by determining the total length of the timeline we want to create.

Let's say we want to include the entire Phanerozoic Eon, which spans approximately 541 million years.
To represent this on our timeline, we would need a total length of 541 centimeters.

However, we need to keep in mind that 100 cm is equal to 1 meter, which is a little longer than 3 feet.

Therefore, a timeline that spans 541 centimeters would be equivalent to a length of 5.41 meters or approximately 17.75 feet.

To  learn more about the unit conversion visit:

https://brainly.com/question/13016491

#SPJ1

The option that is true about the equations for these two lines iis that they represent the same lines.

The trick to questions like this is to get both equations into the slope-intercept form.  That is done for our first equation (y = 3x + 5).  However, for the second, some rearranging must be done:

5y – 25 = 15x; 5y = 15x + 25; y = 3x + 5

Note: Not only do these equations have the same slope (3), they are totally the same; therefore, they represent the same equation.

Learn more about equations on;

https://brainly.com/question/22688504

#SPJ1

Two lines are described by the equations:

y = 3x + 5 and 5y – 25 = 15x

Which of the following is true about the equations for these two lines?They represent perpendicular lines.

None of the other answers

They represent non-perpendicular, intersecting lines.

They represent the same lines.

They represent parallel lines.

Answer:

28°

Step-by-step explanation:

If the angles are supplementary, they add up to 180°.

(3x) + (2x + 40) = 180

5x + 40 = 180

     - 40   - 40

5x = 140

x = 28°

Solving the system of equations using matrices is : = -66, y = 163, and z = 11.

To solve this system of equations using matrices, we can write it in the form AX = B, where:

A = coefficient matrix

X = variable matrix (containing x, y, and z)

B = constant matrix (containing the constants on the right-hand side of each equation)

So, we have:

| 2  -1  3 |   | x |   | 180 |

| -4  2  3 | x | y | = | 225 |

| 3  -4  0 |   | z |   | 270 |

We can solve for X by multiplying both sides of the equation by the inverse of A:

X = A^-1 * B

First, we need to find the inverse of A. We can do this by using the formula:

A^-1 = (1 / det(A)) * adj(A)

where det(A) is the determinant of A and adj(A) is the adjugate (transpose of the cofactor matrix) of A.

| 2  -1  3 |

| -4  2  3 |

| 3  -4  0 |

det(A) = 2(20 - 3(-4)) - (-1)(-40 - 33) + 3(-4*(-1) - 2*3) = 16

| 2  -1  3 |

| -4  2  3 |

| 3  -4  0 |

The cofactor matrix is:

| 2  9  6 |

| 12  0  -2 |

| 13  -9  8 |

Taking the transpose of the cofactor matrix gives us the adjugate of A:

| 2  12  13 |

| 9  0  -9 |

| 6  -2  8 |

So, we have:

A^-1 = (1 / det(A)) * adj(A) = (1 / 16) *

| 2  12  13 |

| 9  0  -9 |

| 6  -2  8 |

Multiplying A^-1 by B gives us:

| x |   | -66 |

| y | = | 163 |

| z |   | 11  |

Therefore, x = -66, y = 163, and z = 11.

Learn more about matrix here:https://brainly.com/question/94574

#SPJ1

Answer:

One possible rational function that satisfies the given properties is:

r(x) = (x-2)(x-6) / [(x-3)(x-5)]

Step-by-step explanation:

x-intercepts at (2,0) and (6,0)

The x-intercepts are the points where the function crosses the x-axis, i.e., where the function value is zero. Since we are given that the function has x-intercepts at (2,0) and (6,0), we know that the function can be factored as:

r(x) = A(x-2)(x-6)

where A is a constant that we need to determine.

A hole at x=1 and vertical asymptotes at x=5 and x=3

A hole in a rational function occurs when there are factors in the numerator and denominator that cancel out, leaving a "hole" in the graph. In this case, we are given that there is a hole at x=1, which means that there must be a common factor of (x-1) in both the numerator and denominator. So, we can write:

r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5))

where B is another constant that we need to determine.

We are also given that there are vertical asymptotes at x=5 and x=3, which means that the denominator must have factors of (x-5) and (x-3) that do not cancel out with any factors in the numerator. So, we can write:

r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5)) = [A(x-2)(x-6)] / [(B(x-1))(x-3)(x-5)]

End behavior given by x → ∞ ,f(x) → 1 and x → -∞ ,f(x) → 1

The end behavior of a rational function is determined by the degree of the numerator and denominator. Since the numerator and denominator in this case have the same degree (3), we know that the end behavior is given by the ratio of the leading coefficients, which is A/B. We are told that the end behavior approaches 1 as x approaches infinity or negative infinity, so we can set A/B = 1 and solve for A in terms of B:

A/B = 1, so A = B

Putting it all together

We now have enough information to write the equation for the rational function with the given properties:

r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5))

Using A = B, we get:

r(x) = A(x-2)(x-6) / [A(x-1)(x-3)(x-5)]

Canceling out the common factor of (x-1) in the numerator and denominator, we get:

r(x) = (x-2)(x-6) / [(x-3)(x-5)]

which is the equation for the desired rational function.

a. It will take 7 months to pay off the credit card. b. it will take 4 months to pay off the credit card.

APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance. We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

= log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

= 6.18

Therefore, it will take approximately 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

= log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

= 3.43

Therefore, it will take approximately 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

To know more about APR, visit:

https://brainly.com/question/13597527

#SPJ1

Answer: The actual difference between the numbers is:

87.71 - 5.8 = 81.91

Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91. Brainliest?

Step-by-step explanation:

To round 87.71 to the nearest whole number, we look at the digit in the ones place, which is 1. Since 1 is less than 5, we round down to 87. To round 5.8 to the nearest whole number, we look at the digit in the ones place, which is 8. Since 8 is greater than or equal to 5, we round up to 6.

Using these rounded values, Yasmine estimated the difference between the numbers to be 87 - 6 = 81.

The actual difference between the numbers is:

87.71 - 5.8 = 81.91

Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91.

Answer:

Yasmine estimated the difference to be 82. The actual difference is 81.91.

Step-by-step explanation:

The rounded whole number of 87.71 is 88 and the rounded whole number of 5.8 is 6.

So, the difference between the numbers 87.71 and 5.8 by rounding each number to the nearest whole numbers will be

(88 - 6) = 82.

The actual difference between the numbers 87.71 and 5.8 is (87.71 - 5.8) = 81.91.

Therefore, Yasmine estimated the difference to be 82. The actual difference is 81.91.

to find the mean you add al the numbers together and divide it by how many numbers there were. so to find the mean it would be (682+612+756+674+714+790+668+652+776)÷9=702.6 which can be rounded up to 703. Also pls mark as brainliest answer

Answer:

Step-by-step explanation:

I think its 42 because 7/20ths of 120 is 42

7/20 x 120 =42

Step-by-step explanation:

the answer is 115 remainder 1

Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.

A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.

The vertex of the parabola is located at this lowest or highest point.

Vertex form of a quadratic function:

f(x) = a(x – h)² + k, where a, h, and k are constants.

The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).

(h,k) are the vertex of parabola.

From the given graph:

f(b) is the given function:

Vertex (h,k) = (8, 4)

Thus, h= 8 and k = a = 1, x = b.

Put the values in quadratic function:

f(b) = 1(b – 8)² + 4

f(b) = (b – 8)² + 4

Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.

Know more about the quadratic function in vertex form:

https://brainly.com/question/28201865

#SPJ1

Step-by-step explanation:

6^2 / 6^1   x    6^12 / 6^8   =

6^(2-1)      x    6^(12-8)   =

6^1          x    6^4   =

6^(1+4)  =   6^5     or  = 7776

The type of the relation are

A linear expression is an algebraic expression in which each term has a degree of 1 (or 0), and the variables are raised only to the first power.

In the given expressions:

Therefore, the linear expressions are "5x", "6x + 1", and "17". The nonlinear expressions are "10xy" and "4x^2".

Read more about linear relations at

https://brainly.com/question/30318449

#SPJ1