Find the amount owed at the end of 4 years if $3,000 is loaned at a rate of 7% compounded semiannually (twice a year).
\($3,932.39\)
\($3,950.43\)
\($5,154.56\)
\($3,442.57\)

Answer:

51/8

Step-by-step explanation:

each bracelet length as a fraction will be 51/8 inches if the artist uses the 51 inches of the string to make 8 bracelets

Answer: 35%

Step-by-step explanation:

$70,000 was the down payment for a total price of $200,000.

Down payment percentage = 70,000 / 200,000

= 0.35

= 35%

We have the following:

Over 8 months, an investment of $84,000 at a simple interest rate of 12% would earn $8,400 in interest.

To calculate the interest earned on a simple interest investment, we use the formula: Interest = Principal × Rate × Time. In this case, the principal is $84,000 and the rate is 12% or 0.12 (converted to decimal form). The time is 8 months.

First, we convert the time to years by dividing 8 months by 12 (number of months in a year). This gives us 0.67 years.

Next, we plug in the values into the formula: Interest = $84,000 × 0.12 × 0.67.

Calculating this, we find that the interest earned over 8 months is $8,400. This means that after 8 months, the investment would have grown to a total of $92,400 ($84,000 principal + $8,400 interest).

It's important to note that simple interest assumes a constant interest rate over the entire period and does not take compounding into account. If compounding were involved, the interest earned would be higher.

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Part (a)

The error is that the 0.15 should be 0.85 because 1-0.15 = 0.85

If the laptop loses 15% of its value, then it keeps the remaining 85%.

Therefore, the formula should be \(a_n = 1500(0.85)^{n-1}\)

I'm assuming the "$1,5000" should have been "$1,500".

===========================================

Part (b)

Plug n = 4 into the formula.

\(a_n = 1500(0.85)^{n-1}\\\\a_4 = 1500(0.85)^{4-1}\\\\a_4 = 1500(0.85)^{3}\\\\a_4 = 1500(0.614125)\\\\a_4 = 921.1875\\\\a_4 \approx 921.19\\\\\)

The laptop's value is approximately $921.19 at the beginning of the 4th year.

The answer is (d) 6 variables, 1 of which is categorical.

The given data set consists of 6 variables, indicating that there are six distinct pieces of information being recorded or measured. Among these variables, only one is categorized as categorical. Categorical variables are qualitative in nature and represent characteristics or categories rather than numerical values. Examples of categorical variables include gender, color, type, or any other non-numeric attribute.

By deductive reasoning, since there is only one categorical variable in the dataset, the remaining five variables are likely to be quantitative. Quantitative variables are numerical and represent measurable quantities, such as age, weight, temperature, or time.

Identifying the number of categorical variables in a dataset is crucial for understanding the nature of the information being collected. In this case, we can confidently conclude that the data set contains 6 variables, with 1 of them being categorical, while the other 5 variables are likely to be quantitative.

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Answer:

110

Step-by-step explanation:

54+14=68+14=82+14=96+14=110

adding 14

Answer:

\(\huge\boxed{Answer\hookleftarrow}\)

\({\boxed{\boxed{\tt { ✎ \ 345688}}}} \ \)

⇻ 300000 + 40000 + 5000 + 600 + 80 + 8

\({\boxed{\boxed{\tt {✎ \ 5682003}}}} \ \)

⎇ 5000000 + 600000 + 80000 + 2000 + 0 + 0 + 3

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

To find the area below z=1.04 for an Upper N(0,1) density, you will need to use the standard normal distribution table or a calculator with a z-table function. Here are the steps:

1. Locate the value of z=1.04 in the table or use the calculator's function.
2. Find the corresponding area value (which represents the probability or percentage of values below z=1.04).

The area below z=1.04 is approximately 0.851, rounded to three decimal places.

(b) To find the area above z=-1.4 for an Upper N(0,1) density, follow these steps:

1. Locate the value of z=-1.4 in the table or use the calculator's function.
2. Find the corresponding area value.
3. Since we need the area above z=-1.4, subtract the area value found in step 2 from 1.

The area above z=-1.4 is approximately 1 - 0.0808 = 0.919, rounded to three decimal places.

(c) To find the area between z=1.1 and z=2.1 for an Upper N(0,1) density, follow these steps:

1. Locate the values of z=1.1 and z=2.1 in the table or use the calculator's function.
2. Find the corresponding area values for both z=1.1 and z=2.1.
3. Subtract the area value of z=1.1 from the area value of z=2.1 to find the area between them.

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

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Bentley needs to ride an average of 7.9 miles each day for the next 4 days to meet his goal of riding 39.6 miles in a week.

The equation to determine the average number of miles Bentley needs to ride each day is:

31.6/4 = x

Let x be the average number of miles Bentley must bike each day for the next four days in order to reach his objective. The total distance Bentley needs to ride is 39.6 miles, and he has already ridden 8 miles.

Therefore, he needs to ride an additional (39.6 - 8) = 31.6 miles in the remaining 4 days.

The equation to determine the average number of miles Bentley needs to ride each day is:

31.6/4 = x

Simplifying this equation, we get:

x = 7.9

Therefore, Bentley needs to ride an average of 7.9 miles each day for the next 4 days to meet his goal of riding 39.6 miles in a week.

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Answer:

2nd Bullet point / (B)

Step-by-step explanation:

divide by b on both sides

Answer:

  56.3 units

Step-by-step explanation:

You want the side opposite a 102° angle in a triangle with a side of length 27 opposite a 28° angle.

The law of sines tells you side lengths are proportional to the sine of the opposite angle.

  b/sin(102°) = 27/sin(28°)

  b = 27(sin(102°)/sin(28°)) ≈ 56.3

The length of side b is about 56.3 units.

__

Additional comment

The side labeled b is not the "hypotenuse" in this triangle. The term "hypotenuse" is reserved for the long side of a right triangle.

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Identify the equation: Write down the given equation in the form |x - a| = b, where 'a' represents the number being subtracted or added and 'b' represents the absolute value.

Graphing absolute value equations on a number line is a process that involves several steps. First, you need to identify the equation and rewrite it in the form |x - a| = b, where 'a' represents the number being subtracted or added and 'b' represents the absolute value.

This form helps determine the critical points of the graph. Next, you set the expression inside the absolute value bars equal to zero and solve for 'x' to find the critical points. These points indicate where the graph may change direction. Once the critical points are determined, you plot them on the number line, using an open circle for critical points and a closed circle for any additional points obtained by adding or subtracting the absolute value.

After plotting the points, you can draw the graph by connecting them with a solid line for the portion of the graph that is positive and a dashed line for the portion that is negative. This representation helps visualize the behavior of the absolute value equation on the number line.

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Answer:

The radius (r) of a soccer ball with a volume of 288 cm3 is 6 cm.

Answer:

-1 -1. Answer for X and Y if that's the case.

The predicted number of adults in Oak City whose main source of news is newspapers or the radio is 85

To predict the number of adults in Oak City whose main source of news is newspapers or the radio, we need to add the number of adults who answered "Newspapers" to the number of adults who answered "Radio".

According to the sample data

Number of adults who answered "Newspapers": 64

Number of adults who answered "Radio": 21

Therefore, the predicted number of adults in Oak City whose main source of news is newspapers or the radio we have to use the addition

64 + 21 = 85

Rounding this answer to the nearest whole number, we get

85 ≈ 85

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The given question is incomplete, the complete question is:

There are 44,000 adults living in Oak City. In examining attitudes toward the news, a research group asked a random sample of Oak City adults "What is your main source of news?" The results are shown below. Main Source of News Newspapers Number of Adults 64 Internet 80 Television 126 Radio 21 Other 40 Based on the sample, predict the number of adults in Oak City whose main source of news is newspapers or the radio. Round your answer to the nearest whole number.

Answer:

-1, -1, 1/2, and 2

Step-by-step explanation:

Sorry if I’m wrong

Alex has $15.78 and Rick has $12.15 money.

According to the question,

We have the following information:

Alex had $3.63 more than Rick. Together they had $27.93.

Let's take the money Rick has to be $x.

Now, we have the following expression for the money Alex has:

3.63+x

Now, we have:

x+3.63+x = 27.93

2x+3.63 = 27.93

Subtracting 3.63 from both the sides:

2x = 27.93-3.63

2x = 24.3

Dividing by 2 on both the sides:

x = 24.3/2

x = $12.15

So, Rick has $12.15.

Now, the money Alex has:

3.63+12.15

$15.78

Hence, Alex has $15.78 and Rick has $12.15 money.

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The value of \(\bar{\nabla} \cdot(\bar{\nabla} \phi)\) is \(e^z\cos y\).

The gradient is a vector operation that transforms a scalar function into a vector with a magnitude equal to the highest rate of change of the function at the gradient's point and a direction pointing in the same direction.

To find \(\bar{\nabla} \cdot(\bar{\nabla} \phi)\), we need to calculate the divergence of the gradient of the function ϕ.

The gradient of ϕ is given by:

\(\bar{\nabla} \phi\) = (∂x/∂ϕ​, ∂y/∂ϕ, ∂z/∂ϕ)

Let's calculate the partial derivatives of ϕ with respect to each variable:

\(\frac{\partial \phi}{\partial x}=e^{z}\sin y\)

\(\frac{\partial \phi}{\partial y}=xe^{z}\cos y\)

\(\frac{\partial \phi}{\partial z}=xe^{z}\sin y\)

Now, we can find the divergence of \(\bar{\nabla} \phi\) by taking the sum of the partial derivatives:

\(\bar{\nabla} \cdot(\bar{\nabla} \phi)\) =  \(\frac{\partial}{\partial x}(e^z\sin y)+\frac{\partial}{\partial y}(xe^z\cos y)+\frac{\partial}{\partial z}(xe^z\sin y)\)

Simplifying each partial derivative:

\(\bar{\nabla} \cdot(\bar{\nabla} \phi)\) = \(e^z\cos y\) + \((-xe^z\sin y)\) + \((xe^z\sin y)\)

Combining like terms, we find:

\(\bar{\nabla} \cdot(\bar{\nabla} \phi)\) = \(e^z\cos y\)

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The complete question is:

Given that \(\phi(x, y, z)=x e^{z} \sin y\) Find \(\bar{\nabla} \cdot(\bar{\nabla} \phi)\).

r = (sin theta + C)^(-1) where C is an arbitrary constant of integration.

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation. Assuming that a function's rate of change with regard to x is inversely proportional to y, we may write it down as dy/dx = k/y.

r = (cos(theta) - d/d(theta) of sec(theta)) / sec(theta)

The differential equation assists us in presenting a relationship between the changing quantity with respect to the change in another variable. The derivative represents nothing more than a rate of change. Be a function with the form: y=f(x), where x is an independent variable, f is an unknown function.

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here's the solution,

rumba got 250 marks !!

if she had got 30 more marks then she would had passed the exam,

So, passing marks :

=》250 + 30

=》 280 marks

now, passing percentage :

=》

\( \dfrac{passing \: \: marks}{total \: \: marks} \times 100\)

=》

\( \dfrac{280}{700} \times 100\)

=》

\( \dfrac{280}{7} \)

=》

\(40\)

Hence, the passing percentage is 40%

Answer:

-5   and   1

Step-by-step explanation:

Answer:

-5×1 = -5 so , -5 plus 1 = -4

Answer: 3 • (-10.50)

Step-by-step explanation:

it told me bc i got it wrong lol

The expression for total change in Anaya's account on Monday is \(-10.50\times 3\) or \(3\times (-10.50)\).

Important information:

Value of one entry is \(-\$10.50\).

It means, the change in account by one entry is \(-\$10.50\).

The value of three entries is the product of the value of one entry and 3.

\(-10.50\times 3\)

Therefore, the expression for total change in Anaya's account on Monday is \(-10.50\times 3\) or \(3\times (-10.50)\).

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Answer:

Regular polygon of 10 sides or 10-gon

Explanation:

The angle of rotation symmetry is equal to

θ = 360/n

Where n is the order of rotation. In a regular polygon, the order of rotation for symmetry is the number of sides.

In this case, we can replace θ by 36 degrees and solve the equation for n

36 = 360/n

n = 360/36

n = 10

Therefore, the shape of rotation should be a regular polygon of 10 sides.

Check the picture below, I'll be referring to the material in the picture.

we know the outer cube has a surface area of 24, we also know is a cube, so it has 6 equal sides which are squares each, let's say the side of one of those squares in the cube is say of length "s", so the area of one square will just be  s², and for 6 squares that'll be an area of 6s², that is the area of the outer cube, which we know is 24.

\(24=6s^2\implies \cfrac{24}{6}=s\implies 4=s^2\implies \sqrt{4}=s\implies 2=s\)

now, we know the sphere is inscribed in the outer cube, so it's touching its edges, like you see in the picture in blue, so if we get a cross-section of the whole lot, we'd get the picture to the right of blue cube in the picture, an outer cube with a side of 2, and therefore an sphere with a diameter of 2, and thus a radius of 1, as you can see in the red triangle.

Let's notice that the red triangle is a 45-45-90 triangle, and thus we can use the 45-45-90 rule to get its sides, as you can see in the picture on the far-right, which gives us half of one side of the inner cube to be 1/√2.

\(\stackrel{\textit{half a side}}{\cfrac{1}{\sqrt{2}}}\qquad \stackrel{\textit{a full side}}{\cfrac{1}{\sqrt{2}}+\cfrac{1}{\sqrt{2}}}\implies \cfrac{2}{\sqrt{2}}\implies \cfrac{2\sqrt{2}}{\sqrt{2}\sqrt{2}}\implies \cfrac{2\sqrt{2}}{2}\implies \sqrt{2}\)

now as you can see in the picture, the inner cube in orange, has 6 sides, each side is √2 long, so let's get the 6 squares area.

\(\stackrel{\textit{area of one square}}{\sqrt{2}\cdot \sqrt{2}\implies 2}\qquad \stackrel{\textit{area of all 6 sides of the inner cube}}{6\cdot 2\implies 12}\)

The required cycle-time is approximately 57.6 seconds.

To find the required cycle time, we need to divide the total available time by the number of units to be produced.

Total available time: 16 hours = 16 * 60 minutes = 960 minutes = 960 * 60 seconds = 57,600 seconds

Number of units to be produced: 1,000 units

Required cycle time: Total available time / Number of units

Cycle time = 57,600 seconds / 1,000 units

Cycle time ≈ 57.6 seconds

Therefore, the required cycle time is approximately 57.6 seconds.

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Answer: It is 6x+12

Step-by-step explanation: Distribute 2 to the parenthesis, then do the same at the second parenthesis, 10x+6-4x+6, combine like terms, 10x-4x and +6+6, so 6x+12 is the final result.

Answer:r=6cm :)

Step-by-step explanation:

V = pi r^2 h

720pi = pi r^2 20
720/pi = (pi r^2 20) / pi

720 = r^2 20

720/20 = r^2

36 = r^2

r = 6cm