Robert uses f(x)=1000(1. 0375)^x to calculate the interest he earns each year for his savings account. What is the annual rate as a percent?

Let's represent the width of the rectangular course as $w$. Then the length of the rectangular course can be represented as $2w$, since the ratio of the length to the width is given as 2:1.

We know that the total length of the course is 2.4 kilometers, so we can write an equation:

$\sf\implies\:2w + 2(2w) = 2.4$

Simplifying the equation:

$\sf\implies\:6w = 2.4$

$\sf\implies\:w = \frac{2.4}{6}$

$\bigstar\implies\sf{\textbf{\boxed{w = 0.4}}}$

Therefore, the width of the course is 0.4 kilometers.

The length of the course is $\sf\:2w = 2(0.4)=$

${\boxed{\sf{0.8 kilometers.}}}$

Hence, the length of the course is 0.8 kilometers and the width of the course is 0.4 kilometers.

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[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]

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The area of the triangle is approximately 31.3049 square inches.

The area of a triangle can be found using the formula: A = (1/2)bh, where b is the length of the base of the triangle, and h is the height (or perpendicular distance from the base to the opposite vertex).

However, in this case, we don't have the height. Instead, we can use

Heron's formula, which only requires the lengths of the three sides of the triangle:

A = √[s(s-a)(s-b)(s-c)],

where a, b, and c are the lengths of the sides of the triangle, and s is the semiperimeter (half the perimeter):  s = (a + b + c)/2.

Using the given values, we have:

s = (7 + 9 + 12)/2 = 14

A = √[14(14-7)(14-9)(14-12)]

A = √[14(7)(5)(2)]

A = √(980)

A ≈ 31.3049 square inches

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The equation y=1/2x can be graphed using either number graph or the slope-intercept form. In either case, the result is a straight line that passes through the same points.

In mathematics, a graph is a visual representation of a mathematical relationship. The equation y=1/2x ​is a linear equation, which means that it describes a straight line. This equation can be graphed using the number graph.

To graph the equation y=1/2x, one must first plot points on the graph. To do this, one can use the given equation to calculate the x and y values of the points. For example, if x is equal to 1, then y is equal to 1/2. Therefore, the point (1, 1/2) can be plotted on the graph. This process can be repeated for other values of x, such as 2, 3, and 4. The result is a straight line that passes through the points (1, 1/2), (2, 1), (3, 1 1/2), and (4,2).

The equation y=1/2x can also be graphed using the slope-intercept form of the equation. This form of the equation is written as y=mx + b, where m is the slope of the line and b is the y-intercept. For the equation y=1/2x, the slope is 1/2 and the y-intercept is 0. To graph the line, one must first plot the y-intercept, which is the point (0,0). Then, one must calculate the slope and draw a line through (0,0) in the direction of the slope. The result is a straight line that passes through the points (0, 0), (1, 1/2), (2,1), (3, 1 1/2), and (4, 2).

In conclusion, the equation y=1/2x can be graphed using either number graph or the slope-intercept form. In either case, the result is a straight line that passes through the same points.

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The slope-intercept form or a number graph can both be used to visualise the equation y=1/2x. The outcome is a straight line that goes through the same spots in both scenarios.

A graph in mathematics is a picture of a mathematical connection. A linear equation is one that describes a straight line, such as y=1/2x. The number graph can be used to graph this equation.

The graph must first have points drawn on it before the equation y=1/2x can be graphed. To do this, one can compute the x and y values of the points using the above equation. For instance, y is equal to 1/2 if x is equal to 1. As a result, the graph's point (1, 1/2) can be drawn. You can repeat this procedure for x values of 2, 3, and 4. Consequently, a straight line that traverses the coordinates (1, 1/2), (2, 1), (3, 1 1/2),and (4,2).

The slope-intercept form of the equation can also be used to graph the equation y=1/2x. Y=mx + b, where m is the line's slope and b is its y-intercept, is how this form of the equation is expressed. The slope and y-intercept of the equation y=1/2x are 1/2 and 0, respectively.

Plotting the y-intercept, or the point, is required before the line can be graphed. (0,0). The next step is to determine the slope and draw a line through (0,0) in the slope's direction. A straight line is created as a result, passing through the points (0, 0), (1, 1/2), (2, 1), (3, 1 1/2), and (4, 2).

In conclusion, the slope-intercept form or a number graph can both be used to graph the equation y=1/2x. The outcome is a straight line that goes through the same spots in both scenarios.

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You should always measure your following distance in seconds. The correct answer for measuring following distance is A.  

It is important to keep a safe distance between vehicles on the road, which is known as following distance. Measuring following distance in seconds is a more reliable method than measuring it in car lengths or feet.

The recommended following distance is typically two to three seconds. This means that when the vehicle in front of you passes a fixed point on the road, you should not reach that same point before two to three seconds have elapsed.

Measuring in seconds is more effective as it takes into account the speed at which both vehicles are traveling. If you measure in car lengths or feet, it may not be accurate as the length of the cars may differ, and it does not account for the speed of the vehicles. By measuring in seconds, you can maintain a safe distance and reduce the risk of accidents or collisions.

The correct answer for measuring following distance is A.  

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Complete question is:

You should always measure your following distance in __________

A. seconds. B. car lengths. C. feet.

Answer:

Angle 1 is 77

Angle 2 is 103

Angle 4 is 103

Step-by-step explanation:

Angles that are vertical to each other like 2 and 4, 1 and 3

will always equal each other

since 3 is = to 77, 1 is also = to 77

You can also find the angles by thinking of supplementary angles (180 degrees) Straight angle basically

You see that 3 is 77 and 4 is part of the straight line so it needs to equal 180

so 180-77 it will equal 103.

Hope this helps

The original price of the novel is $21.5

The first step is to write out the parameters given in the question

Last year, Gloria buys a novel for $18.70

This price is with a discount of 15% form the original price

The original price of the novel can be calculated as follows

15/100 × 18.70

= 0.15 × 18.70

= 2.805

The next step is to add 2.805 to the price of the novel last year($18.70)

= 18.70 + 2.805

= 21.5

Hence the original price of the novel before the addition of the discount is $21.5

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Answer:

55 degrees

Step-by-step explanation:

sin Φ = cos 35

sin Φ = .81915

Φ = arc sin (.81915) = 55 degrees

Or you could just know that the cos of an angle is equal to the sin of its comeplement

Answer:

The missing point of this parallelogram is (6, 5).

Original percentage: 100%

Percentage off: 25%

Percentage left over: 75%

Complete the number sentence to show how to find the sale price of the bunch of flowers:

Sale price = (100% - 25%) x $32 = 75% x $32 = $24

It takes approximately 10 hours for the drug concentration to decrease.

We can use exponential decay to model the concentration of the drug in the bloodstream. Let C(t) be the concentration of the drug in milligrams at time t in hours since the person took the drug. Then we have:

[tex]C(t) = 125(0.7)^t[/tex]

where 0.7 is the factor by which the concentration decreases each hour.

We want to find the time t such that C(t) = 1. Substituting this into the equation above, we get:

[tex]1 = 125(0.7)^t[/tex]

Dividing both sides by 125, we get:

[tex]0.008 = (0.7)^t[/tex]

Taking the logarithm of both sides with base 0.7, we get:

[tex]t = log(0.008) / log(0.7)[/tex]

Using a calculator, we can evaluate this expression to get:

t ≈ 10.07

Therefore, it will take approximately 10.07 hours for the concentration of the drug in the bloodstream to be 1 milligram.

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Normal Distribution: Finding Values

Press the "2nd" key, then press the "vars" key to access the DISTR menu.

Scroll down to "Normalcdf" and press enter.

Enter the lower bound, upper bound, mean, and standard deviation. For example, if you want to find the probability that X is between 60 and 70, given that the mean is 65 and the standard deviation is 5, you would enter "60, 70, 65, 5".

Press enter to get the result. The calculator will give you the probability that X falls between the two values you entered.

Press the "2nd" key, then press the "vars" key to access the DISTR menu.

Scroll down to "InvNorm" and press enter.

Enter the probability you want to find. For example, if you want to find the z-score that corresponds to the 90th percentile, you would enter "0.9".

Enter the mean and standard deviation. For example, if the mean is 65 and the standard deviation is 5, you would enter "65, 5".

Press enter to get the result. The calculator will give you the z-score that corresponds to the probability you entered.

Sampling Distributions and the Central Limit Theorem: Press the "2nd" key, then press the "vars" key to access the DISTR menu.

Scroll down to "1-PropZTest" or "2-PropZTest" and press enter, depending on the type of test you want to perform.

Enter the sample statistics and the population parameters, if known. The calculator will use these values to calculate the test statistic and p-value.

Press enter to get the result. The calculator will give you the test statistic and the p-value, which you can use to make inferences about the population.

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The length of the minor arc GD is approximately 0.196π units.

To get the length of the minor arc GD, we need to subtract the measure of the major arc mDUG from the circumference of the circle, and then divide by 360° to find the length of one degree of arc.
First, we need to find the circumference of the circle. Since GA = 29, we know that the radius of the circle is also 29. The formula for the circumference of a circle is C = 2πr, so for this circle we have: C = 2π(29) = 58π
Next, we need to subtract the measure of the major arc mDUG from the circumference of the circle. Since mDUG = 185°, we have:
58π - (185/360)(58π) = (175/360)(58π)
Simplifying this expression, we get: (175/360)(58π) = 29(175/72)π ≈ 70.48π
Finally, we divide this value by 360° to find the length of one degree of arc:
(70.48π)/360 ≈ 0.196π
Therefore, the length of the minor arc GD is approximately 0.196π units.

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The equation of the tangent plane to the surface at the point (u,v) = (3,U) is z = x + 34 + U.

To calculate TT, we need to find the partial derivatives of O(u,v) with respect to u and v:

TT = (∂O/∂u) x (∂O/∂v)
  = (2, 0, 8) x (0, 0, 1)
  = (-8, 0, 0)

To find n(u,v), we normalize TT:

n(u,v) = TT/|TT|
      = (-1, 0, 0)

At the point u=3, v=U, O(u,v) = (2u + 0.0 - 40, 8u) = (-34, 24).

To find the equation of the tangent plane, we first find the normal vector to the plane, which is n(u,v) = (-1, 0, 0). Then we use the point-normal form of the equation of a plane:

(-1)(x + 34) + 0(y - 24) + 0(z - U) = 0
-x - 34 + z - U = 0
z = x + 34 + U

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It should be noted that m⁸m⁻⁶ is equivalent to (m²)¹, which is equal to m².

Using the product of powers rule for exponents, we can simplify m⁸m as follows:

m⁸m⁻⁶ = m⁸⁻⁶) = m²

Therefore, m⁸⁻⁶ is equal to m².

Now, we can further simplify by expressing m² as (m²)¹. Multiplying the exponents, we get:

(m²)¹ = m²

We can say that m⁸m⁻⁶ is equivalent to (m²)¹, which is equal to m².

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The total surface area of a cylinder is the sum of the areas of its top and bottom circles, along with the area of its lateral surface (the curved surface that connects the two circles).

The formula for the lateral surface area of a cylinder is:

Lateral surface area = 2πrh

where r is the radius of the cylinder, h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14.

The formula for the area of a circle is:

Area of circle = πr^2

Using these formulas, we can calculate the total surface area of the cylinder as follows:

Area of top and bottom circles = 2 × π × r^2

= 2 × 3.14 × 2^2

= 25.12 square feet

Lateral surface area = 2 × π × r × h

= 2 × 3.14 × 2 × 6

= 75.36 square feet

Total surface area = Area of top and bottom circles + Lateral surface area

= 25.12 + 75.36

= 100.48 square feet

Therefore, the total surface area of the cylinder is 100.48 square feet.

Answer:

i think the answer is 96

Step-by-step explanation:

Answer:

c=4

Step-by-step explanation:

as there is only one solution for this quadratic equation which is supposedly have 2 or more answers, c can only be 4 in order to be the same equation as the the first one x-4=0

Prepare adjusting journal entries, close the book, open a new set of books for the partnership, record the contributions of both partners, and prepare the balance sheet of the partnership.

Adjusting Journal Entries:

Debit Interest Receivable: (calculate accrued interest amount based on notes receivable and interest rate)

Credit Interest Revenue: (same amount as above)

Debit Interest Expense: (calculate accrued interest amount based on notes payable and interest rate)

Credit Interest Payable: (same amount as above)

Debit Furniture and Fixtures: 1,000

Credit Accumulated Depreciation - Furniture and Fixtures: 1,000

N. Lustre's Contribution:

Debit Cash: (amount contributed by N. Lustre)

Debit Delivery Truck: 20,000

Credit N. Lustre's Capital: (total contributed amount)

J. Reid's Capital:

Credit J. Reid's Capital: 62,200

Balance Sheet of the Partnership:

Include the capital balances of N. Lustre and J. Reid

List the current assets, fixed assets, current liabilities, and long-term liabilities of the partnership

Calculate the total assets, total liabilities, and partners' equity

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a. The volume of the funnel is 167.6 in³.

b. The amount in quarts of oil are there in the funnel is approximately 2.9 quarts.

a. To find the volume of a cone, you can use the formula V = (1/3)πr²h, where r is the radius and h is the height. Substituting in the values given, we get V = (1/3)π(4 in)²(10 in) ≈ 167.6 in³. Rounded to the nearest tenth, the volume of the funnel is 167.6 in³.

b. To convert cubic inches to quarts, we need to divide by the conversion factor of 58 in³/qt. So, V = 167.6 in³ ÷ 58 in³/qt ≈ 2.9 qt. Rounded to the nearest tenth, there are approximately 2.9 quarts of oil in the funnel.

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We know that the measure of AB is 240°.

Given that AC is a diameter of D and MBDC = 150°, we know that angle ABC is a right angle (90°) because it is inscribed in a semicircle.

Using the fact that the sum of angles in a triangle is 180°, we can find angle MBC:

MBC + 150° + 90° = 180°
MBC  = -60°

Since angle MBC is negative, we know that it must actually be 360° - 60° = 300°.

Finally, using the fact that angles on a straight line add up to 180°, we can find angle ABM:

ABM + MBC = 180°
ABM + 300° = 180°
ABM = -120°

Again, since angle ABM  is negative, we know that it must actually be 360° - 120° = 240°.

Therefore, the measure of AB is 240°.

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The original number was 17 to which when Angad adds 20, then doubles it and gets an answer of 53.

To solve this problem, we need to work backwards from the final answer. If Angad added 20 to the original number, we can subtract 20 from 53 to get 33. This means that after Angad doubled the number, he had 33.

To find the original number, we need to undo the doubling process. If Angad had 33 after doubling the number, we can divide 33 by 2 to get the original number.

33 divided by 2 equals 16.5. However, we know that the original number must be a whole number since we cannot add 20 to a decimal. Therefore, we can round up to the nearest whole number to get 17.

So, the original number was 17.

In summary, to find the original number, we worked backwards from the final answer and undid the steps that Angad took. We subtracted 20 to undo the addition, then divided by 2 to undo the doubling. We rounded up to the nearest whole number since the original number must be a whole number.

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The road with alternating white and black stripes and each 50 cm wide is 7.5 m wide.

The road consists of alternating white and black stripes

No. of white stripes = 8

As the first and last stripe is white so in between the black stripes will be 7

No. of black stripes = 7

Total no. of stripes = 15

Width of black stripe = 50 cm

Width of white stripe = 50 cm

Width of whole road = total no. of stripes × width of each stripe

Width of whole road = 15 × 50

Width of whole road = 750 cm

To convert m into cm

Now, 1 m = 100 cm

1 cm = 1/100 m

750 cm = 750/100 m

750 cm = 7.5 m

Hence the width of the road is 7.5 m

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The third term in the sequence has a value of 1.

Here, we have,

Sequence

Given:

f(3) = 1

Let f(x) b a function.

Here x is replaced by "3", f(3) represents the value of the 3rd term of the function, which is 1.  

In this case f(3) = 1 means the value of a  member of the sequence when x = 3 is 1.

For example, if the sequence is the values of x^2-8  from 1 to infinity, then f(1) would have a value 1-8 = -7 and f(3)  would be 9- 8 = 1

The third term in the sequence has a value of 1.

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The height of the Key West Lighthouse in meters is approximately 26.21 meters.

Here's how you can calculate it:

- There are 3.28 feet in a meter.

- Divide the height of the lighthouse in feet by the number of feet in a meter: 86 ÷ 3.28 = 26.21 meters (rounded to two decimal places).

- Therefore, the height of the Key West Lighthouse in meters is approximately 26.21 meters.

_________________________________

_________________________________

Answer:

Sure. Here is the equation for the cost, C, after h hours of babysitting:

```

C = 3 + 5h

```

This equation can be found by combining the flat fee of $3 with the hourly rate of $5. For example, if Nicole babysits for 2 hours, she will make $3 + (2 * $5) = $13.

To find how much Nicole will make after babysitting for 8 hours, we can simply substitute h = 8 into the equation. This gives us:

```

C = 3 + 5(8) = 3 + 40 = $43

```

Therefore, Nicole will make $43 after babysitting for 8 hours.

Answer:c= 3 + 5(8)

Step-by-step explanation:

3 is flat fee, and then plus $5 and hour. you know she's going for 8 hours, so you multiply hourly rate by the number of hours plus flat fee and you get your answer

Answer:

Step-by-the answer is (a) 16

The value of integral ∫(x^2+10x-9)e^-4x dx is  (-1/4)(x^2+10x-9)e^-4x - (1/8)(x+5)e^-4x - (1/32)e^-4x + C.

To evaluate the integral ∫(x^2+10x-9)e^-4x dx using integration by parts, we need to choose two functions to multiply together, one of which we differentiate and the other we integrate. A common choice is to let u = x^2+10x-9 and dv = e^-4x dx, which gives du = (2x+10) dx and v = (-1/4)e^-4x.

Using the formula for integration by parts, we have:

∫(x^2+10x-9)e^-4x dx = uv - ∫v du

= (-1/4)(x^2+10x-9)e^-4x - ∫(-1/4)(2x+10)e^-4x dx

= (-1/4)(x^2+10x-9)e^-4x + (1/2)∫(x+5)e^-4x dx.

Now we can use integration by substitution to evaluate the second integral on the right-hand side:

(1/2)∫(x+5)e^-4x dx = (-1/8)(x+5)e^-4x - (1/32)e^-4x + C,

where C is the constant of integration.

Substituting this back into our previous equation, we get:

∫(x^2+10x-9)e^-4x dx = (-1/4)(x^2+10x-9)e^-4x - (1/8)(x+5)e^-4x - (1/32)e^-4x + C.

Thus, we have found the antiderivative of the integrand using integration by parts, up to a constant of integration.

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Complete question is:

Use integration by parts to evaluate the integral: ∫(x^2+ 10x – 9)e ^-4x dx

For a purchase of a new desktop computer for $1250, loan description that would result in the smallest amount of interest she would have to pay is 12 months at 6. 25% annual simple interest rate. Therefore, the correct option is option 1.

To determine which loan description results in the smallest amount of interest for Roxie, we'll calculate the interest for each option using the simple interest formula:

Interest = Principal × Rate × Time.

1. 12 months at 6.25% annual simple interest rate:

Interest = $1250 × 6.25% × (12/12)

Interest = $1250 × 0.0625 × 1

Interest = $78.13

2. 18 months at 6.75% annual simple interest rate:

Interest = $1250 × 6.75% × (18/12)

Interest = $1250 × 0.0675 × 1.5

Interest = $126.56

3. 24 months at 6.5% annual simple interest rate:

Interest = $1250 × 6.5% × (24/12)

Interest = $1250 × 0.065 × 2

Interest = $162.50

4. 30 months at 6.00% annual simple interest rate:

Interest = $1250 × 6.00% × (30/12)

Interest = $1250 × 0.06 × 2.5

Interest = $187.50

Comparing the interest amounts, the smallest interest is for the first option, 12 months at 6.25% annual simple interest rate, with an interest amount of $78.13.

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The equation oe: y + 1 = -4/6(x + 5) represents a line perpendicular to line m.

The equation of line m is given as y + 2 = (3/2)(x + 4). To determine the equations that represent lines perpendicular to line m, we need to find the negative reciprocal of the slope of line m and use it as the slope in the perpendicular lines.

The slope of line m is (3/2), so the negative reciprocal is -2/3. We can eliminate options oa, oб, and of because they do not have a slope of -2/3.

Now, let's check the remaining options:

oc: y = (2/3)x + 4

This equation has a slope of 2/3, which is not the negative reciprocal of -2/3. Therefore, it is not perpendicular to line m.

od: y = (3/2)x + 4

This equation has the same slope as line m, which means it is not perpendicular to line m.

oe: y + 1 = (-4/6)(x + 5)

Simplifying the equation, we get y + 1 = (-2/3)(x + 5), which has a slope of -2/3. Therefore, this equation represents a line that is perpendicular to line m.

Therefore, the equation oe: y + 1 = -4/6(x + 5) represents a line perpendicular to line m.

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