Michael is building a fence around his garden to keep the rabbits out. The perimeter of his garden is 42 feet. If the length of the garden is 5 more than the width, what are the dimensions of the fence? Hint: draw a rectangle, and label all 4 sides for the length and width, given what you know this is the last question on my test please help me

If firm issues​ commercial paper with $1000000 face-value and pays EAR of​ 7.4%, then amount the firm will receive is $981500.

To calculate the amount the firm receives from issuing the three-month commercial paper, we need to determine the total interest earned over the three-month period.

The Effective Annual Rate (EAR) of 7.4% indicates the annualized interest rate. Since the commercial paper has 3-month term, we adjust the EAR to account for the shorter period.

To find the quarterly interest rate, we divide the EAR by the number of compounding periods in a year. In this case, since it is a 3-month period, there are 4-compounding periods in a year (quarterly compounding).

Quarterly interest rate = (EAR)/(number of compounding periods)

= 7.4%/4

= 1.85%,

Now, we calculate interest earned on "face-value" of $1,000,000 over 3-months,

Interest earned = (face value) × (quarterly interest rate)

= $1,000,000 × 1.85% = $18,500,

So, amount firm receives from issuing 3-month commercial paper is the face value minus the interest earned:

Amount received = (face value) - (interest earned)

= $1,000,000 - $18,500

= $981,500.

Therefore, the amount that firms receives is $981500.

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Answer:

erm

Step-by-step explanation:

The sides will be:

6cm

6cm

4cm

Answer:

In isosceles triangle two sides are equal . Let the length be x .hence perimeter can be given as x + x + 6 . Therefore 2x + 6 = 16 . And 2x = 10 .and hence x =5 . So the length of each side is 5 cm

Step-by-step explanation:

Answer:

-1116

Step-by-step explanation:

The expression is simplified to give 2(9x + 2√3x - 5)

First, we need to know that surds are mathematical forms that can no longer be simplified to smaller forms

From the information given, we have that;

(2√3x - 2)(3√3x + 5)

expand the bracket, we get;

6√9x² + 5(2√3x) - 6√3x - 10

Find the square root factor

6(3x)  + 10√3x - 6√3x - 10

collect the like terms, we have;

18x + 4√3x - 10

Factorize the expression, we have;

2(9x + 2√3x - 5)

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The  Maclaurin series for f(x) is f(x) = 7 - 14x + 14\(x^2\) - 28/3 \(x^3\) + ...

a. To find the Maclaurin series for the function f(x) = 7e(-2x), we can use the formula for the Maclaurin series:

f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x3/3! + ...

where f(n)(0) is the nth derivative of f(x) evaluated at x = 0.

First, we can find the derivatives of f(x):

f(x) = 7e(-2x)

f'(x) = -14e(-2x)

f''(x) = 28e(-2x)

f'''(x) = -56e(-2x)

Then, we can evaluate these derivatives at x = 0:

f(0) = 7\(e^0\) = 7

f'(0) = -14\(e^0\) = -14

f''(0) = 28\(e^0\) = 28

f'''(0) = -56\(e^0\) = -56

Using these values, we can write the Maclaurin series for f(x) as:

f(x) = 7 - 14x + 14\(x^2\) - 28/3 \(x^3\) + ...

b. We can write the power series using summation notation as:

∑[infinity]n=0 (-1)n (7(2x)n)/(n!)

c. To determine the interval of convergence of the series, we can use the ratio test:

The series converges if this limit is less than 1, and diverges if it is greater than 1.

Since this limit approaches 0 as n approaches infinity, the series converges for all values of x.

Therefore, the interval of convergence is (-∞, ∞).

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a. The Maclaurin series for the function f(x) = 7e^-2x can be found by using the formula:

f^(n)(0) / n! * x^n

where f^(n)(0) represents the nth derivative of f(x) evaluated at x=0.

Using this formula, we can find the first four nonzero terms of the Maclaurin series:

f(0) = 7e^0 = 7
f'(0) = -14e^0 = -14
f''(0) = 28e^0 = 28
f'''(0) = -56e^0 = -56

So the first four nonzero terms of the Maclaurin series for 7e^-2x are:

7 - 14x + 28x^2/2! - 56x^3/3!

b. The power series using summation notation is:

Σ[n=0 to infinity] (7(-2x)^n / n!)

c. To determine the interval of convergence, we can use the ratio test:

lim[n->infinity] |a(n+1) / a(n)| = |-14x / (n+1)|

Since this limit approaches zero as n approaches infinity, the series converges for all values of x. Therefore, the interval of convergence is (-infinity, infinity).

a. To find the first four nonzero terms of the Maclaurin series for the given function 7e^(-2x), we need to find the derivatives and evaluate them at x=0:

f(x) = 7e^(-2x)
f'(x) = -14e^(-2x)
f''(x) = 28e^(-2x)
f'''(x) = -56e^(-2x)

Now, evaluate these derivatives at x=0:

f(0) = 7
f'(0) = -14
f''(0) = 28
f'''(0) = -56

The first four nonzero terms are: 7 - 14x + (28/2!)x^2 - (56/3!)x^3

b. To write the power series using summation notation, we use the Maclaurin series formula:

f(x) = Σ [f^(n)(0) / n!] x^n, where the sum is from n=0 to infinity.

For our function, the power series is:

f(x) = Σ [(-2)^n * (7n) / n!] x^n, from n=0 to infinity.

c. Since the given function is an exponential function (7e^(-2x)), its Maclaurin series converges for all real numbers x. Thus, the interval of convergence is (-∞, +∞).

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Answer:

1. A triangle weighs more than a square.

2. A triangle could weigh more than a circle.

3. A triangle cannot possibly weigh more than 4 squares and a circle.

Answer:

x=-13/2=-6 1/2

Step-by-step explanation:

13 3/4 +x-7 1/4=

6 2/4+x

x= -6 1/2

Answer:

x=-13/2=-6 1/2

Step-by-step explanation:

If the length on the scale model car is 17 cm and the scale is 2 cm colon 50 centimeters the length of a car  is 425 cm

To find the length of the actual car, we can use the given scale ratio. The scale ratio is 2 centimeters colon 50 centimeters, which means that for every 2 centimeters on the scale model car,

it represents 50 centimeters on the actual car.
We can set up a proportion to solve for the length of the actual car.

Let's call the length of the actual car "x". The length on the scale model car is given as 17 centimeters.
Using the proportion, we have:
2 cm / 50 cm = 17 cm / x
To solve for x, we cross-multiply:
2 cm × x = 50 cm × 17 cm
2x = 850 cm
Divide both sides by 2 to isolate x:
x =  850/ 2

x = 425 cm
Therefore, the length of the actual car is 425 centimeters.

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Based on the given scale and the length of the scale model car, the length of the actual car is 425 centimeters. The scale model car is 17 centimeters long, and the scale is 2 centimeters colon 50 centimeters.

To find the length of the actual car, we can set up a proportion.

Let's label the length of the actual car as "x".

Using the scale, we can write the proportion:

    2 cm (scale model car) / 50 cm (actual car) = 17 cm (scale model car) / x cm (actual car)

To solve for x, we can cross multiply:

    2 cm * x cm = 50 cm * 17 cm

=> 2x = 850 cm

Dividing both sides of the equation by 2:

    x = 425 cm

Therefore, the length of the actual car is 425 centimeters.

In conclusion, based on the given scale and the length of the scale model car, the length of the actual car is 425 centimeters.

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We have been given that a company manufactures mountain bikes. The research department produced the marginal cost function C′(x)=300−3x​, 0≤x≤900, where C′(x) is in dollars and x is the number of bikes produced per month.

We need to compute the increase in cost going from a production level of 600 bikes per month to 720 bikes per month.Let the cost of producing x bikes be C(x), then by definition,

C(x) = ∫[0, x] C'(t) dt

Given C'(x) = 300 - 3x, we can compute C(x) by integrating

C'(x).C(x) = ∫[0, x] C'(t) dtC(x)

= ∫[0, x] (300 - 3t) dtC(x)

= [300t - (3/2)t²]

evaluated from 0 to xC(x)

= 300x - (3/2)x²

Also, we can find out the cost of producing 600 bikes,720 bikes, respectively as shown below.

Cost of producing 600 bikes per month,

C(600) = 300(600) - (3/2)(600)²C(600)

= 180000 dollars

Cost of producing 720 bikes per month,

C(720) = 300(720) - (3/2)(720)²C(720)

= 205200 dollars

Therefore, the increase in cost going from a production level of 600 bikes per month to 720 bikes per month is

C(720) - C(600)

= 205200 - 180000C(720) - C(600)

= 25200 dollars.

Hence, the required answer is 25200 dollars.

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Answer:

\((4 \times 25) - (7 \times 5) - 6 = 100 - 41 = 59\)

Answer:

59

Step-by-step explanation:

Can give me brainliest????

The graph shows the relationship between the number of students who attend a homecoming dance and the amount of money raised. The graph is a straight line with a slope of $10, passing through the point (0, $80) and another point on the line. The fixed cost for decorations is $80, which is a constant cost that does not depend on the number of students attending the dance. For each additional student that attends the dance, the amount of money raised will increase by $10.

Answer:

y = 10x - 80

Therefore your answer is B, hope this helps! :)

Answer:

\( \sf 9,802 \frac{1}{3} \)

Step-by-step explanation:

\( \sf = \frac{588,140}{60} \)

\( \sf = \frac{58,814}{6} \)

\( \sf = 9,802 \frac{2}{6} \)

\( \sf = 9,802 \frac{1}{3} \)

The sides of the triangle are: opposite = 7 adjacent = 24 hypotenuse =25. The correct option is A and B.

To determine which of the given trigonometric equations is not correct, we first need to label the sides of the triangle with respect to the angle x. Using the Pythagorean theorem, we can find the length of the missing side as follows:
a^2 + b^2 = c^2
24^2 + 7^2 = 25^2
576 + 49 = 625
√625 = 25

Therefore, the sides of the triangle are:
opposite = 7
adjacent = 24
hypotenuse = 25

Now we can evaluate each of the given trigonometric equations:
A. sinx = opposite/hypotenuse = 7/25
B. cosy = adjacent/hypotenuse = 24/25
C. tanx = opposite/adjacent = 7/24
D. Not Here

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Answer: S and T.

Step-by-step explanation:

I watched a video on how to do this just to answer, so it might not be right LOL. But since the angles are the same if you draw them from each other they both show the angles are equal which means the lines are parallel.

Answer:

Pretty sure it's B, the second one from the top

Answer:

Soda tax — Should people have to pay an extra tax on soda or junk food?

Your conversation should include the following:

A total of at least five entries for each side (10 entries total—two to three sentences each)

Accurate facts used to support both perspectives

At least two properly cited sources used for research

Step-by-step explanation:

Preconditions for Binary Search Tree is a valid binary search tree and Postconditions are Operations maintain tree validity. Insertion increases size, deletion decreases size. Search returns element or indication. Minimum/maximum return respective values.

The preconditions and postconditions for some common operations of an ADT (Abstract Data Type) Binary Search Tree. Preconditions and Postconditions for Binary Search Tree Operations are

Insertion

Preconditions:

The tree is a valid binary search tree.

Postconditions:

The tree remains a valid binary search tree.

The element to be inserted is added to the tree.

The size of the tree is incremented by 1.

Deletion

Preconditions:

The tree is a valid binary search tree.

The element to be deleted is present in the tree.

Postconditions:

The tree remains a valid binary search tree.

The element to be deleted is removed from the tree.

The size of the tree is decremented by 1.

Search

Preconditions:

The tree is a valid binary search tree.

Postconditions:

The tree remains unchanged.

If the searched element is found, it is returned along with its location (node).

If the searched element is not found, an appropriate indication (such as null or false) is returned.

Minimum

Preconditions:

The tree is a valid binary search tree.

Postconditions:

The tree remains unchanged.

The minimum element (smallest value) in the tree is returned.

Maximum

Preconditions:

The tree is a valid binary search tree.

Postconditions:

The tree remains unchanged.

The maximum element (largest value) in the tree is returned.

Traversal (In-order, Pre-order, Post-order)

Preconditions:

The tree is a valid binary search tree.

Postconditions:

The tree remains unchanged.

The nodes of the tree are visited and processed in the specified order.

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Answer:

Lima bean

Step-by-step explanation:

It sounds weird but a cell is actually the size of a lima bean

The height of the tower is approximately 28.510 feet, rounded to 3 decimal places."

we can use trigonometry. Let's call the height of the tower "h" and the distance from the first point to the tower "x". Then, we can set up two right triangles: Triangle 1: Opposite side = h, Adjacent side = x, Angle = 37º.

Triangle 2:
Opposite side = h
Adjacent side = x - 15
Angle = 42º

Using the tangent function, we can write:
tan(37º) = h/x
tan(42º) = h/(x-15)

We can solve these equations for h:
h = x * tan(37º)
h = (x-15) * tan(42º)

Setting the two equations equal to each other, we get:
x * tan(37º) = (x-15) * tan(42º)

Simplifying, we get:
x = 15 / (tan(42º) - tan(37º))

Now that we have x, we can use either of the original equations to find h:
h = x * tan(37º) = (15 / (tan(42º) - tan(37º))) * tan(37º).

Evaluating this expression on a calculator, we get:
h ≈ 67.819 feet, So the height of the tower is approximately 67.819 feet, rounded to 3 decimal places.To find the height of the tower,

we can use the tangent function in right triangles. Let's denote the height of the tower as h and the initial distance from the tower as x.

From the first point, we have:
tan(37º) = h / x

From the second point, which is 15 feet closer:
tan(42º) = h / (x - 15)

We have two equations and two unknowns (h and x). To solve for h, we can first find x:
h = x * tan(37º) and h = (x - 15) * tan(42º)

Setting the two equations equal to each other:
x * tan(37º) = (x - 15) * tan(42º)

Now, solve for x:

x = (15 * tan(42º)) / (tan(42º) - tan(37º))

Plug the angles into your calculator and solve for x:
x ≈ 38.384

Now, use the value of x in either equation to find the height h:
h = 38.384 * tan(37º)

h ≈ 28.510 feet , So, the height of the tower is approximately 28.510 feet, rounded to 3 decimal places.

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Answer:

  no

Step-by-step explanation:

In terms of area per hour, Bob's works at the rate of ...

  1460 ft²/(4 h) = 365 ft²/h

Rhonda's rate is ...

  753 ft²/(1.5 h) = 502 ft²/h

The rates are different, so they are not proportional.

___

Additional comment

Toni's rate is 803 ft²/(2.2 h) = 365 ft²/h . . . the same as Bob's

Bob's and Toni's rates are proportional.

Using the Newton's law of cooling, the time it takes to cool to 100°F is 116 mins.

According to the Newton's law of cooling, the when an object is exposed to the surrounding it looses heat rapidly untill it is at a thermal equilibrium with the suurroundings.

Now;

T(t) = T(s) + (To - Ts)e^-kt

T(t) = temperature at time T

To = initial temperature

Ts = temperature of the surrounding

k = colling constant

t = time taken

200 = 68 + (230 - 68)e^-15k

200 = 68 + 162e^-15k

200 - 68/162 = e^-15k

ln(0.815) = -15k

k = ln(0.815)/-15

k = 0.014 min-1

Now;

100 = 68 + (230 - 68)e^-( 0.014t)

100 -68/162 = e^-( 0.014t)

0.198 =e^-( 0.014t)

ln(0.198) = -( 0.014t)

t = ln(0.198)/-0.014

t = 116 mins

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Answer:

\( \sqrt{ \frac{9}{2} } \)

Answer:

\(x = \sqrt{70} \)

Step-by-step explanation:

Please see the attached pictures for the full solution.

Answer:i thing the anwser is 56

Step-by-step explanation:

Hey does this help you by any chance

The four corners of a square are 90 degrees.

They are evenly split by the diagonal lines, so each corner is now two 45 degree angles.

The lines form triangles, which have 3 angles that need to equal 180 degrees.

Two of the angles are 45, so 45 + 45 = 90 degrees.

X = 180 -90 = 90 degrees.

Answer:

90 degrees

By 90 * 4 is 360

Step-by-step explanation:

The given function is

The expression f(-16) means we have to evaluate the function when x = -16.

Answer:

3

Step-by-step explanation:

B. Stacy states that a plane has two dimensions because it is made up of an infinite number of lines is the correct answer

Answer:

the inflation rate was 4.7% it is acceptable

Step-by-step explanation:

The Federal reserve has not established a formal inflation target

Option A is the correct solution for this question. 5% was the inflation rate in 2021.

This is an acceptable inflation rate so option A which is Yes is the correct solution.

Whether a 5% inflation rate is considered acceptable or not depends on various factors such as the economic conditions of a country, the target inflation rate set by the central bank, and the expectations of consumers and businesses.

In some cases, a 5% inflation rate may be considered acceptable or even desirable if it is part of a deliberate government policy to stimulate economic growth or if it is a result of temporary supply-side shocks. However, in other cases, a 5% inflation rate may be seen as a sign of an overheating economy or a lack of monetary policy control.

In general, most central banks aim to keep inflation rates within a range of 2-3%, although there can be variations depending on the specific circumstances.

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sorry i cant help im not there yet im not that high a grade yet