Jessica wants to make a ramp using a board so that she can ride her bike onto the front porch. The ramp must reach from the ground to the floor of the porch, which is 212
ft above the ground. Jessica has decided that the ramp cannot have an incline of more than 35°.

What length board should Jessica buy if she uses the maximum angle of incline?

Enter your answer in the box. Round only your final answer to the nearest tenth

Answer:

V = 3 × 2 × 6 = 36 cubic centimeters

The angle of incline of the tram is 19.4 degree.

According to the question:

h=(10450-6311)ft

= 4139 ft

We know that, sinθ=Opposite/Hypotenuse

So, sinθ=h/12463

sinθ= 4139/12463

sinθ= 0.3321

Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.

θ=19.39

θ≈19.4°

Therefore, the angle of incline of the tram is 19.4 degree.

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The monthly payments and total cost of interest depend on the interest rate and the length of the loan. Generally, a lower interest rate or a shorter loan term results in lower total interest costs.

To calculate the monthly payments, we can use the formula for the present value of an annuity:

[tex]PV = P * (1 - (1 + r)^{-n}) / r[/tex]

where PV is the present value of the loan, P is the principal (the amount borrowed), r is the monthly interest rate, and n is the number of monthly payments.

(a) 30 years, 5%:

PV = 0.9 * $90,000 = $81,000 (since she puts 10% down)

r = 0.05 / 12 = 0.0125(monthly interest rate)

n = 30 * 12 = 360 (number of monthly payments)

Using the formula, we get:

PV = $81,000

Monthly payment = $436.82

Total cost of interest = $57,255.85

(b) 30 years, 5.12%:

r = 0.0512 / 12 = 0.00427 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $439.88

Total cost of interest = $59,956.19

(c) 30 years, 6%:

r = 0.06 / 12 = 0.005 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $485.24

Total cost of interest = $95,687.34

(d) 15 years, 3.78%:

n = 15 * 12 = 180 (number of monthly payments)

r = 0.0378 / 12 = 0.00315 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $591.93

Total cost of interest = $34,147.07

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Answer: 2.35619

Step-by-step explanation: Hope this helps! :)

A symbolic representation of the contrapositive is

letter D

Answer:

b

Step-by-step explanation:

The correct statement regarding the graph is given as follows:

C. The graph is non-proportional and has the equation y = -2x + 18.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The slope and the intercept of the line in this problem are given as follows:

Thus the equation is:

y = -2x + 18.

The equation is non-proportional, as it has an intercept which is different of zero.

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The value of x if the object is a square with a perimeter of 94 cm is 23.5 cm

From the question, we have the following parameters that can be used in our computation:

The permieter of object A is 94cm

Assuming the object is a square

So, we have

4x = 94

Divide both sides by 4

So, we have

x = 94/4

Evaluate

x = 23.5

Hence, the value of x is 23.5cm

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Compare the data by observing the shape, center, and spread of the data in both representations.

1. Understand the data: Before comparing two representations of data, it is important to understand what the data represents and its context.

2. Identify the type of data: Identify the type of data represented in each representation to ensure the data is comparable.

3. Plot the data: Plot the data in each representation, such as a line plot, box plot, or histogram.

4. Compare the data: Compare the data by looking at the shape, center, and spread of the data in both representations.

Example: To compare data in two-line plots, plot the data as two lines on the same graph. Observe the difference in the shape of the two lines, the difference in center (the average value of the data), and the difference in spread (the range of the data).

Example: To compare data displayed in a box plot, plot the data as two box plots side by side. Observe the difference in the shape of the two box plots, the difference in center (the median value of the data), and the difference in spread (the interquartile range of the data).

Example: To compare data displayed in histograms, plot the data as two histograms side by side. Observe the difference in the shape of the two histograms, the difference in center (the mean value of the data), and the difference in spread (the standard deviation of the data).

List the steps to create a back-to-back stem-and-leaf plot:

1. Organize the data: Organize the data into two sets of numerical data.

2. Create stems: Create a stem for each set of data by dividing the values by a common multiple.

3. Create leaves: Create leaves for each set of data by recording the remainder of the original values after dividing them by the common multiple.

4. Plot the data: Arrange the stems and leaves into a back-to-back stem-and-leaf plot.

5. Compare the data: Compare the data by observing the shape, center, and spread of the data in both representations.

Therefore, compare the data by observing the shape, center, and spread of the data in both representations.

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Answer:

25000

Step-by-step explanation:

The amount that Katherine, who is going to invest in an account paying an interest rate of 5.8% compounded monthly, would need to invest, to the nearest ten dollars for the future value of the account for the account to reach $960 in 26 years, is $380 (present value).

The future value is the present value compounded at an interest rate.

The present value is the future value discounted at an interest rate.

The future value and the present value can be computed using an online finance calculator.

N (# of periods) = 192 months (16 years x 12)

I/Y (Interest per year) = 5.8%

PMT (Periodic Payment) = $0

FV (Future Value) = $960

Results:

Present Value (PV) = $380.38

Total Interest = $579.62

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The intervals for which each function is decreasing are f(x) = [0, ∝) and g(x) = (-∝, ∝)

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

From the graph of the functions, we can see that

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The measure of the angles for the similar triangles are ∠G = 105°; ∠H = 55° and ∠I = 20°

Two triangles are said to be similar if the ration of their corresponding sides are in the same proportion. Also, all their corresponding angles are congruent with each other.

From the diagram shown:

∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)

20 + 105 + ∠Z = 180

∠Z = 55°

Since triangle XYZ and triangle GHI are similar, hence:

∠X = ∠G = 105°; ∠Z = ∠H = 55° and ∠Y = ∠I = 20°

The measure of the angles are ∠G = 105°; ∠H = 55° and ∠I = 20°

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The exact value of tan2θ in simplest radical form is  -21/√7.

The value of tan2θ at the given quadrant is calculated as follows;

From Pythagorean identity, we know that;

sin² θ + cos² θ = 1

cos² θ is calculated as follows;

(3/4)² + cos² θ = 1

9/16 + cos² θ = 1

cos² θ = 1 - 9/16

cos² θ = 7/16

cos θ = √(7/16)

The value of tan θ is calculated as follows;

tan θ = sin θ / cos θ = 3/4 x 4/√7 = 3/√7

Now, we will find tan 2θ;

tan 2θ = 2tan θ / (1 - tan² θ)

tan 2θ = 2(3/√7) / (1 - (3/√7)²)

tan 2θ = (6/√7) / (-2/7)

tan 2θ = -21/√7

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Conversion models can be used to express numbers of different bases to base-2 and base-5. To convert a number from base-10 to base-2, we use division-by-2, and for base-5, we divide by 5. To convert between bases, we convert to base-10 first and then to the desired base. for example 25 in binary is 11001, 45 in base-5 is 104, 89 to base-2 is 1011001.

In computer science and mathematics, binary (base-2) and quinary (base-5) numbering systems are commonly used to represent numbers. However, it is often necessary to express numbers in other bases as well. This is where conversion models come into play.

To convert a number from base-10 to base-2, we can use the division-by-2 method.

The process involves repeatedly dividing the decimal number by 2 and keeping track of the remainders until the quotient becomes 0. We then write the remainders in reverse order to get the binary representation of the number.

For example, to convert the number 25 to binary

25 / 2 = 12 R1

12 / 2 = 6 R0

6 / 2 = 3 R0

3 / 2 = 1 R1

1 / 2 = 0 R1

Therefore, 25 in binary is 11001.

To convert a number from base-10 to base-5, we can use a similar method. Instead of dividing by 2, we divide by 5 and keep track of the remainders. For example, to convert the number 45 to base-5

45 / 5 = 9 R0

9 / 5 = 1 R4

1 / 5 = 0 R1

Therefore, 45 in base-5 is 104.

We can also convert a number from base-2 to base-5 or vice versa. To convert a number from base-2 to base-5, we can first convert it to base-10 and then to base-5. For example, to convert the binary number 101110 to base-5

1*2⁵ + 0*2⁴ + 1*2³ + 1*2² + 1*2¹ + 0*2⁰ = 46

46 to base-5 is 141

To convert a number from base-5 to base-2, we can first convert it to base-10 and then to base-2. For example, to convert the quinary number 324 to base-2

3*5² + 2*5¹ + 4*5⁰ = 89

89 to base-2 is 1011001

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This prompt has to do with the analysis of random outcomes. See the attached tables and graphs accordingly.

An exhaustive depiction of all possible marble combinations that may arise out of a chance experiment involving two random selections has been depicted in this table.

The table enlists five different-colored marbles available in a bag and elaborates its varying conclusions based on two distinct selections.

The columns indicate colors, whereas each result depicts two correlated choices made during an experiment's progression to illustrate randomness accurately.

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An inequality to find the least number of bananas your character slipped on: -3x ≤ -27

And  the least amount of race time character took to slip on bananas = 18 seconds.

Let us assume that x represents the number of bananas your character slipped on.

Here, based on the informtaion we get an inequality to find the least number of bananas your character slipped on -3x ≤ -27

We solve this inequality to find  the least number of seconds of race time.

-3x ≤ -27

⇒ x ≥ 9

When the character slips, it takes 2 seconds for him to resume the race.

Therefore, the least amount of race time your character took to slip on bananas would be,

9 × 2 = 18 seconds

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The complete question is:

In an online game, you receive -3 points for every banana your character slips on during a race. The total points from slipping on bananas during one race were at most -27. When the character slips, it takes 2 seconds for him to resume the race. Write and solve an inequality to find the least number of bananas your character slipped on. At least how many seconds of race time

The number of days it would take for the investment to be valued at £3,800 is 4.4 days

From the question, we have the following parameters that can be used in our computation:

A = 1200 × 1.3^n

For the investment to be valued at £3,800, the value of A would be

A = 3800

Substitute the known values in the above equation, so, we have the following representation

1200 × 1.3^n = 3800

Divide both sides by 1200

1.3^n = 3800/1200

So, we have

n = ln(3800/1200)/ln(1.3)

Evaluate the quotient

n = 4.4

Hence, it would take 4.4 days

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Answer:

π(5^2)(8) + (1/2)(4/3)π(5^3)

= 200π + 250π/3 = 850π/3 cubic meters

= about 889.67 cubic meters

The value of the variable x;

1. x = -4, BC = 4x + 3 = -13

2. x = 72 degrees

3. x = 5/2, SV = 6.5, ZU = 6.4

4. x = 4

5. x = 5

6. x = 3

Tangent are simply described as any straight line that is drawn from the curve at a point but never reaches the center of the circle.

It is also important to note that tangent segments of a circle are equal.

From the information given, we have that;

1. The tangents are;

4x + 1 = 5x - 3

collect the like terms

-x = 4

x = -4

Then BC = 4x + 3 = -13

2. 2x - 1 = 143

collect the like terms

2x = 143 + 1

2x = 144

x = 72 degrees

3. 3x - 1 = 5x - 6

collect the like terms

-2x = -5

x = 5/2

Then,

SZ = ZU =  3(5/2) - 1 = 15/2 - 1 = 6.5

4. 5x² + 10 = x² + 74

collect the like terms

4x² = 64

x² = 16

x = 4

5. 2x + 7 = 5x - 8

collect the like terms

-3x = -15

divide the values

x = 5

6. 3x - 1.2 = 2x + 1.8

x = 3

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The opposite side of the right triangle is determined as 10.6 cm.

The value of x is calculated by applying trigonometry ratio as shown below;

we will use the short form; SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The hypotenuse side of the right triangle is given, and we are required to find the opposite side of the right triangle.

sin (62) = x/12

x = 12 sin (62)

x = 10.6 cm

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Answer:

Step-by-step explanation:

your supposed to learn things in class pay attetion

The surface area of each square pyramid, we used the formula Surface Area = Base Area + 4 x (1/2 x Base x Height of Face) is 1049.2, 1285.8 and 2100mm². The cost to cover each pyramid was $1.05, $1.29 and $2.10

To calculate the surface area of each pyramid, we need to use the formula

Surface Area = Base x Height of face + 2 x ((Base/2) x Slant Height)

For the small pyramid, we have

Surface Area = 20 x 25 + 2 x ((20/2) x 26.46)

Surface Area = 500 + 2 x 10 x 26.46

Surface Area = 1049.2 mm²

Cost to cover the small pyramid

Cost = Surface Area x 0.001

Cost = 1049.2 x 0.001

Cost = $1.05

For the medium pyramid, we have

Surface Area = 20 x 40 + 2 x ((20/2) x 42.43)

Surface Area = 800 + 2 x 10 x 42.43

Surface Area = 1285.8 mm²

Cost to cover the medium pyramid

Cost = Surface Area x 0.001

Cost = 1285.8 x 0.001

Cost = $1.29

For the large pyramid, we have

Surface Area = 30 x 40 + 2 x ((30/2) x 50)

Surface Area = 1200 + 2 x 15 x 50

Surface Area = 2100 mm²

Cost to cover the large pyramid

Cost = Surface Area x 0.001

Cost = 2100 x 0.001

Cost = $2.10

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[tex]-37 < -12v+1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ v=-11\hspace{5em}-37 < -12(-11)+1\implies -37 < 133 ~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=-9\hspace{5em}-37 < -12(-9)+1\implies -37 < 109~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=-5\hspace{5em}-37 < -12(-5)+1\implies -37 < 61~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=6\hspace{5em}-37 < -12(6)+1\implies -37 < -71 ~~ \bigotimes[/tex]

Answer: 84 in

Step-by-step explanation:

A = h(b)/2

h= 7

b= 24

24x7= 168

168/2= 84

The equation that could be used to find the distance that the tornado traveled is: log d = 0.7

We are told that The wind speed near the center of a tornado is represented by the equation S = 93 log d + 65,

where:

d is the distance, in miles, that the tornado travels.

S is the wind speed, in miles per hour.

When S = 130, we have:

130 = 93 log d + 65

93 log d = 130 - 65

93 log d = 65

log d = 65/93

log d = 0.7

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The limit as a definite integral is  given as   lim (n → ∞) Σ(8i²)/n³ = 8/3n³

The area under the curve f(x) from x= a to x  = b is represented by the definite integral of f(x  )

There are 2 kinds of    integrals

To express the limit as a definite integral, we can use the following formul

lim(n → ∞  ) Σf(i)/n = ∫  a^bf(x)dx

where....

a and b are the lower and upper limts of the definite integral

f (x) is the function being integrated

In this case, we have

lim(n → ∞) Σ(8i²)/n³

Let f  (x) = x ²

So, f(i/n) = (i/n) ²

And, the sum can be written as

Σ(8i^2)/n³ = 8/n³ Σi²

= 8/n³ Σ(i/n)²

= 8/n³ Σ[f(i/n)]

= 8/n³ ∫0¹ f(x) dx (using the formula above)

Therefore, the limit can be   expressed as

lim(n → ∞) Σ(8i²)/n³ = 8/n³ ∫0¹ x² dx

Simplifying the integral, we get....

8/n³  ∫0¹ x₂ dx = 8/n^3 [x³/3] from 0 to 1

= 8/3n ³

Se we can say here that  the limit as a definite integral is lim(n → ∞) Σ(8i ₂)/n^3 = 8/3n ₃

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The graph of the function f(x) = 4(2/3)^x is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x)=4⋅(

2

3

​)

x

Express the equation properly

So, we have

f(x) = 4(2/3)^x

The above expression is a an equation of a exponential function

Next, we plot the graph using a graphing tool

To plot the graph, we enter the equation in a graphing tool and attach the display

See attachment for the graph of the function

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If Mark  used 12.4 lbs to make a sculpture, and 0.75 lbs for each mug then the number of mugs he can make is 57.

Mark bought 55 lbs of clay for his art projects

He used 12.4 lbs to make a sculpture

The left over clay is 55-12.4 = 42.6

We know that 0.75 lbs for each mug

We have to find the number of mugs he can make from left over clay

To find this we have to divide 42.6 by 0.75

Number of mugs = 42.6/0.75

=56.8

=57

Hence, if Mark  used 12.4 lbs to make a sculpture, and 0.75 lbs for each mug then the number of mugs he can make is 57.

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