From the top of a 72 m high vertical cliff,
a boat has an angle of depression of 32
degrees. How far is the boat from the
base of the cliff? Round your answer to
the nearest whole number.

Answer:

To find the account balance after 5 years, we need to calculate the compound interest earned during this period. The formula for compound interest is:

A = P × (1 + r/n)^(nt)

where:

A = the final amount of the investment

P = the principal investment amount ($1000)

r = the annual interest rate (7.2%)

n = the number of times that interest is compounded per year (1)

t = the number of years the investment is held (5)

So, plugging in the values into the formula, we get:

A = 1000 * (1 + 0.072/1)^(1 * 5)

A = 1000 * (1.072)^5

A = 1000 * 1.44444444

A = $1444.44

So, the account balance after 5 years would be $1444.44.

Answer:

Step-by-step explanation: I could mostly say $36,000. How I did it was:

1000x7.2x5=36,000

Could you find this helpful???

Answer:

NPV = -$57,937

Step-by-step explanation:

NPV = ($1.50 - $1.80) * 256,000 - $206,000 - $51,000 + $15,450 / (1 + 0.15)^10 - ($206,000 + $51,000) * 0.35

Answer: Matt completes his homework faster than Jill by 14 minutes

Step-by-step explanation:

5*12= 60 so if I multiply 3 by 12 I get how many minutes it took Matt to finish her homework. (which was 36 minutes)

6*10=60 so if I multiply 5 by 10 I get how many minutes it took Jill to finish her homework (which was 50 minutes)

50 minus 36 is a difference of 14

Note that the angle labeled ∠PQR is given as 70°

First, note that the Lengths of tangents drawn from external points to a circle are equal in length. This means that:

Length of PT = Lenght of TR

This makes Δ TPR and Isosceles Triangle.

This also makes ∠P = ∠R..............................1

Thus:

∠P + ∠R + ∠T = 180°

Given expression 1 above,

we can say:

x + x + 38° = 180°

Thatis 2x = 180 - 40

2x = 140°

x = 140/2

x = 70°

Note that Line TP is parallel to Line QR and Line PQ is a transversal line. Thus, ∠P and ∠Q are co-interior angles. This means that:

∠P + ∠Q = 180°

Recall that:

70 + 40 + ∠Q = 180°
∠Q = 180 -70 -40

∠Q = 70°

Thus: ∠ PQR = 70°

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Full Question:

See attached image.

The minimum = (-11, -2)

And the maximum = (2, 5).

Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.

Given:

The function,

f(x) = ∛(x + 3).

The graph of the function is given in the attached image.

f'(x) = d/dx{∛(x + 3)}

     = 1/{3(x + 3[tex])^{2/3}[/tex]}

The critical point = (-3, 0)

The minimum = (-11, -2)

And the maximum = (2, 5).

Therefore, all the required values are given above.

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We can write radicals  [tex]9^{\frac{3}{2}[/tex] as [tex](3^2)^{\frac{3}{2}[/tex] forms to help us communicate our answers.

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Suppose, We have a radical [tex]16^{\frac{1}{4}[/tex].

Now, We know 2⁴ = 16.

So, We can rewrite [tex]16^{\frac{1}{4}[/tex] as [tex](2^4)^{\frac{1}{4}[/tex] and multiply the exponents which

results to 1.

Again say we have [tex]9^{\frac{3}{2}[/tex] and we know 3² = 9, Se we can rewrite [tex]9^{\frac{3}{2}[/tex] as [tex](3^2)^{\frac{3}{2}[/tex] , and the exponent multiplies to 3 so it is now 3³ which is 27.

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Answer:

Step-by-step explanation:

The monthly compound interest formula.

Future Value = monthly deposit x (1 + r) - 1/r

r = .07/12 = .00583

n = total number of time for compound = 35 years x 12 months/1 year = 420 months

PMT = monthly deposit = $200

Future Value = $200 x (1 + .00583)⁴²⁰ - 1/.00583

Future Value = $394,001.64 in 35 years

Total money you put into the account.

$200 x 420 months = $84,000

Total interest earned.

$394,001.64 - $84,000 = $310,001.64

Answer:

f(x) = 2[tex](\frac{1}{2}) ^{x}[/tex]

Step-by-step explanation:

The y intercept is 2 where in the parent function it is 1.  In the parent function, as x is increasing y is increasing.  In this function as the x is increasing the y is decreasing.

The number of square centimeters of icing that would be needed for one cake is equal to: C. 1,755 cm².

Since everything but the circular bottom of the cake was iced, the number of square centimeters of icing that would be needed for one cake can be calculated by using this mathematical expression:

Total surface area of cake = Curved surface area of cake + area of the top

Total surface area of cake = 2πrh + πr²

Where:

By substituting the given parameters into the total surface area of cake formula, we have;

Total surface area of cake = (2 × 3.14 × 13 × 15) + (3.14 × 13²)

Total surface area of cake = 1224.6 + 530.66

Total surface area of cake = 1755.26 ≈ 1755 square centimeter.

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Answer: C. 1,755 cm2

Hope this helps

The given function

g(x)  = [x² - 3x -10][x²+ 2x² -5x +4  ]

is continuous at  x = -1,

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  =  [x² - 3x -10][x²+ 2x² -5x +4  ]

To check whether it is continuous at x = -2

First taking LHL,

[tex]\lim_{h \to \00}[/tex]  [(-1-h)² - 3(-1-h) -10][(-1-h)²+ 2(-1-h)² -5(-1-h) +4  ]

[tex]\lim_{h \to \00}[/tex]  [(-1-0)² - 3(-1-0) -10][(-1-0)²+ 2(-1-0)² -5(-1-0) +4  ]

⇒   -6 x 12

⇒     -72

Now, taking RHL

[tex]\lim_{h \to \00}[/tex]  [(-1+h)² - 3(-1+h) -10][(-1+h)²+ 2(-1+h)² -5(-1+h) +4  ]

[tex]\lim_{h \to \00}[/tex]  [(-1+0)² - 3(-1+0) -10][(-1+0)²+ 2(-1+0)² -5(-1+0) +4  ]

⇒   -6 x 12

⇒     -72

The value at x = -1

F(-1)  =  [(-1)² - 3(-1) -10][(-1)²+ 2(-1)² -5(-1) +4  ]

⇒ -6 x 12

⇒   -72

RHL = LHL =  F(-1)

Hence Proved,  the function is continuous at x = -1

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The mass of the sample after 4 days is 1.54 kg.

Exponential decay can be defined as the process in which a quantity decreases over time with the rate of decrease becoming proportionally smaller as the quantity gets smaller.

The formula for exponential decay is given by:

m(t) = m0 * e^(-kt)

where m(t) is the mass of the substance after time t

M0 is the initial mass

k is the decay rate parameter

E is the base of natural logarithms

Plugging in the values:

m(4) = 2.05 * e^(-0.04 * 4)

m(4) = 1.54 kg

Therefore, The mass of the sample after 4 days is 1.54 kg.

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1) X2 + 6x + 3 = 0. is resolved using the discriminant technique, and the value of s for the second equation, 52 + 2s - 6 = 0, is 9.5.

The statistic is said to be in its simplest form is divided into its smallest equivalent fraction. What to do to find the most basic form. Look for common factors in the denominator and numerators. Confirm a fractional integer to verify if it qualifies as a prime number. A statement having two equal sides and an equaled sign in the middle is called an equation in mathematics. The general form of any equation contains the diplomas of all the variables in descending order. The conventional form of an equation is an x + b = 0. The general form of a linear function with two variables is an x + b y + c = 0. (or something similar). An identification holds true no matter what value is given to the variables.

given

equation 1 ) X2 +6x +3=0

by discriminant method

x =(6+√48)/2

=3+2√ 3

= 6.464.

equation 2) 5^2 + 2s - 6 = 0

= 25 + 2s - 6 = 0

= 19 = - 2s

s = 9.5

1) X2 + 6x + 3 = 0. is resolved using the discriminant technique, and the value of s for the second equation, 52 + 2s - 6 = 0, is 9.5.

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The relationship between x and y is y = (1/2)x. When x is 2, then the value of 'y' is 1.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

If x and y are in direct proportion. Then the equation is given as,

y ∝ = x

y = kx

At x = 12 and y = 6, then the value of 'k' is given as,

6 = 12k

k = 1/2

Then the equation is given as,

y = (1/2)x

If the value of the variable 'x' is 2. Then the value of y is given as,

y = (1/2) 2

y = 1

The relationship between x and y is y = (1/2)x. When x is 2, then the value of 'y' is 1.

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Kevin's solution is incorrect because he used wrong formula.

Correct area of triangle = 20 square inches.

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height,

i.e. A = 1/2 × b × h

Given,

Height of triangle h = 8 inches

Base of the triangle b = 5 inches

Formula for area of triangle A = 1/2(b h)

A = 1/2 (8 × 5)

A = 40/2

A = 20 square inches.

Area by given formula for area of the triangle A = b h

A = 8 × 5

A = 40

Since actual area of the triangle is 20 square inch, Kevin found the area with wrong formula.

Actual area of triangle is 20 square inches.

Hence, Kevin's solution is incorrect, as the formula used is wrong.

20 square inches is correct area of the triangle.

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Answer: Let's call the number of hamburgers sold "x". Then the number of cheeseburgers sold would be x + 53. The total number of hamburgers and cheeseburgers sold is 553, so we can set up the equation:

x + (x + 53) = 553

Expanding the left side:

2x + 53 = 553

Subtracting 53 from both sides:

2x = 500

Finally, dividing both sides by 2:

x = 250

So on Wednesday, 250 hamburgers were sold.

Step-by-step explanation:

Refer to the given image

well, the line y = -5 is simply a horizontal line, a perpendicular line to that will simply be a vertical one, Check the picture below.

We can conclude, the number -7/5 is less than the number 1 1/5.

One of the ways to know how a fraction compares to another is by simplifying the fraction, which can be done by dividing the numerator by the denominator.

Let's simplify the fractions given:

-7/5 = -1.4

-1 1/5 = 1 + 0.2 = -1.2

Moreover, in the case of negative numbers those that are closer to 0 are greater. Based on this, -1.2 is greater than -1.4, which means -7/5 is less than the number 1 1/5.

Note: This question is incomplete; here is the missing section:

The number -7/5 is less or greater than the number 1 1/5.

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The solution of the system of equations -6x -12= (1/2)x -4 include the following: D. x = -4 and x = -2.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-axis, which is given by  x = -4 and x = -2.

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Step-by-step explanation:

x = number of children

y = number of adults

x + y = 364

x = 364 - y

1.75x + 2.25y = 707.5

using the first equation in the second :

1.75(364 - y) + 2.25y = 707.5

637 - 1.75y + 2.25y = 707.5

637 + 0.5y = 707.5

0.5y = 70.5

y = 70.5/0.5 = 141

x = 364 - y = 364 - 141 = 223

there were 223 children at the public pool.

there were 141 adults at the public pool.

the answer is -13. And this is why, because the negative sign is bigger so same sign add keep the same sign that’s why I got -13

the simplified Answer to the given expression 36 x 5 +59 x(234)(51) will be 7,04,286.

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

Given, an expression 36 x 5 +59 x(234)(51)

Simplifying using PEMDAS

=> 36 x 5 +59 x(234)(51)

First, we will open a bracket

=> 36 * 5 + 59 * 11934

Now multiple of the given terms:

=> 180 + 704106

Addition of the last two-term

=> 7,04,286

Therefore, the simplified Answer to the given expression will be 7,04,286.

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The measure of angle D, m∠D, found using the specified lengths of the three sides of the triangle and the law of cosines is; m∠D = 75.7°

The law of cosines specifies the relationship between the measures of an angle, and the lengths of the three sides of a triangle. Specifically, the law of cosines states that the square of the length of a (reference) side of a triangle, is equivalent to the sum of the squares of the lengths of the other two sides, less the product of 2, the lengths of the other two sides and the cosine of the angle opposite to the reference side.

Mathematically, the law of cosines can be presented as follows;

Where;

a, b, and c are the lengths of the three sides of the triangle

Angle A, ∠A, is the opposite angle to side a.

Therefore, according to the law of cosines, we get;

38² = 36² + 24² - 2 × 36 × 24 × cos(∠D)

2 × 36 × 24 × cos(∠D) = 36² + 24² - 38² = 428

2 × 36 × 24 × cos(∠D) = 428

cos(∠D) = 428/(2 × 36 × 24) = 428/1728 = 107/432

cos(∠D) = 107/432

m∠D = arccos(107/432) ≈ 75.7°

The measure of angle D, m∠D ≈ 75.7°

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The likelihood of getting the loan cannot be ascertained. Hence the answer is D. There is not enough information given to determine the answer.

To determine whether Jared is likely to be approved for the home loan, it would be necessary to calculate his debt-to-income ratio, which is one of the main factors that lenders consider when evaluating loan applications. This ratio is calculated by dividing a person's total recurring monthly debt payments by their gross monthly income. If the debt-to-income ratio is higher than 28% or 36% (depending on the lender), the loan application may be declined.

Based on the information provided, it is not possible to determine Jared's debt-to-income ratio. In order to determine the ratio, it would be necessary to know Jared's gross monthly income, which is not provided. Therefore, it is not possible to say whether Jared is very likely, somewhat likely, or not likely to be approved for the home loan.

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Rounding to the nearest hundredth of a meter, the height of the goalpost is 3.74 meters.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Let's call the height of the goalpost "h". We can use similar triangles to solve for h. Morgan walks a total of 13.85 and placed the mirror and walk 4.25 more, let d = 13.85.

The mirror forms a right triangle with the height of the goalpost, the distance from her eyes to the ground, and the distance d.

So, we have:

h / d = 1.15 / 4.25

Solving for h:

h = (1.15 ×13.85 ) / 4.25

h = 6371 / 1700

Rounding to the nearest hundredth of a meter, the height of the goalpost is 3.74 meters.

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