Given a right triangle with = 60° and the hypotenuse equal to 25 feet, which trigonometric
function would you use to solve for the opposite side?

cosine
secant
sine
tangent

The formula for the future value of an annuity is FV = Pmt * (((1 + r)n - 1) / r) to calculate the balance of the IRA at age 65. To compare this amount to the total deposits made over the time period, Total Deposits = Pmt * n = $45,600.

To calculate the balance of the IRA at age 65, we need to use the formula for the future value of an annuity:

FV = Pmt * (([tex](1 + r)^n[/tex] - 1) / r)

Where:

Pmt = $95 (the monthly deposit amount)

r = 4% / 12 = 0.003333 (the monthly interest rate)

n = (65 - 25) * 12 = 480 (the total number of months, assuming retirement at age 65)

Plugging in these values, we get:

FV = 95 * (([tex](1 + 0.003333)^480[/tex] - 1) / 0.003333)

FV = $98,052.52

Therefore, the IRA will contain $98,052.52 at age 65.

Part 2

To compare this amount to the total deposits made over the time period, we can calculate the total deposits as:

Total Deposits = Pmt * n

Plugging in the values, we get:

Total Deposits = 95 * 480

Total Deposits = $45,600

Therefore, the IRA will contain significantly more than the total deposits made over the time period, due to the power of compounding interest.

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Answer:

26° 180 -81 - 73 = 26

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

triangle= 180

81 + 73 = 154

180 - 154= 26

The tοtal price οf the game including tax is $29.96.

Physical assets such as prοperty and transactiοns such as the sale οf stοck οr a hοme are subject tο taxatiοn. Taxes include incοme, cοrpοrate, capital gains, prοperty, inheritance, and sales taxes.

Because the tax rate is 7%, the tax amοunt is 7% οf the purchase price. Tο calculate the tax, multiply the purchase price by the tax rate expressed as a decimal:

0.07 x $28 = $1.96 in taxes

As a result, the purchase tax is $1.96.

Tο calculate the tοtal price, add the purchase price and the tax:

Purchase price + Tax = Tοtal Price

Tοtal cοst: $28 + $1.96 = $29.96

As a result, the tοtal cοst οf the game, including tax, is $29.96.

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The principle of mathematical induction is a method of proof used in mathematics to prove that a statement is true for all natural numbers.

It is based on the idea that if the statement is true for one number, then it can be used to prove that it is true for the next number. Mathematical induction can be expressed mathematically as follows:

Let P(n) be a statement involving an integer n

Base Case: P(m) is true for some m

Induction Hypothesis: Assume P(k) is true for some k>m.

Induction Step: Show that P(k+1) is true.

Therefore, P(n) is true for all n>m

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The corresponding point on the graph is (9, 21). This point is within the normal respiratory rate region, which is defined by the system of linear inequalities. Therefore, model breakdown has not occurred.

The given problem involves the normal respiratory rates of children aged 3 to 15 years. The respiratory rate, measured in breaths per minute, is represented as a function of age using a system of linear inequalities. The graph depicts a normal respiratory rate region that models the respiratory rate ranges shown in the table. The problem requires us to identify a specific point on the graph that corresponds to a respiratory rate of 21 breaths per minute for a 9-year-old child. The ordered pair (9, 21) represents the corresponding point on the graph.

Further, we need to determine if this point lies within the normal respiratory rate region or if model breakdown has occurred. The system of linear inequalities defines the normal respiratory rate region, and we can determine if the point (9, 21) satisfies these inequalities. In this case, the point (9, 21) lies within the normal respiratory rate region and satisfies the system of linear inequalities. Therefore, model breakdown has not occurred, and the given model is an appropriate approximation of the normal respiratory rate region for children aged 3 to 15.

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Answer:

44 students

Step-by-step explanation:

1200 for the first year

a third of that is 400

400 for the second year

a third of that is 133.4

133.4 for the third year

a third of that is 44

the fraction of the class that are boys is 4/9. And the fraction of the class that are girls is 5/9.

What is ratio?

A ratio is a comparison of two or more quantities that are related in some way. It expresses the relationship between these quantities in terms of the number of times one quantity contains another. Ratios are usually expressed as a fraction, where the numerator represents the first quantity and the denominator represents the second quantity. For example, the ratio of boys to girls in a class of 40 students may be expressed as 2:3 or 2/3, meaning there are 2 boys for every 3 girls. Ratios can also be expressed in other forms, such as percentages or decimals. Ratios are commonly used in mathematics, science, engineering, and everyday life to compare quantities and make predictions or decisions.

A fraction is a number that represents a part of a whole or a ratio of two quantities. It consists of two numbers, a numerator and a denominator, separated by a line. The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole or in the comparison. Fractions are used in many areas, such as mathematics, science, engineering, cooking, and everyday life. They can be added, subtracted, multiplied, and divided, and can be converted to decimals or percentages.

a) The total ratio of boys to girls in the class is 4+5 = 9. Therefore, the fraction of the class that are boys is 4/9.

b) The question is unclear as it seems to be asking for the same answer as in part (a). If you meant to ask for the fraction of the class that are girls, you can use the same approach: the fraction of the class that are girls is 5/9.

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Answer:

-2cotxcscx

Step-by-step explanation:

Step 1: Find a common denominator

Step 2: Simplify

Answer:

To determine which statements are true, we can use the standard form of the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius.

Using this form, we can rewrite the given equation as:

(x - 1)^2 + y^2 = 3^2 + 1^2 = 10

Comparing this to the standard form, we can see that the center of the circle is (1, 0), so the statement "The center of the circle lies on the x-axis" is true. However, the statement "The center of the circle lies on the y-axis" is false.

To find the radius, we can rearrange the equation as follows:

x^2 - 2x + y^2 = 8

Completing the square for x, we get:

(x - 1)^2 + y^2 = 9

This shows that the radius of the circle is 3, so the statement "The radius of the circle is 3 units" is true, as well as the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."

Therefore, the three true statements are:

1.The radius of the circle is 3 units.

2.The center of the circle lies on the x-axis.

3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Step-by-step explanation:

hope its help <:

There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Each classroom has 6 rows of 5 desks.

So the total number of desks in one classroom.

= 6 rows x 5 desks per row

= 30 desks

To find the total number of desks in 45 classrooms, we can multiply the number of desks in one classroom by the number of classrooms.

= 30 desks per classroom x 45 classrooms

= 1,350 desks

Therefore,

There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.

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Answer:

2n + 14 = 30

Step-by-step explanation:

Since you know that 2n + 14 = 30, we can determine the values by first subtracting 14 from 30. Our equation would then be 2n = 16. Divide 2 from both sides and n = 8.

This model represents the total on the top and the 2 parts on the bottom.

The lumpsum amount invested in 18 years ago for the given value Future value and interest is = Rs 2763,18.3268

What about lumpsum?

In mathematics, a lump sum refers to a single, fixed amount of money or quantity of something that is paid or received all at once, rather than being paid or received in installments or over a period of time.

The term "lump sum" can be used in various mathematical contexts, such as in finance, where it can refer to a single payment or investment, or in statistics, where it can refer to a single value or data point.

Define future value:

In mathematics, future value (FV) refers to the value of an investment or cash flow at a specified date in the future, assuming a certain rate of return.

The future value of an investment is the amount of money that an investor would expect to have at a specified date in the future if they were to invest a certain amount of money today, and if that investment earns a certain rate of return over time.

⇒ The formula for calculating the future value of an investment is:

[tex]FV = PV x (1 + r)^n[/tex]

According to the given information:

Interest Rate = 5%

Time Period =  18 years

Future Value = Rs 6649,93.

Using the concept of TVM calculation we have that,

Present value = [tex]\frac{Future Value}{(1+r)^{t} }[/tex]

So, the Present Value = [tex]\frac{664993}{(1+0.05)^{18} } = 2763,18.3268[/tex]

Hence, the Lumpsum Amount is Rs 2763,18.3268

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Answer:

Experimental Procedure:

Materials:

Piece of wood

Electronic balance

Bunsen burner

Heat-resistant mat

Stopwatch or timer

Safety goggles

Lab coat

Safety Precautions:

Wear safety goggles and a lab coat to protect your eyes and clothing from any sparks or flames.

Place the heat-resistant mat under the Bunsen burner to prevent any accidental fires.

Use the Bunsen burner only under adult supervision.

Be cautious when handling hot objects, and allow them to cool before touching.

Procedure:

Measure the initial mass of the piece of wood using an electronic balance, and record it in a table.

Light the Bunsen burner, and place the piece of wood over the flame using tongs. Ensure that the wood is fully engulfed in the flame.

Use a stopwatch or timer to time how long the wood burns for (in this case, 15 minutes).

After 15 minutes, turn off the Bunsen burner and remove the piece of wood from the flame using tongs.

Allow the wood to cool, and then measure its final mass using the electronic balance, and record it in the table.

Calculate the difference between the initial and final mass of the wood, and record it in the table.

Repeat steps 1-6 three times to obtain three sets of data.

Calculate the average mass of the burned wood and compare it to the initial mass of the unburned wood to determine if the student's prediction was correct.

Conclusion:

If the average mass of the burned wood is less than the initial mass of the unburned wood, the student's prediction was correct, and he can conclude that the wood underwent a chemical change when it was burned. If the average mass is greater than or equal to the initial mass, the prediction was incorrect, and the student may need to revise his hypothesis or experimental design.

Answer: The building is approximately 16.6 feet tall.

Step-by-step explanation:

Use Pythagorean theorem (a²+b²=c²) to solve this.

We know that the ladder is 26 feet long so that would be our hypotenuse (c²). and the distance between the ladder and the building is 20 feet. So, this is the base. The remaining side is x.

Your equation would be: 20²+x²=26²

subtract 20² from 26² --> 276=x²

then take the square root --> 16.6=x

The total distance that the water tanker has covered in March of 2022 is given as follows:

1860 kilometers.

Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

The parameters for this problem are given as follows:

Hence the total distance is then obtained as follows:

d = v x t

d = 60 x 31

d = 1860 kilometers.

The complete question is:

"Assuming that the water tanker travels an average of 60 kilometers a day, calculate the total distance that the water tanker has covered in March 2022​".

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The type of transformation represented in the figure is the translation transformation i.e. (c) none of these

Given the triangles ABC and A'B'C'

The transformation between the triangles is translation

The translation transformation is a type of transformation that moves an object without changing its size, shape, or orientation.

This transformation involves sliding an object in a particular direction by a certain distance, either horizontally or vertically.

In this case, the direction is horizontally and vertically

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Answer:

The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.

In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:

The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.

The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.

The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.

Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).

Answer:

We can rewrite the function as:

f(x) = 3(8√3)^(2x) = 3(2^3√3)^(2x)

Using the properties of exponents, we can rewrite this as:

f(x) = 3(2^(3*2x)√3^(2x)) = 3(2^(6x)√(3^(2x)))

Therefore, the base of the exponent is 2.

The correct answer is B. Symmetric property.

The symmetric property states that if a = b, then b = a. In the context of geometry, this property can be used to show that if one side of a figure is congruent to another side, then the second side is also congruent to the first. In the case of the given proof, it is possible that the symmetry of the figure is used to show that opposite sides of the rhombus are congruent.

The reflective property (A) is not typically used to prove that a figure is a rhombus, as it relates to the reflection of a figure across a line. The transitive property (C) and the addition property (D) are also unlikely to be used in this context, as they relate to the properties of equality and addition, respectively, rather than geometric properties of figures.

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a) The expected (mean) number of shots that Zlatan Ibrahimović must make to score a goal is 3.11.

b) The standard deviation of the distribution is 2.46.

The expected number or mean (μ) of a distribution is computed as sum resulting from the multiplication of each value of the random variable by its probability and adding the products.

The formula for the mean is given as E(x) = ∑x P(x).

On the other hand, to compute the standard deviation (σ) of a probability distribution, we find each deviation from its expected value, square it, multiply it by its probability, add the products, and take the square root.

No. of shots    Probability    Expected        Squared      Squared Deviation

                       of scoring    No. of shots     Deviation     x Probability

0                         0.02               0                   9.6721            0.193442

1                          0.13                0.13               8.8804           1.154452

2                         0.34               0.68              5.9049          2.007666

3                         0.32               0.96              4.6225          1.4792

4                         0.16                0.64              6.1009          0.976144

5                         0.02               0.1                9.0601            0.181202

6                         0.01               0.6                6.3001            0.063001

The expected (mean)

 number of shots =                3.11                                     6.055107

Standard Deviation = Square root of 6.055107 = 2.46

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Answer:

     6.75 inches.

Step-by-step explanation:

[tex]183.69 = 2*3.14*3^2 + 2*3.14*3*h[/tex]

[tex]= 56.52 + 18.84h[/tex]

[tex]183.69 - 56.52 = 18.84h[/tex]

[tex]127.17 = 18.84h[/tex]

[tex]=\frac{127.17}{18.84}[/tex]

[tex]=6.75[/tex]

The volume of the cone is  2119. 5 cubic centimeters

The formula used for calculating the volume of a cone is expressed as;

V = πr² h/3

Given that the parameters are namely;

Now, substitute the values, we have;

Volume , V = 3.14 × 15² × 9/3

Divide the values, we have;

Volume = 3.14 × 225 × 3

Multiply the values, we get;

Volume, V = 2119. 5 cubic centimeters

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Answer:

I got 28

Step-by-step explanation:

use the formula k=y/x. 6/8=0.75

21/0.75=

Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

in our case

length = width + 3

and

2×length + 2×width = 30

using the first equation in the second :

2×(width + 3) + 2×width = 30

width + 3 + width = 15

2×width + 3 = 15

2×width = 12

width = 12/2 = 6 ft

length = width + 3 = 6 + 3 = 9 ft

Answer:

Step-by-step explanation:

adjacent:   [tex]\angle BOC, \angle EOD[/tex]   (both are adjacent)

complementary:  [tex]\angle BOC[/tex]

supplementary:   [tex]\angle EOD[/tex]

vertical angles:   [tex]\angle AOE[/tex]

Using trigonometric functions, we can find that the value of the angle N is 3°.

The six fundamental trigonometric operations make up trigonometry. Trigonometric ratios are useful for describing these methods. The sine, cosine, secant, co-secant, tangent, and co-tangent functions are the six fundamental trigonometric functions. On the ratio of a right-angled triangle's sides, trigonometric identities and functions are founded. Trigonometric formulas are used to determine the sine, cosine, tangent, secant, and cotangent values for the perpendicular side, hypotenuse, and base of a right triangle.

Here, using the cosine theorem:

CosM = n² + l² - m²/2nl

⇒ Cos 149° = 27² + 70² - m²/2 × 27 × 70

⇒ -0.981 = 729 + 4900 - m²/3780

⇒ 5629 - m² = -3708

⇒ m² = 9337.

Now Cos N = m² + l² - n²/2ml

= (9337 + 4900 - 729) / (2 × √9337 × 70)

= 0.9985

Cos N = 0.9985

Putting [tex]Cos^{-1}[/tex] on both sides:

[tex]Cos^{-1}[/tex] Cos N = [tex]Cos^{-1}[/tex] 0.9985

⇒ N ≈ 3°

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The complete question is:

In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.

Answer:

We are given the function S = m^2 + 6m + 8 which models the growth of book sales in m months, where S is an amount in thousands of dollars. We want to find in how many months book sales reach $80,000.

We can set up an equation as follows:

S = m^2 + 6m + 8 = 80

Subtracting 80 from both sides, we get:

m^2 + 6m - 72 = 0

We can factor this quadratic equation as:

(m + 12)(m - 6) = 0

This gives us two possible solutions:

m + 12 = 0 or m - 6 = 0

Solving for m in each case, we get:

m = -12 or m = 6

Since we are looking for a number of months, we can discard the negative solution.

Therefore, book sales reach $80,000 in 6 months.

So, the answer is: 6 months.

Answer: Sally will earn $4,830.00 in interest over 7 years.

Step-by-step explanation:

If the interest is not compounded, then Sally will earn simple interest, which can be calculated using the formula:

I = P * r * t

where:

I = the interest earned

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

t = the time period, in years

In this case, we have:

P = $9,000 (the initial deposit)

r = 7% = 0.07 (the annual interest rate)

t = 7 (the number of years)

So, plugging in the values:

I = $9,000 * 0.07 * 7

I = $4,830.00

Therefore, Sally will earn $4,830.00 in interest over 7 years.

The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

What is a piecewise function ?

A piecewise function is a function that is defined by different equations on different parts of its domain. The graph of a piecewise function consists of several distinct parts, each corresponding to a different equation.

The graph shown is an example of a piecewise function. The function is defined using different equations on different intervals of the domain.

On the interval from negative infinity to negative 2, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

On the interval from negative 2 to 2, the function is defined by the equation y = -x. This means that the value of the function is equal to the negative of x on this interval.

On the interval from 2 to positive infinity, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

At the point x = -2, the function experiences a discontinuity, because the two equations that define it have different values at this point. The function is not differentiable at this point, because it does not have a well-defined tangent line.

The domain of the function is the set of all real numbers, because there are no restrictions on the values of x that are allowed.

Therefore, The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

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