A newscaster earns $25,100 and wants to invest 10% of his/her monthly salary to save for
retirement in 29 years. If he/she invests this money at 4.1% compounded monthly, how much
money will he/she have at retirement?
a) How much will be saved each year?
b) What will be the monthly deposit?
c) What will be the amount in the account after 29 years?

Answer:

data given

principal 300

rate12%

time 4 years

Step-by-step explanation:

from

A=P[1+r/100]^n

where

A is amount

p is principal

r is rate

n is interest period

now,

A= 300[1+12/(100×12)]^(12×4)

A=300×1.01^48

A=483.67

: .would be 483.67

verbal phrase can be represented by 7.16.

Part A:

The verbal phrase can be represented by the following expression:

[tex]2.19g + 0.59[/tex]

Here, "Two and nineteen hundredths times a number g" can be written as 2.19g, and "plus fifty-nine hundredths" can be written as [tex]0.59[/tex]  .

Part B:

To evaluate the expression when  [tex]g = 3[/tex], we substitute 3 for g in the expression and simplify:

[tex]2.19g + 0.59[/tex]

[tex]= 2.19(3) + 0.59 [\ Substitute g = 3][/tex]

[tex]= 6.57 + 0.59[/tex]

[tex]= 7.16[/tex]

Therefore, the correct answer is [tex]7.16.[/tex]

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The given question is incomplete. the complete question is given below:

Consider the verbal phrase.

Two and nineteen hundredths times a number g, plus fifty-nine hundredths

Part A

Enter an expression to represent the verbal phrase.

g +

Part B

Evaluate the expression when g = 3.

3.96

7.16

8.34

8.93

The range is the best measure of variability for this data, and its value is 4.

The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).

The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:

Range = Maximum value - Minimum value = 4 - 0 = 4

Therefore, the range is the best measure of variability for this data, and its value is 4.

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The two consecutive natural numbers whose sum of squares is 181 are 9 and 10

Let's assume that the two consecutive natural numbers are x and x+1. Then, we can write an equation based on the given information:

x² + (x+1)² = 181

Expanding the equation:

x² + x² + 2x + 1 = 181

Combining like terms:

2x² + 2x - 180 = 0

Dividing both sides by 2:

x² + x - 90 = 0

Now, we can use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 1, and c = -90

x = (-1 ± √(1 + 360)) / 2

x = (-1 ± √(361)) / 2

x = (-1 ± 19) / 2

We discard the negative value, as it does not correspond to a natural number:

x = 9

Therefore, the two consecutive natural numbers are 9 and 10, and their sum of squares is 81 + 100 = 181.

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The continuous compounding rate earned by the investment is given as follows:

8.022%.

The balance of an account after t years, using continuous compounding, is  modeled by the equation presented as follows:

A(t) = A(0)e^{kt}.

In which:

For this problem, the parameters are given as follows:

A(11) = 58, A(0) = 24, t = 11.

Hence the rate is obtained as follows:

24e^(11k) = 58

e^(11k) = 58/24

11k = ln(58/24)

k = ln(58/24)/11

k = 8.022%.

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Therefore, the answer is (A) 7x-9 when it is given that function F(x) = 4x - 8 and g(x) = -3x + 1.

In mathematics, a function is a relationship between two sets of values, where each input (or domain element) is associated with a unique output (or range element). In other words, a function is a rule or a process that takes an input (or inputs) and produces a corresponding output. Functions can be expressed using various mathematical notations, such as algebraic formulas, graphs, tables, or even verbal descriptions. They are widely used in many fields of mathematics, science, engineering, economics, and computer science, to model and solve problems that involve relationships between variables or quantities.

Here,

To find (f - g)(x), we need to subtract g(x) from f(x), so we get:

(f - g)(x) = f(x) - g(x)

Substituting the given functions, we get:

(f - g)(x) = (4x - 8) - (-3x + 1)

Simplifying the expression by distributing the negative sign, we get:

(f - g)(x) = 4x - 8 + 3x - 1

Combining like terms, we get:

(f - g)(x) = 7x - 9

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An observation is considered an outlier if it is below 35.5 or above 79.5 in this dataset.

To determine the outliers in a dataset using the five-number summary, we need to calculate the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).

IQR = Q3 - Q1

Where

Q1 = 52

Q3 = 63

So, we have

IQR = 63 - 52

IQR = 11

An observation is considered an outlier if it is:

Below Q1 - 1.5 × IQR

Above Q3 + 1.5 × IQR

Substituting the values, we get:

Below 52 - 1.5 × 11 = 35.5

Above 63 + 1.5 × 11 = 79.5

Therefore, an observation is considered an outlier if it is below 35.5 or above 79.5 in this dataset.

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The polynomial in factor form is y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3).

In this problem we find a representation of polynomial set on Cartesian plane, whose expression is described by the following formula in factor form:

y(x) = a · (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄)

Where:

Then, by direct inspection we get the following information:

y(0) = - 3, r₁ = - 3, r₂ = - 1, r₃ = 2, r₄ = 3

First, determine the lead coefficient:

- 3 = a · (0 + 3) · (0 + 1) · (0 - 2) · (0 - 3)

- 3 = a · 3 · 1 · (- 2) · (- 3)

- 3 = 18 · a  

a = - 1 / 6

Second, write the complete expression:

y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3)

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Answer:

Step-by-step explanation:

36 26 so 36 +26 = 89

If no accessories are sold, $3 will be paid out. In the event that accessories are sold, the compensation is $2.00 plus $1.00 plus 1.5 percent of their worth.

Based on the information given, the KPI payouts are:

$1.00 for each Prepaid Ring-out Only

$2.00 for each Prepaid Activation

1.5% of the value of each Accessories sale

$1.00 for each Equipment Protection sale

We need to know the values of the prepaid activation and equipment protection in order to compute the payment for activating a prepaid device with equipment protection. Assume that the equipment protection is worth $Y and the prepaid activation is worth $X.

The following would be the total payment for activating a prepaid device with equipment protection:

Payout = $2.00 (for activation) + $1.00 (for equipment protection) + 1.5% (of the value of accessories sold)

If no accessories are sold, the payout would be:

Payout = $2.00 + $1.00

= $3.00

If accessories worth $Z are also sold, the payout would be:

Payout = $2.00 + $1.00 + 1.5% of $Z

= $2.00 + $1.00 + 0.015Z

So the payout for activating a prepaid device with equipment protection depends on the value of the accessories sold.

Therefore,  If no accessories are sold, the payout is $3.00. If accessories are sold, the payout is $2.00 + $1.00 + 1.5% of the value of the accessories sold.

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Using equations, we can find that the number of pop tarts that Taylor has with him, p = 13.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others.

Let the cost of one granola bar = x.

Let the cost of one pop tart = y.

Now, assume Taylor had money, m.

So, as per the question:

90x = m

⇒ x = m/90

78y = m

⇒ y = m/78

75x + py = m

Substituting the values of x and y:

⇒ 75 × m/90 + p × m/78 = m

⇒ 75m/90 + pm/78 = m

⇒ (5850m + 90pm) / 7020 = m

⇒ 5850m + 90pm = 7020m

⇒ 90pm = 7020m - 5850m

⇒ 90pm = 1170m

⇒ p = 1170m/90m

⇒ p = 13.

Therefore, the number of pop tarts, p = 13.

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The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.

A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).

The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).

Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.

To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:

g(x) = 0{-10≤x≤10}

Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].

However, if the formula is something like:

g(x) = 2 * 0{-10≤x+3≤10}

Then we can describe the transformations as follows:

Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.

Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.

Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.

To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.

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The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.

A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).

The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).

Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.

To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:

g(x) = 0{-10≤x≤10}

Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].

However, if the formula is something like:

g(x) = 2 * 0{-10≤x+3≤10}

Then we can describe the transformations as follows:

Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.

Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.

Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.

To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.

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Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.

The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.

Here,

a.

P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)

= (4/52) * (1/12)

= 1/78

b.

P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)

= (13/52) * (5/12)

= 65/624

c.

P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)

= (12/52) * (6/12)

= 1/4

d.

P(Bert gets a red card and Ernie rolls a fifteen) = 0

e.

Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:

A regular 52-card deck contains 48 cards that are not Jacks,

so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.

On a 12-sided dice with 11 possible outcomes,

Ernie rolls a non-12th-number (1, 2, 3, etc.).

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With given compound interest, the final amount of the investment after 15 years at 8% interest compounded semiannually, quarterly and daily are $2,067.87, $2,094.28, and $2,101.62, respectively.

What is Compound interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit, or the interest earned on both the principal and any previously accrued interest. In other words, interest is computed not only on the original amount of money but also on any past interest gained. The interest generated on the cumulative interest can compound exponentially, resulting in enormous growth of an investment or loan sum over time. Compound interest is computed using a formula that takes the principle amount, interest rate, and compounding frequency into consideration.

Now,

To find the final amount of the investment, we can use the formula for compound interest:

A = P(1 + r/n)ⁿˣ

where:

A = final amount

P = principal (initial investment)

r = annual interest rate

n = times the interest is compounded per year

x = time in years

For semiannual compounding, n = 2 and x = 15:

A = 750(1 + 0.08/2)²*¹⁵= $2,067.87

For quarterly compounding, n = 4 and x = 15:

A = 750(1 + 0.08/4)⁴*¹⁵ = $2,094.28

For daily compounding, n = 365 (assuming no leap years) and x = 15:

A = 750(1 + 0.08/365)³⁶⁵*¹⁵ = $2,101.62

Therefore, the final amount of the investment after 15 years at 8% interest compounded semiannually, quarterly and daily are $2,067.87, $2,094.28, and $2,101.62, respectively.

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The radius of the cylinder is approximately 6.75 inches.

We can use the formula for the volume of a cylinder to solve this problem:

[tex]V = \pi r^2h[/tex]

We know that the volume V is 2,035.75 [tex]in^3[/tex], and the height h is 3 times the radius r. So we can write:

[tex]V = \pi r^2(3r)[/tex]

Simplifying this expression, we get:

V = 3π[tex]r^3[/tex]

To solve for r, we can divide both sides of the equation by 3π[tex]r^2[/tex]:

V/(3π[tex]r^2[/tex]) = r

Substituting the given value for V, we have:

2,035.75/(3π[tex]r^2[/tex]) = r

Multiplying both sides by 3πr^2, we get:

2,035.75 = 3π[tex]r^3[/tex]

Dividing both sides by 3π, we have:

[tex]r^3[/tex] = 2,035.75 / (3π)

Taking the cube root of both sides, we get:

r = [tex](2,035.75 / (3\pi ))^{1/3[/tex]

Using a calculator, we find that:

r ≈ 6.75 inches

Therefore, The cylinder has a radius of about 6.75 inches.

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Two lines parallel to AD are BF and CE.

Two lines skew to DE are EF and DF.

The number of base edges is three: DE, EF, and DF.

The number of lateral faces is three: ABDF, BCEF, and ACDE.

The base area is 6 square units.

The lateral area is 72 square units.

The volume is 36 cubic units.

What is volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

1. Name two lines parallel to AD.

BF, CE

2. Name a line skew to DE.

EF, DF

3. State the number of base edges.

DE, EF, DF

4. State the number of lateral faces.

3, Which are ABDF, BCEF, ACDE.

5. Find the base area,

the base of a prism is ΔDEF,

DE = AC = 3,

EF = BC = 4,

DF = 5

A = √(s(s-a)(s-b)(s-c))

s = (3 + 4 + 5)/2 = 6

A = √(s(s-a)(s-b)(s-c))

A = √(6(6-3)(6-4)(6-5))

A = √(6(3)(2)(1))

A = √36

A = 6

6. Find the lateral area.

the lateral area would be the sum of the area of the four rectangular faces.

A = lb

ABDF

A1 = 5* 6 = 30,

BCEF,

A2 =  4 * 6 = 24

ACDE

A3 = 3  *6 = 18

lateral area = 30 + 24 + 18

= 72

7. Find the volume.

The volume of a prism can be calculated by multiplying the area of the base by the height of the prism. Therefore, the formula for the volume of a prism is:

V = Bh

Where V is the volume, B is the area of the base, and h is the height of the prism.

V = 6 * 6 = 36

hence,

Two lines parallel to AD are BF and CE.

Two lines skew to DE are EF and DF.

The number of base edges is three: DE, EF, and DF.

The number of lateral faces is three: ABDF, BCEF, and ACDE.

The base area is 6 square units.

The lateral area is 72 square units.

The volume is 36 cubic units.

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The control group for the experiment would be option C: some plants will receive no sunlight.

The control group in an experiment is the group that does not receive the treatment or intervention being tested, so that the effects of the treatment can be compared to a baseline or reference point. In this experiment, the treatment being tested is the provision of sunlight as an energy source for plant growth.

Therefore, the control group should not receive sunlight, so that the effects of sunlight can be compared to the baseline of plant growth without sunlight.

Therefore, the control group for the experiment would be option C: some plants will receive no sunlight.

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Answer:

The circumference of the circle is 119.32 ft.

Step-by-step explanation:

The circumference of a circle can be solved through the formula:

C = πd

where d is the diameter

Given: d = 38 ft

π = 3.14

Solve:

C = πd

C = 3.14 (38 ft)

C = 119.32 ft

We can see that the choice falls within the range of (A) less than 1 hour. Therefore, the answer is (A), Kristen spends less than 1 hour .

Finding the value of a single unit using the unitary technique allows us to determine the value of the necessary number of units based on this value.

To find out approximately how much time Kristen spent gardening each day, we can divide the total time she spent gardening by the number of days she gardened.

Total time = 4 hours

Number of days = 7

So, Kristen spent approximately 4/7 = 0.57 hours or about 34 minutes each day gardening.

Since the answer choices are in ranges, we can see that this falls within the range of (A) less than 1 hour. Therefore, the answer is (A).

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f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞),f(x) is concave down on the interval (-√(6/7), √(6/7)) ,The inflection points occur at x = -√(6/7) and x = √(6/7).

An inflection point is a point on a curve where the concavity changes, from concave up to concave down or vice versa, indicating a change in the curvature of the curve.

According to the given information:

To determine the intervals where f(x) is concave up or down, we need to find the second derivative of f(x) and determine its sign.

First, we find the first derivative of f(x):

f'(x) = (14x)/(7x²+6)²

Then, we find the second derivative of f(x):

f''(x) = [28(7x²+6)²- 28x(7x²+6)(4x)] / (7x²+6)^4

Simplifying the expression, we get:

f''(x) = 28(42x² - 72) / (7x^2+6)³

To determine where f(x) is concave up or down, we need to find the intervals where f''(x) is positive or negative, respectively.

Setting f''(x) = 0, we get:

42x² - 72 = 0

Solving for x, we get:

x = ±√(6/7)

These are the possible inflection points of f(x). To determine if they are inflection points, we need to check the sign of f''(x) on both sides of each point.

We can use a sign chart to determine the sign of f''(x) on each interval.

Intervals where f''(x) > 0 are where f(x) is concave up, and intervals where f''(x) < 0 are where f(x) is concave down.

Here is the sign chart for f''(x):

x  |   -∞   | -√(6/7) | √(6/7) |   ∞

f''(x)|   -    |     +      |     -     |   +

From the sign chart, we can see that:

a) f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞).

b) f(x) is concave down on the interval (-sqrt(6/7), √(6/7)).

c) The inflection points occur at x = -√(6/7) and x = √(6/7).

Therefore, the open intervals where f(x) is concave up are (-∞, -√(6/7)) and (√(6/7), ∞), and the open interval where f(x) is concave down is (-√(6/7), √(6/7)). The inflection points occur at x = -√(6/7) and x = √(6/7).

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The f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞),f(x) is concave down on the interval (-√(6/7), √(6/7)) ,The inflection points occur at x = -√(6/7) and x = √(6/7).

What is inflection Point?

An inflection point is a point on a curve where the concavity changes, from concave up to concave down or vice versa, indicating a change in the curvature of the curve.

According to the given information:

To determine the intervals where f(x) is concave up or down, we need to find the second derivative of f(x) and determine its sign.

First, we find the first derivative of f(x):

f'(x) = (14x)/(7x²+6)²

Then, we find the second derivative of f(x):

f''(x) = [28(7x²+6)²- 28x(7x²+6)(4x)] / (7x²+6)^4

Simplifying the expression, we get:

f''(x) = 28(4x² - 72) / (7x^2+6)³

To determine where f(x) is concave up or down, we need to find the intervals where f''(x) is positive or negative, respectively.

Setting f''(x) = 0, we get:

42x² - 72 = 0

Solving for x, we get:

x = ±√(6/7)

These are the possible inflection points of f(x). To determine if they are inflection points, we need to check the sign of f''(x) on both sides of each point.

We can use a sign chart to determine the sign of f''(x) on each interval.

Intervals where f''(x) > 0 are where f(x) is concave up, and intervals where f''(x) < 0 are where f(x) is concave down.

Here is the sign chart for f''(x):

x  |   -∞   | -√(6/7) | √(6/7) |   ∞

f''(x)|   -    |     +      |     -     |   +

From the sign chart, we can see that:

a) f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞).

b) f(x) is concave down on the interval (-sqrt(6/7), √(6/7)).

c) The inflection points occur at x = -√(6/7) and x = √(6/7).

Therefore, the open intervals where f(x) is concave up are (-∞, -√(6/7)) and (√(6/7), ∞), and the open interval where f(x) is concave down is (-√(6/7), √(6/7)). The inflection points occur at x = -√(6/7) and x = √(6/7).

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the simplified form of the equation 6Y + 4 = 8 + 2Y + 2Y is Y = 2.

How to solve the question ?

To simplify the equation 6Y + 4 = 8 + 2Y + 2Y, we can combine like terms. Like terms are terms that have the same variable and the same exponent. In this case, we have two terms with Y as the variable, so we can combine them.

First, let's add the 2Y terms on the right side of the equation: 6Y + 4 = 8 + 4Y

Next, we can subtract 4Y from both sides of the equation to isolate the variable on one side: 6Y - 4Y + 4 = 8

Simplifying further, we can combine the Y terms: 2Y + 4 = 8

Finally, we can subtract 4 from both sides to isolate the variable: 2Y = 4

And we can solve for Y by dividing both sides by 2: Y = 2

Therefore, the simplified form of the equation 6Y + 4 = 8 + 2Y + 2Y is Y = 2.

In summary, to simplify an equation, we want to combine like terms and isolate the variable on one side of the equation. Once we have the variable on one side, we can solve for its value.  

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Answer:

Step-by-step explanation:

The distance formula is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

x1 is a,

x2 is 0,

y1 is 0 and

y2 is b. Fitting those into the formula where they belong:

[tex]d=\sqrt{(0-a)^2+(b-0)^2}[/tex] and

[tex]d=\sqrt{(-a)^2+(b)^2}[/tex]

Since a negative squared is a positive, then

[tex]d=\sqrt{a^2+b^2}[/tex]

which is the second choice down.

The length of arc FED is approximately 51.1 yards, rounded to the nearest tenth.

The length of a section of a circle's circumference is known as an arc length.

The radius of the circle and the angle the arc subtends at the centre of the circle are two variables that affect an arc's length.

To find the length of FED, we need to first find the measure of the arc EGD. Since a circle has 360 degrees, we can find the measure of arc EGD by subtracting the measures of arcs DGC, CGF, and FGE from 360:

m(EGD) = 360° - m(DGC) - m(CGF) - m(FGE)

m(EGD) = 360° - 80° - 47° - 90°

m(EGD) = 143°

The formula for arc length is:

Arc length = (central angle / 360) x (2πr)

We can use this information to find the radius of the circle:

FG = 2r

27 yd = 2r

r = 13.5 yd

Now we can use the formula for arc length to find the length of arc FED:

Arc length FED = ((∠FED) / 360) x (2πr)

We know that ∠(EGD) + ∠(FED) = 360, so we can solve for ∠(FED):

∠(FED) = 360° - ∠(EGD)

∠(FED) = 360° - 143°

∠(FED) = 217°

Plugging in the values, we get:

Arc length FED = (217° / 360) x (2π x 13.5 yd)

Arc length FED = (0.6028) x (84.78 yd)

Arc length FED = 51.11 yd

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The value of Tanθ is 20/21.

What is Pythagorean Theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we have

Given: sinθ = -20/29 and that angle terminates in quadrant III.

We have to find the value of tanθ.

Using the definition of sine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

Sinθ = Perpendicular/hypotenuse

Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.

Adjacent = - √Hypotenuse² - perpenducualr²

Replace the known values in the equation.

Adjacent = -√29² - (-20)²

Adjacent = -21

Find the value of tangent.

Tanθ = Perpendicular/base

Tanθ = -20/(-21)

Hence, the value of Tanθ is 20/21.

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So according to the given figure ∠mah is right angle(90°), The value of x is 17, ∠mat is 38° and ∠tah is equal to 52°.

(A) ∠mah is right angle(90°) [GIVEN IN THE FIGURE]

(B) (2x+4)+(3x+1) = 90

5x+5 = 90

x= 17

(C) 2x+4 = 2×17 + 4 = 38°

(D) 3X + 1 = 3 × 17 + 1 = 52°

A graph is a visual representation or diagram that displays facts or values in an organised manner in mathematics. The points on a graph are typically used to depict the relationships between two or more things.

A graph in discrete mathematics is made up of vertices, which are groups of points, and edges, which are the connections between those vertices. There are numerous different types of graphs besides linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs.

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The required graph of the function given; h (x) has been attached.

In mathematics, graph theory is the study of graphs, which are mathematical structures used to represent pairwise interactions between objects. In this definition, a network is made up of nodes or points called vertices that are connected by edges, also called links or lines. In contrast to directed graphs, which have edges that connect two vertices asymmetrically, undirected graphs have edges that connect two vertices symmetrically. Graphs are one of the primary areas of study in discrete mathematics.

Here as per the question the graph of the function, h (x) has been attached.

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Answer: Rectangle

Step-by-step explanation: The shape created by the cross-section is a rectangle because the cross-section shows a 2-dimensional slice of a 3-dimensional rectangular prism. Since a rectangular prism has rectangular faces, any cross-section taken perpendicular to the length of the prism will be a rectangle.