What is perimeter in math?

The value of the principal investment is $21,597.30. The solution has been obtained by using the concept of compound interest.

What is compound interest?

When interest is calculated, both the principal and the interest that has accumulated over the previous period are used. Compound interest accounts for the principal when calculating the interest for the subsequent month, as opposed to simple interest, which does not. In algebra, the letter C.I. is frequently used to denote compound interest.

We are given that after 16 years in an account with a 6.2% annual interest rate compounded continuously, an investment is worth a total of $58,226.31.

This means that

P(t) = $58,226.31

t = 16 years

r = 6.2%

We know that formula for continuous compounding interest is

[tex]P(t) = P_{0} e^{rt}[/tex]

So, using this, we get

⇒58,226.31 = Pe^(0.062*16)

⇒58,226.31 = Pe^(0.992)

⇒58,226.31 = P*2.696

⇒P = $21,597.30

Hence, the value of the principal investment is $21,597.30.

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Answer:

2%

Step-by-step explanation:

Answer:

7.75

Step-by-step explanation:

Multiply y-4 both sides

(y-4) 3/y-4 =4/5(y-4)

3=4/5(y-4)

3/(4/5)=y-4

(3/(4/5))+4

Put in calculator

y=31/4

y=7.75

Answer:

y = 7.75

Step-by-step explanation:

3 = 4/5 x y-4

3x5 = 4 x y-4

15 = 4y-16

15+16 = 4y

31/4 = y

y = 7.75

Answer:

Step-by-step explanation:

The sum of the first 20 terms of a linear sequence can be found using the formula for the sum of an arithmetic series:

S = n/2 * (a1 + a20)

where n = number of terms = 20, a1 = first term = 1, and a20 = 20th term = 1 + 4 * (20 - 1) = 77

Substituting these values, we have:

S = 20/2 * (1 + 77) = 20/2 * 78 = 20 * 39 = 780

So, the sum of the first 20 terms of the sequence 1, 5, 9, 13 is 780.

In the line of symetry for this parabola is x = -1.

The maxima or minima of the parabola is [tex]-\frac{21}{4}[/tex]

Estimate the gradient of the curve at x = 4 is 5.

The equation of the tangent of the point (4, 1) is 5x² - y² - 40x + 2y + 89 = 0.

The gradient of the curve at the point (-1, 1) is -1.

The steps are as follows:

The function of parabola y = x² - 3x - 3

(i) In the line of symetry for this parabola.

Symetry of the parabola:

x =  [tex]-\frac{b}{2a}[/tex]    → for y = ax² + bx + c

x =  [tex]-\frac{-3}{-3}[/tex]

x = -1

(ii) The maxima or minima of the parabola.

The maximum or minimum parabola can be found when the derivative is 0

y = x² - 3x - 3

y' = 2x - 3

0 = 2x - 3

2x = 3

x =  [tex]\frac{3}{2}[/tex]

The maxima or minima of the parabola

y = x² - 3x - 3

  = ( [tex]\frac{3}{2}[/tex] )² - 3 (  [tex]\frac{3}{2}[/tex] ) - 3

  =  [tex]\frac{9}{4}[/tex]  -   [tex]\frac{9}{2}[/tex]  - 3

  =   [tex]\frac{9}{4}[/tex]  -  [tex]\frac{18}{4}[/tex]  -  [tex]\frac{12}{4}[/tex]

  = [tex]-\frac{21}{4}[/tex]

(iii) Estimate the gradient of the curve at x = 4

y = x² - 3x - 3

y' = 2x - 3

y' = m = 2(4) - 3

          = 8 - 3

          = 5

y = x² - 3x - 3

y = 4² - 3(4) - 3

  = 16 - 12 - 3

  = 1

(iv) The equation of the tangent of the point (4, 1)

(y - b)² = m (x - a)²

(y - 1)² = 5 (x - 4)²

y² - 2y + 1 = 5 (x² - 8x + 16)

y² - 2y + 1 = 5x² - 40x + 90

5x² - y² - 40x + 2y + 90 - 1 = 0

5x² - y² - 40x + 2y + 89 = 0

(v) The gradient of the curve at the point (-1, 1)

y = x² - 3x - 3

y' = 2x - 3

y' = m = 2(1) - 3

          = 2 - 3

          = -1

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The parallel segments are MN & LK, MP & JK and NP & JL

The side lengths are listed below and the perimeter is 84 units

By definition, parallel segments are segments that extend indefinetely and do not meet

Using the above as a guide, we have the following:

The midsegments are given as

MP = 17, LK = 24 and PN = 13

This means that

JK = 2 * MP

JK = 2 * 17

JK = 34

Also, we have

MN = 1/2 * LK

MN = 1/2 * 24

MN = 12

Lastly, we have

JL = 2 * PN

JL = 2 * 13

JL = 26

For the perimeter, we have

Perimeter = JK + LK + JL

Perimeter = 34 + 24 + 26

Perimeter = 84

Hence, the perimeter is 84 units

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Answer:  A=4.5m²

Step-by-step explanation:  length: 1.5 Width: 300

Unit Conversion:l=1.5mw

A=wl=3·1.5=4.5m²

Answer:

Step-by-step explanation:

As stated in the question that One vehicle transports 14 tourists and there are 34 tourists

Number of vehicles required = 34/14 = 2 vehicles + 6 people left

So, the remaining 6 people will be transported through 3rd vehicle.

So, there are 3 vehicles needed to transport 34 tourists.

a) The vectors a and b are collinear when compa b=compb a. This means that they have the same direction, so that they're pointing in the same direction or opposite directions. In other words, if the angle between them is 0° or 180°, then they are collinear.

b) The vectors a and b are orthogonal when proja b=proj b a. This means that they are perpendicular to each other, so that the angle between them is 90°. Furthermore, it means that the projection of one vector onto the other is equal to zero.

This is because the projection of a vector onto itself is equal to the magnitude of the vector, while the projection of a vector onto a vector orthogonal to it is equal to zero.

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An algebraic expression which is equivalent to the expression

csc[arccos(x -1)] is equal to 1 / √2x - x² .

Let us consider the expression arccos(x - 1 ) = y .

arccos(x - 1 ) = y

⇒ cos y = (x - 1 ) ___( 1 )

Now the required algebraic expression is equivalent to :

csc[arccos(x -1)]

= csc y

= ( 1 / sin y )

= 1 / √ 1 - cos²y   __(2)

Substitute the value of cosy from (1 ) in the expression ( 2 ) we get,

= 1 / √ 1 - ( x - 1 )²

= 1 / √ 1 -  ( x² -2x + 1 )

= 1 / √ 1 - x² + 2x - 1

= 1 / √ 2x - x²

Therefore, the expression csc[arccos(x -1)] is equivalent to an algebraic expression is  1 / √ 2x - x².

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Answer:

3°

Step-by-step explanation:

33 +19x = 90     subtract 33 from both sides of the equation

19x = 57             divide both sides by 19

x = 3°

the area of the given kite will be 60 feet².

What is area of Kite?

A polygon with four vertices and four sides enclosing four angles is called a quadrilateral. A unique quadrilateral known as the kite has successive sides that are all congruent, but the opposite sides are not. A rhombus is a kite that has four congruent sides. A kite's diagonals are perpendicular. The area of a kite is calculated as half of the diagonal product, which is the same as the area of a rhombus. The formula: can be used to express the area of a kite.

Area of Kite = 1/2*D1 * D2

D1 = long diagonal of kite

D2 = short diagonal of kite

The diagonals intersect each other so that the shorter diagonal is split into parts that are 2 feet and 2 feet and the longer diagonal is split into parts that are 10 feet and 20 feet.

So Area = 1/2 * 4 * 30 = 60 feet²

Hence the area of the given kite will be 60 feet².

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(a) Each xi in the vector (x1, x2, ..., xn) can be either 0 or 1.

Therefore, there are 2 possibilities for each xi.

The number of vectors that can be formed by combining these values is equal to the number of combinations of 2 possibilities, taken n times.

The number of vectors (x1, x2 . . ., xn) such that each xi is either 0 or 1 and n where k is a non-negative integer less than or equal to n is 2^n.

the same problem as before but under the condition thatx1 + x2 + · · · + xn ≥ k,

This is equivalent to 2^n. For example, if n = 2, then there are 2 possibilities for x1 (either 0 or 1) and 2 possibilities for x2 (either 0 or 1). The total number of vectors that can be formed is 2 * 2 = 2^2 = 4. In general, the number of vectors that can be formed is equal to 2^n.

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The complete question is :-

determine the number of vectors (x1, x2 . . ., xn) such that each xi is either 0 or 1 and n where k is a non-negative integer less than or equal to n.

(A) The point (2, 80) represents that at 2 hours there are 80 miles of water in a tank.

(B) Writing an equation for the relationship in the form of y = mx, we get y = 40x.

What is Proportionate Relationship?

It is given that there is a proportional relationship between hours, x, and number of miles, y, of water in a tank.

Also, the point (2, 80) is on a graph of this relationship.

(A) The point (2, 80) represents that at 2 hours there are 80 miles of water in a tank.

(B) We have the given point, (2, 80)

Writing the relationship in the form of equation, y = mx using the point (2, 80), we get

80 = m × 2

⇒ m = 80/2

⇒ m = 40

Thus, writing an equation for the relationship in the form of y = mx when m = 40, we get y = 40x.

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Answer:

Step-by-step explanation:

Given that sin θ = -4/9 and 3π/2 ≤ θ ≤ 2π, we can use the trigonometric identities to find cot θ.

cot θ = 1/tan θ = 1/ (sin θ / cos θ) = cos θ / sin θ

As we know the sin θ = -4/9, we can find cos θ = √(1 - sin^2 θ) = √(1 - (-4/9)^2) = √(1 - 16/81) = √(65/81)

So cot θ = (√(65/81)) / (-4/9) = -9/4 * √(65/81) = -(9/2) √(65/81)

Note that, since 3π/2 ≤ θ ≤ 2π, the value of cot θ will be negative

The equation to find the distance between Professor Burger's house and Lila's house is x + 5 = 12 and the solution of the equation is 7 miles.

Distance between Professor Burger's house and Chris' house = 12 miles

Lila's house falls between Professor's house and Chris' house.

Distance between Lila's house and Chris' house = 5 miles

Let's assume x to be the distance between Professor Burger's house and Lila's house.

Thus the equation to solve this problem will be

x + 5 = 12

The next step will be,

x = 12 - 5

x = 7

Therefore, the distance between Professor Burger's house and Lila's house is 7 miles.

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Answer:12.405 would be correct

Step-by-step explanation:

In probability theory and statistics, variance is the squared deviation from the mean of a random variable. The variance is also often defined as the square of the standard deviation. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value

The variance is a measure of variability

Therefore c is your answer!

The compass bearing measure is N60°E and the three figure bearing measure is 060°

From the question, we ae to write the measurement of the bearing in both compass bearing and three figure bearing

Compass bearing

The line is between the North and E poles. The line measures 60°. Therefore, N60°E.

Hence, the compass bearing measure is N60°E

Three figure bearing

Reading from the North pole in the clockwise direction, the bearing of the line is 60°.

Hence, the three figure measure is 060°

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Answer: this is the answer it is a screenshot of the graph

Assuming you graph lines f and g on the same coordinate plane and they intersect at point (4, 5), a statement which is not true include the following: D. Other points that are on line f are also solutions of the system.

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.

Based on the graph of the lines representing the system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant I and it is denoted by the point of intersection of both the x-axis and y-axis, which is given by the ordered pair (4, 5).

In conclusion, the ordered pair (4, 5) is a solution to the system of equations and it is located on both lines f and g.

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350% of the correct pre-test questions - 7

50% of the correct pre-test questions - 1

100% of the correct pre-test questions - 2

A diagram that resembles a piece of tape that is used to show how numbers relate to one another. Also known as length model, fraction strip, bar model, and strip diagrams.

Given:

There are 7 units to represents 14 Questions and 350%.

So, 14/7 = 2 and 350/ 7= 50%

one unit represent 2 questions and 50%.

and, 2 units represents 4 questions and 100%.

then, 350% of the correct pre-test questions - 7

50% of the correct pre-test questions - 1

100% of the correct pre-test questions - 2

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The length of the rectangle is 23 km and the width of the rectangle is 15 km.

A rectangle is 8 km longer than it is wide.

Its area is 345 sq-km.

Let the width of the rectangle is x.

The length is 8 km longer than the width.

So the width of the rectangle is x + 8 km.

The formula of the area of rectangle is:

A = length × width

We know A = 345 sq-km.

Now putting the value

x × (x + 8) = 345

Now simplifying

x^2 + 8x = 345

Subtract 345 on both side, we get

x^2 + 8x - 345 = 0

Now factor the equation

x^2 + (23 - 15)x - 345 = 0

x^2 + 23x - 15x - 345 = 0

x(x + 23) - 15(x + 23) = 0

(x - 15)(x + 23) = 0

Now equation the factor equal to zero.

x - 15 = 0           or             x + 23 = 0

x = 15                or              x = -23

Since the dimension of the rectangle can't be negative. So

The width of the rectangle is 15 km.

Now we determine the value of length

x + 8 = 15 + 8 = 23

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The number of piles when the newspaper is 15 will be 3.

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.

20 newspapers in 4 piles.

We know that the ratio of the newspaper to pile is constant. Then 15 newspapers in piles will be given as,

15 / x = 20 / 4

15 / x = 5

x = 15 / 5

x = 3

The number of piles when the newspaper is 15 will be 3.

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Answer:

1/4

Step-by-step explanation:

The probability of the spinner landing on any one number = 1/8 since there are 8 possible outcomes and we are looking for the probability of one outcome out of those

So P(2) = P(4) = 1/8

P(4) and P(2) is the sum of these two probabilities = 1/8 + 1/8 = 2/8 = 1/4

The length of side CE is 5/6 units

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

The triangle

On the triangle, we have the following ratio

x - 2 : 2 = x + 1 : 8

Express as fraction

(x - 2)/x = (x + 1)/8

So, we have

8x - 16 = 2x + 1

Evaluate the like terms

6x = 17

So, we have

x = 17/6

The value of CE is

CE = x - 2

CE = 17/6 - 2

So, we have

CE = 5/6

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Answer:

5

Step-by-step explanation:

A kilogram is a unit of mass in the metric system and is often used to measure the weight of food items. One kilogram is equivalent to 35.27 ounces. To determine how many ounces of peanut butter you used for your sandwich, you need to convert the mass in kilograms to ounces.

In this case, the jar contains 1.41 kg of peanut butter. To find the amount of peanut butter you used, you multiply the total amount by the percentage of the peanut butter you used. In this case, 8.0% of 1.41 kg is 0.11 kg of peanut butter.

Finally, you convert the 0.11 kg of peanut butter to ounces using the conversion factor of 35.27 ounces per kilogram. So 0.11 kg * 35.27 oz/kg = 3.88 ounces of peanut butter.

This answer is expressed to two significant figures because the original mass of the peanut butter is given to two significant figures (1.41 kg) and the percentage of peanut butter used is also given to two significant figures (8.0%).

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Answer:

110.0%

Step-by-step explanation:

25% of 88 is 22. 88+22=110 Fahrenheit

to get this you divide 88 by 100 which is 0.88, then multiply by 25 which gets you 22.