Calculate the present value. (Round your answer to two decimal
places.)
A = $35,000, r = 7% compounded monthly, t = 6 years

The value of x in the triangle based on Pythagoras Theorem will be 13

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle. The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a²+b²=c². However, it can also be written in the form of c²=a²+b²

This will be:

x² = 12² + 5²

x² = 144 + 25

x² = 169

x = ✓169

x = 13

Learn more about Pythagoras on:

https://brainly.com/question/343682

#SPJ1

a. The inverse of a linear transformation T₁,  which is obtained is:

T₁⁻¹(x,y) = (37x - 9y)/2 , (-8x + 2y)/2

b. The inverse of T₂ does not exist.

c. Entering the values of T₁ into the equations gives:  

d. Entering the values of T₂ into the equations gives:  

a. To find the inverse of a linear transformation T₁ , we need to solve the system of equations:

2x + 9y = a
8x + 37y = b

We can use the determinant of the matrix associated with this system to find the inverse:

[tex]\left[\begin{array}{cc}2&9\\8&37\end{array}\right][/tex]

The determinant Δ is:

Δ = (2)(37) - (9)(8)

Δ = 74 - 72

Δ =  2

The inverse of T₁ is:

T₁⁻¹(a,b) = (1/2)(|37 -9| |a|) = (37a - 9b)/2 , (-8a + 2b)/2

T₁⁻¹(x,y) = (37x - 9y)/2 , (-8x + 2y)/2

b. To find the inverse of a linear transformation T₂, we need to solve the system of equations:

x + z = a
x + y = b
y + z = c

We can use the determinant of the matrix associated with this system to find the inverse:

[tex]\left[\begin{array}{ccc}1&0&1\\1&1&0\\0&1&1\end{array}\right][/tex]

The determinant Δ is:

Δ =  (1)(1)(1) + (0)(0)(1) + (1)(1)(0) - (1)(0)(0) - (1)(1)(1) - (0)(1)(1)

Δ = 1 - 1

Δ = 0

Since the determinant is 0, the inverse of T₂ does not exist.

c. To find x and y given T₁(x,y) = (5,-1), we can plug in the values into the equations for T₁:

2x + 9y = 5
8x + 37y = -1

We can use substitution to solve for x and y. From the first equation, we can solve for x:

x = (5 - 9y)/2

Plugging this into the second equation:

8(5 - 9y)/2 + 37y = -1

Simplifying:

20 - 36y + 37y = -2

y = -22

Plugging this back into the first equation to solve for x:

x = (5 - 9(-22))/2

x = 101/2

d. To find x, y, and z given T₂(x,y,z) = (5,-3,-1), we can plug in the values into the equations for T₂:

x + z = 5
x + y = -3
y + z = -1

We can use substitution to solve for x, y, and z. From the first equation, we can solve for x:

x = 5 - z

Plugging this into the second equation:

5 - z + y = -3

Simplifying:

y = -8 + z

Plugging this back into the third equation:

-8 + z + z = -1

2z = 7

z = 7/2

Plugging this back into the equations to solve for x and y:

x = 5 - 7/2

x = 3/2

y = -8 + 7/2

y = -9/2

More information about linear transformation here: https://brainly.com/question/12963276

#SPJ11

The length of DC is √102, which is the simplest radical form.

The proportion of corresponding sides in similar triangles is the same. This is known as the similar triangles theorem.

In other words, if two triangles are similar, then the ratio of the lengths of any two corresponding sides is the same.

Since DE is parallel to AB, we can use similar triangles to set up the following proportion:

DC/AC = DE/AB

Substituting the given values, we get:

DC/17 = 6/AB

Since AB is the same length as DC, we can replace AB with DC:

DC/17 = 6/DC

Cross-multiplying and simplifying, we get:

DC^2 = 17 * 6

DC^2 = 102

DC = √102 in simplest radical form

Learn more about similar triangles at:

https://brainly.com/question/2644832

#SPJ1

Answer: A, C, and D all have the sums of -12.45

Step-by-step explanation:
A) -21.89 + 9.44 = -12.45
C) -3.18 - 9.27 = -12.45
D) -5.75 + -6.7 = -12.45

The correct answer is (e) Between 890,000 and 900,000 people.

To find out how many people from this city will have a monthly income between £2,000 and £2,300, we need to use the z-score formula:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

First, we'll find the z-score for £2,000:

z = (2000 - 2075) / 162 = -0.46

Next, we'll find the z-score for £2,300:

z = (2300 - 2075) / 162 = 1.39

Using a z-table, we can find the corresponding probabilities for these z-scores. The probability for a z-score of -0.46 is 0.3228, and the probability for a z-score of 1.39 is 0.9177.

To find the probability of having a monthly income between £2,000 and £2,300, we need to subtract the smaller probability from the larger probability:

0.9177 - 0.3228 = 0.5949

This means that approximately 59.49% of the population will have a monthly income between £2,000 and £2,300. To find out how many people this represents, we'll multiply the probability by the total population:

0.5949 * 1,500,000 = 892,350

Therefore, the answer is (e) Between 890,000 and 900,000 people.

To know more about normal distribution refer here:

https://brainly.com/question/29509087#

#SPJ11

Answer: 25%

Step-by-step explanation:

To find the percentage, you divide 6 by 24. That equals 0.25, which is a decimal. You need to make it a percent, so multiply 0.25 by 100 which is equal to 25%.

0 and variance 1.

For (a), L follows a Chi-squared distribution with 6 degrees of freedom. This is because L is a sum of squares of 6 random variables (the 5 Yi - Y plus Y^3).

For (b), J follows a Student's t-distribution with 6 degrees of freedom. This is because it is the ratio of two independent normally distributed random variables with mean 0 and variance 1.

Learn more about Chi-squared

brainly.com/question/14082240

#SPJ11

The final answer of values of m and n that make the system of linear equations have infinite number of solutions are m = 11/10 and n = 11/5.

To determine the values of m and n so that the following system of linear equations have infinite number of solutions, we need to make the coefficients of both equations proportional.

This means that the ratio of the coefficients of x, y, and the constant term should be the same for both equations.

Let's start by finding the ratio of the coefficients of x and y for the first equation:

(2m-1)/3 = 3/(n-1)

Cross-multiplying gives us:

3(2m-1) = 3(n-1)

Simplifying:

6m-3 = 3n-3

6m = 3n

Dividing both sides by 3:

2m = n

Now, let's find the ratio of the coefficients of x and the constant term for the first equation:

(2m-1)/(-5) = 3/(-2)

Cross-multiplying gives us:

-10m + 5 = -6

Simplifying:

-10m = -11

Dividing both sides by -10:

m = 11/10

Substituting this value of m back into the equation 2m = n, we get:

2(11/10) = n

n = 22/10

n = 11/5

Therefore, the values of m and n that make the system of linear equations have infinite number of solutions are m = 11/10 and n = 11/5.

To know more about linear equations refer here:

https://brainly.com/question/11897796#

#SPJ11

1 meter = 1000 millimeter

Answer: :)

Step-by-step explanation:

The metric system is based on the International System of Units (SI), which is a standardized system of measurement used worldwide. The SI unit for length is the meter, and all other units of length in the metric system are derived from it.

The relationship between millimeters and meters can be expressed mathematically as follows:

1 mm = 0.001 m

1 m = 1000 mm

This means that if you have a length measurement in millimeters, you can convert it to meters by dividing by 1000. Conversely, if you have a length measurement in meters, you can convert it to millimeters by multiplying by 1000.

For example, if you have a piece of wire that measures 500 mm long, you can convert this to meters as follows:

500 mm ÷ 1000 = 0.5 m

Similarly, if you have a piece of fabric that measures 2.5 m long, you can convert this to millimeters as follows:

2.5 m x 1000 = 2500 mm

In summary, the relationship between millimeters and meters is that they are both units of length in the metric system, with one meter being equal to 1000 millimeters.

The total number of popsicle sticks needed to make one snowman using the given conditions for system of equations is equal to 9.

Let us consider 'x' is the number of popsicle sticks required to make one pencil cup.

And 'y' represents the number of popsicle sticks required to make one snowman.

The required set up two equations are,

8x + 15y = 271  ___(1)

14x + 15y = 373 ___(2)

Multiplying both sides of equation (1) by 14 and both sides of equation (2) by -8 we get,

112x + 210y = 3794

-112x - 120y = -2984

Add both the above equations to eliminate the x variable we get,

⇒ 112x + (-112x) + 210y + (-120y) = 3794 + (-2984)

Simplifying the equation we get,

⇒90y = 810

Dividing both sides by 90 we get,

⇒ y = 9

Therefore, number of popsicle sticks required to make one snowman is equal to 9.

learn more about popsicle sticks here

brainly.com/question/20312588

#SPJ4

The axis of symmetry of a quadratic function can be found by taking the negative of the coefficient of the x term, and then dividing it by 2. In this case, the coefficient of the x term is -2, so the axis of symmetry is located at x = -1.

The key features of the quadratic function are the vertex, the y-intercept, and the x-intercepts. To find the vertex, substitute the x-value for the axis of symmetry into the equation. In this case, the vertex is located at (x, y) = (-1, 27).

The y-intercept is found by setting x = 0 and solving for y. This gives us y = -24, so the y-intercept is located at (0, -24).

To find the x-intercepts, set y = 0 and solve for x. In this case, the x-intercepts are located at (2, 0) and (6, 0).

To know more about quadratic function refer to-

brainly.com/question/18958913#
#SPJ11

3a and 4b are not like terms, hence they cannot be added, and the result of the expression is 3a + 4b and not 7ab.

Like terms are terms that share these two features:

If two terms are like terms, then they can be either added or subtracted.

3a and 4b on this problem are not like terms, as the letters, in this case a and b, are different.

Thus, the expression cannot be simplified, as only like terms, which are terms whose definition we gave in this explanation, can be simplified.

More can be learned about like terms at brainly.com/question/17471184

#SPJ1

Answer: Y=6/5

Step-by-step explanation:

Y=1/4X+6/5

(set X to zero 1/4(0) = 0)

Y=0+6/5

Y=6/5

The solution to the inequality 2r - 5 ≤ 9 in interval notation is (-∞, 7].

To solve the inequality 2r - 5 ≤ 9, we need to isolate the variable r on one side of the inequality. Here are the steps to do so:

Now, we can present our answer in interval notation. Interval notation is a way to represent an interval on the number line. It is written in the form of [a, b], where a and b are the endpoints of the interval. The square brackets mean that the endpoints are included in the interval.

Since our inequality is r ≤ 7, our interval notation would be (-∞, 7], where -∞ represents negative infinity and 7 is the endpoint. The square bracket on the 7 means that 7 is included in the interval.

Therefore, the solution to the inequality 2r - 5 ≤ 9 in interval notation is (-∞, 7].

For more information about inequality, visit:

https://brainly.com/question/30238989

#SPJ11

The correct name for the polynomial -2x^(3)+5x^(4)-3x is a quartic trinomial.

The student made an error when naming the polynomial as a "cubic trinomial". A cubic polynomial is one where the highest degree is 3, and a trinomial is a polynomial with three terms.

While this polynomial does have three terms, its highest degree is actually 4, as seen in the 5x^(4) term.

Therefore, the correct name for this polynomial would be a "quartic trinomial".

To summarize, the error the student made was naming the polynomial as a cubic trinomial instead of a quartic trinomial. The correct name for the polynomial -2x^(3)+5x^(4)-3x is a quartic trinomial.

To know more about cubic polynomial click on below link:

https://brainly.com/question/28081769#

#SPJ11

The measure of angle IHJ is 131 degree.

The angle subtended by an arc at the center is twice the angle subtended at the circumference . More simply, the angle at the center is double the angle at the circumference.

From the figure,

3) Given that, arc ML=53 degree

∠LHM = 1/2 ×53

= 26.5

Arc MI = 89°

∠MHI=1/2 × 89°

= 44.5°

Here, ∠IHJ+∠MHI+∠LHM+∠LHK+∠KHJ=360°

∠IHJ+44.5°+26.5°+88°+70°=360°

∠IHJ=360°-229°

∠IHJ=131°

4) Arc WV= 1/2 ×55° = 27.5°

Here, Arc WT = Arc TU + Arc UV + Arc WV

= 50°+100°+27.5°

= 177.5°

5) Here, HG= 1/2 ×40 =20°

Arc FH= Arc FG+ Arc HG°

= 60°+20°

= 80°

Therefore, the measure of angle IHJ is 131 degree.

To learn more about the circle theorems visit:

https://brainly.com/question/19906313.

#SPJ1

The rate at which the water level is rising when the water is 3m deep is 0.159 m/min.  The rate at which the tip of his shadow is moving when he is 40ft from the pole is 3ft/sec. The volume of a cone is given by V = 1/3πr^2h.

We are given that the base radius is 2m and the height is 4m. We are also given that the rate at which water is being pumped into the tank is 2 m^3/min. We need to find the rate at which the water level is rising when the water is 3m deep.

To find the rate at which the water level is rising, we need to take the derivative of the volume with respect to time. This gives us:

dV/dt = (1/3)π(2r)(dr/dt)(4) + (1/3)π(2^2)(dh/dt)

We know that dV/dt = 2 and r = 2, so we can plug these values into the equation and solve for dh/dt:

2 = (1/3)π(2)(2)(dr/dt)(4) + (1/3)π(2^2)(dh/dt)

Solving for dh/dt gives us:

dh/dt = (6 - 4π(dr/dt))/(4π)

We are given that the water level is 3m deep, so we can plug this value into the equation for the volume of a cone and solve for r:

V = (1/3)πr^2h

3 = (1/3)πr^2(3)

r = √(3/π)

We can now plug this value of r into the equation for dh/dt and solve for dr/dt:

dh/dt = (6 - 4π(√(3/π))(dr/dt))/(4π)

Solving for dr/dt gives us:

dr/dt = (6 - 4π(dh/dt))/(4π√(3/π))

We can now plug this value of dr/dt back into the equation for dh/dt and solve for dh/dt:

dh/dt = (6 - 4π((6 - 4π(dh/dt))/(4π√(3/π))))/(4π)

Solving for dh/dt gives us:

dh/dt = 0.159 m/min

The street light is mounted at the top of a 15ft tall pole and the man is 6ft tall. The man is walking away from the pole with a speed of 5ft/sec along a straight path. We need to find the rate at which the tip of his shadow is moving when he is 40ft from the pole.

We can use the properties of similar triangles to relate the height of the pole, the height of the man, the distance of the man from the pole, and the length of the shadow. Let x be the distance of the man from the pole and y be the length of the shadow. Then we have:

15/x = 6/(x + y)

Cross-multiplying gives us:

15(x + y) = 6x

Simplifying gives us:

9x = 15y

Taking the derivative of both sides with respect to time gives us:

9(dx/dt) = 15(dy/dt)

We are given that dx/dt = 5ft/sec, so we can plug this value into the equation and solve for dy/dt:

9(5) = 15(dy/dt)

Solving for dy/dt gives us:

dy/dt = 3ft/sec

To learn more about cone here:

https://brainly.com/question/28109167#

#SPJ11

Answer: The correct response is "Interest rates vary between lenders and can drastically change the monthly payment."

The interest rate is one of the most important things to consider when shopping around for loans because it determines the cost of borrowing money. Different lenders offer different interest rates, and even a small difference in interest rates can have a big impact on the total cost of the loan. A higher interest rate will result in a higher monthly payment, and a longer repayment period, which can make the loan more expensive overall. Therefore, it is important to shop around and compare interest rates from different lenders to find the best deal.

Step-by-step explanation:

6 hairless chimpanzees should the biologist expect to find in the troop.

What is the percentage?

A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

The sample number is 150.

Given that 3% of the chimpanzees are hairless, another sample indicates that 5% are hairless, and a third sample indicates that 4% are hairless.

The average percentage of chimpanzees of hairless is

(3% + 5% + 4%)/3

= 12%/3

= 4%

Now calculate 4% of 150:

4% of 150

= (4/100) × 150

= 6

To learn more about average percentage, click on the below link:

https://brainly.com/question/27024118

#SPJ1

Answer:

Step-by-step explanation:

big semicircle circumference=1/2*3.14*64

100.48cm

small semicircle circumference=1/2*3.14*16=25.12cm

total perimeter=125.6cm

It is feasible to close Hargett St. between Blount Street and Person Street for a day.

Given the traffic flow model described, it is feasible to close Hargett St. between Blount Street and Person Street for a day. The model states that the average daily traffic flow on Hargett St. is 8,000 vehicles per day, with 3,000 vehicles per hour during peak hours. By closing Hargett St. between Blount Street and Person Street for a day, the average daily traffic flow would be reduced by 8,000 vehicles per day. Thus, the total number of vehicles that would be diverted from Hargett St. on the day of the event would be 8,000 vehicles. This amount of traffic would not be too overwhelming for the surrounding streets to handle, since the model states that the average daily traffic flow for those streets is approximately 4,000 vehicles per day.

Learn more about average here:

https://brainly.com/question/30873037

#SPJ4

A1. We can use Gaussian Elimination to determine if the system has a unique solution, infinite many solutions, or no solution. Gaussian Elimination is a method of solving linear equations by reducing a system of equations to a simpler form.

First, we need to write the system of equations in matrix form:

| 2 4 3 | | x1 | = | f |
| 1 d -3 | | x2 | = | g |
| 1 2 c | | x3 | = | h |

Next, we will use Gaussian Elimination to reduce the matrix to row echelon form:

| 1 2 c | | x1 | = | h |
| 0 (d-2) (-3-c) | | x2 | = | (g-h) |
| 0 (4-2d) (3-2c) | | x3 | = | (f-2h) |

Now, we can check for the conditions that determine the number of solutions:

1. If the rank of the coefficient matrix is less than the rank of the augmented matrix, then the system has no solution.

2. If the rank of the coefficient matrix is equal to the rank of the augmented matrix, and the rank is equal to the number of variables, then the system has a unique solution.

3. If the rank of the coefficient matrix is equal to the rank of the augmented matrix, and the rank is less than the number of variables, then the system has infinite many solutions.

In this case, if (d-2) ≠ 0 and (4-2d) ≠ 0, then the system has a unique solution. If (d-2) = 0 and (4-2d) = 0, then the system has infinite many solutions. If (d-2) = 0 and (4-2d) ≠ 0, or (d-2) ≠ 0 and (4-2d) = 0, then the system has no solution.

Therefore, we can find a relation which gives a unique solution or infinite many solutions by using Gaussian Elimination and checking the conditions for the number of solutions.

Know more about Gaussian Elimination here:

https://brainly.com/question/30400788

#SPJ11

The equation that models the objective function for the cost,  C=1x+.80y. (A)

This equation is the correct model because it represents the cost, C, as a function of the number of x and y items. The cost of each x item is $1, and the cost of each y item is $0.80.

Therefore, the total cost will be the sum of the cost of x items and the cost of y items, which is represented by the equation C=1x+.80y.

In contrast, options B, C, and D do not accurately represent the cost as a function of the number of x and y items. Option B includes a subtraction of the cost of y items, which would not accurately represent the total cost.

Options C and D include incorrect coefficients for the cost of x and y items, which would also not accurately represent the total cost.

Therefore, the correct equation to model the objective function for the cost, C, is option A. C=1x+.80y.

To know more about objective function click on below link:

https://brainly.com/question/29185392#

#SPJ11

it should be +60 not +78

when you multiply 18x by X - 3 you obtain 18x² - 54x . Subtract what you have gotten from 18x²-6x you obtain 60x

Two parts of a family budget is Income and expenses. The correct option is c.

The fundamental family budgets cover housing, food, childcare, transportation, health care, other necessities, and taxes.

It's easy to understand the difference between income and expenses: income refers to the funds your organisation receives, whereas expenses refer to the funds it spends.

Net income is typically defined as your revenue, or the total amount of money coming into your business, minus all of your expenses. Your company is profitable if that number is positive.

Therefore, the correct option is c. Income and expenses.

Learn more about income and expense, here:

brainly.com/question/14185533

#SPJ1

Complete question:

What are the two parts of a family budget?

Responses:

Answer: 43.96 inches^2

Step-by-step explanation:

By answering the above question, we may state that A kite has graphs perpendicular diagonals, and the larger diagonal splits the shorter diagonal in half.

Mathematicians use graphs to visually express or chart facts or values in a logical way. Usually, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph

The measurements of the numbered angles in each kite cannot be given without a reference image or particular kite. We can, however, offer some general knowledge on kites and their angles.

With two sets of neighboring congruent sides and angles, a kite is a quadrilateral with congruent sides on all four sides. A kite has perpendicular diagonals, and the larger diagonal splits the shorter diagonal in half.

Let's give a generic kite's angles the labels displayed in the accompanying diagram:

  A-------B

 /         \

D-----------C

To know more about graphs visit:

https://brainly.com/question/11950136

#SPJ1

Answer:

A. y = 52x

Step-by-step explanation:

The equation is set up in slope-intercept form y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0,0) (4, 208)

We see the y increase by 208 and the x increase by 4, so the slope is

m = 208/4 = 52

Y-intercept is located at (0,0)

So, our equation is y = 52x

The answer is option A

Answer:

x=16 and y=9

Step-by-step explanation:

(x+19)+(9x+1)=180

Combine Like Terms

10x+20=180

Subtract 20 from both sides

10x=160

Divide 10 by both sides

x=16

Fill in for x in (9x+1) to help find y

9*16+1

145

3y+8+145=180

Combine like terms

3y+153=180

Subtract 153 from both sides

3y=27

Divide 3 by both sides

y=9

Since the park is isosceles trapezoid-shaped, the two sides, AB and CD, that make up the parallel sides of the trapezoid are of equal length.

An isosceles triangle is a type of triangle with two sides of equal length. It has two equal angles opposite of the two equal sides, and the third angle is usually different. Isosceles triangles are named after the Greek term isoskelēs, which means “equal legs”. They are very common in geometry and are used in many applications, including architecture and engineering.

We can then use the midpoints of the adjacent sides of the trapezoid, E and F, to form a rhombus. Since the rhombus is formed from the midpoints of the two parallel sides, we know that the two sides AE and CF of the rhombus are of equal length. Similarly, the two sides BE and FD of the rhombus are also equal in length. This means that the trail, if constructed in the shape of the rhombus, will have all sides of equal length, satisfying the criteria set by the Parks Commission.

To learn more about isosceles
https://brainly.com/question/29793403
#SPJ1