Andres Michael bought a new boat. He took out a loan for $24,180 at 4.5% interest for 4 years. He made a $4,650 partial payment at 4 months and another partial payment of $3,400 at 6 months. How much is due at maturity? (Do not round intermediate calculations. Round your answer to the nearest cent.)

The length of segment EC is 24 in the given triangle

A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.

3x=2(x+4)

Apply distributive property on RHS

3x=2x+8

Subtract 2x from both sides

x=8

The segment EC =3x

=3(8)

=24

Hence, the length of EC is 24 in the given triangle

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Answer:

27.23 inches

Step-by-step explanation:

question wants circumference over 2π/3 radians

2π/3 times 180/π = 120 degrees

120 is 1/3 of 360

so question wants 1/3 of the circumference

circumference is π times diameter

π times 26 = 81.6814089933

81.6814089933 divided by 3 =

27.2271363311 =

27.23

Answer:

y=2x-6

Step-by-step explanation:

y+4=-2(x-1)

Since the slope intercept form is in the form of:

y=mx+c

Making above equation in this form.

y+4=-2(x-1)

opening bracket

y+4=2x-2

subtracting both side by 4.

y+4-4=2x-2-4

y=2x-6

This equation is the slope intercept form.

The speed of the second pedestrian is 5 kilometers per hour.

Let's say that the speed of the second pedestrian is S.

We know that the other pedestrian walks at a speed of 4km/h, and they (together) travel a distance of 27km in 3 hours, then we can write the linear equation:

(4km/h + S)*3h = 27km

It says that both pedestrians work, together, a total of 27km in 3 hours.

Now we can solve that linear equation for S, to do this, we need to isolate S in the left side of the equation.

4km/h + S = 27km/3h = 9 km/h

S = 9km/h - 4km/h = 5km/h

The speed of the second pedestrian is 5 kilometers per hour.

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The magnitude and direction of the vectors are

11.  <0,4> :

Magnitude = 4

Direction =  90°

12.  <-3,0>:

Magnitude = 3

Direction = 0°

13. <6,5>:

Magnitude = √(61)

Direction =  39.8°

14. <3,7>:

Magnitude = √58

Direction =  66.8°

15. <-2,1>:

Magnitude = √5

Direction =  -26.57°

16. <-10,13>:

Magnitude =  √(269)

Direction =  -37.57°

17. <2,-5>:

Magnitude = √(29)

Direction = -68.2°

18. <8,-4>:

Magnitude =  √(80)

Direction =  -26.57°

19. <-4.-6>:

Magnitude =  √(52)

Direction =  56.3°

20.  <-1,9>:

Magnitude = √(82)

Direction =  -83.66°

We are asked to find the magnitude and direction of the vectors given as <x, y>. We have the formulas for magnitude and direction of the vectors.

Magnitude = √(x²+y²)

and direction, θ = tan⁻¹(y/x)

11. The vector is <0,4>

Magnitude = √(0²+4²) = 4

Direction = tan⁻¹(4/0) = tan⁻¹∞ = 90°

12. The vector is <-3,0>.

Magnitude = √(-3²+0²) = 3

Direction = tan⁻¹(0/-3) = tan⁻¹0 = 0°

13.The vector is <6,5>

Magnitude = √(6²+5²) = √(61)

Direction = tan⁻¹(5/6) = 39.8°

14. The vector is <3,7>

Magnitude = √(3²+7²) = √58

Direction = tan⁻¹(7/3) = 66.8°

15.The vector is <-2,1>

Magnitude = √(-2²+1²) = √5

Direction = tan⁻¹(1/-2) = -26.57°

16.The vector is <-10,13>

Magnitude = √(13²+-10²) = √(269)

Direction = tan⁻¹(-10/13) = -37.57°

17.The vector is <2,-5>

Magnitude = √(2²+-5²) = √(29)

Direction = tan⁻¹(-5/2) = -68.2°

18.The vector is <8,-4>

Magnitude = √(8²+-4²) = √(80)

Direction = tan⁻¹(-4/8) = -26.57°

19.The vector is <-4.-6>

Magnitude = √(-4²+-6²) = √(52)

Direction = tan⁻¹(-6/-4) = 56.3°

20. The vector is <-1,9>

Magnitude = √(-1²+9²) = √(82)

Direction = tan⁻¹(9/-1) = -83.66°

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The number of sodas sold at the baseball game was 119, while the number of hot dogs sold was 72.

Let's assume the number of sodas sold as 'x' and the number of hot dogs sold as 'y'.

According to the problem, the total number of sodas and hot dogs sold is 191, so we can write the equation:

x + y = 191   ...(1)

The problem also states that the number of hot dogs sold was 47 less than the number of sodas sold. Mathematically, we can express this as:

y = x - 47   ...(2)

To find the values of x and y, we can solve the system of equations (1) and (2). Substituting equation (2) into equation (1), we have:

x + (x - 47) = 191

Simplifying the equation:

2x - 47 = 191

2x = 191 + 47

2x = 238

Dividing both sides by 2:

x = 238/2

x = 119

Substituting the value of x back into equation (2):

y = 119 - 47

y = 72

As a result, the total amount of sodas sold is 119, and the total amount of hot dogs sold is 72.

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Answer:

1.5x = 30 - 1.5

Step-by-step explanation:

30 grams minus the weight of the bag 1.5

1.5x x is the number of marbles and the bag so take 1 out and you have an answer which is 28.5 19 marbles

Answer:

132ft

Step-by-step explanation:

Mathius Distance = 3/8 mile

Eva Distance        = 2/5 mile

1 mile = 5,280ft

1. Start by multiplying the mile distance of Mathius to the distance of 1 mile in feet.

5,280ft x 3/8 = 15840ft/8 = 1980ft

2. Do the same thing as number 1 but for Eva's distance now.

5,280ft x 2/5 = 10560ft/5 = 2112ft

3. Subtract Eva's Distance from Mathius' Distance for the answer.

2112ft (Eva) - 1980ft (Mathius) = 132ft

Answer: y= 3/5x 6.8

Step-by-step explanation: The slope for these coordinates is 3/5 because the difference between 5 and 8 is 3, and the difference between -3 and 5 is 5. The y intercept is 6.8 because only with this y intercept the line goes through the points.

Answer:

28. B

29. D

30. A

Step-by-step explanation:

28.

2 5/8 yd × 5/6 yd =

= 21/8 × 5/6 yd²

= 105/48 yd²

= 35/16 yd²

= 2 3/16 yd²

Answer: B

29.

2641 becomes 6241.

In 6241, the 6 is in the thousands place.

6 × 1000 = 6000

Answer: D

30.

90 + 7 × (7 - 1) =

Use the correct order of operations.

= 90 + 7 × 6

= 90 + 42

= 132

Answer: A

Answer: 112.36cm^2

Step-by-step explanation:

Un cuadrado tiene 4 lados de igual longitud.

Si dibujamos la diagonal del cuadrado, podemos ver la imagen como dos triángulos rectángulos.

Donde los lados del cuadrado son los catetos, y la diagonal es la hipotenusa.

Ahora, recordando el teorema de Pitágoras, tenemos que, si A y B son catetos, y H es la hipotenusa:

A^2  + B^2 = H^2

En este caso sabemos que los catetos son iguales (por que es un cuadrado)

A = B.

Y también sabemos que H = 15cm.

A^2 + A^2 = (15cm)^2

2*A^2 = (15cm)^2

A = √((15cm)^2/2) = 15cm/√2 = 10.6 cm.

Ahora conocemos L, el largo de los lados de nuestro cuadrado.

L = 10.6cm

Y sabemos que el área de un cuadrado es igual a el cuadrado de uno de los lados:

Área = L^2 = (10.6cm)^2 = 112.36cm^2

Answer:(24/60)*7=2.8 miles

Step-by-step explanation:

24/60x7

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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The consumer surplus is approximately $145.83.

To find the consumer surplus, we first need to find the demand function's inverse, which gives us the willingness to pay for each unit of the product. The demand function is:

D(x) = √(739 - 3x)

Setting D(x) equal to the equilibrium price of $25, we get:

25 = √(739 - 3x)

Squaring both sides, we get:

625 = 739 - 3x

Solving for x, we get:

So at a price of $25 per unit, the consumer is willing to buy 38 units per month.

Now we can calculate the consumer's surplus.

The consumer\(x = (739 - 625) / 3 = 38\) surplus is the difference between the total amount that consumers are willing to pay for a certain quantity of a good and the total amount they actually pay. In this case, the consumer's surplus can be calculated as:

\(CS = \int_0^{38} [D(x) - 25] dx\)

where D(x) is the demand function, and the integral is taken over the range of 0 to 38, which represents the quantity demanded at a price of $25 per unit.

Evaluating this integral, we get:

\(CS = \int_0^{38} [\sqrt{(739 - 3x)} - 25] dx\\\\= [1/6 (739 - 3x)^{(3/2)} - 25x]_0^{38}\\\\= \$ 145.83\)

Therefore, the consumer surplus is approximately $145.83.

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Answer:

I can't see the table...?

Step-by-step explanation:

I will answer if you have the table.

Answer:

Step-by-step explanation:

The correct answer is a. A larger sample size was used.As per the Law of Large Numbers, the more times an experiment is repeated, the closer the actual results will be to the expected probability. In this case, rolling the cube 100 times provides a larger sample size than rolling it only 20 times. The more rolls that are made, the greater the likelihood that the actual results will converge towards the expected probability of 1/2 for rolling an even number.Option b, The 100 tosses were controlled better, is not relevant to this scenario since the fairness of the cube is assumed.Option c, The expected probability changed when the cube was rolled 100 times, is not true. The expected probability of rolling an even number on a fair six-sided die is always 1/2, regardless of the number of times it is rolled.Option d, The thrower considered only the even rolls, and disregarded the odd rolls, is not a valid assumption. The question states that the number of even rolls was recorded, but it does not imply that odd rolls were disregarded.

Answer:

280 pupils

Step-by-step explanation:

27 + 38 + x = 100 Find what percentage is the Year 9 which is 35%

800 x 0.35 = 280 pupils

Answer: 11/9

Step-by-step explanation:

you would cross out the two 4s(using butterfly method) and make them 1s. So 11 x 1 and 1 x 9 = 11/9

Answer:

11/4 times 4/9 is 11/9

Step-by-step explanation:

We have to find,

(11/4) times 4/9

\((11/4)(4/9) = (11*4/4*9)\)

We can cancel the 4s from the numeratorand denominator to get,

\((11*4/4*9) = (11*1/1*9) = 11/9\\=11/9\)

The answer is 11/9

Answer:

30ft

Step-by-step explanation:

I am pretty sure. Please correct me kindly, if I am wrong.

The expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)

Complex numbers are square root of negative numbers. They are expressed as a + bi

Using the expression

(4+7i)-2i(2+3i)

Expand

4 + 7i - 4i -2i(3i)

4 + 3i - 2(-3)

4 + 6 + 3i

10 + 3i

Hence the expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)

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Answer:

x=0

Step-by-step explanation:

Answer:

0.13 ft/min

Step-by-step explanation:

We are given that

\(\frac{dV}{dt}=15ft^3/min\)

We have to find the increasing rate of change of height of pile  when the pile is 12 ft high.

Let d be the diameter of pile

Height of pile=h

d=h

Radius of pile,r=\(\frac{d}{2}=\frac{h}{2}\)

Volume of pile=\(\frac{1}{3}\pi r^2 h=\frac{1}{12}\pi h^3\)

\(\frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}\)

h=12 ft

Substitute the values

\(15=\frac{1}{4}\pi(12)^2\frac{dh}{dt}\)

\(\frac{dh}{dt}=\frac{15\times 4}{\pi(12)^2}\)

\(\frac{dh}{dt}=0.13ft/min\)

Answer:

56

Step-by-step explanation:

Given data:

Total: 11210

7761 good risk

2499 medium risk

950 poor risk

a) Probability of choose a customer with good risk (gr):

b) Probability that a customer is not a poor risk (pr):

The probability that a randomly selected integer from the first 100 positive integers is divisible by 3 or 5 is 47/100. The events of choosing an integer divisible by 3 and choosing an integer divisible by 5 are not independent.

To find the probability that a randomly selected integer from the first 100 positive integers is divisible by 3 or 5, we need to count the number of integers in this range that are divisible by 3 or 5, or both.

There are 33 integers in the range from 1 to 100 that are divisible by 3: 3, 6, 9, ..., 99. Similarly, there are 20 integers in this range that are divisible by 5: 5, 10, 15, ..., 100. However, some of these integers are divisible by both 3 and 5, which means we have counted them twice. To find the total number of integers that are divisible by 3 or 5, we need to subtract the number of integers that are divisible by both 3 and 5 (which are the multiples of 15):

33 + 20 - 6 = 47

So, there are 47 integers out of the first 100 positive integers that are divisible by 3 or 5.

To find out whether the two events of choosing an integer divisible by 3 and choosing an integer divisible by 5 are independent, we need to check whether the probability of one event changes if the other event has already occurred.

Let A be the event of choosing an integer divisible by 3, and B be the event of choosing an integer divisible by 5. We can find the probabilities of these events as follows:

P(A) = 33/100

P(B) = 20/100

To check for independence, we need to compare the probability of A given that B has occurred (i.e., the probability of choosing an integer divisible by 3, given that we know it is also divisible by 5) with the probability of A without any information about B:

P(A|B) = P(A and B) / P(B)

Since the multiples of 15 are the only integers that are divisible by both 3 and 5, we have:

P(A and B) = P(15) / 100 = 1/20

So,

P(A|B) = (1/20) / (20/100) = 1/4

This means that if we know an integer is divisible by 5, the probability that it is also divisible by 3 is 1/4.

Now, let's compare this with the probability of A without any information about B:

P(A) = 33/100

Since P(A|B) ≠ P(A), we can conclude that the events of choosing an integer divisible by 3 and choosing an integer divisible by 5 from the first 100 positive integers are not independent.

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Answer:

Below

Step-by-step explanation:

3.15 can be read as  3 and 15 hundredths =   3   15/100  = 3  3/20

Answer:  63/20

Step-by-step explanation:

Solution :

The standard time for doing a job in minutes is given by :

Standard time = Normal time + normal time x allowance factor.

Here, it is given that ,

Allowance factor = 20%

                            = 0.20

Normal time of doing a a job = 12 minutes.

Therefore,

Standard time = Normal time + normal time x allowance factor

Standard time = 12 + 12 x 0.20

                        = 12 + 2.4

                        = 14.4

Thus, the standard time for doing the job is 14.4 minutes.

Answer:

\( 129° + (x + 19) ° = 180° \: (angles \: on \: a \: straight \: line) \\ x = 180° - (129° + 19°) \\ x = 32°\)