Your classmate tells you the details of the great deal he got on his mortgage: 30-year 1.1% fixed rate with a 20% down payment

If his new home costs $136,000, what is his down payment?

Answer:

kkrg=u/d

-678/09

=12 ans

Using proportions, it is found that the total amount budgeted for entertainment is of $720.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Researching the problem on the internet, it is found that the day trip amount is 10% of the budget for entertainment, hence:

0.1x = 72

x = 72/0.1

x = 720.

Hence the total amount budgeted for entertainment is of $720.

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Answer:

2.

Step-by-step explanation:

There are 2 complex solutions to this equation:

x^2 = -9

= 3i and -3i.

Answer:

okay but what about

Step-by-step explanation:

x² = 9

Answer:

-4

Step-by-step explanation:

if you switch it you get 12-16 and you have to get a negative so 16-12 is 4 so switch it to a nrgative to get -4

The length of the side of the square is given as follows:

20 cm.

In the figure, there are two expressions used to give the side length to each square, as follows:

In a square, all the four side lengths have the same length, hence the value of x is obtained as follows:

6x - 1 = 4x + 6

2x = 7

x = 3.5 cm.

Then the side length of the square is obtained as follows:

6(3.5) - 1 = 20 cm.

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Answer:

a) s = (4-t)/(t^2+4)^2,   a(t) = (2t^3-24t)/(t^2+4)^3

b) s = 0.2ft, v = 0.12 ft/s,  a = -0.176 ft/s^2

c) t = 2s

d) slowing down for t < 2, speeding up for t > 2

e) 0.327 ft

Step-by-step explanation:

The position function of a particle is given by:

\(s(t)=\frac{t}{t^2+4},\ \ \ t\geq 0\)   (1)

a) The velocity function is the derivative, in time, of the position function:

\(v(t)=\frac{ds}{dt}=\frac{(1)(t^2+4)-t(2t)}{(t^2+4)^2}=\frac{4-t^2}{(t^2+4)^2}\)   (2)

The acceleration is the derivative of the velocity:

\(a(t)=\frac{dv}{dt}=\frac{(-2t)(t^2+4t)^2-(4-t^2)2(t^2+4)(2t)}{(t^2+4)^4}\\\\a(t)=\frac{(-2t)(t^2+4)-4t(4-t^2)}{(t^2+4)^3}=\frac{2t^3-24t}{(t^2+4)^3}\) (3)

b) For t = 1 you have:

\(s(1)=\frac{1}{1+4}=0.2\ ft\\\\v(1)=\frac{4-1}{(1+4)^2}=0.12\frac{ft}{s}\\\\a(1)=\frac{2-24}{(1+4)^3}=-0.176\frac{ft}{s^2}\)

c) The particle stops for v(t)=0. Then you equal equation (2) to zero ans solve the equation for t:

\(v(t)=\frac{4-t^2}{(t^2+4)^2}=0\\\\4-t^2=0\\\\t=2\)

For t = 2s the particle stops.

d) The second derivative evaluated in t=2 give us the concavity of the position function.

\(\frac{d^2s}{dt^2}=a(2)=\frac{2(2)^3-24(2)}{(2^2+4)^3}=-0.062<0\)

Then, the concavity of the position function is negative. For t=2 there is a maximum. Before t=2 the particle is slowing down and after t=2 the particle is speeding up.

e) Due to particle goes and come back. You first calculate s for t=2, then calculate for t=5.

\(s(2)=\frac{2}{2^2+4}=0.25\ ft\)

\(s(5)=\frac{5}{5^2+4}=0.172\ ft\)

The particle travels 0.25 in the first 2 seconds. In the following three second the particle comes back to the 0.172\ ft. Then, in the second trajectory the particle travels:

0.25 - 0.127 = 0.077 ft

The total distance is the sum of the distance of the two trajectories:

s_total = 0.25 ft + 0.077 ft = 0.327 ft

Answer:

Step-by-step explanation:

log(x²+8)=1+log(x)

log(x²+8)-log(x)=1

\(log\frac{x^2+8}{x} =1\\\frac{x^2+8}{x} =10^1\\x^2+8=10x\\x^2-10x+8=0\\x=\frac{10 \pm \sqrt{(-10)^2-4*1*8} }{2} \\=\frac{10 \pm \sqrt{100-32} }{2} \\=\frac{10 \pm \sqrt{68} }{2} \\=\frac{10 \pm 2\sqrt{17} }{2} \\=5 \pm \sqrt{17}\)

Answer:

x = 2 2/3

Step-by-step explanation:

(1/3)/(1/8) = 2 2/3

Answer:

5 is a prime that's the answer

Answer:

The answer is "\(\bold{\frac{(m-1)(m-2)}{(m-n)}}\)"

Step-by-step explanation:

Given:

\(\bold{\frac{(m-n)}{m^2-n^2} + \frac{?}{(m-1)(m-2)} - \frac{2m}{m^2-n^2}=0}\\\\\)

let,  ? = x then,

\(\Rightarrow \frac{(m-n)}{m^2-n^2} + \frac{x}{(m-1)(m-2)} - \frac{2m}{m^2-n^2}=0\\\\\Rightarrow \frac{(m-n)}{m^2-n^2} - \frac{2m}{m^2-n^2}=- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{(m-n)-2m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{m-n-2m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-n-m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-(m+n)}{(m+n)(m-n)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-1}{(m-n)} =- \frac{x}{(m-1)(m-2)} \\\\\)

\(\Rightarrow -((m-1)(m-2))=-x(m-n) \\\\\Rightarrow x= \frac{- (m-1)(m-2)}{- (m-n)} \\\\\Rightarrow \boxed{x= \frac{(m-1)(m-2)}{(m-n)}} \\\)

Answer:

226 cm^3

The mass of plastic used to make cylinder is greater

Step-by-step explanation:

Given:-

- The density of cone material, ρc = 1.4 g / cm^3

- The density of cylinder material, ρl = 0.8 g / cm^3

Solution:-

- To determine the volume of plastic that remains in the cylinder after gouging out a hemispherical amount of material.

- We will first consider a solid cylinder with length ( L = 10 cm ) and diameter ( d = 6 cm ). The volume of a cylinder is expressed as follows:

                                  \(V_L =\pi \frac{d^2}{4} * L\)

- Determine the volume of complete cylindrical body as follows:

                                 \(V_L = \pi \frac{(6)^2}{4} * 10\\\\V_L = 90\pi cm^3\\\)

- Where the volume of hemisphere with diameter ( d = 6 cm ) is given by:

                                 \(V_h = \frac{\pi }{12}*d^3\)

- Determine the volume of hemisphere gouged out as follows:

                                 \(V_h = \frac{\pi }{12}*6^3\\\\V_h = 18\pi cm^3\)

- Apply the principle of super-position and subtract the volume of hemisphere from the cylinder as follows to the nearest ( cm^3 ):

                               \(V = V_L - V_h\\\\V = 90\pi - 18\pi \\\\V = 226 cm^3\)

Answer: The amount of volume that remains in the cylinder is 226 cm^3

- The volume of cone with base diameter ( d = 6 cm ) and height ( h = 5 cm ) is expressed as follows:

                               \(V_c = \frac{\pi }{12} *d^2 * h\)

- Determine the volume of cone:

                              \(V_c = \frac{\pi }{12} *6^2 * 5\\\\V_c = 15\pi cm^3\)

- The mass of plastic for the cylinder and the cone can be evaluated using their respective densities and volumes as follows:

                             \(m_i = p_i * V_i\)

- The mass of plastic used to make the cylinder ( after removing hemispherical amount ) is:

                           \(m_L = p_L * V\\\\m_L = 0.8 * 226\\\\m_L = 180.8 g\)

- Similarly the mass of plastic used to make the cone would be:

                           \(m_c = p_c * V_c\\\\m_c = 1.4 * 15\pi \\\\m_c = 65.973 g\)

Answer: The total weight of the cylinder ( m_l = 180.8 g ) is greater than the total weight of the cone ( m_c = 66 g ).

The volume of the remaining plastic in the cylinder is large, which

makes the weight much larger than the weight of the cone.

Responses:

Density of the plastic for the cone = 1.4 g/cm³

Density of the plastic used for the cylinder = 0.8 g/cm³

From a similar question, we have;

Height of the cylinder = 10 cm

Diameter of the cylinder = 6 cm

Height of the cone = 5 cm

(a) Radius of the cylinder, r = 6 cm ÷ 2 = 3 cm

Volume of a cylinder = π·r²·h

Volume of a hemisphere = \(\mathbf{\frac{2}{3}}\) × π×  r³

Volume of the cylinder after it has been hollowed out, V, is therefore;

Which gives;

\(V = \pi \times 3^2 \times 10 - \frac{2}{3} \times \pi \times 3^3 \approx \mathbf{ 226}\)

(b) Volume of the cone = \(\mathbf{\frac{1}{3}}\) × π × 3² × 5 ≈ 47.1

Mass of the cone = 47.1 cm³ × 1.4 g/cm³ ≈ 66 g

Mass of the hollowed cylinder ≈ 226 cm³ × 0.8 g/cm³ = 180.8 g

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Answer:

It is not a valid sample because it is not a random sample of the population.

Answer:It is not a valid sample because it is not a random sample of the population.

Step-by-step explanation:

got it right

The angle of elevation of the top of the tower from the point on the ground is approximately 30.96 degrees.

To find the angle of elevation of the top of the tower, we can use trigonometry.

Let's denote the angle of elevation as θ.

In a right triangle, the tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

In this case, the side opposite the angle is the height of the tower (10√3 m), and the side adjacent to the angle is the distance from the point on the ground to the foot of the tower (30 m).

Using the tangent function, we can write:

tan(θ) = opposite/adjacent

= (10√3 m) / (30 m)

= (√3/3)

To find the angle θ, we can take the inverse tangent (arctan) of (√3/3):

θ = arctan(√3/3)

Calculating this angle using a calculator, we get:

θ ≈ 30.96 degrees

Therefore, the angle of elevation of the top of the tower from the point on the ground is approximately 30.96 degrees.

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In this problem we have that

EG=2HJ

substitute the given values and solve for x

9x-47=2(35-2x)

9x-47=70-4x

9x+4x=70+47

13x=117

x=117/13

x=9

Find EG

9(9)-47

81-47=34

answer is 34 units

The best representation of the number of tiles that will be needed to cover the Floor is 80 tiles.

The number of tiles needed to cover the floor, we can calculate the total area of the floor and divide it by the area of each tile.

The area of the floor is given by the product of its length and width: 15 feet * 12 feet = 180 square feet.

The area of each tile is given by the product of its length and width: 1.5 feet * 1.5 feet = 2.25 square feet.

To find the number of tiles needed, we divide the total area of the floor by the area of each tile:

Number of tiles = (Total area of the floor) / (Area of each tile) = 180 square feet / 2.25 square feet = 80 tiles.

therefore, the best representation of the number of tiles that will be needed to cover the floor is 80 tiles.

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Answer:

a. x = roses

   y= lavender

b. x + y=36

c. 25x + 5y = 480

d. 19 rose bushes and 1 lavender bush

The width of the duck pond is,

⇒ 27 feet

We can see that the given diagram is a rectangle,

And we know that,

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

Now, By given diagram we have;

We have to given that;

Use the scale drawing to determine how wide the duck pond is.

And there are 4.5 feet in 1 square,

Therefore,

1 square is equal to 4.5 feet

So, we get;

The width of the duck pond is,

⇒ 6 square

We know that,

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Then to find width of duck pond in feet,

Multiply 6 with 4.5

⇒ 6 × 4.5 feet

⇒ 27 feet

Thus, The width of the duck pond is,

⇒ 27 feet

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Answer:

6/8 2/8

Step-by-step explanation:

theres eight sections 6 are gray and 2 are blue

the probability of you getting gray on the first time is 6/8

The probability of you getting blue on the second time is 2/8

Answer:

240

Step-by-step explanation:

60 = 1/4 of x

so: x = 60*4

x = 240

check:

240/4 = 60

60 = 60 true!!

Answer:

240÷4=60

Step-by-step explanation:

docientos cuarenta dividido entre cuatro es igual a sesenta.

True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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Answer:

nice

Step-by-step explanation:

if u have a question j comment this answer

The values of the expressions are;

z³³

d⁻¹⁶

Note that index forms are described as forms used in the representation of numbers or variables too large or small.

Some rules of index forms are;

Then, from the information given, we have that;

(z⁻⁴/z⁶  × z⁵/z⁻⁶)⁻¹¹

Subtract the exponents, we have;

(z⁻² × z⁻¹)⁻¹¹

expand the bracket

z²² ⁺ ¹¹

z³³

(d⁴)⁻³/(d⁶)⁻²  ÷  (d⁴/d⁶)⁻⁸

expand the brackets

d⁻¹²/d¹²  ÷    (d⁻²)⁻⁸

subtract the exponents

d⁰  ÷  d¹⁶

d⁻¹⁶

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Given:

Total number of students, n=12.

The average score of 12 students, a=85.

After Bob took the test, the number of students attended the test, N=13.

The new average score, A=82.

The total score of 12 students is the product of their average score and the number of students.

Hence, the total score of 12 students is,

The total score of 13 students is,

Now, Bob's score can be calculated as,

Therefore, Bob's score on the test is 46.

Answer: No real solutions.

Step-by-step explanation: −x2=8x+20

Step 1: Subtract8x+20  from both sides.

−x2−(8x+20)=8x+20−(8x+20)

−x2−8x−20=0

For this equation: a=-1, b=-8, c=-20

−1x2+−8x+−20=0

Step 2: Use quadratic formula with a=-1, b=-8, c=-20

Answer:  

tan theta = -1

we know tan = opposite/ adjacent

So opposite/adjacent = -1

Multiply by adjacent on each side

opposite = - adjacent

We also know from pythagorean theorem that

opposite ^2 + adjacent ^2 = hypotenuse ^2

Substituting in for adjacent

opposite ^2 + (-opposite ) ^2 = hypotenuse ^2

opposite ^2 + opposite ^2 = hypotenuse ^2

2 opposite ^2 = hypotenuse ^2

Taking the square root on each side

sqrt(2 opposite ^2)   =  sqrt(hypotenuse ^2)

sqrt(2) opposite = hypotenuse

We are now set to find the sec

sec theta = hypotenuse / adjacent

              = sqrt(2) opposite/ adjacent

Replace the opposite = -adjacent

                = sqrt(2) (-adjacent)/adjacent)

                = -sqrt(2)

Step-by-step explanation:

Answer:

tan theta = -1

we know tan = opposite/ adjacent

So opposite/adjacent = -1

Multiply by adjacent on each side

opposite = - adjacent

We also know from pythagorean theorem that

opposite ^2 + adjacent ^2 = hypotenuse ^2

Substituting in for adjacent

opposite ^2 + (-opposite ) ^2 = hypotenuse ^2

opposite ^2 + opposite ^2 = hypotenuse ^2

2 opposite ^2 = hypotenuse ^2

Taking the square root on each side

sqrt(2 opposite ^2)   =  sqrt(hypotenuse ^2)

sqrt(2) opposite = hypotenuse

We are now set to find the sec

sec theta = hypotenuse / adjacent

             = sqrt(2) opposite/ adjacent

Replace the opposite = -adjacent

               = sqrt(2) (-adjacent)/adjacent)

               = -sqrt(2)

Step-by-step explanation:

The probability that at most 2 of the next 10 callers will have to wait more than 8 minutes to have their calls answered is 0.810.

As per the question an online customer service department estimates that about 15 percent of callers have to wait more than 8 minutes to have their calls answered by a person.

The department conducted a simulation of 1,000 trials to estimate the probabilities that a certain number of callers out of the next 10 callers will have to wait more than 8 minutes to have their calls answered.

The simulation is shown in the following histogram(graph provided at the end of solution)

Based on the simulation, according to the bar graph , probability of at most 2 callers out of next 10 callers getting awaited by more than 8min is

P(x≤2) = P(0)+P(1)+P(2) {x is number of persons)

= 0.181+0.345+0.284= 0.810

So required probability is 0.810.

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Answer:

6 red and 1 yellow

Step-by-step explanation:

Multiply 2 and 1/3 by the same value

* 2

4 Red and 2/3 Yellow

*3

6 red and 1 yellow

Etc.

The substance will weigh 9 pounds after  4.5123 hours.

Here it is given that every 3 hours the weight of the substance doubles.

At 12 noon it weighed 2 pounds. Hence we will consider the initial weight to be 2.

Let the weight after x hours be w(x)

Here it doubles in 3 hours, hence the growth rate is 100%

Since the growth rate is given, the equation for the growth rate will be

w(x) = w₀.eˣ

where x = no. of 3-hour spans.

Here

w₀ = 2

and w(x) is given 9

Hence,

2eˣ = 9

or, e²ˣ = 9/2

Taking log on both sides we get

loge²ˣ = ln(9/2)

or, 2xloge = ln(9/2)

Since loge = 1 we get

2x = log(9/2)

or, x = 1.5041

Hence they will become 9 pounds after

3 X 1.5041 hours

= 4.5123 hours

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Answer:

Rounded to whole numbers, if he slept for 33% of the year, he slept for a total of 4 months.

Step-by-step explanation:

Given that in a year there are a total of twelve months, if he slept for 33% of the year, to determine how many months are spent sleeping the following calculation must be performed:

12 - (12 x 33/100) = X

12 - (12 x 0.33) = X

12 - 3.96 = X

8.04 = X

12 - 8.04 = 3.96

Thus, rounded to whole numbers, if he slept for 33% of the year, he slept for a total of 4 months.

Answer:

1) B

2) B

Step-by-step explanation:

1) funtion 1 slope is 4

function 2 we use y2-y1/x2-x1

10-6/3-1

4/2

2 is the slope of function 2

so function 1 is bigger

1) only b is correct because it lands on the same line of y=x

hopes this helps please mark brainliest