Prove that cyclic trapezium is always isosceles and its diagonal are equal​

The tοtal interest paid οver the full 40 years the Jacksοns have a lοan fοr the hοuse is apprοximately $137,986.85.

Tο sοlve this prοblem, we can use the fοrmula fοr a fixed-rate mοrtgage payment:

[tex]P = (Pv\times r) / (1 - (1 + r)^{(-n))[/tex]

Where:

Pv = present value οf the mοrtgage

r = mοnthly interest rate

n = tοtal number οf payments

a) Mοnthly payment οn the οriginal 5.75% mοrtgage:

Pv = $150,000

r = 5.75% / 12 = 0.004792

n = 30 years × 12 mοnths per year = 360

[tex]P = (150,000 \times 0.004792) / (1 - (1 + 0.004792)^{(-360))[/tex]

P ≈ $875.25

Therefοre, the mοnthly payment οn the οriginal 5.75% mοrtgage was apprοximately $875.25.

b) Remaining balance after 10 years:

Using an οnline amοrtizatiοn calculatοr οr fοrmula, we can find that the remaining balance after 10 years is apprοximately $111,138.77.

c) Interest paid during the first 10 years:

Using the same amοrtizatiοn calculatοr οr fοrmula, we can find that the tοtal interest paid during the first 10 years is apprοximately $54,316.57.

d) Mοnthly payment οn the refinance 4.375% mοrtgage:

Pv = $111,138.77

r = 4.375% / 12 = 0.003646

n = 30 years × 12 mοnths per year = 360

[tex]P = (111,138.77\times 0.003646) / (1 - (1 + 0.003646)^{(-360))[/tex]

P ≈ $554.62

Therefοre, the mοnthly payment οn the refinance 4.375% mοrtgage is apprοximately $554.62.

e) Tοtal interest paid οver the 30 year term οf the refinance:

Using the same amοrtizatiοn calculatοr οr fοrmula, we can find that the tοtal interest paid οver the 30 year term οf the refinance is apprοximately $82,670.28.

f) Tοtal interest paid οver the full 40 years:

Tο find the tοtal interest paid οver the full 40 years, we can add up the interest paid during the first 10 years and the interest paid οver the 30 year term οf the refinance:

Tοtal interest = $54,316.57 + $82,670.28

Tοtal interest = $137,986.85

Therefοre, the tοtal interest paid οver the full 40 years the Jacksοns have a lοan fοr the hοuse is apprοximately $137,986.85.

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Answer:

l=(60÷w)

Step-by-step explanation:

since area =l×w

thats 60=l×w

l=60÷w

The correct options are A) Pull two times as many green cubes as blue cubes , B) Pull a blue cube 28 times, and E) Pull a red cube 16 times.

To determine which of the following amounts you would expect to pull, we need to calculate the probabilities of drawing each color cube and then apply that probability to 100 draws.

1. Calculate the total number of cubes in the bag:

Total cubes = 7 blue + 4 red + 14 green = 25 cubes

2. Calculate the probability of drawing each color:

P(blue) = 7/25

P(red) = 4/25

P(green) = 14/25

3. Apply the probabilities to 100 draws:

Blue: 100 × (7/25) = 28

Red: 100 × (4/25) = 16

Green: 100 × (14/25) = 56

Now we can evaluate the given statements:

A) Pull two times as many green cubes as blue cubes

56 green cubes is exactly 2 times 28 blue cubes, so A is correct.

B) Pull a blue cube 28 times

As calculated earlier, you would expect to pull a blue cube 28 times. B is correct.

C) Pull 60 red cubes

The expected number of red cubes is 16, not 60. C is incorrect.

D) Pull more blue cubes than green cubes

You would expect to pull 28 blue cubes and 56 green cubes, so D is incorrect.

E) Pull a red cube 16 times

As calculated earlier, you would expect to pull a red cube 16 times. E is correct.

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When the denominator is zero, the divisor is undefined.

In mathematics, division is the process of dividing a quantity into equal pieces or groups. Division reverses the effects of multiplication because it is the inverse operation of multiplication. The amount being divided is referred to as the dividend in division, and the number by which it is being divided is referred to as the divisor. The quotient is the outcome of a division operation.

Explanation:

Left side               Right side

0 ÷ 70 = 0            ⇒ Zero

862 / 0                ⇒ Undefined

97 ÷ 0                  ⇒ Undefined

[tex]\frac{0}{764}[/tex]  = 0                 ⇒ Zero                    

When the denominator is zero, the divisor is undefined.

When the molecule is zero, the divisor is zeros.

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As a result, the rectangle is 2x^2y^3 inches long.

The Latin word rectus, which meaning "right" or "straight," is where the "recto" in "rectangle" comes from. A rectangle possesses straight sides due to its right angles. Rectitude, a different term derived from the same root and denoting moral uprightness.

We may employ the following formula to determine the rectangular area:

area = length x width

Since we are aware of the surface and the breadth in this instance, we can determine the length:

area = 24x^3y^5

width = 12xy^2

area = length x width

24x^3y^5 = length x 12xy^2

When we multiply both sides by 12xy^2, we get:

2x^2y^3 = length

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The student's test score is 0.76 standard deviations above the mean of the class.

A z-score is a measure of how many standard deviations a data point is from the mean of the data set. It is calculated by subtracting the mean from the data point and dividing by the standard deviation. In this case, the teacher wants to convert the test scores into z-scores relative to the mean and standard deviation of the students in the class.

The formula for calculating a z-score is:

z-score = (data point - mean) / standard deviation

Using the mean and standard deviation provided in the question, the teacher can calculate the z-score for each student's test score by plugging in the values into the formula. For example, if a student scored 150 on the test, their z-score would be:

z-score = (150 - 130) / 26.2
z-score = 0.76

This means that the student's test score is 0.76 standard deviations above the mean of the class. The teacher can use this information to understand how each student's test score compares to the rest of the class.

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There are a variety of factors that can lead to violent protests, but two significant factors are perceived injustice and lack of political representation.

Perceived injustice: When people feel that they have been wronged, marginalized, or oppressed by a system or institution, they may resort to violent protest as a way to express their anger and frustration. This is particularly true when people believe that peaceful means of protest have been ignored or have failed to bring about change. For example, if a community feels that they are being unfairly treated by the police, and previous attempts to seek redress through peaceful protests or other channels have failed, they may turn to violent protest as a last resort.

Lack of political representation: When people feel that their voices are not being heard, they may resort to violent protests as a way to force attention to their concerns. This can happen when marginalized groups feel excluded from the political process, or when they feel that their interests are being ignored by those in power. If people feel that their concerns are not being taken seriously, they may turn to violent protest as a way to make their voices heard.

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Answer:

X AXIS WILL BE ON 4,2 AND Y AXIS WILL BE 4,2 ON BEHALF OF BOTH ANGLES HAVING QUADILATERAL AND THEN APPLY THEOREMS FOR THE EASY SOLUTIONS..

Answer: slope is 1/9

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

i  used a website math-way . its a very accurate response. it usually is at least but you should use it.

Therefore , the solution of the given problem of angles comes out to be k can be any number, so θ = 0 + k180 or θ = 180 + k180

A tilt is a form in Euclidean geometry made up of two lines, or conical faces, that divide at the structure's centre and apex. At their junctions, two rays may combine to form an angle. Angle is another outcome of two entities interacting. Dihedral shapes best describe them. A two-dimensional curve can be created by arranging two line beams in various configurations at their ends. The term "angle" was first used in the Latin term "angulus," which is translated as "horn" in English.

Here,

The solution can be factored to begin with:

=> tanθ(tanθ + 3) = 0

Either

=>  tanθ = 0 or tanθ + 3 = 0

will result in the satisfaction of this equation.

When sin = 0, can be any integer multiple of 180 degrees, including zero.

We can find tan by solving for 3 when tan + 3 = 0.

=> tanθ = -3

There are no answers to this problem because there isn't any angle whose tangent is -3.

As a result, the following are the answers to the equation

tan²θ + 3tanθ = 0 :

k can be any number, so θ = 0 + k180 or θ = 180 + k180

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Answer:

1,4,5

Step-by-step explanation:

Jist Multiply these

The current drawn by R2 is 3.333A or 3333mA in parallel combination in ohms.

In a parallel combination, the voltage across both resistors is the same. However, the current is divided between the two resistors based on their individual resistances. Using Ohms law (V = IR), we can find the voltage across the resistors:

According to the specific resistances of the resistors in a parallel circuit, the current is distributed among them. More current will flow through the resistor with the lower resistance than the one with the greater resistance. This is due to the fact that the lower resistance provides less resistance to the current flow. In this instance, R1 will draw more current than R2 since it has a lower resistance than R2.

V = IR1 = (10A)(5Ω) = 50V

V = IR2 = (I)(15Ω)

We can find current I by solving this particular equation:

I = V/R2 = (50V)/(15Ω) = 3.33A

Convert this ampere value to milliamps, in which we have to multiply by 1000:

I = 3.33A * 1000 = 3333mA or 3.333A

Current drawn by R2 is 3.333A or 3333mA.

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Answer:

223.67

Step-by-step explanation:

Answer:

x = 115 , y = 40

Step-by-step explanation:

in a trapezoid

• each lower base angle is supplementary to the upper base angle on the same side.

∠ ART = 40° + 25° = 65°

then

∠ PAR = 180° - ∠ ART = 180° - 65° = 115° , so

∠ PAR = x = 115

the sum of the 3 angles in Δ PAR = 180° , that is

x + y + 25 = 180

115 + y + 25 = 180

140 + y = 180 ( subtract 140 from both sides )

y = 40

The value of the expression 4x+1/3y² when x = 2 and y = 3 is 1/3

In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem.

Finding the value of the expression, we substitute the given values for the variables

(4x+1)/(3y²

when x = 2 and y = 3

4( 2) +1/3(3)²

= 8 + 1/( 3 × 9)

= 9/27

= 1/3

therefore the value of the expression is 1/3

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Answer:

Step-by-step explanation:

A(8) = 9/7A(-5) = -1/3A(3/1) = 2A(-71/1) = -5/36

Function: A(t) = (t+1)/(t-1)For the given function A(t), the following values are to be calculated: A(8), A(-5), A(3/1), and A(-71/1)A(8):We need to substitute t=8 in the function. A(8) = (8+1)/(8-1) = 9/7Therefore, A(8) = 9/7A(-5):We need to substitute t=-5 in the function. A(-5) = (-5+1)/(-5-1) = -1/3Therefore, A(-5) = -1/3A(3/1):We need to substitute t=3/1 in the function. A(3/1) = (3/1+1)/(3/1-1) = (4)/(2/1) = 4*1/2 = 2Therefore, A(3/1) = 2A(-71/1):We need to substitute t=-71/1 in the function. A(-71/1) = (-71/1+1)/(-71/1-1) = (-70/1)/(-72/1) = (-5/36)Therefore, A(-71/1) = -5/36Therefore, the respective answers for the given values of the function A(t) are as follows: A(8) = 9/7A(-5) = -1/3A(3/1) = 2A(-71/1) = -5/36

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Answer:

look on the yt theres alot of helpful things on there and ive had to do this simliar things and stuff so thats why yt viedo of this should help you

Step-by-step explanation: try a yt viedo to help on this math i wish you luck

Answer:

Your anser is u = 6

Step-by-step explanation:

[tex]\frac{6}{7} =\frac{8}{u+5}[/tex]

Cross multiply.

[tex]6*(u+5) =7*8\\\\6u+30=56\\\\6u=56-30\\\\6u=36\\\\u=6[/tex]

Answer:

21/136

Step-by-step explanation:

The probability of selecting a boy from the class on the first draw is 7 boys out of 17 students total, or 7/17.

After the first boy is selected, there will be 6 boys and 10 girls left in the class.

So the probability of selecting a boy on the second draw, given that a boy was already selected on the first draw, will be 6 boys out of 16 remaining students, or 6/16.

To find the probability that both students selected are boys, we can multiply the probabilities of selecting a boy on the first and second draws:

P(boy and then boy) = P(boy on first draw) x P(boy on second draw | boy on first draw)

P(boy and then boy) = (7/17) x (6/16)

P(boy and then boy) = 21/136

Therefore, the probability of selecting two boys from Mr. Smith's class is 21/136.

Answer:

[tex] \frac{21}{136} [/tex]

Step-by-step explanation:

[tex] \frac{7}{17} \times \frac{6}{16} = \frac{7}{17} \times \frac{3}{8} = \frac{21}{136} [/tex]

Jina is taller than 90% of US women if her height is at least 67.3 inches. Jina's height is approximately 67.3 inches.

Jina's height can be found using the z-score formula: z = (x - μ) / σ, where x is Jina's height, μ is the mean height of US women, and σ is the standard deviation of the heights. We need to find the z-score such that the area under the normal curve to the right of it is 0.10 (since Jina is taller than 90% of the population).

Using a z-score table or a calculator, we find that the z-score corresponding to an area of 0.10 is approximately 1.28. Substituting into the z-score formula and solving for x, we get:

1.28 = (x - 64.5) / 2.2

x - 64.5 = 2.816

x = 67.316

Rounding to one decimal place, Jina's height is approximately 67.3 inches.

In other words, Jina is taller than 90% of US women if her height is at least 67.3 inches.

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The coordinate set that describes the image of rectangle MPAT after the translation of 1 unit right and 2 units up is:

M'(2, 4), P'(2, 5), A'(4, 5), and T'(4, 4).

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for the ordered pairs of the vertices of a figure are defined as follows:

The vertices of the original rectangle are given as follows:

M(1, 2), P(1, 3), A(3, 3), and T(3, 2).

The translation is given as follows:

Hence the equation is:

(x, y) -> (x + 1, y + 2).

Then the coordinates of the vertices are given as follows:

M'(2, 4), P'(2, 5), A'(4, 5), and T'(4, 4).

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The response will be P(neither blue nor white) = 0, in accordance with the information provided.

A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, in which the both the numerator and the denominator are divided. In a simple fraction, both are integers. The numerator or decrease of a complicated fraction contains a fraction. The numerator of an appropriate fraction is less than the denominator.

The total probability of all potential outcomes must equal 1. As P(blue) and P(white) are both 1, there cannot be any other card colors. P(neither blue nor white) is therefore equal to zero.

If there are additional cards of different colors and the information provided is insufficient or inaccurate, we can also apply the following formula:

P(neither blue nor white) = 1 - P(blue) - P(white)

Assuming that there are just three possible card colors (blue, white, and another color), the following equation can be constructed using the provided data:

P(blue) + P(white) + P(another color) = 1

P(white) and P(blue) are both 1, so we have:

1 + 1 + P(another color) = 1

When we simplify this equation, we obtain:

P(another color) = -1

The presented information does not support the notion that there are merely three possible card colors, hence this is not a legitimate probability. Hence, the only viable response is.

P(neither blue nor white) = 0

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The answer is 0/1, which can be simplified to 0.

what is probability?

Probability is a measure of the likelihood or chance of an event occurring.

If P(blue) and P(white) are both 1, it means that all the cards are either blue or white.

Let's assume there are a total of n cards. Then,

P(blue) + P(white) = 1

=> Number of blue cards + Number of white cards = n

Given that P(blue) = P(white) = 1, we can conclude that there are n/2 blue cards and n/2 white cards.

Therefore, the probability of choosing a card that is neither blue nor white is the probability of choosing a card of a different color. There are no other colors given, so we can assume that there are no cards of any other color.

Hence, the probability of choosing a card that is neither blue nor white is 0.

So, P(neither blue nor white) = 0.

Therefore, the answer is 0/1, which can be simplified to 0.

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The correct answer is (A): "its sampling distribution is centered exactly at the parameter it estimates."

An estimator is a statistic that is used to estimate an unknown parameter in a population. A point estimator is a single value that is used to estimate the population parameter. The goal of a point estimator is to provide an estimate that is as close to the true value of the parameter as possible.

One way to evaluate the quality of a point estimator is to look at its bias, which is the difference between the expected value of the estimator and the true value of the parameter it is estimating. An estimator is unbiased if its expected value is equal to the true value of the parameter it estimates. In other words, an unbiased estimator is centered exactly at the parameter it estimates.

In the context of the given problem, the sample mean of weekly computer usage time (8.5 hours) is a point estimator for the population mean weekly computer usage time. To evaluate whether this estimator is unbiased, we would need to look at its sampling distribution and check whether its expected value (i.e., the mean of the sampling distribution) is equal to the true population mean.

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The answer is [tex]\(\frac{dy}{dx} = 24x\left( 2x^{2}-1 \right)^{2}-8x\)[/tex]To find [tex]( \frac{d y}{d x} \)[/tex]), let's apply the Chain Rule.

It is the most popular technique for differentiating composite functions, and it involves applying the derivative to the outer function and then to the inner function, multiplied by the derivative of the inner function.

Expression [tex]\(y = u^3 - 2u\) and \(u = 2x^2 - 1\),[/tex] Let us apply the chain rule; [tex]\( \frac{d y}{d x}= \frac{dy}{du}\frac{du}{dx}\)[/tex] , So [tex]\( \frac{d y}{d x}= \left( 3u^{2}-2 \right)\left( 4x \right) \).[/tex]

Put the value of u in the above equation, we have\[tex]( \frac{d y}{d x}= \left( 3\left( 2x^{2}-1 \right)^{2}-2 \right)\left( 4x \right) \)[/tex] , Thus [tex]\(\frac{dy}{dx} = 24x\left( 2x^{2}-1 \right)^{2}-8x\)[/tex] is the answer.

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The correct answer is A. Definition of midsegment. In this step, the proof is demonstrating that the midsegment of a triangle is parallel to the median of the triangle.

A triangle is a three-sided polygon. It is one of the basic shapes in geometry. It has three sides and three angles, with the sum of the angles of a triangle being always 180 degrees. Triangles come in various shapes and sizes, and are classified by their angles or sides. Examples of triangle shapes include equilateral, isosceles and scalene.

The midsegment is defined as the line segment that connects the midpoints of two sides of the triangle. The median is defined as the line segment that connects a vertex of the triangle with the midpoint of the opposite side. Therefore, in order to prove that the midsegment is parallel to the median, the definition of the midsegment must be used. The definition of the midsegment states that it is the line segment that connects the midpoints of two sides of the triangle, which is necessary in order to prove that it is parallel to the median. Therefore, A. Definition of midsegment is the correct answer for this step in the proof.

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If u is indirectly proportional to t³ - 3, the value of u when t = 3 is 5.

Proportional relationships are relationships between two variables where their ratios are equivalent.

Given that;

u is indirectly proportional to t³ - 3;

u ∝ 1/( t³ - 3)

u = k/( t³ - 3)

Where k is the proportionality constant.

First, we determine the proportionality constant.

To find k, we can use the initial condition that;

24 = k / (2³- 3)

24 = k / (8 - 3)

24 = k / 5

k = 24 × 5

k = 120

Hence, the equation relating u and t is:

u = k/( t³ - 3)

Plug in k = 120

u = 120/( t³ - 3)

To find u when t = 3, we can substitute t = 3 into the equation:

u = 120/( t³ - 3)

u = 120/( 3³ - 3)

u = 120/( 27 - 3)

u = 120/24

u = 5

Therefore, the value of u is 5.

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Answer:

ab = -2

Step-by-step explanation:

3ab - 1 = 2ab - 3

(minus 2ab on both sides of the equation)

ab - 1 = -3

(plus one of both sides of the equation)

ab = -2

Answer:

10[tex]x^{5}[/tex]

Step-by-step explanation:

The list is: 30[tex]x^{7}[/tex], 60[tex]x^{5}[/tex], 110[tex]x^{8}[/tex]

Find the GCF

We see

30, 60, and 110 have the greatest common factor is 10.

[tex]x^{7}[/tex], [tex]x^{5}[/tex], [tex]x^{8}[/tex] have the greatest common factor is [tex]x^{5}[/tex]

So, the greatest common factor for the list of terms is 10 [tex]x^{5}[/tex]