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10. Mr. and Mrs. Rainer took out a $240,000 to purchase their home. If the interest rate on the loan is 1.2% compounded bimonthly, how much interest will they have paid after 30 years?

The theorems that demonstrate that AC ⊥ BD are Angle Bisector Theorems and Perpendicular Bisector Postulate.

Recall that according to the angle bisector theorem, an angle bisector of a triangle divides the opposing side into two segments that are proportionate to the triangle's other two sides. An angle bisector is a ray that splits a given angle into two equal-sized angles.

In this case

∠1 ≅ ∠2 - Given

hence they is bisected by AX

Also ∠5 ≅ ∠6. This means that they are bisected by CX

Since AX and CX form AC, and

AC = CA (Reflexive Property)
Also

BD = DB  (Reflexive Property)

Then it means that AC ⊥ BC (QED)

Recall that the perpendicular bisector principle deals with congruent triangle segments, allowing for congruent diagonals from the vertices to the circumcenter.

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There are 2 positive residuals and 4 negative residuals.

The residual with the greatest absolute value is -4.8, and the residual with the least absolute value is 0.5.

The absolute values of the residuals are relatively large, indicating that the model does not fit the data well. In general, the data points are not evenly dispersed about the line of fit.

Using the equation y=−x+9.6, we can calculate the predicted values for y as follows:

When x = 1: y = -(1) + 9.6 = 8.6

When x = 2: y = -(2) + 9.6 = 7.6

When x = 3: y = -(3) + 9.6 = 6.6

When x = 4: y = -(4) + 9.6 = 5.6

When x = 5: y = -(5) + 9.6 = 4.6

When x = 6: y = -(6) + 9.6 = 3.6

We can then calculate the residuals by subtracting the predicted values from the actual values of y:

When x = 1: residual = 5.8 - 8.6 = -2.8

When x = 2: residual = 8.7 - 7.6 = 1.1

When x = 3: residual = 2.9 - 6.6 = -3.7

When x = 4: residual = 0.8 - 5.6 = -4.8

When x = 5: residual = 5.1 - 4.6 = 0.5

When x = 6: residual = 1.7 - 3.6 = -1.9

There are 2 positive residuals and 4 negative residuals.

The residual with the greatest absolute value is -4.8, and the residual with the least absolute value is 0.5.

The absolute values of the residuals are relatively large, indicating that the model does not fit the data well. In general, the data points are not evenly dispersed about the line of fit.

Therefore, we can say that the equation y=−x+9.6 is not a good fit for this data.

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The length of the PR is 14 cm by pythagoras theorem

We have to find the length of PR

By using pythagoras theorem we know that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

PR² + RQ² = 50 ²

PR² + 48² = 50 ²

PR² +2304=2500

PR²=2500-2304

PR²=196

PR=14

Hence, the length of the PR is 14 cm by pythagoras theorem

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By making x the subject of the formula in this equation u = cos(0.5x)​ gives x = 2cos⁻¹(u).

In Mathematics and Geometry, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) expressions that are connected by an equal sign.

In this exercise, you are required to make "x" the subject of the formula in the given mathematical equation by using the following steps.

By taking the arc cosine of both sides of the equation, we have the following:

u = cos(0.5x)

cos⁻¹(u) = 0.5x

By multiplying both sides of the mathematical equation by 2, we have the following:

2 × cos⁻¹(u) = 0.5x × 2

x = 2cos⁻¹(u)

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Based on the image attached, The the shape of the distribution is option c) data skewed right.

The term Right skewed is one where the mean  is more prominent than the middle. The mean overestimates the foremost common values in a emphatically skewed dispersion. Cleared out skewed: The mean is less than the median. The mean  is one that has little of the common values in a rightly skewed dissemination.

So, therefore, if  most of the information are on the cleared out side of the histogram but many larger values are on the proper, the information are said to be skewed to the right.

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See text below



Gabriela recorded the ages of her shirts.

·

0 1 2 3 4 5 6 7 8 9 10

Age (years)

Which of these best describes the shape of the distribution?

Choose 1 answer:

Roughly symmetric

Skewed left

Skewed right

Good Question (141)

Answer:

[tex]\textsf{Area}=\dfrac{5\pi -3}{12} \approx 1.06\; \sf square\;units \;(3\;s.f.)\end{aligned}[/tex]

Step-by-step explanation:

To find the area of the shaded region, subtract the area of the isosceles triangle from the area of the sector.

An isosceles triangle is made up of two congruent right triangles.

To find the height of the right triangles (and thus the height of the isosceles triangle), use the cosine trigonometric ratio.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given values:

Substitute these values into the cosine ratio to calculate the height of the right triangles (and thus the height of the isosceles triangle):

[tex]\cos \left(\dfrac{5\pi}{12}\right)=\dfrac{x}{1}[/tex]

[tex]x=\cos \left(\dfrac{5\pi}{12}\right)[/tex]

[tex]x=\dfrac{\sqrt{6}-\sqrt{2}}{4}[/tex]

The base of one of the right triangles can be found by using the sine trigonometric ratio.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given values:

Substitute these values into the sine ratio to determine the base of the right triangle:

[tex]\sin \left(\dfrac{5\pi}{12}\right)=\dfrac{y}{1}[/tex]

[tex]y=\sin \left(\dfrac{5\pi}{12}\right)[/tex]

[tex]y=\dfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]

The base of the isosceles triangle is twice the base of the right triangle, so the base of the isosceles triangle = 2y.

Therefore the area of the isosceles triangle is:

[tex]\begin{aligned}\textsf{Area of isosceles triangle}&=\dfrac{1}{2} \cdot \sf base \cdot height\\\\&=\dfrac{1}{2}\cdot 2y \cdot x\\\\&=\dfrac{1}{2} \cdot 2\left(\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) \cdot \left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)\\\\&=\left(\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) \cdot \left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)\\\\&=\dfrac{4}{16}\\\\&=\dfrac{1}{4}\sf \;square\;units\end{aligned}[/tex]

To find the area of the sector of the circle, use the area of a sector formula (where the angle is measured in radians).

[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\dfrac12 r^2 \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]

Given values:

Substitute the values into the formula:

[tex]\begin{aligned}\textsf{Area of the sector}&=\dfrac{1}{2} \cdot (1)^2 \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{1}{2} \cdot 1 \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{1}{2} \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{5\pi}{12}\;\; \sf square\;units\end{aligned}[/tex]

Finally, to find the area of the shaded region, subtract the area of the isosceles triangle from the area of the sector:

[tex]\begin{aligned}\textsf{Area of the shaded region}&=\sf Area_{sector}-Area_{isosceles\;triangle}\\\\&=\dfrac{5\pi}{12}-\dfrac{1}{4}\\\\&=\dfrac{5\pi}{12}-\dfrac{3}{12}\\\\&=\dfrac{5\pi -3}{12}\\\\&=1.05899693...\\\\&=1.06\; \sf square\;units \;(3\;s.f.)\end{aligned}[/tex]

Therefore, the area of the shaded region is (5π - 3)/12 or approximately 1.06 square units (3 significant figures).

The Triangle is Equilateral and Equiangular.

We will use theses property of Equilateral Triangle as

We have a Triangle.

The Triangle all three angles measured 60 degree each.

and, We know the equilateral Triangle all angles measures 60 degree.

Now, from the figure all the three sides of triangle are equal.

and, we know Equilateral triangle have the three sides equal

Thus, the Triangle is Equilateral and Equiangular.

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Answer:

Step-by-step explanation:

Given:

a₁ = 3

an+1 = (an)² + 1To find:

a₃Solution:

We can use the recursive formula given to find the value of a₃.a₂ = a₁ + 1² = 3 + 1 = 4

a₃ = a₂² + 1 = 4² + 1 = 17Therefore, the value of a₃ is 17.Answer: a₃ = 17

Step-by-step explanation:

To find the expected value of the number of bids won, E(X), we need to multiply each value of X with its corresponding probability and then sum these products.

E(X) = (X1 * P1) + (X2 * P2) + (X3 * P3)

Here, X1 = 0, X2 = 1, X3 = 2, and their corresponding probabilities are P1 = 0.81, P2 = 0.18, and P3 = 0.01.

E(X) = (0 * 0.81) + (1 * 0.18) + (2 * 0.01)

E(X) = (0) + (0.18) + (0.02)

E(X) = 0.20

The expected value of the number of bids won is 0.20.

The expected value of the investment is $600,000.

The expected value of the investment is calculated by multiplying the possible outcomes by their respective probabilities and summing them up. In this case, the possible outcomes are a success or a failure, with probabilities of 0.3 and 0.7 respectively.

If the company succeeds, the investment will be worth $2,000,000. If it fails, the investment will be worth $0. Therefore, the expected value is:

(0.3 x $2,000,000) + (0.7 x $0) = $600,000

This means that the expected value of the investment is $600,000.

Since the expected value of the investment is positive, Mr. Sharp should invest the $100,000. However, it's important to note that expected value is just an estimate and does not guarantee a positive return on investment. There is always a risk associated with any investment, and Mr. Sharp should carefully consider his risk tolerance and financial goals before making any investment decisions.

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Note that in  Circle Q, m∠1  = 66° (Option A)

Note that inthe circle above, the angle which creates the arc 114° lies ont he same line with ∠1. Since sum of angles on a Straight line sum up to 180°.

∠1 = 180 -114 = 66°

A circle is defined as a form made up of points in a two-dimensional plane that are equidistant from a particular location. A circle is defined as a closed curve with no corners or vertices. Circles define several circular forms in our everyday lives.

Circular shapes include:

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The statement that describes the mean is the last one:

"the sum of the prices divided by 7"

For any set of N values {x₁, ..., xₙ}, the mean is given by:

M = (x₁ + ... + xₙ)/N

In this particular case, we have a set of 7 values which is {8, 10, 10, 12, 15, 15, 18}

The mean will be the sum of these 7 values divided by the number of values, which is 7, so the mean is:

M = (8 + 10 + 10 + 12 + 15 + 15 + 18)/7

M = 12.57

The correct option is the last one; The sum of the prices divided by 7

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Step-by-step explanation:

Fred has two possible outcomes on his first test: he either scores less than 60 or he scores 60 or higher.

If he scores less than 60, there is a 55% chance he will pass the course, and a 45% chance he will fail. We know there is a 70% chance he will score less than 60, so the probability that he scores less than 60 and fails the course is 0.7 * 0.45 = 0.315.

If he scores 60 or higher, there is a 70% chance he will pass the course, and a 30% chance he will fail. We don't know the exact probability that he scores 60 or higher, but we know that it is 1 - 0.7 = 0.3 (since there is a 70% chance he scores less than 60). So the probability that he scores 60 or higher and fails the course is 0.3 * 0.3 = 0.09.

Adding these two probabilities together gives us the total probability that Fred gets more than 60 on the first test but fails the course: 0.315 + 0.09 = 0.405. However, we are looking for the probability that he gets more than 60 but fails, so we need to subtract the probability that he scores less than 60 and fails: 0.405 - 0.315 = 0.09. Therefore, the answer is B. 0.09.

i think so...

The value of f(4) for the piecewise function f(x) is found to be 23, hence, option A is correct answer.

The given function is a piecewise function which means it is defined by different formulas for different intervals of x. We need to evaluate f(4) using the formula that applies for the interval that contains 4. Since 4 is in the interval -3 ≤ x ≤ 4, we use the formula f(x) = 2x² - 9 for f(4). To find f(4), we substitute 4 for x in the formula,

f(4) = 2(4)² - 9

Evaluating 2(4)²,

f(4) = 2(16) - 9

Simplifying 2(16) - 9:,

f(4) = 23

Therefore, f(4) = 23. So, the correct answer is Option A.

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Complete question - Determine f(4) for A piecewise function

f(x) = x³ ____ x<-3

f(x) = 2x²-9 ____ -3 ≤ x≤ 4

f(x) = 5x+ ____ when x>4

A. 23

B. 24

C. 41

D. 64

Given that a randomly selected applicant has more than 10 years of experience, the likelihood that they have a graduate degree is roughly 0.4016.

To find the probability that a randomly chosen applicant has a graduate degree given that they have over 10 years of experience, we need to use conditional probability. We can use the formula:

P(grad degree | over 10 years of experience) = P(grad degree and over 10 years of experience) / P(over 10 years of experience)

From the given information, we know that:

P(grad degree and over 10 years of experience) = 51 (number of applicants with over 10 years of experience and a graduate degree)

P(over 10 years of experience) = 127 (number of applicants with over 10 years of experience)

So, plugging in these values:

P(grad degree | over 10 years of experience) = 51 / 127

Using a calculator, we get:

P(grad degree | over 10 years of experience) ≈ 0.4016

Therefore, the probability that a randomly chosen applicant has a graduate degree, given that they have over 10 years of experience, is approximately 0.4016.

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Answer:

The correct answer is option C. (-4,2) lies in the Quadrant II .

Answer:

2a+15b+11

Step-by-step explanation:

2*a + 2*4b + 5 + 7b + 6

2a + 8b + 5 + 7b + 6

2a + 8b + 7b + 5 + 6

2a + 15b + 11

Answer:

Step-by-step explanation:

I don't quite understand the problem but:

2 2/4 -1 =1 1/2, and 3/4 can't be simplified more.

Answer:

? ≈ 9.09

Step-by-step explanation:

using the Sine rule in the triangle

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

where a, b , c are the sides opposite angles A , B , C

we require the third angle in the triangle

third angle = 180° - (51 + 109)° = 180° - 160° = 20°

then with

a = 4 , ∠ A = 20°

b = ? , ∠ B = 51°

[tex]\frac{4}{sin20}[/tex] = [tex]\frac{?}{sin51}[/tex] ( cross- multiply )

? × sin20° = 4 × sin51° ( divide both sides by sin20° )

? = [tex]\frac{4sin51}{sin20}[/tex] ≈ 9.09 ( to the nearest hundredth )

A transformation that would take Figure A to Figure B include the following: D. A counterclockwise rotation of 90° about the origin.

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise around the origin to vertices, the coordinates of the vertices of the image are as follows:

(x, y)                               →                (-y, x)

Ordered pair (-4, 9)        →           Ordered pair (-9, -4)

In conclusion, we can logically deduce that a rotation of 90° counterclockwise around the origin is a type of transformation that would take Figure A to Figure B.

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The solution is: the interest rate and principal is 6% and Rs 65,000

The interest rate, r = 6% and the principal, P = Rs 65,000

Here, we want to find the interest rate and principal

Compound interest:

A = P(1 + r/n)^t

Simple interest :

I = P * r * t

Simple interest for 2 years = Rs 7800

Simple interest for 1 year = Rs 7800 / 2

= Rs 3900

Compound interest for 2 years = Rs 8034

Compound interest for the second year = Rs 8034 - Rs 3900

= Rs 4134

Interest on Rs 3900 = Rs 4134 - Rs 3900

= Rs 234

Therefore,

Interest rate, r = 234/3900 × 100

= 0.06 × 100

r = 6%

Recall,

Simple interest :

I = P * r * t

Then,

P = I / r * t

= 3900 / 6% * 1

= 3900 / 0.06

= 65,000

P = Rs 65,000

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complete question:

compound interest on a sum of money for 2 years compounded annually is Rs 8034 simple interest on the same sum for the same period and at the same rate is Rs 7800 find the sum and the rate of interest​

(a). The ratio of blue marbles to all marbles as 5/14.

(b). The number of blue marbles by the number of red marbles: 5/9

(a) The ratio of blue marbles to all marbles in the bag is 5/14.

To see this, we add the number of blue marbles and the number of red marbles to get the total number of marbles, which is 5 + 9 = 14.

Then we can express the ratio of blue marbles to all marbles as 5/14.

(b) The ratio of blue marbles to red marbles is 5/9. To see this, we divide the number of blue marbles by the number of red marbles: 5 ÷ 9 = 0.55555..., which we can simplify to 5/9.

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Step-by-step explanation:

it follows practically the same rules as a division between plain numbers.

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴

we take the first term (x⁵) and divide it by the x term(s) of the divisor (we ignore constants for the moment). the resulting x term : x⁴

as x⁵/x = x⁴

now we multiply the intermediate result with the full divisior and subtract that result from the left side of the dividend :

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴

- x⁵ - x⁴

--------------

0 0

now we "pull down" the next term of the dividend and we calculate

(0 + 0 + 9x³) / x = 9x²

so, we have now

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x²

and we do the same thing as before (multiply intermediate result with divisor and subtract the result)

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x²

0 0 9x³

- 9x³ - 9x²

---------------

0 0

and, again, we pull down the next term of the dividend abd divide by the x term(s) of the divisor

(0 + 0 + 0 + 0 + 9x) / x = 9

so, we have now

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x² + 9

and we do the same thing as above again

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x² + 9

- 0 0 0 0 9x - 9

-----------

0 - 1

since we ran out of additional terms, we are finished.

the quotient is

x⁴ + 9x² + 9

the remainder is

-1

which makes the full division result

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) =

= x⁴ + 9x² + 9 - 1/(x - 1)

let's check :

(x⁴ + 9x² + 9 - 1(x - 1)) × (x - 1) =

= x⁵ + 9x³ + 9x - x⁴ - 9x² - 9 - 1 =

= x⁵ - x⁴ + 9x³ - 9x² + 9x - 10

perfect.

The length of the pool is 5 meters

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

The length of the pool is calculated as

Length = Surface area / Width

substitute the known values in the above equation, so, we have the following representation

Length = 20/ 4

EValuate

Length = 5

Hence, the length is 5 meters

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The number of jerseys they can purchase for $430 is 53 jerseys.

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Based on the information provided about the cost of the jerseys, we have the following quadratic function;

C = 0.1x² + 2.4x + 25

430 = 0.1x² + 2.4x + 25

0.1x² + 2.4x + 25 - 430 = 0

0.1x² + 2.4x - 405 = 0

By solving the quadratic function using the quadratic formula, we have:

[tex]x = \frac{-(-2.4)\; \pm \;\sqrt{(2.4)^2 - 4(0.1)(-405)}}{2(0.1)}\\\\[/tex]

x = 52.76 ≈ 53 jerseys.

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The rate of change of the number of oil changes with respect to the number of hours will be 3.

The table is given below.

Number of hours              Number of oil changes

            1.5                                          4.5

             3                                             9

           5.5                                         16.5

             8                                            24

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the line gradient linking the interval's ends on the graph depicting the function.

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

The rate of change is calculated as,

Average rate = (24 - 9) / (8 - 3)

Average rate = 15 / 5

Average rate = 3

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14 inches taller by the tallest player than the shortest player on the basketball team. The correct option is A .

To determine how much taller the tallest player is than the shortest player on the basketball team, we need to examine the given line plot and calculate the difference between their heights.

To find the height difference, we need to identify the tallest and shortest players on the team. The line plot should display the heights of each player, allowing us to determine these values.

Once we have these heights, we can subtract the height of the shortest player from the height of the tallest player to calculate the difference.

Based on the options provided, we can consider each possibility:

A. If the height difference is 14 inches, then the tallest player is 14 inches taller than the shortest player. B. If the height difference is 10 inches, then the tallest player is 10 inches taller than the shortest player.

C. If the height difference is 13 inches, then the tallest player is 13 inches taller than the shortest player. D. If the height difference is 12.5 inches, then the tallest player is 12.5 inches taller than the shortest player.

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Answer:

18.85 meters

Step-by-step explanation:

V=πr2h=π·12·6≈18.84956