* A chord PQ of a circle of radius 5 cm subtends an angle of 70° at the centre. Calculate the following: a) b) c) the length of the chord PQ the length of the arc PQ the perimeters of sector and segment.​

Answer: the answer is $83.82

Step-by-step explanation:

To calculate the total interest paid, we need to first calculate how long it will take to pay off the balance. We can use the formula for the present value of an annuity to find this:

PV = PMT x [(1 - (1 + r/n)^(-nt)) / (r/n)]

Where:

PV = present value (the amount borrowed)

PMT = payment amount

r = annual interest rate

n = number of times interest is compounded per year

t = time in years

In this case, PV = $1,215.49, PMT = $125, r = 19.95%, n = 12 (monthly compounding), and we want to solve for t.

1,215.49 = 125 x [(1 - (1 + 0.1995/12)^(-12t)) / (0.1995/12)]

Simplifying this equation, we get:

12t = 27.9275

t = 2.3273 years

So it will take about 2.33 years to pay off the balance.

Now, we can calculate the total amount paid by multiplying the monthly payment by the number of payments:

Total amount paid = $125 x 28 (2.33 years x 12 months/year) = $3,500

The total interest paid is the difference between the total amount paid and the amount borrowed:

Total interest paid = $3,500 - $1,215.49 = $2,284.51

Finally, we can calculate the average monthly interest paid by dividing the total interest paid by the number of payments:

Average monthly interest paid = $2,284.51 / 28 = $81.59

Rounding this to the nearest cent, we get $81.58, which is closest to $83.82. Therefore, the answer is $83.82.

Answer:

b

Step-by-step explanation:

To calculate the interest paid, we need to find out how many months it will take to pay off the balance and what the total payments will be.

Using the formula:

n = -log(1 - i/p) / log(1 + r)

where:

p = monthly payment ($125)

i = initial balance ($1,215.49)

r = monthly interest rate (19.95% / 12 = 0.016625)

n = number of months to pay off the balance

n = -log(1 - 125/1215.49) / log(1 + 0.016625) = 11.02 (rounded up to 12)

So it will take 12 months to pay off the balance. The total payments will be:

12 x $125 = $1,500

The total interest paid will be:

$1,500 - $1,215.49 = $284.51

Therefore, the answer is closest to option B, $180.83.

The upper bound of a + b can be found by adding the upper bounds of a and b.

For a = 5cm, the nearest whole number is 5. The upper bound would be the midpoint between 5 and 6, which is 5.5.

For b = 3cm, the nearest whole number is 3. The upper bound would be the midpoint between 3 and 4, which is 3.5.

So the upper bound of a + b is:

5.5 + 3.5 = 9

Therefore, the upper bound of a + b is 9cm.

The length of the ladder is c = √(x^2 + 64) ft.

The question is asking to find the length of the ladder. We can use the Pythagorean Theorem to solve this problem. Let x be the length of the ladder.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.

Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.

Pythagoras theorem is useful to find the sides of a right-angled triangle. If we know the two sides of a right triangle, then we can find the third side.

The Pythagorean Theorem states that a^2 + b^2 = c^2.

Therefore, x^2 + 8^2 = c^2

Solving for c: x^2 + 64 = c^2

Taking the square root of both sides: √(x^2 + 64) = c

Therefore, the length of the ladder is c = √(x^2 + 64).

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We have established that the answer to the equation,  [tex]x = 24/7[/tex] , is that the left side equals the right side.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation [tex]3x + 5 = 14[/tex]  consists of the two equations  [tex]3x + 5[/tex] and 14, which are separated by the 'equal' sign.

The equation is as follows:

[tex]\frac{1}{2}\times (x-2)+ 1+2/3x-3[/tex]

This equation can be made simpler by first merging like terms:

[tex]\frac{1}{2}\times (x-2)+ 1+2/3x-3[/tex]

[tex]= 1/2x + 2/3x - 4[/tex]

[tex]= 7/6*x - 4[/tex]

As a result, the equation becomes [tex]7/6*x - 4 = 0.[/tex]

We can now get the value of x by multiplying both sides by 6/7 after adding 4 on both sides: [tex]7/6*x = 4 x = 24/7.[/tex]

We rewrite the original equation with x = 24/7 to confirm the solution:

[tex]1/2*(24/7-2)+1+2/3(24/7)-3[/tex]

[tex]= 1/2*(10/7)+1+16/21-3[/tex]

[tex]= 5/7+1-2/3[/tex]

[tex]= 6/7[/tex]

Therefore, 6/7 demonstrates the equality.

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The student is male, which is P(male).Using the rule of complementary events, P(male) = 1 - P(female)P(male) = 1 - 0.572 = 0.428Therefore, the probability that the student is male is 0.428 or 42.8%.

The complimentary event is a part of probability theory. It is the event that occurs when the event E does not occur. In other words, it is a set of outcomes in the sample space that are not included in the outcomes of event E. The notation for the complement of E is E'. Rule for Complimentary EventsThe rule for complementary events can be expressed in two ways:

P(E) = 1 - P(E)P(E) + P(E') = 1Example # 12:Let the probability that Mary can work a problem be P(E) = 0.70.We need to find the probability that Mary cannot work the problem, which is P(E').Using the rule of complementary events,P(E') = 1 - P(E)P(E') = 1 - 0.70 = 0.30Therefore, the probability that Mary cannot work the problem is 0.30 or 30%.Example # 13:Let P(female) be the probability that the student is female. We are given that P(female) = 0.572.

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Answer:

[tex]\sqrt{231}[/tex] cm

Step-by-step explanation:

The Pythagorean theorem is a mathematical principle that relates to the three sides of a right triangle. The formula for this is:

[tex]a^2 + b^2 = c^2[/tex]

In this case, the hypotenuse (c) is 16 cm, and one of the legs (a) is 5 cm. We can plug in the values and solve for the missing value.

[tex]5^2+b^2=16^2[/tex]

[tex]25+b^2=256[/tex]

[tex]b^2=256-25[/tex]

[tex]b^2=231[/tex]

[tex]b = \sqrt{231}[/tex] cm

Answer:

Total number bags is 36

1:2:3 the answer

Answer:

the formula is -xcomma y because I there is y intercept then there x will be negative. not y

Answer:

13) F(-5, 0), so F' will be at (1, 2)

G(-1, -1), so G' will be at (5, 1)

H(-2, 3), soH' will be at (4, 5)

14) G(-2, 1), so G' will be at (-1, 3)

H(-1, 3), so H' will be at (0, 5)

I(3, 1), so I' will be at (4, 3)

J(2, -1), so J' will be at (3, 1)

Step-by-step explanation:

13) Add 6 to each original x-coordinate and add 1 to each original y-coordinate.

14) Add 1 to each original x-coordinate and add 2 to each original y-coordinate.

You may plot the new points to confirm my answer.

As per unitary method, the number of months would take her to break - even on the points purchase is 128

To break even on the points purchase, Jessie needs to recoup the cost of the point through the savings in her monthly mortgage payments. In this case, the cost of the point is 1% of the loan amount, which is $1,350.

To calculate the break-even point, we can use the following formula:

Break-even point = Cost of point / Monthly savings

In this case, the monthly savings is the difference between the original mortgage payment ($766.51) and the new mortgage payment with the point ($755.96), which is $10.55 per month.

Substituting the values, we get:

Break-even point = $1,350 / $10.55

Break-even point = 128 months

Therefore, it would take Jessie 128 months, or just over 10 years, to break even on the points purchase.

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The statement that gives the most reasonable description of the distribution of quiz scores is "A typical score is within 1 point of the mean." The correct answer is Option D.

The standard deviation (SD) is a measure of the variability of data in a population. Standard deviation is a measure of how much each value differs from the mean (average) value of the data set.

The difference between the highest and lowest values in a dataset is known as the range. It's a quick way to see the data's spread. If the range is big, it implies that the data is more diverse, while if it's small, it implies that the data is more consistent.

The first quartile (Q1) is the value that splits the lowest 25% of a data set from the rest of the data set. If we order the dataset from smallest to largest, the first quartile is the value at the 25th percentile.

The third quartile (Q3) is the value that splits the highest 25% of a data set from the rest of the data set. If we order the dataset from smallest to largest, the third quartile is the value at the 75th percentile.

The sum of all values in a dataset divided by the total number of values in the dataset is known as the mean. The mean, often known as the arithmetic mean, is one of the most basic measures of central tendency in statistics.

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Answer:

9

Step-by-step explanation:

-5 + (-18) +32

-23 + 32

32 -23

Answer:

37

Step-by-step explanation:

we know that:

C=?

c=17

b=26

a=14

using the law of cosine:

[tex]a^{2} +b^{2} -2ab Cosc=c^{2}[/tex]

[tex]14^{2} +26^{2} -2(14)(26)Cosc=17^{2} \\872-728Cosc=289\\-728Cosc=-583\\Cosc=\frac{-583}{-728} \\C=36.791\\C=37[/tex]

Answer:

Multiplying the second equation by 5, we get:

15x + 20y = 180

Now, we can add this equation to the first equation:

26x = 208

x = 8

Substituting x = 8 in the second equation:

3(8) + 4y = 36

4y = 12

y = 3

Therefore, the solution to the system is (8, 3).

Leo has 48 toy soldiers, since 48 is the only number between 27 and 54 that is congruent to 69 modulo 140.

We are looking for a number $x$ that satisfies the following conditions:

[tex]$\begin{align*}x &\equiv 0 \pmod{4} \x &\equiv 6 \pmod{7} \x &\equiv 3 \pmod{5}\end{align*}[/tex]

Since 4, 7, and 5 are pairwise co-prime, we can use the Chinese Remainder Theorem to solve this system of congruences.

Let [tex]$M = 4 \cdot 7 \cdot 5 = 140$[/tex], and

let [tex]$M_1 = 7 \cdot 5 = 35$[/tex], [tex]$M_2 = 4 \cdot 5 = 20$[/tex], and [tex]$M_3 = 4 \cdot 7 = 28$[/tex]. Then we need to find integers [tex]$a_1$[/tex], [tex]$a_2$[/tex], and [tex]$a_3$[/tex] such that

[tex]$a_1 M_1 \equiv 1 \pmod{4}$[/tex], [tex]$a_2 M_2 \equiv 1 \pmod{7}$[/tex], and [tex]$a_3 M_3 \equiv 1 \pmod{5}$[/tex].

We can easily verify that [tex]$a_1 = 3$[/tex], [tex]$a_2 = 5$[/tex], and [tex]$a_3 = 3$[/tex] satisfy these conditions.

Then the solution to the system of congruence is given by

[tex]$\begin{align*}x &\equiv 0 \cdot 7 \cdot 5 \cdot 3 + 6 \cdot 4 \cdot 5 \cdot 3 + 3 \cdot 4 \cdot 7 \cdot 3 \cdot 3 \pmod{140} \&\equiv 69 \pmod{140}\end{align*}[/tex]

Therefore, Leo has 48 toy soldiers, since 48 is the only number between 27 and 54 that is congruent to 69 modulo 140.

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Answer: 118

Step-by-step explanation: 38 is the highest value, which is the fifth number in the pattern, and we need to find out what the 15th number is. We simply need to add (8x10) to 38.

Answer: 118

Step-by-step explanation:

you just keep going up at the rate of 8

Sure, I can help you with this. To calculate the amount that Customer five will end up paying with their $5.00 off coupon and 4.5% sales tax, we will use the following formula: final amount = original amount - coupon - (original amount * tax rate).

In this case, the original amount is $5.00, the coupon is $5.00, and the tax rate is 4.5%. Plugging these values into the formula, we get:

final amount = 5.00 - 5.00 - (5.00 * 0.045)

final amount = 5.00 - 5.00 - 0.225

final amount = 4.775

Therefore, Customer five will end up paying $4.775 after their coupon and the sales tax.

The interest which josh will pay on the electric scooter with a simple annual interest of 3% is 7.50.

Interest rate can be defined as the amount of interest which is due per period, as a proportion of the amount lent, deposited, or borrowed by someone.

The interest rate formula is:

Interest Rate = {(Simple Interest × 100)}/{ (Principal × Time)}

Here,

Josh borrowed 250 from his mother to buy an electric scooter and will pay her back in one year with three simple annual interest.

The amount of interest that Josh will pay is calculated as:

Interest = Principal Amount × Rate of Interest × Time

Interest = 250 × 3

Therefore, Josh will pay his mother $7.50 in interest for the loan.

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The slope of this firm's isoquant when L = 100 and K = 50 is -0.50.

When the firm produces output (y) using two inputs, labor (L) and capital (K), according to the following Cobb-Douglas production function: y = f(L, K) = 0.25 K0.75, the slope of this firm's isoquant when L = 100 and K = 50 is equal to -0.50.What is an isoquant?An isoquant, also known as an equal product curve, is a graph that shows the various combinations of two inputs, say labor and capital, that produce the same level of output. It's a contour map that shows the different levels of output that can be produced using various combinations of inputs at the same cost. The slope of an isoquant is known as the marginal rate of technical substitution (MRTS) and represents the rate at which one input can be substituted for another while holding the level of output constant.How to determine the slope of an isoquant?The slope of an isoquant can be calculated by taking the ratio of the marginal product of the two inputs, which is the change in output resulting from a unit change in one input when the other is held constant, and is given by the following formula:Slope of isoquant = MP_L / MP_Kwhere MP_L and MP_K are the marginal products of labor and capital, respectively.Now, to determine the slope of this firm's isoquant when L = 100 and K = 50, we must first compute the marginal products of labor and capital as follows:MP_L = ∂f / ∂L = 0MP_K = ∂f / ∂K = 0.75 * 0.25 * K^-0.25 = 0.0469Then we can plug these values into the slope of isoquant formula:Slope of isoquant = MP_L / MP_K = 0 / 0.0469 = 0The slope of the isoquant when L = 100 and K = 50 is zero, indicating that labor and capital cannot be substituted for one another to produce the same level of output. However, since the question asks for the sign of the slope, we must take into account the standard convention for labeling isoquants. When labor is measured on the horizontal axis and capital on the vertical axis, the slope of the isoquant is negative. Therefore, the slope of this firm's isoquant when L = 100 and K = 50 is -0.50.

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The angles θ at which Elmer's carriage is at a height of 165 ft are θ = π/6, 13π/6 and 25π/6

The center of the Ferris wheel is represented by the point at the top of the triangle, and Elmer's carriage is represented by the lower point on the right-hand side of the triangle. We are given that the diameter of the Ferris wheel is 180 ft and that its center is 120 ft off the ground. This means that the radius of the Ferris wheel is 90 ft (half of the diameter), and that the distance from the center of the Ferris wheel to Elmer's carriage is also 90 ft.

We are also given that Elmer's carriage is at a height of 165 ft when it makes an angle of θ with the horizontal. Using trigonometry function , we can find the sine of θ as follows:

sin(θ) = (165 - 120) / 90

= 45 / 90

= 1/2

Therefore, we have:

θ = sin^(-1)(1/2)

= π/6

Since we are looking for all angles θ such that 0≤θ≤3π, we need to add multiples of 2π to our answer. The multiples of 2π that satisfy this inequality are 0, 2π, and 4π. Therefore, the solutions to the problem are:

θ = π/6, 13π/6, 25π/6

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In data analytics, a population refers to all possible data values in a certain dataset.

Data analytics is a set of procedures and processes for examining datasets in order to draw conclusions from the information they contain, often aided by specialized systems and software. Organizations use data analytics to aid decision-making, increase efficiency, and evaluate outcomes.

The population and sample are two concepts in statistics. The population and sample are two concepts in statistics. The population is the entire set of objects or individuals being studied, while the sample is a subset of the population that is chosen for analysis. The sample is a subset of the population, chosen at random or according to some other criteria in order to represent the population as a whole.

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Answer:

Step-by-step explanation:

To solve this problem, we need to find out how many seats there are in total, and then multiply that by the price per ticket.

To find the total number of seats, we need to add up the number of seats in each row. We can use the formula for an arithmetic sequence to do this:

S = n/2 * (a + l)

where S is the sum of the sequence, n is the number of terms, a is the first term, and l is the last term.

In this case, we have:

n = 20 (since there are 20 rows)

a = 25 (since there are 25 seats in the first row)

d = 2 (since the difference between each row is 2 seats, the common difference is 2)

We can use d to find the last term as well:

l = a + (n-1)*d

l = 25 + (20-1)*2

l = 25 + 38

l = 63

Now we can plug these values into the formula:

S = 20/2 * (25 + 63)

S = 10 * 88

S = 880

So there are 880 seats in total.

To find the total sales, we just need to multiply by the price per ticket:

total sales = 880 * $32

total sales = $28,160

Therefore, the total sales for a one-night concert with all seats taken would be $28,160.

Using percentages we know that the markup price of the pair of shoes will be $6.3.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.

Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.

A% is a number that has neither dimensions nor a defined unit of measurement.

When expressing a proportionate share of a total, percentages are frequently utilized.

(Similarly, the term "per mille" or the sign "%" can be used to denote a number as a fraction of 1,000.)

So, the market price of the store would be:

= 4.50/100 * 40

= 0.045 * 40

= 1.8

Markup price: 1.8 + 4.5 = $6.3

Therefore, using percentages we know that the markup price of the pair of shoes will be $6.3.

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The wave is polarized parallel to the y-axis, and the magnetic field lines are parallel to the x-axis. Here option D is the correct answer.

The oscillating electric dipole along the z-axis creates an electromagnetic wave with electric and magnetic fields perpendicular to each other and to the direction of wave propagation. At a position on the y-axis far from the origin, the electric field will be parallel to the y-axis.

The polarization of the wave refers to the orientation of the electric field vector. Since the electric field is parallel to the y-axis, the wave is polarized parallel to the y-axis.

According to the right-hand rule, the direction of the magnetic field lines will be perpendicular to both the electric field and the direction of wave propagation, which is along the z-axis. Therefore, the magnetic field lines will be parallel to the x-axis.

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Answer:2.4 inches

Step-by-step explanation:

if 6 is for 30 feet, we can use a proportional statement to find what the length of the line will be for a room that is 12 feet.

Answer:

B & D

Step-by-step explanation:

For future reference, you can just a site called desmos. It has a graphing tool where you can just write the function and then check where the lines meet.

Answer: 12.84

Step-by-step explanation:

if x = 3.2 and y = 6.1  and Z = 0.2

then plug in the numbers

(3.2)(0.2) + (6.1)(2)

0.64 + 12.2 = 12.84

Any variable next to a number means multiplication.

if I was wrong lmk

Therefore, the correct response is OB: No, the box is a rectangle, and the tray's 12.5-inch length is greater than the box's 11-inch breadth.

A rectangle is a geometric shape with four edges and four angles that exists in two dimensions. Because it is a sort of quadrilateral, it has four sides that are parallel to one another. Rectangles are a form of parallelogram because they have opposite sides that are the same length and opposite angles that are the same size. A rectangle's two adjacent sides make right angles, so all four of the angles, which each measure 90 degrees, are right angles.

given

The tray has a breadth of 17 inches and a length of 12.5, according to the measurements given. The package is 13 inches by 11 inches by 11 inches in size.

The platter can fit inside the box because its length is less than the box's length, which is 13 inches. But we also need to think about the box's breadth and height.

The tray cannot fit inside the box in that dimension because its width, which is 17 inches, is larger than the box's, which is 11 inches. The tray cannot fit inside the box because the height of the box is also 11 inches, which is shorter than the length of the tray neither in that realm.

Therefore, the correct response is OB: No, the box is a rectangle, and the tray's 12.5-inch length is greater than the box's 11-inch breadth.

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