An arc of length 21 meters subtends a central angle of 287° in a
circle.
a) Find the circumference of the circle & area.

A recursive formula for this geometric sequence is;

Option C:

a₁ = -1/8

aₙ = (-1/8)a⁽ⁿ⁻¹⁾

The geometric sequence is given as;

-1/8, -1/4, -1/2, -1, . . .

The general formula used to find the nth term of a geometric sequence is;

aₙ = a(r)⁽ⁿ⁻¹⁾

where;

a is first term

d is common ratio

where;

r = (-1/4)/(-1/8)

r = 2

Thus;

aₙ = -1/8(2)⁽ⁿ⁻¹⁾

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Step-by-step explanation:

4x^3 + 7x^2 + 10    <====standard form

    degree  is 3 (this is the largest exponent)     and there is three terms

`C(p,k) * C(n-p,k)`

a. Proof: We will apply the same method we used in formula (1) in our class notes on this question. For this purpose, we choose a set containing `n + 1` elements. It contains all elements of the set of `n` elements and another element `y` that has not been included in the set of `n` elements.Let the number of sets of `n` elements that contain `k` particular elements `a` be `P(n, k)`. To count the number of sets of `n + 1` elements that contain `k` elements, we use the concept of permutations with repetition, such as -{n + 1} can be placed in any of the `k` places of the k-element subsets of `{1, 2,...,n}`, or it can be one of the remaining `n-k+1` elements in each of the `P(n,k)` sets that contain `k` elements.Let us use `A` to denote the set of sets of `n` elements that do not contain the element `y` and `B` to denote the set of sets of `n` elements that contain the element `y`. Then, `P(n+1,k)=|A|+|B|=P(n,k)+(n−k+1)P(n,k−1)`.b. Proof: To count the number of `k` element subsets from a set of `n` elements, we use `C(n, k)`.Let us consider two sets, `A` and `B`, where `|A|=n-k` and `|B|=p-k`. We want to choose `k` elements from these two sets such that the number of subsets we get from `A` is `x` and the number of subsets we get from `B` is `y`. In the set `A`, we select `x` elements by choosing `k-x` elements from the remaining `n-k` elements. Similarly, in the set `B`, we select `y` elements by choosing `k-y` elements from the remaining `p-k` elements.Thus, the total number of ways of choosing `k` elements from `A` and `B` is given by `C(n-k, x) * C(p-k, y)`. The total number of ways of choosing `k` elements from `n` elements is given by `C(n, k)`. Therefore, the total number of ways of choosing `k` elements from `n` elements such that `x` elements are chosen from `A` and `y` elements are chosen from `B` is `C(n-k, x) * C(p-k, y) * C(n, k)`.To get the total number of ways of choosing `k` elements from `n` elements such that `k` elements are chosen from `A` and `p-k` elements are chosen from `B`, we must sum over all possible values of `x` and `y`. Thus, the total number of ways of choosing `k` elements from `n` elements such that `k` elements are chosen from `A` and `p-k` elements are chosen from `B` is given by: `C(p,k) * C(n-p,k)`  which is the required result.

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In three years, the villa would cost roughly $18,375.64.

We can apply the compound interest formula if a villa's price is rising at a pace of 7% annually:

[tex]A = P(1 + r)^t[/tex]

The principal is the sum that was either lent or borrowed. It is the initial sum of money borrowed or lent in a loan, exclusive of interest or other costs. It serves as the baseline from which interest is determined. The total sum that must be repaid at the conclusion of the loan term is known as the principal amount. It is often referred to as the loan's face value or par value.

from the question:

We can apply the compound interest formula if a villa's price is rising at a pace of 7% annually:

[tex]A = P(1 + r)^t[/tex]

where A represents the overall sum, P represents the initial sum, r represents the annual interest rate in decimal form, and t is the number of years.

In this case, P = $15,000, r = 0.07, and t = 3. Plugging in these values, we get:

A = $15,000[tex](1 + 0.07)^3[/tex]

= $15,000[tex](1.07)^3[/tex]

= $15,000(1.225043)

= $18,375.64 (rounded to two decimal places)

As a result, the villa's price would be roughly $18,375.64 after three years.

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Mr. Yang invested the $1000 approximately 8.55 years ago

To calculate the time that Mr. Yang invested the money, you can use the formula for compound interest: A=P(1+r/n)^nt where A is the amount of money after t years, P is the initial principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years. We are given A= $1435.77, P=$1000, r=0.06, and n=2 (since interest is compounded twice per year). We want to solve for t, so we will rearrange the formula to solve for t:t=ln(A/P)/(n ln(1+r/n))Plugging in the values, we have: t= ln(1435.77/1000)/(2 ln(1+0.06/2)) ≈ 8.55 years, rounded to two decimal places.Therefore, Mr. Yang invested the $1000 approximately 8.55 years ago.

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Answer:

If you multiply a function by a constant value, it will result in a vertical scaling of the graph. In this case, multiplying by 1/3 would compress the graph vertically by a factor of 3. Specifically, the y-coordinates of each point on the graph would be multiplied by 1/3, resulting in a graph that is one-third as tall as the original.

We can use the Pythagorean theorem to find the length of the diagonal of the rectangle. The Pythagorean theorem states that in a right triangle with legs of length a and b and hypotenuse of length c, we have:

a^2 + b^2 = c^2

In this case, the rectangle has dimensions of 14 centimeters by 48 centimeters, so we can let the length and width of the rectangle be the legs of a right triangle, and the diagonal be the hypotenuse. Then:

a = 14 cm b = 48 cm c = ?

We can plug these values into the Pythagorean theorem and solve for c:

14^2 + 48^2 = c^2 196 + 2304 = c^2 2500 = c^2 c = sqrt(2500) c = 50

Therefore, the length of the diagonal of the rectangle is 50 centimeters.

Answer:

50 cm

Step-by-step explanation:

the equation is d=sqrt(w^2+l^2)

so you get sqrt(14^2+48^2) which equals 50.

Answer:

45

Step-by-step explanation:

Draw an imaginary line from F to S. We then break this into 2 parts:

1. Evaluate the area of triangle SFN

The base of the triangle is FS, who has length 9. The height is the vertical line that passes through point N and FS, and that line has length 6. The area would then be 9*6/2=27.

2. Evaluate the area of rectangle SCWF

WC has length 9. FW has length 2. The area would then be 9*2=18.

a) True. This is an example of sampling without replacement because once a person is selected for jury duty, they are no longer available for selection again.

b) 0.5238 is the probability.

a) Sampling without replacement is the technique of choosing a sample from a population without replacing the selected individuals in the population after each selection. In this case, once an eligible person is chosen, they cannot be chosen again.
Hence, the given statement is true.

b) We have to find the probability of all four of the excused jurors being women. We are picking four people out of 70 men and 80 women, or 150 people in total. Since we are dealing with independent events, we may use the multiplication principle for probabilities.
There are 80 women in the 150-person sample, so the probability of selecting one woman is 80/150.
After the first woman is selected, there are 79 women remaining in the 149-person sample, so the probability of selecting another woman is 79/149.
Similarly, the probabilities of selecting a third and fourth woman are 78/148 and 77/147, respectively.

Therefore, the probability that all four excused jurors are women is:
P(4 women) = (80/150) × (79/149) × (78/148) × (77/147)
P(4 women) = 0.5238 (rounded to four decimal places)
The probability that all four of the excused jurors are women is 0.5238.

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Since Lourdes garage is in the shape of a square pyramid, the surface area of the square pyramid roof is 1440 ft²

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The surface area (SA) of a pyramid is given as:SA = B + (1/2)Ph

where B is the base area, P is the perimeter and h is the slant height

Since the roof is a square pyramid with base 40 feet and slant height of 18 ft, hence:

h = 18 ftP = 40 + 40 + 40 + 40 = 160 ft.

Surface area of only roof = (1/2)Ph

Therefore, Substituting:

SA = (1/2)(160)(18) = 1440 ft²

The surface area of the roof is 1440 ft²

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Answer:

The formula for the surface area of a cuboid is:

SA = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the cuboid, respectively.

In this case, l = 6 cm, w = 4 cm, and h = 3 cm. Substituting these values into the formula, we get:

SA = 2(6)(4) + 2(6)(3) + 2(4)(3)

SA = 48 + 36 + 24

SA = 108

Therefore, the surface area of the cuboid is 108 square centimeters.

Step-by-step explanation:

Answer: Surface Area is [tex]72cm^2[/tex].

Step-by-step explanation: Let surface area be a.

[tex]a= 2(5*4)+(5*2)+(4*2)\\a= 2(20+10+8)\\a=2(38)\\a=72 cm^2[/tex]

This means the surface area of the solid cuboid is [tex]72cm^2[/tex].

Hope this helps!

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The resulting constant is 2/5 when (2-4/3) is subtracted from (-3/5 plus 5/3).

Mathematical subtraction includes calculating the difference between two numbers. It is the inverse of addition and is denoted by the symbol "-". When we subtract one number from another, we are essentially finding out how much smaller the second number is than the first number.

We can simplify the expressions inside the parentheses first:

2 - 4/3 = 6/3 - 4/3 = 2/3

-3/5 + 5/3 = -9/15 + 25/15 = 16/15

So the expression (-3/5 + 5/3) - (2 - 4/3) becomes:

(16/15) - (2/3)

To subtract these fractions, we need to find a common denominator, which is the least common multiple of 15 and 3, which is 15. Then we can rewrite both fractions with this denominator:

(16/15) - (2/3) = (16/15) - (10/15)

Now we can subtract the numerators and keep the denominator:

(16/15) - (10/15) = 6/15 = 2/5

Therefore, the resulting constant is 2/5.

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The value of k that solves the proportion is given as follows:

k = 100/9.

The proportional relationship for this problem is defined as follows:

9/10 = 10/k.

Then we cross-multiply, that is we multiply the numerator of one ratio by the denominator of the other ratio, and vice versa, hence:

9k = 10 x 10

9k = 100.

Then we solve for the unknown variable k, applying the division, which is the inverse operation of the multiplication, hence the value of k that solves the proportion is given as follows:

k = 100/9.

The proportional equation for this problem is defined as follows:

9/10 = 10/k.

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Part A:  The amount of unearned interest is $3,225.

Part B: The amount needed to repay the loan using the Rule of 78 is $8,443.75.

Part C: To support our answers to Part A and Part B, the total interest that Christopher would have paid, which is 3,900$. the amount needed to repay the loan using the Rule of 78, which is $8,443.75.

What is an interest?

To determine the amount of unearned interest, we need to find out how much interest Christopher would have paid if he made all 24 payments.

First, we can calculate the total amount he would have paid if he made all 24 payments:

Total amount paid = 475 x 24 = 11,400$

Next, we can subtract the amount borrowed from the total amount paid to find the total interest:

Total interest = Total amount paid - Amount borrowed

Total interest = 11,400$ - 7,500$

Total interest = 3,900$

Since Christopher paid off the loan after 18 months instead of 24 months, he did not pay the full amount of interest he would have paid if he made all 24 payments. The unearned interest is therefore:

Unearned interest = Total interest - (Number of remaining payments / Total number of payments x Total interest)

Unearned interest = 3,900 - (6 / 24 x 3,900)

Unearned interest = 3,225$

Therefore, the amount of unearned interest is $3,225.

What is repay?

Part B:

To determine the amount needed to repay the loan using the Rule of 78, we need to calculate the proportion of the total interest that has been earned by the lender up to the point when Christopher repays the loan.

The Rule of 78 is a method of allocating interest charges based on the sum of the digits of the loan term. In this case, since the loan term is 24 months, the sum of the digits is:

1 + 2 + ... + 4 + 5 = 15

We can use this sum to calculate the proportion of the total interest earned by the lender up to the point when Christopher repays the loan:

Proportion of earned interest = (Number of payments made / Total number of payments) x (Sum of digits of loan term / Total sum of digits)

Proportion of earned interest = (18 / 24) x (15 / 120)

Proportion of earned interest = 0.09375

The total interest paid is 3,900$, so the amount needed to repay the loan using the Rule of 78 is:

Amount needed to repay loan = Amount borrowed + Total interest x Proportion of earned interest

Amount needed to repay loan = 7,500$ + 3,900$ x 0.09375

Amount needed to repay loan = 8,443.75$

Therefore, the amount needed to repay the loan using the Rule of 78 is $8,443.75.

Part C:

To support our answers to Part A and Part B, we calculated the total interest that Christopher would have paid if he made all 24 payments, which is 3,900$. We also calculated the unearned interest, which is the difference between the total interest and the interest that Christopher actually paid when he paid off the loan early.

Using the Rule of 78, we calculated the proportion of the total interest earned by the lender up to the point when Christopher repaid the loan, which is 0.09375. We then used this proportion to calculate the amount needed to repay the loan using the Rule of 78, which is $8,443.75.

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According to the problem, Alvin is 12 years younger than Elga, and the sum of their ages is 66. So, we have to use algebra to find Elga's age.

Step-by-step explanation:

Let's assume Elga's age to be x.

Alvin's age can be found as: x - 12

The sum of their ages is 66. So,

x + (x - 12) = 66 ⇒ 2x - 12 = 66

⇒ 2x = 78

⇒ x = 39

Therefore, Elga's age is 39 years old.

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Using the length and breadth οf the rectangular kitchen, fοund using the distance fοrmula, we fοund the area as 165 sq. feet.

The internal angles οf a rectangle, which has fοur sides, are all exactly 90 degrees. At each cοrner οr vertex, the twο sides cοme tοgether at a straight angle.

Here, Pοints (7,6) and (7.-9) lie οn the same hοrizοntal line as the x values are the same

Sο the distance between these pοints can be taken as the length οf the rectangle.

The distance can be fοund using the distance fοrmula.

Length l = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

             = [tex]\sqrt{(7-7)^2 + (6--9)^2} = \sqrt{15^2} = 15[/tex]

Nοw the pοints  (7,6) and (-4,6) lie οn the same vertical line as the y values are the same.

Sο the distance between these pοints can be taken as the breadth οf the rectangle.

Breadth b = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex] = [tex]\sqrt{(7--4)^2 + (6-6)^2} = \sqrt{11^2} = 11[/tex]

Since it is a rectangle, the οppοsite sides will have the same measurements.

Nοw the area = l * b = 15 * 11 = 165 sq. feet.

Therefοre using the length and breadth οf the rectangular kitchen, fοund using the distance fοrmula, we fοund the area as 165 sq. feet.

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Answer: When do you need it done?

Step-by-step explanation: ?

Answer:

Step-by-step explanation:

x+y=17

x-y = 7

From equation 2, x = 7 + y

put this in equation 1.

(7+y) + y = 17

7+2y = 17

2y = 10

y = 5.

We said that x = 7+y

thus, x = 7 + 5

x = 12.

2x+2y=36

2(x+y) = 36

Thus, x + y = 18.

x+y = 18

x-y=6 using elimination (literally simplifying this)

2x = 24 (y-y=0. ELIMINATED!)

x = 12

When x = 12,

x+y=18

12+y=18

y=6.

3x = y

x + y = 20

From 1, y = 3x.

x + (3x) = 20

4x = 20

x = 5.

when x = 5,

y = 3x

y = 3(5)

y = 15.

x+y = -4

xy = -21

from 1, x = -4-y

=> y(-4-y)= -21

-y²-4y = -21

Therefore,

y² + 4y -21 = 0

y= 3 or -7.

When y = 3,

x + 3 = -4

x= -7.

When y = -7,

x + (-7) = -4

x-7=-4

x = 3.

Hope these help! :)

*fingers cracking*

Answer: Let's use the following system of equations to represent the given information:

h + c = 131    (the total number of burgers sold is 131)

2.5h + 2.75c = 342    (the total value of the burgers sold is $342)

where h represents the number of hamburgers sold and c represents the number of cheeseburgers sold.

We can use the first equation to solve for one of the variables in terms of the other:

h + c = 131

h = 131 - c

Substituting this into the second equation, we can solve for c:

2.5h + 2.75c = 342

2.5(131-c) + 2.75c = 342

327.5 - 2.5c + 2.75c = 342

0.25c = 14.5

c = 58

So, 58 cheeseburgers were sold. We can use the first equation to find the number of hamburgers sold:

h + c = 131

h + 58 = 131

h = 73

Therefore, 73 hamburgers were sold.

Let x be the number of medium bags of chips that Bradford bought. Then, he bought 20 - x large bags of chips.

According to the problem, the total cost of the chips was $53. We can set up an equation for the total cost in terms of x:

diff

2x + 3(20-x+6) = 53

2x + 54 - 3x + 18 = 53

-x = -19

x = 19

So, Bradford bought 19 medium bags of chips and 20 - 19 = 1 large bag of chips.

Enjoy!

Step-by-step explanation:

The values of ST and QR based on the information regarding the square will be 7 and 9.9

The square is a geometric figure that belongs to the parallelograms. The square has the following properties:

All four sides have the same length. The four angles measure 90. The sum of its angles is equal to 360

The diagonals are congruent. The diagonals bisect each other.

We get a PQRS square with PR=14. We are required to find ST and QR.

First, since the figure is a square, we must know that the diagonals are congruent. Therefore, we are required to find ST and QR:

PR = SQ = 14.

ST = 14/2 = 7

QR = sin 45 × 14

QR = 9.9

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Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

part A)

the table shows that in 10 attempts

Blue was hit 5 times

Yellow was hit 2 times

Green was hit 2 times

Purple was hit 1 time

so the experimental probabilities are

Blue 5/10 = 1/2 = 0.5

Yellow 2/10 = 1/5 = 0.2

Green 2/10 = 1/5 = 0.2

Purple 1/10 = 0.1

part B)

the theoretical probability of Purple with an equally spaced spinner of 4 colors is 1/4 = 0.25

Answer: 130 degrees

Step-by-step explanation:

The line equals 180 degrees

50+j=180

180-50=130

Answer:

130 Degrees

Step-by-step explanation:

180-50 = 130

Answer: -2

Step-by-step explanation: Find the midpoint of both points so they are equidistant meaning that the ratios between them are 1:1.

To do so, add both quantities given and divide by 2.

[tex](-7+3)/2\\(-4)/2\\-2[/tex]

Which is the answer!

Answer:

plot the point at -2

Step-by-step explanation:

The length of arc AB for the given circle is found to be 13.60 units.

Plotting two lines from the arc's ends to the circle's center, measuring the angle at the point where the two lines intersect the center, and then solving for L by cross-multiplying are useful methods for calculating an arc's length.

And use the arc length method, one may determine a circle's arc length given its radius and center angle.

So,

Radius r = 13 units

Central Angle Ф = 60 degree.

Arc length AB = 60 * 3.14 * 13 /180

Arc length AB = 13.60

Thus, the length of arc AB for the given circle is found to be 13.60 units.

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Answer:

17

Step-by-step explanation:

To find the median of 16 even numbers, we need to arrange the numbers in order from least to greatest, and then find the middle value.

Since the numbers are even, the middle two values will need to be averaged to find the median.

Let's assume the 16 even numbers are:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32

Now, we arrange them in order from least to greatest:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32

The middle two numbers are 16 and 18. So, we need to average them to find the median:

Median = (16 + 18) / 2 = 17

Therefore, the median of 16 even numbers is 17.

Answer:

P=(1100+1400)2

Step-by-step explanation:

Therefore , the solution of the given problem of probability comes out to be there is a 0.7569 percent chance that more than 82 executives agree that Tuesdays are when workers are most effective.

The primary goal for every procedure's criteria-based methods is to ascertain the probability that a statement is true or that a specific event will occur. Chance can be represented by any number range between 0 and 1, where 0 usually represents probability and 1 usually reflects degree of certainty. A probability illustration displays the possibility that a specific event will take place.

Here,

a.

=> P(X < 90) = F(89)

We can determine: Using a computer or a spreadsheet

=> Binom.dist(89, 200, 0.48, TRUE) = 0.0016 when

=> P(X  90) = F(89) (rounded to 4 decimal places)

Therefore, there is a 0.0016 percent chance that fewer than 90 of the executives agree that workers are most effective on Tuesdays.

b.

=> P(X > 100) = 1 - P(X < 100) = 1 - F(100)

We can determine: Using a computer or a spreadsheet

=> Binom.dist(100, 200, 0.48, TRUE)

=> 0.0668 for P(X > 100) = 1 - F(100) = 1 - (rounded to 4 decimal places)

Therefore, there is a 0.0668 percent chance that more than 100 executives agree that Tuesdays are when workers are most effective.

c.

=> P(X > 82) = 1 - P(X < 82) = 1 - F(82)

We can determine: Using a computer or a spreadsheet

=> Binom.dist(82, 200, 0.48, TRUE) = 0.7569, P(X > 82) = 1 - F(82) = 1

Therefore, there is a 0.7569 percent chance that more than 82 executives agree that Tuesdays are when workers are most effective.

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The solution of the system of equations from the graph is x = 2.

The point of intersection formula is used to determine where two lines meet, or the point at which they intersect. In Euclidean geometry, the intersection of two lines can be either an empty set, a point, or a line. Two lines must meet certain requirements in order to intersect, including being in the same plane and not being skew lines. The intersection of these lines may be determined using the intersection formula.

The solution of the system of equations can be determined from the graph by determining the point of intersection between the two lines.

From the graph we observe that the point of intersection of the two lines is at (0, 2).

Hence, the solution of the system of equations is x = 2.

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Answer:

[tex]\huge\boxed{\sf x = 6.5 }[/tex]

Step-by-step explanation:

Given that, both the expressions are equal.

So,

7x - 5 = 5x + 8

7x - 5x - 5 = 8

2x - 5 = 8

2x = 8 + 5

2x = 13

x = 13/2

[tex]\rule[225]{225}{2}[/tex]

Answer:

[tex] \sf \: x = 6.5[/tex]

Step-by-step explanation:

Given expressions,

→ 7x - 5

→ 5x + 8

Now we have to,

→ Find the required value of x.

Forming the equation,

→ 7x - 5 = 5x + 8

Then the value of x will be,

→ 7x - 5 = 5x + 8

→ 7x - 5x = 8 + 5

→ 2x = 13

→ x = 13 ÷ 2

→ [ x = 6.5 ]

Hence, the value of x is 6.5.