On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction.
The number b varies directly with the number a. For example b = 22 when a = -22. Which equation represents this
direct variation between a and b?
b=-a
0-b=-a
O b-a=0
Ob(-a)=0

Hello !

Answer:

[tex]\large \boxed{\sf \sum\limits^6_{k=3}(-2k+5)=-16}[/tex]

Step-by-step explanation:

We want to calculate the following sum :

[tex]\sf \sum\limits^6_{k=3}(-2k+5)[/tex]

Let's remember the following property :

[tex]\fbox{\begin{tabular}{1\textwidth}\star\ \underline{\sf Linearity:}\\ \sf \sum\limits^n_{k=n_0}(\alpha a_k+\beta b_k)=\alpha\sum\limits^n_{k=n_0} a_k+\beta \sum \limits^n_{k=n_0}b_k\end{tabular}}[/tex]

Now we can apply this property to our formula :

[tex]\sf \sum\limits^6_{k=3}(-2k+5)\\=-2\sf \sum\limits^6_{k=3}(k)+\sum\limits^6_{k=3}5[/tex]

Now we can calculate :

[tex]\sf \sum\limits^6_{k=3}(-2k+5)\\=-2(3+4+5+6)+(6-3+1)5\\=-2\times18+4\times 5\\=-36+20\\\boxed{\sf \sum\limits^6_{k=3}(-2k+5)=-16}[/tex]

Have a nice day ;)

The proportion by which the later temperature exceeds the earlier temperature is 3/5 or 3:5.

To determine the proportion by which one temperature exceeds the other, we need to calculate the difference between the two temperatures and express it as a proportion of the starting temperature.

First, calculate the temperature difference between 7:00 am and 3:00 pm:

temperature difference = 24°C - 15°C = 9°C

Now, express the temperature difference as a proportion of the starting temperature (15°C).

Proportion = Temperature difference / Starting temperature

Proportion = 9/15

Proportion = 3/5

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Question in English

In a city the temperature was measured at 7:00 am and the value was 15°C, then it was measured at 3:00 pm the value was 24°C. Starting from the level of measurement of this variable, in what proportion does one temperature exceed the other, analyze your answer.

Similarity statement and justification for two similar figures with given measurements. The given figures are AB = 40, AC = 50, and BC = 60. For the second figure, YX = 37.5, YZ = 30, and ZX = 45.

To write a similarity statement, we compare the ratios of corresponding sides of the two figures. So, we can compare AB/BC to YX/ZX and AC/BC to YZ/ZX.AB/BC = 40/60 = 2/3YX/ZX = 37.5/45 = 5/6AC/BC = 50/60 = 5/6YZ/ZX = 30/45 = 2/3Since the ratios of the corresponding sides of both figures are the same, we can say that the two figures are similar.

A similarity statement for these figures can be written as:ΔABC ~ ΔXYZThis statement indicates that the two triangles ABC and XYZ are similar. The symbol ~ is used to denote similarity.

The justification for this similarity statement is based on the fact that the ratios of the corresponding sides of the two figures are equal.

Therefore, by the definition of similarity, we can conclude that the two triangles are similar.

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The three arithmetic means between 10 and 130 are 40, 70, and 100.

To find the three arithmetic means between 10 and 130, we need to calculate the common difference between consecutive terms.

The common difference (d) can be found using the formula:

d = (last term - first term) / (number of terms - 1)

In this case, the first term is 10, the last term is 130, and we need to find three arithmetic means.

d = (130 - 10) / (3 + 1) = 120 / 4 = 30

Now, we can calculate the three arithmetic means by adding the common difference to the previous term:

First arithmetic mean = 10 + 30 = 40

Second arithmetic mean = 40 + 30 = 70

Third arithmetic mean = 70 + 30 = 100

So 40, 70, and 100 are the three arithmetic means between 10 and 130.

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Answer:

The y-intercept of a function is the point where the graph of the function intersects the y-axis. To find the y-intercept of f(x), we can substitute x=0 into the equation for f(x):

f(0) = -3(1.02)^0 = -3

Therefore, the y-intercept of f(x) is -3. To find the y-intercept of g(x), we can look at the table and see that when x=0, g(x)=-3. Therefore, the y-intercept of g(x) is also -3.

Comparing the y-intercepts of the two functions, we see that they are equal. Therefore, the correct answer is:

The y-intercept of f(x) is equal to the y-intercept of g(x).

Step-by-step explanation:

Answer:

The correct answer is A, the y-intercept of f(x) is equal to the y-intercept of g(x).

Step-by-step explanation:

First, note that the y intercept is what y is equal to when x is equal to 0.

The given function, f(x), is an exponential function. Exponential functions are written in the formula [tex]f(x) = a(1 + r)^x[/tex], where a = y-intercept!

a in the function f(x) is -3, so this means that the y intercept is -3.

In the given table, g(x), the y value is -3 when the x value is 0.

This means that in the g(x) table, the y-intercept is also -3.

Thus, A is correct and the y-intercept of f(x) is equal to the y-intercept of g(x).

Answer:

? = 157°

Step-by-step explanation:

the measure of the secant- secant angle KLM is half the difference of the intercepted arcs , that is

[tex]\frac{1}{2}[/tex] (CJ - KM) = ∠ KLM , that is

[tex]\frac{1}{2}[/tex] (? - 53) = 52° ( multiply both sides by 2 to clear the fraction )

? - 53° = 104° ( add 53° to both sides )

? = 157°

Answer:

Step-by-step explanation:

Remember PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction)

35 - 12 : 2 + 8² =

35 - 6 + 64 =

93

Answer:

The five-number summary of the data represented by the given box plot is: Min: 72, Q1: 76, Median: 79, Q3: 80.5, Max: 84. Therefore, the correct option is: Min: 72, Q1: 76, Median: 79, Q3: 80.5, Max: 84.

Step-by-step explanation:

Answer:

The correct answer is

A.    [tex]pq^4r^4[/tex]

Step-by-step explanation:

The answer is:

3x + 12

Work/explanation:

To simplify this expression, we will use the distributive property:

[tex]\sf{3(x+4)}[/tex]

Distribute the 3:

[tex]\sf{3\cdot x + 3 \cdot 4}[/tex]

[tex]\sf{3x+12}[/tex]

Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.

To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest earned

P = Principal (initial investment)

r = Interest rate per year (expressed as a decimal)

t = Time (in years)

Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:

4850 * 0.076 * t = 8000

Simplifying the equation:

369.8t = 8000

To find t, we divide both sides of the equation by 369.8:

t ≈ 8000 / 369.8 ≈ 21.62 years

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The surface area of a cylinder is 284m² and it's volume is 366.9m³

To find the surface area and volume of a cylinder, we need to know the radius (r) and height (h) of the cylinder. The formulas for the surface area (A) and volume (V) of a cylinder are as follows:

From the given question, the data are;

a. The surface area of the cylinder is;

SA = 2π(4)² + 2π(4)(7.3)

SA = 283.999≈284m²

b. The volume of the cylinder is

v = πr²h

v = π(4)²(7.3)

v = 366.9m³

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Answer:

  A. The multiplication that takes place while distributing comes before addition and subtraction in order of operations.

Step-by-step explanation:

You want to know the error that adding -4+4 on the left and 1+1 on the right represents in the solution of the equation ...

The correct solution procedure would be to eliminate the parentheses using the distributive property as a first step:

  4x -6x +8 +4 = -x +3x +3 +1

Comparing this to Maricella's first step, we see that she ignored the step of using the distributive property to multiply the constants inside parentheses by the factor outside. The appropriate description of Maricella's mistake is ...

A. The multiplication that takes place while distributing comes before addition and subtraction in order of operations.

__

Additional comment

Adding like terms would give ...

  -2x +12 = 2x +4

  8 = 4x . . . . . . . . . . . add 2x-4 to both sides

  2 = x . . . . . . . . . . divide by 4

<95141404393>

Answer:25.12

Step-by-step explanation:

Use the second equation

C = 8(3.14) = 25.12

Answer:

Area = 50.24 feet²

Circumference = 25.12 feet

Step-by-step explanation:

If the circle's diameter is 8 feet, then the radius will be 4 feet.

A=4²(3.14)

=16(3.14)

=50.24

C=2π(4)

C=8π

C≅25.12

The present value of the stream of savings estimates is approximately $200,256.

To determine whether the firm should make the investment in new software, we need to calculate the present value of the stream of savings estimates and compare it to the cost of the software.

The present value (PV) of the savings estimates can be calculated using the formula:

[tex]PV = C1/(1+r)^1 + C2/(1+r)^2 + ... + Cn/(1+r)^n[/tex]

Where C1, C2, ..., Cn represent the savings in each year, r is the minimum annual return required (8% or 0.08), and n is the number of years (5).

Given the savings estimates in the table, we have:

C1 = $35,000

C2 = $45,000

C3 = $50,000

C4 = $55,000

C5 = $60,000

Plugging these values into the present value formula and using the minimum annual return rate of 8% (0.08), we can calculate:

[tex]PV = 35000/(1+0.08)^1 + 45000/(1+0.08)^2 + 50000/(1+0.08)^3 + 55000/(1+0.08)^4 + 60000/(1+0.08)^5[/tex]

Evaluating this expression, we find that the present value of the stream of savings estimates is approximately $200,256.

Since the present value of the savings estimates is greater than the cost of the software ($172,395), the firm should make this investment. The investment is expected to provide a return greater than the minimum required annual return of 8%.

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The present value of the stream of savings estimates is $149,622.

To determine if the firm should make the investment, we need to calculate the present value of the stream of savings estimates and compare it to the initial cost of the software.

The present value (PV) of the savings estimates can be calculated using the formula:

PV = C1/(1+r)¹ + C2/(1+r)² + ... + Cn/(1+r)ⁿ

Where:

PV = Present value

C1, C2, ..., Cn = Cash flows in each period

r = Discount rate (minimum annual return)

Given the savings estimates in the table over a 5-year period and a minimum annual return of 8% (0.08), we can calculate the present value as follows:

PV = $15,000/(1+0.08)¹ + $35,000/(1+0.08)² + $50,000/(1+0.08)³ + $45,000/(1+0.08)⁴ + $40,000/(1+0.08)⁵

PV = $13,888.89 + $30,864.20 + $41,152.46 + $34,682.34 + $29,034.09

PV = $149,621.98 (rounded to the nearest dollar)

The present value of the savings is higher than the initial cost of the software ($172,395), the firm should make this investment if it requires a minimum annual return of 8% on all investments.

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Part I- a) y = (x + 25)(x + 9)

b) y = x^2 + 34x + 225

c) y=  (x + 17)^2 - 64

d) The y-intercept is (0, 225), The y-intercept is (0, 225).

e) The graph of the parabola has the vertex at (-17, -64), x-intercepts at (-25, 0) and (-9, 0), and the y-intercept at (0, 225).

f) Only positive values of x make sense because the dimensions of a pool and deck cannot be negative.

g) y = 465 square yards

Part II- a) y = (6 + 2x)^2

b) 169 = (6 + 2x)^2

c) x = 3.5 feet

Part I:

y = (x + 25)(x + 9)

b) To rewrite the equation in standard form using the FOIL method:

y = x^2 + 9x + 25x + 225

= x^2 + 34x + 225

c) To rewrite the equation in vertex form by completing the square:

y = (x^2 + 34x) + 225

= (x^2 + 34x + (34/2)^2) + 225 - (34/2)^2

= (x^2 + 34x + 289) + 225 - 289

= (x + 17)^2 - 64

d) The vertex of the parabola is (-17, -64). The x-intercepts are found by setting y = 0 and solving the equation:

0 = (x + 17)^2 - 64

64 = (x + 17)^2

x + 17 = ±√64

x + 17 = ±8

x = -17 ± 8

x = -25, -9

Therefore, the x-intercepts are (-25, 0) and (-9, 0).

The y-intercept is obtained by setting x = 0 in the equation:

y = (0 + 17)^2 - 64

y = 17^2 - 64

y = 289 - 64

y = 225

Therefore, the y-intercept is (0, 225).

e) The graph of the parabola has the vertex at (-17, -64), x-intercepts at (-25, 0) and (-9, 0), and the y-intercept at (0, 225).

f) Only positive values of x make sense because the dimensions of a pool and deck cannot be negative. In this context, negative values for x would not provide meaningful solutions for the width of the deck.

g) The point on the graph that represents the total area including the pool but not the pool deck is the y-intercept (0, 225).

h) When x = 6 yards, the total area of the pool and deck can be found by substituting the value into the equation from Part b:

y = (6 + 17)^2 - 64

y = 23^2 - 64

y = 529 - 64

y = 465 square yards

Part II:

a) The equation for the area of the enclosed space in the form y = (side length)^2, considering the hot tub and the deck around it, is:

y = (6 + 2x)^2

b) Substituting the area of the enclosed space (169 square feet) for y in the equation:

169 = (6 + 2x)^2

c) Solving the equation for x:

√169 = √((6 + 2x)^2)

13 = 6 + 2x

2x = 13 - 6

2x = 7

x = 7/2

x = 3.5 feet

Therefore, the width of the deck space around the hot tub is 3.5 feet.

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The number of paperback copies sold is 366,300.

Let's solve the problem :

Calculate the number of hardback copies sold.

We are given that 35,000 hardback copies were sold before the paperback version was issued.

Calculate the number of paperback copies sold.

From the time the first paperback copy was sold until the last copy of the novel was sold, nine times as many paperback copies as hardback copies were sold.

Let's assume the number of hardback copies sold is H.

Therefore, the number of paperback copies sold would be 9H.

Set up the equation for the total number of copies sold.

The problem states that a total of 442,000 copies of the novel were sold in all. We can set up the equation as follows:

H + 9H + 35,000 = 442,000

Solve the equation for H.

Combining like terms, we have:

10H + 35,000 = 442,000

10H = 442,000 - 35,000

10H = 407,000

H = 40,700.

Calculate the number of paperback copies sold.

We already know that the number of paperback copies sold is 9 times the number of hardback copies sold.

Therefore, the number of paperback copies sold would be:

9H = 9 [tex]\times[/tex] 40,700 = 366,300

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The resulting equation after multiplying the first equation by 2 and subtracting the second equation is:

-5y = -375

1. Given equations:

  - x + 3y = 350    (Equation 1)

  - 2x + 4y = 625   (Equation 2)

2. Multiply Equation 1 by 2:

  - 2(x + 3y) = 2(350)

  - 2x + 6y = 700    (Equation 3)

3. Subtract Equation 2 from Equation 3:

  - (2x + 6y) - (2x + 4y) = 700 - 625

  - 2x - 2x + 6y - 4y = 75

  - 2y = 75

4. Simplify Equation 4:

  -2y = 75

5. To isolate the variable y, divide both sides of Equation 5 by -2:

  y = 75 / -2

  y = -37.5

6. Therefore, the resulting equation is:

  -5y = -375

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The ages of the seven family members are 12, 16, 16, 45, 45, 45, and 80 years.

To solve this problem, let's break it down step by step:

1. We are given that the mean age of the family is 23 years. The mean is calculated by summing up all the ages and dividing by the number of family members. Since there are seven family members, the total sum of their ages is 7 * 23 = 161 years.

2. The median age is 16 years. This means that when the ages are arranged in ascending order, the fourth age is 16. Since there are seven family members, the fourth age is the middle age. Therefore, the ages in ascending order are: _ _ 12 16 _ 45 _.

3. The modes are 12 years and 45 years, which means these two ages occur more frequently than any other age. Since the median is 16, it can't be one of the modes. Hence, we can conclude that the family members' ages are: _ _ 12 16 16 45 _.

4. The range is 35 years, which is the difference between the highest and lowest ages. Since the ages are arranged in ascending order, the highest age must be 45 + 35 = 80 years. Therefore, the ages of the family members are: _ _ 12 16 16 45 80.

In summary, the ages of the seven family members are 12, 16, 16, 45, 45, 45, and 80 years.

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The ordered pairs which are in the solution set of the system of linear inequalities are (5, –2), (3, 1), (4, 2).

The correct answer to the given question is option C.

The system of linear inequalities is:y > -1/2 x y < 1/2 x + 1

On a coordinate plane, two straight lines are shown.

The first solid line has a negative slope and goes through (0, 0) and (4, -2).

Everything above the line is shaded.

The second dashed line has a positive slope and goes through (-2, 0) and (2, 2).

Everything below the line is shaded.

We will check which of the given ordered pairs lie in the solution set of this system of linear inequalities. 1. (5, -2) Putting x = 5 and y = -2, we get:

y > -1/2 x   ⇒   -2 > -1/2 (5)   ⇒   -2 > -2.5  which is false.

xy < 1/2 x + 1   ⇒   (5)(-2) < 1/2 (5) + 1   ⇒   -10 < 3.5  which is false.

Therefore, the ordered pair (5, -2) is not in the solution set of the system of linear inequalities. 2. (3, 1) Putting x = 3 and y = 1, we get:

y > -1/2 x   ⇒   1 > -1/2 (3)   ⇒   1 > -1.5  which is true.

xy < 1/2 x + 1   ⇒   (3)(1) < 1/2 (3) + 1   ⇒   3 < 2.5  which is false.

Therefore, the ordered pair (3, 1) is not in the solution set of the system of linear inequalities. 3. (-4, 2) Putting x = -4 and y = 2, we get:y > -1/2 x   ⇒   2 > -1/2 (-4)   ⇒   2 > 2  which is false. xy < 1/2 x + 1   ⇒   (-4)(2) < 1/2 (-4) + 1   ⇒   -8 < -0.5  which is true.

Therefore, the ordered pair (-4, 2) is in the solution set of the system of linear inequalities. Hence, the answer is (5, –2), (3, 1), (4, 2).

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The best deal over 5 years would be investing at 7.8% compounded quarterly.

Although the interest rates of 7.87% compounded semi-annually and 7.72% compounded every minute may appear slightly higher, the frequency of compounding plays a significant role in determining the overall return.

Compounding more frequently leads to a higher effective annual rate. In this case, compounding quarterly provides a greater compounding frequency than semi-annual or minute-by-minute compounding, resulting in higher returns over time.

When interest is compounded quarterly, the compounding occurs four times a year, whereas semi-annual compounding only occurs twice a year. Compounding every minute may seem more frequent, but the actual effect on the return is minimal since there are a large number of minutes in a year.

Therefore, the 7.8% compounded quarterly is the best deal over 5 years as it offers a higher effective annual rate compared to the other options.

In summary, investing at 7.8% compounded quarterly is the most advantageous choice over a 5-year period. The frequency of compounding plays a crucial role in determining the overall return, and compounding quarterly provides a greater compounding frequency compared to semi-annual or minute-by-minute compounding.

It is essential to consider both the interest rate and the compounding frequency when evaluating investment options to make an informed decision.

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Step-by-step explanation:

87,959 ==> 88,000 is the nearest hundred

The answer is:

Work/explanation:

When rounding to the nearest hundredth, round to 2 decimal places (DP).

Which means we should round to 5.

5 is followed by 9, which is greater than or equal to 5. So, we drop 9 and add 1 to 5 :

87. 96

Answer:

6b + 5n = 101

Step-by-step explanation:

The correct system of equations that can be used to find b, the number of bracelets Ily sold, and n, the number of necklaces she sold is:

b + n = 18

6b + 5n = 101

In this system, the first equation represents the total number of items sold, which is 18. Since b represents the number of bracelets and n represents the number of necklaces, the equation b + n = 18 reflects that the total number of bracelets and necklaces sold should add up to 18.

The second equation represents the total amount of money Ily earned from selling bracelets and necklaces. Since bracelets were sold for $6 each and necklaces for $5 each, the equation 6b + 5n = 101 represents the total amount of money earned, which is $101.

Therefore, the correct system of equations is:

b + n = 18

6b + 5n = 101

The different coordinates after respective rotation are:

1) A'(2, 0)

2) A'(0, -2)

3) A'(-2, 0)

There are different methods of transformation such as:

Translation

Rotation

Dilation

Reflection

Now, the coordinate of the given point A is: A(0, 2)

1) The rule for rotation of 90 degrees clockwise is:

(x, y) →(y,-x)

Thus, we have:

A'(2, 0)

2) The rule for rotation of 180 degrees is:

(x, y) → (-x,-y)

Thus, we have:

A'(0, -2)

3) The rule for rotation of 180 degrees is:

(x, y) → (-y,x)

Thus, we have:

A'(-2, 0)

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The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

The sample variance (s²) is approximately 29.5 and the sample standard deviation (s) is approximately 5.4.

To find the sample variance and standard deviation,

Calculate the mean (average) of the given data set.

21 + 12 + 6 + 7 + 10 = 56

Mean = 56 / 5 = 11.2

Square the result of subtracting the mean from each data point.

(21 - 11.2)² = 96.04

(12 - 11.2)² = 0.64

(6 - 11.2)² = 27.04

(7 - 11.2)² = 17.64

(10 - 11.2)² = 1.44

Calculate the sum of the squared differences

96.04 + 0.64 + 27.04 + 17.64 + 1.44 = 142.8

Divide the sum by (n-1), where n is the number of data points (in this case, 5).

142.8 / (5-1) = 35.7

The result is the sample variance (s²).

Take the square root of the sample variance to determine the sample standard deviation (s).

s = √35.7 ≈ 5.4

Therefore, the sample variance is approximately 29.5 (rounded to one decimal place) and the sample standard deviation is approximately 5.4 (rounded to one decimal place).

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OThe presence of identical fossil plants in both Antarctica and Australia, within the same rock formations, supports the hypothesis of a supercontinent and the process of plate tectonics by providing evidence of past land connections and the subsequent separation of continents due to tectonic activity.

The presence of identical fossil plant species in rock formations of both Antarctica and Australia suggests that these two regions were once connected geographically. The similarity in the fossil record indicates that the plants existed in a shared ecosystem or environment at some point in the past.

The geological formations in which the fossil plants are found can provide further evidence. If the rock layers containing the fossils can be matched across Antarctica and Australia, it suggests that these regions were once part of the same landmass. This correlation supports the idea of a supercontinent.

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Answer:

Step-by-step explanation:

If {0, 3, 6, 9} are are your x's or domain  or input and there are no repeats, then yes TRUE it is a function.

The measure of the angle m∠RQS subtended by the arc RS at the circumference is equal to 70°

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

arc RS = 2(m∠RQS)

Also arc AD = 140°

2(m∠RQS) = 140°

m∠RQS = 140°/2 {divide through by 2}

m∠RQS = 70°

Therefore, the measure of the angle m∠RQS subtended by the arc RS at the circumference is equal to 70°

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The joint probability is found by multiplying the probability of event J by the probability of event K P(J and K) = P(J) * P(K) Option C.

When two events J and K are independent, it means that the occurrence or non-occurrence of one event does not affect the probability of the other event. In other words, the probability of event J happening is completely unrelated to the probability of event K happening.

The joint probability of two independent events J and K is the probability that both events J and K occur simultaneously. Since the events are independent, the probability of their intersection is equal to the product of their individual probabilities.

The joint probability is found by multiplying the probability of event J by the probability of event K.

This formula holds true for independent events because there is no interaction or dependency between the events. Each event has its own probability, and when they occur together, the joint probability is simply the product of their individual probabilities. Option C is correct.

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