NEED HELP ASP PLEASE

The probability that either event A or B will occur is 11/17.

We have,

The Addition Rule for Probability:

P(A U B) = P(A) + P(B) - P(A ∩ B),

where P(A U B) represents the probability of the union of events A and B, P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A ∩ B) represents the probability of the intersection of events A and B.

Now,

P(A) = 9/17

P(B) = 2/17

There is no intersection of Q and B so,

P(A ∩ B) = 0

Now,

P(A U B) = P(A) + P(B) - P(A ∩ B),

Substituting the values.

P(A U B) = The probability that either event A or B will occur.

So,

P(A U B)

= 9/17 + 2/17 - 0

= 11/17

Thus,

The probability that either event A or B will occur is 11/17.

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The cash cycle, also known as the operating cycle or cash conversion cycle, is a financial metric that measures the time it takes for a company to convert its investments in inventory and other resources into cash flow from sales. It provides insight into the efficiency of a company's working capital management.

The cash cycle can be calculated using the following formula:

Cash Cycle = Inventory Conversion Period + Receivables Conversion Period - Payables Conversion Period

1. Inventory Conversion Period (ICP):

ICP measures the average number of days it takes for the company to convert its raw materials into finished goods. It is calculated as:

ICP = (Average Inventory / Cost of Goods Sold) x Number of Days in a Year

Average Inventory = (Opening Inventory + Closing Inventory) / 2

Cost of Goods Sold = Total Sales - Closing Inventory

2. Receivables Conversion Period (RCP):

RCP measures the average number of days it takes for the company to collect payment from its customers. It is calculated as:

RCP = (Average Receivables / Total Sales) x Number of Days in a Year

Average Receivables = (Opening Receivables + Closing Receivables) / 2

Opening Receivables = Total Sales x Percentage of Sales on Credit

Closing Receivables = Total Sales x Percentage of Sales on Credit - Collections

3. Payables Conversion Period (PCP):

PCP measures the average number of days it takes for the company to pay its suppliers. It is calculated as:

PCP = (Average Payables / Total Purchases) x Number of Days in a Year

Average Payables = (Opening Payables + Closing Payables) / 2

Opening Payables = Total Purchases x Percentage of Purchases on Credit

Closing Payables = Total Purchases x Percentage of Purchases on Credit - Payments

Now, let's calculate the cash cycle using the provided information:

Given data:

Opening balances:

Raw material: ₹1,00,000

WIP: ₹45,000

Finished goods: ₹1,35,000

Debtors: ₹6,00,000

Creditors: ₹8,60,000

Closing balances:

Raw material: ₹2,00,000

WIP: ₹65,000

Finished goods: ₹1,25,000

Debtors: ₹5,45,000

Creditors: ₹9,75,000

Costs incurred during the year:

Manufacturing costs: ₹11,60,000

Excise duty: ₹18,80,000

Selling and distribution expenses: ₹6,20,000

Admin. overheads: ₹2,00,000

Total sales: ₹2,01,96,800

Total purchases: ₹1,46,00,000

Percentage of sales on credit: 40%

Percentage of purchases on credit: 70%

1. Calculate the Inventory Conversion Period (ICP):

Average Inventory = (Opening Inventory + Closing Inventory) / 2

Opening Inventory = Raw Material + WIP + Finished Goods

Closing Inventory = Raw Material + WIP + Finished Goods

Opening Inventory = ₹1,00,000 + ₹45,000 + ₹1,35,000 = ₹2,80,000

Closing Inventory = ₹2,00,000 + ₹65,000 + ₹1,25,000 = ₹3,90,000

Average Inventory = (₹2,80,000 + ₹3,90,000) / 2 = ₹3,35,000

Cost of Goods Sold = Total Sales - Closing Inventory

Cost of Goods Sold = ₹2,01,96,800 -

Answer:

The complex number represented by the polar coordinates (4, -π/4) is 4(cos(-π/4) + i*sin(-π/4)).

The expression √(x²y²)  when simplified is i. xy

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

√(x²y²)

When the expression is expanded, we have

√(x²y²) = √(x² * √(y²)

Evaluae the exponents in the expression

So, we have

√(x²y²) = x * y

Evaluae the products in the expression

So, we have

√(x²y²) = xy

Hence, the expression when simplified is i. xy

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The angle measures of the numbered angles from <1- 8 would be listed below as follows:

<1=147°

<2= 33°

<3= 147°

<4=33°

<5=33°

<6=147°

<7=33°

<8=147°

When two parallel lines a crossed by a transverse line then the following occurs:

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The dimensions (length and breadth) of the box are 10r x 8r.

We are given that;

π = 3,142

Number of tins=4,5

Now,

To calculate the area of sheet metal needed to make a soup tin, we can use the formula for surface area of a cylinder which is given by:

Surface Area = 2πrh + 2πr^2

where r is the radius of the cylinder and h is the height of the cylinder.

Using the given values, we can calculate the surface area of the soup tin as follows:

Surface Area = 2π(4.5)(8) + 2π(4.5)^2 Surface Area = 226.08 cm^2

To calculate the total surface area of the label, we can use the formula for surface area of a cylinder which is given by:

Surface Area = 2πrh

where r is the radius of the cylinder and h is the height of the cylinder.

Using the given values, we can calculate the surface area of the label as follows:

Surface Area = 2π(4.5)(8) Surface Area = 226.08 cm^2

To find out the dimensions (length and breadth) of the box in which tins are packed, we can use the given information that 4 tins fit in the width of the box and 5 tins fit in the length of the box. Let’s assume that each tin has a diameter of d cm.

4d = width of box 5d = length of box

We know that diameter (d) = 2r where r is radius.

So, width of box = 4d = 8r length of box = 5d = 10r

Therefore, by the area the answer will be 10r x 8r.

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Answer: -3 and -17

Step-by-step explanation:

     When completing the square we add and subtract [tex]\frac{b}{2} ^2[/tex] in the form ax² + bx + c.

[tex]\frac{b}{2} ^2 = \frac{-6}{2} ^2=(-3)^2=9[/tex]

x² - 6x - 8 = (x - __)² - __

(x² - 6x) - 8 = (x - __)² - __

(x² - 6x + 9) - 8 - 9 = (x - __)² - __

(x - 3)² - 17 = (x - __)² - __

     The blanks are 3 and 17.

Answer:

Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.

Step-by-step explanation:

To find the volume and surface area of a diversion tunnel, we can use the formulas for the volume and lateral surface area of a cylinder.

The volume of a cylinder is given by the formula:

V = πr^2h

Where:

V is the volume,

π is a mathematical constant approximately equal to 3.14159,

r is the radius of the cylinder, and

h is the height (or length) of the cylinder.

Substituting the given values:

r = 56 feet

h = 4,000 feet

V = π(56^2)(4,000)

V ≈ 3.14159 * 56^2 * 4,000

Calculating the volume:

V ≈ 9,839,916,800 cubic feet

The surface area of the lateral (curved) part of a cylinder is given by the formula:

A = 2πrh

Where:

A is the surface area,

π is a mathematical constant approximately equal to 3.14159,

r is the radius of the cylinder, and

h is the height (or length) of the cylinder.

Substituting the given values:

r = 56 feet

h = 4,000 feet

A = 2π(56)(4,000)

A ≈ 2 * 3.14159 * 56 * 4,000

Calculating the surface area:

A ≈ 1,000,530.9 square feet

Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.

Data set: 6, 8, 10, 12, 14, 16, 18

To draw a dot plot representing this data set, we can place a dot above the corresponding value on a number line. Here's the dot plot:

Value    |

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

   6    |      o

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

   8    |      o

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

  10    |      o

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

  12    |      o

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

  14    |      o

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

  16    |      o

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

  18    |      o

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

In the dot plot, each "o" represents a data point. The values are shown on the left side, and the dots are placed above their respective values on the number line.

Hello !

Answer:

[tex]\boxed{\sf V_{hemisphere}=144\pi\ mm^3}[/tex]

Step-by-step explanation:

The volume of a sphere is given by the following formula : [tex]\sf V_{sphere}=\frac{4}{3}\pi r^3[/tex] where r is the radius.

Moreover, we know that the volume of a hemisphere is half the volume of a sphere : [tex]\sf V_{hemisphere}=\frac{1}{2} V_{sphere}[/tex]

We obtain : [tex]\sf V_{hemisphere}=\frac{2}{3}\pi r^3[/tex]

Given :

[tex]\sf r=\frac{1}{2} d=\frac{12}{2} \\\underline{\sf r=6mm}[/tex]

Let's substitue r with it value in the previous formula :

[tex]\sf V_{hemisphere}=\frac{2}{3} \pi\times 6^3\\\boxed{\sf V_{hemisphere}=144\pi\ mm^3}[/tex]

Have a nice day ;)

Answer:

  15.  f(-2) = 2

  17.  f(x) = 1 for x = ±1.7

Step-by-step explanation:

You want various values of the function and its inverse relation for f(x)=x²-2.

The value of f(x) is found by locating the value x on the x-axis and following the vertical line until it intersects the graph. Find the y-coordinate of that point.

The value of x for f(x) = k is found by locating k on the y-axis and following the horizontal line to the points of intersection with the graph. The x-coordinates of the points are the values of interest. Interpolation is often required.

The graph intersects the vertical line at x=-2 where y = 2.

  f(-2) = 2

The horizontal line at y=1 intersects the graph in two places, located symmetrically about the y-axis. The leftmost point is approximately (-1.7, 1). The rightmost point is approximately (1.7, 1).

  x ≈ -1.7 or +1.7

__

Additional comment

The instructions are to use the figure to answer the question. We interpret that to mean that you are to read the answers from the graph.

You can also use the figure to determine the equation for the graph (part of our problem statement, above). Then you can find the solutions by using the equation.

  f(x) = 1

  x² -2 = 1

  x² = 3

  x = ±√3 ≈ ±1.732 . . . . the values for problem 17

<95141404393>

Answer:

  0.90

Step-by-step explanation:

You want the probability of either event A or event B given the Venn diagram shown.

The probability of an event shown in the diagram is the ratio of counts for that event to the total of all counts in the diagram. That total is 50.

The number of counts that are not part of either event is shown as 5.

  P(A or B) = 1 - P(not (A or B)) = 1 - 5/50

  P(A or B) = 0.90

__

Additional comment

Using the given formula, ...

  P(A or B) = (25+5)/50 +(15 +5)/50 -5/50 = (25 +15 +5)/50 = 45/50

  P(A or B) = 0.90

<95141404393>

Answer:

x = 9 and y = 4

Step-by-step explanation:

-2x + 7y = 10    (call this equation '1')

x - 3y = -3      (call this '2')

multiply '2' by 2:

2x - 6y = -6  (call this '3')

add '1' and '3':

(-2x + 7y = 10)  +  (2x - 6y = -6)

0x + y = 4

y = 4

sub that back into '1':

-2x + 7y = 10

-2x + 7(4) = 10

-2x + 28 = 10

-2x = 10 - 28 = -18

x = -18/-2 = 9

sub both y = 4 and x =9 into '2' to check if everything adds up:

x - 3y = -3

9 - 3(4) = 9 - 12 = -3

so x = 9 and y = 4

Answer:f(x) = (x-10)^2-49

f(x) = (x-10+7)(x-10-7)

f(x) = (x-3)(x-17)

The zeros of the function are 3 and 17.

Step-by-step explanation:

According to the figure of the trapezoid

angle XMZ = 115 degrees

angle XMY = 102 degrees

Angle YMZ = 78 degrees

The given figure is an isosceles trapezoid, hence

angle XMZ + angle XYZ = 180

angle XYZ = 39 + 26 = 65

angle XMZ + angle XYZ = 180

angle XMZ = 180 - 65

angle XMZ = 115 degrees

angle XMY

angle XMY =  180 - 39 - 39 = 180 - 78 = 102 degrees

Angle YMZ + angle XMY = 180 (angle on a straight line)

Angle YMZ = 180 - angle XMY = 180 - 102 = 78 degrees

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Answer:

17.5

Step-by-step explanation:

You can find the mean of a data set by adding all numbers in the data set together and dividing by the amount of numbers in the given data set.

In this case, your data set is:

15 , 16 , 17 , 23 , 11 , 19 , 20 , 15 , 18 , 22 , 15 , 19   (12 numbers).

Firstly, add all the numbers together: [tex]15 + 16 + 17 + 23 + 11 + 19 + 20 + 15 + 18 + 22 + 15 + 19 = 210[/tex]

Next, divide 210 (total sum) with the amount of terms in total (12):

[tex]\frac{(210)}{(12)} = 17.5[/tex]

17.5 is already in the tenth digit place value, and so you do not need to round.

17.5 is your answer.

~

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The volume of the solid obtained by rotating the region enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0 about the y-axis is 288π cubic units.

To find the volume of the solid obtained by rotating the region enclosed by the given graphs about the y-axis, we can use the method of cylindrical shells.

First, let's sketch the region to visualize it better.

The region is enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0.

Let's find the intersection points of these curves by setting them equal to each other:

18 - x = 3x - 6

Simplifying the equation, we have:

4x = 24

x = 6

So, the intersection point is (6, 12).

Now, we can integrate to find the volume of the solid.

The radius of each cylindrical shell is the distance from the y-axis to the curve y = 18 - x.

This can be expressed as x.

The height of each cylindrical shell is the difference between the two curves, which is (18 - x) - (3x - 6).

The volume of each cylindrical shell is given by the formula:

V = 2πrhΔx, where r is the radius, h is the height, and Δx is the width of each shell.

Integrating from x = 0 to x = 6, we can find the total volume:

V = ∫[0,6] 2πx[(18 - x) - (3x - 6)] dx

V = ∫[0,6] 2πx(24 - 4x) dx

V = 2π ∫[0,6] (24x - 4x²) dx

V = 2π [12x² - (4/3)x³] | [0,6]

V = 2π [(12(6)² - (4/3)(6)³) - (12(0)^2 - (4/3)(0)^3)]

V = 2π [(12(36) - (4/3)(216)) - (0 - 0)]

V = 2π [(432 - 288) - (0 - 0)]

V = 2π (432 - 288)

V = 2π (144)

V = 288π

Therefore, the volume of the solid obtained by rotating the region enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0 about the y-axis is 288π cubic units.

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In the given expression, 2x³-4x²+2x-x-3, there are five terms. An expression is a mathematical phrase that can be constructed using variables, constants, and operators.

It can include any mathematical operations such as addition, subtraction, multiplication, and division. Additionally, an expression can be made up of one or more terms.In the given expression, 2x³-4x²+2x-x-3, there are five terms. The terms are:2x³: This is the first term in the expression.

It is a cubic term, which means it has an exponent of 3.4x²: This is the second term in the expression. It is a quadratic term, which means it has an exponent of 2.2x: This is the third term in the expression. It is a linear term, which means it has an exponent of 1.-x:

This is the fourth term in the expression. It is also a linear term, but it has a negative coefficient.-3: This is the fifth term in the expression. It is a constant term since it does not have any variable attached to it.In summary, the given expression has five terms, which are 2x³, -4x², 2x, -x, and -3.

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Answer:

Step-by-step explanation:

To solve this problem, we can use the following formula:

(quantity of tea 1 x price of tea 1) + (quantity of tea 2 x price of tea 2) = total quantity x price of mixture

Let x be the number of pounds of black tea that the store owner needs to mix with the oolong tea.

We know that:

The store owner has 35 pounds of oolong tea that sells for $2.40 per pound.

The store owner wants to sell the final mixture for $2.10 per pound.

The black tea is worth $1.80 per pound.

Using the formula above, we can write:

(35 x 2.40) + (x x 1.80) = (35 + x) x 2.10

Simplifying this equation, we get:

84 + 1.8x = 73.5 + 2.1x

0.3x = 10.5

x = 35

Therefore, the store owner needs to mix 35 pounds of black tea with the oolong tea.

I hope this helps! Let me know if you have any other questions.

Answer:

Step-by-step explanation:

Let's assume the store owner needs to mix x pounds of black tea with the 35 pounds of oolong tea.

The cost of the oolong tea is $2.40 per pound, so the total cost of the oolong tea is:

Cost of oolong tea = 35 pounds × $2.40/pound = $84

The cost of the black tea is $1.80 per pound, and the final mixture needs to be sold for $2.10 per pound. To achieve an average price of $2.10 per pound, the total cost of the mixture should be:

Total cost of mixture = (35 + x) pounds × $2.10/pound = $73.5 + $2.10x

Since the cost of the mixture should equal the sum of the costs of the oolong and black teas, we can set up the equation:

$73.5 + $2.10x = $84

Now, let's solve for x to find the amount of black tea needed:

$2.10x = $84 - $73.5

$2.10x = $10.5

x = $10.5 / $2.10

x ≈ 5

Therefore, the store owner needs to mix approximately 5 pounds of black tea with the 35 pounds of oolong tea in order to sell the final mixture for $2.10 per pound.

Answer:

d)  171.8°

e)  72

f)  60°

Step-by-step explanation:

The Polygon Interior Angle Theorem states that measure of the interior angle of a regular polygon with n sides is [(n - 2) · 180°] / 2.

The number of sides of a 44-gon is n = 44. Therefore, the measure of its interior angle is:

[tex]\begin{aligned}\textsf{Interior angles of a 44-agon}&=\dfrac{(44-2) \cdot 180^{\circ}}{44}\\\\&=\dfrac{42\cdot 180^{\circ}}{44}\\\\&=\dfrac{7560^{\circ}}{44}\\\\&=171.8^{\circ}\;\sf(nearest\;tenth)\end{aligned}[/tex]

Therefore, the interior angle of a 44-gon is 171.8°.

[tex]\hrulefill[/tex]

The Polygon Interior Angle Theorem states that measure of the interior angle of a regular polygon with n sides is [(n - 2) · 180°] / 2.

Given the interior angle of a regular polygon is 175°, then:

[tex]\begin{aligned} \textsf{Interior angle}&=175^{\circ}\\\\\implies \dfrac{(n-2) \cdot 180^{\circ}}{n}&=175^{\circ}\\\\(n-2)\cdot 180^{\circ}&=175^{\circ}n\\\\180^{\circ}n-360^{\circ}&=175^{\circ}n\\\\5^{\circ}n&=360^{\circ}\\\\n&=72\end{aligned}[/tex]

Therefore, the number of sides of the regular polygon is 72.

[tex]\hrulefill[/tex]

According the the Polygon Exterior Angles Theorem, the sum of the measures of the exterior angles of a polygon is 360°.

Therefore, to find exterior angle of a regular hexagon, divide 360° by the number of sides:

[tex]\begin{aligned}\sf Exterior\;angle&=\dfrac{360^{\circ}}{\sf Number\;of\;sides}\\\\&=\dfrac{360^{\circ}}{6}\\\\&=60^{\circ}\end{aligned}[/tex]

Therefore, the exterior angle of a regular hexagon is 60°.

Answer:

4. a. 171.818°

b. 72 sides

c. 60°

Step-by-step explanation:

d. The interior angle of a regular polygon with n sides can be calculated using the formula:

[tex]\bold{Interior Angle =\frac{ (n-2) * 180\°}{n}}[/tex]

For a regular 44-gon, the interior angle would be:

[tex]\bold{Interior Angle =\frac{ (44-2) * 180\°}{44}=171.818^o}[/tex]

[tex]\hrulefill[/tex]

e. The number of sides in a regular polygon with an interior angle of 175° can be found using the formula:

[tex]\bold{n = \frac{360\° }{180\° - Interior \:Angle}}[/tex]

For an interior angle of 175°, the number of sides would be:

substituting Value,

[tex]\bold{n =\frac{ 360\° }{ 180\° - 175\°} = \frac{360\° }{ 5\° }= 72 \:sides}[/tex]

[tex]\hrulefill[/tex]

f.

The sum of the exterior angles of any polygon is always 360°.

Since a regular hexagon has six sides,
n=6

exterior angle would be [tex]\bold{\frac{360\° }{ n}}[/tex]

substituting value,

exterior angle=[tex]\bold{\frac{360\° }{ 6}=60\°}[/tex]

[tex]\hrulefill[/tex]

Answer:

156yd²

Step-by-step explanation:

area of parallelogram = base X vertical height

= 12 X 13

= 156yd²

1. Create a horizontal axis labeled "Time Spent on Homework Problem (Minutes)."

2. Choose an appropriate scale for the axis, such as labeling every other unit of time from 0 to 18.

3. Plot a dot for each student's data point along the horizontal axis.

4. Arrange the dots in order from smallest to largest time spent on the problem.

5. Title the dot plot to reflect the data set being represented, such as "Math Homework Problem Time Spent: Mean 9 Minutes, MAD 7 Minutes."

6. Include a legend or key if needed to clarify the meaning of the dot plot.(The dot plot is attached below)

To draw a dot plot representing a data set where the mean amount of time spent on one math homework problem is 9 minutes and the MAD is 7 minutes for a group of ten students, we can follow these steps:

The resulting dot plot may show a spread of data between 2 and 16 minutes, with more dots around the center or mean of 9 minutes and fewer dots at the tails. The MAD of 7 minutes suggests a relatively high degree of variability in the data, with some students spending significantly less or significantly more time on the math homework problem. The dot plot can help to visualize these differences and identify any potential outliers in the data.

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Answer: Pretty sure it should be 2.

Step-by-step explanation:

maybe -2 but i dont think so

(f x g)(x) = √(1/x + 2)

(g x f)(x) = 1/(√(x + 2))

To find (f x g)(x), we need to evaluate the composition of functions f and g, which is denoted as f(g(x)).

Similarly, to find (g x f)(x), we need to evaluate the composition of functions g and f, which is denoted as g(f(x)).

Let's calculate (f x g)(x) and (g x f)(x) for the given pair of functions f(x) = √(x + 2) and g(x) = 1/x:

1. (f x g)(x):

We start by substituting g(x) into f(x) wherever we see an x in f(x):

(f x g)(x) = f(g(x)) = f(1/x)

Substitute 1/x into f(x):

(f x g)(x) = f(g(x)) = f(1/x) = √(1/x + 2)

2. (g x f)(x):

We start by substituting f(x) into g(x) wherever we see an x in g(x):

(g x f)(x) = g(f(x)) = g(√(x + 2))

Substitute √(x + 2) into g(x):

(g x f)(x) = g(f(x)) = g(√(x + 2)) = 1/(√(x + 2))

Therefore, we have:

(f x g)(x) = √(1/x + 2)

(g x f)(x) = 1/(√(x + 2))

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The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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Answer:

x = 8

Step-by-step explanation:

Intersecting tangent and secant theorem:

If a tangent and a secant are drawn to the circle from a point from outside, the square of the measure of the tangent is equal to the product of the measures of the secant segment and its external secant segment.

         x² = (4+12)*4

         x² = 16 * 4

         x² = 64

        x = √64

         x = 8

The surface area of the sphere is 98 yd².

To find the surface area of a sphere, we can use the formula:

Surface Area = 4πr²

Given that the radius, r, of the sphere is 7/3.14 yd, we can substitute this value into the formula:

Surface Area = 4 x 3.14 x (7/3.14)²

= 4 x 3.14 x 49/9.86

= 4 x 49/2

= 98 yd²

Therefore, the surface area of the sphere is 98 yd².

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The coordinates of midpoint P are P(-1/2, 3/2) and coordinates of midpoint Q are Q(-3/2, -4).

To find the coordinates of the midpoints P and Q of sides AB and AC, we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint of a line segment between two points (x1, y1) and (x2, y2) are given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Using this formula, we can find the coordinates of P and Q as follows:

Coordinates of midpoint P:

P = ((2 + (-3)) / 2, (-1 + 4) / 2)

= (-1/2, 3/2)

Therefore, the coordinates of midpoint P are P(-1/2, 3/2).

Coordinates of midpoint Q:

Q = ((2 + (-5)) / 2, (-1 + (-7)) / 2)

= (-3/2, -4)

Therefore, the coordinates of midpoint Q are Q(-3/2, -4).

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Let the points A(2,-1), B(-3,4), and C(-5,-7) be the vertices of triangle A B C. Let P and Q be the midpoints of the sides AB and AC respectively. Find the coordinates of P and Q. (2 marks)

The shop initially has 0.884 jars of jam

The probability that both customers chose strawberry jam, is 0.25.

a) Let's assume the number of jars of strawberry jam is 3x and the number of jars of raspberry jam is x.

So, the total number of jars of jam in the shop is 3x + x = 4x.

According to the given information, the probability that both customers select strawberry jam is 11/20.

So, the probability of the first customer selecting a jar of strawberry jam = (3x/4x) = 3/4,

and the probability of the second customer

=  ((3x-1)/(4x-1)).

Now, (3/4) ((3x-1)/(4x-1)) = 11/20

(3/4) ((3x-1)/(4x-1)) = 11/20

20(3/4) ((3x-1)/(4x-1)) = 11

15 (3x-1) = 44  (4x-1)

45x - 15 = 176x - 44

176x - 45x = 44 - 15

131x = 29

x ≈ 29/131

Therefore, the value of x is 0.221

To find the initial number of jars of jam in the shop, we can substitute this value of x into the equation:

4x =  0.884

b) The probability of the first customer selecting strawberry jam is

= (3x)/(4x)

= 3/4.

Therefore, the probability that both customers chose strawberry jam is:

= (3/4) x ((3x-1)/(4x-1))

= (3/4)  ((3 x 0.221 - 1)/(4 x 0.221 - 1))

= (3/4) ((3 x 0.221 - 1)/(4 x 0.221 - 1))

≈ 0.25

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