18. In the diagram below, PQRS is a square Find the equation of the circle that will pass through the four vertices of the square

R(2, - 2)

S

P(- 2, 2)

Q

The probability that the next person chosen will be in the 40-49 or 50-59 age groups is 0.32

The frequency table is added as an attachment

From the attached image, we have:

40 - 49 or 50 - 59 = 6869 + 6323

40 - 49 or 50 - 59 = 13192

The probability that the next person chosen will be in the 40-49 or 50-59 age groups is then calculated as:

P = 13192/41557

Evaluate

P = 0.32

Hence, the probability that the next person chosen will be in the 40-49 or 50-59 age groups is 0.32

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The quantity of baking powder needed to bake 100 muffins is 6 tablespoons of baking powder

Number of muffins : quantity of baking powder

= 50 : 3

How much baking powder is needed for 100 muffins

let

Equate the ratio of muffins to baking powder

50 : 3 = 100 : b

50/3 = 100/b

50 × b = 3 × 100

50b = 300

b = 300/50

b = 6 tablespoons

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Answer: W = 113/20

What we know:

Set up equation                                                W + 3/5 = 6 1/4

Expand                                                              W + 3/5 = 6*4+1 /4

Simplify                                                              W + 3/5 = 25/4

Common denominator                                     W + 3*4/5*4 = 25*5 / 4*5

Simplify                                                              W + 12/20 = 125/20

Subtract                                                                   -12/20    -12 /20

Solve                                                                  W = 113/20

Check:

By converting our answers into decimals, we can see if the sides are equal:

113/20 = 5.65

3/5 = 0.6

5.65 + 0.6 = 6.25

Does 6.25 = 6 1/4?

1/4 = 0.25

6 + 0.25 = 6.25

6.25 = 6.25

Therefore, W = 113/20 is the correct answer.

The two factors multiplied together to make a trinomial is (x-1)(3x-2).

Given equation is 3x²-5x+2.

An algebraic equation which of the second degree in x is known as quadratic equation. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

In the given equation,

Multiply the first coefficient 3 with the last coefficient 2  so we get 2×3=6

Use any two numbers which on multiply give 6 and on adding or subtracting give -5.

Such two numbers are -2 and -3

On multiplying, (-3)×(-2)=6

On Adding, -3-2=-5

So, break -5x into -3x and -2x and we get

3x²-3x-2x+2

Taking out 3x common from the first two terms and -2 from the last two terms as

3x(x-1)-2(x-1)

Taking out the common term (x-1) as common and get

(x-1)(3x-2)

Hence, the two factors of the equation 3x²-5x+2 that can be multiplied together to make this trinomial is (x-1)(3x-2).

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Answer: 1st graph (3,2)

Step-by-step explanation:

Answer:

30,000

Step-by-step explanation:

place value of 3 is tens of thousands (10,000)

therefore its total value is : 3×10,000=30,000

Answer:

$5750

Step-by-step explanation:

For simple interest,

I = prt

115 = p × 0.03 × 8/12

p = 5750

Emil starts the day with 16 liters of lemonade if he is left with 4 liters by the end of the day. Computed using the fractional values given.

Let the initial quantity of lemonade with Emil be x liters.

Quantity sold by Emil in the morning = Half of his lemonade = (1/2)x liters, that is half fraction of x.

Quantity left with Emil = x - x/2 = x/2 liters, that is half fraction of x.

Quantity sold by Emil at lunchtime = Quarter of what was left = (1/4)(x/2) liters = x/8 liters, that is the one-eight fraction of x.

Quantity left with Emil = x/2 - x/8 = 3x/8 liters, that is the three-eight fraction of x.

Quantity sold by Emil in the afternoon = One-third of what was left = (1/3)(3x/8) liters = x/8 liters, that is the one-eight fraction of x.

Quantity left with Emil = 3x/8 - x/8 = x/4 liters, that is the quarter fraction of x.

Now, we are said that Emil closes for the day with 4 liters remaining.

Therefore, x/4 = 4, or, x = 4*4 = 16 liters.

Therefore, Emil started the day with 16 liters of lemonade.

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Answer:

71°

Step-by-step explanation:

So, angle A measures 66+5=71°

The company should focus attention on 17515 people.

The term percentage means a denominator of 100. We can proceed to find the people to which the company must reach as follows;

The percentage that is over the age of 65, and immunocompromised =  27%

so;

27/100 × 50,000 = 13500 people

50,000 - 13500 = 36,500

Now;

11% of this number are under 65 and immunocompromised so;

11/100 ×  36,500 = 4015 people

Total number that the company should reach = 13500 + 4015  = 17515 people

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Answer:

what is the price of an article costing rs 2000 after levying 13 value added tax find it

Answer:

B

Step-by-step explanation:

subtract 1/3 from both sides

m< -2 7/12

Isabella’s error is  Isabella should have divided the product of 12π and 9 by 3 to get V = 12π(9)/3 option fourth is correct.

It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.

[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]

Isabella equation:

[tex]\rm V = \dfrac{1}{3}(12)^2(9)\pi[/tex]

The area of the base = 12π square cm

[tex]\rm V = \dfrac{12\pi (9 )}{3}[/tex]

Thus, Isabella’s error is  Isabella should have divided the product of 12π and 9 by 3 to get V = 12π(9)/3 option fourth is correct.

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Answer:

y = 95

Step-by-step explanation:

x + 120 = 180

25 + x + y = 180

flipping the first equation 180 - 120 = 60 so x is 60.

so plug in 60 into the second equation

25 + 60 + y =180 --> 85 + y =180 flip equation 180 - 85 = 95

so y is 95

Using the permutation formula, it is found that the probability that the CDs end up in alphabetical order is:

[tex]p = \frac{1}{8,204,716,800}[/tex]

For this problem, the order in which the CDs are chosen is important, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

8 CDs are chosen from a set of 21, hence the number of ways they can be chosen is:

[tex]P_{(21,8)} = \frac{21!}{13!} = 8204716800[/tex]

Only one arrangement is in alphabetical order, hence the probability is:

[tex]p = \frac{1}{8,204,716,800}[/tex]

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Answer:

Olive's age = 32

Lisbeth's age = 8

Step-by-step explanation:

Declaration

Let Eisbeths present age = x

Let Olive's age = y

Equations

(x - 2) = 1/5 (y - 2)

x + 4 = 1/3(Y + 4)

Solution

1st equation

(x - 2) = 1/5 (y - 2)                 Multiply both sides by 5

5(x - 2) = y - 2                       Remove the brackets

5x - 10 = y - 2                       Add 10 to both sides

5x -10+10 = y - 2+10            Combine

5x = y + 8                            Subtract 8 from both sides

5x - 8 = y + 8 - 8                 Combine

5x - 8 = y

2nd Equation

x + 4 = 1/3(y + 4)                 Multiply both sides by 3

3(x + 4) = y + 4                   Remove the brackets

3x + 12 = y + 4                     Subtract 3 from both sides

3x + 12 - 4 = y + 4 - 4          Combine

3x + 8 = y

Note Since y is the same in both equations, the left side of each can be thought of as equal to each other.

3x + 8  = 5x - 8                    Add 8  to both sides

3x + 8 + 8 = 5x - 8 + 8        Combine

3x + 16 = 5x                         Subtract 3x from both sides

3x - 3x + 16 = 5x - 3x           Combine

16 = 2x                                  Divide by 2

16/2 = 2x/2

8  = x

y = 3x + 8

y = 32

Answer:

factors are (x-1),(x+2),(x+4),(x+3)

Answer:

x = 25, y = 10

Step-by-step explanation:

I'll add a drawing of my own so that it's easier for me to explain, and for you to understand.  

Since line BC and line DE are parallel and line AE is being shared, angle ACB and angle CED will be the same. So the square will also be 3y.

Since line AB and line CD are parallel and line AE is being shared, angle CAB and angle ECD will be the same. So the heart will be 2x.

Now that we figured out two unknown angles, we can see that the two triangles share two angles with the same value. Since angles in a triangle add up to 180 (Added angles in every triangle are the same), the triangle shape (I drew) will be 4x.

We have a few clues to find the value of x and y.

1) 2x + 4x + 3y = 180 (all angles in a triangle add up to 180)

2) 3y + 2x = 180 - 100 (If you look near point C, we can see that 3y + 100 + 2x equals a flat line. A flat line equals 180)

We can use substitution. 3y + 2x can be replaced with 80.

So our new equation will be: 4x = 100

x = 25.

Now we can replace x with 25 in our second clue.

3y + 2(25) = 80

3y + 50 = 80

3y = 30

y = 10.

We can conclude that x = 25, and y = 10

Answer:

x = 25 and y = 10

Step-by-step explanation:

The arrows on the line segments mean the lines are parallel.

Therefore, the diagram shows two similar triangles, which means their interior angles are the same size.  (Refer to the attached diagram).

Interior angles of a triangle sum to 180°:

⇒ 2x + 4x + 3y = 180

⇒ 6x + 3y = 180

⇒ 3(2x + y) = 180

⇒ 2x + y = 60

⇒ 2x = 60 - y

Angles on a straight line sum to 180°:

⇒ 3y + 100 + 2x = 180

⇒ 2x + 3y = 80

⇒ 2x = 80 - 3y

Substitute the first equation into the second equation, and solve for y:

⇒ 60 - y = 80 - 3y

⇒ 60 + 2y = 80

⇒ 2y = 20

⇒ y = 10

Substitute the found value of y into one of the equations and solve for x:

⇒ 2x = 60 - 10

⇒ 2x = 50

⇒ x = 25

Therefore, x = 25 and y = 10.

Answer:

DC= 32.3 units

Step-by-step explanation:

Use Pythag theorem to find BC   first

15 ^2 +  BC ^2 = 22^2      then BC = sqrt 259

Then use the Pythagorean Theorem again to find DC

DC^2 = 28^2 + sqrt(259)^2

       DC=32.3

Step-by-step explanation:

1. Right angled triangle , scalene triangle

2. isosceles triangle, obtuse angled triangle

3. equilateral triangle

4. right angled triangle, isosceles triangle

5. scalene triangle, obtuse angled triangle

6. scalene triangle, acute angled triangle

Answer:

Step-by-step explanation:

Answer:

  22

Step-by-step explanation:

The segment addition theorem tells us the whole is the sum of the parts. We can use this to write an equation relating the expressions for segment length.

  OQ = OP +PQ . . . . . segment addition theorem

  4x +2 = (3x -3) +(4x -10) . . . . substitute given expressions

  15 = 3x . . . . . . add 13 -4x to both sides

  5 = x . . . . . . . divide by 3

  OQ = 4x +2 = 4(5) +2 = 22

The length of OQ is 22 units.

Hello,

[tex]\boxed{P(X = k) =( {}^{n} _{k}) \times p {}^{k} \times (1 - p) {}^{n - k} }[/tex]

[tex]P(X= k) = ( {}^{12} _{6}) \times 0.51 {}^{6} \times (1 - 0.51) {}^{12 - 6} [/tex]

We have :

[tex]( {}^{n} _{k}) = \frac{n!}{k!(n - k)!} [/tex]

[tex]( {}^{12} _{6}) = \frac{12!}{6!(12 - 6)!} = \frac{12!}{6!6!} = \frac{12 \times 11 \times 10 \times ... \times 1}{2(6 \times 5 \times 4 \times... \times 1) } = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7 }{6 \times 5 \times 4 \times 3 \times 2 \times 1} = 924[/tex]

[tex]P(X = k) = 924 \times 0.51 {}^{6} \times 0.49 {}^{6} = 0.2250[/tex]

The point J connote that the mixture has more than the expected volume and has the optimal butterfat percentage.

Note that in the question, it was supplied that  Otto intended to make a mixture of 12% butter fat.

Since:

Milk = 2% butter fat

Whipping cream = 30% butter fat.

This implies that  the milk contains the smallest of butter fat and it also implies that Otto would require  a lot more milk than cream, to be able to attain the 12% mixture.

This is known to be when point J is said to meet, and by using that data from point J, Otto require more of milk than the cream to get what he wants.

Therefore, The point J connote that the mixture has more than the expected volume and has the optimal butterfat percentage.

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Answer:

4

Step-by-step explanation:

i dont cap

The solution of the expression [tex]\dfrac{60-48}{6\times 7}[/tex] is [tex]\dfrac{2}{7}[/tex].

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The expression is solved as,

[tex]\dfrac{60-48}{6\times 7}= \dfrac{12}{42}[/tex]

Solve the fraction [tex]\dfrac{12}{42}[/tex].

[tex]\dfrac{60-48}{6\times 7}= \dfrac{2}{7}[/tex]

Therefore, the solution of the expression [tex]\dfrac{60-48}{6\times 7}[/tex] is [tex]\dfrac{2}{7}[/tex].

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The multiples of 5 and 6 based on the information have been illustrated below.

It should be noted that a multiple is a number that can be divided by another number without a remainder.

Here, the multiples of 5 will be:

5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.

6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...

In this case, the multiples of the numbers have been illustrated.

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Answer:

[tex]C-\frac{1}{3(lnx- \pi)^3}.[/tex]

Step-by-step explanation:

[tex]\int\ {\frac{1}{x(lnx- \pi)^4} } \, dx=\int\ {\frac{d(lnx- \pi)}{(lnx- \pi)^4}} \, dx=-\frac{1}{3(lnx- \pi)^3} +C.[/tex]

Answer:

Original Salary: [tex]5,957.14[/tex]

Increase in 3%: [tex]6,135.85[/tex]

Step-by-step explanation:

So when something increases by x%, the new value is (100+x)% the original value. So 6255, is 105% the original value. This means to find the original value, we have to find the number that has 6255 as 105% of it's value. Whenever you try to find x% of a number, you multiply it by the decimal value of the percentage, which is found by dividing by 100. So to find x%, you do: [tex]o*\frac{x}{100}[/tex] where o = original value, x=percent. In this case the percent is 105%, which when divided by 100 is 1.05. So this gives us the equation: [tex]o*1.05=6255 \implies o = \frac{6255}{1.05} = 5,957.14[/tex]. This is his original salary. You need to do this process, do not make the mistake of subtracting 5% from 6255. This is because 5% of 6255 does not equal the 5% of the original value. 5% of 6255 should be greater than 5% of the original value, since the new value is an increase of 5%. So since we have his original salary, we can calculate the salary increase had it been 3%. to do this we multiply by 1.03 (103% divided by 100). This gives us the equation: [tex]5,957.14*1.03=6,135.85[/tex]

The answers to the statements that have been made here are:

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Hello !

[tex]F(x) = \frac{1}{3} \times {4}^{x} [/tex]

[tex]F(3) = \frac{1}{3} \times {4}^{3} \\ = \frac{1}{3} \times 64 \\ = \frac{64}{3} [/tex]

==> B

Have a nice day ;)

Hello,

Answer: 64/3

B

Step-by-step explanation:

F(x) = 1/3 × 4ˣ

F(3) = 1/3 × 4³ = 1/3 × 64 = 64/3