14. A baker needs to make 3 batches of
3 cups of
cupcakes. If each recipe uses
sugar, how much sugar will the baker need?
(Example 5)

(7-4i)√2/7 is the simplified form of (4-i√2)/(4+i√2)

a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit

The given expression is

(4-i√2)/(4+i√2)

Now we have to rationalize the above expression

((4-i√2)/(4+i√2))×((4-i√2)/(4-i√2))

(4-i√2)(4-i√2)/(4+i√2)(4-i√2)

16-4i√2-4i√2-2/16-2

16-8i√2-2/14

14-8i√2/14

2(7-4i√2)/2(7)

(7-4i)√2/7

Hence (7-4i)√2/7 is the simplified form of (4-i√2)/(4+i√2)

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The solutions are;

The joint probability of y1 and y2 is  [tex]\left[\begin{array}{ccc}0\\1\\2\end{array}\right][/tex][tex]\left[\begin{array}{ccc}1/9&2/9&1/9\\2/9&2/9&0\\1/9&0&0\end{array}\right][/tex] and F(1,0) = 1/3.

Given data;

Let y1 signify the number of contracts awarded to firm a and y2 the number of contracts assigned to firm b. Recall that each firm can receive 0, 1, or 2 contracts. Contracts for two construction tasks are randomly assigned to one or more of three firms, a, b, and c.

To find,

(a) The joint probability function for  y₁ and y₂

Let y₁ denote the number of contracts assigned to firm A,

y₂ the number of contracts assigned to firm B

      y₁

      [tex]\left[\begin{array}{ccc}0&1&2\\\\\end{array}\right][/tex]

        y₂

[tex]\left[\begin{array}{ccc}0\\1\\2\end{array}\right][/tex][tex]\left[\begin{array}{ccc}1/9&2/9&1/9\\2/9&2/9&0\\1/9&0&0\end{array}\right][/tex]

(b) Find F(1,0)

F(1,0) =  p(y₁ ≤ 1, y₂ ≤ 0)

         = p(0,0) + p(1,0)

         = 1/9 + 2/9

         = 1/3.

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The measures of those two angles are 35° and 50°.

It's important to note that the sum of angles on a quadrilateral is 360°. In this case, two angles of a quadrilateral measure 260° and 15º.

The remaining angles will be:

= 360° - (260° + 15°)

= 85°

Since the other two angles are in a ratio of 7:10, the measure will be:

= 7 / (7 + 10) × 85°

= 7/15 × 85°

= 35°

Also, 10/17 × 85°

= 50°

The angles are 35° and 50°.

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Answer:

He drives 2921 a week.

Step-by-step explanation:

If Tia drives 127 miles in a week, and Mac drives 23 times as many miles as Tia, then we multiply. 127x23=2921.

Hope this helped :)

2/3 of cookies were she saved.

A fraction represents a part of a whole.

The first batch consisted of 120 gingerbread cookies

Second batch consisted of 150 shortbread cookies.

And, the same fractions of cookies from each batch were saved.

Let x parts of each of cookies were saved.

Then The number of the saved gingerbread cookies = 120 x

While, The number of the saved shortbread cookies = 150 x

150x-120x=20

30x=20

x=20/30

x=2/3

Hence 2/3 of cookies were she saved.

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hola buenas tardes como está el día de hoy ? yo estoy bien gracias por preguntar, espera...hablas español verdad...?

Answer: All real numbers

Step-by-step explanation: It is pretty simple. Just see if the x can be undefined. In this case x works with every number. So, it's all real numbers

Answer:

so that means they would each get 2 and a half of apple and orange slices

Step-by-step explanation:

48 ÷ 24 =2

36 ÷ 24 =1.5

=2 1.5

Step-by-step explanation:

I gone through your work and I don't see anything wrong.

Try reaching out to your teacher.

Answer:

You answered every question correctly. All ten of them. The program you are using has some issues. lol

Step-by-step explanation:

Answer:

x = -9

Step-by-step explanation:

Below:-

Answer:

x = -9

Step-by-step explanation:

Given equation,

→ x + (-9) = -18

Now the value of x will be,

→ x + (-9) = -18

→ x - 9 = -18

→ x = -18 + 9

→ [ x = -9 ]

Hence, the value of x is -9.

Answer:

5

Step-by-step explanation:

Answer: The answer to that would be 5.

Step-by-step explanation:

Hope this helps!

Four friends go out to eat and their meal cost $86. 50. The sales tax 6. 75% and they should tip the waiter 20%.each person must pay $27.7 for their meal

Four friends go out to eat and $86.50 for their meals.

The sales tax is 6.75%, and the waiter is tipped 20%.

M = 86.5 * 10675 / 10000 = 92.34

92.34$, and the total amount of money that four friends will give, including waiter tip, is

T=92.35 * 120 / 100 = 110.80

and each person must give

110.8/4= $27.7

each person must pay $27.7

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Answer:

204 feet^2

Step-by-step explanation:

rectangle area = 18 * 10 = 180 feet^2

triangle width = 18 - 10 = 8 feet

triangle area = 6 * 8 /2 = 24 feet^2

total area = 180 + 24 = 204 feet^2

The inverse function of the given is [tex]y^-1[/tex]= [tex]\frac{x}{2}[/tex]-4 .

What is inverse function?

The domain of the original function becomes the range of the inverse function, and the range of the given function becomes the domain of the inverse function. The inverse function is denoted by the notation f-1 in relation to the original function f. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function. Only when f is both a one-one and an onto function does it have an inverse, indicated by the symbol f-1. Keep in mind that f-1 is NOT f's inverse. The domain value of x is given by combining the function f and the reciprocal function f-1.

Here the given function is,

=> y = 2x+8

Now interchange x and y then

=> x=2y+8

Now simplify the expression with respect to y then,

=> x-8=2y

=> y = [tex]\frac{x}{2}[/tex]-4

=>[tex]y^-1[/tex]= [tex]\frac{x}{2}[/tex]-4

Hence inverse function is [tex]y^-1[/tex]= [tex]\frac{x}{2}[/tex]-4 .

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Answer:

[tex]x=\frac{-8+y}{6}[/tex]

Step-by-step explanation:

Let us evaluate this problem.

First, add Y to both sides

[tex]-6x-y+y=-8+y[/tex]

Always remember to simplify.

[tex]-6x=-8+y[/tex]

Divide both sides by -6

[tex]\frac{-6x}{6} =\frac{8}{-6} +\frac{y}{-6}[/tex]

Simplify one more time.

[tex]x=\frac{-8+y}{6}[/tex]

Your final answer is:
[tex]x=\frac{-8+y}{6}[/tex]

The equation 3 + 4 = 7 and 4 + 3 = 7, shows the existence of Commutative Property of Addition.

What are Properties of Addition?

The properties of addition are the rules we can follow while adding numbers. Using these properties can make the calculation more straightforward and helps to solve complex problems in Math.

Solution:

Using Commutative Property of Addition the above mentioned equation can be solved.

Commutative Property of Addition - When we add two or more numbers, their sum is the same regardless of the order of the addends. We can write this property in the form of A + B = B + A.

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Answer:

Step-by-step explanation:

1. Find decrease.

If the car dealer bought the car for 100$ and only received 100$ for selling the car, he had 400$ in disadvantage!

2. Caculate Percent Loss:

400/ 500*100=

400/5=

80

There was a 80% decrease from the starting value!

Answer: 80% decrease!

Total cost  to tile the kitchen =$273.78

Let the width of kitchen = w

The length of the kitchen is nine feet shorter than three times its width, w  = 3 w-9    equation-----1

The perimeter of the kitchen is six times the width = 6 w

= 2(length+width) =6 w    equation----2

from equation 1 and 2

= 2(3 w-9+w) = 6 w

= 6 w-18+2 w = 6 w

   2 w = 18

   w = 9

Length = 3 w-9

length  = 3×9-9

length  = 18

Area of kitchen = length×width

                          = 18×9

                          = 162 square foot

Cost of tiles per square = $1.69

Total cost  to tile the kitchen = Area of kitchen × cost of tiles per square

                                                = 162×$1.69

                                                =$273.78

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If the tiles cost $1.69 a square foot, the total cost to the tiles of the kitchen is $273.28.

According to the question:

Let the width be = x

Then, the length of the rectangular kitchen is L = 3x - 9

The perimeter is = 6x

It is given that the cost of the tile = $1.69 a square foot.

Then the total costs of tiles the kitchen is :

The Perimeter of the rectangle =  2(L + b)

The Perimeter of the rectangle =  2(3x - 9 + x)

The Perimeter of the rectangle =  2(4x-9)

We know that, according to the question,

the perimeter of the kitchen is six times the width = perimeter of rectangle

⇒ 6x = 8x - 18

⇒ - 2x = - 18

⇒ x = 18/2

⇒ x = 9

Thus, the width = x = 9 feet

Putting the value of x = 9

then, The length = 3x - 9 = 3(9) - 9

the length = 27 - 9

the length = 18 feet

Therefore, as we know that,

Area = Length × Width

Area = (18 × 9) feet  

Area =   162 square feet.

Now,

Cost of a Tile = $1.69 per sq. ft.

Thus,

Total Cost of tile = $1.69 × 162

Total Cost of tile =  $273.28

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The after simplification of the expression 1 over 6x + 3 over 4 ( 1 over 2x - 4), we get (26 - 144)/48x.

We need to simplify 1 over 6x + 3 over 4 ( 1 over 2x - 4)

1/6x + 3/4 (1/2x - 4)

1/6x +3/4 ((1 - 8x)/2x)

1/6x + (3 - 24x)/8x

(8 + 6(3 - 24x))/(6x8) x

(8 + 18 - 144x)/48x

(26 - 144)/48x

Therefore, the after simplification of the expression 1 over 6x + 3 over 4 ( 1 over 2x - 4), we get (26 - 144)/48x.

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Probability that a continuous random variable (x) will take on a value between 34 and 35 is 1/8

Uniform distribution is a type of probability distribution which consists constant probability.

It is also known as Rectangular distribution and

denoted by U( x,y ) .

let X be a continuous random variable then

X ~ U( x,y) where x is maximum value and y is minimum value .

Probability density function of uniform distribution is f(X) = 1/(b-a) , where

b---> maximum value , a---> minimum value

we have provided the interval of uniform distribution as 30 to 38 i.e b = 38 , a = 30

then , f( X) = 1/ (38-30) = 1/8

Probability that X will take on value between c and d is

P ( c ≤X≤ d ) =( d -c )/ (b-a )

Probability that X will take on a value between 34 and 35 is

P ( 34≤X≤35) = ( 35-34)/ 8 = 1/8

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Answer:

Find the angle measurement like a 90 degree angle or something for both of them and then find the solution following it. If you need further help post the question with the name where these questions are posted!

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The 95% confidence interval for the average apple weight is (119.14, 125.86).

Given info,

The average weight per apple, according to one manufacturer, is 120 grams, with a standard deviation of 12 grams. The average weight per apple, according to data produced from a sample of 49 apples drawn at random from a shipment, was 122. 5 grams.

Let,

n = 49

x = 122.5

σ = 12

To calculate and interpret a 95% confidence interval for the mean weight per apple;

∴ A 95% confidence interval is given by,

(x ± 1.96*σ/√n)

(122.5 ± 1.96*12/√49)

(119.14, 125.86)

Hence, a 95% confidence interval for the mean weight per apple is  (119.14, 125.86).

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If I || m, find the value of x and y.

Given (7x + 12)

(12x - 28)

(9y-77)

What does the term " l || m " represents?

This term indicates that the line 'l' is parallel to the line 'm'.

It can be seen that, ∠(7x + 12) and ∠(12x - 28) from alternate interior angles as line 'l' and 'm' are parallel. These angles will be equal to each other. Therefore, we can write -

7x + 12 = 12x - 28

12x - 7x = 12 + 28

5x = 40

x = 8

Now, ∠(12x - 28) and ∠(9y - 77) form a straight angle. Therefore, we can write -

(12x - 28) + (9y - 77) = 180

(12 x 8 - 28) + (9y - 77) = 180

68 + 9y - 77 = 180

9y = 180 + 9

9y = 189

y = 21

Hence the answer is, the values of [x] and [y] will be 8 and 21 respectively.

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Answer:

1/x

Step-by-step explanation:

With the exception of x=4/5, the domain of s(x) over t(x) is all real numbers. Except when x=-3/2, all real numbers fall within the domain of w(x).

Given,

The value of the independent variable, often x, for which the supplied function is specified is the domain of a function.

When the value of the denominator falls to zero, a function that is composed of the fraction of two polynomials is not defined.

The numerator of t(x) should not be zero since the domain of s(x) over t(x) will be all real integers except the numerator of zero.

t(x) = 0

5x + 4 = 0

5x = -4

x = -4/5

With the exception of x=-4/5, all real numbers fall into the domain of s(x) over t(x).

Similar to w(x), s(x) should not be zero because the domain of w(x) will be all real numbers except for the one that makes the denominator equal to zero.

s(x) = 0

2x - 3 = 0

2x = 3

x = 3/2

With the exception of x=-3/2, all real numbers fall within the domain of w(x).

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Answer:

Step-by-step explanation:

n = some unknown natural number

n/2 = half of that natural number

n-1 = number right before the unknown natural number

2*(n-1) = twice the number before the natural number n

Answer:

24 and 41 inches.

Step-by-step explanation:

Let the lengths of the two pieces be a and b.

The total length of the two-piece should be the length of the original board.

Therefore:

a + b = 65

One piece, say b, is 7 inches shorter than twice the length of the other, a.

Therefore, we can write the following equation:

b = 2a - 7

The “2a” represents the twice, and the “-7” represents the 7 shorter inches.

We now have a system of equations:

a + b = 65

b = 2a - 7

We can solve using substitution. Substitute the second equation with the first. Hence:

a + (2a - 7) = 65

Combine like terms:

3a - 7 = 65

Add 7 to both sides:

3a = 72

Divide both sides by 3:

a = 24

So, the shorter piece is 24 inches.

Then, we can use our second equation again:

b = 2a - 7

Since we now know a substitute 24 for a and evaluate. Hence:

b = 2(24) - 7

  = 48 - 7

  = 41

Therefore, the length of the other two pieces is 24 and 41 inches.

Using the concepts of  probability, we got that an experiment may have d) several events

Event is called one or more outcomes of an experiment. Example of this is -rolling a dice, we get a possible outcomes as {1,2,3,4,5,6}.

In an experiment there can be one outcome, two outcomes, more than two outcomes or several outcomes.

An event is the collection of one or more of the outcomes of an experiment. An event that actually includes one and only one of the (final) outcomes for an experiment is called the simple event and is denoted by Ei.

Hence, an experiment may have d)several events

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