Yasmin is making some pancakes. Her recipe makes 6 pancakes.
Flour
Eggs
Milk
100g
2
250ml
Yasmin wants to make 15 pancakes.
Complete the table to show how much she will need of each ingredient.

a. np = 8.91 and nq = 18.09 where n = 27 and p = 0.33

b. np = 3.75 and nq = 21.25 where n = 25 and p = 0.15

c. np = 9.68 and nq = 34.32 where n = 44 and p = .22

a. Given n =  27

          p = 0.33

np = 27 x 0.33

     = 8.91

nq = 27 x (1 - 0.33)

    = 18.09

For the approximation of binomial distribution, the sample size must be greater than 10 for both the products np and n(1-p) to approximate the binomial distribution by a normal distribution.

Since here np < 10 approximation is not applicable.

μp = np = 27 x 0.33  

             = 8.91

σp = √npq = √(27)x (.33) x (1 - 0.33)

              = 2.443

b.  n = 25 and p = 0.15

   np = 25 x 0.15

         = 3.75

   nq = 25 x (1 - 0.15)

    = 21.25

Approximation is not possible because np < 10.

c. n = 44 and p = .22

   np = 44 x 0.22

         = 9.68

   nq = 44 x (1 - 0.22)

    = 34.32

Since here np< 10 approximation is not possible.

μp = np = 44 x 0.22  

             = 9.68

σp =√npq = √(44)x (.22) x (1 - 0.22)

              = 2.747

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Answer:

Inconsistent: parallel lines.

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y=4x+4\\-12x+3y=3\end{cases}[/tex]

Use arithmetic operations to isolate y in the second equation:

[tex]\implies -12x+3y+12x=3+12x[/tex]

[tex]\implies 3y=12x+3[/tex]

[tex]\implies\dfrac{3y}{3}=\dfrac{12x}{3}+\dfrac{3}{3}[/tex]

[tex]\implies y=4x+1[/tex]

Therefore, we can see that both equations have the same slope and so the graphs of these equations are parallel.

The solution to a system of linear equations is the point of intersection.

As parallel lines never intersect, there are no solutions to this system and the system is said to be inconsistent.

$128,000 represents 100%

To find how much is 4% we can use the next proportion:

Solving for x:

Her commission is $5,120

Answer:

k = ± [tex]\sqrt{\frac{2A-3t\p}{\pi } }[/tex]

Step-by-step explanation:

2A = πk² + 3t ( subtract 3t from both sides )

2A - 3t = πk² ( isolate k² by dividing both sides by π )

[tex]\frac{2A-3t}{\pi }[/tex] = k² ( take square root of both sides )

± [tex]\sqrt{\frac{2A-3t}{\pi } }[/tex] = k

Answer:

There is no dot plot below

Step-by-step explanation:

part 1 of the question is asking us to evaluate expressions to the power of 2. To do that let's remember the following:

Ther is, when a number is elevated to second power it means we have to multiply that number by itself. For example:

In the second part of this question, we are asked to evaluate the square root of a number. Let's remember that the square root is the inverse operation of elevating a number to the second power. That is if we have:

it means:

For example:

The third part of the questions asks us to solve for "x" the following equation:

To do that we take square root on both sides:

Since the square root of a number to the second power is the same number and the square root of 9 is 3, we get:

We have that:

then, in this case, we have:

therefore, the velocity of the cart is 0.9 meters per second.

the answer would be (0,5)

Answer:

6.5625 gal per hour

Step-by-step explanation:

Since there are 60 minutes per hour, we need to multiply 14 by 60 to change per minute into per hour. Combining these: 14 fl oz / min x (1 gal / 128 fl oz) x (60 min / hr) = 6.5625 gal per hour. Written as a mixed fraction: 6 9/16 gal per hour.

Total 250 adult tickets are sold.

Let a = number of adult tickets sold

Let s = number of student tickets sold

a + s = 553

s = a + 53

From above equations;

a + a + 53 = 553

2a = 553 - 53

2a = 500

a = 250

Total 250 adult tickets are sold.

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The value of x = -12.

Define Function.

A special relationship where each input has a single output. It is often written as "f(x)" where x is the input value. Example: f(x) = x/2 ("f of x equals x divided by 2")

The given expression is

H(x)=-5/6 x

also, H(x) = 10

so, put H(x) value in given expression,

10 = -5/6 x

Now, solve for 'x'

-5x = 60

x = 60/(-5)

x = -12

Therefore, the value of x = -12

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The length of the line segment will be 10 units.

What is Distance?

The distance between two points (x₁ , y₁) and (x₂, y₂) is defined as;

D = √( y₂ - y₁)² + (x₂ - x₁)²

Given that;

Two endpoints of the line segment are (6, -5) and (0, 3).

Now,

The length of the line segment is distance between two endpoints (6, -5) and (0, 3).

So, The distance between two endpoints (6, -5) and (0, 3) is calculated as;

D = √(0 - 6)² + (3 - (-5))²

D = √36 + 64

D = √100

D = 10 units

Thus, The length of the line segment will be 10 units.

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letter D is the answer

Answer:

y = 5

Step-by-step explanation:

since the triangles are congruent then corresponding sides are congruent, so

AB = CD , that is

7y = 3y + 20  ( subtract 3y from both sides )

4y = 20 ( divide both sides by 4 )

y = 5

Answer:

4:2 and 14:7

Step-by-step explanation:

The ratios equivalent to 8:4 would be:

4:2

14:7

5:10 wouldn't be equivalent because if you simplify that, it is 1/2 and if you simplify 8/4, it is 2. 1/2 and 2 are not the same.

:D

Answer:

They are all equivalent except for 5:10

Step-by-step explanation:

You can write ratios as fractions

[tex]\frac{8}4}[/tex]   [tex]\frac{4}{2}[/tex]  [tex]\frac{14}{7}[/tex]   [tex]\frac{5}{10}[/tex]  If I simplify each fraction, I can see that they all equal 2 expect for the the last one.

2   2   2   1/2

Answer:

Length in inches → 11

1 inch = 2.5 centimeters

Length in Centimetres → 11 × 2.5 → 27.5 cm

Answer:

Step-by-step explanation:

Substitute and calculate:

Answer:

d. y= 2x³

Step-by-step explanation:

All of the other equations represent linear functions, and are in the form y = mx + b. D on the other hand contains an exponent, making it a non-linear (in this case cubic) function.

The distance between the translated points C and D is 5 units

From the question, the coordinates are given as

A (-2,3) , B (3,3) , C (4,6) , and D (-1 , 6)

The sequence of transformations is given as

The above sequence of transformations are rigid transformations.

This means that the lengths are preserved

In other words,

CD = C'D'

So, we have the distance to be

Distance = √[(x₁ - x₂)² + (y₁ - y₂)²]

Where

(x, y) = C (4,6) , and D (-1 , 6)

So, we have

Distance = √[(4 + 1)² + (6 - 6)²]

Evaluate

Distance = 5

Hence, the distance is 5 units

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A)

If the order of choice is taken into consideration, we consider four possibilities for the first choice and three for the second. Then the total number of ways is given by:

B)

If the order of choices is not taken into consideration, we must divide the the previous result by 2, which is the total number of ways by which we can organize two letters (ex: AB and BA):

Answer:

-16

Step-by-step explanation:

fog(18)=f(g(18))

g(18)=[tex]\sqrt{18-9} =\sqrt{9} =3[/tex]

f(3)=-8(3)+8

=-16

Integer Numbers

It can be defined as the number that can be written without a fractional (decimal) component.

Integers can be positive, negative, or 0.

From the numbers on the list only -4, 0, and 2 are integers. The rest of the numbers cannot be written without a decimal component.

For example:

-2/3 = -0.666

π = 3.14

The square root of 6 is 2.45

4.111... has an evident decimal component.

Answer: -4, 0, and 2

If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.

Total number of registered voters in Central city = 29791 voters

Total number of voting centers = 93 voting centers

The number of population serves by each center = Total number of registered voters in Central city ÷ Total number of voting centers

Substitute the values in the equation

The number of population serves by each center = 29791/93

= 320.33

≈ 320

Hence, If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.

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The solution of the system of linear equations 2x + 3y = 6 and -3x + 5y = 10 is (0, 2).

Linear equation:

Linear equation refers an equation in which the highest power of the variable is always 1. It is also called as a one-degree equation.

Given,

Here we have the following system of linear equations.

2x + 3y = 6

-3x + 5y = 10

Now, we need to find the solution for the equations.

Here we have to use the substitution method to solve this one,

To do the substitution method we have to follow the following steps:

Step 1) Solve anyone of the equations either for the variable x or y

Step 2) Now, substitute the value obtained from step 1 to the other equation

Step 3) Finally, solve the equation to find the value of the remaining variable.

Here we have to take the equation (2), and we have to solve it for the value of y,

For that we have to rewrite the equation as,

5y = 10 + 3x

y = (10 + 3x)/5

Apply the value of y on the equation (1), in order to get the value of x,

So,

2x + 3(10 +3x)/5 = 6

2x + (30 + 9x)/5 = 6

(10x + 9x + 30)/5 = 6

19x + 30 = 30

19x = 0

x = 0

Now, apply the value of x on the equation in order to get the value of y,

y = (10 + 3(0))/5

y = 10/5

y = 2.

Therefore, the resulting ordered pairs for the system of linear equation is (0, 2).

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Using ratio and proportion, Louie is correct.

Ratio is defined as the relationship between two quantities. On the other hand, proportion is defined as the equality between two or more ratios.

From the given graph (see attached photo), the coordinates of Point F and Point G is (4, 8) and (-6, -7).

If the ratio of FP to PG is 4 to 1, then the ratio of the horizontal distance and vertical distance between the two endpoints is also 4 to 1.

FP : PG = 4 : 1

FP/PG = 4/1 = 4

x-coordinate of P

(4 - x)/(x - -6) = 4

(4 - x) = 4(x + 6)

4 - x = 4x + 24

-5x = 20

x = -4

y-coordinate of P

(8 - y)/(y - -7) = 4

(8 - y) = 4(y + 7)

8 - y = 4y + 28

-5y = 20

y = -4

Hence, the coordinates of Point P is (-4, -4).

Therefore, Louie is correct, while Nicky is mistaken probably while setting up the proportion and solving for the coordinates.

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The system of inequalities that can be used to determine the number of each type of plant to be sold are :

x + y  ≥ 15

$150x + $125y  ≥  $2000

The first step is to determine the inequality signs that would be used in the system of inequalities:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used is the greater than or equal to sign, ≥.

Two system of inequalities would be formed using the information provided in the question. The form of the system of inequalities would be:

number of Mediterranean palms sold + number of palmetto sold  ≥ least number of plants

(number of Mediterranean palms sold x cost of Mediterranean palms) + (number of palmetto sold x cost of palmetto sold   ≥ least number of sales

x + y  ≥ 15

$150x + $125y  ≥  $2000

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The equations of the lines are:

7. y = 3/2x - 3/2

8. y = -1/3x - 8/3

The equation that represents a line, in slope-intercept form is, y = mx + b.

7. Find the slope (m) between (5, 6) and (1, 0):

Slope (m) = (6 - 0)/(5 - 1) = 6/4

Slope (m) = 3/2

Find the y-intercept of the line, b, by substituting m = 3/2 and (x, y) = (1, 0) into y = mx + b:

0 = 3/2(1) + b

-3/2 = b

b = -3/2

To write the equation, substitute m = 3/2 and b = -3/2 into y = mx + b:

y = 3/2x - 3/2

8. Find the slope (m) between (-5, -1) and (1, -3):

Slope (m) = (-1 -(-3))/(-5 - 1) = 2/-6

Slope (m) = -1/3

Find the y-intercept of the line, b, by substituting m = -1/3 and (x, y) = (1, -3) into y = mx + b:

-3 = -1/3(1) + b

-3 = -1/3 + b

-3 + 1/3 = b

-8/3 = b

b = -8/3

To write the equation, substitute m = -1/3 and b = -8/3 into y = mx + b:

y = -1/3x - 8/3

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Answer:

x = 10

Step-by-step explanation:

-3x - 6 = -7x + 34

+7x

4x - 6 = 34

+6

4x = 40

/4

x = 10

Answer:

x = 10

Step-by-step explanation:

-3x - 6 = -7x + 34  Add 7x to both sides

4x - 6 = 34  Add 6 to both sides

4x = 40  Divide both sides by 4

x = 10