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This is grade 6 maths
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Answer:

A) [tex]y = \frac{1}{10}x + 28[/tex]

B) $116.5

Step-by-step explanation:

The data we are given is:

• for 440 minutes of usage, the total cost is $72

• for 940 minutes of usage, the total cost is $122

A)

In order to find an equation in the form [tex]y = mx + b[/tex], we must first express the given data as coordinates in the form [tex](x, y)[/tex].

We are told that [tex]x[/tex] is the number of monthly minutes, and [tex]y[/tex] is the total monthly fee. Therefore the first piece of data expressed as coordinates is (440, 72), and for the second piece of data, it is (940, 122).

Now that we have the coordinates, we can make an equation using the formula:

[tex]\boxed{\frac{y - y_1}{y_2 - y_1}= \frac{x - x_1}{x_2 - x_1}}[/tex],

where [tex](x_1, y_1)[/tex] is (440, 72) and [tex](x_2, y_2)[/tex] is (940, 122).

Substituting the values into the formula, we get:

[tex]\frac{y - 72}{122 - 72}= \frac{x - 440}{940 - 440}[/tex]

⇒ [tex]\frac{y - 72}{50} = \frac{x - 440}{500}[/tex]

⇒ [tex]50 \times \frac{y - 72}{50} =50 \times \frac{x - 440}{500}[/tex]       [Multiplying both sides of the equation by 50]

⇒ [tex]y - 72 = \frac{x - 440}{10}[/tex]

⇒ [tex]10y - 720 = x - 440[/tex]    [Multiplying both sides by 10]

⇒ [tex]10y = x +280[/tex]            [Adding 720 to both sides]

⇒ [tex]y = \frac{1}{10}x + 28[/tex]    (Answer)

B)

To find the total cost if 885 minutes are used, we have to replace [tex]x[/tex] in the above equation with 885:

[tex]y = \frac{1}{10}(885) + 28[/tex]

⇒ [tex]y = 88.5 + 28[/tex]

⇒ [tex]y = 116.5[/tex]    

Therefore, the total cost will be $116.5.   (Answer)

Percentage of the cupcakes that had sprinkles = 30 %

Percentage

Percentage, often referred to as percent, is a fraction of 100. Percentage means "per 100," and denotes part a total amount. For example, 45% represents 45 out of 100.

Proportion

The proportion formula is used to depict if two ratios or fractions are equal. We can find the missing value by dividing the given values. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The first step is to divide 12 by 40 to get the answer in decimal form:

12 / 40 = 0.3000

Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:

0.3000 * 100 = 30.00%

Percentage of the cupcakes that had sprinkles = 30 %

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Jonas have to repay $13888 after 4 years.

Given

Principle amount of loan (P) = $12,400

Rate of interest (R) = 3%

Time period (T) = 4 years

Also the interest is not compounded, hence it is simple interest.

The formula for simple interest is (PTR)/100

Where,

P = Principle amount

T = time period

R = rate of interest

By substituting the values in the formula we get,

Simple interest =  (12400 x 4 x 3) / 100

Simple interest = 1488

Hence adding this interest to Principle sum we get

12400 + 1488 = 13888

Jonas has to repay $13888 after 4 years.

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Answer:

[tex]\frac{14}{25}[/tex]

Step-by-step explanation:

per cent means 'out of 100 ' , then

56%

= [tex]\frac{56}{100}[/tex] ( divide numerator/ denominator by 4 )

= [tex]\frac{14}{25}[/tex] ← in simplest form

For 6 hours

Grace will pay = $11 + 6 x $4

= $11 + $24

= $35

for t hours

Grace will pay = $11 + t x $4

= $11 + $4t

= $( 11 + 4t )

The value of the quadratic equation given as -9- -8x^2= -209 is 5

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The quadratic equation is given as

-9- -8x^2= -209

Add 9 to all sides of the equation

So, we have

-8x^2= -200

Divide both sides of the equation by -8

x^2= 25

Take the square roots

x = 5

Hence, the solution of the equation is 5

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Answer:

X=1

Step-by-step explanation:

9x -4 = 2x+3 :

9x-4=2x+3

9x -4 + 4= 2x + 3+4

Simplify

subtract 2x from both sides

Simplify

Divide both sides by the same factor

simplify

X=1

P(A). P(Y)= 0.5*0.6=0.3

Probability: - Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

Number of cases of A, N(A)= 250,

So,

     P(A)=250/500 =0.5

and

      N(Y)= 300, so P(Y)=300/500 =0.6

N(A and Y)= 175 so P(A and Y)= 175/500=0.35

A and Y are mutually exclusive implies A and Y donot have any elements in common, but here there are 175 people who are below 30 years and under the influence of alcohol, So they are not mutually exclusive!!

For A and Y to be independent, the Probability of A intersection Y should be equal to the product of their respective probabilities,

in this case P(A). P(Y)= 0.5*0.6=0.3 which is not equal to P( A intersection Y) (0.35)

So, A and Y are not mutually Independent also.

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1.     [tex]i^{23}[/tex] = - i

2.   [tex]\sqrt{-128}[/tex]  = 8i√2

Steps to simplify complex numbers:

1.  To simplify  [tex]i^{23}[/tex]

We can rewrite [tex]i^{23}[/tex] as [tex](i^{4)^{5} } (i^{2} . i )[/tex]

write [tex]i^{4}[/tex] as [tex](i^{2} )^{2}[/tex]

[tex](i^{4)^{5} } (i^{2} . i )[/tex]  = [tex]((i^{2} )^{2} )^{5} (i^{2} . i)[/tex]

we  know [tex]i^{2}[/tex] = -1

((-1²))⁵  [tex](i^{2} .i)[/tex]

we know that -1² = 1

= 1⁵ [tex](i^{2} .i)[/tex]

= 1 [tex](i^{2} .i)[/tex]

= [tex](i^{2} .i)[/tex]

here [tex]i^{2}[/tex] =-1

-1 . [tex]i^{}[/tex]

= - i

so [tex]i^{23}[/tex] is -i

2. To simplify [tex]\sqrt{-128}[/tex]

= [tex]\sqrt{(- 1) . (128)}[/tex]

= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{128}[/tex]

= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{(2) . (64)}[/tex]

= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{(2) . (8) . (8)}[/tex]

here [tex]}\sqrt{-1}[/tex]  = i

substituting i we get

= i . 8 √2

= 8i√2

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The value of b for which the difference between the fractions

 (2b - 1) / 2 and  (1 + 5b) / 4 negative will be;

⇒ b < -3

What is Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts.

Given that;

Two fractions are,

⇒ (2b - 1) / 2 and  (1 + 5b) / 4

Since, The difference between the fractions  (2b - 1) / 2 and  (1 + 5b) / 4 negative.

So, we can formulate;

⇒ (1 + 5b) / 4 - (2b - 1) / 2 < 0

Solve for b, as;

⇒ 1 + 5b - 2 (2b - 1) < 0 x 4

⇒ 1 + 5b - 4b + 2 < 0

⇒ b + 3 < 0

Subtract 3 both side;

⇒ b + 3 - 3 < 0 - 3

⇒ b < -3

Therefore, The value of b for which the difference between the fractions  (2b - 1) / 2 and  (1 + 5b) / 4 negative will be;

⇒ b < -3

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Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.

Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.

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Answer:

Answer:

9 [tex]\frac{3}{4}[/tex]

13[tex]\frac{2}{3}[/tex]

3[tex]\frac{4}{6}[/tex] or 3 [tex]\frac{2}{3}[/tex] simplified

Step-by-step explanation:

For the fraction part, could how many total spaces between the numbers then count how many spaced over to the pointer.

For #16, there are 4 spaced between 9 and 10.  The pointer is pointing to 3 spaces from 9 so the fraction is 3/4.

For #18, there are 6 spaces and the pointer is at the 4th space.  You can see that if you counted every 2 spaces as I unit, you would have a total of 3 spaces and the pointer is over 2 of those three spaces.  That would get your simplified answer of 2/3.

Answer:

y=3x+3

Step-by-step explanation:

i use point (-1,0) and (0,3) then 3-0/0-(-1)=3/1=3 so (0,3) 3 is the y intercept plug in so y=3x+3is the equation

Answer:

See below

Step-by-step explanation:

Find two convenient points to calculate the slope:

0,3   and   -1,0         slope =  m =  (3-0) / ( 0 - -1) = 3

  and the y axis intercept = 3   (from looking at graph)

line equation is   y = mx + b             ( where b is the y-axis intercept)

                     y = 3x + 3

Answer:

a) 78.75

b) 62.5

a) 2 minutes

b) 19 minutes

c) 24 minutes and 48 seconds

Answer:

slope is 3

Step-by-step explanation:

8-5/-2-(-3)=3/1=3 3 is the slope

Answer: 60 divided by 4

Step-by-step explanation:

Answer:

The average would be $15 for each shirt.

Step-by-step explanation:

divide the amount of money by the amount of shirts.

The linear function to model the amount of money in her checking account at any time t is 185 + 5.55t.

An interest simply means the extra amount that's borrowed when one borrows money or when one saves.

In this case, the checking account pays simple interest at 3% per year. She has $185 in her account.

The amount of money in the account at anytime will be:

= 185 + (PRT/100)

P = principal

R = rate

T = time

= 185 + [(185 × 3 × t)/100]

= 185 + 5.55t

The function is 185 + 5.55t.

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Answer:

A = 101250 meter²

Step-by-step explanation:

Answer:

Maximum area enclosed will be 101250 meter².

Step-by-step explanation:

Let the length of the rectangular plot is x meters and the width is y meters.

900 meters is the length of the fence which represents the length of the three sides of the plot.

Therefore,

x + 2y = 900

y =  meters

Now the area of the rectangular plot will be

A = Length × Width

  = (x)(y)

  = 

  = 450x - 

We know for the maximum area we will differentiate the area and equalize it t the zero.



= 450 - x

For the maximum area, 

Therefore, 450 - x = 0

x = 450

and y = 

y = 

y = 450 - 225

  = 225 meters

Now the area enclosed A = 450 × 225

A = 101250 meter²

If about 5% of americans have blue eyes, the probability of 3 people selected at random having blue eyes is 1/8000.

About 5% of americans have blue eyes

The probability of a person having blue eyes = 5% = 5/100

Eyes colour of a person is an indepedent event, which means the eye colour of one individual is independent of the other. The probability of one individual having blue eyes or not is independent of another person.

In case of independent event the probability of A intersection B = probability of A multiplied with probability of B

P(A∩B) = P(A) x P(B)

P(A∩B∩C) = P(A) x P(B) x P(C)

The probability that all 3 have blue eyes = 5/100 x 5/100 x 5/100

= 125/1000000

= 1/8000

Therefore, if about 5% of americans have blue eyes, the probability of 3 people selected at random having blue eyes is 1/8000.

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The area in square inches of the tile is 9 / 4 t .

She makes rectangular kitchen tiles with an area of t square inches.

Therefore,

area of the rectangular kitchen tiles = lw

t = lw

l = t / w

w = t / l

Therefore, the tile is 3 / 4 as long and 3 times wide as her kitchen tiles.

Hence,

area of the tile = 3 / 4 t / w × 3(t / l)

area of the tile = 9 / 4 × t² / lw

where

lw = t

Hence,

area of the tile  = 9 / 4 × t² / t

area of the tile  = 9 / 4 × t

Therefore,

area of the tile  = 9 / 4 t

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Note the in such type of questions the term 'probability' and 'proportion' can be used in place of each other. It is because the probability gives the proportion of favorable outcomes to the total outcomes.

Let X be the random variable representing the number of data points greater than or equal to 22.

Given that the mean and standard deviation is 18.5 and 3.25, respectively.

Consider the formula for z-score as,

So the probability is calculated as,

From the Standard Normal Distribution Table,

Substitute this value,

Thus, there is 0.1401 or 14.01% probability that a data will be greater than or equal to 22.

So, the 14.01% of the data is expected to be 22 or greater.

Step-by-step explanation:

Let's say first piece is x. First and third ratio is 1:4 so it would be

4x - x = 360

3x = 360

x = 120 Third piece is 120g. Now we just multiply the rest.

2 × 120 = 240g

4 × 120 = 480g, total 840g

Answer:

840 g

Step-by-step explanation:

  Ratio of weight of 3 pieces = 1 : 2 : 4

Weight of 3 pieces = x , 2x , 4x

Weight of third piece - weight of first piece = 360 g

           4x - x = 360

                3x = 360

Divide both sides by 3,

                  x = 360÷ 3

                 x = 120 g

Weight of first piece = x = 120 g

Weight of second piece = 2x = 2*120 = 240g

Weight of third piece = 4x = 4 *120 = 480 g

Weight of the whole cake = 120  + 240 + 480

                                          = 840 g

Answer:

8a)

D: [tex]1\leq x\leq 3[/tex].

R: [tex]0\leq y\leq 4[/tex]

8b)

D: [tex]x\geq 0[/tex]

R: [tex]y\geq 1[/tex]

Step-by-step explanation:

8a) The domain is the set of all possible numbers the x values could be. If there is no corresponding y value for an x value, that x value would not be considered part of the domain.

In the question, the function starts at x = 1 and continues until 3. The ends of the function are closed, so it is inclusive. This can be written as [tex]1\leq x\leq 3[/tex].

The range is all the possible y values. The function does not go below y = 0 and has a maximum of 4. The ends of the function are closed, so it is inclusive. This can be written as [tex]0\leq y\leq 4[/tex]

8b) We can do the same for this problem. The x has a minimum at 0 and continues to go on without an upper bound(as indicated by the arrow), is also includes the point where x=0. Therefore, the domain can be written as [tex]x\geq 0[/tex].

As for the range, the y minimum is 1 and the function continues to increase as shown by the upwards slope and arrow. The function also includes the point where y=1, so it can written as [tex]y\geq 1[/tex]

Answer:

24a -12b + 15

Step-by-step explanation:

Answer:

=24a - 12b + 15

Step-by-step explanation:

3(8a-4b+5)

Apply the distributive law:  m(a+b+c) = ma + mb + mc

3 (8a - 4b + 5 ) = 3 · 8a + 3( -4b)+ 3 · 5

= 3 · 8a + 3( - 4b) + 3 · 5

Simplify 3 · 8a + 3( -4b) + 3 · 5 :   24a - 12b + 15

= 24a - 12b + 15

From the linear model we can see that the height of the balloon after 15 seconds is 0 feet.

Depending on the context, the phrase "linear model" is used differently in statistics.

From the linear model we can see that the water balloon is thrown from a height of 40 feet upwards.

Now the balloon reaches a height of 70 feet and then falls back down on earth due to gravity.

At about 10 seconds the balloon falls on the ground and splashes.

Hence for further time the balloon is always at the ground.

Therefore at time of 15 seconds the height of the balloon is always 0 feet as represented in the linear model.

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Answer:

Coordinate A would be (12,3)

Coordinate B would be (12,7)

Coordinate C would be  (10,5)

The probability of making no sales in 100 tries is 0.97^100. That's equal to about 0.0476, so the probability of getting at least one sale is 0.9524. About 95%.

If the probability of making a sale is 0.03 then the probability of not making a sale must be 1-0.03 which is 0.97.

So looking at contacting 100 prospects, you could say there are two general outcomes. Either the salesman makes no sales at all, or he makes at least one sale. There are no other possible outcomes, so the probability of those two outcomes must add up to 1.

So the probability of making of at least one sale is 1 minus the probability of making no sales.

The probability of making no sales in 100 tries is 0.97^100. That's equal to about 0.0476, so the probability of getting at least one sale is 0.9524. About 95%.

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