In 2018, the population of Sydney was 5.48 million.
This was 22% of the total population of Australia.
Work out the total population of Australia in 2018
Give your answer correct to 3 significant figures.

Answer:

A) 4 batches

B) 1 1/2 batches

C) 10 batches

D) 1 2/3 batches

Step-by-step explanation:

A) A 1/4 goes into 1, 4 times so it would make 4 batches.

B) 1/4 = 2/8 so 3/8 = 1.5/4 and that would make 1.5 batches.

C) since 1 cup of sugar can make 4 batches, 2 cups can make 8 batches and 1/2 cup makes 2, so 8+2= 10 batches

D) 1/4=3/12 that means 5/12 = 1/4+1/6 and 1/6 divided by 1/4 = 2/3 so that means that it can make 1 2/3 batches.

The value of x on the diagram is given by the following option:

D) 50º.

When two parallel lines are cut by a transversal line, the corresponding angles are the angles that are in the equivalent position for each parallel line.

The parallel lines for this problem are given as follows:

L1 and L2.

Hence the corresponding angles are given as follows:

The bases of the rectangle are also parallel, hence two extra pairs of corresponding angles are given as follows:

As all these angles are corresponding, they have the same measure, hence:

4a = 100º

a = 100º/4

a = 25º.

The angle x is twice the measure of these angles, hence:

x = 2 x 25º

x = 50º.

Meaning that option D is correct.

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Using the decay constant on the exponential function, the mass of the sample that will be left in 2013 is 35g

An exponential function is a function that can be expressed in the form     f(x) = b^x, where b is a positive real number and x is a real number. The graph of an exponential function is a curve that increases or decreases rapidly as x increases or decreases.

In the exponential decay, the decay function can be given as;

y = ae⁻ⁿˣ

The disintegration constant is also know as the rate of decay and we can calculate it as;

260 = 470e⁻ⁿ⁽³⁾

n = 0.197

n = 0.2

The disintegration constant is 0.2

The amount left in 2013 will be;

y = 470e⁻⁽⁰.²⁾⁽¹³⁾

y = 34.90

The mass in 2013 is 35g

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Answer: The inequality that can be used to determine the maximum number of days Alyssa can afford to rent for while staying within her budget is:

43d + 0.1(275) <= 100

Step-by-step explanation: The rental car company charges $43 per day to rent a car and $0.10 for every mile driven.

Alyssa wants to rent a car for d days, and she plans to drive 275 miles.

The cost of renting the car for d days is 43d, and the cost of driving 275 miles is 0.1(275)

To determine the maximum number of days Alyssa can afford to rent for while staying within her budget, we can write the inequality:

43d + 0.1(275) <= 100

This inequality represents the total cost of renting the car and the cost of driving, which should be less than or equal to $100 (Alyssa's budget)

On solving the inequality we can determine the maximum days Alyssa can afford.

a. The probability that both adults think most celebrities are good role models is 0.0359

b. The probability that neither of adults think that celebrities are good model is 0.6559.

P(adult think most celebrities are good role models) = 209 / 1100

Since the first selected adult is not replaced, there are 1099 total adults left.

P(second adult think most celebrities are good role models) = 208 / 1099

So, P(both adults think most celebrities are good role models) = 209 / 1100 * 208 / 1099

= 0.19 × 0.1893

= 0.0359

b) The probability that neither of adults think that celebrities are good model is,

P(Neither adult) = P(1st adult does not think)P(2nd adult does not think)

= ((1100 – 209)/1100)((1100 – 209– 1)/1099) =0.6559

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Complete question

In a sample of 1100 us adults 209 think the most celebrities are good role models. Two U.S adults are selected from this sample

Calculate the probability that both adults think most celebrities are good role models.

Calculated the probability that neither of adults think that celebrities are good model.

Answer: [tex]5 \text{ cm}^2[/tex]

Step-by-step explanation:

[tex]4 \times 1 \frac{1}{4}=4 \times \frac{5}{4}=5[/tex]

Therefore, the answer is [tex]5 \text{ cm}^2[/tex].

Answer:

Step-by-step explanation:

Given-: Y= -X+1  (1)

            3X-Y=3  (2)

we will put the value of Y from equation (1) in equation (2)

  3X-(-X+1)=3

   3X+X-1=3

   4X-1=3

Taking -1 to R.H.S

  4X=3+1

 4X=4

 X=4/4

 X=1

Now put the value of X in equation (1)

Y=-X+1

Y=-1+1

Y=0

So the option will be B (1,0)

On solving the provided question we can say that quadratic equation is  y = 3x + 2x^2 => y = 14

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here,

quadratic equation is

y = 3x + 2x^2

y = 6 + 8

y = 14

as x = 2

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The height of the pebble after 2 seconds is 201 feet.

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

y = 265 − 16t2.

The height of the pebble after 2 seconds is given by

y = 265 - 16 * 2^2.

Plugging in the values:

y = 265 - 16 * 4

y = 265 - 64

y = 201 feet

So, the height of the pebble after 2 seconds is 201 feet.

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Complete question

The deck of a bridge is suspended 265 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by

y = 265 − 16t2. What is the height after 2 seconds

Answer:

x = 20

Step-by-step explanation:

Corresponding angles are congruent (have the same measurements).

5x + 15 = 115  Subtract 15 from both sides

5x + 15- 15 = 115 - 15

5x = 100   Divide both sides by 5

x = 20

Answer:

-320

Step-by-step explanation:

Use the formula

Tₙ = a + (n - 1)d where

a is the first term (in this case, -2)

n is the required term ( in this case, 54)

d is the common difference (in this case, -6)

54th term = -2 + 53 x -6 = -320

Pls mark as brainliest if possible. Cheers

Answer:

see explanation

Step-by-step explanation:

∠ 2 and ∠ 5 are on opposite ( alternate) sides of the transversal and are in between ( in the interior of ) the parallel lines.

The pair are then alternate interior angles.

Answer:

11.64

Step-by-step explanation:

24.68/2.12=11.64

The rays in the figure are (b) EA, EF, ED and EG

A ray in geometry is a part of a line that has one endpoint and continues infinitely in one direction.

It is represented by an arrow with the endpoint of the arrow being the endpoint of the ray

Using the above definition as a guide, we have the rays to be

option (b) EA, EF, ED and EG

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Answer:

0.4

Step-by-step explanation:

4.00-3.55 = 0.45 = 0.4

The tip she gives is given by approximately 12.7% of the price.

The cost of a medium coffee is given by = $ 3.55

Mary Anne brings $ 4 with her and buy a coffee.

So, the remaining dollars with her is given by = 4 - 3.55 = $ 0.45

According question she gives this remaining amount as tip.

Therefore she gives a tip of $ 0.45 on the price of $ 3.55

The percentage of her tip = (0.45/3.55) * 100% = 12.7 % [Rounding off to one decimal place]

Hence the tip she gives is given by approximately 12.7% of the price.

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We are aware that P = 2(a + b) units is the perimeter of a parallelogram.Consequently, the parallelogram's sides are 50 cm, 25 cm, 50 cm, and 25 cm.

We are aware that P = 2(a + b) units is the perimeter of a parallelogram.Adding up all four sides will reveal a parallelogram's perimeter.An area of a circle of radius r is known as r2 in geometry.

The circumference-to-diameter ratio, which is always the same and is roughly equivalent to 3.14159 in this context, is denoted by the Greek letter.

Let side a and the side next to it in the parallelogram be a and b, respectively.

The parallelogram's perimeter is equal to 2(a+b)=150, where a+b=75.

Since an is 25 cm taller than b, a=b+25.

By changing it in equation 1, b+25+b=75 2b=50 b=25 is obtained.

a+b=75\sa=75=25\sa=50

Consequently, the parallelogram's sides are 50 cm, 25 cm, 50 cm, and 25 cm.

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Answer: C

Step-by-step explanation: If you solve each of them (1 x 4=4, 2x4=8, 3x4=12, 6x4=24), You can see that the are rational.

Answer:

12,375

Step-by-step explanation:

that x mean time each number by x

The answer should be 4x(2x-3) so Renuka does not score full marks.

A number system is defined as a system of writing to express numbers.

The given expression is 8x²-12x.

To factorise this we have to find the highest common factors from both the terms.

Factors of 8 are 1, 2, 4, 8

Factors of 12 are 1, 2, 3, 4, 6,12

The highest common factor is 4.

So we have to take common 4 but Renuka has taken out 2.

So she does not got full marks.

The answer should be 4x(2x-3)

Hence, the answer should be 4x(2x-3) so Renuka does not score full marks.

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Answer:

Step-by-step explanation:

2940.1667

Answer:

2940.16667

Step-by-step explanation:

Answer:

To solve this problem, we will use the following steps:

Step 1: Let's assume that the number of adult tickets sold is x and the number of senior/child tickets sold is y

Step 2: We know that the number of senior/child tickets sold was 27 less than twice the number of adult tickets sold, so we can write the equation: y = 2x - 27

Step 3: We also know that the total value of tickets sold was $2,647.50. Since adult tickets sold for $10 each and senior/child tickets sold for $7.50 each, we can write the equation: 10x + 7.5y = 2,647.50

Step 4: Now we have two equations with two unknowns, we can substitute one equation into another to find the value of x and y.

y = 2x - 27

10x + 7.5(2x - 27) = 2,647.50

10x + 15x - 405 = 2,647.50

25x = 3,052.50

x = 122

Step 5: We can substitute the value of x in one of the equation, to find the value of y

y = 2(122) - 27

y = 245

Final Answer: 122 adult tickets and 245 senior/child tickets were sold.

Note: We can check our solution by multiplying the number of adult tickets by $10 and the number of senior/child tickets by $7.5 to check if the total money is $2,647.50 which is true.

Answer: A rational function is a function that is a fraction and has the property that both its numerator and denominator are polynomials.

Step-by-step explanation:

From the coordinates we can see the rule for this transformation:

This is a rotation by 180 degrees and translation 5 units down, therefore shape or size remain as is. So this is a congruence transformation.

Answer:

Rotation of 180° about the origin (0, 0) followed by a translation of 5 units down.

Congruence transformation.

Step-by-step explanation:

Given vertices of ΔPQR:

Given vertices of ΔSTU:

From observation, the mapping rule the transforms ΔPQR to ΔSTU is:

Rotation of 180° about the origin (0, 0) followed by a translation of 5 units down.

This is a congruence transformation as the two triangles have the same shape and same size.

Step-by-step explanation:

directly proportional means

y = kx

with k being a constant factor for all values of x.

we get k by using the given data point (10, 15).

15 = k×10

k = 15/10 = 1.5

so, now for the other tree we know k and x and calculate y

y = 1.5×14.4 = 21.6 m

it is 21.6 m tall (its height is 21.6 m).

Answer:

To find the greatest possible price of the calculator, we can use the information given about the total sales.

We know that the total sales of the calculator on three days are $180, $414, and $306. We can assume that the calculator is sold at a single price p on all three days, and the total number of calculators sold is x, y and z respectively.

So, we can set up the following equation:

px = $180 (1)

py = $414 (2)

p*z = $306 (3)

From (1) and (2) we can say x < y and from (2) and (3) we can say y > z

so the greatest possible price of the calculator will be the one from equation (2)

p = $414 / y

Therefore, the greatest possible price of the calculator is $414 / y.

It is important to note that we don't know the actual numbers of calculators sold, but we know that y is greater than x and z, and that is why we can say that the greatest possible price of the calculator is $414 / y.

Using exponential function, the value of x that makes f(x) = g(x) is x = 6.7 (rounded to the nearest integer).

The value of x that makes f(x) = g(x) is approximately x = 76.

To solve this, you can set f(x) = g(x) and solve for x.

[tex]f(x)=400(0.90)^x\\g(x)=70(1.10)^x\\400(0.90)^x = 70(1.10)^x\\Divide both sides by 400 to get:\\(0.90)^x = (1.10)^x / (400/70)\\[/tex]

Take the logarithm of both sides and use the power rule:

[tex]x(log 0.90) = (log (1.10)) / (log (400/70))\\x = (log (1.10)) / (log (400/70)) / (log 0.90)\\x = 76.3 (round to the nearest integer)\\[/tex]

Therefore, the approximate value of x that makes f(x) = g(x) is x = 76.

To solve this, we can set the two equations equal to each other and solve for x.

[tex]f(x)=400(0.90)^x = 70(1.10)^x\\400(0.90)^x = 70(1.10)^x\\(0.90)^x = 70/400 (1.10)^x\\(0.90)^x / (1.10)^x = 70/400\\(0.90/1.10)^x = 70/400\\(0.81818)^x = 70/400\\[/tex]

Take the logarithm of both sides.

[tex]xlog(0.81818) = log(70/400)\\x = log(70/400) / log(0.81818)\\x = 6.7 (rounded to the nearest integer).[/tex]

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Answer:

22

Step-by-step explanation:

Range : Maximum - Minimum

Minimum = 6

Maximum = A (Let maximum be A)

Hence,

16 = A - 6

A = 22

Maximum = 22

Answer:

Step-by-step explanation:

2 x 12 - (9 - 3) x 2 / 2

Answer:

54.027

Step-by-step explanation:

54 x 1.0005 = 54.027

Answer:

67.96 inches

hope this help

The evaluation of the given fraction is 1 2/19

From the question, we are to evaluate the given fraction

From the given information,

The given fraction is

(11/15 + 2/3) ÷ (1 1/2 - 7/30)

Simplifying

((11 + 10)/15) ÷*(3/2 - 7/30)

(21/15) ÷ ( (45 - 7)/30)

(21/15) ÷ (38/30)

Then,

21/15 × 30/38

(21 × 30) / (15 × 38)

630 / 570

21/19

= 1 2/19

Hence, the evaluation is 1 2/19

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