The population of Australia was 14.692 million in 1980 and 17.065 million in 1990. Estimate the population of Australia in 2000.

Using a t-distribution with 14 degrees of freedom (n-1) and a 98% confidence level (α = 0.02/2 = 0.01 for each tail), we have:

sample mean (x) = (2051+2061+2162+2167+2169+2171+2180+2183+2186+2195+2196+2198+2205+2210+2211)/15 = 2180.6

sample standard deviation (s) = 39

standard error of the mean (SEM) = s/√n = 39/√15 ≈ 10.077

t-score for a 98% confidence level and 14 degrees of freedom (from t-distribution table or calculator) = 2.977

Margin of error (ME) = t-score × SEM = 2.977 × 10.077 ≈ 30.05

Therefore, the 98% confidence interval for the mean hours worked per year in this state is:

(x- ME, x+ ME) = (2180.6 - 30.05, 2180.6 + 30.05) = (2150, 2211)

Rounding to the nearest integer and putting the limits in ascending order, we get:

(2150, 2211)

Visit here to learn more about confidence level brainly.com/question/22851322

#SPJ11

Answer:

21

Step-by-step explanation

Answer: 400

Step-by-step explanation:

Answer:

26V^5+2V^7

Step-by-step explanation:

The value of angle A is 100⁰.

option D is the correct answer.

The measure of angle A is calculated by applying the following formula as shown below;

If line AB is similar to line AC, then angle B must be equal to angle C.

∠ B = ∠ C = 40 ⁰

The value of angle A is calculated as follows;

∠ A = 180⁰ - ( ∠ B + ∠ C ) ( sum of angles in a triangle )

∠ A = 180⁰  -  ( 40⁰ + 40⁰ )

∠ A = 180⁰ - ( 80 ⁰ )

∠ A = 100⁰

Learn more about angles in a triangle here: https://brainly.com/question/25215131

#SPJ1

Answer:

slope= -6/8 or -3/4

Step-by-step explanation:

(-10-(-4)/(-12-(-20)= -6/8

The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.

To find the area of triangle EFG, we can use the formula:

\(Area = (1/2) \times base \times height\)

In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.

First, let's find the length of FG. We can use the law of cosines:

FG² = EF² + EG² - 2 * EF * EG * cos(∠F)

EF = 72 inches

EG = 34 inches

∠F = 21°

Plugging these values into the equation:

FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)

Solving for FG, we get:

FG ≈ 83.02 inches

Next, we need to find the height. We can use the formula:

height = \(EF \times sin( \angle F)\)

Plugging in the values:

height = 72 * sin(21°)

height ≈ 25.52 inches

Now we can calculate the area:

\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)

Area ≈ 1060.78 square inches

For more such questions on triangle

https://brainly.com/question/1058720

#SPJ8

Answer:

Slope(M)=0

Step-by-step explanation:

Slope(M)=0

Answer:

11 months

Step-by-step explanation:

185 - 20 = 165

165 ÷ 15 = 11

Answer:

100%

Step-by-step explanation:

It doubles in height, which makes it 100%

Answer:

100%

Step-by-step explanation:

The tree grew from 6 feet to 12 feet, which is a growth of 6 feet. 6 feet/6feet is 1, which in percent is 100%.

Now, you could say as the tree doubled in size, the change is 200%, however you must subtract the original height to gain the amount of change. So, 12-6 = 6, and 6/6 = 1, 1*100 = 100%.

Answer:

for the first equation

f(-3) = 34

f(4) = 6

for the 2nd equation

f(-3) = -56

f(4) ÷ 70

Step-by-step explanation:

my work is attached in a picture.

all you do is substitute each x value into each equation

The height of the building is about 364 feet.  

Let's use a proportion to solve the problem. We know that the height of the building and the length of its shadow are proportional to the height of the pole and the length of its shadow. That is:  

height of building/length of building shadow = height of pole/length pole shadow

We are given that the height of the pole is 10 feet, and its shadow is 5.5 feet long. We are also given that the length of the building shadow is 200 feet. We don't know the height of the building, so we'll use "h" to represent it. Substituting the given values into the proportion, we get:

h / 200 = 10 / 5.5

We can solve for "h" by cross-multiplying:

h = 200 * 10 / 5.5

h ≈ 363.6

Therefore, the height of the building is approximately 363.6 feet. Rounding to the nearest foot gives us the final answer:

The height of the building is about 364 feet.

To learn more about proportion:

brainly.com/question/29774220

#SPJ4

The value of the given expression 3 x 2,746 is 8,238.

We are given the expression:-

3 x 2,746

We have to find the value of the given expression using place value.

According to the data given in the question, we can write,

In 2746,

The place value of 6 is 6

The place value of 4 is 4*10 = 40

The place value of 7 is 7*100 = 700

The place value of 2 is 2*1000 = 2000

Hence, we can write,

3*2746 = 3*2000 + 3*700 + 3*40 + 3*6 = 6000 + 2100 + 120 + 18 = 8,238.

To learn more about place value, here:-

https://brainly.com/question/27734142

#SPJ1

Answer:

The center is (4, 7), and the radius is 3.

\( {(x - 4)}^{2} + {(y - 7)}^{2} = 9\)

Answer:

1 mile

Step-by-step explanation:

Jamal's Distance = 3 miles

Since Brendan lives 2 miles closer than Jamal, you do 3 - 2 = 1

Since Jamal lives 1 mile closer than Aisha, you do 3 - 1 = 2

Then, you do 2 - 1

Answer: 1

Answer:

t=2

Step-by-step explanation:

16-2t=3/2t+9

you multiply everything with 2

32-4t = 3t+18

4t-3t=18-32

-7t=-14

t=2

Step 1: Minus the 16 from the 9

Step2: Multiply the 2t wirh the -2t.

Step 3: Divide -4 by -4

We can use a normal distribution to model phat and construct a confidence interval. We are 90% confident that 6.85% to 10.15% of first-time site visitors will register using the new design.

(a) The visitors are from a simple random sample, so independence is satisfied. The success/failure condition is also satisfied, with both 64 and 752 − 64 = 688 above 10. Therefore, we can use a normal distribution to model phat and construct a confidence interval.

(b) The sample proportion is phat = 0.085, SE = 0.010

(c) For a 90% confidence interval, use z⋆ = 1.65. The confidence interval is 0.085 ± 1.65 × 0.010 → (0.0685, 0.1015). We are 90% confident that 6.85% to 10.15% of first-time site visitors will register using the new design.

Normal distribution is a statistical concept that describes the probability distribution of a random variable that is continuous and symmetric around its mean. It is also known as Gaussian distribution or bell curve because of its characteristic bell-shaped curve. The normal distribution is important in statistical analysis because it occurs naturally in many real-world situations, such as the distribution of heights, weights, and test scores. It is also used in hypothesis testing and in the construction of confidence intervals.

The normal distribution is characterized by two parameters: the mean, which is the central tendency of the distribution, and the standard deviation, which measures the spread or dispersion of the distribution. The standard deviation determines the width of the bell curve, with a larger standard deviation indicating a wider curve.

To learn more about Normal distribution visit here:

brainly.com/question/17199694

#SPJ4

Answer:

The leading coefficient in the polynomial 10x2 + 3x - 5 is 10.

Step-by-step explanation:

To find the leading coefficient of the polynomial function, we must first locate the leading term. In a polynomial function, the leading term is the term containing the highest power of x. In this polynomial function, the leading term is 10x2. The leading coefficient of a polynomial function is the coefficient of the leading term, and so the leading coefficient of this polynomial function is 10.

Answer:its c

Step-by-step explanation: hope this helped have a good day or night :)

Answer:

UV = 45

Step-by-step explanation:

ZY is the perpendicular bisector of UV , then

UV = 2 × UY = 2 × 22.5 = 45

Answer

q≤ -11

thats your answer i believe, just typing this because it said it was too short to post

Answer:

\(a_{n}\) = 20 - 12n

Step-by-step explanation:

the explicit rule for an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

a recursive rule has the form

\(a_{n}\) = \(a_{n-1}\) + d

given recursive rule

\(a_{n}\) = \(a_{n-1}\) - 12 : a₁ = 8

then a₁ = 8 and d = - 12

explicit rule is therefore

\(a_{n}\) = 8 - 12(n - 1) = 8 - 12n + 12 = 20 - 12n

Answer:

A)

Step-by-step explanation:

Given function:  

\(h(t)=-16t^2+75t+25\)

The domain (input values) will be the x-intercepts, so the values of t when h(t) = 0.

The quickest way to find these is to use the quadratic formula.

Quadratic Formula

\(x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0\)

\(\implies t=\dfrac{-75 \pm \sqrt{75^2-4(-16)(25)} }{2(-16)}\)

\(\implies t=\dfrac{-75 \pm \sqrt{7225}}{-32}\)

\(\implies t=\dfrac{75 \pm 85}{32}\)

\(\implies t=5, t=-\dfrac{5}{16}\)

Time cannot be negative.

When h(t) = 0, the disk will hit the floor.

Therefore, the domain is restricted to 0 ≤ t ≤ 5

Answer: 36132

Step-by-step explanation:

81+283=364

100*364=36400

67*4=268

36400-268=36132

Answer:

Step-by-step explanation:

100*(81+283)-67*5

=36400-268

=36132

Step-by-step explanation:

a²+ab+b²

(0)^2 + (0)(1) + (1^2)

  0    +    0    +    1        = 1  

Answer:

-9h² - 12h - 3

Step-by-step explanation:

Follow the FOIL method:

FOIL = First, Outside, Inside, Last

Multiply the terms together:

First: 9h * -h = -9h²

Outside: 9h * -1 = -9h

Inside: 3 * -h = -3h

Last: 3 * -1 = -3

Combine like terms: 9h² + (-9h - 3h) - 3

9h² - 12h - 3

-9h² - 12h - 3 is your answer.

~

-0.05 is the average rate of change in median age per year from 1930 to 1960.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,  a data set that gives the median age of an American man at the time of his first marriage.

Year                             Median age

1910                              25.1

1920                             24.6

1930                             24.3

1940                             24.3

1950                             22.8

1960                             22.8

1970                             23.2

1980                             24.7

1990                             26.1

2000                             26.8

The average rate of change from 1930 to 1960 = (-24.3 + 22.8) / (1960-1930)

The average rate of change from 1930 to 1960 = -0.05

Therefore, the average rate of change in median age per year from 1930 to 1960 is -0.05.

Learn more about ratios here:

https://brainly.com/question/13419413

#SPJ1

The speed of the current is 5 mph.

Let the speed of the current be x mph.Speed of the boat downstream = (Speed of the boat in still water) + (Speed of the current)= 15 + x.Speed of the boat upstream = (Speed of the boat in still water) - (Speed of the current)= 15 - x.

Let us assume the distance between two places be d .According to the question,20 = (15 + x) × 6 - d    (1)
Distance covered upstream in 10 hours = d. Distance covered downstream in 6 hours = d + 20.

We know that time = Distance/Speed⇒ Distance = Time × Speed.

According to the question,d = 10 × (15 - x)     (2)⇒ d = 150 - 10x         (2)

Also,d + 20 = 6 × (15 + x)⇒ d + 20 = 90 + 6x⇒ d = 70 + 6x     (3)

From equation (2) and equation (3),150 - 10x = 70 + 6x⇒ 16x = 80⇒ x = 5.

for such more question on speed

https://brainly.com/question/13943409

#SPJ8

Answer:

The value of x is 6.

Step-by-step explanation:

You have to use Pythagorean Theorem, a² + b² = c². Make (4x+1)cm as the hypotenuse because any values substitute into x will give the highest length among these 3 expressions of length :

\( {a}^{2} + {b}^{2} = {c}^{2} \)

Let a = side = (x+1)cm,

Let b = side = 4x cm,

Let c = hypotenuse = (4x+1)cm,

\( {(x + 1)}^{2} + {(4x)}^{2} = {(4x + 1)}^{2} \)

\( {x}^{2} + 2x + 1 + 16 {x}^{2} = 16 {x}^{2} + 8x + 1\)

Then you have to simplify :

\(17 {x}^{2} + 2x + 1 = 16 {x}^{2} + 8x + 1\)

\(17{x}^{2} + 2x + 1 - 16 {x}^{2} - 8x - 1 = 0\)

\( {x}^{2} - 6x = 0\)

Next you have to solve it :

\( {x}^{2} - 6x = 0\)

\(x(x - 6) = 0\)

\(x = 0 \: (rejected)\)

\(x - 6 = 0\)

\(x = 6cm\)

The value of x in the right triangle is 6 cm.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

Right triangle:

The three sides are:

x + 1, 4x and 4x + 1

Applying the Pythagorean theorem.

(x + 1)² + (4x)² = (4x + 1)²

x² + 2x + 1 + 16x² = 16x² + 8x + 1

17x² + 2x + 1 = 16x² + 8x + 1

17x² - 16x² = 8x - 2x

x² = 6x

x gets canceled.

x = 6

Thus,

The value of x is 6.

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ2

In response to the query, we can state that Hence, P"s coordinates are coordinates  (3, 4).

When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.

A point's y-coordinate changes sign when it is reflected across the x-axis, but its x-coordinate stays the same.

Hence, we must modify the sign of the y-coordinate while leaving the x-coordinate unaffected in order to reflect point P(3,-4) across the x-axis. The reflected point P' will therefore have coordinates (3, 4).

Hence, P"s coordinates are (3, 4).

To know more about coordinates  visit:

https://brainly.com/question/27749090

#SPJ1