A county planner is looking at trends in population growth for two towns, Hapville and Merton.

The population of Hapville in the year 2000 was 18,000. Since then, the population has increased at a steady rate of 500 per year.
The population of Merton is increasing according to the equation y=12,000(1.04)t , where y = the population in thousands and t = the number of years since the year 2000.
If these trends continue, how will the populations of the two towns compare in 2030?

Answer: \(\dfrac15\)

Step-by-step explanation:

Given : A cloth bag contains 6 cards numbered 1 through 6. Two cards are drawn without replacement.

Favorable outcome: sum of the numbers on the two drawn cards is 7

Since 1+6 = 7 , 2+5=7, 4+3 = 7

So, sum of 7 can be obtained as (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1)

Probability of getting (first 1, second 6) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 2, second 5) = (\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 3, second 4) =\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 4, second 3) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 5, second 2) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 6, second 1) =\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Required probability =\(6\times\dfrac{1}{30}=\dfrac15\)

Hence, the required probability = \(\dfrac15\)

113

Hope this helped you- have a good day bro cya)

Answer:

15:24, 20:32 and 40:64.

Step-by-step explanation:

hope this helps

Answer:

The ratios that work is 15:24 because 5 x 3= 15, 24 x 3 = 24 as they both have a 3 as factors. There's also 20:32 as they both have a 4 as factors and  lastly 16:10 because they both have a 2 as factors.

Step-by-step explanation:

The ratios that work is 15:24 because 5 x 3= 15, 24 x 3 = 24 as they both have a 3 as factors. There's also 20:32 as they both have a 4 as factors and  lastly 16:10 because they both have a 2 as factors.

The required area of the coat button with given radius of 6 millimeters is equal to 113.04 square millimeters.

Radius of the coat button is equals to 6 millimeters

let us consider 'A' be the area of the circle.

And 'r' be the radius of the circle.

Use the formula for the area of a circle we have,

A = πr^2

π (pi) is a mathematical constant approximately equal to 3.14.

Plugging in the given value of the radius we have,

⇒ A = π(6mm)^2

⇒ A = 36π mm^2

⇒ A = 36 × 3.14mm^2

⇒ A = 113.04 mm^2

Therefore, the area of the coat button is 113.04 square millimeters.

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Answer:

j

Step-by-step explanation:

v

Solution :

a). The point estimate of proportion of college graduates among women who work at home,

\($\hat p =\frac{166}{506}$\)

  = 0.3281

99.5% confidence interval

\($=\left( \hat p \pm Z_{0.005/2} \sqrt{\frac{\hat p (1- \hat p)}{n}} \right)$\)

\($=\left( 0.3281 \pm 2.81 \sqrt{\frac{0.3281 \times (1- 0.3281)}{506}} \right)$\)

\($=(0.3281 \pm 0.0586)$\)

\($=(0.2695, 0.3867)$\)

The option A is correct because the value of the statement is 6+3/n-8.

According to the statement

we have given that the statement and we have to write the statement in the numerical form.

So, For this purpose

we know that the given statement is

"Six more than the quotient of three and a number, decreased by eight".

In this statement "Six more than" indicates the sum between the quotient and 6.

And "The quotient of three and a number" indicates a fraction where the numerator is 3 and the denominator is , a number.

"Decreased by eight" indicates a subtraction between the quotient an 8 units".

If we unit all parts of the statements, we would have

6+3/n-8

So, From the given statement, The option A is correct because the value of the statement is 6+3/n-8.

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The length of side AB in right angled triangle ABC  will be 48 cm.

Every triangle with one 90° angle is said to have a right angle. The triangle with a right angle is known as a right triangle because a right angle is 90 degrees.The longest side of a right angle is known as the hypotenuse, and it is opposite the right angle.

Given,

∠B= 90°, AC = 96 cm, ∠C = 30°

Now, we know, Trignometric ratio sin θ in triangle can be given by-:

sin θ = \(\frac{perpendicular}{hypotenuse}\)

From given figure,

Perpendicular= AB= ?

and Hypotenuse= AC = 96

and θ= 30°

Hence,

sin 30° =\(\frac{perpendicular}{hypotenuse}\)= \(\frac{AB}{96}\)

\(\frac{1}{2} = \frac{AB}{96}\)                                      (∵ sin 30°= 1/2)

\(AB=\frac{96}{2}\)

\(AB= 48 cm\)

Thus, AB= 48 cm

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Correct Question:ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB = ?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The total number of people want in all is 531.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of buses = 9

Number of buses that has 63 people = 5

Number of buses that has 54 people = 4

The total number of people in all the buses.

= 5 x 63 + 4 x 54

= 315 + 216

= 531

Thus,

The total number of people want in all is 531.

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The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

Answer:

pretty sure it’s addition property of equality since you’re adding 5 to 10

(1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

Given are the polynomials,

1) x² - 2 x - 8

Factors = (x+2)(x-4)

2) x² + 2 x - 8

Factors = (x-2)(x+4)

3) x²-2x-4 = There will be no integral root.

4) x²+2x-4 = There will be no integral root.

Hence the (1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

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Answer:

1/2

Step-by-step explanation:

cuz you take away 2/3 over two and then you get a half simply put

The correct solution set for the given graph include the following: D. {infinite set of points on the line}.

In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.

This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:

Generally speaking, the solution set of a graph simply refers to all of the points that lie on its line. By critically observing the graph of lines a and b, we can reasonably infer and logically deduce that they both have the same slope, solution set, as well as increasing and decreasing infinitely.

In this context, the correct solution set lies in both Quadrant II and Quadrant III because both lines move towards negative and positive infinity i.e [-∞, ∞].

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Answer:

8 and 9

Step-by-step explanation:

8 times 9 is 72

Answer:

66.6666

Step-by-step explanation

This is the answer because I found it up here and I got the answer right.

to find the interest you simply just multiply the amount by the percentage, so:

$3000 × 3.5%

= $3000÷100×3.5

=$105

Answer:

B

Step-by-step explanation:

201.06

Step-by-step explanation:

pie which is 3.14^2 = 3.14 x 8^2 = 201.06193 but

201.06 is right

Answer:

c. y = x^2 - 4

Step-by-step explanation:

If you graph both y = x^2 and y = x^2 - 4, you'll be able to see that the equation of function, y = x^2 - 4, is 4 units down from the equation of function y = x^2.

Answer:

(x+4)^2  -25

Step-by-step explanation:

x²+8x-9 in the form  (x+k)² +h.

We need to complete the square.

x^2 +8x   -9

Take the coefficient of x.

8

Divide by 2.

8/2 =4

Square it.

4^2 = 16

Add this then subtract i.

x^2 +8x+16    -16   -9

The x^2 +8x+16 becomes  (x+4) ^2  and we can simplify the remaining terms.

(x+4)^2  -25

Here is your answer.

A tank contains 5832 litres of water.

Total amount of water in tank = 5832 litres.

Each day one-third of the water in the tank is removed and not replaced.

Since one third of the water is removed for six days.

1st day = 1/3rd of 5832 litres is removed

\( = \dfrac{5832}{3} = 1944\)

Amount of water left = 5832 - 1944 = 3888 litres

2nd day = 1/3rd of 3888 litres is removed

\( = \dfrac{3888}{3} = 1296 \)

Amount of water left = 3888 - 1296 = 2592 litres

3rd day = 1/3rd of 2592 litres is removed

\( = \dfrac{2592}{3} = 864 \)

Amount of water left = 2592 - 864 = 1728 litres

4th day = 1/3rd of 1728 litres is removed

\( = \dfrac{1728}{3} = 576 \)

Amount of water left = 1728 - 576 = 1152 litres

5th day = 1/3rrd of 1152 litres is removed

\( = \dfrac{1152}{3} =384 \)

Amount of water left = 1152 - 384 = 768 litres

6th day = 1/3rrd of 768 litres is removed

\( = \dfrac{768}{3} = 256 \)

Amount of water left = 1768 - 256 = 512 litres

So, 512 litres water remains in the tank at the end of 6 days

Answer:

12inches

Explanation

Area of a square A = L^2

L is the side length

Given

Area of the square = 9sq. in

Substitute the given value into the formula and find L

9 = L^2

Swap

L^2 = 9

L = \sqrt{9}

L = 3units

Get the perimeter

Perimeter of the square = 4L

Perimeter of the square = 4(3)

Perimeter of the square = 12in

Hence the Perimeter of the square is 12inches

Answer:

140

If that's wrong, try 147

Step-by-step explanation:

With this brief sequence of numbers, we can see that the function is linear, and increases by 7 each term, with the first term at -21, and therefore, the "0th" term, or the y-intercept, at -28. With this information we can create a function in slope intercept form (y=mx+b):

\(y=7x-28\\\),

where our m (slope) is 7, and our b (y-intercept) is -28.

If this doesn't make sense, then the easiest way is to just keep adding seven to the previous number until you get to the 24th term.

Hope this helps!

The transformation in the picture is option c Reflection.

Given,

Reflection transformation:

A reflection is a transformation that works similarly to a mirror by switching all pairs of points that are directly across from one another along the line of reflection. A mathematical formula or the two sites it passes through can be used to define the line of reflection.

According to the law of reflection, r = I the angle of incidence and reflection are equal. θ r = θ I . At the point where the ray strikes the surface, the angles are measured in relation to the perpendicular to the surface.

Here,

In the picture the transformation is reflection.

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