A population of 1200 leopards decreases by 12% per year. How many leopards will there be in the population after 6 years? Round your answer to the nearest whole number

Answer:

The directrix of the ellipse is:

x= -3.25 and x=9.25

Step-by-step explanation:

As we know that for any ellipse equation of the type:

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex] and a>b

The directrix is given by:

[tex]x=h\pm \dfrac{a}{e}[/tex]

where,

[tex]e=\sqrt{1-\dfrac{b^2}{a^2}}[/tex]

Here we have the equation of parabola as:

[tex]\dfrac{(x-3)^2}{5^2}+\dfrac{(y-2)^2}{3^2}}=1[/tex]

Hence, we have:

[tex]h=3,\ k=2,\ a=5,\ b=3\\\\and\\\\e=\sqrt{1-\dfrac{3^2}{5^2}}\\\\e=\sqrt{1-\dfrac{9}{25}}\\\\e=\sqrt{\dfrac{25-9}{25}}\\\\\\e=\sqrt{\dfrac{16}{25}}\\\\e=\dfrac{4}{5}[/tex]

Hence, we have: the directrix as:

[tex]x=3\pm \dfrac{5}{\dfrac{4}{5}}\\\\\\x=3\pm \dfrac{25}{4}\\\\Hence, x=9.25\ and\ x=-3.25[/tex]

Hence, the equation of directrix is:

x= -3.25 and x=9.25

Answer:

B

Step-by-step explanation:

On edge

The 7th term in the geometric sequence described by this explicit formula will be 31,250 so option (D) will be correct.

A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.

For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.

Given explicit formula is

[tex]a_{n}[/tex] = 2 × [tex]5^{(n-1)}[/tex]

Where n represents a number of terms and [tex]a_{n}[/tex] is an nth term in the GP series.

By substituting n = 7 into the formula

[tex]a_{7}[/tex] = 2 × [tex]5^{(7 - 1)}[/tex]

[tex]a_{7}[/tex] = 2 × 5⁶

[tex]a_{7}[/tex] = 2 × 15625 = 31250 hence, it will the correct answer.

For more information about the geometrical progression

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The confidence level for the interval x ± 2.88σ/√n is approximately 99.9%. The term 'confidence level' speaks to how frequently the true value of the parameter would be inside the interval for replicated experiments. Without additional information, we cannot compute the confidence level for just 'x'.

In statistics, a formula exists to find the confidence interval. For the interval x ± 2.88σ / √n, the confidence level is nearly 99.9%. We find this by referring to the z-table (standard normal table) with a z-score of 2.88. This leaves 0.05% in each tail of the distribution.

On the topic of confidence levels, a 95% confidence interval implies that if you were to take 100 random samples from your population, approximately 95 of those samples would capture the true population parameter.

For the other part of your question, when we talk about the interval x, it doesn't provide enough detail to calculate a confidence level. It needs to be stated in context of the standard deviation and the sample size.

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Answer:

High

Step-by-step explanation:

The triange may be classified as (2) isosceles triangle

The vertices are given as:

A(0,0), B(3,2), and C(0,4)

Calculate the side lengths using:

d = √(x2 - x1)^2 +(y2 - y1)^2

So, we have:

AB = √(3 - 0)^2 +(2 - 0)^2

AB = √13

AC = √(0 - 0)^2 +(4 - 0)^2

AC = 4

BC = √(3 - 0)^2 +(2 - 4)^2

BC = √13

Side lengths BC and AB are equal

i.e. AB = BC = √13

Hence, the triange may be classified as (2) isosceles triangle

Read more about triangles at:

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O.5 is the correct answer

Varna's package weighs 3 pounds, priced at $7.50, matching Elliot's $12.50 package with 5 pounds at same unit price.

To find the weight of Varna's package of ground beef, we can set up a proportion based on the unit price.

Elliot's package:

Price: $12.50

Weight: 5 pounds

Varna's package:

Price: $7.50 (same unit price as Elliot's)

Weight: Let's call it x pounds

We can set up the proportion:

[tex]\[\frac{12.50}{5} = \frac{7.50}{x}\][/tex]

Now, we can cross multiply:

[tex]\[12.50x = 5 \times 7.50\]\[12.50x = 37.50\][/tex]

Now, let's solve for \( x \):

[tex]\[x = \frac{37.50}{12.50}\]\[x = 3\][/tex]

So, the weight of Varna's package of ground beef is 3 pounds.

Complete question:

Elliot buys a 5 pound package of ground beef for 12.50

1)varna buys a package of ground beef for 7.50 at the same unit price. 2)What is the weight of the package

Combining like terms gives

9x−30=180. Adding 30 to both sides yields

9x=210. Dividing by 9, we find x=23.3333.

To solve the equation

4x+5x−30=180, we first combine like terms:

4x+5x=9x

So the equation becomes:

9x−30=180

Next, we isolate the variable

x by adding 30 to both sides:

9x=180+30

9x=210

Finally, we divide both sides by 9 to solve for

Final answer:

The land area of Australia is roughly 7.62 trillion square meters, calculated by multiplying the area in square miles (2,941,526) by the conversion factor of 2,590,000 square meters per square mile.

Explanation:

The student is asking for the conversion of Australia's land area from square miles to square meters. To convert square miles to square meters, we use the conversion factor that 1 square mile is equal to 2.59 square kilometers or 2,590,000 square meters. Therefore, the land area of Australia in square meters is calculated by multiplying the area in square miles by the conversion factor:

2,941,526 mi2 × 2,590,000 m2/mi2 = 7,619,652,340,000 m2

The land area of Australia is approximately 7.62 trillion square meters.

Answer:

D!!

Step-by-step explanation:

Hope it helps!!

The solution to the inequality 11x + 14 < -8 is x < -2. On a number line, this would be a circle at -2 with a line extending to the left.

To find the solution to the inequality 11x + 14 < –8, we will first subtract 14 from both sides, which gives us:

11x < -8 - 14

This simplifies to 11x < -22.

Next, we divide both sides by 11 for: x < -2

The solution is x < -2. On a number line, this would be represented by a circle around -2 (not filled in, because the inequality does not include 'equal to') with a line extending to the left (indicating 'less than').

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