A scientist wants to estimate the number of lions living in a region.

On Thursday, he locates and tags some lions. I

On Friday he returns and locates 10 less lions than he had on Thursday.

He notices that 4 of the lions are tagged

The scientist works out an estimate for the total number of lions living in the

region.

He notices that the number of lions that he had caught on Thursday, was a

fifth of the total number of lions.

How many lions live in the region?

Answer:

Ava

Step-by-step explanation:

Ava's = 100/10 = 10

Ian's = 110/20 = 5.5

Answer:

4

Step-by-step explanation:

An object's radius is half of the object's diameter.

Solving for diameter

Solving for radius

d = r * 2

  = 2 * 2

  = 4

The diameter of Harry's table is 4 feet.

The cones are not congruent because one cone is oblique, which makes the length of the slant heights different.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

The two cones below have the same radius, height, and volume.

One cone is oblique.

The cones have different slant heights.

The lengths of all corresponding edges are not equal.

Since, Congruent cones must have congruent corresponding measures, including slant height.

The cones are not congruent because one cone is oblique, which makes the length of the slant heights different.

Learn more about congruent;

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Answer:

Sample Response: The cones are not congruent because one cone is oblique, which makes the length of the slant heights different. Having the same radius, height, and volume does not make the cones congruent when the corresponding slant heights are not equal. Congruent cones must have congruent corresponding slant heights, with all other corresponding parts being congruent.

What did you include in your response? Check all that apply.

One cone is oblique.

The cones have different slant heights.

The lengths of all corresponding edges are not equal.

Congruent cones must have congruent corresponding measures, including slant height.

Step-by-step explanation:

circumference = 2 pi r = 2 r pi

= d pi

= 6 × 3.14 = 18.84

Answer:

total cost= 24.6

Step-by-step explanation:

12 ÷ 20 = 0.6 per straight line

arc 0.6 × 3/2 = 0.9

12 + 0.9 × 14

12 + 12.6 = 24.6

The required cost of the metal used in the pattern is £24.6.

Given that,
A different pattern is made using 20 straight lines and 14 arcs.
The straight lines and arcs are made from metal. 20 straight lines cost £12 cost of one straight line is cost one arc = 2 : 3.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let the cost of the total arcs be x,
As per the given condition,
The cost of the one straight line is 12/20 and cos if the one arc is x/14,
According to the question,
[12/20]/[x/14] = 2/3
12×14/20 = 2x / 3
x = £12.6
The total cost of a metal arc is £12.6
And the total cost of the metal line in the pattern is = £12.

Total cost of metal = 12 + 12.6 = £24.6

Thus, the required cost of the metal used in the pattern is £24.6.

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#SPJ5

congruent angles are of similar measures

congruent angles that are congruent to ∠7:

See how

From both

Similarly

And

<6 and <2 are corresponding and equal so

Answer:

1.75

Step-by-step explanation:

Answer:

[tex]\textsf{D.}\quad\dfrac{b}{\sqrt{a^2+b^2}}[/tex]

Step-by-step explanation:

Tan trig ratio

[tex]\tan(x)=\sf \dfrac{O}{A}[/tex]

where:

Using the given information:

[tex]\implies x=\tan^{-1}\left(\dfrac{a}{b}\right)[/tex]

[tex]\implies \tan(x)=\tan\left(\tan^{-1}\left(\dfrac{a}{b}\right)\right)[/tex]

[tex]\implies \tan(x)=\left(\dfrac{a}{b}\right)[/tex]

Comparing this with the trig ratio, we can say that:

[tex]x[/tex] is the angle opposite side [tex]a[/tex]

Cos trig ratio

[tex]\cos(x)=\sf \dfrac{A}{H}[/tex]

where:

Therefore:

[tex]\implies \cos\left(\tan^{-1}\left(\dfrac{a}{b}\right)\right)=\cos(x)= \dfrac{b}{\sqrt{a^2+b^2}}[/tex]

When the bay shoots are 82.55 mm, Derek should cut them according to the guidebook for growing fresh herbs option (c) is correct.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, multiplication by a conversion factor.

The book says that it is best to cut bay shoots when they are 3.25 in long.

As it is given that the:

1 mm = 0.03937 in

To find how many millimeters long should the bay shoots be when Derek cuts them, we must convert 3.25 in to mm

From the 1 mm = 0.03937 in, we can find how many mm is there in 1 in;

[tex]\rm 1 \ in= \frac{1}{0.03937} \ mm[/tex]

To convert 3.25 in into mm, we must multiply it by 1/0.03937

= 3.25×(1/0.03937)

= 82.55 mm

Thus, when the bay shoots are 82.55 mm, Derek should cut them according to the guidebook for growing fresh herbs option (c) is correct.

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The absolute value function represented by the graph is:

y = -3*|x|

So the correct option is B.

In the graph, we can see a "V" shape, which belongs to the absolute value functions, but this graph opens down, so our function will be something like:

y = -a*|x - b|

The value of b is the value of x where we have the vertex, in this case, is at x = 0, so b = 0

y = -a*|x|

To get the value of 1, we ise one of the points that we can see on the graph. For example, for x = 1, we have y = -3, replacing that we get:

-3 = -a*|1| = -a

3 = a

So we can conclude that our function is:

y = -3*|x|

So the correct option is B.

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We will see that the fourth statement:

"-0.3*|3 + 8x| = 0.9 has no solutions."

Is the true statement.

Here we need to see which statement regarding absolute value equations is true.

Here you can see that the fourth statement is:

-0.3*|3 + 8x| = 0.9   has no solutions.

Now, if you look at the left side of the above equation, the left side will always be negative, while the right side is positive, then the equation can't have a solution.

There is no value of x that makes that equation true, so it is true that the given equation has no solutions. This is the correct statement.

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Answer:

10 hours = 60 mph

you will need to go 60 mph to make the trip 10 hours

explaination:

Multiplying the amount of hours and the mph, 12 times 50 is 600 miles.

10 times 60 is 600 miles. They both have the same answer, but 60 mph is the fastest. 60 mph is how fast you would need to go to make it in 10 hours.

I dont know if i explained it good.

Answer: 2500

Step-by-step explanation: 250 spins times the amount of greens expected equals 2500.

Answer:

c is 7

Step-by-step explanation:

becuase 4x4=16 then u divide 16\2=7

Answer:

x = 7.5, x = -5

Step-by-step explanation:

1. Plug a(2), b(-5), and c(-75) into the qudratic formula:

[tex]x_{1,2} =\frac{-(-5)+-\sqrt{(-5)^{2}-4(2)(-75) } }{2(2)}[/tex]

2. Find the square:

[tex]x_{1,2} =\frac{-(-5)+-\sqrt{25-4(2)(-75) } }{2(2)}[/tex]

[tex]x_{1,2} =\frac{-(-5)+-\sqrt{25+600} }{2(2)}[/tex]

[tex]x_{1,2} =\frac{-(-5)+-25 }{4}[/tex]

3. Separate the solutions:

[tex]x_{1} = \frac{-(-5)+25}{4} , x_{2} =\frac{-(-5)-25}{4}[/tex]

4. Solve for both:

[tex]x_{1} =\frac{5+25}{4} \\\\x_{1} =\frac{30}{4} \\\\x_{1} =\frac{15}{2}\\\\x_{1} =7.5[/tex]

--------------------

[tex]x_{2} =\frac{5-25}{4} \\\\x_{2} =\frac{-20}{4} \\\\x_{2} =-5[/tex]

In conclusion, the solutions are x = 7.5 and -5.

hope this helps!

Answer:

14

Step-by-step explanation:

using the formula:

(theta/360 pi r^2)-(1/2ab(the radius)sin theta)

theta is obtained by multiplying 1/4 and 360 therfore theta is 90°

Answer:

216 outcomes.

Just as one die has six outcomes and two dice have 62 = 36 outcomes, the probability experiment of rolling three dice has 63 = 216 outcomes

Answer:

B. plant from variety Always grow taller than plant from variety B

Answer:

No

Step-by-step explanation:

Linear equations, when graphed, look like straight lines.

Examples include:

y= mx + b

y = 3

x + 2 = 0

y + 6 = 0

y = 7x +2

Answer:

[tex]\boxed{\sf x < -3\quad \mathrm{or}\quad \:x > -1}[/tex]

Step-by-step explanation:

[tex]\sf x^2+4x+3 > \:0[/tex]

In order to solve inequality, we need to factor the left hand side. we can use the transformation [tex]ax^2+bx+c=a(x-x_1)(x-x_2)[/tex] to factor quadratic polynomials. where  x(1) & x(2)  are the solutions of the quadratic equation  ax²+bx+c=0 .

[tex]\sf x^2+4x+3=0[/tex]

Quadratic formula:-

[tex]\boxed{\sf x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]

[tex]\sf a=1\\b=4\\c=3[/tex]

[tex]\sf \cfrac{-4\pm \sqrt{4^2-4\times \:1\times \:3}}{2\times \:1}[/tex] ← Calculate

[tex]\sf \sqrt{4^2-4\times \:1\times \:3}=\boxed{2}[/tex]

[tex]\sf \cfrac{-4\pm \:2}{2\times \:1}[/tex]

Now, let's Separate the solutions,

[tex]\sf x_1=\cfrac{-4+2}{2\times \:1},\:x_2=\cfrac{-4-2}{2\times \:1}[/tex]

Do the calculations,

[tex]\sf x_1=\cfrac{-4+2}{2\times \:1}=\boxed{-1}[/tex]

[tex]\sf x_2=\cfrac{-4-2}{2\times \:1}=\boxed{-3}[/tex]

[tex]\boxed{\sf x < -1\quad \mathrm{or}\quad \:x > -3}[/tex]

Answer:

7

Step-by-step explanation:

I assume x with dash on top is mean

The sum of all x's is 175 and there are 25 x's.

To find the mean:

175/25 = 7

Answer:

Step-by-step explanation:

Sum of all angles of triangle = 180

17x + 10x -5 +  50 = 180

Combine like terms

27x + 45 = 180

To find the valu of x, we have to isolate x. To isloate x

Step 1: Subtract 45 from both sides

           27x = 180 - 45

           27x = 135

Step 2: Divide both sides by 27

               x = 135/27

x = 5

Answer:

B

Step-by-step explanation:

-5 is less than -4 is true. it cannot be the first one because they are equal. It cannot be the third one because the absolute value of 5 (which is 5) is not greater than 7. And, it cannot be the last on because the absolute value of -5 (which is also 5) is not less than -4.

Answer:

27 hours

Step-by-step explanation:

160.65 = 8.50x-68.85

x=27

Answer:

Hey i believe this is the answer

Step-by-step explanation:

Take a look at the screenshot

Also Desmos graphing calculator is a big help :) It might make you a little more confident

Answer:

ACUTE TRIANGLE

Step-by-step explanation:

If the sum of the squares of the two shorter sides of a triangle is greater than the square of the longest side, the triangle is acute. However, if the sum of the squares of the two shorter sides of a triangle is smaller than the square of the longest side, the triangle is obtuse.

Therefore, the triangle with sides 11, 9, and 7 is an acute triangle since 9² + 7² is greater than 11²

[tex] {9}^{2} \: + \: {7}^{2} > \: {11}^{2} \\ 130 > 121[/tex]

solution:

3x^2+9x-5

i hope this helps

:)