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We can expect there to be 684 trout in the lake.

In the given statement is:

To determine the number of trout in a lake, a conservationist catches 171 trout, tags them and throws them back into the lake. Later 52 trout are caught; 13 of them are tagged.

Proportion:

A ratio gives us the measure of one quantity as compared to another quantity, and it is represented either as a fraction, decimal or a notation like a : b. When the same ratio is applicable to other quantities.

Now, According to the question:

Number of trout / number of trout = number of trout caught / caught that were tagged

Number of trout / 171 = 52/13

Number of trout = (171 x 52) / 13

Number of trout = 8,892 / 13 = 684

Hence, We can expect there to be 684 trout in the lake.

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The given sequence is not arithmetic as the difference of each consequent term with the previous term is not the same.

Given: 1, 3, 9, 27, ...

Here, 3 - 1 ≠ 9 - 3 ≠ 27 - 9

Since the sequence does not follow the definition of an arithmetic progression, it is not one.

Hence, The given sequence is not arithmetic as the difference of each consequent term with the previous term is not the same.

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Answer:

W = -57.6         PS: I'm in 8th grade.

Step-by-step explanation:

W/6 + 7.2 = -2.4   Step 1: Use Inverse operations (subtract 7.2 on both sides)

W/6 = -2.4 - 7.2    Step 2: Combine Like terms (-2.4 - 7.2)

W/6 = -9.6            Step 3: Use Inverse Operations (multiply by 6 on both sides)

W = -9.6 x 6         Step 4: Simplify

W = -57.6            

An inequality that matches the wingspan of the common sparrow is       9 ≤ x ≤ 15, where x represents the wingspan of the common sparrow.

In this question, we have been given a statement 'The common sparrow has a wingspan of 9 to 15 centimeters. '

We need to write an inequality that matches the wingspan of the common sparrow.

Let x represents the wingspan of the common sparrow.

According to given statement, the common sparrow has a wingspan of 9 to 15 centimeters.

So, the required inequality would be,

9 ≤ x ≤ 15

Therefore, an inequality that matches the wingspan of the common sparrow is 9 ≤ x ≤ 15, where x represents the wingspan of the common sparrow.

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Answer:26

Step-by-step explanation:

-3(2-4)2+14= -3*-2*2+14=12+14=26

The equation of the parabola that has vertex at the center and focus at the point (6,0) is x = y²/24

We define what a parabola is

 The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

The canonical equation of a parabola is given by

(y - k)² = 4p(x - h)

The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

Since the vertex and the focal axis are on the same axis, we analyze that:

v (0, 0)

f (6, 0) the focus is on the right so the parabola is of the form X = Y².

(y - 0)² = 4p(x - 0)

f = (0 + p, 0)

0 + p = 6

p = 0 + 6

p= 6

(y - 0)² = 4*6(x - 0)

(Y)² = 24(X)

x = y²/24

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Answer:

Step-by-step explanation:

-9

The dividend is 50 , the quotient is 25 .

Let the no . ( the divisor ) be x .

Forming linear equation in one variable using given info .

Given : divisor = 2 , result = 33 , quotient increased by 8 .

Division Formula : Dividend = Divisor * Quotient .

Hence , the equation is ,

( x / 2 ) + 8 = 33

( x / 2 )  =  25

x = 50

Hence the dividend is 50 .

The quotient is 25 .

Therefore , option B ) is correct + 8 = 33 ; 82 .

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The measure of each angles are 21 and 83degrees

A line is defined as the distance between two points while an angle is the point where two lines intersect.

From the diagram shown, the expression below is true;

<EFH + <HFG = <EFG

Substitute the given parameters to have:

5x+1 + 62 = 18x + 11

Collect the like terms

5x - 18x = 11 - 63

-13x = -52

x = 52/13

x = 4

Find each measure

<EFH = 5(4) + 1

<EFH = 21

degrees

<EFG = 18(4) +11

<EFG = 72 + 11

<EFG  = 83 degrees

Hence the measure of each angles are 21 and 83degrees

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The value of angle 4 is 57°

From the image shown, we can see  that angle 3 and angle 4 are on a straight line.

It is important to note that angles on a straight line sum up to 180 degrees.

We have angles 1 and 2 are supplementary, that is, they sum up to 180 degrees

Angles 3 and 4 are also supplementary and sum up to 180 degrees

Angles 5 and 6 are also supplementary.

Then, if angle 3 = 123 , we have;

angle 3 + angles 4 = 180

123 + angle 4 = 180

Angle 4 = 180 - 123

Angle 4 = 57°

Thus, the value of angle 4 is 57°

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The probability of getting a number that is greater than four is G. 0.33

Probability:

Probability defines the possible occurrence of the selected event across the total number of events.

Given,

A die is rolled.

And we need to find the probability of rolling a number greater than 4.

If you roll a single die there are 6 possible outcomes  are

=> {1,2,3,4,5,6}

So, the numbers that are greater than 4 are,

=> 5 and 6.

So, there are 2 of which are greater than 4.  

So in a single roll the probability of getting a number greater than 4 is

=> 2/6

=> 1/3.  

For the decimal form it can be written as,

=> 0.33.

So, the correct option is G. 0.33.

Therefore, the probability of getting the number greater than 4 is 0.33.

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Answer:

the answer is

[tex] \frac{27}{4} [/tex]

The distance between X(5,4) and Y(2,1) is 4.24 rounded to the nearest tenth.

Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

The distance between two points (x₁, y₁) and (x₂, y₂)  is given by ;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

So,

Distance between A(1,5) and B(-2,-3)

[tex]d = \sqrt {\left( {1 + 2 } \right)^2 + \left( {5 + 3 } \right)^2 }[/tex]

d = 8.544

Roud to nearest tenth ⇒ 8.54  units.

Hence "The distance between A(1,5) and B(-2,-3) is  8.54 rounded to the nearest tenth".

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The nth term of seuence is 4^n and the formula for finding the nth term of the given sequence is [tex]a_{n} = 4^{n}[/tex] .

According to the given question.

We have a sequence 4, 16, 64, 256, 1024...

As we know that, a sequence or number pattern is an ordered set of numbers or diagrams that follow a rule.

Here,

The first term of the given sequence is 4, or we can say that 4^1 is 4.

The second term of the sequence is 16, or we can say that 4^2 is 16.

The third term of the sequence is 64, or we can say that 4^3 is 64.

The fourth term of teh sequence is 256, or we can say that 4^4 is 256.

So, if we follow the same pattern or the rule we can say that the nth term of the given sequence is 4^n.

Thereofre, the formula for finding the nth term of the given sequence 4,16,64,256,1024, ...... is [tex]a_{n} = 4^{n}[/tex] where n = 1, 2, 3 , 4....

Hence, the nth term of seuence is 4^n and the formula for finding the nth term of the given sequence is [tex]a_{n} = 4^{n}[/tex] .

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Answer:

12°

Step-by-step explanation:

The angles of the shape should all add to 360°.

We divide this by 30, because the shape has 30 angles.

360° ÷ 30 = 12°.

This is the measure of each angle, and also the degree of rotation. The shape will look like the original figure each time it is rotated 12°.

The proof of Theorem 4.3 with an example is shown.

To prove Theorem 4.3:

Let,s take two triangles, that is △ABC and △ADC.

Since two pairs of angles are congruent, then the △ABC≅△ADC is under AA condition.

Therefore, the proof of Theorem 4.3 with an example is shown.

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The Simplified value of the complex fraction 1 + 2/x / 2 + 3 / 2x is (4x+7)/(4x+3) .

A complex fraction is defined as an expression that has fraction in it's numerator and a fraction in its denominator.

For Example : [tex]\frac{\frac{2}{3} }{\frac{5}{7} }[/tex] is an example of complex fraction.

The given question is

=1 + 2/x / 2 + 3 / 2x

[tex]=1+\frac{\frac{2}{x} }{2+\frac{3}{2x} }[/tex]

Taking LCM in the denominator and solving further,

[tex]=1+\frac{\frac{2}{x} }{\frac{4x+3}{2x} }[/tex]

[tex]=1+\frac{2}{x} *\frac{2x}{4x+3}[/tex]

Cancelling out "x" from both numerator and denominator

we get,

=1+(2*2)/(4x+3)

=1+(4)/(4x+3)

Taking LCM as 4x+3 and solving further we get,

=(4x+3+4)/(4x+3)

=(4x+7)/(4x+3)

Therefore , the simplified value of the expression 1 + 2/x / 2 + 3 / 2x is (4x+7)/(4x+3).

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The value of expression  [tex]4\frac{7}{12} +2 \frac{3}{4} + 7\frac{5}{12}[/tex]  is [tex]\frac{157}{12}[/tex].

We solve this type of fraction by firstly simplifying it into proper fraction. For simplifying it into proper fraction, we multiply denominator of the complex fraction with whole number given with fraction and then add the numerator of the complex fraction

e.g. [tex]4\frac{7}{12}[/tex] = [tex]\frac{12*4+7}{12}[/tex]

so, The given question can be written down as [tex]4\frac{7}{12} +2 \frac{3}{4} + 7\frac{5}{12}[/tex]

i.e. [tex]\frac{35}{12} +\frac{11}{4} + \frac{89}{12}[/tex]

Taking LCM and then writing the equation again

[tex]\frac{35+33+89}{12}[/tex]= [tex]\frac{157}{12}[/tex]

Final answer, the simplified value will be [tex]\frac{157}{12}[/tex]

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When the supermarket wants to find the percent of shoppers who use coupons. A manager interviews every shopper entering the greeting card aisle. This is a convenience sampling.

A non-probability sampling technique called convenience sampling includes taking a sample from the nearest area of the population. Pilot testing benefits the most from this kind of sample. The most popular kind of convenience sampling concentrates on gathering data from individuals (the sample) who are 'convenient' for the researcher to reach.

Convenience sampling techniques include inviting friends to take part in your study, gathering information from local sites, mailing surveys, and posting links on social media.

In conclusion, the correct option is A.

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A supermarket wants to find the percent of shoppers who use coupons.  A manager interviews every shopper entering the greeting card aisle.

convenience sample

Self-selected sample

systematic sample

random sample

Which property does the equation 3(g+h)+2 g=(3 g+3 h)+2 g illustrate?

Distributive property .

What is distributive property?

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The measure of angles ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 will be 40°, 140°, 40°, 140°, 40°, 140°, 40°, and 140°, respectively.

The angle is the separation of the crossing surfaces or lines. Additionally, the angle is specified in degrees. One whole spin has an arc of 360 degrees.

If the total of two angles is 180 degrees, they are said to be supplementary angles.

In the third line, if two lines are parallel. Equal angles are formed by matching angles.

When two lines intersect, then their opposite angles are equal.

The measure of angle ∠1 is 40°.

Angle ∠1 and angle ∠2 are supplementary angles. Then the measure of angle ∠2 will be

∠1 + ∠2 = 180°

40° + ∠2 = 180°

∠2 = 140°

The vertical angles are given below.

∠1 = ∠3 = 40°

∠2 = ∠4 = 140°

The corresponding angles are given below.

∠1 = ∠5 = 40°

∠2 = ∠6 = 140°

∠3 = ∠7 = 40°

∠4 = ∠8 = 140°

Then the measure of angles ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 will be 40°, 140°, 40°, 140°, 40°, 140°, 40°, and 140°, respectively.

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Answer:

66

Step-by-step explanation:

After solving for equation or inequality 4 x+6 ≥ -6, the value of  x ≥ -3

⇒ 4 x+6 ≥ -6

⇒ 4x ≥ -6-6

⇒ 4x ≥ -12

⇒ x ≥  -12/4

⇒ x ≥ -3

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The approximate length of each side of the park is 85m .

Pythagoras Theorem states that the sum square of two sides of triangle is equal to the  square of longest side.

According to the question

given that the park is a square

and in square the longest side is it's diagonal and the diagonal is  given to be 120m.

In square all sides of square is same .

let the side be x.

By Applying Pythagoras Theorem in the given ΔABC

[tex]AB^{2} +BC^{2} =AC^{2}[/tex]

Substituting the values  we get

[tex]x^{2} +x^{2} =120^{2}[/tex]

[tex]2x^{2} =120^{2} \\ \\ 2x^{2} =14400\\ \\ x^{2} =7200[/tex]

[tex]x=\sqrt{7200} =60\sqrt{2}[/tex] = 84.85 ≅ 85

Therefore ,  the approximate length of each side of the park is 85m .

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Answer:

I'll go with the last option. c=√Em

Answer:

[tex]\frac{613}{1000}[/tex]

Step-by-step explanation:

Converting Mexican pesos to US dollars,  Kyle will get 2224 Mexican pesos for 200 US dollars.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.

A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.

If 278 Mexican pesos is equivalent to 25 US dollars,

278 Mexican pesos = 25 US dollars

Dividing both sides by 25,

278/25 Mexican pesos = 25/25 US dollars

11.12 Mexican pesos = 1 US dollar

Therefore, 1 US dollar is equivalent to 11.12 Mexican pesos.

The conversion factor is 11.12 Mexican pesos/1 US dollar.

If Kyle wants to convert 200 US dollars to Mexican pesos for spending money, and 1 US dollar is equivalent to 11.12 Mexican pesos, multiply the amount by the conversion factor.

200 US dollars (11.12 Mexican pesos/1 US dollar)

= 2224 Mexican pesos

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Each subtraction equation as an addition equation is  mathematically given as

a - 9 = 6 ==> a=6+9

p - 20 = -30==> p+30=20

z - (-12) = 15 ==>  z+12=15

x - (-7) = -10 ==> x+17=0

This is further explained below.

Generally, In mathematics, the summation is the process of adding together a string of any form of numbers, which are referred to as operands or summands; the result is the sum or total of the figures.

In conclusion,

a - 9 = 6 ==> a=6+9

p - 20 = -30==> p+30=20

z - (-12) = 15 ==>  z+12=15

x - (-7) = -10 ==> x+17=0

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By solving a system of equations we can see that the quadratic equation is:

y = x^2 + 3x + 10

A general quadratic equation is given by:

y = a*x^2 + b*x + c

We want this quadratic equation to pase through the points (-2, 8), (1, 14), and (0, 10).

using the last point, we know that when x = 0, we must have y = 10, then:

10  = a*0^2 + b*0 + c

10 = c

So our quadratic equation is:

y = a*x^2 + b*x + 10

Now we use the other two points to write a system of equations:

8 = a*(-2)^2 + b*(-2) + 10

14 = a*(1)^2 + b*1 + 10

If we simplify these, we get:

-2 = 4*a - 2b

4 = a + b

Isolating a in the second equation we get:

a = 4 - b

Now we replace that in the other equation:

-2 = 4*(4 - b) - 2b

-2 = 16 - 4b -2b

-2 - 16 = -6b

-18/-6 = b = 3

Now that we know the value of b, we replace it in the equation for a:

a = 4 - b = 4 - 3 = 1

Then the quadratic equation is:

y = x^2 + 3x + 10

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