t on rn . 14. let t be a one-to-one linear transformation from a vector space v into rn . show that for u, v in v , the formula hu; vi d t .u/t .v/ defines an inner

∠SWV is congruent to ∠TWU because vertically opposite angle.

If one of the geometric figures can be superimposed on the other so that their entire surface coincides, then the two are said to be congruent, or to be in the relation of congruence. Two triangles are said to be congruent if their two sides and their included angle are the same in both of them. Congruence appears to be based on the concept of a "rigid body," which may be transported from one location to another without affecting the internal relationships between its components.

Given

∠SWV ≅ ∠TWU

Vertically opposite angle

∠SWV is congruent to ∠TWU because vertically opposite angle.

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Answer:

|
|
|
∆∆∆∆∆∆∆∆∆∆∆∆∆∆

Step-by-step explanation:

get better

Answer:

[tex] \huge{ \boxed{x = 3}}[/tex]

Step-by-step explanation:

[tex] {x}^{2} - 6x + 9 = 0[/tex]

Using the quadratic formula that's,

[tex] \bold{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}} \\ [/tex]

Comparing the equation to the general form of a quadratic equation ( ax² + bx + c), we have.

[tex]a = 1 \\ b = - 6 \\ c = 9[/tex]

Substituting the values into the formula we have.

[tex]x = \frac{- ( -6) \pm \sqrt{( - {6})^{2} - 4(1)(9) } }{2(1)} \\ x = \frac{6 \pm \sqrt{36 - 36} }{2} \\ x = \frac{ 6 \pm\sqrt{0} }{2} \\ x = \frac{6}{2} \: \: \: \: \: \\ \\ x = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

We have the final answer as

The Answers to the Question are solved below.

A number's cube root is the factor that we multiply three times to get that number.

The symbol for cube root is 3 ​cube root of, end cube root(∛) .

Given:

1. [tex]5^{-2[/tex]

Using Exponents

[tex]a^{-m[/tex] = 1 / [tex]a^m[/tex]

So,  [tex]5^{-2[/tex] = 1/5² = 1/25.

2. z+ 5= 12

z= 12-5

z= 7

3. Pythagorean triplet: m²-1, 2m, m²+1

2m= 6

m=3

and, m²-1 = 9-1= 8

and, m²+1 = 9+1= 10

3. Cube root of 64 = ∛64= ∛(4 x 4 x 4)= 4

4. 4z+ 3= 6+ 2z

2z = 3

z= 3/2

5. a- b+ ab, b- c + bc, c- a +ac

Adding: (a- b+ ab) + (b- c + bc) + (c- a +ac)

= ab+ bc+ ac

6. -1 x -2/5

= 2/5

The Multiplicative inverse = -5/2

7. y+3 = 10

y=7

8. 10³= 10 x 10 x 10= 1000

9. [tex]3^{-2[/tex]

= 1/3²

= 1/9

10. Volume = Base Area x height

900 = 180 h

h= 900/180

h = 5

11. 16 as sum of 4 add number

= 1 + 3 + 5 + 7

12. 78 x 82

(80- 2)(80+ 2)

= 80² - 2²

= 6400 - 4

= 6396

13. 2/3 x 100

= 200/3 %

14. (ab- bc)+ (bc - ca)  + (ca- ab)

= [tex](-4)^5[/tex]  ÷ [tex](-4)^8[/tex]

= [tex](-4)^{5-8}[/tex]

= [tex](-4)^{-3[/tex]

15. 4p² - 9q²

= (2p)² - (3q)²

= (2p - 3q) (2p + 3q)

16. 2y-1 = 14- y

3y= 15

y= 5

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They like best brand C) A: 11%; B: 16%; C: 34%; D: 39%.

What is probability ?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Have given ,

Ida made four brands A , B , C and D

Mostly students like A brand 11% , B brand 16% , C brand 34% and D brand 39%

So this is best brand like by students male and female

They like best brand C) A: 11%; B: 16%; C: 34%; D: 39%.

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Answer:

Area = 5π/2 in^2

Perimeter = 3π + 2 in

Step-by-step explanation:

A=area of a circle.   P=Perimeter of a circle

F=Area of first semi-circle

T=Area of Figure

Solve for Area:

A=πr^2

F=A/2

A=π(2)^2  ==> solve for A

A=4π

F=(4π)/2
F=2π   ==> this is for the first semi-circle

S=Area of second semi-circle

S=(πr^2)/2

S=(π(2/2)^2)/2  ==> the radius is half the diameter, and the diameter is 2 in

S=(π(1)^2)/2

S=π/2

T=F+S  ==> The total area is the area of both semi-circles

T=2π + π/2  ==> plugin 2π for F and π/2 for S

T = 4π/2 + π/2  ==> common denominators

T = 5π/2 in^2

Now solve for perimeter

P = 2πr.

q = perimeter of first semi-circle

q = P/2

q = 2πr/2

q = 2π(2)/2  ==> plugin 2 for r

q = 2π

R = Perimeter of second semi-circle

R = 2π(1)/2  ==> we calculated that the radius of the semi-circle is half of the

                          radius of the first semi-circle

R = 2π/2  ==> simplify

R = π

Also, add in side length DC into the perimeter as it is part of the perimeter.

E = Entire perimeter of figure

E = q + R + DC

E = 2π + π + 2

E = 3π + 2 in

Part (a)

Given data table.

[tex]\begin{array}{|c|c|} \cline{1-2}t & T\\\cline{1-2}0 & 81\\\cline{1-2}5 & 69\\\cline{1-2}10 & 60.5\\\cline{1-2}15 & 54.2\\\cline{1-2}20 & 49.3\\\cline{1-2}25 & 45.4\\\cline{1-2}30 & 42.6\\\cline{1-2}\end{array}[/tex]

where,

It's unfortunate that T is used twice for these variables. It might cause some confusion.

This is what happens when we subtract 24 from each temperature.

[tex]\begin{array}{|c|c|} \cline{1-2}t & T-24\\\cline{1-2}0 & 57\\\cline{1-2}5 & 45\\\cline{1-2}10 & 36.5\\\cline{1-2}15 & 30.2\\\cline{1-2}20 & 25.3\\\cline{1-2}25 & 21.4\\\cline{1-2}30 & 18.6\\\cline{1-2}\end{array}[/tex]

The graph of each set of points is shown in figure A. I used GeoGebra to make the graph.

The first set of data points are in red. The second set in blue. Notice the set of blue points is the result of shifting the red points 24 units down.

The green exponential model is also shown as the curve through the set of red points.

The green regression exponential model doesn't go through each point perfectly. Rather it tries to get as close as possible.

To go from

T-24 = 54.4(0.964)^t

to

T = 54.4(0.964)^t + 24

we simply add 24 to both sides. This means there isn't much to show in terms of steps when solving for T.

=======================================================

Part (b)

Use spreadsheet technology or something like GeoGebra to generate this data table.

[tex]\begin{array}{|c|c|} \cline{1-2}t & ln(T-24)\\\cline{1-2}0 & 4.043051\\\cline{1-2}5 & 3.806662\\\cline{1-2}10 & 3.597312\\\cline{1-2}15 & 3.407842\\\cline{1-2}20 & 3.230804\\\cline{1-2}25 & 3.063391\\\cline{1-2}30 & 2.923162\\\cline{1-2}\end{array}[/tex]

The values in the 2nd column are approximate.

Then plot each of those points on the same xy grid. Use technology of your choice to determine the regression line is roughly

y = -0.03723x + 3.99739

So we can say

ln(T-24) = -0.03723t + 3.99739

the right hand side fits the format at + b where

both of which are approximate.

Then,

e^(ln(T-24)) = e^(at+b)

T-24 = e^(at+b)

T-24 = e^(-0.03723t + 3.99739)

T-24 = e^(-0.03723t)*e^(3.99739)

T-24 = e^(-0.03723t)*54.45583

T-24 = 54.45583*e^(-0.03723t)

T = 54.45583*e^(-0.03723t) + 24

T = 54.456*e^(-0.037t) + 24

Let's verify that this is equivalent to the model found in part (a).

T = 54.456*e^(-0.037t) + 24

T = 54.456*(e^(-0.037))^t + 24

T = 54.456*(0.963676)^t + 24

T = 54.5*(0.964)^t + 24

which is very close to the model mentioned in part (a). There's some slight rounding error. That's to be expected in problems like this.

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

Answer: T = 54.456*e^(-0.037t) + 24

See figure B for the graph. Like with the other regression curve, this straight line doesn't go through all of the points. It tries to get as close as possible.

=======================================================

Part (c)

Refer to the 2nd table mentioned in part (a).

We'll apply the reciprocal to each item in the column labeled T-24.

For instance, the item 57 becomes 1/57 = 0.017544 approximately.

This is what the data table looks like:

[tex]\begin{array}{|c|c|} \cline{1-2}t & 1/(T-24)\\\cline{1-2}0 & 0.017544\\\cline{1-2}5 & 0.022222\\\cline{1-2}10 & 0.027397\\\cline{1-2}15 & 0.033113\\\cline{1-2}20 & 0.039526\\\cline{1-2}25 & 0.046729\\\cline{1-2}30 & 0.053763\\\cline{1-2}\end{array}[/tex]

The values in the 2nd column are approximate.

The set of points and regression line are shown in figure C1. This line does not go through all of the points. Like with the others, it tries to get as close as possible to each point.

Use technology to determine the equation of the regression line is approximately:

y = 0.00121x + 0.01613

Which tells us that

1/(T-24) = 0.00121t + 0.01613

Let's solve for uppercase T.

1/(T-24) = 0.00121t + 0.01613

T-24 = 1/(0.00121t + 0.01613)

T = 1/(0.00121t + 0.01613) + 24

T = 1/(0.0012t + 0.0161) + 24

which is the approximate final answer.

Figure C2 shown below represents the original data points (t, T) in red. The blue curve is y = 1/(0.0012x+0.0161)+24, which is the rational regression curve we just found. This curve tries its best to get as close as possible to each red point.

Compare the regression curves of figure A and figure C2. We have a very close tie in terms of which curve does a better job of fitting the original data.

The number of times a large popcorn without butter is sold is, 49.

The conditional relative frequency of no.of Item2 sold given that

50% off is 0.27.

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

The number of times a large popcorn without butter is sold is,

= 49.

The total no. of items that is 50% off is (12 + 20 + 32) = 74.

The no. of Item2 which is 50% off is 20.

So, The conditional relative frequency of no.of Item2 sold given that 50% off is,

= 20/74.

= 0.27.

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Answer:

x = 40

Step-by-step explanation:

since lines PQ and BC are parallel , then

∠ BCQ and ∠ AQP are corresponding angle and are congruent , that is

∠ BCQ = 80°

the sum of the 3 angles in Δ ABC = 180° , then

x + 80 + 60 = 180

x + 140 = 180 ( subtract 140 from both sides )

x = 40

The probability that at most 195 of those purchases are paid with a credit or debit card i.e P(X ≤ 195 ) is 0.9625..

We have given that,

Sample size , n=250

Sample proportion, p= 73.2% = 0.732

np = 183

n(1-p) = 67

both np & n(1-p) values are greater than 5, So normal approximation is applicable

mean, µ = np = 183

std. dev, σ = √np(1-p) =√250×0.732 ×(1-0.732) =7.0031

we have to calculate probability that at most 195 of those purchases are paid with a credit or debit card i.e P(X ≤ 195 )

= P( X < 195.5 )

= P((x - µ) / σ < (195.5 -183)/ 7.0031)

= P( Z < 1.78 )

= 0.9625

Required probability using Excel function ,

Excel command: =NORM.S.DIST(z,1)

= Norm.S.DIST(1.78,1)

= 0.9625

Hence, required probability is 0.9625..

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The slope and y-intercept, or the points, should be used to graph the line.  Slope: 3 y-intercept: (0, 1 )

g ( x ) = − 3 x − 1

Create an equation using the function.

y = − 3 x − 1

Calculate the slope and y-intercept using the slope-intercept form.

Less steps by tapping...

In the slope-intercept form, y = m x + b denotes the slope and the y-intercept, respectively.

y = m x + b

With the use of the formula y = m x + b, determine the values of m and b.

m = − 3 b = − 1

m is the line's slope, and is the value of the y-intercept.

B. Slope: 3 Y-intercept: (0, 1 )

Two points are all that are required to graph any line. To determine the associated y values, enter two x values into the equation.

Less steps by tapping...

Assign the x and y values to a table.

x     y

0   − 1

1    − 4

The slope and y-intercept, or the points, should be used to graph the line.

Slope: 3 y-intercept: (0, 1 )

x        y

0        1

1         4.

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The radius of the sphere of surface area 320 cm² is 5.04 cm.

A radius is defined as half of a diameter. The unit of radius is meter.

To calculate the radius of the sphere, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the radius of the sphere is 5.04 cm.

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I don't see the full picture but your answer should look like this:

4ab+(-12ab)+9ab+(-5ab)

= 4ab-12ab+9ab-5ab

= (4-12+9-5)ab

= -4ab

Step-by-step explanation:

tan(x) = sin(x)/cos(x) = 3/4

in the trigonometric triangle sin(x) and cos(x) are the legs, and the radius is the Hypotenuse, the baseline (opposite of the 90° angle).

so, we can use Pythagoras to find the radius.

c² = a² + b²

with c being the Hypotenuse, a and b being the legs.

let's stay integer.

if sin(x) is equivalent to 3, and cos(x) to 4, then what is the radius ?

3² + 4² = c²

9 + 16 = c²

25 = c²

c = radius = 5

so,

3 = sin(x) × 5

4 = cos(x) × 5

sin(x) = 3/5 = 0.6

cos(x) = 4/5 = 0.8

The value of sin x is 3/5 and the value of cos x is 4/5.

What are trigonometry ratios?

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Given that tan x = 3/4.

The tangent of an angle is the ratio of height to the base of the right triangle.

Here the height of the triangle is 3 and the base is 4.

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the base and height.

Thus,

hypotenuse = √(3² + 4²)

hypotenuse = 5.

The sine of an angle is the ratio of height to the hypotenuse.

Sin x = Height/ hypotenuse

sin x = 3/5

The cosine of an angle is the ratio of the base to the hypotenuse.

cos x = base/ hypotenuse

cos x = 4/5

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The solution to the systems are (1, 1), (-3, -1), (1, -2), (2, -1), (7, -1) and (-2, 2)

System 1

In this case, the system of equations is given as

y = -3x + 4

y = 3x - 2

Next, we plot the graph of the system of equations

In this case, the point of intersection of the equations represent the solution to the system

From the graph, the lines intersect at (1, 1)

So, the solution is (1, 1)

System 2

In this case, the system of equations is given as

y = x + 2

x = -3

Next, we plot the graph of the system of equations

In this case, the point of intersection of the equations represent the solution to the system

From the graph, the lines intersect at (-3, -1)

So, the solution is (-3, -1)

System 3

In this case, the system of equations is given as

4x + y = 2

x - y = 3

Next, we plot the graph of the system of equations

In this case, the point of intersection of the equations represent the solution to the system

From the graph, the lines intersect at (1, -2)

So, the solution is (1, -2)

System 4

We have

y = 4x - 9

y = x - 3

Substitute y = 4x - 9 in y = x - 3

4x - 9 = x - 3

Evaluate the like terms

3x = 6

So, we have

x = 2

Recall that:

y = x - 3

So, we have

y = 2 - 3

y = -1

So, the solution is (2, -1)

System 5

We have

x + 7y = 0

2x - 8y = 22

Make x the subject in x + 7y = 0

x = -7y

Substitute x = -7y in 2x - 8y = 22

-14y - 8y = 22

Evaluate the like terms

-22y = 22

So, we have

y = -1

Recall that:

x = -7y

So, we have

x = -7(-1)

x = 7

So, the solution is (7, -1)

System 6

We have

-7x + 2y = 18

6x + 6y = 0

Make x the subject in 6x + 6y = 0

x = -y

Substitute x = -y in -7x + 2y = 18

7y + 2y = 18

Evaluate the like terms

9y = 18

So, we have

y = 2

Recall that:

x = -y

So, we have

x = -2

So, the solution is (-2, 2)

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Answer:

They are equivalent ratios because if you multiply 10 to 2 by 2.5 you get 25 to five

Answer:

equals 25

Step-by-step explanation:

Answer:

$47.48

Step-by-step explanation:

Let x = the amount owed Sept.

x + x - 2.23 = 292.43  Combine like terms

2x -2.23 = 292.43  Add 2.23 to both sides

2x - 2.23 + 2.23 = 292.43 + 2.23

2x = 294.66  Divide both sides by 2

[tex]\frac{2x}{2}[/tex] = [tex]\frac{294.66}{2}[/tex]

x = 147.33 this is the bill for September

Oct. 147.33 -2.23 = 145.10 This is the Bill for Oct.

Total:

147.33 + 145.10 = 292.43

292.43 ÷ 3 = 97.48  This is what each will owe rounded to the nearest penny.

This is a SAS situation, only one triangle is possible. Then the correct option is C.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

In triangle ΔABC, the angle ∠A is 22°. And the measure of the side BC is 18.9 cm and the measure of the side AC is 15.1 cm.

To fix a triangle, the known dimensions of the triangle should be three which one must be a side.

This is a SAS circumstance, just a single triangle is conceivable. Then the right choice is C.

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Answer:

[tex]E[/tex]ach pajama costs $32

Step-by-step explanation:

So, the said person bought:

2 slippers at a price, 3 pajamas at another price. (The prices are unknowns, s, and p)

Each slippers cost $12

We are to find the cost of each pajama, where the total purchase price is $120

With the given conditions, we formulate an equation: 2s + 3p = 120

Since s = 12, we replace for the value of s in the equation. s becomes 2 × 12 = 24.

The new equation is then: 24 + 3p = 120, where we are to find the value of p.

Collect like terms: 3p = 120 - 24 → 3p = 96

Divide both sides of the equation by 3 to find the value of p: 3p/3 = 96/3 → p = 32

Therefore, the price of each pajama is $32

x3y2 is the result of the expression employing the common factor (x - 6y).

Here,

The sentence is,

x⁴y² - 6x³y³

We must use the common factor to solve.

Mathematical expression refers to the combining of numbers and variables utilizing the operations addition, subtraction, multiplication, and division.

Now,

The sentence is,

x⁴y² - 6x³y³

The common factor is used to solve as,

6x3y3 - x4y2 equals x*x*x*y*y - 6*x*x*x*y*y.

= x³y² (x - 6y) (x - 6y)

Consequently, x3y2 is the value of the expression employing the common factor (x - 6y).

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Answer:

The answer is approximately 770 bacteria after 3 hours.

In a case whereby In 1950, a U.S. population model was y = 151. (1.013)^t-1950 million people, where t is the year, the model predict the U.S. population would be 288 million in the year 2000.

Population models are mechanical theories that link alterations in population structure and density to responses at the individual level (life history features in eco-evolutionary theory or vital rates in demographic theory).

The model was given as y=151x(1.013)^t-1950

where the future time t = 2000

Then we can substitute the given year 2000 as the value of 't'

then we will have y=[151x(1.013)^(2000-1950)] = 288 million

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Explanation:

You can make use of the properties of parallel lines to prove ∠ACB≅∠DAC.

Statement . . . . Reason

2. ∠DAB +∠ABC = 180° . . . . definition of a right angle

3. AD║BC . . . . consecutive interior angles are supplementary

4. ∠ACB≅∠DAC . . . . alternate interior angles are congruent

Answer:

Equation of side AB:

We know the coordinates of A and B, so we can use the point-slope form to create the equation of the line:

y - 3 = (3/5)(x - 5)

y - 3 = 3/5x - 15/5

5/3y - 15/3 = x - 5

5/3y - x = -15/3 + 5

5/3y - x + 15/3 = 5

5/3y - x + 15/3 = 0

Equation of side AB: 5/3y - x + 15/3 = 0

Equation of side DC:

We know the coordinates of C and D, so we can use the point-slope form to create the equation of the line:

y - 1 = (2/5)(x - 10)

y - 1 = 2/5x - 20/5

5/2y - 10 = x - 10

5/2y - x = -10

5/2y - x - 10 = 0

Equation of side DC: 5/2y - x - 10 = 0

Equation of side BD:

We know the equation of side BC (x - 2y = 8) and that consecutive sides are perpendicular, so we can use the slope-intercept form to find the equation of line BD:

Slope of BC = -2/1

Slope of BD = -1/-2 = 1/2

y = (1/2)x + b

We can use the coordinates of B to find b:

1 = (1/2)(8) + b

2 = 4 + b

b = -2

Equation of side BD: y = (1/2)x - 2

Step-by-step explanation:

The function h is defined, for all real numbers h(-3) = -1/2 , h(2) = -2 and h(4) = -4.

What is a function ?

When it comes to arithmetic, a function is represented as a rule that produces a different result for each input x. Mathematicians refer to functions as mapping or transformations.

The given function,

h(x) =  -1/2 x^2 + 4 if x≠ 2

                 -2         if x=2

So, h(-3) = -1/2 (-3)^2 + 4

             = - 9/2 + 4

             = -1/2

     h(2) = -2 ( given )

     h(4) = -1/2 (4)^2 + 4

            = -8 + 4

            = -4 .

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The 95% confidence interval for this population proportion is (0.10, 0.23).

A confidence interval is a range of values that are constrained by the statistic's mean and that are likely to include an unidentified population parameter. The proportion of likelihood, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn several times is referred to as the confidence level.

Sample size n = 125

number of people who planned to take an extended vacation = 21

sample proportion p = 21/125 = 0.168

Confidence level = 0.95

significance level α = 1-0.95 = 0.05

Z score =[tex]Z_{\alpha 2}[/tex] = Z(0.05) = 1.96, from Z table.

The confidence interval for population proportion is-

p±[tex]Z_{\alpha 2}[/tex] x √{p(1-p)}/n =0.168±1.96 x 0.168 x √{(1-0.168)}/125

                        =0.168±1.96 x 0.0334

                        =0.168±0.0655

                        =(0.1025, 0.2335)

                        =(0.10, 0.23)

Therefore, the confidence interval is (0.10, 0.23).

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Answer:

1

Step-by-step explanation:

The probability of needing to catch 8 fish to get the first salmon is D) 0.2 (0.8)^7.

How to calculate probability of needing to catch 8 fish to get the first salmon?

Given that he probability of fishing a salmon in a certain river is 20% i.e. 0.2. Now, the probability of not getting a salmon will be

1 - probability of not getting salmon  = 1 - 0.2 = 0.8.

So, the first fish should be salmon and the others should not be salmon. So, the required probability of independent events can be calculated as,

P =0.2×0.8×0.8×0.8×0.8×0.8×0.8×0.8×0.8

P = 0.2× (0.8)^7

Hence,the probability of needing to catch 8 fish to get the first salmon is 0.2 (0.8)^7.

The probability of needing to catch 8 fish to get the first salmon is D) 0.2 (0.8)^7.

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The reason behind this is that when the negative root goes from the RHS to LHS, its sign gets converted, and it appears like (x + 4).

A 2nd equation in x is known as a quadratic function. Ax2 + bx + c = 0 is the quadratic equations in standard form, wherein there a and b are the coefficient, x is the constant, and c is the constant.

The presence of a non-zero component in the coefficient of x2 (a ≠ 0) is the first prerequisite for an expression to be a quadratic equation.

As per the given information in the question,

The root obtained is -4 or,

We can also write this thing as,

x = -4

So, when -4  will come to the LHS the sign will be converted to positive, and then it can be written as (x + 4).

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