22
Select the correct answer.
Consider functions fand g.
f(x) = ^x4 + 9x^2 - 3
g(x) = (1/2) ^x-2
Using a table of values, what are the approximate solutions to the equation f(x) = g() to the nearest quarter of a unit?
OA -0.5 and
OB.
I-0.25 and
OC
OD. I
0.5
1.5
-0.25 and ≈ 2.5
I ~ -1 and I ~ 0.75
Reset
Next

The ratio of cups of mixed nuts to cups of granola is 2:11.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0

Given:

Rolled oats= 6 cups

Mixed nuts=2 cups

Sesame seeds=1/2 cup

Cranberries= 1 cup

Dried unsweetened coconuts=1

Honey =1/2 cup

As, the ingredients listed

Total cups of granola= Rolled oats + Mixed nuts + Sesame seeds + Cranberries + Dried unsweetened coconuts + Honey

=6 + 2 + 1/2 + 1 + 1 + 1/2

=11 cups

Hence, the ratio of cups of mixed nuts to cups of granola is 2:11.

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The complete question is

Granola 6 cups rolled oats 2 cups mixed nuts 1 2 cup sesame seeds 1 cup dried cranberries. What is the ratio of cups of mixed nuts to the total number of cups of granola? The ratio of cups of mixed nuts to cups of granola is to . 1 cup dried unsweetened coconut 1 2 cup honey

The value of x in the triangle is (a) 30√2

The complete question is in the attached image.

From the attached image of the triangle, we can see that the triangle is a right triangle, and x can be solved using the following sine function

[tex]\sin(45) = \frac{30}{x}[/tex]

Evaluate sin(45)

[tex]\frac 1{\sqrt 2} = \frac{30}{x}[/tex]

Solve for x

[tex]x = 30 * \sqrt 2[/tex]

Evaluate

[tex]x = 30 \sqrt 2[/tex]

Hence, the value of x in the triangle is (a) [tex]30 \sqrt 2[/tex]

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The combination of possible outcomes that we get exactly four tails is 1365.

According to the statement

The times for which coin is flipped (n) is 15

The number for which we get exactly the tails (r) is 4

So, use Combination formula which is written below

C(n,r)= n! / r!(n−r)!

Substitute the values in it

C(15,4)= 15! / 4!(15−4)!

C(15,4)= 15! / 4! * 11!

C(15,4)= 15*14*13*12*11! / (4*3*2*1) * 11!

C(15,4)= 32760 / 24

C(15,4)= 1365

So, the combination of possible outcomes that we get exactly four tails is 1365.

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Answer: non of those numbers

Step-by-step explanation:

all the numbers couldn't form a triangle

the answer is 30 because 3*4=12/2=6 and for the other triangle it is 8*6=48/2 =24 and 24+6=30

The shape of a data flow diagramming process is a  open box.

Given nothing and we have to tell the shape of a data flow diagramming process.

A data flow diagram expresses  the flow of information for any process or system. It uses symbols like rectangles, circles and arrows to show data inputs, outputs, storage points and the routes between each destination.

In this diagram the information is presented in rectangles and circles which are then joined through arrows.

It can present a process of coordination between departments.

Because there is no shape in which these rectangles , circles and arrows are present. That's why we have said that it is a open box.

Hence the shape of a data flow diagramming process is a open box.

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Since the length of the ladder is 40ft, the length of the zip line Z will be 222.47m.

Note that: one has to derive b using the law of sine.

[tex]\frac{b}{sin (15)} = \frac{40}{sin 90}[/tex]

b  = [40  x  Sin (15)] / sin (90)

So:

Sin (15) = √3−1)/(2√2

= 0.2588190451

Then: Sin (90)  = 1

So,  b  = (0.2588190451 *40)/1

= 10.35/1

= 10.35

So one has to also derive for h

= [tex]\frac{b}{sin (15)} = \frac{h}{sin 75}[/tex]

Note that b = 10.35

Hence : h = 10.35 * [(√3 + 1) / 2√2] / [(√3−1)/(2√2)]

h  = 10.35 * 3.73

h = 38.62

Using  simple trigonometric analysis, we can say that:

∠ GJH = 90°; and

∠ GHJ = 10°

Therefore, to obtain Z

Z/ Sin (90) = h/Sin (10)

(Then make Z the subject of the formula)

Thus Z = h * Sin (90)/ Sin (10)

Z = 38.62 * 1/ 0.1736

Z = 222.47m

Therefore, Since the length of the ladder is 40ft, the length of the zip line Z will be 222.47m.

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Total 36 outcomes are possible on rolling two dices simultaneously

A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment

A dice has 6 possibilities (1,2,3,4,5,6) , thus two when dices thrown together will have 36 outcomes in it's sample space. It's sample space is shown in picture attached below.

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Answer:

no it does not pass the vertical line test choose D

Step-by-step explanation:

Answer:

x = 55°

Step-by-step explanation:

given 2 inscribed angles intercept the same arc then they are congruent, so

x = 55°

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the value of a in the equation 3a+b=54, if b=9?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Put in 9 for b.

[tex]\bf{3a+9=54}[/tex] | subtract 9 on both sides

[tex]\bf{3a=45}[/tex] | divide the entire equation by 3

[tex]\bf{a=15}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

       [tex]\bf{\bigcirc 15}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]

Answer:

a = 15

Step-by-step explanation:

3a + b = 54 ← substitute b = 9

3a + 9 = 54 ( subtract 9 from both sides )

3a = 45 ( divide both sides by 3 )

a = 15

Answer:

108

Step-by-step explanation:

Since 3n is a perfect square, that means that n has to be a multiple of 3. Since 2n is a perfect cube, then n has to be divisible by 2^2=4. Since n is a multiple of 3, then n also has to be divisible by 3^3=27. Therefore, the smallest value for n is 4*27=108.

According to the dilation formula, the location of the four vertices of the quadrilateral A'B'C'D' are A'(x, y) = (0, 0), B'(x, y) = (0, 7.5), C'(x, y) = (12.5, 7.5) and D'(x, y) = (12.5, 0).

Dilation are a kind of rigid transformations defined by the following formula:

P'(x, y) = O(x, y) + r · [P(x, y) - O(x, y)]     (1)

Where:

If we know that r = 2.5, O(x, y) = (0, 0), A(x, y) = (0, 0), B(x, y) = (0, 3), C(x, y) = (5, 3) and D(x, y) = (5, 0), then the resulting points are obtained:

A'(x, y) = (0, 0) + 2.5 · [(0, 0) - (0, 0)]

A'(x, y) = (0, 0)

B'(x, y) = (0, 0) + 2.5 · [(0, 3) - (0, 0)]

B'(x, y) = (0, 7.5)

C'(x, y) = (0, 0) + 2.5 · [(5, 3) - (0, 0)]

C'(x, y) = (12.5, 7.5)

D'(x, y) = (0, 0) + 2.5 · [(5, 0) - (0, 0)]

D'(x, y) = (12.5, 0)

Lastly, we proceed to graph the two figures.

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Answer:

-726

Step-by-step explanation:

So whenever you have a fraction raised to some power, you can distribute the exponent: [tex](\frac{a}{b})^n=\frac{a^n}{b^n}[/tex] the reason for this can be explained, using the definition of an exponent. You can see: [tex](\frac{a}{b})^n[/tex] as [tex]\frac{a}{b} * \frac{a}{b} * \frac{a}{b}... \text{ n amount of times}[/tex] multiplying fractions simply multiplying the numerators by the other numerators, and the denominators by the other denominators. So you're going to have the fraction: [tex]\frac{a * a * a \text{ n amount of times...}}{b * b * b\text{ n amount of times...}}[/tex] which can be rewritten as an exponent, since this is the very definition of an exponent. This simplifies to: [tex]\frac{a^n}{b^n}[/tex].

Anyways now that you hopefully understand that, let's simplify the expression

The first step is to distribute the exponent to get the fraction:

[tex]\frac{6}{2}-\frac{81^2}{3^2}[/tex]

Now square both values to get

[tex]\frac{6}{2}-\frac{6,561}{9}[/tex]

The fraction simplifies to:

[tex]\frac{6}{2}-729[/tex]

the left fraction simplifies to 3, so you get

[tex]3-729[/tex]

This simplifies to

-726

22 students study both subjects.

What is Venn diagram in math ?

N=55,n(M)=23,n(P)=24,n(C)=19,n(M∩P)=12,n(P∩C)=7,n(M∩C)=9,n(M∩P∩C)=4

Now, number of students who studying only Mathematics

n(M∩P)∩C =n(M)−n(M∩P)−n(M∩C)+n(M∩P∩C)    (by  Venn diagram) diagram=23−9−12+4=6

number of students who studying only Physics

n(P∩M )∩C  =n(P)−n(P∩M)−n(P∩C)+n(P∩M∩C)    (by Venn diagram)

                =24−12−7+4=9

Now, number of students  who studying only Chemistry

n(C∩M  )∩P =n(C)−n(C∩M)−n(C∩P)+n(M∩P∩C)    (by Venn diagram)

                    =19−9−7+4=7

So, how many students study only one of the three disciplines in detail                                                            6+9+7=22

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The coordinates for the center of the circle and the length of the radius are  ( -7, -1 ) and 6 respectively.

Option D) is the correct answer.

Given the equation;

x² + y² + 14x + 2y + 14 = 0

We subtract 14 from both sides

x² + y² + 14x + 2y + 14 - 14 = 0 -14

x² + y² + 14x + 2y = -14

Next, we complete the square for x² + 14

We have, ( x + 7 )² - 49

Next, we complete the square for y² + 2y

We have, ( y + 1)² - 1

We substitute these squares into the given equation

x² + y² + 14x + 2y = -14

( x + 7 )² - 49 + ( y + 1)² - 1 = -14

Collect like terms

( x + 7 )² + ( y + 1)² = -14 + 49 + 1

( x + 7 )² + ( y + 1)² = 36

( x + 7 )² + ( y + 1)² = 6²

Note that, the form of a circle is given as;

( x-h )² + ( y-k)² = r²

Hence, we match the values into the form and determine our center and radius.

( x-(+7) )² + ( y-(+1))² = 6²

( x-7 )² + ( y-1 )² = 6²

Hence Center = ( -7, -1 ) and radius = 6

The coordinates for the center of the circle and the length of the radius are  ( -7, -1 ) and 6 respectively.

Option D) is the correct answer.

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The statement that describes the error that Jamal has made is option A: He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.

An expression is often seen as a form of mathematical statement about a thing.

Note that from the expression:

[tex]\sqrt{75x^{5} y^{8} }[/tex]

[tex]\sqrt{25 x 3 x x^{4} x x x y^{8} }[/tex]

=   5x² y² [tex]\sqrt{3x}[/tex]

So, The statement that describes the error that Jamal has made is option A: He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.

See options below

Which describes the error Jamal made?

A. He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.

B. He should have written the square root of x Superscript 4 in the answer as x, not x squared.

C. He should have written the 5 inside of the radical in the answer.

D. He should have written the 3 outside of the radical in the answer.

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Answer:

A)

Step-by-step explanation:

Answer:

B.) y = x² + 3, x < 4
          x + 4, x ≥ 4

Step-by-step explanation:

Remember, the x-values associated with closed dots are not included in the function. Therefore, only greater than/less than signs can be applied to these points.

The exponential function includes all x-values before x = 4. Therefore, the domain for the parabola is x < 4.

The linear function includes all x-values after and including x = 4. Therefore, the domain for the linear portion of the function is x ≥ 4.

Answer:

A

Step-by-step explanation:

[f(x) + g(x)]=x²+3x-6+1

=x2+3x-5

The value of the composite function is A: x² + 3x - 5.

Option A is the correct answer.

We have,

To find (f + g)(x), you simply need to add the two functions f(x) and g(x) together.

So, (f + g)(x) = f(x) + g(x).

Given:

f(x) = 3x + 1

g(x) = x² - 6

Now, add the two functions:

(f + g)(x) = (3x + 1) + (x² - 6)

Now, combine like terms:

(f + g)(x) = 3x + 1 + x² - 6

Finally, rearrange the terms in descending order of powers of x:

(f + g)(x) = x² + 3x - 5

Thus,

The value of the composite function is A: x² + 3x - 5.

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We can use the following identity:

(Xm, Ym) = X1+X2/2, Y1+Y2/2, where Xm and Ym are the midpoints of X and Y.

So, let's use it.

For question 11, X1 is -3, Y1 is 9, X2 is 3, and Y2 is -7.

Plugging in the points, we get:

-3 + 3 = 0 / 2 = 0 for x, and 9 + (-7) = 2 / 2 = 1 for y. Thus the midpoint is (0,1).

For question 12, X1 is -9, Y1 is -4, X2 is 1, and Y2 is 6. Plugging in the values we get:

-9 + 1 = -8 / 2 = -4 for x, and -4 + 6 = 2 / 2 = 1 for y. So the midpoint is (-4,1)

Answer:

Step-by-step explanation:

#11 (first photo): M = (0, 1)

basically, if you just count the units out (like i went from (-3,9) to (0,9) so i went 3 units to the right) and then do the same for the other point (making sure the number of units is equal so you would want to move 3 left) and then draw a line, you can then connect the other 2 points to create 2 triangles and where they intersect is the midpoint.

so in the picture, the bold green line is the original line, the purple line is the line created when you move units for both points, and the blue lines are the lines created when you fill in the blanks to make the triangles

#12 (picture 2): M = (-4, 1)

and the process is the exact same just change it for the points used

Answer:

The second graph

Step-by-step explanation:

Let's start with the top equation, 4y+3x=0

Isolate the y by moving the 3x to the other side. 4y=-3x

Divide both sides by 4 to fully isolate the y which will give you y=-3/4x

There's your first equation.

Then take 4y-x=16 and do the same thing

4y=16+x

y=4+x/4

y=x/4+4

Now you know that one equation is going to go left, or the negative direction, while the other will go right, or positive, meaning there will be a point where they intersect. So just basically look for the one where x/4+4 is rising while going right. Leaving you with either the 1st or 2nd graph.

Then,

Graph both using the rise/run method or just look for an answer choice where one of the equations is positive and intersects at y=4 (since the second equation is x/4+4) which makes it the second graph.

Let me know if you need any extra explanation

Answer:

(-4,3)

Step-by-step explanation:

To solve a system of equations by graphing, we'll need to graph both equations, and find their points of intersection.

Note that both equations are linear (no exponents, no radicals, no variables in a denominator, no variables multiplied to other variables, etc -- just numbers multiplied to a variable and added to other numbers multiplied to a variable).

To graph linear equations, often they are graphed by putting the equation in slope-intercept form.  Alternatively, since it is a line, two points can be found on the line, and then the line can be graphed.

Slope intercept form is [tex]y=mx+b[/tex], where "m" is the slope of the line, and "b" is the y-intercept (the place where the line crosses the y-axis).

To convert to slope intercept form, isolate "y".

First equation:

[tex]4y+3x=0[/tex]

[tex](4y+3x)-3x=(0)-3x[/tex]

[tex]4y=-3x[/tex]

[tex]\dfrac{4y}{4}=\dfrac{-3x}{4}[/tex]

[tex]y=\frac{-3}{4}x[/tex]

Second equation:

[tex]4y-x=16[/tex]

[tex](4y-x)+x=(16)+x[/tex]

[tex]4y=x+16[/tex]

[tex]\frac{1}{4}*(4y)=\frac{1}{4}*(x+16)[/tex]

[tex]y=\frac{1}{4}*x+\frac{1}{4}*16[/tex]

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

To graph the lines, plot their y-intercepts first, then use their slopes to determine the rest of the line.

Recall that the slope is [tex]\frac{rise}{run}[/tex].

Once the equations are graphed, find the intersection from the diagram, (-4,3).

The equations currently are in an implicit form (a form where the variables aren't isolated, so neither variable is written in terms of the other).  To graph any line, find and plot two points, then draw the line between them.

To find points on the line, recall that the equation for a line relates the x-coordinate and y-coordinate through the equation.  So, if you want to find the y-coordinate for the line when the x-coordinate is 0, substitute 0 for x, and solve for y.  Often zero is used, because multiplying by zero cancel out the term, and makes the calculations easier.

Equation 1 - finding a point where x=0

[tex]4y+3x=0[/tex]

[tex]4y+3(0)=0[/tex]

[tex]4y+0=0[/tex]

[tex]4y=0[/tex]

[tex]\dfrac{4y}{4}=\dfrac{0}{4}[/tex]

[tex]y=0[/tex]

So, if x=0, then y=0.  So, the point (0,0) is on line 1.

To find another point, we need to choose another number.  As mentioned previously, often zero is used, and we could find a point on the line where the y-coordinate is zero.  However, since we just found that the point (0,0) is on the line, x=0 when y=0, and so y=0 when x=0.  We'll need a new number.

Another number that it often an easy choice mathematically is to choose the coefficient of the other variable.  So, for instance, in equation 1, the coefficient of the y term is "4", so let's choose the x-coordinate to be 4, and find the y-coordinate that goes with it:

Equation 1 - finding a second point, where x=4

[tex]4y+3x=0[/tex]

[tex]4y+3(4)=0[/tex]

[tex]4y+12=0[/tex]

[tex](4y+12)-12=(0)-12[/tex]

[tex]4y=-12[/tex]

[tex]\dfrac{4y}{4}=\dfrac{-12}{4}[/tex]

[tex]y=-3[/tex]

So, if x=4, then y=-3.  So, the point (4,-3) is also on line 1.

Those two points can be plotted, and the line drawn.

Equation 2 - finding a point where x=0

[tex]4y-x=16[/tex]

[tex]4y-(0)=16[/tex]

[tex]4y=16[/tex]

[tex]\dfrac{4y}{4}=\dfrac{16}{4}[/tex]

[tex]y=4[/tex]

So, if x=0, then y=4.  So, the point (0,4) is on line 2.

To find another point, this time, we can choose the y-coordinate to be zero, because we don't already know the x-coordinate that is associated with it.

Equation 2 - finding a second point, where y=0

[tex]4y-x=16[/tex]

[tex]4(0)-x=16[/tex]

[tex]0-x=16[/tex]

[tex]-x=16[/tex]

[tex]-1*(-x)=-1*(16)[/tex]

[tex]x=-16[/tex]

So, if y = 0, then x = -16.  So, the point (-16,0) is also on line 2.

Those two points can be plotted and the line drawn.  Once the lines are drawn, the intersection can be found.  From the diagram, the intersection is (-4,3).

Answer: 1226

Step-by-step explanation:

Answer:

The product is the difference of squares is [tex]$$(7w+10x)(7w-10x)=49{{w}^2}-100{{x}^2}$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(7 w+10 x)(7 w-10 x)=(7 w)^{2}-(10 x)^{2} \\&(7 w+10 x)(7 w-10 x)=49 w^{2}-100 x^{2}\end{aligned}$$[/tex]

The area of wood needed for the frame is 5. 5 + 106 square inches. Option A

The amount of wood needed for the window frame will be equal to area of window frame.

It is important to note that the upper part of window is semicircle

Area of the upper part = π [tex]\frac{R^2 - r^2}{2}[/tex]

where,

R = Outer radius,

r = Inner radius.

Area of upper part = π ×  [tex]\frac{6^2 - 5^2}{2}[/tex]

Area of upper part = 11π/2

Area of upper part = 5. 5π

To find the area of the lower part, it is important to note that the area of lower part of frame will be area of 3 different rectangles. Two are the same rectangles with length 48 inches and width 1 inch and one rectangle with length 10 inches (12-2) and width 1 inch.

Area of lower part = 2 × 48 × 1 + 10 × 1

Area of lower part = 96 + 10

Area of lower part  = 106 inches

Thus, the area of wood needed for the frame is 5. 5 + 106 square inches. Option A

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Answer:

20 years

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\sf \implies 10000=5000e^{0.035t}[/tex]

[tex]\sf \implies \dfrac{10000}{5000}=e^{0.035t}[/tex]

[tex]\sf \implies 2=e^{0.035t}[/tex]

[tex]\sf \implies \ln 2=\ln e^{0.035t}[/tex]

[tex]\sf \implies \ln 2=0.035t\ln e[/tex]

[tex]\sf \implies \ln 2=0.035t(1)[/tex]

[tex]\sf \implies \ln 2=0.035t[/tex]

[tex]\sf \implies t=\dfrac{\ln 2}{0.035}[/tex]

[tex]\implies \sf t=19.80420516...[/tex]

Therefore, it will take 20 years (to the nearest year) for the initial investment to double.

The true statements about the synthetic division are

The synthetic division is given as:

3)2 -2 -12

       6 12

    2 4 0

In the above representation of the synthetic division, we have:

Because the remainder is 0, then

(2x^2 - 2x - 12) ÷ (x - 3) = (2x + 4) --- option C

Set the divisor to 0

x - 3 = 0

Solve for x

x = 3

This means that 3 is a root of 2x^2 - 2x - 12 --- option (D) and x - 3 is a factor of 2x^2 - 2x - 12 --- option (E)

Hence, the true statements are (C), (D) and (E)

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Answer:

A quadratic equation can be solved using the quadratic formula, the factoring method, or completing the square. You expect to get either one or two answers.

Step-by-step explanation:

First, we have to understand how to solve a quadratic equation. There are three methods, the first of which is the quadratic formula. For any quadratic equation that takes the standard form of

[tex]f(x)=ax^2+bx+c[/tex]

you can solve for x by using the following formula:

x=(-b±√(b^2-4ac))/2a

Sometimes, however, the quadratic expression is factorable, meaning it can be converted into a product of two smaller expressions. For example:

[tex]x^2-4=(x-2)(x+2)[/tex]

As you can see, factoring gives you the roots easily (set each smaller expression to 0 and solve for x). If the quadratic is factorable, it would be easiest to use this method first.

Completing the square is another method that can be used to solve a quadratic function. It is often preferred because it converts the function into something factorable. In order to complete the square, you have to first ensure that the quadratic term's coefficient is 1. After that, you can take the linear term's coefficient, divide it by 2, and square it. Take the new term you found and add it to the equation. Because you are adding something to an equation, you must also subtract. Now, you can complete the square and factor. An example can be found below:

[tex]x^{2}-6=0\\\\(x^2-6+9)-9=0\\\\(x-3)^2-9=0\\\\(x-3-3)(x-3+3)=0\\\\x(x-6)=0\\\\x=0, x=6[/tex]

A quadratic equation can only have up to two solutions. You can imagine the graph of a quadratic. It looks like a parabola and only changes directions once. This means that it only crosses the x-axis two times. You can also look at the examples given and see that factoring only gives you two smaller expressions (leading to 2 roots). Sometimes, however, you might get a double root, leading to an equation with only one solution. This happens when the discriminant of the quadratic equation is 0. You can calculate this in advance to save yourself some time.

The classical probability of the given event is 1/4 or 0.25 or 25%.

The classical property of an event is the ratio of the total number of outcomes favorable to the event to the total number of outcomes in the experiment.

If we suppose an event A.

The total number of favorable outcomes to event A to be n.

The total number of possible outcomes in the experiment to be S.

Then, the classical probability of event A is given as:

P(A) = n/S.

In the question, we are informed that in a random experiment there are 8 possible outcomes, and two of them correspond to a favorable event.

We are asked to find the classical probability of the event.

As we know, the classical probability of an event is the ratio of the number of favorable outcomes to the event to the total number of possible outcomes in the experiment.

Thus, the classical probability = 2/8 = 1/4 or 0.25 or 25%.

Thus, the classical probability of the given event is 1/4 or 0.25 or 25%.

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Answer:

Negative linear relationship

Step-by-step explanation: