What are the zeros of the quadratic function f(x)=6x^2+12x-7?

What Are The Zeros Of The Quadratic Function F(x)=6x^2+12x-7?

Answers

Answer 1

The zeroes of the quadratic function f(x) = 6x² + 12x – 7 will be given below. Then the correct option is A.

What is a quadratic function ?

The quadratic function is given as ax² + bx + c = f(x).

For finding the zeroes of the polynomial we have to find the roots of the polynomial , The value of f(x) = 0

The given function is f(x) = 6x² + 12x – 7

Then the zeroes of the quadratic function will be

[tex]roots = \dfrac {-b \pm \sqrt{b^2 -4ac}}{2a}\\\\[/tex]

Here a =6 , b = 12 ,c = -7

Therefore the zeroes are

[tex]\rm roots = \dfrac {-12 \pm \sqrt{12^2 -4 * 6 * (-7)}}{2 *6}\\\\[/tex]

[tex]\rm root_1 = -1 + \sqrt{\dfrac {13}{6}}\\\\\rm root_2 = -1 - \sqrt{\dfrac {13}{6}}[/tex]

Therefore the correct option is A.

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Related Questions

The depth of a certain part of the Earth's seabed is 36,024 feet. How deep is it in (a) fathoms? (b) leagues (marine)?

Answers

The depth of the sea bed is 5104 fathom and 1.986 league

What is a Seabed ?

The bottom of an ocean , the ocean floor is called Seabed .

It is given that

The depth of a certain part of the Earth's seabed is 36,024 feet

The depth in fathom is given by =  depth in feet / 6

The depth in fathom is = 36024 / 6

= 5104 fathom

1 league = 6046.1 * 3 feet = 18138.1 feet

The depth in League (marine) = Depth in feet / 18138.1

The depth in League (marine) = 36024/18138.1

= 1.986 league

Therefore the depth of the sea bed is 5104 fathom and 1.986 league.

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AB and CD intersect at point E if measure angle AED equals 6x-24 and measure angle CEB equals 4y+32 find the values of x and y such that AB is perpendicular to CD

Answers

The values of x and y such that AB is perpendicular to CD will be 19 and 14.5.

What is an angle?

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

AB and CD intersect at point E.

If measure angle AED equals 6x – 24 and measure angle CEB equals 4y + 32.

Then the values of x and y such that AB is perpendicular to CD will be

6x – 24 = 90

        6x = 114

          x = 19

Then we have

4y + 32 = 90

       4y = 58

         y = 14.5

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I don’t understand this question can someone please help

Answers

Answer:

the second option listed

(A = 53 degrees)

(a = 13.3)

(c = 16.6)

Step-by-step explanation:

SOH CAH TOA

(sin = opposite / hypotenuse)

(cos = adjacent / hypotenuse)

(tan = opposite / adjacent)

For this question, you are provided an angle (37), and its opposite (10)

so, we can solve for either sin or tan first.

tan = opposite / adjacent

tan 37 = 0.7535540501

0.7535540501 = 10/a  [multiply by a]

0.7535540501a = 10 [divide by [0.7535540501]

a = 13.2704482163

rounded to the nearest tenth, a = 13.3

we know that the three angles shown here must add up to 180

so,

90 + 37 + A = 180

127 + A = 180

- 127           - 127

A = 53

--this is enough information to answer, but I will also solve side c to prove my answer

c = hypotenuse

a²+ b²=c²

[13.3]² + [10]² = c²

176.89 + 100 = c²

276.89 = c²

√276.89 = √c²

16.6400120192 = c

c = 16.6 (rounded to the nearest tenth)

**I am assuming this is a right triangle, otherwise there wouldn't be a matching answer

Solve 22x = 5.3 by graphing.
a x ≈ 0.3
b x ≈ 0.7
c x ≈ 1.2
d x ≈ 0.4

Answers

The solution is  x ≈ 0.3 , Option A is the right Answer.

What is an Equation ?

An Equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

To find the value of

22x = 5.3

A graph has to be plotted for the line

From the graph it can be clearly seen the point at which the line intersect x axis is  x = 0.24 , which is approx equal to 0.3.

Therefore the solution is  x ≈ 0.3 ,

Option A is the right Answer.

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1

x

If
y
=
3
when
x
=
36
find,
y
when
x
=
9

Answers

Answer:

3y= 36×9x

3y=324x

y=324÷3

y=108 ans

NEED HELP PLEASE!! Don’t know how to do this

Answers

By working with percentages we will see that the down payment is of $11,010 and the first monthly payment is of $275.25

How to work with percentages?

First, the total cost is $110,100.

And we know that you initially pay the 10% of that, so the amount that you pay initially is:

P = 0.10* $110,100 = $11,010

So the down payment is of $11,010

The rest is financed over 30 years, so the rest is:

$110,100 - $11,010 = $99,090

Dividing by the number of months:

N = ( $99,090)/(30*12)  = $275.25

And there is an interest of the 9%, then the amount that you pay on month x is given by:

[tex]P(x) = $275.25*(1.09)^{x-1}[/tex]

Currently (on the first month, so x = 1)

Your pay will be of $275.25

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2, 9, 11, 18, 20, 27,
the next 3 numbers.

Answers

Answer:

29, 36, 38

Step-by-step explanation:

The pattern is add 7 then 2, then 7, then 2, then 7, then 2. You should get the hang of it. All you have to do is just do the same thing for the next three numbers.

Use two different methods to find an explain the formula for the area of a trapezoid that has parallel sides of length a and B and height H. Consider these ideas or others: combine two copies of a trapezoid to make a parallelogram. Subdivide the trapezoid into two triangles one with base b and one with base a.

Answers

Answer:

Formula of Trapezoid:

A = (a + b) × h / 2

The formula can be derived in different ways. for now, we have discussed two ways:

1. By using the formula of a triangle

2. By dividing into different sections

Step-by-step explanation:

1. By using the formula of a triangle

One of the ways to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.

Assume a trapezoid PQRS with lower base SR and upper base PQ (they are parallel) and sides PS and QR.

The image is attached below.

Connect vertices P and R with a diagonal.

Consider triangle ΔPQR as having a base PQ and an altitude from vertex R down to point M on base PQ (RM⊥PQ).

Its area is

S1=[tex]\frac{1}{2} *PQ*RM[/tex]

Consider triangle ΔPRS as having a base SR and an altitude from vertex P up to point N on-base SR (PN⊥SR).

Its area is

S2=[tex]\frac{1}{2} *SR*PN[/tex]

Altitudes RM and PN are equal and constitute the distance between two parallel bases PQ and SR.

They both are equal to the altitude of the trapezoid h.

Therefore, we can represent areas of our two triangles as

S1=[tex]\frac{1}{2}*PQ*h[/tex]

S2=[tex]\frac{1}{2}*SR*h[/tex]

Adding them together, we get the area of the whole trapezoid:

S=S1+S2=[tex]\frac{1}{2} (PQ+SR)h,[/tex]

which is usually represented in words as "half-sum of the bases times the altitude".

2. By dividing into different sections

Trapezoid PQRS is shown below, with PQ parallel to RS.

Figure 1 - Trapezoid PQRS with PQ parallel to RS(image is attached below.)

We are going to derive the area of a trapezoid by dividing it into different sections.

If we drop another line from Q, then we will have two altitudes namely PT and QU.

Figure 2 - Trapezoid PQRS divided into two triangles and a rectangle. (image is attached below.)

From Figure 2, it is clear that Area of PQRS = Area of PST + Area of PQUT + Area of QRU. We have learned that the area of a triangle is the product of its base and altitude divided by 2, and the area of a rectangle is the product of its length and width. Hence, we can easily compute the area of PQRS. It is clear that

=> [tex]A_{PQRS} = (\frac{ah}{2}) + b_{1}h + \frac{ch}{2}[/tex]

Simplifying, we have

=>[tex]A= \frac{ah+2b_{1+C} }{2}[/tex]

Factoring we have,

=> [tex]A_{PQRS} = (a+ 2b_{1} + c)\frac{h}{2} \\= > {(a+ b_{1} + c) + b_{1} }\frac{h}{2}[/tex]

 But, [tex]a+ b_{1} + c[/tex]  is equal to [tex]b_{2}[/tex], the longer base of our trapezoid.

Hence, [tex]A_{PQRS}= (b_{1} + b_{2} )\frac{h}{2}[/tex]

We have discussed two ways by which we can derive area of a trapezoid.

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What do large differences of the mean of each group indicate

Answers

The Actual Question:

What do large differences of the means of each group indicate? Select the correct answer.

A. The large differences do not indicate any Significant meaning in the given context.

B. The peppers with different weights aren't properly distributed between the two groups.

C. There is not enough information to analyze the differences.

D. The peppers with different weights are properly distributed between the two groups

Answer:

B. The peppers with different weights aren't properly distributed between the two groups.

What is a mean?

A quantity having a value intermediate between the values of other quantities; an average, especially the arithmetic mean.

The considerable discrepancies in the means of each group imply that: B. the peppers with varying weights are not adequately divided across the two groups.

So in the given situation above in the question, it can be concluded that large differences of the means from each group indicates that the peppers that are not properly distributed between the 2 different groups have different weights.

1 If the population of a town increases by 280 people per year, then the growth is LINEAR (or constant). If the population in 2022 is 120,500, then what will the population be in 2023?

Answers

The population in the year 2023 is 120,780.

The growth is linear hence, the equation of the growth is
y=ax+b where b represents the initial population and a is the number of people growing yearly.

So, according to the question statement, we have that

y=280x+b where x is the number of years past and y is the population in the xth year.

According to the given problem population in 2022 will be 120,500.

Suppose that the initial population is taken at 2000.

Hence, 120,500=280×(2022-2000)+b

⇒b=120,500-280×22

⇒b=120,500-6,160

    =114,340

So, the Linear equation becomes

y=280x+114,340

⇒y=280×(2023-2000)+114,340

⇒y=120,780

Hence, the population in the year 2023 is 120,780.

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4. You must make 3000 bags of product for a customer by 5 pm. You started work at 7 am today. By 9 am you have
made 500 bags. If you continue at this pace with no interruptions or machine issues, what percent (%) of 3000
will be complete by 11 am?

Answers

Answer:

33.33%

Step-by-step explanation:

from 7 to 9 it's 2 hours and you make 500
and 7 to 11 is 4 hours so you make 1000
then do 1000/3000 to find the percentage you have made
1000/3000 is 33.3333333333...% (the 3333.... never ends)

The answer is 33.33%

Which graph represents y = RootIndex 3 StartRoot x + 6 EndRoot minus 3?
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = negative 3 and it crosses the x-axis at x = negative 1.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = negative 3 and it crosses the x-axis at x = negative 5.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = 6 and it crosses the x-axis at x = 7.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = 6 and it crosses the x-axis at x = 5.

Answers

The graph is: On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5

A cubic function in mathematics is one with the formula f(x)=ax3+bx2+cx+d, where aneq 0 and the coefficients a, b, c, and d are complex numbers, and the variable x has real values. In other words, it is a real function as well as a polynomial function of degree three.

The function we have is:

y = ∛(x - 5)

So cubic root is given

Here we notice that when x = 0, we have:

y = ∛-5, this is the y-intercept

And when x = 5 we have:

y = ∛0 = 0 which is the x-intercept, and also the inflection point because here we have the change of sign.

Hence option which describes graph best is On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5

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Answer:A

Step-by-step explanation: Edge 2022

suppose the theoretical probability of winning a prize in the carnival game 0.18 based on this probability how many more customers would u have expected to win a prize​

Answers

The number of customers I would have expected to win the prize is 6.

How many more customers would I have expected to win the prize?

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Based on the probability, the number of customers I would have expected to win: 0.18 x 300 = 36

How many more people I would have expected to win : 36 - 30 = 6

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College students (ages 18-26) tend to make decisions which are
tentative (more short-range) and support a desire for autonomy.
a result of a greater sense of commitment and stability.
more permanent choices.

Answers

College students (ages 18-26) tend to make decisions that are tentative (more short-range) and support a desire for autonomy. This depicts more permanent choices.

How to illustrate the information?

It should be noted that values are a compass that helps us make decisions and choices.

Choices characterize the stage of life we are in. For example 18-26 ages tend to make tentative choices, later 27-31 ages tend to make permanent choices, and ages 32-42 people make stable choices.

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Celia needs 75% of the marks in an exam to pass. She gets 4/5 of the marks. Does she pass the course? Show your working to justify your answer

Answers

Answer:

Yes, she passes with 80%

Step-by-step explanation:

4 divided by 5 = 0.8

0.8 multiplied by 100 = 80%

80% is greater than the required 75% needed to pass

Answer:

Yes

Step-by-step explanation:

First lets establish the key points

We know she needs 75% to pass and she gets 4/5 of the marks

Lets make 4/5 a decimal 4/5 X 2/2 is 8/10 better know as .8

.75 = 75%

.8 = 80%

80% > 75%

Meaning She PASSED!!!

Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 90.

Answers

The transformation of a function may involve any change. The transformation of the function is Right shift by 90 units.

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Right shift by c units:

y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]

Horizontal stretch by a factor k: [tex]y = f\left(\dfrac{x}{k}\right)[/tex]

Since the function is transformed from f(x)=x to g(x)=x-90, therefore, the transformation of the function is Right shift by 90 units.

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What’s a 106.7 gpa into weighted form like on the 4.0 scale??

Answers

A 106.7 GPA into weighted form like on the 4.0 scale will be 4.26.

What is rounding a number to some specific place?

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

As 106.7 out of 100 gives 106.7% calculated below:

Percentage formula = (Obtained value/total value) x 100.......eq(1)

Putting values:

= (106.7/100) x 100

= 106.7%

Now finding 106.7% of 4:

Putting values in eq (1):

106.7% = (Obtained value/4) x 100

106.7/100= (Obtained value/4)    

1.067= (Obtained value/4)

4 x 1.067 = Obtained value

4.268 = Obtained value

Then 106.7% of 4 will be equal to 1.067 x 4  = 4.268

A 106.7 GPA into weighted form like on the 4.0 scale will be 4.26.

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5.2 Two concentric circles have radii 7cm and 4cm respectively. PQ, a chord to the larger circle, is 13cm. 5.2.1 Draw the sketch. (2) 5.2.2 Calculate AB (a chord to a smaller circle), correct to 2 decimal places. (6)​

Answers

The length of the chord AB will be 6.08 cm

A chord of a circle is a section of a straight line whose ends both fall on an arc of a circle. A secant line, often known as secant, is a chord's infinite line extension. A chord is, more broadly speaking, a line segment connecting two points on any curve, such as an ellipse.

Given two concentric circles have radii 7cm and 4cm respectively. PQ, a chord to the larger circle, is 13cm

We have to find the length of chord AB drawn to smaller circle

Given:

PQ = 13 cm

R = 7 cm

r = 4 cm

The formula to find length of chord is as follow:

Length of chord = 2 x √(R²-d²)

Where,

R = radius of circle

D = Perpendicular distance from center of circle to chord

So,

PQ = 2 x √(R²-d²)

13 = 2 x √(7²-d²)

d = 2.59 cm

Now,

AB = 2 x √(r²-d²)

AB = 2 x √(4²-2.59²)

AB = 6.08 cm

Hence the length of chord AB will be 6.08 cm

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Acontinous random variable X has a pdf given by p(x) = (5x4 0≤x≤1 0, otherwise) Let Y=X3. Find the probability distribution function ​

Answers

I'll use the method of transformations.

If [tex]f_X(x)[/tex] denotes the PDF of [tex]X[/tex], and [tex]y=g(x)=x^3 \iff x=g^{-1}(y) = y^{1/3}[/tex], we have

[tex]f_Y(y) = f_X\left(g^{-1}(y)\right) \left|\dfrac{dg^{-1}}{dy}\right|[/tex]

[tex]\dfrac{dg^{-1}}{dy} = \dfrac13 y^{-2/3}[/tex]

[tex]\implies f_Y(y) = f_X\left(y^{1/3}\right) \left|\dfrac13 y^{-2/3}\right| = \boxed{\begin{cases} \dfrac53 y^{2/3} & \text{if } 0 \le y \le 1 \\ 0 & \text{otherwise} \end{cases}}[/tex]

PLEASE HELP!!
Write Y=x^2+4x+3 in standard form

Answers

Answer:

already in standard form

Step-by-step explanation:

the equation of a quadratic in standard form is

y = ax² + bx + c ( a ≠ 0 )

y = x² + 4x + 3 ← is in standard form

with a = 1 , b = 4 , c = 3

How to translate a graph of y= absolute value of x to obtain the graph of y= absolute value of x-6

Answers

Answer: Translate the graph of y=|x| 6 units to the right.

6ac+bd-3bc-2ad help​

Answers

Answer:

(2a-b)(3c-d)

The table has data reflecting the measured population of Complete the descriptors of the regression equation for
North Carolina in terms of years since 1920
this data
The data is best modeled by
function
The value of a is
and the value of c is
the value of b is

Answers

The function can be best modeled by a linear regression and the values of a, b and c are -6, 100 and 240, respectively

The function type

From the table, we can see that as the number of years increases, the population increases.

This implies that the function can be best modeled by a linear regression.

The values of a, b and c

A linear regression equation is represented by

ax + by = c

Next, we enter the data in a statistical calculator.

From the statistical calculator, we have the following summary:

Sum of X = 225Sum of Y = 27.505Mean X = 37.5Mean Y = 4.5842Sum of squares (SSX) = 3937.5Sum of products (SP) = 231.4875

The regression equation is then represented as:

y = bx + a

Where:

b = SP/SSX = 231.49/3937.5 = 0.05879

a = MY - bMX = 4.58 - (0.06*37.5) = 2.37952

So, we have:

y = 0.05879x + 2.37952

Approximate

y = 0.06x + 2.4

Multiply through by 100

100y = 6x + 240

Rewrite as:

-6x + 100y = 240

Hence, the values of a, b and c are -6, 100 and 240, respectively

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Answer:

The data is best modeled by an exponential function.

The value of a is 2.653, the value of b is 1.01, and the value of c is not used

Step-by-step explanation:

EDGE answers

Select the correct answer from each drop-down menu.

Need helpp
(1st image of dropdown menu is the drop down menu on top an the second image is the second dropdown menu beneath it)

Answers

Triangle ABC and triangle XYZ are similar based on angle-side-angle criterion.

Triangle ABC and triangle RQP are similar based on side-angle-side criterion.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent.

Triangle ABC and triangle XYZ are similar based on angle-side-angle criterion.

Triangle ABC and triangle RQP are similar based on side-angle-side criterion.

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Please answer all three of the questions <3

Answers

Answer:

1) D because the answer to 8.42*10^3=8420

and 8420 lies between 8400 and 8500

2) C because when you take the absolute value of -2.3 and -3.2, they become positive numbers => 2.3 < 3.2

3)D because 6 < 6.3 < 6.6

Hope it helps!

2. (06.03)
What is the solution to the following system of equations? (2 points)
y = -x2 – 5x − 4
y = -x² + 9x - 18
O (-1,-10)
O (1,-10)
O (-1,10)
(1.10)

Answers

Answer: (1, -10)

Step-by-step explanation:

Since both of the equations are set equal to y, we can conclude that:

[tex]-x^2 -5x-4=-x^2 + 9x-18\\\\-5x-4=9x-18\\ \\ -14x-4=-18\\\\-14x=-14\\\\x=1[/tex]

If x=1, then [tex]y=-(1)^{2}+9(1)-18=-10[/tex]

Thus, the solution is (1, -10)

What is the quotient of -27.375 divided by 7.5

A)–3.65
B)–0.365
C)0.365
D)3.65

Answers

The answer is A) -3.65

Answer: A. -3.65

Step-by-step explanation: The best way to figure this out is by using a calculator. One specific rule to remember is the positive/negative rule. When it applies to multiplication, it also applies to division.

[tex](+)*(+)=+\\(+)*(-)=-\\(-)*(+)=-\\(-)*(-)=+\\[/tex]

Knowing this, we can input it into the calculator and find the answer's sign.

[tex]-27.375/7.5=-3.65[/tex]

Therefore, the answer is A. -3.65.

I hope this helps! Pls mark brainliest!! :)

Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3

Answers

Answer:

[tex](x,y) = (5,-6)[/tex]

Step-by-step explanation:

[tex]\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\[/tex]

                     [tex]~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)[/tex]

[tex]\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\[/tex]

[tex]\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5[/tex]

[tex]y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6[/tex]

[tex]\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)[/tex]

True or False? A corollary is a statement that can be easily proved by using theorem.

Answers

Corollary - It is a theorem in geometry that the angles opposite two congruent sides of a triangle are also congruent. So I’d say true

The Wilson family had 5 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Wilson family had

at least 3 girls?

at most 3 girls?

Answers

The expression represents the probability of getting exactly 3 heads is,

[tex]C(n,r)(0.5)^3(0.5)^6[/tex]

We have given

Aron flips a penny 9 times.

We have to determine

Which expression represents the probability of getting exactly 3 heads

What is binomial distribution?

The binomial distribution is determined as the probability of mass or discrete random variable which yields exactly some values.

The binomial probability formula shown has variables that represent:

[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]

Where n is the total number of trials (here, we flip penny 9 times, hence n = 9).

r is the number we want to find (here, we want the probability of 3 heads, so r = 3).

p is the probability of success (here, success means getting heads.

So, in a coin flip the probability of heads is always 1/2, so p = 1/2).

Therefore, The expression represents the probability of getting exactly 3 heads is;

[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]

[tex]=C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex]

Hence, the expression represents the probability of getting exactly 3 heads is [tex]C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex].

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The probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.

What is Binomial distribution?

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

Given the probability of a child being girl is 0.5, therefore, the probability of a child being boy is 0.5. Now, the probability of at least 3 girls out of 5 is,

Probability (x≥3)

= ⁵C₃ (0.5)³(0.5)² + ⁵C₄ (0.5)⁴(0.5)¹ + ⁵C₅(0.5)⁵(0.5)⁰

= 0.5

Probability (x≤3)

= ⁵C₃ (0.5)³(0.5)² + ⁵C₂(0.5)²(0.5)³ + ⁵C₁(0.5)¹(0.5)⁴ + ⁵C₀(0.5)⁰(0.5)⁵

= 0.8125

Hence, the probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.

Learn more about Binomial Distribution:

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