The degree of the polynomial function f(x) is 4. The roots of the equation f(x) =0 are -2,-1,1 and 3. Which graph could be the graph of f(x)?

Answer:

−4304

Step-by-step explanation:

1. The given determinant is :

[tex]\begin{vmatrix}7 &31 \\ 142& 14\end{vmatrix}[/tex]

We need to find its determinant . It can be solved as follows :

[tex]\begin{vmatrix}7 &31 \\ 142& 14\end{vmatrix}=7(14)-142(31)\\\\=-4304[/tex]

So, the value of determinant is equal to −4304.

Answer:

A= -4269

B= 1768

C= 647.36

Step-by-step explanation:

9514 1404 393

Answer:

  B (-2, 1)

Step-by-step explanation:

The trauma center will be located at the circumcenter of the triangle. That is the point of intersection of the perpendicular bisectors of the sides. Once the points are graphed, it is pretty easy to see where that will be. It is on the line x=-2, above the x-axis. Only one answer choice is appropriate:

  (-2, 1)

_____

Line AC has a slope of 1. Those points are separated by 7 units horizontally and vertically, so the midpoint is 3.5 units horizontally and vertically from either point, at (-2.5, 1.5). The perpendicular line with slope -1 through that point will intersect x=2 at y=1.

Answer:

Step-by-step explanation:

Answer:

(4,3,0,-4)

May this

help you

Answer:

Both are true.

Step-by-step explanation:

Answer:

7.5 pi

Step-by-step explanation:

The formula for arc length of a sector is denoted as

[tex]\frac{x}{360}2\pi r[/tex], where x is the central angle of the sector.

Since the sector is 3/4 of a circle, the central angle will be 3/4 of 360 degrees.

3/4 of 360 is 270, so we have our central angle. We also have our radius which we can plug into the formula.

[tex]\frac{270}{360}2(5)\pi[/tex]

2 times 5 is equal to 10, and 270/360 simplifies to 3/4. 3/4 times 10 is equal to 7.5, so the answer is 7.5 pi

Answer:

[tex]y=-5x-3[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0).

To solve for the equation of the line, we would need to:

1) Find the point of intersection between the two given lines

[tex]2x - 3y + 11 = 0[/tex]

[tex]5x + y + 3 = 0[/tex]

Isolate y in the second equation:

[tex]y=-5x-3[/tex]

Plug y into the first equation:

[tex]2x - 3(-5x-3) + 11 = 0\\2x +15x+9 + 11 = 0\\17x+20 = 0\\17x =-20\\\\x=\displaystyle-\frac{20}{17}[/tex]

Plug x into the second equation to solve for y:

[tex]5x + y + 3 = 0\\\\5(\displaystyle-\frac{20}{17}) + y + 3 = 0\\\\\displaystyle-\frac{100}{17} + y + 3 = 0[/tex]

Isolate y:

[tex]y = -3+\displaystyle\frac{100}{17}\\y = \frac{49}{17}[/tex]

Therefore, the point of intersection between the two given lines is [tex](\displaystyle-\frac{20}{17},\frac{49}{17})[/tex].

2) Determine the slope (m)

[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the two points [tex](\displaystyle-\frac{20}{17},\frac{49}{17})[/tex] and (-1,2):

[tex]m=\displaystyle \frac{\displaystyle\frac{49}{17}-2}{\displaystyle-\frac{20}{17}-(-1)}\\\\\\m=\displaystyle \frac{\displaystyle\frac{15}{17} }{\displaystyle-\frac{20}{17}+1}\\\\\\m=\displaystyle \frac{\displaystyle\frac{15}{17} }{\displaystyle-\frac{3}{17} }\\\\\\m=-5[/tex]

Therefore, the slope of the line is -5. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-5x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=-5x+b[/tex]

Plug in the point (-1,2) and solve for b:

[tex]2=-5(-1)+b\\2=5+b\\-3=b[/tex]

Therefore, the y-intercept is -3. Plug this back into [tex]y=-5x+b[/tex]:

[tex]y=-5x+(-3)\\y=-5x-3[/tex]

I hope this helps!

Answer:

25 cm.

Step-by-step explaination:

Given,

Two sides of a triangle:

a = 7cm

b = 24 cm

To find,

Third side:

c = ?

By Pythagorean Theorem;

a² + b² = c²

[where c is the longest side,hypotenuse]

Putting the value of a and b;

we get,

7² + 24² = c²

49 + 576 = c²

625 = c²

25² = c² (square root)

25 = c

c = 25

Therefore, the length of the third side will be equal to 25 cm.

The lengths of two sides of the right triangle ABC shown in the illustration given

a= 7cm and b= 24cm

> a= 7cm

> b= 24cm

Side c (third side)

Using Pythagoras theorem,

▶️ a² + b² = c

▶️ 7cm ² + 24cm² = c²

▶️ 49cm + 576cm = c²

▶️ 625cm = c²

▶️ 25² = c² (25×25 = 625)

▶️ c = 25

The value of c is 25 cm.

Answer:

your mom

Step-by-step explanation:

Answer:

Workers can plant 0.72 acres per day.

Answer:

A child who weighs 84 pounds should be given 94.5 milligrams of the drug.

Step-by-step explanation:

Givens:

1kg=2.5 milligrams of dosage

Weight of child = 84 pounds

1 pound = 0.45 kg

Solution:

Convert pounds to kilograms --> 84lbs*0.45kg = 37.8 kg

Convert weight to dosage --> 37.8kg * 2.5 mg = 94.5 mg of dosage.

Step-by-step explanation:

c=3.14×3.14×10.1

=99.58196

Answer:

[tex]{ \sf{ {x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy }}[/tex]

Step-by-step explanation:

[tex]{ \tt{ {(x + y)}^{2} = (x + y)(x + y) }} \\ { \tt{ {(x + y)}^{2} = ( {x}^{2} + 2xy + {y}^{2}) }} \\ { \tt{( {x}^{2} + {y}^{2} ) = {(x + y)}^{2} - 2xy}}[/tex]

Answer:

B. The question may not be directly stated.

Answer:

Step-by-step explanation:

#1

A) P(FEMALE|APPLE)

apple total = 346

apple/female = 194

194/346 = .56 = 56 %

B) P(APPLE|MALE)

male total = 320

apple male = 152

152/320 = .475 = 47.5%

C) female prefer Microsoft

152:168 = 76:84 = 38:42 = 19:21

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Answer:

can you please send the picture of the diagram.

Step-by-step explanation:

Answer:

ABC:

AB-5 units

BC-12.65 units

AC-15 units

FGH:

FG-5 units

GH-12.65 units

FH-15 units

Step-by-step explanation:

PLATO SAMPLE ANSWER

Answer:

h²=p²+b²

(7√2)²=x²+x²

(49×2)=2x²

2x²=49ײ

x²=49×2/2

x²=49

x=√49=7

x=7

OAmalOHopeO

Answer:

1/8=12.50%

Step-by-step explanation:

Take the pizza as a whole = 100

Then consider 1/8 of 100

or   1/8 * 100  

= 1/4 * 50

=   1/2 * 25

= 12.50

Therefore it is 12.50%

Answer:

5/12

Step-by-step explanation:

5/12 , 2/3, 5/6,3/4

Get a common denominator of 12

5/12, 2/3 *4/4, 5/6*2/2, 3/4 *3/3

5/12, 8/12, 10/12, 9/12

The numerator closest to 0 is the fraction closest to 0

5/12

Answer:

The correct graph is A.

Answer:

A i got it right

Step-by-step explanation:

9514 1404 393

Answer:

  {x ∈ ℝ | x ≤ 3}

Step-by-step explanation:

Subtracting 5 from both sides, we see the solution is ...

  x ≤ 3

In set notation, this can be written ...

  {x ∈ ℝ | x ≤ 3}

9514 1404 393

Explanation:

Definition

The determinant of a square matrix is a single number that is computed (recursively) as the sum of products of the elements of a row or column and the determinants of their cofactors. The determinant of a single element is the value of that element.

The cofactor of an element in an n by n matrix is the (n-1) by (n-1) matrix that results when the row and column of that element are deleted. The "appropriate sign" of the element is applied to the cofactor matrix. The "appropriate sign" of an element is positive if the sum of its row and column numbers is even, negative otherwise. (Rows and columns are considered to be numbered 1 to n in an n by n matrix.)

Uses

The inverse of a square matrix is the transpose of the cofactor matrix, divided by the determinant. Hence if the determinant is zero, the inverse matrix is undefined. This means any system of equations the matrix might represent will have no distinct solution. (There may be zero solutions, or there may be an infinite number of solutions. The determinant by itself cannot tell you which.)

Cramer's Rule for the solution of linear systems of equations specifies that the value of any given variable is the ratio of the determinants of two matrices. The numerator matrix is the original matrix with the coefficients of the variable replaced by the constants in the standard-form equations; the denominator matrix is the original coefficient matrix. This rule lets you solve a system of 3 equations in 3 variables by computing 3+1 = 4 determinants, for example.

Let's look at an example.

If we wanted to solve this system of equations

[tex]\begin{cases}2x-y = 2\\x+y = 7\end{cases}[/tex]

Then it's equivalent to solving this matrix equation

[tex]\begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}2\\7\end{bmatrix}[/tex]

We can then further condense that into the form

[tex]Aw = B[/tex]

Where,

[tex]A = \begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\\\\w = \begin{bmatrix}x\\y\end{bmatrix}\\\\B = \begin{bmatrix}2\\7\end{bmatrix}[/tex]

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

To solve the matrix equation Aw = B, we could compute the inverse matrix [tex]A^{-1}[/tex] and left-multiply both sides by this to isolate w.

So we'd go from [tex]Aw=B[/tex] to [tex]w = A^{-1}*B[/tex]. The order of multiplication is important.

For any 2x2 matrix of the form

[tex]P = \begin{bmatrix}a & b\\c & d\end{bmatrix}[/tex]

its inverse is

[tex]P^{-1} = \frac{1}{ad-bc}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}[/tex]

Notice the expression ad-bc in the denominator of that fractional term outside. This [tex]ad-bc[/tex] expression represents the determinant of matrix P. Some books may use the notation "det" to mean "determinant"

[tex]P^{-1} = \frac{1}{\det(P)}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}[/tex]

or you may see it written as

[tex]P^{-1} = \frac{1}{|P|}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}[/tex]

Those aren't absolute value bars, even if they may look like it.

Based on that, we can see that the determinant must be nonzero in order to compute the inverse of the matrix. Consequently, the determinant must be nonzero in order for Aw = B to have one solution.

If the determinant is 0, then we have two possibilities:

So a zero determinant would have to be investigated further as to which outcome would occur.

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

Let's return to the example and compute the inverse (if possible).

[tex]A = \begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\\\\A^{-1} = \frac{1}{2*1 - (-1)*1}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}\\\\A^{-1} = \frac{1}{3}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}\\\\[/tex]

In this case, the inverse does exist.

This further leads to

[tex]w = A^{-1}*B\\\\w = \frac{1}{3}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}*\begin{bmatrix}2\\7\end{bmatrix}\\\\w = \frac{1}{3}\begin{bmatrix}1*2+1*7\\-1*2+2*7\end{bmatrix}\\\\w = \frac{1}{3}\begin{bmatrix}9\\12\end{bmatrix}\\\\w = \begin{bmatrix}(1/3)*9\\(1/3)*12\end{bmatrix}\\\\w = \begin{bmatrix}3\\4\end{bmatrix}\\\\\begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}3\\4\end{bmatrix}\\\\[/tex]

This shows that the solution is (x,y) = (3,4).

As the other person pointed out, you could use Cramer's Rule to solve this system. Cramer's Rule will involve using determinants and you'll be dividing over determinants. So this is another reason why we cannot have a zero determinant.

Answer:

The answer is in the picture below

Step-by-step explanation:

Sorry just realised the answers were different ;-;

Answer:

The arm spans for Class A are roughly symmetric, while those for Class B are skewed left.

Step-by-step explanation:

Solution :

We have given two baskets :

[tex]$H_1$[/tex] : 8 apples + 2 bananas + 6 cantaloupes = 16 fruits

[tex]$H_2$[/tex] : 6 apples + 4 bananas = 10 fruits

A fair coin is made to flipped. If the [tex]\text{flip}[/tex] results is head, then the fruit is selected from a basket [tex]$H_1$[/tex].

If the flip results in tail, then the fruit is selected from the basket [tex]$H_2$[/tex].

Probability of head P(H) = [tex]1/2[/tex]

Probability of tail P(T) = [tex]1/2[/tex]

if given event is :

B = selected fruit is BANANA

We have to calculate : P(T|B)

Probability of banana if the flip results is head P(B|H) = [tex]$\frac{2}{16}$[/tex]

Probability of banana if the flip results is tail P(B|T) = [tex]$\frac{4}{10}$[/tex]

From the Bayes' theorem :

Probability of flip results is tail when selected fruit is BANANA.

[tex]$P(T|B) = \frac{P(B|T)\ P(T)}{P(B|T) \ P(T) + P(B|H)\ P(H)}$[/tex]

            [tex]$=\frac{\frac{4}{10} \times \frac{1}{2}} {\frac{4}{10} \times \frac{1}{2} + \frac{2}{16} \times \frac{1}{2}}$[/tex]

            [tex]$=\frac{\frac{1}{5}}{\frac{1}{5}+\frac{1}{16}}$[/tex]

            [tex]$=\frac{\frac{1}{5}}{\frac{21}{80}}$[/tex]

            [tex]$=\frac{16}{21}$[/tex]

∴  [tex]$P(\ T|B\ )=\frac{16}{21}$[/tex]

Answer:

[0.6969, 0.7695]

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

They randomly survey 401 drivers and find that 294 claim to always buckle up.

This means that [tex]n = 401, \pi = \frac{294}{401} = 0.7332.

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.7332 - 1.645\sqrt{\frac{0.7332*0.2668}{401}} = 0.6969[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.7332 + 1.645\sqrt{\frac{0.7332*0.2668}{401}} = 0.7695[/tex]

The 90% confidence interval for the population proportion that claim to always buckle up is [0.6969, 0.7695]

Answer:

y = 3/4 x - 3

Step-by-step explanation:

the slope of a line is the factor of x in the equation and is expressed as ratio of y/x : defining how many units y changes, when x changes a certain number of units.

in our graph here we can see that when increasing x from e.g. 0 to 4 (the x-axis intercept point, a change of +4), y changes from -3 to 0 (a change of +3).

so, the slope and factor of x is y/x = 3/4

and for x=0 we get y=-3 as y-axis intercept point.

so, the line equation is

y = 3/4 x - 3

Answer:

The correct answer is "0.7289".

Step-by-step explanation:

The given values are:

Mean,

[tex]\mu = 15.5[/tex]

Standard deviation,

[tex]\sigma = 3.6[/tex]

As we know,

⇒ [tex]z = \frac{(x - \mu)}{\sigma}[/tex]

The probability will be:

⇒ [tex]P(11< x< 19) = P(\frac{11-15.5}{3.6} <z<\frac{19-15.5}{3.6})[/tex]

                             [tex]=P(z< 0.9722)-P(z< -1.25)[/tex]

By using the z table, we get

                             [tex]=0.8345-0.1056[/tex]

                             [tex]=0.7289[/tex]