What is the probability of A given B.

Answer:  1. [tex]\dfrac{9}{8}[/tex] .

Step-by-step explanation:

The given expression  [tex]2x^2-3x+1[/tex]

Using completing the square method.

First, we divide the entire expression by 2 and write in the form of [tex]x^2+bx=c[/tex] , we get

[tex]x^2-\dfrac{3}{2}x+\dfrac{1}{2}[/tex]

Such that [tex]b=\dfrac{3}{2}\ \ \ , c=\dfrac{1}{2}[/tex]

Now add and subtract [tex](\dfrac{b}{2})^2[/tex] on both sides.

[tex](\dfrac{b}{2})^2=(\dfrac{\dfrac{3}{2}}{2})^2\\\\=(\dfrac{3}{2\times2})^2\\\\=(\dfrac{3^2}{4^2})\\\\=\dfrac{9}{8}[/tex]

Here, we add and subtract [tex]\dfrac{9}{8}[/tex] .

Hence, the correct answer is  1. [tex]\dfrac{9}{8}[/tex] .

Answer:

15

Step-by-step explanation:

you need to get to 35. if one bag is 5 pounds what else plus 5 is 35. so each bag is 15 pounds

Answer: 15

Step-by-step explanation:

35 - 5 = 30

30 ÷ 2 = 15

Hope this helped.

(15 each)

Answer:

See explanation below for further details.

Step-by-step explanation:

A rational consist of two real numbers such that:

[tex]\frac{a}{b} =c[/tex]

If c is a polynomial with a certain grade, then, both the numerator and the denominator must be also polynomials and the grade of the numerator must be greater than denominator.

If c is linear function, that is, a first order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example:

If [tex]a = x^{2}[/tex] and [tex]b = x[/tex], then:

[tex]c = \frac{x^{2}}{x}[/tex]

[tex]c = x[/tex]

If c is a quadratic function, that is, a second order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example

If [tex]a = 3\cdot x^{3}[/tex] and [tex]b = x[/tex], then:

[tex]c = \frac{3\cdot x^{3}}{x}[/tex]

[tex]c = 3\cdot x^{2}[/tex]

But if c is an exponential, both the numerator and the denominator must be therefore exponential function and grade of each exponential function must different to the other.

Example

If [tex]a = 10^{2x}[/tex] and [tex]b = 3\cdot 10^x[/tex], then:

[tex]c = \frac{10^{2\cdot x}}{3\cdot 10^{x}}[/tex]

[tex]c = \frac{1}{3}\cdot 10^{2\cdot x -x}[/tex]

[tex]c = \frac{1}{3}\cdot 10^x[/tex]

Otherwise, c would be equal to a constant function, that is, a polynomial with a grade 0.

If [tex]a = 5\cdot e^{x}[/tex] and [tex]b = -3\cdot e^{x}[/tex], then:

Example

[tex]c = \frac{5\cdot e^{x}}{-3\cdot e^{x}}[/tex]

[tex]c = -\frac{5}{3}[/tex]

It is worth to add that exponential functions can be a linear combination of single exponential function, similar to polynomials.

Example

[tex]5\cdot a^2\cdot x -9[/tex]

Answer:

A. 10/(3x^2+3x)

Step-by-step explanation:

2x5=10

3x(x+1) = 3x^2+3x

Answer:

3) ED

Step-by-step explanation:

3)ED

as u can see, AC has a 90 degree angle with ED

Answer:

3) DE

Step-by-step explanation:

A segment is tangent to a circle when it intercepts with the circle at only one point, which is the case for DE.

Answer:

45

Step-by-step explanation:

g(4) = 3 * 4 - 7 = 5

f[g(4)] = f(5) = 2 * 5² - 5 = 45

Answer:

45

Step-by-step explanation:

Answer:

27. 4x + 44  (D)

28. 17.5 in (A)

29. 189 cm² (C)

Step-by-step explanation:

27. 4 (2x + 11 - x) → 4 (x + 11) → 4x + 44

28. 369.25 ÷ 42.2 = 8.75 → 8.75 × 2 = 17.5 in

29. 21 × 9 = 189 cm²

Hope this helps! :)

Answer:

27.D

28.A

29.C

Step-by-step explanation:

27.   8x+44-4x= 4x+44         D

28. (369.25*2)/42.2=17.5      A

29.     9*21=189 cm^2           C

Answer:

12x<22+x

11x<22

x<2

Answer:

x < 2

Step-by-step explanation:

12x < 22 + x

Subtract x on both sides.

12x - x < 22 + x - x

11x < 22

Divide 11 into both sides.

11x/11 < 22/11

x < 2

The correct expression with the correct statement has matched below.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is equivalent to the quantity of that value between 1 and 100, and it is highly helpful for forecasting. For instance, if you say 678, we must also know the whole number, but if you say 80%, it is obvious.

The price of a game that’s been discounted by 18% of its list price

It will be (x - 0.18x)  =  0.82x

The price of a toy that sells for 18% more than the amount needed to build the toy

It will be (x + 0.18x) = 1.18x

The volume of water remaining in a tank after 3/10 of its original volume is drained out.

It will be [ x - (3/10)x ] = 7/10x

The total amount of flour in a bakery after receiving new stock equal to 3/10 of the current stock.

It will be [ x + (3/10)x ] =  13/10x

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Answer:

[tex]1.\ \ p^2q = (\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}}[/tex]

[tex]2.\ \ pq^{\frac{3}{2}}} = (\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}[/tex]

[tex]3.\ \ pq^2 = \frac{(pq^3)^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}[/tex]

[tex]4.\ \ p^2q^{\frac{1}{2}} = (p^6q^{\frac{3}{2}})^{\frac{1}{3}}[/tex]

Step-by-step explanation:

Required

Match each expression to their simplified form

1.

[tex](\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}}[/tex]

Simplify the expression in bracket by using the following law of indices;

[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]

The expression becomes

[tex](\frac{p^{5-(-3)}}{q^{-4}})^{\frac{1}{4}}[/tex]

[tex](\frac{p^{5+3}}{q^{-4}})^{\frac{1}{4}}[/tex]

[tex](\frac{p^8}{q^{-4}})^{\frac{1}{4}}[/tex]

Split the fraction in the bracket

[tex](p^8*\frac{1}{q^{-4}})^{\frac{1}{4}}[/tex]

Simplify the fraction by using the following law of indices;

[tex]\frac{1}{a^{-m}} = a^m[/tex]

The expression becomes

[tex](p^8*q^4)^{\frac{1}{4}}[/tex]

Further simplify the expression in bracket by using the following law of indices;

[tex](ab)^m = a^m * b^m[/tex]

The expression becomes

[tex](p^{8*\frac{1}{4}}\ *\ q^4*^{\frac{1}{4}})[/tex]

[tex](p^{\frac{8}{4}}\ *\ q^{\frac{4}{4}})[/tex]

[tex]p^2q[/tex]

Hence,

[tex](\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}} = p^2q[/tex]

2.

[tex](\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}[/tex]

Simplify the expression in bracket by using the following law of indices;

[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]

The expression becomes

[tex]({p^2q^{7-4}}})^{\frac{1}{2}}[/tex]

[tex]({p^2q^3}})^{\frac{1}{2}}[/tex]

Further simplify the expression in bracket by using the following law of indices;

[tex](ab)^m = a^m * b^m[/tex]

The expression becomes

[tex]{p^{2*\frac{1}{2}}q^{3*\frac{1}{2}}}}[/tex]

[tex]pq^{\frac{3}{2}}}[/tex]

Hence,

[tex]pq^{\frac{3}{2}}} = (\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}[/tex]

3.

[tex]\frac{(pq^3)^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}[/tex]

Simplify the numerator as thus:

[tex]\frac{p^{\frac{1}{2}} * q^3*^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}[/tex]

[tex]\frac{p^{\frac{1}{2}} * q^{\frac{3}{2}}}{(pq)^{\frac{-1}{2}}}[/tex]

Simplify the denominator as thus:

[tex]\frac{p^{\frac{1}{2}} * q^{\frac{3}{2}}}{p^{\frac{-1}{2}}q^{\frac{-1}{2}}}[/tex]

Simplify the expression in bracket by using the following law of indices;

[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]

The expression becomes

[tex]p^{\frac{1}{2} - (\frac{-1}{2} )} * q^{\frac{3}{2} - (\frac{-1}{2}) }[/tex]

[tex]p^{\frac{1}{2} +\frac{1}{2} } * q^{\frac{3}{2} + \frac{1}{2} }[/tex]

[tex]p^{\frac{1+1}{2}} * q^{\frac{3+1}{2}}[/tex]

[tex]p^{\frac{2}{2}} * q^{\frac{4}{2}}[/tex]

[tex]pq^2[/tex]

Hence,

[tex]pq^2 = \frac{(pq^3)^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}[/tex]

4.

[tex](p^6q^{\frac{3}{2}})^{\frac{1}{3}}[/tex]

Simplify the expression in bracket by using the following law of indices;

[tex](ab)^m = a^m * b^m[/tex]

The expression becomes

[tex]p^6*^{\frac{1}{3}}\ *\ q^{\frac{3}{2}}*^{\frac{1}{3}}[/tex]

[tex]p^{\frac{6}{3}}\ *\ q^{\frac{3*1}{2*3}}[/tex]

[tex]p^2 *\ q^{\frac{3}{6}}[/tex]

[tex]p^2 *\ q^{\frac{1}{2}[/tex]

[tex]p^2q^{\frac{1}{2}[/tex]

Hence

[tex]p^2q^{\frac{1}{2}} = (p^6q^{\frac{3}{2}})^{\frac{1}{3}}[/tex]

Answer:

a and b

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

I'm guessing that each number represents the number of rectangles that overlap. Where you see 1, there is only one rectangle, 2 shows where two rectangles overlap, and so on.

At the question mark, it appears as though four rectangles overlap. So a 4 would go there.

Answer:

Step-by-step explanation:

Let width = w units

Length = 4w - 3

Cost for lining corners of wall = $ 18.50

Perimeter of the wall = 18.50/0.25 =  74 ft

2*(length  +width ) = 74

2*(4w - 3 + w) =74

2*(5w - 3) =74

10w - 6 = 74   {Add 6 to both sides}

10w - 6 + 6 = 74 + 6

10w = 80

Divide both sides by 10

10w/10 = 80/10

w =  8 ft

Length = 4w - 3 = 4*8 - 3 = 32 - 3

Length = 29 ft

Area of the wall = length * width

                           = 29 * 8

                           =  232 square ft

Cost of painting the wall per square feet = 20 cents = 0.20

Cost of painting 232 square feet = 232 * 0.20

                                                             = $ 46.40

Answer:

see below

Step-by-step explanation:

1.the equations have different slopes?  They will intersect at one point so one solution

2.the equations have the same slope and different y-intercepts.  They are parallel lines with a different y intercept so they will never intersect - no solutions

3.the equations have the same slope and same y-intercepts. they are the same line so they have infinite solutions

Answer:

1. One solution

2. no solution

3. infinite number of solutions.

Step-by-step explanation:

How many solutions a system of linear equations have if: Questions.

(assuming a system of two equations)

1.the equations have different slopes?

One unique solution, which is at the intersection point.

2.the equations have the same slope and different y-intercepts.

The equations/lines are then parallel but NOT coincident.  They will never meet, therefore NO solution.

3.the equations have the same slope and same y-intercepts.

The two lines/equations are in effect coincident.  Therefore there is an infinite number of solutions.

Answers. A.no solutions. B.infinetly as many solutions C.two solutions. D.one solution

Step-by-step explanation:

What was Given was that Point G is rotated 90°. The coordinate of the pre-image point G was (7, –5), and its image G’ is at the coordinate (5, 7).

What you need to find was : What is the direction of the rotation.

So coming to conclusions is we have given that Point G is rotated 90°.

The Pre-image of G = ( 7, -5).

Translated image G' = ( 5 ,7).

By the Rotation rule of 90° is : (-y, x) 90 degree rotation counterclockwise around the origin.

(y, -x) 90 degree rotation clockwise about the origin.

We can from G (7,-5) and G'( 5 ,7) it is rotation counterclockwise around the origin.

Therefore, Direction of rotation is counterclockwise around the origin.

Answer:

The answer is COUNTERCLOCKWISE

Step-by-step explanation:

edg

The function that models the inverse variation is y=96/x. Thus, the correct option is A.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as

p∝q where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

Given that x and y vary inversely. Therefore, the relation can be written as,

y  ∝ 1/x

y = k × 1/x

y = k/x

Also, when y =8, the value of x is 12, therefore, if we substitute the points in the above-formed equation,

y = k/x

8 = k /12

k = 96

Hence, the function that models the inverse variation is y=96/x. Thus, the correct option is A.

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Answer:

40/46+x=30/46-x

Step-by-step explanation:

Speed=distance/time

s=d/t

x=speed of the boat

Downstream speed=x+46

Upstream speed=x-46

Downstream

s=d/t

x+46=40/t

t=40/(x+46)

Upstream

s=d/t

x-46=30/t

t=30/(x-46)

Equate upstream and downstream

30/x-46=40/x+46

30(x+46)=40(x-46)

30x+1380=40x-1840

30x+1380-40x+1840=0

-10x+3220=0

-10x=-3220

Divide both sides by -10

x=322

x=322 miles/hour

Answer:

-7.9, -7.881, -7.88, 0.07, 7.03.  

Step-by-step explanation:

Ascending, is just another word for "least to greatest."

To arrange these numbers from least to greatest, we start with the negative numbers. The negative numbers are: -7.88, -7.9, -7.881.

The greatest of these numbers would be the number that is closest to 0, and that would be -7.88.

Arranging these numbers should give us: -7.9, -7.881, -7.88.

The positive numbers are naturally greater than the negatives, and we see that 7.03 is greater than 0.07. Thus, we have the list of numbers to be: -7.9, -7.881, -7.88, 0.07, 7.03.  

Let me know if this helps :)

There are 55 two-bedroom units  in the apartment.

Let x represent the number of one bedroom units and y represent the number of two bedroom units.

Since the apartment building contains 100 units, hence:

x + y = 100      (1)

The total monthly rent paid by the tenants is $55,275, hence:

495x + 600y = 55275   (2)

Solving equation 1 and 2 simultaneously gives:

x = 45, y = 55

Hence, there are 55 two-bedroom units  in the apartment.

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Answer:

24 Combinations Total

Step-by-step explanation:

METHOD 1 (no advanced math skills needed)

i. Number the friends: a, b, c, and d

ii. List all possible combinations...

To speed up the process instead of sitting here and listing 24 combinations, after two sections you can see that with friend "a" sitting all the way at the left there are six combinations and the same goes for friend "b". You can then multiply 6 (number of combinations with that friend first) and 4 (friends) to get 24.

METHOD 2

n! means the total number for permutations calculation (1 x 2 x ... until you reach n ) = 24

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

Explanation:

Label the friends A,B,C,D,E

There are 5 choices for the first ticket, then 4 for the second, and 3 for the third. We have 5*4*3 = 20*3 = 60 permutations. One permutation is ABC and another permutation is CBA if order mattered. However, order does not matter. All that counts is the group overall rather than the individual. This is because there is no ranking and all the friends are effectively treated equally.

With a set like {A,B,C} there are 3! = 3*2*1 = 6 ways to arrange this set of three items. This means we have overcounted by a factor of 6. Divide the previous result (60) by 6 to get 60/6 = 10

So there are exactly 10 different groups possible.

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

You can use the combination formula

[tex]_n C _r = \frac{n!}{r!(n-r)!}[/tex]

with n = 5 and r = 3 to get the same result.

Or you could use Pascal's triangle to find "10" located in the row that has 1,5,10,10,5,1. Notice how 10 is located in slot 3. You start counting at slot 0.

Answer:

119

Step-by-step explanation:

I believe you meant the question to be " [tex]m^4[/tex] + 1 / [tex]m^4[/tex], if m - 1 / m = 3. "

I presume that we want to take this second equation at hand here, and " simplify " it further. After doing so this first expression will have a value with respect to the simplified value of the equation, and, plugging in it's value we can solve for the expression (  [tex]m^4[/tex] + 1 / [tex]m^4[/tex]. )

m - 1 / m = 3 - Take each value squared on either side of the equation,

[tex]( m - 1 / m )^2 = 3^2[/tex] - Simplify,

[tex]( m - 1 / m )^2 = 9[/tex]

If you don't know how to expand expressions such as the one in the third step, " [tex]( m - 1 / m )^2[/tex] " here is a quick recap. Remember that [tex]( a - b )^2 = a^2 - 2ab + b^2[/tex]. Therefore,

[tex]( m - 1 / m )^2 = m^2 - 2( m )( 1 / m ) + ( 1 / m )^2,\\( m - 1 / m )^2 = m^2 - 2 + 1 / m^2[/tex]

Now let's continue,

[tex]m^2 - 2 + 1 / m^2 = 9[/tex] - Add 2 on either side,

[tex]m^2 + 1 / m^2 = 11[/tex]

_______________

So now we have the " simplified equation " as you can say, for the equation. Let's " simplify " the expression now,

[tex]m^4+1/m^4 = 75+4(m^2+1/m^2)[/tex] - Substitute the value of 11,

[tex]m^4+1/m^4 = 75+4(11),\\m^4 + 1 / m^4 = 119[/tex]

Solution = 119

Answer:

A, C and D

Step-by-step explanation:

The missing inequality is:

y > 2x -4

To verify if a point is a solution, replace x into the equation, compute y, and see their relationship.

Option A: (-2,-5)

2(-2) -4 = -8

y = -5 > -8

then, the point is solution

Option B: (0,-4)

2(0) -4 = -4

y = -4 = -4

then, the point is not solution

Option C: (1,1)

2(1) -4 = -2

y = 1 > -2

then, the point is solution

Option D: (3,5)

2(3) -4 = 2

y = 5 > 2

then, the point is solution

Option E: (5,5)​

2(5) -4 = 6

y = 5 < 6

then, the point is not solution

Answer:

B and D

Step-by-step explanation:

Given

4x² + 32x + 60 = 0 ( divide all terms by 4 )

x² + 8x + 15 = 0

Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)

The factors are + 5 and + 3 , since

5 × 3 = 15 and 5 + 3 = 8 , thus

(x + 5)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5 → B

x + 3 = 0 ⇒ x = - 3 → D

The solution of the equation are,

x = - 5

x = - 3

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Now, We can simplify as;

4x² + 32x + 60 = 0

divide all terms by 4;

x² + 8x + 15 = 0

x² + 5x + 3x + 15 = 0

(x + 5)(x + 3) = 0

x = - 5

x = - 3

Thus, The solution of the equation are,

x = - 5

x = - 3

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Answer:

-2

Step-by-step explanation:

The product of the slope of perpendicular lines= -1.

Slope of given line= ½,

since the equation is in the form of y=mx +c, where m is the slope of the line.

½(slope of line)= -1

slope of line

= -1 ÷½

= -1 ×2

= -2

Answer:

Step-by-step explanation:

Slope of perpendicular line = -1

y = (1/2)x + 5

Slope [tex]m_{1}\\[/tex] = 1/2

[tex]m_{1}*m_{2}=-1\\\\\frac{1}{2}*m_{2}=-1\\\\m_{2} = -1*\frac{2}{1}\\\\ m_{2}= -2[/tex]

y = -2x + 7

Answer:

Step-by-step explanation:

Well since AB/DE = 3/4 and AB/DE = BC/EF, then BC/EF must also be 3/4.

We now only need to find a fraction that simplifies to 3/4.

8/12 = 2/3 [tex]\neq[/tex] 3/4

12/16 = 3/4 ✅

4/6 = 2/3 [tex]\neq[/tex] 3/4

6/9 = 2/3 [tex]\neq[/tex] 3/4

This means that the correct answer is B. 12 and 16.

Answer:

B. 12 and 16

Step-by-step explanation:

Answer:

Your correct answer is option C. Equilateral triangles

Step-by-step explanation:

In similar polygons, it is all the corresponding angles that are congruent.

Answer:

Table 2

Step-by-step explanation:

The question is to identify the table where the relative frequency of orders for blue pants is half the relative frequency of their orders for black shorts.

We are interested in the number of blue pants and black shorts.

If we name them as p and b respectively, then we are looking for a table where s/p=2

Let's verify relevant data in all tables:

Table 1:

Table 2:

Table 3:

Table 4:

So only one of tables- the second one from top represents the required data.

Answer:

The second table

Step-by-step explanation:

I did the test.