An ordinary fair die is a cube with the numbers 1 through 6 on the sides. Imagine that such a die is rolled twice in succession and that the faces of the 2 rolls are added together. This sum is recorded of single trial of a random experiment. Event A: The sum is greater than 8. Event B: the sum is not divisible by 5

By evaluating f(x) in x = 0 we will see that the value is 1, then we will get:

f²⁰²³(0) = 1²⁰²³ = 1

Remember that 1 is the identity of the multiplication, this means that any number times 1, is equal to the same number.

Then, for any real value n, we know that:

1ⁿ = 1

Now we have the function:

f(x) = 1/(1 + x²)

Evaluating in x = 0, we get:

f(0) = 1/(1 + 0²) = 1

Now we can apply the exponent n = 2023 we will get:

f²⁰²³(0) = 1²⁰²³ = 1

The answer is 1.

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The mid point of the line segment with the end coordinates of:

(0, 2) and (8,8) is (4,5).

For the given question;

The given coordinates are-

(x1, y1) = (0, 2)

(x2, y2) =  (8,8)

The mid point is found by the formula;

x = (x1 + x2 )/2

y = (y1 + y2)/2

Put teh values,

x = (0 + 8)/2

x = 4

y = (2 + 8)/2

y = 5

Thus, the mid point of the line segment with the end coordinates of:

(0, 2) and (8,8) is (4,5).

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The volume of the largest box that can be made from the rectangular cardboard obtained by using the value of the derivative of the function for the volume at the extremum point is 18 cubic feet

An extremum of a function is the point where the value of the function is a maximum or a minimum.

The side length of the cut out squares = x

The width of the rectangular cardboard = 5 feet

The length of the rectangular cardboard = 8 feet  

The length of the side of the cut square = 8 - 2·x

Width of the side of the cut square = 5 - 2·x

Height of the cut square = x

Volume of the cut square, V = (8 - 2·x) × (5 - 2·x) × x = 4·x³ - 26·x² + 40·x

When the volume of the box is largest, we have;[tex]V' = \dfrac{d}{dx} \left(4\cdot x^3 - 26\cdot x^2 + 40\cdot x\right) = 12\cdot x^2 - 52\cdot x + 40=0[/tex]

12·x² - 52·x + 40 = 0

3·x² - 13·x + 10 = 0

Which gives;

(3·x - 10)·(x - 1) = 0

The dimensions of the cut square that gives the maximum volume are therefore;

x = 1 or x = 10/3

When x = 10/3, we have;

V = (8 - 2×(10/3)) × (5 - 2×(10/3)) × (10/3) ≈ -200/27 < 0

When x = 1, we have;

V = (8 - 2×1) × (5 - 2×1) × 1 = 18

The value of x that gives the maximum volume is therefore, x = 1

The dimensions of the box that give the maximum volume are therefore;

Height = x = 1

Length = 8 - 2×1 = 6

Width = 5 - 2 × 1 = 3

The dimensions of the box that gives the maximum volume are;

Height = 1 ft

Length = 6 ft

Width = 3 ft

The volume of the largest box that can be formed is 18 cubic feet

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Step-by-step explanation:

In general equation, y = mx+c, c represents y-intercept.

So, y-4 = 6x+42

y = 6x+46

So, y intercept will be 46

According to the product rule of logarithms, the given equation is written as,  log₄(x² + 13x + 40) = 1

Product rule of logarithm

Basically, the product rule states that the sum of two logarithms is equal to the product of the logarithms.  

And it is the first law and it can be represented as;

logₐ(x) + logₐ(y) = logₐ(xy)

Given,

Here we have the logarithmic equation log 4(x+8) + log 4(x+5) = 1

And we have to rewrite the equation.

Here we have the logarithmic equation,

=> log₄(x+8) + log₄(x+5) = 1

By using the product property of logarithms, 

We have to rewrite the equation as,

=> log₄(x+8)(x+5) = 1

Now, we have to expand (x+8)(x+3) using the FOIL Method.

Then we get,

=> log₄(x² + 5x + 8x + 40) = 1

=> log₄(x² + 13x + 40) = 1

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Juan have earned of interest after 36 months at the rate of 7.5% interest per year.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. The formula of simple interest is as follows:

S.I = p×r×t

Where p is principle value, r is rate and t is time in years.

Here, the principle amount is $7,850 and rate is 7.5% i.e  [tex]\frac{7.5}{100}=0.075[/tex] and time is 36 months i.e 3 years.

Now, putting the values,

SI = 7850×0.075×3

= $ 1766

Therefore, the interest Juan have earned in 36 months is $1,766.

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Answer:

21y-7/11

Step-by-step explanation:

First you would multiply everything outside of the prhthises to the inside. Second multiply 7 times 3y that would equal 21y. Third multiply 7 times - 1/11    that would equal to 21y-7/11

Answers:

1 yard by 72 yards

4 yards by 18 yards

6 yards by 12 yards

8 yards by 9 yards

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

Explanation:

Let's list out all the ways to multiply to 72 using two values

1*72

2*36

3*24

4*18

6*12

8*9

Then cross off something like 2*36 since 2 is prime. We also cross off 3*24 since 3 is prime.

We're left with this list

1*72

4*18

6*12

8*9

which represent the possible dimensions of this rectangle.

Keep in mind that 1 is not prime.

The graph of the equation y = 3x + 2 + 3 is shown below .

In the question ,

it is given that ,

the equation of the line is y [tex]=[/tex] 3x [tex]+[/tex] 2 [tex]+[/tex] 3 ,

we need to draw the graph of it .

Do draw the graph we need at least two points .

for the first point

put x = 0

we get ,

y = 3(0) + 2 + 3

y = 0 + 2 + 3

y = 2 + 3

y = 5

the first point is (0,5)

for the second point put y = 0,

we get ,

0 = 3x + 2 + 3

3x = - 2 - 3

3x = -5

x = -5/3 ,

So , the second point is (-5/3 , 0)

the graph of the given equation is shown below .

Therefore , The graph of the equation y [tex]=[/tex] 3x + 2 [tex]+[/tex] 3 is shown below .

The given question is incomplete , the complete question is

What is the graph of the equation y = 3x + 2 + 3 ?

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Answer:

Step-by-step explanation:

no idea

The number of oranges with first women are 200 and the number of oranges with other women are 100.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, 2 market women shared 300 oranges.

The share of first woman is twice the other.

Let the number of oranges with other women be x.

Then, the number of oranges with first women will be 2x.

Now, x+2x=300

3x=300

x=100

So, 2x=200

Therefore, the number of oranges with first women are 200 and the number of oranges with other women are 100.

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The volume of the cube is 1/125b⁹

From the question, we understand that

Shape = Cube

Side length = 1/5b³

Rewrite the side length as

a = 1/5b³

The volume of a cube can be expressed as V = a³

where a is the length of any side

And v is the volume

Substitute the known values in the above equation So, we have the following equation

V = (1/5b³)³

Evaluate

V = 1/125b⁹

Hence, the volume is V = 1/125b⁹

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The weighted dollar amount of the savings account as per the an investment portfolio is; $67.20.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

Given that An investment portfolio is;

Investment Amount   Invested    ROR

Savings Account  $3,200     2.1%

Municipal Bond  $4,900       4.5%

Preferred Stock   $940         10.5%    

Common Stock A       $1,675     -3.5%

The weighted dollar amount of the savings account is;

= 2.1% of $3200

=  ( 2.1 / 100)  × $3200

= ($6720) /100

= $ 67.20

Therefore, the weighted dollar amount of the savings account as per the an investment portfolio is; $67.20.

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Answer:71/40 or 1 31/40 or 1.775  

Step-by-step explanation:1 31/40 is the mixed number

The total amount Frank pays back to the bank = $210642.72

Assuming the given interest rate- that is the simple interest rate.

so the future value A for the simple interest rate is given by,

A = P(1 + rt)

here, P = $56022

r = 0.04

t = 69

Substitute these values in above formula.

A = 56022 (1 + 0.04 * 69)

A = 56022 * 3.76

A = $210642.72

Therefore, the total amount Frank pays back to the bank = $210642.72

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Answer:

C: x-axis

Step-by-step explanation:

It is the x-axis.

The elements of set (AnB)' = {1,2,3,5,6,7,8,9,10} and The elements of A'uB' = {1,2,3,5,6,7,8,9,10}

The complement of a set is the set that includes all the elements of the universal set that are not present in the given set. For example, if A is a set of all coins which is a subset of a universal set that contains all coins and notes, so the complement of set A is a set of notes (which do not includes coins).

Therefore if U={1,2,3,5,6,7,8,9,10} and A={4,8,9,10} B= {2,3,4,6,7} then,

(AnB) = {4}

(AnB)' = {1,2,3,5,6,7,8,9,10}

A' = {1,2,3,5,6,7} and B' = {1,5,8,9,10}

therefore A'uB'= {1,2,3,5,6,7,8,9,10}

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Answer:

Step-by-step explanation:

1) first we find the x and y intercepts. Remember the intercepts are where x=0 and y=0

2) To find the x-intercept, substitute y = 0 and solve for x.

given equation:  x +2y= -4

then substitute y=0    so

x+ 2(0) = -4    -> any number multiplied by 0 it will always equal zero

then,  it will be  x=-4

the coordinates will be (-4,0)

3) To find the y-intercept, substitute x =0 and solve for y.

given equation:  x +2y= -4

then substitute x=0    so

(0)+ 2y = -4    -> x disappears since is zero

then,  it will be  2y=-4

then we multiply by 2 :

2y/2 = -4/2

y=-2

the coordinates for the y-intercept will be (0,-2)

The slope is -3/(2+3a)² and the equation of the line is y - 1/8 = [-3/(2+3a)²](x - 2).

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

​f(x) = 1 / 2+3x and point P = (2 , 1/8)

f(x+h) = 1/(2 + 3a + 3h)

f(a) = 1/(2 + 3a)

m(tan) = [1/(2 + 3a + 3h) - 1/(2 + 3a)]/h

After simplifying:

m(tan) = -3/[(2+3a)(2+3a+3h)]

h = 0

m(tan) = -3/(2+3a)²

The equation of the line:

y - 1/8 = [-3/(2+3a)²](x - 2)

Thus, the slope is -3/(2+3a)² and the equation of the line is y - 1/8 = [-3/(2+3a)²](x - 2).

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Probability of drawn ticket at random with the condition of first ticket drawn is red and for second ticket drawing blue is equal to 0.253.

As given in the question,

Number of blue tickets in a box is equal to 25

Number of red tickets in a box is equal to 20

Total number of tickets in a box = 25 + 20

                                                     =  45

Drawing a ticket one at a time and not replaced

Probability of drawing a ticket first is red and second drawn is blue

= ( 20 / 45 ) × ( 25 / 44 )

= ( 500 / 1980 )

= 0.2525..

= 0.253

Therefore, probability of drawn ticket at random with the condition of first ticket drawn is red and for second ticket drawing blue is equal to 0.253.

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By the principle of mathematical induction, it has been proved that

[tex]p^3 + 11p[/tex] is divisible by 6

What is Principle of mathematical induction?

Let the statement be given by P(n). At first P(n) is proved to be true for 1. Then it is assumed that P(n) is true for all n. If P(n) is true for (n+1) then by Principle of Mathematical induction, P(n) is true for all natural numbers

The given expression is [tex]p^3 + 11p[/tex]

For p = 1

[tex](1)^3 + 11 \times 1\\12[/tex]

which is a multiple of 6

Let it be true for p = m

[tex]m^3 + 11m[/tex] is a multiple of 6

[tex]m^3 + 11m = 6k[/tex], where k is any integer

For p = m + 1

[tex](m+1)^3 + 11(m+1) \\m^3+3m^2+ 3m +1+11m+11\\m^3+11m +3m^2+3m+12\\m^3+11m + 3m(m+1) + 12[/tex]

Now,

[tex]m^3 + 11m[/tex] is divisible by 6

We know that the product of two consecutive integers are divisible by 6

[tex]3m(m+1)[/tex] is divisible by 6

12 is divisible by 6

[tex](m+1)^3 + 11(m+1)[/tex] is divisible by 6

So it is true for p = m + 1

By the principle of Mathematical induction, it is true for all natural numbers and eventually for all integers

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The equations you use to find the price of one tire patch are 4x + 1.9 = 22.20 and  22.2 – 4x = 1.9, so options A and E are correct.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given:

The Balance on the gift card =  $22.20,

The no of patches bought = 4,

The left balance on the card =  $1.90.

The equation for the statement in the question is,

The no of patches bought × The price of patches  + The left balance on the card = The Balance on the gift card

Let x be the price of one batch

Substitute the values,

4x + 1.9 = 22.20 or 22.2 – 4x = 1.9

Therefore, the equations you use to find the price of one tire patch are   4x + 1.9 = 22.20 and  22.2 – 4x = 1.9.

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The probability that the person obtains a note with C written in it is of:

0.1538 = 15.38%.

The probability of an event in an experiment is obtained as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.

The total number of notes in this problem is composed as follows:

Hence the total number is of:

Total = 7 x 4 + 8 x 3 = 52 notes.

The desired number of outcomes is the number of notes with C, hence:

Desired = 8 notes.

Thus the probability is calculated as follows:

Probability = Desired/Total = 8/52 = 0.1538 = 15.38%.

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After the firm work year reduced to 48 weeks at the same rate, the architect annual pay decrease to 43,392 dollars.

An entry level architect's annual pay is $47,008 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its architects

The company cuts the work year to 48 weeks but keeps the same rate of pay.  The amount the architect should expect his annual pay to decrease can be calculated as follows:

Let's find the rate.

Therefore,

52 weeks = 47008

1 week = ?

cross multiply

rate = 47008 / 52

rate = 904 dollars per weeks

He collects the same rate after the company cuts the work year to 48 weeks.

Therefore,

annual pay of the architect after the cut = 48 × 904

annual pay of the architect after the cut = 43,392 dollars

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Step-by-step explanation:

let angles of a triangle a=86

b= 180-3z , c= 180-4z

a+b+c = 180 {angle sum property}

86 +180+180-3z-4z=180

446 -7z = 180

-7z = -266

[tex]z = \frac{ - 266}{ - 7} = 38[/tex]

so other angle are

3z = 3 x 38 = 114

4z = 4 x 38 = 152

The simplest form is 4xy

From the question, we have

xy + 3xy = 4xy

The simplest form is 4xy.

Addition:

The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.

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Answer:

I 728.Two beetles sit at the verticesAandHof a cubeABCDEFGHwith edge length40√110 units. The beetles start moving simultaneously alongACandHFwiththe speed of the first beetle twice that of the other one.....ADCBEFGH✈s✈s. . . . . . . . . . . . . . . . . . . . . . . . ......................................................................What will be the shortest distance between the beetles?29.In the diagram,4PQRhas an area of 960 square units. The pointsS,TandUare the midpoints of the sidesQR,RPandPQ, respectively, and the linesPS,QTandRUintersect atW.......PQRSUTNMLW✓✓✼. . . . . . . . . . . . . . .....................The pointsL,MandNlie onPS,QTandRU, respectively, such thatPL:LS= 1 : 1,QM:MT= 1 : 2 andRN:NU= 5 : 4.What is the area, in square units, of4LMN?30.A 40×40 white square is divided into 1×1 squares by lines parallel to its sides.Some of these 1×1 squares are coloured red so that each of the 1×1 squares,regardless of whether it is coloured red or not, shares a side with at most one redsquare (not counting itself). What is the largest possible number of red squares?

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Answer:

i got 48000

Step-by-step explanation:

20x40x60

when solving volume you multiply the length times width times height.

After dilation with center (0, 0) and scale factor 4 the required image vertices of the given image is given by A' =(-12 , 4), B' =(16 , -12),

C' = (8 , 12),  D' = (-4 , 16).

As given in the question,

From the given graph of quadrilateral  the vertices of the given image is given by :

A and D are second quadrant , C is first quadrant and B is in fourth quadrant.

Each unit on both the axis represents 1 unit only.

Coordinates of each vertices are:

A = (-3 , 1) , B = (4 , -3) ,C = (2 , 3), D = (-1 , 4)

Now for dilation scale factor is equal to 4

Image vertices for a dilation with center (0 , 0) multiply the vertices by scale factor 4.

Required image vertices are given by:

A' = (-12 , 4),

B' = (16 , -12)

C' = (8 , 12)

D' = (-4 , 16)

Therefore, after dilation with center (0, 0) and scale factor 4 the required image vertices of the given image is given by A' =(-12 , 4),  B' =(16 , -12),

C' = (8 , 12),  D' = (-4 , 16).

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Answer:

A ≈ 2.88×108km²

Step-by-step explanation:

A= 4 π r² = 4·π· 47902 ≈ 2.88324×10 power 8 km²