The diameter of a circle is 3 m. What is the circle's circumference?

Answer: 16t^6−40t^3+25 is the answer

first lets set the equation as a binomial *remember 2 binomial= trinomial*

so its going to look something like..........

(4t^3-5) (4t^3-5)

now we do the foil method so 4t^3* 4t^3= 16t^6 (add exponents)

do the same for the other terms:

4t^3*-5= -20t^3

-5*4t^3= -20t^3

-5*-5= 25

now the whole equation is...

16t^6-20t^3-20t^3+25 (combine like terms like -20t^3 and -20t^3)

therefor the answer is... 16t^6-40t^3+25

Converting the given decimal numbers to hexadecimal and then to binary, we find that

(a) 757.1710 is equivalent to 2F5.2E16 in hexadecimal and 1011110101.001011002 in binary.

(b) 356.2510 is equivalent to 164.4016 in hexadecimal and 101100100.01000011012 in binary.

To convert a decimal number to hexadecimal, we divide the whole number part and the fractional part separately by 16 and convert the remainders to hexadecimal digits.

For the whole number part of (a) 757, dividing it by 16 gives us a quotient of 47 and a remainder of 5, which corresponds to the hexadecimal digit 5.

Dividing the fractional part 0.17 by 16 gives us a hexadecimal digit of 2. Combining these digits, we get the hexadecimal representation 2F5.

To convert (b) 356 to hexadecimal, we divide it by 16, obtaining a quotient of 22 and a remainder of 4, which corresponds to the hexadecimal digit 4.

For the fractional part 0.25, dividing by 16 gives us a hexadecimal digit of 1. Combining these digits, we get the hexadecimal representation 164.

To convert hexadecimal numbers to binary, we simply replace each hexadecimal digit with its equivalent four-digit binary representation. Converting (a) 2F5 to binary, we get 1011110101.

Similarly, converting (b) 164 to binary, we get 101100100.

For the fractional parts, converting 0.2E to binary gives us 0010, and converting 0.401 to binary gives us 01000011.

Therefore, (a) 757.1710 is equivalent to 2F5.2E16 in hexadecimal and 1011110101.001011002 in binary, while (b) 356.2510 is equivalent to 164.4016 in hexadecimal and 101100100.01000011012 in binary.

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The linear factors of the polynomial function are f(x) = - (1/1500) · (x + 20) · (x + 5) · (x - 15).

Cubic equations are polynomials of third grade, whose standard and factor forms are shown below:

Standard form

y = a · x³ + b · x² + c · x + d

Factor form

y = (x - r₁) · (x - r₂) · (x - r₃)

Where r₁, r₂, r₃ are the zeros of the cubic equation.

There are several approaches to find the roots of the polynomial, in this question we decided to use the graphical approach, which offers sufficiency and quickness for analysis. The roots of the polynomials are the points that pass through the x-axis.

In accordance with the image attached below, the polynomial has three real roots: r₁ = - 20, r₂ = - 5, r₃ = 15. Then, the linear factors of the polynomial function are f(x) = - (1/1500) · (x + 20) · (x + 5) · (x - 15).

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Answer:

Option B is the correct answer

Step-by-step explanation:

B. x2 + y2 = 25

Number of license plates = 24 x 24 x 7 x 7 x 7

= 197568

Answer:

x=1/2

Step-by-step explanation:

4/5x-1/10=3/10

4/5x=2/5

x= 1/2.

Hope this helps :D

Therefore, an orthonormal basis for the λ2-eigenspace is given by the matrix:

[ 3/7 | 0.43 ]

[ 4/7 | 0.57 ]

[-5/7 | -0.71 ]

To find an orthonormal basis for the λ2-eigenspace, we can use the Gram-Schmidt process. Given that v1 and v2 are an eigenbasis for the λ1-eigenspace, we can start with v3 = [0, 1, 0] as a candidate vector for the λ2-eigenspace. We will perform the Gram-Schmidt process to orthogonalize and normalize v3.

Orthogonalization:

To orthogonalize v3, we subtract its projection onto v1 and v2 from itself.

u3 = v3 - proj(v3, v1) - proj(v3, v2)

To find the projections, we use the dot product:

proj(v3, v1) = (v3 · v1) / (v1 · v1) * v1

proj(v3, v2) = (v3 · v2) / (v2 · v2) * v2

Calculating the projections:

proj(v3, v1) = ([0, 1, 0] · [-2, 0, 2]) / ([-2, 0, 2] · [-2, 0, 2]) * [-2, 0, 2]

= (-2) / 8 * [-2, 0, 2]

= [-1/2, 0, 1/2]

proj(v3, v2) = ([0, 1, 0] · [-2, -2, -2]) / ([-2, -2, -2] · [-2, -2, -2]) * [-2, -2, -2]

= (-2) / 12 * [-2, -2, -2]

= [-1/3, -1/3, -1/3]

Substituting the values:

u3 = [0, 1, 0] - [-1/2, 0, 1/2] - [-1/3, -1/3, -1/3]

= [1/2, 4/3, -5/6]

Normalization:

To normalize u3, we divide it by its magnitude.

v3_orthonormal = u3 / ||u3||

Calculating the magnitude:

||u3|| = sqrt((1/2)^2 + (4/3)^2 + (-5/6)^2)

= sqrt(1/4 + 16/9 + 25/36)

= sqrt(9/36 + 64/36 + 25/36)

= sqrt(98/36)

= sqrt(49/18)

= 7/3

Dividing u3 by its magnitude:

v3_orthonormal = [1/2, 4/3, -5/6] / (7/3)

= [3/7, 4/7, -5/7]

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Answer:

6 miles

Step-by-step explanation:

Answer:

4/9

Step-by-step explanation:

8/18 x 7/17 x 6/16 = 336/4896 = 0.06863 = 6.863% = 6.9\%

≈0.06863=6.863%≈6.9%

The percentage of people who do not like to listen to radio as well as watch the television is 65%.

It is important to note that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

From the information, 36% like to listen to radio as well as watch the television.

Therefore, the percentage of the people who do not like to listen to radio as well as watch the television will be:

= 1 - 35%

= 65%

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In a survey of a community. 55% of the people like to listen the radio, 65% like to watch the television and 35% like to listen the radio as well as watch the television

Find the percentage of the people who do not like to listen radio as well as watch the television.

Answer:

La arista de la bodega debe medir 6 metros.

Step-by-step explanation:

Podemos encontrar la arista de la bodega sabiendo su volumen:

\( V = a^{3} \)

En donde:

V: es el volumen de un cubo = 216 m³

a: es la arista del cubo =?

La arista del cubo es:

\( a = \sqrt[3]{V} = \sqrt[3]{216 m^{3}} = 6 m \)

Por lo tanto, la arista de la bodega debe medir 6 metros.

Espero que te sea de utilidad!

The answers are explained in the solution.

Given that, a bus and a car have speed of 100km/hr and 120km/hr.

They are covering a distance of 340 km, they started travelling at 7:00 am,

Speed = distance / time

A) Bus travelled in 30 minutes = 100 × 0.5 = 20 km

After 30 minutes = 100 × 0.5 = 20 km

Total distance by bus in 1 hour = 40 km

Car covered in 30 minutes = 120 × 0.5 = 60 km

Distance between them = 60-40 = 20 km

Relative speed = 120-100 = 20 km/h

Time to catch up = 20/20 = 1 hour

Distance from Nairobi = 60 + (1 × 120) = 180 km

Therefore, the car catches up with the bus 180 km from Nairobi,

B) Time taken = 30 + 30 + 1 = 2 hours.

7:00am + 2 hours = 9:00 am

C) Time taken by bus to reach the destination = 340 / 100

= 3.4 hours

Hence, bus took 3.4 hours to reach the destination.

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The correct answers are: c) vomiting and d) weight loss. Gastroesophageal reflux can cause frequent vomiting, which can lead to weight loss in infants.

A nurse caring for an infant with gastroesophageal reflux may observe the following findings associated with this condition:
b) wheezing
c) vomiting
d) weight loss

Infants and children diagnosed with gastroesophageal reflux should not sit or lie down immediately after a meal; patients will be advised to lie face down for at least the first hour after a meal; Sleeping in this position has been shown to reduce the frequency of gastroesophageal reflux. Expressed milk can be thickened as described, in addition to increasing the frequency of feedings; in addition, early teaching (at three (3) months) to eat rice can be attempted; small meals are also recommended; oily and spicy. foods that promote postprandial reflux by increasing gastric emptying and slowing digestion; Chocolate, mint, tomato, citrus fruits, and caffeine should be avoided, which lowers LES pressure.

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The speed of the plane with no wind is 273 miles/hour.

What exactly is speed?

Speed is a measure of how fast an object is moving, usually measured in distance per unit of time. It is a scalar quantity, which means it has magnitude but no direction.

The formula for speed is:

Speed = Distance / Time

where distance is the total path traveled by an object, and time is the duration of the motion.

Now,

Let's use the following equations to solve for x and y:

x - y = 1680/5 (the speed of the plane against the wind)

x + y = 1680/4 (the speed of the plane with the wind)

Simplifying each equation, we get:

x - y = 336

x + y = 420

Adding the two equations together, we get:

2x = 756

Solving for x, we get:

x = 378

Substituting x into either equation, we can solve for y:

378 + y = 1680/4

y = 105

Therefore, the speed of the plane with no wind (i.e., the airspeed) is:

x - y = 378 - 105 = 273 miles per hour.

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9514 1404 393

Answer:

  UW = 24

Step-by-step explanation:

Midsegment XY is half the length of base UW, so we can write ...

  UW = 2·XY

  73 -7x = 2(54 -6x) . . . . substitute the given expressions

  73 -7x = 108 -12x . . . . . eliminate parentheses

  5x = 35 . . . . . . . . . . . . . add 12x-73

  x = 7 . . . . . . . . . . . . . . . divide by 5

Now, we can find UW:

  UW = 73 -7x = 73 -7·7

  UW = 24

ΔXYZ will also be an equilateral triangle.

What is equilateral triangle?

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean space, an equilateral triangle also is equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others. It's also referred to it as a regular triangle because it is a regular polygon.

As X,Y,Z are the midpoints of sides of equilateral triangle so when we will join the X,Y,Z we will find that distances XY=YZ=XZ are three are equal because this is proved by similarity of triangles which in itself is a detailed and vast topic

Hence XYZ will also be an equilateral triangle

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The consumers’ surplus (CS) if the market price is set at $6 is 16.67 (per unit thousands).

Let,

The wholesale unit price in dollars = p

The quantity demanded each week = x (in thousand units)

The demand function =  \(-0.01x^2-0.2x+9\\\)

Market price = $6

Substitute p = 6 into the demand function:

6= -0.01\(x^2\)-0.2x+9

0= -0.01\(x^2\)-0.2x+3 (subtract 6 on both sides of the equation)

0.01\(x^2\)+0.2x-3=0 (rewrite the equation)

\(x^2\)+20x-300=0 (multiply 100 on both sides of the equation)

(x+30)(x-10)=0 (factor the equation)

(x+30)=0 and (x-10)=0 (zero product property of multiplication)

Therefore, x=-30, x=10.

x=10 as negative numbers are not feasible in this situation.

Consumer surplus (CS) of a production can be found using the integral,

CS = \($$ \int_{0}^{x}(p)dx $$ -px\)

CS = \($$ \int_{0}^{x} (-0.01x^2-0.2x+9)dx $$ -px\)

Substitute x=10 and p=6 :

CS = \($$ \int_{0}^{10} (-0.01x^2-0.2x+9)dx $$ - (6\times10)\)

CS = \($$ \int_{0}^{10} (-0.01x^2-0.2x+9)dx $$ -60\)

CS = \($$ \left[\frac{x^3}{300}-\frac{x^2}{10}+9x\right]_{0}^{10} $$ -60\)(evaluate the integral)

CS = \((((10^3/300)-(10^2/10)+(9$$ \times $$10))-(0)) - 60\) (evaluate the limit)

CS = (230/3)-60

CS = 50/3

CS \($$ \approx $$\) 16.67

Therefore, The consumers’ surplus (CS) is 16.67 if the market price is set at $6(per unit thousands).

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Answer: The answer in this photo thanks for a little quiz

The number of day it will be until Addison and Bert each have  read the same number of pages in total is 8 days.

In mathematics, an equation is a statement of equality between two expressions, indicated by the equals sign (=). Solutions to equations are the values for unknowns which, when substituted into the expression, make it true.

Given that, the book they're reading right now is 256 pages long.

Let the number of days be x.

Addison has read 102 pages so far and decides to read 16 pages every day until she finishes the book.

102+16x -------(i)

Bert has read 142 pages, and he plans to read 11 pages every day.

142+11x -------(ii)

Addison and Bert have each read the same number of pages in total.

So, (i)=(ii)

102+16x=142+11x

16x-11x=142-102

5x=40

x=8

Hence, the number of day it will be until Addison and Bert each have  read the same number of pages in total is 8 days.

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Answer:

2,323. 13 dollars

We can read 91 books in a year if you increase your reading speed so that each page takes you 30 seconds less than it did before.

Now If each page now takes 30 seconds less to read than before,

then you will save 30*200 = 6000 seconds (or 100 minutes) on each book.

So, the time it will take you to read a 200-page book will be

20 minutes - 100 minutes = -80 minutes,

which means you will finish a 200-page book in 80 minutes (or 1 hour and 20 minutes).

In a year, there are 365 days. If you read for 20 minutes per day, then you will read for a total of

365 * 20 = 7300 minutes (or 121.67 hours) in a year.

Since you can finish a 200-page book in 80 minutes, you can read 7300/80 = 91.25 books in a year.

However, since you cannot read a fraction of a book, the maximum number of 200-page books you can read in a year is 91 books.

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Complete question is :

If you increase your reading speed so that each page takes you 30 seconds less than it did before,

and you begin reading 20 minutes per day,

How many 200 page books can you now read in a year?

Answer:

3349.5 \(cm^{3}\)

Step-by-step explanation:

see image

Answer:

145

Step-by-step explanation:

\( \frac{36}{48} \\ \\ = \cancel \frac{36}{48} \\ \\ \fbox {cancelling \: by \: 6} \\ \\ = \frac{6}{8} \\ \\ = \cancel \frac{6}{8} \\ \\ \fbox{now \: cancelling \: by2} \\ \\ = \frac{3}{4} \)

So \( \frac{3}{4} \) is the most simplified form of \( \frac{36}{48} \)

Answer:

3/4

Step-by-step explanation:

Factor 12 out of 36

Factor 12 out of 48

Which gives you 3/4

[3 for the 36 b/c \(12*3\) = 12] [4 for the 48 b/c \(12*4\) = 48]

Making it  \(\frac{3}{4}\)

Or in decimal form: 0.75

We can use Coulomb's law to calculate the magnitude of the electric field at a distance r away from a point charge Q:

E = k * Q / r^2

where k is Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge.

In this problem, we have a point charge Q of -10 nC located at (1.2 cm, 0 cm), and we want to find the x-component of the electric field at a distance r = 5.3 cm away at position (-4.1 cm, 0 cm).

To find the x-component of the electric field, we need to use the cosine of the angle between the electric field vector and the x-axis, which is cos(180°) = -1.

So, the x-component of the electric field at position (-4.1 cm, 0 cm) is:

E_x = - E * cos(180°) = - (k * Q / r^2) * (-1)

where k = 9 x 10^9 N*m^2/C^2 is Coulomb's constant.

Substituting the given values, we get:

E_x = - (9 x 10^9 N*m^2/C^2) * (-10 x 10^-9 C) / (0.053 m)^2

E_x ≈ -30,566.04 N/C

Rounding this to two significant figures and including the appropriate units, we get:

The x-component of the electric field is about -3.1 x 10^4 N/C (to the left).

To solve for x, we have to find a way to make x the subject of the equation (get x on one side and everything else on the other side)

since    -4 = (2/3)x     [mutiply both sides by 3]

⇒    -4 × 3 = 2x     [divide both sides by 2]

⇒   (-12/2) = x      [simplify by dividing -12 by 2]

∴            x = -6

Answer:

X = 6

Step-by-step explanation:

2/3 x 6/1 = 4

2 x 6 = 12

3 x 1 = 3

12/3 = 4

12 divided by 3 is 4

The answer is 6 , x = 6

Answer: 140

Step-by-step explanation:

We know that the angle measures must add to 180 deg, so:

40 + x = 180

x = 140.

The probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

If the average number of units rented per week is 2.3 and the distribution is Poisson, then the parameter lambda is also equal to 2.3.

The probability of renting exactly three apartments in a week is given by the Poisson probability function:

\(P(X = 3) = (e^(-lambda) * lambda^x) / x!\)

Substituting the values, we get:

\(P(X = 3) = (e^(-2.3) * 2.3^3) / 3!\)

P(X = 3) = (0.09963 * 12.167) / 6

P(X = 3) = 0.2018

Therefore, the probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

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