I will give you branilest

To transmit information on the internet, large files are broken into packets of smaller sizes. Each packet has 1,500 bytes of information. An equation relating packets of information is given by b = 1500p where p represents the number of packets and b represents the number of bytes of information.

a. How many packets would be needed to transmit 30,000 bytes of information?

The coefficient of x^2 in the expansion of (x + 2)^3 is 6

From the question, we have the following parameters that can be used in our computation:

(x + 2)^3

Next, we expand the expression

So, we have the following representation

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

Evaluate the expression

(x + 2)^3 = x^3 + 6x^2 + 12x + 8

The coefficient of x^2 in the expression  x^3 + 6x^2 + 12x + 8 is 6

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Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

The linear and exponential equations for the amount of money in the banks indicates;

TCF Bank Equation

y = 100·x + 1000

Well Fargo Bank Equation

y = (1.06)ˣ

The number of years it will take for both accounts to have the same amount of money is about 17 years

An exponential equation is an equation of the form; y = a·bˣ, where the input variable, x is an exponent.

The equation for calculating the amount in each bank, based on the details are;

TCF Bank;

Amount invested = $1,000

Amount added each year = 100·x

Well Fargo Bank Equation

The percentage of the amount earned as interest each year = 6% = 0.06

The exponential equation for compound interest amount is; y = 1000·(1 + 0.06)ˣ

Therefore; y = 1000·(1.06)ˣ

When the amount in the two accounts have the same amount of money, we get;

1000·(1.06)ˣ = 100·x + 1000

Therefore; (1.06)ˣ = (100·x + 1000)/1000 = 0.1·x + 1

(1.06)ˣ = 0.1·x + 1

Solving the above equation using the substitution method and graphing indicates that we get;

x = 0, and x ≈ 17.125732

Therefore, it takes about 17 years for the two accounts to have the same amount of money

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Answer:

Angle A = tan^-1(11/5)
Angle C = 90 - tan^-1(11/5)
AC = sqrt(146)

Step-by-step explanation:

As this is a right triangle, we can apply the Pythagorean theorem a^2 + b^2 = c^2, where c is the hypotenuse while a and b are the legs, to solve for AC.

11^2 + 5^2 = AC^2

121 + 25 = AC^2

146 = AC^2

sqrt(146) = AC^2

Next, to find angle A, we can use one of the trigonometric functions. Let’s use tangent for simplicity. Tangent of an angle is “opposite divided by adjacent”. If we set the angle to A, opposite is side BC and the adjacent is side AB. Thus, tan(A) = 11/5 and tan^-1(11/5) = A.
Since the sum of angles in a triangle is 180, we can find angle C by setting up this equation: C = 180 - 90 - tan^-1(11/5), which is 90 - tan^-1(11/5)

Answer:

6.  ∠PVU = 58°

7.  y = 74°

Step-by-step explanation:

Angles on a straight line sum to 180°.

⇒ ∠USP + ∠PSV = 180°

⇒ 148° + ∠PSV = 180°

⇒ 148° + ∠PSV - 148° = 180° - 148°

⇒ ∠PSV = 32°

The interior angle of a rectangle at each vertex is 90°.

⇒ ∠VPS = 90°

Interior angles of a triangle sum to 180°.

⇒ ∠PVS + ∠PSV+ ∠VPS = 180°

⇒ ∠PVS + 32° + 90° = 180°

⇒ ∠PVS + 122° = 180°

⇒ ∠PVS + 122° - 122° = 180° - 122°

⇒ ∠PVS = 58°

From inspection of the given diagram:

⇒ ∠PVU = ∠PVS

⇒ ∠PVU = 58°

Opposites sides of a rectangle are parallel.

Therefore, GF is parallel to AB:

⇒ ∠CFG = ∠CBA = 32°

Interior angles of a triangle sum to 180°.

⇒ ∠FGC + ∠GCF + ∠CFG = 180°

⇒ y + 74° + 32° = 180°

⇒ y + 106° = 180°

⇒ y + 106° - 106° = 180° - 106°

⇒ y = 74°

Answer:

15$

Step-by-step explanation:

45 ÷ 3 = 15

Answer:

(3000/(5-3))(3+5)

= (3000/2) 8

= 12000

Step-by-step explanation:

Answer:

19.28

Step-by-step explanation:

91.48 minus 72.2

Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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Explanation:

I'm assuming you meant to write 1/5 instead of 1:5

Add up all the fractions

1/4 + 3/8 + 1/10 + 1/5

20/80 + 30/80 + 8/80 + 16/80

(20+30+8+16)/80

74/80

37/40

He spends 37/40 of his income on rent, foot, clothes, insurance and other items combined.

Subtract this from 1 to find the fraction of his income he saves

1 - 37/40

40/40 - 37/40

(40-37)/40

3/40

He saves 3/40 of his monthly income.

(3/40)*8480 = 636 dollars is the amount saved every month.

Answer:

Yes

Step-by-step explanation:

To find this out. If you divide the denominators by each other, they would need to be the same value as if you divide the numerators by each other

\(45 \div 9 = 5\)

^ 45 and 9 were the denominators, we divide and get 5

Now for the numerators

\(10 \div 2 = 5\)

^ 10 and 2 we're the numerators, dividing also gave 5

Answer:

yes.

Step-by-step explanation:

let us check. to be a proportion they must be equivalent

however, what do we multiply to get there? let us check..

\(\frac{2x}{9x} =\frac{10}{45}\)

cross multiply...

2x * 45 = 9x * 10

90x = 90x

yes, they will be proportional!

you can even do it without the X, i just put x in to make it clearer.

The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).

A function is defined as a relation between the set of inputs having exactly one output each.

On a coordinate plane, a parabola opens down with solid circles along the parabola at (-3, -5), (-2, 0), (-1, 3), (0, 4), (1, 3), (2, 0), (3, -5).

The domain is all real numbers.

The range is all real numbers.

If for an interval I, when x decreases meanwhile staying in interval I, the function's output increases (or can stay same), then we say that the function is increasing in the interval.

The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).

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Answer:

A

Step-by-step explanation:

The correct answer is John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

Let's choose the function "Weekly salary is a function of the hourly pay rate and the number of hours worked."Example: John works as a part-time employee at a grocery store. His hourly pay rate is $12, and he worked for 20 hours in a week. We can evaluate the function to find his weekly salary.

Weekly salary = Hourly pay rate * Number of hours worked

Weekly salary = $12/hour * 20 hours

Weekly salary = $240

So, John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

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Answer:

minimum sample size = 97

Step-by-step explanation:

Margin of error = 20

standard deviation = 100

sample size = n

standard error = 100/sqrt(n)

confidence level, alpha = 95%

Using the standard rule for 95% confidence

standard error <= sample mean \(\pm\) 1.96 standard error, or

20 <= 1.96*100 / sqrt(n)

n >= (1.96*100/20)^2 = 9.8^2 = 96.04  

=>

n >= 97

Answer:

Could you give a little more context. I can help.

Answer:B

Step-by-step explanation:

Hope it helps :)

\(x + 4y = 9 \\

-x - 2y = 3 \\ eliminate \: one \: variable \: by \\ adding \: the \: equations \\ 2y = 12 \\ divide \: both \: sides \\ y = 6 \\ substitute \: the \: value \: of \: y \\ \: into \: equation \: ...2 \\ - x - 2(6) = 3 \\ solve \: the \: equation \\ - x - 12 = 3 \\ - x = 3 + 12 \\ - x = 15 \\ x = - 15 \\ SOLUTION \\ x = - 15 \\ y = 6 \\ Hope \: it \: helps :)\)

The step in which the subtraction property of equality was applied to solve the equation is given as follows:

D. The subtraction property of equality was not applied to solve this equation.

The subtraction property of equality states that subtracting the same number from both sides of an equation does not affect the equality, and hence it is used to isolate a variable that is adding on a side of the expression.

For this problem, to remove the term -7, we add 7 to both sides of the expression, hence the addition property of equality was applied.

In the other step, the multiplication property was applied, hence option D is the correct option for this problem.

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Answer:

15 19/30

Step-by-step explanation:

Answer:

x = 25

Step-by-step explanation:

We have 2 similar triangles:

1) with hypotenuse 15 and short leg 9,

2) with hypotenuse x and short leg 15.

For similar triangles we can write a proportion for corresponding sides.

hypotenuse 1: leg1 = hypotenuse 2 : leg 2

15 : 9 = x : 15

9x = 15 * 15

x = 15*15/9

x = 25

Answer:

\(5x-y+7z-38=0\)

or

\(5x-y+7z=38\)

Step-by-step explanation:

Given vector equation:

\(\textbf{r} = \textbf{i} - 5\textbf{j} + 4\textbf{k} + \lambda(3\textbf{i} + \textbf{j} - 2\textbf{k}) + \mu(-\textbf{i} + 2\textbf{j} + \textbf{k})\)

The vector 3i + j - 2k is perpendicular to n.

The vector -i + 2j + k is perpendicular to n.

\(\textsf{So}\;\;\textbf{n}=\left|\begin{array}{ccc}\textbf{i}&\textbf{j}&\textbf{k}\\3&1&-2\\-1&2&1\end{array}\right|\)

        \(=\textbf{i}\left|\begin{array}{rr}1&-2\\2&1\end{array}\right|-\textbf{j}\left|\begin{array}{rr}3&-2\\-1&1\end{array}\right|+\textbf{k}\left|\begin{array}{rr}3&1\\-1&2\end{array}\right|\)

        \(=\textbf{i}(1 \cdot 1 - (-2) \cdot 2)-\textbf{j}(3 \cdot 1-(-2) \cdot (-1))+\textbf{k}(3 \cdot 2-1 \cdot (-1))\)

        \(=\textbf{i}(1 +4)-\textbf{j}(3-2)+\textbf{k}(6+1)\)

        \(=5\textbf{i}-\textbf{j}+7\textbf{k}\)

So the equation of the plane written in Cartesian form is:

\(5x-y+7z+d=0\)

Substituting (1, -5, 4) gives:

\(5(1)-(-5)+7(4)+d=0\)

\(5+5+28+d=0\)

\(38+d=0\)

\(d=-38\)

Therefore, the given vector equation in Cartesian form is:

\(5x-y+7z-38=0\)

or

\(5x-y+7z=38\)

The angular speed of 14 revolutions per second is equal to 87.96 radians per second.

Angular speed is a measure of how fast an object is rotating or revolving around an axis. It is typically measured in units of angular displacement per unit of time, such as degrees per second, revolutions per minute (RPM), or radians per second.

To convert angular speed from revolutions per second (RPS) to radians per second (RAD/s), we can use the following formula:

Angular speed (RAD/s) = 2π x Revolutions per second (RPS)

Given that the angular speed is 14 revolutions per second, we can substitute this value into the formula:

Angular speed (RAD/s) = 2π x 14 RPS

Angular speed (RAD/s) = 87.96 RAD/s

So, 14 revolutions per second is equivalent to 87.96 radians per second.

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Step-by-step explanation:

Team A time is    1 garden / ( 1 garden/ 2 hr + 1 garden/4 hr) = 1 1/3 hr

Team B =   1 / ( 1/3 + 1/3) =  1 1/2 hr

Team A wins !

Answer:

The answer to the question provided is option 2.

The length of EB is approximately 14.6 units when rounded to the nearest tenth.

To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.

Using the similarity ratio, we can set up the proportion:

DF / CF = DE / EB

Plugging in the given values, we have:

13.1 / 10.9 = 17.5 / EB

To find EB, we can cross-multiply and solve for EB:

13.1 * EB = 10.9 * 17.5

EB = (10.9 * 17.5) / 13.1

EB ≈ 14.6

Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.

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It is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in
the graph intersecting the x- or y-axis at a different point.

Function is an operation that takes an input, performs some processing on it, and returns a result. It is a set of instructions that performs a specific task. Functions are typically used to perform repetitive tasks, like finding the sum of two numbers, adding two strings together, or finding the maximum of a list of numbers. Functions are essential to programming and can be used to make code more organized, reusable, and efficient.


The function f(x) = x is the parent function for linear equations. This equation is generally used to graph a line with a slope of 1 and a y-intercept of (0, 0). In order to translate this parent function, different transformations are applied to it.

A vertical translation down 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function down 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, -4).

A horizontal translation right 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function right 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (4, 0).

A horizontal translation left 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function left 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (-4, 0).

Finally, a vertical translation up 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function up 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, 4).

In conclusion, it is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in the graph intersecting the x- or y-axis at a different point.

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The inequality is used to find the domain of the given function is

5x-5 ≥ 0

A function is a relation from a set of inputs to a set of possible outputs, where each input is related to exactly one output.

Given is function y = √(5x-5)+1, we have to find which inequality can be used to find the domain.

Since, the function is a square root function.

We know that,

The square root function is defined only for the positive values, including 0. i.e. the expression inside the square root must be greater than or equal to 0.

The expression inside the square root is (5x-5) so that must be greater than or equal to 0 which can be written as :

5x-5 ≥ 0

Hence, the inequality is used to find the domain of the given function is 5x-5 ≥ 0

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Answer: 36

Step-by-step explanation:

When handling exponents, we have to remember that we're multiplying a number by itself x amount of times

3^3 + (3^2) Parenthesis first

3^3 + (3 x 3)

3^3 + 9 Next Exponents

3 x 3 x 3 + 9

27 + 9  Add

36

Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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