What is the product of 6/sqrt(3) and 3/sqrt(6) in simplest radical form?

Step-by-step explanation:

\( f(x) = - 3 {x}^{2} + 9x - 2\)

A) f(-2) + f(1) = -32 + 4 = -28

B) f(-2) - f(1) = -32 - 4 = -36

Step-by-step explanation:

By factorization, 6mn-9m-4n+6 becomes

3m(2n-3) -2(2n-3)

= (3m-2)(2n-3).

The value of x from the given exponential function is -8.159.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

The given equation is \(9^{3x}=4^{5x+2}\).

Take the logarithm of both sides of the equation to remove the variable from the exponent.

Here, \(ln(9^{3x})=ln(4^{5x+2})\)

x=2ln(4)/3ln(9)-5ln(4)

x= -8.159

Therefore, the value of x is -8.159.

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The number of portion with each having 12 fruits is at most 6 portions.

To divide the fruits into 12 portions

Total number of fruits = 80

Number of fruits per portion = 12

Number of fruits per portion = (Total number of fruits / Number of fruits per portion )

Number of fruits per portion = 80/12 = 6.67

Therefore, to divide the fruits into 12 fruits , There would be at most 6 portions.

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Answer:

b=d/2a -c

Step-by-step explanation:

b+c=d/2a (Divide 2a on both sides to elimnate the 2a on the left side)

b=d/2a -c (Subtract c on both sides to elimnate the c on the left side)

Answer: b=d/2a -c

Hope this helps!

The value of b is given as follows:

b = 18.

Similar triangles are triangles that share these two features presented as follows:

The bisection, represented by the altitude segment in this triangle, divides the triangle into two similar triangles, hence the equivalent side lengths are given as follows:

Then the proportional relationship for these side lengths is given as follows:

b/(28 - b) = 27/15

Applying cross multiplication, the value of b is obtained as follows:

15b = 27(28 - b)

42b = 27 x 28

b = 27 x 28/42

b = 18.

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Answer:

D. 5

Step-by-step explanation:

Based on the midsegment theorem of a trapezoid, thus:

QR = ½(OP + MN)

Substitute

27 = ½((5x - 7) + (6x + 6))

27 = ½(5x - 7 + 6x + 6)

Add like terms

27 = ½(11x - 1)

Multiply both sides by 2

2*27 = 11x - 1

54 = 11x - 1

54 + 1 = 11x

55 = 11x

55/11 = x

5 = x

x = 5

When events A and B are mutually exclusive or disjoint, the probability of either event A or event B occurring is equal to the sum of their individual probabilities, represented by P(A or B) = P(A) + P(B).

If it is impossible for events A and B to occur simultaneously, the events are said to be mutually exclusive or disjoint.

For mutually exclusive events, the probability of either event A or event B occurring is equal to the sum of their individual probabilities.

Therefore, for mutually exclusive events A and B, the probability of A or B occurring, denoted as P(A or B), is given by:

P(A or B) = P(A) + P(B)

This is because when events A and B are mutually exclusive, they cannot occur together.

Thus, the probability of either event A or event B happening is simply the sum of their individual probabilities.

It is important to note that this statement holds true only for mutually exclusive events.

If events A and B are dependent or not mutually exclusive, we need to consider other factors such as their joint probability and the probability of their intersection.

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The solution to the question is:

c is 6 = \(\sqrt{a^{2} + b^{2} -2abcosC }\)

b is 5 = \(\sqrt{a^{2} + c^{2} -2accosB }\)

cosB is 2 = \(\frac{a^{2} + c^{2} - b^{2} }{2ac}\)

a is 4 = \(\sqrt{b^{2} + c^{2} -2bccosA }\)

cosA is 3 = \(\frac{b^{2} + c^{2} -a^{2} }{2bc}\)

cosC is 1 = \(\frac{b^{2} + a^{2} - c^{2} }{2ab}\)

it is used to relate the three sides of a triangle with the angle facing one of its sides.

The square of the side facing the included angle is equal to the some of the squares of the other sides and the product of twice the other two sides and the cosine of the included angle.

Analysis:

If c is the side facing the included angle C, then

\(c^{2}\) = \(a^{2}\) + \(b^{2}\) -2ab cos C-----------------1

then c =  \(\sqrt{a^{2} + b^{2} -2abcosC }\)

if b is the side facing the included angle B, then

\(b^{2}\) = \(a^{2}\) + \(c^{2}\) -2accosB-----------------2

b =  \(\sqrt{a^{2} + c^{2} -2accosB }\)

from equation 2, make cosB the subject of equation

2ac cosB =  \(a^{2}\) +  \(c^{2}\) - \(b^{2}\)

cosB =  \(\frac{a^{2} + c^{2} - b^{2} }{2ac}\)

if a is the side facing the included angle A, then

\(a^{2}\) = \(b^{2}\) + \(c^{2}\) -2bccosA--------------------3

a =  \(\sqrt{b^{2} + c^{2} -2bccosA }\)

from equation 3, making cosA subject of the equation

2bcosA =  \(b^{2}\) +  \(c^{2}\)  - \(a^{2}\)

cosA =  \(\frac{b^{2} + c^{2} -a^{2} }{2bc}\)

from equation 1, making cos C the subject

2abcosC =  \(b^{2}\) + \(a^{2}\) -  \(c^{2}\)

cos C =  \(\frac{b^{2} + a^{2} - c^{2} }{2ab}\)

In conclusion,

c is 6 = \(\sqrt{a^{2} + b^{2} -2abcosC }\)

b is 5 = \(\sqrt{a^{2} + c^{2} -2accosB }\)

cosB is 2 = \(\frac{a^{2} + c^{2} - b^{2} }{2ac}\)

a is 4 = \(\sqrt{b^{2} + c^{2} -2bccosA }\)

cosA is 3 = \(\frac{b^{2} + c^{2} -a^{2} }{2bc}\)

cosC is 1 = \(\frac{b^{2} + a^{2} - c^{2} }{2ab}\)

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The probability that the alleged father was not the father is: 0.024, or 2.4% and The probability that the alleged father could be the father is: 0.953, or 95.3%.

To calculate the probability that the alleged father was not the father, we first need to calculate the z-score for a pregnancy length of 240 days and for a pregnancy length of 306 days. The z-score formula is:

where x is the pregnancy length, mu is the mean pregnancy length, and sigma is the standard deviation of pregnancy length.

For a pregnancy length of 240 days, the z-score is:

For a pregnancy length of 306 days, the z-score is:

To calculate the probability that the alleged father was not the father, we need to find the area under the normal distribution curve to the left of the z-score for a pregnancy length of 240 days and to the right of the z-score for a pregnancy length of 306 days, and then add these probabilities together. Using a standard normal distribution table or calculator, we find that the probability to the left of z = -3.08 is approximately 0.001, and the probability to the right of z = 2.00 is approximately 0.023. Therefore, the probability that the alleged father was not the father is:

To calculate the probability that the alleged father could be the father, we need to find the area under the normal distribution curve between the z-scores for a pregnancy length of 240 days and a pregnancy length of 306 days. Using a standard normal distribution table or calculator, we find that the probability between z = -3.08 and z = 2.00 is approximately 0.953. Therefore, the probability that the alleged father could be the father is:

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Answer:

Move 4 to the left side of the equation so the equation is equal to 0

The missing coordinates of the three vectors form which makes them an orthonormal basis for R³ are as follow,

v₁ = [-0.8, -0.6, 0]

v₂ = [-0.6, -1, 0.45]

v₃ =[-0.27, -0.36, -0.8].

To form an orthonormal basis for R³, the three vectors must be orthogonal  that is perpendicular to each other.

And have unit length norm equal to 1.

Two of the vectors, find the missing coordinates to satisfy these conditions.

Let us consider the two given vectors,

v₁ = [-0.8, -0.6, 0]

v₂ = [?, -1, ?]

To find the missing coordinates of v₂,

Find a vector that is orthogonal to v₁.

One way to do this is by taking the cross product of v₁ and v₂, which will give us a vector orthogonal to both.

Cross product formula: v₁ × v₂ = [a₁b₂ - a₂b₁, a₂b₀ - a₀b₂, a₀b₁ - a₁b₀]

Using the cross product formula, find the missing coordinates of v₂,

v₂ = [?, -1, ?] = v₁ × [?, -1, ?]

Let us calculate the cross product,

v₂

= [?, -1, ?]

= [-0.8 × ?, -0.6 × (-1) - 0 × ?, 0 × ? - (-0.6 × ?)]

To satisfy the orthogonality condition, the dot product of v₁ and v₂ must be zero,

v₁ · v₂ = -0.8 × ? + (-0.6) × (-1) + 0 × ?

⇒ -0.8 × ? + (-0.6) × (-1) + 0 × ? = 0

Simplifying the equation,

⇒-0.8 × ? + 0.6 + 0 = 0

⇒ -0.8 × ? = -0.6

Dividing both sides by -0.8,

⇒ ? = -0.6 / -0.8

⇒ ? = 0.75

Now substitute this value back into the cross product equation to find the missing coordinates of v₂,

v₂ = [-0.8 × 0.75, -1, 0.6 × 0.75]

   = [-0.6, -1, 0.45]

The missing coordinates for the vector v₂ are [-0.6, -1, 0.45].

To find the missing coordinates for the third vector,

Use the same process.

Let us consider the two given vectors,

v₁ = [-0.8, -0.6, 0]

v₂ = [-0.6, -1, 0.45]

v₃ = [?, ?, ?]

Again, find a vector that is orthogonal to both v₁ and v₂.

Use the cross product to determine the missing coordinates,

v₃ = [?, ?, ?]

   = v₁ × v₂

Calculating the cross product,

⇒ v₃  = [?, ?, ?]

        = [-0.6 × 0.45 - 0 × (-1), 0 × (-0.6) - (-0.8 × 0.45), (-0.8) × (-1) - (-0.6) × 0]

Simplifying the equation,

⇒v₃ = [?, ?, ?]

      = [-0.27, -0.36, -0.8]

The missing coordinates for the vector v₃ are [-0.27, -0.36, -0.8].

Therefore, the missing coordinates that would make the three vectors form an orthonormal basis for R³ are,

v₁ = [-0.8, -0.6, 0]

v₂ = [-0.6, -1, 0.45]

v₃ =[-0.27, -0.36, -0.8].

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The Maclaurin series for cos(x) is given by:

cos(x) = Σ (-1)^n * (x^(2n)) / (2n)!, for n = 0 to ∞

Now, we need to find the Maclaurin series for f(x) = 12x * cos(12x). We can substitute x with 12x in the Maclaurin series for cos(x):

cos(12x) = Σ (-1)^n * (12x)^(2n) / (2n)!, for n = 0 to ∞

Now, multiply the series by 12x:

f(x) = 12x * cos(12x) = 12x * Σ (-1)^n * (12x)^(2n) / (2n)!, for n = 0 to ∞

Simplify the expression:

f(x) = Σ (-1)^n * 12^(2n + 1) * x^(2n + 1) / (2n)!, for n = 0 to ∞

This is the Maclaurin series for the given function f(x) = 12x * cos(12x).

You should be concise and not provide extraneous amounts of detail. You should not ignore any typos or irrelevant parts of the question. Here is the solution to the given problem.Student question: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = 12X COS 12x cos(12)Step 1:We are required to find the Maclaurin series for a function involving cos(x). Let's recall the Maclaurin series for cos(x).cos(x) = Σ(-1)^(n)/(2n)!  (n=0)The same equality would be true for any variable, and in particular for u = x^2.x^2/2! = 1/2!x^4/4! = 1/4! x^6/6! = 1/6!Therefore, the Maclaurin series for cos(x^2) isx^4nΣ(-1)^(n)/n!(2n)!  (n=0)Step 2:Now we can use this to find the Maclaurin series of the given function, treating the term 12x as a constant and using the rule can=canf(x) = 12x cos(12x cos(1+2)) = 12x cos((12x)cos(1+2))= 12xΣ(-1)^(n)/(2n)! [12x cos(1+2)]^(2n) =Σ(-1)^(n)/(2n)!  (24nx)^(2n) =Σ(-1)^(n)/(2n)!  24^(2n) x^(4n+1) (n=0)Therefore, the required Maclaurin series of the given function is Σ(-1)^(n)/(2n)!  24^(2n) x^(4n+1) (n=0).

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Answer:

In a bubble sort, on each pass through the list that must be sorted, the largest value "bubbles" to the end of the list. Therefore, after each pass, the end of the list is guaranteed to be sorted. This means that we can stop making pair comparisons one comparison sooner, which is option B.

Step-by-step explanation:

Bubble sort works by repeatedly comparing and swapping adjacent elements in the list if they are in the wrong order. During each pass through the list, the largest unsorted element "bubbles up" to its correct position. As a result, after the first pass, the largest element is in its correct position, after the second pass, the two largest elements are in their correct positions, and so on.

Therefore, with each subsequent pass, you can stop making pair comparisons one comparison sooner because the elements at the end of the list are already sorted.

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Answer:

She must have to reach $7000 sales to get to her goal.

Step-by-step explanation:

Consider the provided information.

Let her weekly sales is represented by \(x\).

Each week she earns $250 plus a commission equal to 3% of her sales. so this can be written as:

\(250+\frac{3}{100}x\)

Her goal is to earn at least $460. It means she needs to earn more than or equal to $460.

\(250+\frac{3}{100}x\geq 460\)

Now simplify it.

\(0.03x\geq 460-250\)

\(0.03x\geq 210\)

\(x\geq 7000\)

She must have to reach $7000 sales to get to her goal.

Answer:

She must have to reach $7000 sales to get to her goal.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

First, the numbers should be in ascending or descending order . Since, 4 numbers are in ascending order we don't have to do that .

Second, find the "middlest" of them . If there were total of odd numbers it would have been easier but, here is total of even number(4) and mean of 2 middlest number would be its median: (4+4)/2=4 .

Answer: 6

Step-by-step explanation:

Answer: $8

From the table given, we obtained the below information

Number of cars Money ($)

5 40

10 80

15 120

20 160

Calculate the constant rate of change in dollars per car

For the first given data

The total number of cars washed is 5

The total money to washed the 5 cars is $40

Rate of change in dollars per car = Total amount of money / the total number of cars

Rate of change = 40 / 5

= $8

The same procedure applicable to the rest data

For 10 cars and $80

The rate of change in dollars per car =80/10

= $8

For 15 cars and $120

The rate of change in dollars = 120 / 15

= $8

For 20 cars and $160

The rate of change in dollars per car = 160 / 20

= $8

The constant rate of change in dollars per car is $8

The answer is $8

At the end of the year, Achley Company's owner's equity is $4,685,000 and can be calculated by starting with the beginning owner's equity, adding the revenues, subtracting the expenses, and subtracting the owner's withdrawals.

To calculate Achley Company's owner's equity at the end of the year, we start with the beginning owner's equity of $5,175,000. We then add the revenues of $225,000 and subtract the expenses of $165,000. This gives us the net income, which is the difference between revenues and expenses, and represents the increase in owner's equity.

So, net income = revenues - expenses = $225,000 - $165,000 = $60,000. Next, we subtract the owner's withdrawals of $550,000 from the net income. Owner's withdrawals are personal expenses or cash withdrawals made by the owner and reduce the owner's equity.

Owner's equity at the end of the year = Beginning owner's equity + Net income - Owner's withdrawals.Owner's equity at the end of the year = $5,175,000 + $60,000 - $550,000. Calculating the above expression, we find that Achley Company's owner's equity at the end of the year is $4,685,000.

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Answer:

divied by 100 and remove the "%" sign.

Step-by-step explanation:

1.)example 10% becomes 10/100=0.10

2.) example 67.5% becomes 67.5/100=0.675

Answer:

After investing for 10 years at 5% interest, your $2,000 investment will have grown to $3,258

Step-by-step explanation:

Your welcome

Answer:

The answer is Option A

Step-by-step explanation:

Start by dividing 54 by 6 which will give you 9

then divide b² by b^5 which will give you b³ at the denominator

then a^8÷a^-4

using indices...

=a^8-(-4)

=a^12

at the numerator

put everything together and you'll have...

9a^12/b³

A. \( \frac{9 \: {a}^{12} }{ {b}^{3} }\) ✅

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\(54 {a}^{8} {b}^{2} \div 6 {a}^{ - 4} {b}^{5} \)

To solve the expression in a simpler way, single out the like terms.

Now, we have

\( \frac{54}{6} . \frac{ {a}^{8} }{ {a}^{ - 4} } . \frac{ {b}^{2} }{ {b}^{5} } \\ \\ = 9 \: {a}^{8 - ( - 4)} {b}^{2 - 5} \\ \\ (∵ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} ) \\ \\ = 9 \: {a}^{8 + 4} {b}^{ - 3} \\ \\ = 9 \: {a}^{12} {b}^{ - 3} \\ \\ ( \: or \: ) \\ \\ = \frac{9 \: {a}^{12} }{ {b}^{3} } \\ \\ (∵ {a}^{ - m} = \frac{1}{ {a}^{m} } )\)

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}\)

Answer:

sorry this is wrong subject

Answer:

\(x^3 - 4x^2\) = Cubic degree, binomial term

\(3x^3 + 2x^2 -1\) = Cubic degree, trinomial term

2x + 5 = linear degree, binomial term

Step-by-step explanation:

\(x^3 - 4x^2\)  has a cubic degree because the term with the highest exponent is raised to the third power \((x^3)\).  It also has a binomial term because there are two terms in it,

\(3x^3 + 2x^2 -1\)  is also a  cubic degree because the term with the highest exponent is raised to the third power \((3x^3)\). It is also a trinomial term because there are three terms in it: \(3x^3 , 2x^2, and -1\).

2x + 5 is a linear degree because the terms are implicitly assumed to have an exponent of 1: \(2x^1 = 2x\), and \(5^1 = 5\). This is also a binomial term because it has two terms, 2x and 5.

Answer:

they are 4 i think

Step-by-step explanation:

5 x 4 = 20

Answer:

100

Step-by-step explanation:

20 divided by 1/5 = 20 x 5/1 = 100

Answer: x

≥

3

−

3

y

Step-by-step explanation:

The percentage of tires that will have a life of 45,000 to 55,000 miles is  68.27%. So the correct option is 68.27%.

To find the percentage of tires that will have a life of 45,000 to 55,000 miles, we can use the concept of the normal distribution.

First, we calculate the z-scores for both values using the formula:
z = (x - mean) / standard deviation

For 45,000 miles:
z1 = (45,000 - 50,000) / 5,000 = -1

For 55,000 miles:
z2 = (55,000 - 50,000) / 5,000 = 1

Next, we look up the corresponding values in the standard normal distribution table. The table will provide the proportion of data within a certain range of z-scores.

The percentage of tires with a life between 45,000 and 55,000 miles is the difference between the cumulative probabilities for z2 and z1.

Looking at the standard normal distribution table, the cumulative probability for z = -1 is 0.1587, and the cumulative probability for z = 1 is 0.8413.

Therefore, the percentage of tires that will have a life of 45,000 to 55,000 miles is:
0.8413 - 0.1587 = 0.6826

Converting this to a percentage, we get:
0.6826 * 100 = 68.26%

So the correct answer is 68.27%.

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Answer:

O It has the same slope and a different y-intercept.

Step-by-step explanation:

y = mx + b

m = 3/8

b = 12

y = (3/8)x + 12

---

Data in the table:  slope is the rise (y) over the run (x) between two points (assuming the data represent a linear line).

 Change in x and y between two points.  I'll choose (-2/3,-3/4) and (1/3,-3/8).

Change in y:  (-3/8 - (-3/4)) = (-3/8 - (-6/8))  =  3/8

Change in x:  (1/3 - (-2/3)) = (1/3+2/3) = 3/3 = 1

Slope = (Change in y)/(Change in x) = (3/8)/1 = 3/8

The slope of the equation is the same as the data in the table.

Now let's determine if the y-intercept is also the same (12).  The equation for the data table is y = (2/3)x + b, and we want to find b.  Enter any of the data points for x and y and then solve for b.  I'll use (-2/3, -3/4)

y = (3/8)x + b

Use (-2/3, -3/4)

-3/4 =- (3/8)(-2/3) + b

-3/4 = (-6/24) + b

b = -(3/4) + (6/24)

b = -(9/12) + (3/12)

b = -(6/12)

b = -(1/2)

The equation of the line formed by the data table is y = (3/8)x -(1/2)

Therefore, It has the same slope and a different y-intercept.

Answer:

\(y=5\)

Step-by-step explanation:

\(\textsf{If }y \textsf{ is \underline{inversely proportional} to the square root of }x, \textsf{ then}:\)

\(y \propto\dfrac{1}{\sqrt{x}} \implies y=\dfrac{k}{\sqrt{x}}\quad \textsf{(where k is some constant)}\)

\(\textsf{When }x=25, y = 3:\)

\(\implies 3=\dfrac{k}{\sqrt{25}}\)

\(\implies 3=\dfrac{k}{5}\)

\(\implies k=15\)

Inputting the found value of k into the equation:

\(\implies y=\dfrac{15}{\sqrt{x}}\)

To find the value of y when x is 9, substitute x = 9 into the found equation:

\(\implies y=\dfrac{15}{\sqrt{9}}\)

\(\implies y=\dfrac{15}{3}\)

\(\implies y=5\)

Answer:

See explanation below

Step-by-step explanation:

Volume = (11)(10)(7) = 770 cubic centimeters

Surface area = (2)(10)(7) + (2)(11)(7) + (2)(11)(10) = 1774 square centimeters

b) Surface area (How much wax can cover the cube)

c) Volume (How much juice will be inside the cube)

Answer:

x ≥ -6

Step-by-step explanation:

Answer: x ≥-6

explanation: im pretty good at math