A letter is randomly selected from the word 'TABTOR'. What is the probability that the letter will be "T"?

A 5th degree polynomial have five complex roots. This means that the polynomial can be written as the product of five linear or quadratic polynomials.

The general formula to calculate the roots of a 5th degree polynomial is:

\(x^5 + ax^4 + bx^3 + cx^2 + dx + e = 0\)

The roots of the polynomial can be found by solving the following equation:

\(x^4 + (a - x)x^3 + (b - a x + x^2)x^2 + (c - bx + ax^2 - x^3)x + (d - cx + bx^2 - ax^3 + x^4) = 0\)

To calculate the roots of the polynomial, we need to solve the quartic equation, which can be done by using the quadratic formula. Then, we can use the solutions of the quartic equation to find the roots of the 5th degree polynomial.

For example, if we have the polynomial x^5 + 2x^4 + 3x^3 + 4x^2 + 5x + 6 = 0, then the roots can be calculated as follows:

x1 = -1.7177

x2 = -0.3181

x3 = 0.5813

x4 = 1.2520

x5 = 2.1771

These are the five complex roots of the polynomial.

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Answer:

w+d≥14

Step-by-step explanation:

Here is the full question

Morgan is working two summer jobs, washing cars and walking dogs. She must work no less than 14 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours walking dogs, d, that Morgan can work in a given week.

Morgan must not work less than 14 hours. This means that the least amount of hours she can work would be 14 hours. This would be represented by the greater to or equal to sign (≥)

So the time she would spend working = w+d≥14

2

Answer:

Morgan could work 6 hours lifeguarding and 3 hours walking dogs.

Step-by-step explanation:

the total number of hours worked in both jobs,

x+y

x+y, must be less than or equal to 11

solve inequalities for y

x+y≤11

y≤11−x

Morgan makes $19 per hour lifeguarding, so in x hours she will make

19x dollars. Morgan makes $6 per hour walking dogs, so in

y hours she will make 6y dollars. The total amount earned 19x+6y

19x+6y must be greater than or equal to

$120

solve inequalities for y

19x+6y≥120      

6y≥120−19x

y≥20-19/6x

Answer:

Step-by-step explanation:

It could be

ax(x - 4)(x - 3)(x + 3)     where a is some constant ( a could be 1 of course)

For a = 1 the polynomial is

x(x - 4)(x - 3)(x + 3)

In expanded form this is

x^4 - 4x^3 - 9x^2 + 36x

The correct option is: 1 = ∫∫∫r dz dr dθ

By converting the given expression into an equivalent triple integral in cylindrical coordinates, we obtain:

1 = ∫∫∫r dz dr dθ

This option represents the correct conversion of the integral into cylindrical coordinates. The integral is taken over the region defined by the limits of integration for z, r, and θ, which are not provided in the given question.

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Answer:

I dont know the answer, but I am going to give you a lot of luck, so good luck!

Step-by-step explanation:

Answer:

Step by Step Solution

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STEP

1

:

Equation at the end of step 1

STEP

2

:

           3s2 - 2s + 1

Simplify   ————————————

            s2 - s + 2

Trying to factor by splitting the middle term

2.1     Factoring  3s2 - 2s + 1

The first term is,  3s2  its coefficient is  3 .

The middle term is,  -2s  its coefficient is  -2 .

The last term, "the constant", is  +1

Step-1 : Multiply the coefficient of the first term by the constant   3 • 1 = 3

Step-2 : Find two factors of  3  whose sum equals the coefficient of the middle term, which is   -2 .

     -3    +    -1    =    -4

     -1    +    -3    =    -4

     1    +    3    =    4

     3    +    1    =    4

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

The gradient of the stream is 1 meter per kilometre, which means that the stream drops 1 meter for every kilometre travelled. This is a relatively gentle slope and suggests that the stream is not flowing rapidly or eroding its bed very quickly.

The gradient of a stream is a measure of its steepness and is calculated by dividing the change in elevation by the distance travelled. In this case, the stream drops 15 meters in 15 kilometres, which means that the gradient can be calculated as follows:
Gradient = Change in elevation ÷ Distance travelled
Gradient = 15 meters ÷ 15 kilometers
Since we need to express the gradient in terms of meters per kilometre, we can simplify the above equation as follows:
Gradient = (15 meters ÷ 15,000 meters) × 1,000
Gradient = 1 meter per kilometer
Therefore,  understanding the gradient of a stream is important for a range of activities, including flood control, erosion management, and habitat restoration. By monitoring changes in the gradient over time, scientists and engineers can gain insights into the health and behaviour of streams and develop strategies to protect them.

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Answer:

2

Answer:

D) 5

Step-by-step explanation:

cant be 150 or 60 since its bigger than 30 and anything times 11 won't get you 30

6, 12, 18, 24, 30

5, 10, 15, 20, 25, 30

The absolute value of the percent change in the volume of the cylinder is 20%.


When the radius of a right circular cylinder is decreased by 20%, its new radius becomes 0.8 times the original radius (1 - 0.20 = 0.8).

Likewise, when its height is increased by 25%, its new height becomes 1.25 times the original height (1 + 0.25 = 1.25).

The volume of a right circular cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. Let V₁ be the original volume, and V₂ be the new volume after the changes.

V₁ = π(r)²(h) and V₂ = π(0.8r)²(1.25h)

V₂ = π(0.64r²)(1.25h) = 0.8πr²h

Thus, the new volume is 0.8 times the original volume. This represents a 20% decrease in volume (1 - 0.8 = 0.20 or 20%). So, the absolute value of the percent change in the volume of the cylinder is 20%.

In summary, decreasing the radius by 20% and increasing the height by 25% results in a 20% decrease in the volume of the right circular cylinder.

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jAlright, let's take this problem step-by-step:

What is the perimeter:

 ⇒ all the side-lengths added up

    ⇒ need to find side-length using distance formula

                \(Distance_._. Formula=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

                         - (x₁,y₁): first point

                         - (x₂,y₂): second point

Let's solve:

           ⇒ first point: (5,7)

           ⇒ second point: (3,3)

           \(Distance =\sqrt{(3-5)^2+(3-7)^2} =\sqrt{4+16} =\sqrt{20} =4.472\)

          ⇒ first point: (5,7)

          ⇒ second point:(8,6)

           \(Distance=\sqrt{(8-5)^2+(6-7)^2} =\sqrt{9+1} =\sqrt{10}=3.162\)

          ⇒ first point: (8,6)

          ⇒ second point: (3,3)

           \(Distance = \sqrt{(3-8)^2+(3-6)^2} =\sqrt{25+9} =\sqrt{34}=5.831\)

Now let's solve for the perimeter:

  \(Perimeter = 4.472+ 3.126+ 5.831=13.429\)

Answer: 13.43 (rounded to the nearest hundredth)

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The equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six is 1.5 to the eighteenth power over 1.3 to the twenty-fourth power.

Here are the steps to simplify the expression:

Apply the negative power rule: (1.5 cubed over 1.3 raised to the fourth power) raised to the power of negative six is equal to (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six.

Apply the power of a quotient rule: (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six is equal to (1.3 raised to the fourth power)⁶ / (1.5 cubed)⁶.

Apply the power of a power rule: (1.3 raised to the fourth power)⁶ is equal to 1.3(⁴*⁶) = 1.3²⁴.

Apply the power of a power rule: (1.5 cubed)⁶ is equal to 1.5(³*⁶) = 1.5¹⁸.

Therefore, the equivalent expression is 1.5¹⁸ / 1.3²⁴.

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Step-by-step explanation: basically its 6 + 1 = 7x

6 - 14 = 8x  9 + 4 = 13x

Answer: x = 9

Explanation: In this problem, we're given a triangle and information

about each of its angles and we're asked to find the value of x.

The measures of the angle of a triangle always add to 180 degrees.

So we can setup the equation 6x + 1 + 9x + 4 + 6x - 14 = 180.

Simplifying on the left side, we have 21x - 9 = 180.

Adding 9 to both sides, we have 21x = 189.

Now divide both sides by 21 to get x = 9.

The length of the side x is derived to be √2/2 using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

The right triangle is also an Isosceles having same base angles so;

x² + x² = 1²

2x² = 1

x² = 1/2

x = √(1/2) {take square root of both sides}

x = 1/√2

x = √2/2 {rationalize}

Therefore, the length of the side x is derived to be √2/2 using the Pythagoras rule.

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To solve this problem, we will use the formula r(t) = (1 + i/m)^m - 1, where i is the nominal annual rate and m is the number of compounding periods per year.Using i(26) = 4.275%, we can solve for the equivalent nominal rate compounded monthly:r(12) = (1 + 0.04275/12)^12 - 1 = 0.04108 or 4.108%.

Therefore, the correct answer is option (a).

To solve the first problem, we used the formula r(t) = (1 + i/m)^m - 1, where i is the nominal annual rate and m is the number of compounding periods per year. In this case, we were given the nominal rate i(26) = 4.275%, which was compounded monthly. We used the formula to solve for the equivalent nominal rate compounded annually, r(12), which turned out to be 4.108%.This formula can be used to find the equivalent nominal rate compounded at any frequency, given the nominal rate compounded at a different frequency.

It is important to use the correct values for i and m, and to use the correct units (e.g. decimal or percentage) when plugging them into the formula.In the second problem, we are given the amount of money Dayo has ($14,766.80) and the face value of the T-bill she wants to buy ($15,000.00), as well as the annual simple discount rate (2.25%) and the daycount convention (ACT/360). We want to find the last day on which she can still buy the T-bill.This problem can be solved using the formula for the price of a T-bill:P = F - D * r * Fwhere P is the price, F is the face value, D is the discount rate (in decimal form), and r is the number of days until maturity divided by the number of days in a year under the daycount convention (ACT/360 in this case). We want to find the price that Dayo will pay, which is equal to the face value minus the discount:P = F - (D * r * F) = F * (1 - D * r).

We can use this formula to find the price that Dayo will pay, and then compare it to the amount of money she has to see if she can afford the T-bill. If the price is less than or equal to her available funds, she can buy the T-bill. If the price is greater than her available funds, she cannot buy the T-bill.We know that the face value of the T-bill is $15,000.00, and the annual simple Interest rate is 2.25%. To find the discount rate in decimal form, we divide by 100 and multiply by the number of days until maturity (which is 242 in this case) divided by the number of days in a year under the daycount convention (which is 360):D = (2.25/100) * (242/360) = 0.01525We can use this value to find the price that Dayo will pay:

P = F * (1 - D * r)where r is the number of days until maturity divided by the number of days in a year under the daycount convention (which is 242/360 in this case):r = 242/360 = 0.67222P = $15,000.00 * (1 - 0.01525 * 0.67222) = $14,856.78Therefore, the price that Dayo will pay is $14,856.78. Since this is less than the amount of money she has ($14,766.80), she can afford to buy the T-bill.The last day on which she can still buy the T-bill is the maturity date minus the number of days until maturity, which is December 24, 2014 minus 242 days (since the daycount convention is ACT/360):Last day = December 24, 2014 - 242 days = April 22, 2014Therefore, the correct answer is option (b).

To solve the problem, we used the formula for finding the equivalent nominal rate compounded at a different frequency, and we also used the formula for finding the price of a T-bill. We also needed to know how to convert an annual simple discount rate to a decimal rate under the ACT/360 daycount convention. Finally, we used the maturity date and the number of days until maturity to find the last day on which Dayo could still buy the T-bill.

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The underlined part of the sentence can best be described as an adjective phrase.

In formation of sentences in English language, the words that are used usually include the following parts of speech:

An Adjective is a word that describes or modifies a noun or a pronoun. While adjective phrase is the phrase that can be used to modify or describe a noun in a sentence.

From the sentence given, extremely excited is adverbial phrase used to modify the noun vacation.

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Answer:

5

Step-by-step explanation:

I=30

T=5

P=500

r=3

PLS BRAINLIEST

The expansion of (a+b)^15 is: a^15 + 15a^14b + 105a^13b^2 + 455a

To expand (a+b)^15 using the Binomial Theorem, we can use the formula:

(a + b)^n = C(n,0)a^nb^0 + C(n,1)*a^(n-1)*b^1 + C(n,2)*a^(n-2)*b^2 + ... + C(n,n-1)a^1b^(n-1) + C(n,n)a^0b^n

where C(n,k) represents the binomial coefficient "n choose k" which is equal to n!/(k!(n-k)!).

In this case, n = 15, so we have:

(a+b)^15 = C(15,0)a^15b^0 + C(15,1)a^14b^1 + C(15,2)a^13b^2 + ... + C(15,14)a^1b^14 + C(15,15)a^0b^15

We can evaluate each binomial coefficient using the formula above, or we can use Pascal's Triangle to obtain the coefficients:

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

1 10 45 120 210 252 210 120 45 10 1

1 11 55 165 330 462 462 330 165 55 11 1

1 12 66 220 495 792 924 792 495 220 66 12 1

1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1

1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1

1 15 105 455 1365 3003 5005 6435 6435 5005 3003 1365 455 105 15 1

Thus, we have:

(a+b)^15 = 1a^15b^0 + 15a^14b^1 + 105a^13b^2 + ... + 5005a^1b^14 + 32768a^0b^15

Simplifying, we get:

(a+b)^15 = a^15 + 15a^14b + 105a^13b^2 + 455a^12b^3 + 1365a^11b^4 + 3003a^10b^5 + 5005a^9b^6 + 6435a^8b^7 + 6435a^7b^8 + 5005a^6b^9 + 3003a^5b^10 + 1365a^4b^11 + 455a^3b^12 + 105a^2b^13 + 15ab^14 + b^15

Therefore, the expansion of (a+b)^15 is:

a^15 + 15a^14b + 105a^13b^2 + 455a

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Answer:

8

Step-by-step explanation:

the denominator of 5/8 is 8

the denominator of 3/4 is 4

4 can be multiplied by 2 to get 8. If we multiply the entire fraction by 2/2, the fraction changes into 6/8

Now 5/8 and 6/8 share the same denominator and it's the smallest denominator shared between the two.

The maximum shear stress for sigma is 9.375 ksi.

Given: σx = 14 ksi, σy = 10 ksi, and sigma x = 21 ksi, sigma y = 14 ksi, we need to determine the maximum shearing stress using the formula:

Maximum shear stress = (σx - σy) / 2 + [(σx - σy)^2 + 4τ^2]^1/2 / 2

(a) For σx = 14 ksi and σy = 10 ksi:

Substituting the given values, we get:

Maximum shear stress = (14 - 10) / 2 + [(14 - 10)^2 + 4τ^2]^1/2 / 2

= 2 + (16 + 4τ^2) ^1/2 / 2

Now, using the equation τ = σ / 2, we can rewrite the equation as:

σ = 2τ

Therefore, the equation becomes:

2 + (16 + 4σ^2 / 4) ^1/2 / 2

= 2 + (16 + σ^2)^1/2 / 2

Thus, the maximum shear stress for σx = 14 ksi and σy = 10 ksi is 6 ksi.

(b) For sigma x = 21 ksi and sigma y = 14 ksi:

Following the same process, we get:

Maximum shear stress = (21 - 14) / 2 + [(21 - 14)^2 + 4τ^2]^1/2 / 2

= 3.5 + (49 + 4τ^2) ^1/2 / 2

Now, using the equation τ = σ / 2, we get:

σ = 2τ

Therefore, the equation becomes:

3.5 + (49 + 4σ^2 / 4) ^1/2 / 2

= 3.5 + (49 + σ^2)^1/2 / 2

Thus, the maximum shear stress for sigma x = 21 ksi and sigma y = 14 ksi is 9.375 ksi.

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The length of each side of the octagon is 6 cm

It is a polygon with eight sides and eight angles. There are a total of 20 diagonals in it. All its interior angles sum up to 1080°.

Given that, a regular octagon has an area of 288 square centimeters and an apothem of 12 cm.

We need to find the side of the octagon,

We know that area of the octagon = 8/2 × side × apothem

Therefore,

288 = 8/2 × side × 12

side = 288 / 48

side = 6

Hence, the length of each side of the octagon is 6 cm

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Answer:

D

Step-by-step explanation:

.06 =6%

The expression p(1.06)^t represents D. the yearly growth rate of the population is 6%

The country's yearly average rate of change in population size over a certain time period. It expresses the proportion, growth in population size, and the total population for that year.

Given, The population of a city can be modeled by the expression

\(p(1.06)^t\) where t represents the number of years.

This describes the yearly growth rate of the population is 6%.

If in the previous year the population was 100 this year it'll be 106 and next year it'll be 106% of 106 which is 112.36.

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Answer:

$6.75

Step-by-step explanation:

You would have to find how much it would cost you to buy 1 can. So you do $9/4= $2.25

now multiply $2.25 and 3

which equals $6.75

6 dollars 75 cents

Hope this helps :)

Answer:

If it has exactly three sides, then it is not a rectangle.

Step-by-step explanation:

R ------> non T

is the same as

T ------> non R

If the three sides are equal then it will not be a rectangle will be the logically equivalent statement.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

Perimeter of rectangle = 2( length + width).

In a rectangle opposite sides are equal but if the three sides are equal then it will become a square rather than a rectangle.

So, If the three sides are equal then it will not be a rectangle and it will be equivalent to the given statement.

Hence "If the three sides are equal then it will not be a rectangle will be the logically equivalent statement".

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1 meter = 100cm

so:

The value of x in the equation 1/4(4 + x) = 4/3 is x = 4/3.

Multiply both sides of the equation by 4 to eliminate the fraction on the left-hand side:

1/4(4 + x) = 4/3

4 * 1/4(4 + x) = 4 * 4/3

Simplifying:

4 + x = 16/3

Subtract 4 from both sides of the equation:

4 + x - 4 = 16/3 - 4

Simplifying:

x = 16/3 - 12/3

x = 4/3

A fraction is a mathematical concept used to represent a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator (top number) over a denominator (bottom number), separated by a horizontal line. For example, the fraction 1/2 represents one out of two equal parts, or half of a whole. Similarly, the fraction 3/4 represents three out of four equal parts, or three-quarters of a whole.

Fractions are an essential part of mathematics and are used in a wide range of applications, including measurements, cooking, and financial calculations. They can be added, subtracted, multiplied, and divided just like whole numbers, but they require a bit more care in their manipulation due to their unique structure.

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Step-by-step explanation:

3000  ml   /   150 ml/hr =  20 hrs from 0800   would be 0400 the NEXT day.

Answer:

Step-by-step explanation:

1) G = 6x , for x:                G/6

2) U = 2x - 2 , for x:          (1/2)U + 1

3) Z = m - x , for x:              m - Z

4) G = ca , for a:                   G/c

5) U = x - k , for x:                  U + k

6) G = c + x , for x:                G - c

7) U = k/a , for a:                    k/U

8) g = xc , for x:                     g/c

9) 12 am = 4 , for a:                 a = 1/(3m)

10) -3 x + 2c = - 3 , for x:         x = 1 +(2/3)c

11) am = n + p , for a:              (n+p)/m

12) U = ak/b , for a:                      U(b/k)

13) a - c = d - r , for a:                      a = d - r + c

14) xm = np , for x:                np/m

we have

2(4z - 2) = 44

Solve for z

that means

isolate the variable z

step 1

apply distributive property left side

8z-4=44

step 2

Adds 4 both sides

8z-4+4=44+4

simplify

8z=48

step 3

Divide by 8 both sides

8z/8=48/8