The sequence 12, 15, 18, 21, 51, 81, ... consists of all positive multiples of 3 that contain at least one digit that is a 1. what is the 50th term of the sequence? (2006 national target #5)

A binomial is a factor of a polynomial has been determined by using the

polynomial division method.

To determine if a binomial is a factor of a polynomial, you can use the polynomial division method. The basic idea is to divide the polynomial by the binomial and check if the remainder is zero. If the remainder is zero, then the binomial is a factor of the polynomial. Here's the step-by-step process:

Write the polynomial and the binomial in standard form, with the terms arranged in descending order of their exponents.

Perform the long division of the polynomial by the binomial, similar to how you would divide numbers. Start by dividing the highest degree term of the polynomial by the highest degree term of the binomial.

Multiply the binomial by the quotient obtained from the division and subtract the result from the polynomial.

Repeat the division process with the new polynomial obtained from the subtraction step.

Continue dividing until you reach a point where the degree of the polynomial is lower than the degree of the binomial.

If the remainder is zero, then the binomial is a factor of the polynomial. If the remainder is non-zero, then the binomial is not a factor.

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Answer- 9 shelves

In order to find out how many shelves are need we must divided 175 into 20. 175 divided by 20 is 8.75. But, because you cannot have have .75 of a shelf, you have to round this to a whole. This means that 9 shelves will be the least needed number of shelves need to store 175 books. To check this answer 20 books X 8 shelves is 160 books, which means eight shelves can only store 160 books, we will need and additional shelf to store the last 15 books.

HOPE THIS HELPS & GOOD LUCK!

Answer:

This is your answer ☺️☺️☺️

Organizational culture is defined as the common beliefs, values, attitudes, customs, behaviors, and traditions that characterize a specific organization and determine the manner in which it functions. Organizational culture is set by the manager.

In a corporate or business environment, organizational culture can influence the daily operations of employees. It is the responsibility of managers to create a positive culture that emphasizes teamwork, respect, integrity, and accountability. The manager is an essential individual responsible for establishing and maintaining the organization's culture, which will ultimately define the employee's attitudes, behaviors, and productivity levels. He or she sets the tone for the workplace by creating an environment that fosters collaboration, innovation, and success. Employees need to feel connected to their workplace and colleagues to be motivated to do their best work. If a manager promotes a culture of fear, competition, or dishonesty, employees may become unmotivated or unproductive. An effective manager understands the importance of creating a positive workplace culture and works hard to establish and maintain it. Managers can establish a positive culture by encouraging open communication, providing regular feedback and recognition, fostering a sense of teamwork, creating opportunities for professional development, and setting high standards for performance. Managers must lead by example and demonstrate the behaviors and attitudes that they expect from their employees. They must hold themselves and others accountable for their actions, communicate expectations clearly, and provide support when needed. A positive organizational culture will enable an organization to attract and retain top talent, increase employee engagement, and promote collaboration and innovation.

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Answer:

12 minutes I think question kinda confusing

Answer:

the answer is 12pie

Step-by-step explanation:

6mm is radius

circumference is ×2

so its 12

Answer:

$30.47

Step-by-step explanation:

100%-15%=85%
85%=0.85
$35.85*0.85=30.47 (to 2d.p)
Hope this helps

Answer:

(2 , -3)

Step-by-step explanation:

7x +2y = 8

-5x - 2  = -12

The only method that uses addition/subtraction is elimination

5(7x + 2y = 8)

7(-5x = 10) I am getting x coefficient to be the same, LCF of 7 and 5 is 35)

(multiply it out and now we can get ready to subtract) *I got 10 by adding 2 to -12*

35x + 10y = 40

-35x = 70

10y = -30

y = -3

substitute y into original equation

7x + 2 (-3) = 8

7x - 6 = 8

7x = 14

x = 2

(2 , -3 )

Answer:

Step-by-step explanation:

Add 5x to both sides to isolate -2:

-5x + 5x - 2 = -12 + 5x

-2 = -12 + 5x

Add 12 to both sides to isolate the 5x:

-2 + 12 = -12 + 12 + 5x

10 = 5x

Divide both sides by 5:

\(\frac{5x}{5} = 10 \div 5\\\)

x = 2

Substitute this value into the first equation:

7x + 2y = 8

7(2) + 2y = 8

14 + 2y = 8

Subtract 14 from both sides:

14 - 14 + 2y = 8 - 14

2y = -6

Divide both sides by 2:

2y ÷ 2 = -6 ÷ 2

y = -3

So the coordinate set is:

(2, -3)

Hope this helps!

Answer:

10/33

Step-by-step explanation:

2 red discs + 5 pink discs + 4 purple discs = 11 discs

The chance of pulling a pink disc is 5/11

On a 6 sided dice, there are 6 numbers, 4 are greatee than 2. So the chance of rolling a number greater than 2 is 4/6.

5/11 × 4/6 = 20/66 = 10/33

Answer:

50%

Step-by-step explanation:

(V2−V1)|V1|×100

=(7.5−5)|5|×100

=2.55×100

=0.5×100

=50%change

=50%increase

Answer:

Your answer is c = 70°.

Step-by-step explanation:

First, you have to solve for the angle a and b in order to then solve for c.

b is vertical angles with 60° so thus making them congruent :

b = 60° .

For a, a is supplement angle with 130° meaning these two angles add up to 180° : a + 130° = 180° =>

a = 50°

Now solve for c, the triangle adds up to 180°.

a + b + c = 180°

50° + 60° + c = 180°

110° + c = 180°

c = 70°

This problem is related to the concept of continuous compounding, which is a method of calculating the interest earned on an account over a certain period of time. The formula for calculating the principal amount for a continuously compounded account earning 3.9% for 15 years is as follows:

P = A/ (1 + r)^t

Where P is the principal, A is the balance after 15 years, r is the rate of interest and t is the number of years.

In this problem, P = $4,768,549.11, A = $2,656,586.66, r = 3.9% and t = 15.

Therefore, the principal for the continuously compounded account earning 3.9% for 15 years is $4,768,549.11

Answer:

2 blueberry and 5 raspberry scones go in each bag

Step-by-step explanation:

34+85=119

119/17=7

34/85= 2/5

so 2 blueberry and 5 raspberry scones go in each bag

hope that helps :)

Answer:

2 Blueberry scones and 5 Raspberry scones

Step-by-step explanation:

Given:

34 Blueberry scones

85 raspberry scones

17 Bags to fit scones

34 Blueberry so 34 divided by the Bag 17 (34 ÷ 17 = 2)

85 Raspberry scones so 85 divided by the Bag 17 ( 84 ÷ 17 = 5)

Therefore Jason can put 2 Blueberry scones and 5 Raspberry scones in each Bag

Answer:

17 boxes

Step-by-step explanation:

Let x be the number of boxes that you can buy.

14x = 150

x = 250 / 14 = 17.85

We cannot buy 0.85 of a box, so we can only buy 17 boxes.

Therefore , the solution of the given problem of percentage comes out to be invested now is $9,017.67. The response is (B).

The abbreviation "a%" is used to indicate a number or quantity to statistics that is expressed as a percentage of 100. Versions containing the characters "pct," "pct," and "pc" are also rare. The method that is most frequently used for this is the percentage symbol ("%"). Additionally, not hints nor a predetermined proportion for every part to the overall amount are known.

Here,

To calculate the present worth, we can use the compound interest formula:

=> P = A / (1 + r/n)^(n*t)

where P is the value in the present, A is the value in the future, r is the interest rate per year, n is the number of times the interest is multiplied annually, and t is the amount of time in years.

A = $12,868.21, r = 6.1%, n = 1 (compound annually), and t = 7 years in this instance. When these numbers are added to the formula, we obtain:

=>  P = 12,868.21 / (1 + 0.061/1)⁷

=>  P = 12,868.21 / (1.061)⁷

=>  P = $9,017.67

In order to amass $12,868.21 at a compound annual interest rate of 6.1% over a period of seven years,

the present value that should be invested now is $9,017.67. The response is (B).

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90 students are taking both Math 245 and CS 108.

We can use the formula:

n(A or B) = n(A) + n(B) - n(A and B)

where n(A) is the number of students taking Math 245, n(B) is the number of students taking CS 108, and n(A and B) is the number of students taking both courses.

Plugging in the given values, we get:

n(A or B) = 150 + 200 - n(A and B)

n(A or B) = 350 - n(A and B)

We also know that the total number of students taking at least one of the courses is 260:

n(A or B) = 260

Substituting this value, we get:

260 = 350 - n(A and B)

n(A and B) = 90

Therefore, 90 students are taking both Math 245 and CS 108.

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The formula to find the volume of a triangular prism is V = (1/2) x b x h x l, where b is the base of the triangle, h is the height of the triangle, and l is the length of the prism. In this case, the base of the triangle is 10 cm and the height is 8 cm. The length of the prism is 34 cm. So, the volume can be calculated as V = (1/2) x 10 cm x 8 cm x 34 cm = 1360 cubic cm.

The formula to calculate the volume of a triangular prism is used to find the three-dimensional space occupied by the prism. It is calculated by multiplying the area of the base of the triangle by its height and then by the length of the prism. Here, the base of the triangle is 10 cm, and its height is 8 cm. The length of the prism is 34 cm. By substituting these values in the formula, we get the volume of the prism.

The volume of the triangular prism is 1360 cubic centimeters. This calculation is important in real-world applications such as construction, architecture, and engineering, where the volume of different shapes is required for material calculations.

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Answer:

290 in^2

Step-by-step explanation:

front side x 2 = 176

top + bottom = 48

sides x 2 = 66

Sum = 290

Answer:

Total surface area S_tot = 290 in²  thus c. is your answer

Step-by-step explanation:

length l = 8 in

width w = 3 in

height h = 11 in

diagonal d = 13.9283883 in

total surface area S_tot = 290 in²

lateral surface area S_lat = 242 in²

top surface area S_top = 24 in²

bottom surface area S_bot = 24 in²

volume V = 264 in³

Formula and Agenda:

Formulas for a rectangular prism:

Volume of Rectangular Prism:

V = lwh

Surface Area of Rectangular Prism:

S = 2(lw + lh + wh)

l = length

w = width

h = height

d = diagonal

S_tot = total surface area

S_lat = lateral surface area

S_top = top surface area

S_bot = bottom surface area

V = volume

1 pound is equivalent to 16oz

Answer:

i cant see the question :(

Step-by-step explanation:

The polar form of the equation x = 4 is r = 4 / cos(θ).

To convert the equation x = 4 to polar form:

To convert the equation x = 4 to polar form using variables r and θ (theta),

Follow these steps:

Step 1: Recall the polar to rectangular coordinate conversion formulas:
x = r * cos(θ)
y = r * sin(θ)

Step 2: Replace x in the given equation with the corresponding polar conversion formula:
r * cos(θ) = 4

Step 3: Solve for r:
r = 4 / cos(θ)

So, the polar form of the equation x = 4 is r = 4 / cos(θ).

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The solution for question a is -2.00. The solution for question b is  0.6687. The solution for question c is 10 students. We can show the working in the following manner.

a. What is the probability of completing the exam in one hour or less (to 4 decimals)?

To answer this question, we need to convert the time of one hour (60 minutes) to a z-score using the mean and standard deviation provided. We have:

z = (60 - 80) / 10 = -2.00

Using a standard normal distribution table or calculator, we can find that the probability of completing the exam in one hour or less is approximately 0.0228, rounded to 4 decimal places.

b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)?

To answer this question, we need to find the probability of completing the exam in less than 75 minutes and subtract the probability of completing the exam in less than 60 minutes. We have:

z1 = (60 - 80) / 10 = -2.00

z2 = (75 - 80) / 10 = -0.50

Using a standard normal distribution table or calculator, we can find that the probability of completing the exam in less than 75 minutes is approximately 0.6915 and the probability of completing the exam in less than 60 minutes is approximately 0.0228, as calculated in part a.

So, the probability of completing the exam in more than 60 minutes but less than 75 minutes is approximately:

0.6915 - 0.0228 = 0.6687, rounded to 4 decimal places.

c. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to the next whole number)?

To answer this question, we need to find the number of students whose exam time is greater than 90 minutes, which is the maximum time allowed. We can use the normal distribution with the given mean and standard deviation to calculate this.

First, we need to find the z-score corresponding to a time of 90 minutes:

z = (90 - 80) / 10 = 1.00

Using a standard normal distribution table or calculator, we can find that the probability of completing the exam in more than 90 minutes is approximately 0.1587.

Therefore, the expected number of students who will be unable to complete the exam in the allotted time is:

60 x 0.1587 = 9.52, which rounds up to 10 students (to the next whole number).

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Answer:

no

Step-by-step explanation:

a^2 +b^2 = c^2

c^2 - a^2 = b^2

12^2 - 5^2 = b^2

144-25 = b^2

199 = b^2

sqrt(119) = b

10.9 = b

a = distance from the wall = 5

c = length of the ladder = 12

The confidence interval would help Lucy determine the probability that a parameter will fall between two values around the mean.

The question is incomplete, as the needed parameters to answer the question are missing.

So, I will list the normal conditions for constructing the confidence interval

The condition for constructing the confidence interval include:

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Answer:

G. 226 mm

Step-by-step explanation:

C=2(3.14)(36)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\( \cos( \frac{5\pi}{12} ) = \cos( \frac{6\pi}{12} - \frac{\pi}{12} ) = \\ \)

\( \cos( \frac{\pi}{2} - \frac{\pi}{12} ) = \sin( \frac{\pi}{12} ) \\ \)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Also we have :

\( \sin( \frac{5\pi}{12} ) = \cos( \frac{\pi}{12} ) \\ \)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

So :

\( \cos( \frac{\pi}{12} ). \sin( \frac{\pi}{12} ) + \sin( \frac{\pi}{12} ) . \cos( \frac{\pi}{12} ) = \\ \)

\(2 \sin( \frac{\pi}{12} ) . \cos( \frac{\pi}{12} ) \\ \)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Hint :

\( \sin(2 \alpha ) = 2 \sin( \alpha ) . \cos( \alpha ) \)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

So ;

\(2 \sin( \frac{\pi}{12} ) . \cos( \frac{\pi}{12} ) = \\ \)

\( \sin(2 \times \frac{\pi}{12} ) = \sin( \frac{\pi}{6} ) \\ \)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\( \sin( \frac{\pi}{6} ) = \cos( - \frac{\pi}{3} ) \\ \)

Thus the correct answer is the first option.

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Therefore, the equation x^3 - 15x + c = 0 has at most one root in the interval (-2, 2).

To show that the equation x^3 - 15x + c = 0 has at most one root in the interval (-2, 2), we can use the concept of the Intermediate Value Theorem and Rolle's Theorem.

Let's assume that the equation has two distinct roots, denoted as a and b, in the interval (-2, 2). Without loss of generality, we assume a < b.

Since the function is continuous on the closed interval [-2, 2] and differentiable on the open interval (-2, 2), we can apply Rolle's Theorem. According to Rolle's Theorem, there exists a point c in the open interval (a, b) such that the derivative of the function at c is zero.

Consider the derivative of the function f(x) = x^3 - 15x + c:

f'(x) = 3x^2 - 15

Setting f'(c) = 0, we have:

3c^2 - 15 = 0

c^2 - 5 = 0

c^2 = 5

Taking the square root of both sides, we get:

c = ±√5

Now, let's consider the function values at the endpoints of the interval (-2, 2):

f(-2) = (-2)^3 - 15(-2) + c = -8 + 30 + c = 22 + c

f(2) = (2)^3 - 15(2) + c = 8 - 30 + c = -22 + c

If c = √5, then f(-2) = 22 + √5 and f(2) = -22 + √5.

If c = -√5, then f(-2) = 22 - √5 and f(2) = -22 - √5.

In either case, the function values at the endpoints have different signs. This implies that there exists at least one value, say k, in the interval (-2, 2) such that f(k) = 0, according to the Intermediate Value Theorem.

However, we assumed at the beginning that there are two distinct roots in the interval (-2, 2), denoted as a and b. This contradicts our finding that there is at most one root in the interval. Hence, our assumption of having two distinct roots is false.

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Answer:

a. 0.6975

b. 0.25

c. The events are independent and inclusive

Step-by-step explanation:

a. The proportion of five-star football recruits in the nation that go to universities in the three most competitive athletic conferences = 75%

Therefore, the probability of a five-star football recruits chooses to go to a university in the three most competitive athletic conferences p(A) = 75% or 0.75

The proportion of the times five-star football recruits get full football scholarships = 93%

Therefore, the probability that a five-star football recruit get full football scholarships p(B) = 93% or 0.93

Therefore, the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship can be written as -the probability that a randomly selected five-star recruit who chooses one of the best three conferences and will be offered a full football scholarship is therefore;

p(A) ∩ p(B) = p(A) × p(B) = 0.75×0.93 = 0.6975

b. The probability that a randomly selected five star recruit will not select a university from one of the three best conferences = 1 - p(A) = 1 - 0.75 = 0.25

c. The events are independent as the given probability of occurrence of one event does not alter the probability of the other event

The events are inclusive events are exclusive events as P(A)and P(B) can take place simultaneously.

To determine the discontinuities of the function \(\(f(x) = \frac{10x+10}{x-5}\)\), we need to check for any values of \(\(x\)\) that make the function undefined.

Step 1 of 2: Finding the Discontinuous Points:

The function  will be undefined when the denominator \(\(x-5\)\) equals zero since division by zero is undefined. Therefore, we need to find the \(\(x\)\)-value(s) that make the denominator zero.

Setting \(\(x-5 = 0\)\) , we solve for \(\(x\):\)

\(\[x = 5\]\)

So, the function is discontinuous at \(\(x = 5\).\)

Step 2 of 2: Determining the Type of Discontinuity:

To determine the type of discontinuity at \(\(x = 5\)\), we need to examine the behavior of the function as \(\(x\)\) approaches 5 from both sides.

Let's evaluate the limits of the function as \(\(x\)\) approaches 5:

\(\[\lim_{x \to 5^-} \frac{10x+10}{x-5} \quad \text{and} \quad \lim_{x \to 5^+} \frac{10x+10}{x-5}\]\)

For the limit as \(\(x\)\) approaches 5 from the left \((\(x \to 5^-\))\), we substitute values slightly less than 5:

\(\[\lim_{x \to 5^-} \frac{10x+10}{x-5} = -\infty\]\)

For the limit as \(\(x\)\) approaches 5 from the right \((\(x \to 5^+\))\) , we substitute values slightly greater than 5:

\(\[\lim_{x \to 5^+} \frac{10x+10}{x-5} = \infty\]\)

Since the limits from both sides approach different values (negative infinity and positive infinity), the function has a jump discontinuity at \(\(x = 5\).\)

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