Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.)
{1, 7, 13, 19, 25, . . . }

9514 1404 393

Answer:

Step-by-step explanation:

From the law of cosines, you can find the length of side b to be ...

  b = √(a² +c² -2ac·cos(B))

  b = √(184041 +128164 -307164cos(148.5°)) ≈ √574105.36

  b ≈ 757.7

__

From the law of sines, you can find the measure of angle C to be ...

  C = arcsin(c/b·sin(B))

  C ≈ arcsin(358/757.7·sin(148.5°)) ≈ arcsin(0.246872)

  C ≈ 14.3°

  A = 180° -148.5° -14.3°

  A = 17.2°

_____

Some graphing calculators have built-in triangle-solving functions. Apps are available for the purpose for phone or tablet. The screenshot shows a web site that does a nice job of solving the triangle.

Answer: The probability that both events A and B will occur is 5/18 or 0.28.

Step-by-step explanation:

To determine the probability that both events A and B will occur, we need to calculate the probabilities of each event separately and then multiply them together.

Event A: The probability of rolling a 5 or 6 on the first die is 2 out of 6 (since there are two favorable outcomes out of six possible outcomes on a fair six-sided die). Therefore, the probability of event A is 2/6 or 1/3.

Event B: The probability of not rolling a 1 on the second die is 5 out of 6 (since there are five favorable outcomes out of six possible outcomes). Therefore, the probability of event B is 5/6.

To find the probability that both events A and B occur, we multiply the probabilities:

Probability(A and B) = Probability(A) * Probability(B) = (1/3) * (5/6) = 5/18.

SOLUTION

Total no of ties = 45

Number of ties that he feels goes well with jacket = 34

Number of ties that he feels does not go well with jacket = 45 - 34 = 11

a) Probability that tie goes well with jacket =

\(\dfrac{\text{Number of ties that goes well with jacket}}{\text{Total number of ties}}\)

                                \(=\dfrac{34}{45}\)

b) Probability that a tie does not go well with jacket

\(\dfrac{\text{Number of ties that doe not goes well with jacket}}{\text{Total ties}}\)

                                \(=\dfrac{11}{45}\)

Actual time is much longer than the 50-year timeframe suggested by the speaker.

How to verify the statement?

This claim is based on the assumption that the rate of pollution reduction from each factory remains constant at 80%, and the number of factories increases by 3% per annum.

To verify this claim, we can use the following formula to calculate the expected total pollution after n years:

Total pollution after n years = \(Present \: pollution \: level x (1 + 0.03)^n \times (1 - 0.8)^n\)

Here, the first factor represents the increase in pollution due to the growth in the number of factories, and the second factor represents the reduction in pollution due to the 80% reduction in pollution from each factory.

We can set the expected total pollution after n years equal to the present pollution level and solve for n:

\(Present \: pollution \: level = Present \: pollution \: level \times (1 + 0.03)^n \times (1 - 0.8)^n\)

Simplifying this equation, we get:

\(1 = 1.03^n \times 0.2^n\)

Taking the logarithm of both sides of the equation, we get,

\(n \times log(1.03) + n \times log(0.2) = 0 \\ n \times (log(1.03) + log(0.2)) = 0 \\ n = \frac{0} { (log(1.03) + log(0.2))} \\ n = 271.56\)

Therefore, according to this calculation, it would take approximately 272 years for the total annual pollution to return to its present level if the number of factories in the country increases by 3% per annum, and they all immediately reduce the amount of pollution they produce by 80%. This is much longer than the 50-year timeframe suggested by the speaker.

It is important to note that this calculation assumes that the pollution reduction from each factory remains constant at 80% and does not take into account any other factors that may affect pollution levels, such as changes in technology or regulations. Therefore, this should be considered as a rough estimate and not as an exact prediction.

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Correct question is "A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. Verify the statement. (use logarithm)"

Answer: 0.082

Step-by-step explanation: Two Ways: Divide 82.000 by 1000 which equals to 0.082. OR Write 82 and then move the decimal 2 spots to the left, so that it turns into 0.082.

Answer:

x = -15 + y

Step-by-step explanation:

Let next days temperature be x and the temperature rise be y

=> x = -15 + y

The next day's temperature will be more since it "rose".

Answer:

\(\boxed{x=-15+y}\)

Step-by-step explanation:

Let the temperature on Feb 10, 1934 be x.

Let the temperature increase be y.

On Feb 9, the temperature was -15F.

On Feb 10, the temperature increased.

\(x=-15+y\)

Using the concept of the word problem and utilizing the provided conditions and values, The answer is 18, 20, and 22.

A word problem in mathematics is a problem or exercise that is expressed in a natural language, rather than in mathematical notation. These types of problems often present a real-world situation that involves mathematical concepts, such as numbers, operations, or measurements. They typically require the use of mathematical reasoning and problem-solving skills to understand the problem and find a solution. Examples of word problems include: "If a train travels 60 miles per hour and you want to know how far it will travel in 4 hours", "If a rectangle is 6 meters long and 4 meters wide, what is its area?", "If a bag contains 3 red balls and 4 blue balls, what is the probability of picking a blue ball?"

In a mathematical problem, the conditions refer to the specific information or constraints provided in the problem statement that must be taken into account in order to find a solution. These conditions can include information about the quantities involved in the problem, the operations that need to be performed, or the specific requirements that the solution must meet.

Let x be the smallest of the three consecutive even integers. Then the next two integers are x+2 and x+4. We know that:

x + (x+4) * 3 = 84

Expanding and solving for x:

x + 3x + 12 = 84

4x = 72

x = 18

So the three consecutive even integers are 18, 20, and 22.

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Answer:

  $142.32, profit on sale of the policy

Step-by-step explanation:

You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.

The insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...

  0.000456 × $280,000 = $127.68

The company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...

  $270 -127.68 = $142.32

The expected value of the policy to the company is $142.32.

This represents its profit from sale of the policy.

__

Additional comment

Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."

<95141404393>

Answer:

don't know

Step-by-step explanation:

umm

hindsight and then you can you please go see me a few minutes away for my birthday bye day and then go see my doctor tomorrow and get a call

Answer:

Multiply  

634  by  − 11.5 =− 7291

Step-by-step explanation:

that's the answer

Answer:

They lost 15 games

Step-by-step explanation:

Multiply the percent by the number of games they played to find your answer:

75 x %20

75 x 0.2 = 15

Answer:

15 is actual answer. I redid and saw my error sorry. Also I'm still not sure if my process was correct.

Step-by-step explanation:

20% of 75 is 15.

Answer:

24.3

Step-by-step explanation:

18/20 = x/20 (similar triangles)

Step-by-step explanation:

In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.

1. Begin with the equation 0.2 = 0.

2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.

  This simplifies to 0 = -0.2.

3. Observe that the right side of the equation, -0.2, is a negative number.

4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.

5. Rewrite the equation as 0 = +0.2.

6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.

7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.

8. Simplify the equation to 0 = +0.2.

9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.

10. As a result, the original equation 0.2 = 0 is invalid.

11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.

12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.

To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.

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\(-4.46(j + 19)= -8.92\)

Distribute:

\((-4.46)(j)+(-4.46)(19)=-8.92\)

\(-4.46j-84.74=-8.92\)

Add 84.74 to both sides:

\(-4.46j-84.74+84.74=-8.92+84.74\)

\(-4.46j=75.82\)

Divide both sides by -4.46:

\(\dfrac{-4.46j}{-4.46} =\dfrac{75.82}{-4.46}\)

\(=\fbox{j = -17}\)

The value of x in the given polygon is 31 degrees.

An exterior angle is an angle created by the expansion of the neighboring side and one of the sides of a closed shape construction, such as a polygon. Regardless of the number of sides in the polygons, the sum of the measures of the outside angles is equal to 360 degrees.

The sum of the exterior angle of any polygon is 360 degrees.

So,

360 = 57 + 41 + 82 +x + 62 + 87

360 = x + 329

x = 31

Hence, the value of x in the given polygon is 31.

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Answer:

A) PB M(b, m), we have;

b = 1

b = 2

b = 3

B) E(B) = 1.7

C) No they are not independent

Step-by-step explanation:

A) We are told that a shipment can be in 1 box for a small order, 2 boxes for a medium order, 3 boxes for a large order. Thus;

For PB M(b, m), we have;

b = 1

b = 2

b = 3

B) Factory Q is 60 miles from the company. Thus, under factory Q in the table, m = 60

Factory R is 180 miles from the company. Thus under factory R in the table, m = 180

Now;

P_B (b) for b = 1 which is small order is;

P_B (b) = 0.3 + 0.2 = 0.5

P_B (b) for b = 2 which is medium order is;

P_B (b) = 0.1 + 0.2 = 0.3

P_B (b) for b = 3 which is large order is;

P_B (b) = 0.1 + 0.1 = 0.2

Thus;

E(B) = Σb•P_B (b) = (1 × 0.5) + (2 × 0.3) + (3 × 0.2)

E(B) = 0.5 + 0.6 + 0.6

E(B) = 1.7

C) No, they are not independent. This is because from the table we are given, P_B,M at b = 1 and m = 60 is given as 0.3.

Whereas, for B and M to be independent, P_B,M at b = 1 and m = 60 has to be equal to (P_M(m) under m = 0.3) multiplied by P_B(b) for b = 1.

Instead what we have is P_M(m) under m = 0.3 as; 0.3 + 0.1 + 0.1 = 0.5. Which means (P_M(m) under m = 0.3) multiplied by P_B(b) for b = 1 gives;

0.5 × 0.5 = 0.25 which is not equal to P_B,M = 0.3 at b = 1 and m = 60

14. The trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. In the trigonometric equation 2(cos²θ - sin²θ) = 1, θ = 15°

A trigonometric equation is an equation that contains a trigonometric ration.

14. To find the value of (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°, we proceed as follows

Since we have the trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°,

We know that sin47° = sin(90 - 43°) = cos43°. So, substituting this into the equation, we have that

(sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = (cos43°/cos43°)² + (cos43°/cos43°)² - 4cos²45°

= 1² + 1² - 4cos²45°

We know that cos45° = 1/√2. So, we have

1² + 1² - 4cos²45° = 1² + 1² - 4(1/√2)²

= 1 + 1 + 4/2

= 2 + 2

= 4

So, (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. If 2(cos²θ - sin²θ) = 1 and θ is a positive acute angle, we need to find the value of θ. We proceed as follows

Since we have the trigonometric equation 2(cos²θ - sin²θ) = 1

We know that cos2θ = cos²θ - sin²θ. so, substituting this into the equation, we have that

2(cos²θ - sin²θ) = 1

2(cos2θ) = 1

cos2θ = 1/2

Taking inverse cosine, we have that

2θ = cos⁻¹(1/2)

2θ = 30°

θ = 30°/2

θ = 15°

So, θ = 15°

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Answer: Consider me the brainiest. The answer is... Decimal form =4.083

Exact form= 49/12

The mixed number form=4 1/12

How do we solve fractions step by step?

Conversion a mixed number 2  1/3 to a improper fraction: 2 1/3 = 2  1/3 = 2 3 + 1/3 = 6 + 1/3 = 7/3

To find a new numerator

A;   Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3

b) Add the answer from the previous step 6 to the numerator 1. The new numerator is 6 + 1 = 7

c) Write a previous answer (new numerator 7) over the denominator 3.

Two and one-third are seven-thirds.

Conversion a mixed number 1  3/4 to a improper fraction: 1 3/4 = 1  3/4 = 1 · 4 + 3/4 = 4 + 3/4 = 7/4

To find a new numerator:

a) Multiply the whole number 1 by the denominator 4. Whole number 1 equally 1 * 4/4 = 4/4

b) Add the answer from the previous step 4 to the numerator 3. The new numerator is 4 + 3 = 7

c) Write a previous answer (new numerator 7) over the denominator 4. One and three quarters are seven quarters.

Add: 7/3 + 7/4 = 7 · 4/3 · 4 + 7 · 3/4 · 3 = 28/12 + 21/12 = 28 + 21/12 = 49/12 It

is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions.  The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 4) = 12.  It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by cancelling.  In other words - seven thirds plus seven quarters is forty-nine twelfths.

Answer:

An easy way to solve this problem is divide $23.25 by 3 or $54.25 by 7. Either way, you get $7.75. This number represents the amount of money he makes for 1 hour. So with that in mind, the correct equation is:

$7.75x = y

Step-by-step explanation:

Answer: y = 7.75x

Step-by-step explanation:

Find the difference of charges between 6 hours and 8 hours

62-46.5 = 15.5 for 2 hours

15.5/2 = 7.75/hr

62 = 7.75 x 8

Therefore there is no initial charge, and that the relationship is linear

so y = 7.75x

Answer:

x - 4 yards.

Step-by-step explanation:

Given:

Area of rectangle = 3x^2 - 12x square yards

Width = 3x yards

To find:

Length of rectangle

Solution:

The area of a rectangle is equal to the product of its length and width.

Area of rectangle = Length * Width

Substituting the given values, we get:

3x^2 - 12x = Length * 3x

Length =( 3x^2 - 12x )3x

Length = x-4

Therefore, the length of the rectangle is x - 4 yards.

Answer: The length of the rectangle is x - 4 yards.

Step-by-step explanation:

We can create an equation to solve this word problem, where the variable L = length.

3x  ×  L  = \(3x^2 - 12x\)

We need to solve for the variable L, to find the length of the rectangle.

First lets factor the right side of the equation to make it easier to divide with.

3x  ×  L  = \(3x^2 - 12x\)

We can factor out 3x from the right side of the equation.

3x  ×  L  = 3x(x - 4)

Now we need to get the variable L by itself (isolating the variable). In order to do that, we can divide both sides by 3x.

3x ×  L  = 3x(x - 4)

/3x           /3x

L = x - 4

The length of the rectangle is x - 4 yards.

Answer:

12, 24 , and 36

Step-by-step explanation:

Answer:

12 24 36

Step-by-step explanation:

The Circle Sector Area correct answer is: O n(30in)2

To calculate the area of the sector in the circle, you would typically use the formula:

Area = (θ/360) * π *\(r^2\)

where θ is the angle of the sector in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

From the options you provided, the correct choice would be:

O n(30in)2

This option represents the square of the radius (30in) squared, which gives you the value of \(r^2.\)

Therefore, the Circle Sector Area correct answer is: O n(30in)2

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define the domain of the given piecewise function

Given the conditions for the piecewise function, it can be seen that the function starts from negative infinity to positive infinity. Therefore, the domain of the given piecewise function is all set of Real numbers.

STEP 2: Differentitate the given piecewise functions

For the first function,

For the second function,

For the third function,

STEP 3: Determie the domain of the differentiated functions

When you differentitate a piecewise function, the domain at the given points will be undefined. Therefore, these points will be excluded. These points are x=2 and x=4. The domain of a piecewise function after being differentitated will be;

Hence, the answer is given as:

its 5x5 but with a negative

Step-by-step explanation:

Answer:120

Step-by-step explanation:

Answer: 3/2

Step-by-step explanation:

Answer:

3/2 or 1 1/2

Step-by-step explanation:

\(2\frac{1}{4}/1\frac{1}{2} \\\frac{9}{4}/\frac{3}{2} \\(\frac{9}{4})(\frac{2}{3})\\\frac{18}{12} \\\frac{3}{2} or 1\frac{1}{2}\)

Answer:

B

Step-by-step explanation:

a prime polynomial is one which does not factor into 2 binomials.

its only factors are 1 and itself

attempt to factorise the given polynomials

3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )

= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(3x² - 2) ← in factored form

--------------------------------------------------

3x³ - 2x² + 3x - 4 ( factor the first/second terms

= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored

thus this polynomial is prime

----------------------------------------------------

4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )

= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term

= (2x + 1)(2x² + 3) ← in factored form

-------------------------------------------------

4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )

= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(4x² - 3) ← in factored form

--------------------------------------------------

the only polynomial which does not factorise is

3x³ - 2x² + 3x - 4

The volume of the rectangular prism is 208cm³

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Sometimes, volume is also termed capacity.

The volume of a rectangular a prism is expressed as base area × height. The base area is a rectangle and the area of a rectangle is Length × width

length = 2cm

width = 13 cm

height = 8cm

base area = 13× 2 = 26cm²

Volume of the prism = 26× 8 = 208cm³

Therefore the volume of the rectangular prism is 208cm³.

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