Question What is the value of the expression? (9 1/2 − 3 7/8)+(4 4/5 − 1 1/2) Enter your answer as a mixed number in simplest form by filling in the boxes. $$

The nth term of the given sequence is 1/n².

An arithmetic progression (AP) is a sequence of numbers in which each term, starting from the second term, is obtained by adding a fixed constant value to the previous term. This constant value is called the common difference, and it remains the same throughout the sequence.

A geometric progression (GP) is a sequence of numbers in which each term, starting from the second term, is obtained by multiplying the previous term by a fixed constant value. This constant value is called the common ratio, and it remains the same throughout the sequence.

In the given question,

The given sequence is of the form:

1, 1/2², 1/3², 1/4², ...

So, the nth term can be written as:

1/n²

Therefore, the nth term of the given sequence is 1/n².

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Answer:

26

Step-by-step explanation:

triangle=180

81 + 73= 154

180 - 154= 26

Answer:

∠m = 26

Step-by-step explanation:

We know that the sum of the interior angles in a triangle is added up to 180°.

Accordingly,

∠81 + ∠73 + ∠m = 180°

Combine like terms.

∠154 + ∠m = 180°

Subtract 154 from both sides.

∠m = 26

1. Option a, c and e fulfill the Pythagorean triplet rule.

2. Option a, e, and f are the correct options.

3. Yes as per the Pythagoras theorem, all the sides will be proportional to the similar triangle.

The formula for the Pythagoras theorem is written as c² = a² + b², where c is the hypotenuse of the right triangle and a and b are its other two legs.

As a result, the Pythagoras equation can be used to any triangle that has one angle that is exactly 90° to create a Pythagoras triangle.

In question 1,

The Pythagorean triplets we have are:

5, 12, 13 as they fulfill the c² = a² + b², formula.

5, 10, 5√5 and 20, 99, 101

In the second question, we have the triplet 7, 24, 25

So the triangles similar to this will have proportionate sides.

So 14, 48, 50(sides have been doubled)

√7, √24, √25 (sides have been square rooted) and

35, 120 and 125(sides have been multiplied by 5)

are the sides that are proportional.

In the last question,

If the triangle has Pythagorean triplets, then for the other triangle to be similar the sides has to be multiples of the triplets or proportionate to them.

In this case its true, so the triangles are similar to each other.

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Answer:

Therefore, the maturity value of the loan is $2568.75.

Step-by-step explanation:

To calculate the maturity value of the loan, we need to add the interest to the principal.

First, we need to find out how much interest Ricardo will owe for the 180-day period.

The formula for calculating ordinary interest is:

Interest = Principal x Rate x Time

where:

Principal = $2500

Rate = 7.8% = 0.078 (expressed as a decimal)

Time = 180/360 (since the interest is for a 180-day period and the rate is an annual rate)

Time is expressed as a fraction of a year because the rate is an annual rate. In this case, the time is 180/360 because the loan is for 180 days, which is half of a year.

Using the formula above, we can calculate the interest as follows:

Interest = $2500 x 0.078 x 180/360 = $68.75

Therefore, Ricardo will owe $68.75 in interest for the 180-day period.

To find the maturity value of the loan, we add the interest to the principal:

Maturity Value = Principal + Interest = $2500 + $68.75 = $2568.75

Therefore, the maturity value of the loan is $2568.75.

The radius of the Earth's orbit around the sun is approximately 93 million miles.

To calculate the circumference of the Earth's orbit, we can use the formula:

C = 2πr

where C is the circumference and r is the radius. Plugging in the value for the radius, we get:

C = 2π(93,000,000) = 584,336,000 miles

So the Earth travels approximately 584,336,000 miles in one orbit around the sun.

The speed of the Earth in its orbit around the sun can be calculated using the formula:

v = 2πr/T

where v is the velocity, r is the radius, and T is the period (the time it takes for the Earth to complete one orbit). The period of the Earth's orbit is approximately 365.25 days, or 31,557,600 seconds.

Plugging in the values, we get:

v = 2π(93,000,000)/(31,557,600) = 29,784 miles per hour

So the Earth travels at approximately 29,784 miles per hour in its orbit around the sun.

answer: x= 20x

Step-by-step explanation: 2+2 is 4, 4+4 is 8, quick maths

Answer:

Step-by-step explanation:

To convert the mixed angle measure 96° 29' 1" to decimal degrees, we can use the following formula:

decimal degrees = degrees + (minutes / 60) + (seconds / 3600)

Using this formula, we have:

decimal degrees = 96 + (29 / 60) + (1 / 3600)

decimal degrees = 96.4836111

Therefore, mHJ = 96.4836111 degrees (rounded to seven decimal places).

Finally, express the solution as an interval of real numbers or as a set of values that make the inequality. x<10.4, x>3.3, x≥32 and x≤-15.

To solve an inequality, you need to find the set of values that make the inequality true. The process for solving an inequality depends on the type of inequality and the variables involved. Here are the general steps:

Finally, express the solution as an interval of real numbers or as a set of values that make the inequality true. If the inequality is strict (> or <), use an open interval (e.g., (a, b)). If the inequality includes equality (≥ or ≤), use a closed interval (e.g., [a, b]).

by the question.

a. x-3.5>6.9

x>6.9+3.5

x>10.4

b. 6.4>x+3.1

x[tex]\geq 32[/tex]

c. x/4≤8

x≤32

d. 2/3x≤-10

x≤-15

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Answer:

Step-by-step explanation:

Step-by-step explanation:

lol sorry for untidy work

The quantities arranged from smallest to largest are 1.9 g, 24 g, and 210 g.

A quantity is a property or attribute of an object or phenomenon that can be measured or described numerically. Quantities can be either scalar, meaning they have a magnitude (or size) but no direction, or vector, meaning they have both a magnitude and a direction.

First, let's convert all the quantities to the same unit.

2.4 dag = 24 g (since 1 dag = 10 g)

0.21 kg = 210 g (since 1 kg = 1000 g)

190 cg = 1.9 g (since 1 cg = 0.01 g)

Now we can arrange the quantities from smallest to largest:

1.9 g

24 g

210 g

Therefore, the quantities arranged from smallest to largest are 1.9 g, 24 g, and 210 g.

Dag is a weight measuring unit that is rarely applied in daily life. Dag is an abbreviation for "dekagram", which is a metric unit of mass equal to 10 grams. One dekagram is equivalent to 0.01 kilograms or 0.3527 ounces.

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Answer:

0.375

Step-by-step explanation:

3/2 equals 1 and a half, and 1 and a half divided by 4 will get you 0.325

Answer:

4x - 2 = 3x + 1. Solution We substitute the value 3 for x in the equation and see if the left-hand member equals the right-hand member. 4(3) - 2 = 3(3) + 1.

Answer: 160

Step-by-step explanation: The straight line or line X is 180 degrees. So subtracted 20. This is because X is intersected by another line which makes the upper notch 20 degrees.

Answer: 90.32%

Step-by-step explanation:

To calculate your updated grade after receiving a 75% on a quiz that counts 7% of your overall grade, you can use the following formula:

New grade = (Old grade * (100 - weight of quiz)) + (Quiz grade * weight of quiz)

Plugging in your values, we get:

New grade = (97 * (100 - 7)) + (75 * 7)

New grade = (97 * 93) + (5.25)

New grade = 903.16

Therefore, your new grade is 90.32%.

Answer:  The sum of the weight of all your coursework plus your final is equal to 14.00

Step-by-step explanation:

not sure

Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.

Since "percent" is a slang term for "per hundred," when we discuss percentages, we are speaking to a fraction of a hundred. In a variety of contexts, including math, science, finance, and daily living, percentages are used. The percent sign (%) is commonly used to denote percentages. As an illustration, to determine what proportion of 50 apples are red, you would split the number of red apples by the total number of apples and multiply the result by 100.

given

If Jane had phoned 1,000 times and you had allowed 67% of those calls to go to voicemail, then 67% of those calls would have left voicemails for you.

You can multiply the overall number of calls by the proportion of calls that went to voicemail to determine how many voicemails you would have received:

1000 x 67% = 670

Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.

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The complete question is :-  

Jane called one thousand times to tell you she's sorry. If you saw she was calling and let your phone go to voicemail 67% of the time, how many voicemails would you have received if she left one each time?

Possible Answers:

3,700

57,000

67

None of the given answers

670

The sum of the given fractions is (2x + 10)/x.

What is fraction ?

A fraction is a way of representing a part of a whole or a ratio between two quantities. It is written in the form of a numerator and a denominator separated by a horizontal line. The numerator represents the number of equal parts under consideration, while the denominator represents the total number of equal parts that make up the whole. For example, the fraction 3/4 represents three equal parts out of a total of four equal parts. Fractions can be added, subtracted, multiplied, and divided to perform various mathematical operations.

According to the question:
The given fractions can be added if they have a common denominator. In this case, the common denominator is 9x.

So, we need to write the fractions with 9x as the denominator:

2/1 * (9x/9x) = 18x/9x

10/1 * (9/9x) = 90/9x

Now, we can add these two fractions:

18x/9x + 90/9x = (18x + 90)/9x = 9(2x + 10)/9x = 2x + 10/ x

Therefore, the sum of the given fractions is (2x + 10)/x.

Q: Find K by Adding the fractions and simplify if possible k=(2*(9x))+(10*(9x))

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The probability of selecting an even integer is 1/2 or 0.5.

What exactly is probability?

Probability is a measure of an event's possibility or chance of occurring. It is a number between 0 and 1, with 0 indicating that the occurrence is improbable and 1 indicating that the event is unavoidable. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in a wide variety of fields, including mathematics, statistics, economics, physics, engineering, and social sciences, to make predictions and informed decisions.

Now,

There are a total of 27 - 7 + 1 = 21 integers between 7 and 27, inclusive. Of these, half are even and half are odd, since consecutive integers alternate between even and odd.

Therefore, the probability of selecting an even integer is 1/2 or 0.5.

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Answer:

Step-by-step explanation:

(x+3)^2=49

x+3=√(49)

x+3=√(7^2)

x+3=7

x+3-3=7-3

x+3=-√(49)

x+3=-7

x+3-3=-7-3

x = 4,-10

Answer:

130

Step-by-step explanation:

Answer: y=130  x=130

Step-by-step explanation:

The statements that are correct are:

m∠ACB = 44° (Option B)

m∡AC = 156° (Option C)

A) m∠ACB = 44° is correct because the Circle Theorem indicates that the angle at the center is twice or double the one at the circumference.

Since, the one at the center is already 88°, thus, the one at the angle at the circumference = 88°/2 = 44°

Hence, m∠ACB = 44° (Option B) is correct.


B) m∡AC = 156° (Option C)

To get this, we need to state,

360° - 116° - 88° = 156° (Option C)

C) m∡ BAC should be determined using Alternate Segment Theorem.

According to this theorem which states that the angle that lies between a tangent c and a chord is equal to the angle subtended by the same chord in the alternate segment,

∠BAC is supposed to be equal to ∠GAC - ∠GAB

That is:

∠BAC = 90° - 44°
∠BAC = 46°

However, this is questionable because, we have proven that ∠BAO = (180-88)/2 = 46° (Isoceles Δ BOA created by shared Radii)

Thus,

∠BAC = 46°  cannot be equal to ∠BAO.

Thus, the only right answers are:

Option B and

Option C.

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Full Question:

Although part of your question is missing, you might be referring to this full question: See the attached image.

We can compare the amount in the IRA at retirement to the total deposits made over the time period to determine if the interest earned has exceeded the amount deposited.

IRA is an acronym that stands for "Individual Retirement Account." It is a sort of investment account meant to assist individuals in saving for retirement. Individuals can deposit pre-tax income to an IRA, and the money in the account grows tax-free until taken in retirement.

Part 1: To calculate the amount that the IRA will contain when the person retires at age 65, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^(nt)[/tex]

In this situation, the individual establishes the IRA at age a, thus they have t = 65 - a years till retirement. Because the APR is expressed as a percentage, we must divide it by 100 to obtain the annual interest rate in decimal form. Because the individual deposits $d at the end of each month, n = 12 (monthly compounding) and the effective monthly interest rate is r/12.

Therefore, the amount of money in the IRA at retirement can be calculated as:

[tex]A = d * ((1 + r/12)^(12*(65-a)) - 1) / (r/12)[/tex]

Part 2 : We can compare the amount in the IRA at retirement to the total amount of deposits made over the time period. The total amount of deposits can be calculated as:

Total Deposits = 12 * (65-a) * d

The amount in the IRA upon retirement (estimated in Part 1) may then be compared to the total contributions made during the time period. If the amount in the IRA exceeds the total deposits, the interest generated has exceeded the entire deposits. If the amount in the IRA is less than the total deposits, the interest produced will not be sufficient to compensate for the amount contributed.

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The variance of the number of citizens favoring the supermarket is 6.

To find the variance of the number of citizens favoring the supermarket, we need to use the binomial distribution formula:

Variance = n × p × (1 - p)

where n is the number of trials (25 in this case), p is the probability of success (0.6 in this case), and (1 - p) is the probability of failure.

Plugging in the values, we get:

Variance = 25 × 0.6 × (1 - 0.6)

Variance = 25 × 0.6 × 0.4

Variance = 6

The binomial distribution is a probability distribution that models the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes, success or failure. In this case, the trials are the 25 citizens who were chosen, and the success is the event of favoring the supermarket, which has a probability of 0.6.

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The minimum amount of money to be deposited in the bank account is $16,921. The solution has been obtained by using compound interest.

What is compound interest?

Compound interest is the type of interest that is calculated using both the principal and the interest that has accumulated over the preceding period. In contrast to simple interest, compound interest does not factor in the principal when calculating the interest for a subsequent period. In mathematics, compound interest is frequently referred to as C.I.

We are given that we need $25,000 eight years from now and the account pays an annual percentage rate (APR) of 5% which is compounded annually.

So, using the compound interest formula, we get the principal as

⇒ P = [tex]\frac{A}{(1 + \frac{r}{n} )^{nt} }[/tex]

⇒ P = [tex]\frac{25000}{(1 + \frac{0.05}{1} )^{8} }[/tex]

⇒ P = $16,920.98

Hence, the minimum amount of money to be deposited in the bank account is $16,921.

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Answer: D. $722

Step-by-step explanation:

$2,000 - $375 (initial airfare cost which will only be once)

= 1,625

7 x 129 = 903 (cost of the 7 nights in a hotel)

1,625 - 903 = 722

$722 left for the trip

Answer:

19.2 ft

Step-by-step explanation:

Answer:  d.  25 square inches

Step-by-step explanation:

Expression equivalent to 5x - 4 are 5(x - 4/5), 5x - 20/5, 10x/2 - 8/2 and 3(5x/3) - 4

To create an expression equivalent to 5x - 4, we need to use arithmetic operations such as addition, subtraction, multiplication, and division, along with numbers and variables. The goal is to manipulate the numbers and variables in a way that results in the same value as 5x - 4.

Here are some examples of how we can do this:

5(x - 4/5)

In this expression, we start with x and subtract 4/5 from it. Then we multiply the result by 5. This is equivalent to distributing the 5 to x and -4/5, which gives us 5x - 4.

5x - 20/5

Here, we simply subtract 20/5 (which simplifies to 4) from 5x. This gives us 5x - 4.

(25x - 20)/5

In this expression, we start with 25x and subtract 20 from it. Then we divide the result by 5. This is equivalent to simplifying the expression to 5x - 4.

10x/2 - 8/2

This expression might look a bit different, but it's still equivalent to 5x - 4. Here, we start with 10x and divide it by 2, which gives us 5x. Then we subtract 8/2 (which simplifies to 4) from it, giving us 5x - 4.

3(5x/3) - 4

In this expression, we start with 5x and divide it by 3. Then we multiply the result by 3, which gives us 5x. Finally, we subtract 4 from it, giving us 5x - 4.

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Answer:

the chips are marked down by 12%.

Step-by-step explanation:

To calculate the percentage discount, you can use the formula:

percentage discount = (original price - sale price) / original price x 100%

Plugging in the values given in the problem, we get:

percentage discount = (6.00 - 5.28) / 6.00 x 100%

percentage discount = 0.72 / 6.00 x 100%

percentage discount = 0.12 x 100%

percentage discount = 12%

Answer:

The answer is 12%

Step-by-step explanation:

6 - 5.28 = 0.72

0.72/6 = 0.12

0.12 is a decimal, but written as a percent is 12%.