The diameter of a circle is 3 ft. Find its area to the nearest whole number.

After 6 years, the first accοunt with simple interest earn mοre amοunt.

The interest that is calculated using bοth the principal and the interest that has accrued during the previοus periοd is called cοmpοund interest. It differs frοm simple interest in that the principal is nοt taken intο accοunt when determining the interest fοr the subsequent periοd with simple interest.

Here In first bank account ,

Principal P = $1000

Time N = 6

Rate οf interest = 7%

Interest = [tex]\frac{PNR}{100}[/tex]

=> I = [tex]\frac{1000\times7\times6}{100}[/tex] = $420

Tοtal amount = $1000+$420 = $1420.

Now in secοnd bank account,

Principal P = $1000

Times N= 6

Rate οf interest = 6%

Tοtal amount A = [tex]P(1+\frac{R}{100})^N[/tex]

=> A = [tex]1000(1+\frac{6}{100})^6[/tex]

=> A = $1418.00

Now cοmparing bοth account amounts , In first bank have earned more amount that second bank,

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Answer:

Since the fish is swimming down at a constant rate of 12 ft per hour for 6 hours, the distance it travels can be found by multiplying its speed by the time:

distance = speed x time

distance = 12 ft/hour x 6 hours

distance = 72 ft

Therefore, the fish will end up 72 feet down from the surface.

(a)  40.4° or 139.6°

(b)  137.6° or 222.4°

(c)  124.2° or 304.2°

(a) sinθ=0.6264:θ=40.4° or 139.6°

(b) cosθ=-0.6405:θ=137.6° or 222.4°

(c) tanθ=-1.5519:θ=124.2° or 304.2°.What is interval? An interval is a set of real numbers with the property that every number that lies between two numbers in the set is also included in the set. Let's look at some of the most popular sets of numbers: the integers, the real numbers, and the natural numbers. What is an angle? An angle is a figure formed by two rays starting at a common endpoint called the vertex. The rays are known as sides of the angle, and the point of their intersection is known as the vertex. Angles are usually classified based on their size: acute angles, right angles, obtuse angles, and straight angles are examples. The following is how to solve the problem; 1. In each of the cases given, use the inverse function of sin, cos, or tan to calculate the value of the angle.2. Ascertain if the angle you've calculated is in the required interval.3. Since this question asks for an approximation to the nearest 0.1 degrees, express your solutions to one decimal point.Let's look at the following options:(a) sinθ=0.6264θ = 40.4° or 139.6°(b) cosθ=−0.6405θ = 137.6° or 222.4°(c) tanθ=−1.5519θ = 124.2° or 304.2°.Therefore, to the nearest 0.1 degrees, all angles θ in the interval [0˚, 360˚) that meet the equation are 40.4°, 139.6°, 137.6°, 222.4°, 124.2°, and 304.2°.

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Answer:

5760

Step-by-step explanation:

Answer:

c  (2,0)

Step-by-step explanation:

One way to solve this system of inequalities is to graph the inequalities and see which ordered pair lies in the shaded region that is common to both inequalities

See the graph and each of the ordered pairs. Only (2, 0) lies entirely within the shaded region

(-1, 0) lies on the intersection of the two lines so it will satisfy the >= inequality but not the < inequality

Answer (2, 0)

However if you cannot use graphing then a brute force method must be used to see which ordered pair satisfies both inequalities

a. (-1, 0)
Check y < 2x + 2 ?
=>  0 < 2(-1) + 2 ?
=> 0 < -2 + 2
0 < 0 ? False
Eliminate option a

b. (0, 3)
y < 2x + 2?
=> 3 < 2(0) + 2?
3 < 2? False
Eliminate option b

c. (2, 0)
y < 2x + 2?
=> 0 < 2(2) + 2 ?
=>  0 < 4 + 2
=> 0 < 6 True

Move to the second inequality
y ≥ -x - 1?
0 ≥ -2 - 1
0 ≥ -3 True

So option c is the correct choice

While it is not necessary to check option d, let's do it anyway
d. (-1, -4)
y < 2x + 2 ?
-4 < 2(-1) + 2 ?
-4 < -2 + 2 ?
-4 < 0 ? True

Move to the second inequality
y > -x - 1 ?
-4 > -(-1) - 1
-4 > -2? False
Option d is eliminated

Correct answer: (2, 0) which is option c

The midpoint of PQ is -6. The line PQ have endpoints on the real number line at −14 and 2

An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.

The midpoint O between two points A and B on the number line is:

O = (A + B)/2

The endpoints of PQ on the real number line are −14 and 2, hence:

Midpoint = (-14 + 2) / 2 = -12/2 = -6

The midpoint of PQ is -6

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The function that represents the estimated population after t years with an annual rate of decrease of 0.25% is y = [tex]358,000(0.9975)^{t}[/tex]. So  correct option is D) .

Annual rate can also be used to describe growth rates or changes in other types of measurements, such as population growth or inflation. For example, if the population of a city grows by 2% per year, the annual rate of population growth is 2%.

It is important to note that when annual rates are used to describe financial products or investments, they may be compounded over time. Compounding refers to the process of earning interest on interest, which can significantly increase the total amount of interest owed or earned over time. Therefore, it is important to carefully consider the effects of compounding when evaluating financial products or investments.

The function that represents the estimated population after t years with an annual rate of decrease of 0.25% is:

y = [tex]358,000(0.9975)^{t}[/tex]

Therefore, the correct option is D) y = [tex]358,000(0.9975)^{t}[/tex].

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Answer:

C. Simplify

Step-by-step explanation:

1. Subtract 7 from both sides

4x +7 -7 < 15 -7

4x < 8

2. divide both sides by 4

4x/4 < 8/4

answer: x < 2

hope this helps

Answer:

(x + 1) (3x + 5)

Step-by-step explanation:

Let's check

(x + 1) (3x + 5)

3x² + 5x + 3x + 5

3x² + 8x + 5

So, (x + 1) (3x + 5) is the correct answer.

Answer:

$43,200

Step-by-step explanation:

The amount of money you make a year depends on various factors, such as your monthly expenses, debt obligations, and tax liabilities.

To get a rough estimate of your annual income based on the range of affordable rent provided, you can use the rule of thumb that suggests spending no more than 30% of your gross income on housing expenses. Assuming you are willing to spend between $900 and $1080 per month on rent, we can calculate the range of annual incomes that would allow you to meet this guideline:

$900/month rent x 12 months = $10,800/year rent

$10,800/year rent / 0.3 = $36,000/year gross income

$1080/month rent x 12 months = $12,960/year rent

$12,960/year rent / 0.3 = $43,200/year gross income

Therefore, based on the assumption that you can afford rent between $900 and $1080 per month, your estimated annual gross income would need to be in the range of $36,000 to $43,200. However, this is only a rough estimate and may not take into account all of your individual financial circumstances.

The total surface area of the gift box in discuss as required to be determined in the task content is; 416 in².

As evident in the task content; the gift box in discuss can be likened to a cuboid with dimensions; 12 by 10 by 4.

Hence, since the total surface area of a cuboid is given by;

Area = 2 (lw + lh + wh)

Therefore, for the given gift box;

Area = 2 ( (12×10) + (12 × 4) + (10 × 4) )

= 2 ( 120 + 48 + 40 )

= 2 (208)

= 416.

Ultimately, the total surface area of the gift box in discuss is; 416 in².

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14: 2.38 minutes

15: lower bound is 97 km/h and the upper bound is 119 km/h

Question 14: The standard error of the mean (SE) can be calculated using the following formula: SE = s/√n, where s is the standard deviation of the population (43 minutes) and n is the sample size (246 students). Plugging in the values, SE = 43/√246 ≈ 2.38. Therefore, the standard error of the mean is 2.38 minutes and it should be rounded to 2 decimal places, giving us 2.38 minutes.

Question 15: According to the empirical rule, 95.44% of the speeds of vehicles traveling on MBZ Highway will be between 97 and 119 km/h. Therefore, the lower bound is 97 km/h and the upper bound is 119 km/h.

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Answer: A=490

Step-by-step explanation:

Formula - A = 2 ( wl + hl + hw)

2(7•14+7•14+7•7) = 490

Answer:

We can use the formula for exponential growth:

A = P(1 + r)^t

where:

A = final amount

P = initial amount

r = annual growth rate (as a decimal)

t = time (in years)

Let's plug in the values:

P = 540

r = 0.039

t = 2035 - 2015 = 20

A = 540(1 + 0.039)^20

A ≈ 891

Therefore, the local government of Central Village can predict there will be approximately 891 houses in 2035.

Answer:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r)^n

where:

A = the final amount

P = the initial amount

r = the annual interest rate (as a decimal)

n = the number of years

In this case, we want to find the final amount (the number of houses in 2035), given the initial amount (540 houses in 2015), the annual interest rate (3.9%), and the number of years (20 years from 2015 to 2035).

So, we can plug in the values and solve for A:

A = 540(1 + 0.039)^20

A = 540(1.039)^20

A = 540(2.011)

A = 1086.54

Rounding to the nearest whole number, we get:

A ≈ 1087

Therefore, the local government of Central Village can predict there will be about 1087 houses in 2035.

The volume of the hexagonal prism is the amount of space in the prism

The volume of the hexagonal prism is 212.4 cubic units

The given parameters are:

Base area = 36 square units

Height = 5.9 units

The volume is then calculated as:

Volume = Base area x Height

So, we have:

Volume = 36 x 5.9

Evaluate the product

Volume = 212.4

Hence, the volume of the hexagonal prism is 212.4 cubic units

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The probability of at least 2 people having the same birthday in a group of 23 people is 0.5073.

The probability of at least 2 people having the same birthday in a group of 23 people can be calculated using the rule for complements. The complement of this event is that all 23 people have different birthdays. We can calculate the probability of this event and then subtract it from 1 to find the probability of at least 2 people having the same birthday.

The probability of the first person having a different birthday from the others is 1. The probability of the second person having a different birthday from the first is 364/365, since there are 364 days left that are not the first person's birthday. The probability of the third person having a different birthday from the first two is 363/365, and so on.

The probability of all 23 people having different birthdays is:

1 * (364/365) * (363/365) * ... * (343/365)

This simplifies to:

364! / (36522 * 341!)

Using a calculator, we find that this is approximately 0.4927.

Therefore, the probability of at least 2 people having the same birthday is:

1 - 0.4927 = 0.5073

So, the probability of at least 2 people having the same birthday in a group of 23 people is 0.5073.

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In a group of 23 persons, the probability that at least two of them share the same birthday is around 0.5073, or 50.73%.

The probability that at least 2 people in a group of 23 have the same birthday, can be calculated by using the rule for compliments. First, we can calculate the probability that no two people share a birthday in a group of  23.

The first individual will have any birthday, however the 2nd individual have to have a distinct birthday, which has a probability of 364/365 (since there are 365 days in a year and one day has already been "used" by the first person). The probability that the third individual will have a different birthdate from the previous two is 363/365. Continuing in this way,

The probability that all 23 people have different birthdays is:

(365/365) x (364/365) x (363/365) x ...

Since the probabilities of all conceivable outcomes must sum up to 1, subtract the likelihood that at least two persons will have the same birthdate from one:

P(at least 2 people have the same birthday) = 1 - (365/365) x (364/365) x (363/365) x ... x (344/365)

P(at least 2 people have the same birthday) = 0.5073

Therefore, the probability that at least 2 people in a group of 23 have the same birthday is approximately 0.5073 or 50.73%

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Answer: Without further context, it is impossible to determine whose work is correct. (Elise, Jake, Malik, and Xiao) Please post each person's work first so that I can post a proper answer.

Answer:

Maliks

Step-by-step explanation:

Answer:

To show that two fractions are reciprocals, you can multiply them together and check if the product is equal to 1. That is, if we have two fractions a/b and b/a, their product is:

(a/b) * (b/a) = ab / ba = 1

Therefore, if the product of two fractions is equal to 1, they are reciprocals of each other.

For example, let's say we have the fractions 2/5 and 5/2. We can multiply them together to check if they are reciprocals:

(2/5) * (5/2) = 1

Since the product is equal to 1, we can conclude that 2/5 and 5/2 are reciprocals of each other.

Answer: 5x/5 = -6/5 + y/5

Step-by-step explanation:

x = -6 + y/5

and then x = -2 +y

Answer:

We can approach this problem using the following steps:

Calculate the exchange rate after factoring in the agency commission. Since the agency commission is 1.5%, the effective exchange rate will be:

Effective exchange rate = Exchange rate - (Exchange rate * Commission rate)

= 30.075199 - (30.075199 * 0.015)

= 29.6185968

Multiply the amount of South African rands by the effective exchange rate to get the amount in British pounds.

Amount in pounds = Amount in rands / Exchange rate

So, for an amount of 2100 South African rands, the calculation would be:

Amount in pounds = 2100 / 29.6185968

= 70.815 pounds (rounded to three decimal places)

Therefore, Brian will get 70.815 pounds for 2100 South African rands after factoring in the agency commission.

Answer:

6.18km

Step-by-step explanation:

circumference= diameter×π

38.8km÷π=12.350423583931.... this is the diameter

12.3504...÷2=6.1752117919655..... is the radius

radius rounded to 3sf= 6.18km i think

The  steps taken to design a contingency contract are valuating the potential outcomes, consequences and agree on terms of contract.

Identify the potential outcomes. Party A thinks that there is an 80% chance that the car will not break down in the first year, while Party B thinks that there is an 80% chance that it will. These are the two potential outcomes that need to be identified.

Determine the consequences of each outcome. Next, the consequences of each outcome should be determined. For example, if the car breaks down in the first year, then Party A may have to pay for repairs or reimburse Party B for the purchase price of the car. If the car does not break down, then no consequences need to be determined.

Agree on the terms of the contract. Finally, both parties need to agree on the terms of the contract. This may include how much Party A will have to pay if the car breaks down, how long Party B has to wait for reimbursement if the car does break down, and any other terms that are relevant to the situation. Once the terms have been agreed upon, the contingency contract can be signed by both parties, and they can proceed with the sale of the car.

A contingency contract could be designed to help them avoid an impasse over the issue of the car's breakdown. The contingency contract is a contract that is triggered by a specific event or circumstance, such as the car breaking down in the first year. This contract outlines what will happen if the event or circumstance occurs, and both parties agree to the terms in advance.

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The sales price of the item after deduction of percentage discount is: $18

The regular price is defined as the price at which similar goods or services are regularly sold on the market.

The discount is defined as an amount or perhaps percentage deducted from the normal selling price of something.

The sales price is defined as the actual amount for which a good is sold after deduction of discount if any.

The parameters given are:

Regular Price = $20

Percentage Discount = 10%

Thus:

Discount = 10% * 20

Discount = $2

Thus:

Sales Price = $20 - $2

= $18

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[tex]3x^3 + x^2 = 6x[/tex], which is option B, is the right response as Option C,[tex]3x^3 + x^2 = 0[/tex], does not equal the supplied expression.

Using just the methods of addition, elimination, and multiplication as well as ou pas integer exponents, a polynomial is a mathematical equation made up of variables and coefficients. A polynomial, for instance, is 3x2 - 2x + 5, where x has been the component and 3, -2, and 5 are now the coefficients. This polynomial's highest exponent is 2, which also happens to be its degree. Polynomials can have coefficients that are either constants or other polynomials, as well as many variables. Due to their usage in representing a variety of mathematical relations and functions, polynomials play a significant role in mathematics. Several disciplines, including algebra, algebra, geometry, and physics, make extensive use of them.

given

To make [tex]5x^2-x-8x^2 + 3x^3[/tex]simpler, we can rearrange the terms and join comparable terms:

[tex]0 + 3x^3 - x - 3x^2 = 5x^2 - 8x^2 + 3x^3 - x[/tex]

The following step is to factor the final three terms to remove a common factor of x:

[tex]3x^3 - x - 3x^2 = x\\(3x^2 - 1 - 3x)[/tex]

Hence, the abbreviated form is:

[tex]3x^2 - 1 - 3x^3 = 5x^2-x-8x^2 + 3x^3.[/tex]

Due to the fact that Option C,[tex]3x^3 + x^2 = 0[/tex], does not equal the supplied expression, it is incorrect.

Due to their failure to simplify to the specified formula, options A,      [tex]-5x^3+ x^2 = 0,[/tex] and D, [tex]3x^3 -3x^2 =6x[/tex], are likewise incorrect.

[tex]3x^3 + x^2 = 6x[/tex], which is option B, is the right response.

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The complete question is:-  

Simplify: [tex]5x^2-x-8x^2 + 3x^3 = 5x[/tex]

OA.-5x3x2 = 0

B. 3x3 + x2 = 6x

C. 3x3 + x2 = 0

D. 3x3 3x26x

-

Reset Selection

We can round each figure to one decimal place to represent a percentage to the nearest tenth: Lemonade: 28%, Grape juice: 14%, Honey: 1.8% and  Sparkling water: 56.2%. So, the lemonade contributes approximately 28% to the punch mixture.

Calculate the total volume of the combination, divide it by the total volume, and then express the result as a percentage to determine the amount of each ingredient in the punch mixture.

1 quart = 4 cups

1/2 gallon = 8 cups

4 tablespoons = [tex]\frac{1}{4}[/tex] cups

So the total volume of the mixture is:

4 cups (lemonade) + 2 cups (grape juice) + [tex]\frac{1}{4}[/tex] cups (honey) + 8 cups (sparkling water) = [tex]\frac{57}{4}[/tex] cups

Now, we can calculate the percentage of each ingredient in the mixture:

Lemonade:  [tex]\frac{4}{(\frac{57}{4})}*100[/tex] ≈ 28%

Grape juice: [tex]\frac{2}{(\frac{57}{4})}*100[/tex] ≈ 14%

Honey: [tex]\frac{(\frac{1}{4})}{(\frac{57}{4})}*100[/tex] ≈ 1.8%

Sparkling water: [tex]\frac{8}{(\frac{57}{4})}*100[/tex] ≈ 56.2%

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The minutes that it would take for the 0702 bus to go from Birmingham to Coventry is 92 minutes.

The latest time that Steve should leave his house so as to get to work on time is 07 56 hours .

If the bus from Birmingham leaves at 07 02 hours, it would reach Coventry at 08 34. The time taken is therefore :

= 08 34 - 07 02

= 1 hour 32 minutes

In minutes, this is:

= 60 minutes in an hour + 32

= 92 minutes

The total time it would take Steve to reach Coventry from Birmingham would be:

= Time to Coventry + Time spent walking from house + Time spent walking in Coventry

= 92 minutes + 9 + 12

= 113 minutes

The time Steve should leave his house at the latest is:

= 10 am - 113 minutes

= 08 07 hours

However, he would miss the 08 35 bus if he did this so he needs to leave in time for the 08 05 bus which is:

= 08 05 - 9 minutes walking

= 07 56 hours

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Answer:

16

Step-by-step explanation:

Call the 3n+3 angle x. Call the 2n+7 angle y. The right angle, x, and y all lie in a straight line, meaning that the three angles added together equal 180. Adding, 5n + 100=180, so n=16.

Answer:

yes

no

yes

no

no

Step-by-step explanation:

An integer is a positive or negative whole number or zero.

Examples of integers:

-1000, 993, 12, -19, 1000000, -79, 0, 1, 221

Examples of numbers that are not integers:

-5/4, -223.25, 1000.1, 45.2, 1000000.45, 32/7

Is 12 a integer   yes

and is 55.3 a integer   no

and is 18 over 2 a integer = 9, so yes

and is -260.43 a integer   no

and is 12 over 17 a integer =0.70588..., so no

Answer:

he is incorrect because Jackson also has 4 whole bags because 13/3 is a mixed number therefore jackson really has 4 13/3 or 4 1/3 which would be the amount as Fraud

Step-by-step explanation: