Hector designs the piece of jewelry shown below. All lengths are marked in centimeters. What is the total area of the piece of jewelry?

A.30 square centimeters

B.39 square centimeters

C.27 square centimeters

D.33 square centimeters

Answer:

D

Step-by-step explanation:

i multiplied the first equation by 60 to eliminate the fractions: 30x - 45y = 11

i multiplied the second equation by 30 to eliminate the fractions: 12x + 5y = 9

I graphed them and (2/3, 1/5) is the intersection of both lines

The solutions for any integer k can be expressed as kπ, where k is an integer.

Adding integer multiples of π allows us to cover all possible solutions to trigonometric equations. In trigonometry, functions like sine, cosine, and tangent are periodic, meaning they repeat themselves after certain intervals.

For instance, the period of sine and cosine functions is 2π. By adding integer multiples of the period (in this case, π), we generate an infinite set of solutions that accounts for all possible values of the trigonometric functions.

These solutions form a continuous sequence of values that repeats periodically. Hence, the expression kπ, where k represents any integer, encompasses the complete range of solutions.

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given

Find

Product

Explanation

here , we use law of exponents

so ,

Final Answer

Product =

For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.

Given solution to t²y'' - 4ty' + 6y = 0 is

y₁(t) = t²

Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,

y₂ = vt²

y₂' = 2vt + t²v'

y₂'' = 2v + 2tv' + 2tv' + t²v''

y₂'' = 2v + 4tv' + t²v''

Substituting this

t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0

t⁴v'' = 0

v'' = 0

v' = c, c is a constant

v = ct

Therefore, y₂(t) = ct×t²

y₂ (t) = ct³

Therefore general solution will be y(t) = c₁t² + c₂t³

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The estimated probability that of the next 100 speeding summonses issued, there will be at least 90 convictions is about 0.9997 or 99.97%.

The conviction rate for speeding in the county is 85%, it means that out of every 100 speeding summonses issued, 85 are likely to result in convictions. Therefore, we can assume that the probability of a conviction in any given case is 0.85 or 85%.

To estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions, we can use the binomial distribution formula. Let X be the number of convictions out of the 100 summonses. Then,

P(X ≥ 90) = 1 - P(X < 90)
           = 1 - Σ P(X = i) for i = 0 to 89

where Σ denotes the sum from i = 0 to 89.

Using the binomial distribution formula, we can calculate the probability of getting exactly i convictions out of 100 summonses as:

P(X = i) = (100 choose i) * 0.85^i * 0.15^(100-i)

where (100 choose i) denotes the binomial coefficient, which represents the number of ways to choose i items out of 100.

Plugging this formula into the above equation and using a calculator or statistical software, we get:

P(X ≥ 90) = 1 - Σ P(X = i) for i = 0 to 89
           = 1 - 0.0003 (approx.)
           = 0.9997 (approx.)

Therefore, the estimated probability that of the next 100 speeding summonses issued, there will be at least 90 convictions is about 0.9997 or 99.97%. This suggests that it is highly likely that at least 90 out of 100 speeding summonses will result in convictions, given the high conviction rate of 85% in the county.

To estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions, we'll use the binomial probability formula:

P(X ≥ 90) = Σ [C(n, k) * p^k * (1-p)^(n-k)]

Here, n = 100 (number of summonses), p = 0.85 (conviction rate for speeding), and k represents the number of successful convictions (90 to 100).

Step 1: Calculate the individual probabilities for k = 90 to 100:
For each value of k from 90 to 100, compute the binomial probability using the formula. C(n, k) represents the number of combinations of choosing k convictions from n summonses.

Step 2: Sum the individual probabilities:
Add up the probabilities calculated in Step 1 to find the total probability of having at least 90 convictions out of 100 speeding summonses.

By following these steps, you can estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions.

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Total 1,512,000 "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

In the given question, we have to find how many "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

The given word is INQUISITIVE.

The total alphabets in the word INQUISITIVE is 11.

Let us first count the words without U and then insert U wherever applicable.

Now without U we have total 10 alphabets and the alphabet I is repeated by 4 times.

So permutations is 10!/4! = 151,200

Now we need to put U, we can see its 11 alphabets but U should not follow Q so it becomes 10 alphabets.

Hence, Total number of words = 151,200*10

Total number of words = 1,512,000

Hence, 1,512,000 "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

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Answer:

A high 3P% indicates that the player is an accurate shooter from the three-point line, making them a scoring threat and potentially creating spacing on the floor for their team.

Step-by-step explanation:

The answer is two base cases, using induction.

What is induction ?

Weak induction is when an inductive mathematical proof holds true for all integers in a set of countable proofs. Natural numbers typically use this. The base step and inductive step are used to prove a set, making it the simplest type of mathematical induction.

Two examples make up an induction proof. Without requiring any prior knowledge of other examples, the first, or base case, establishes the claim for n = 0. The induction process, which is used in the second case, demonstrates that if the assertion is true for any particular scenario where n = k, it must also be true for the subsequent case where n = k + 1.

If a statement true  for n= k, accordily to induction it have to hold good for n = k+1,

Hence, base cases does a proof by the weak form of the principle of mathematical induction requires 2 bases.

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All functions are relations, but not all relations are functions. A function is a relation that for each input, there is only one output.

Answer: a) 19 degree

b) 71degree

Step-by-step explanation:

Answer:

Last Option is correct

Step-by-step explanation:

\(f(x) = 2x - 10\)

\(y=2x−10\)

\(x=2y−10\)

\(2y−10=x\)

\(2y=x+10\)

\(y = \frac{1}{2} x + 5\)

\(h(x) = \frac{1}{2} x + 5\)

Answer:

The answer is......

COS A

The average rate of change for the interval from x = 7 to x = 8 will be 15. Then the correct option is D.

We have,

Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:

Average rate = (y₂ - y₁) / (x₂ - x₁)

The quadratic equation with the vertex is given as

y = (x -  0)² - 1

y = x² - 1

Then the average rate of change for the interval from x = 7 to x = 8 will be

Average rate = [y(8) - y(7)] / (8 -7)

Then we have

Average rate = (64 -1 - 49 + 1) / 1

Average rate = 15

Thus, the correct option is D.

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a) The present value of $25,000 due 9 periods from now, discounted at 10%, is approximately $10,593.22.

b) The present value of $25,000 to be received at the end of each of 6 periods, discounted at 9%, is approximately $22,935.35.

(a) Present Value of $25,000 due 9 periods from now, discounted at 10%:

To calculate the present value, we need to discount the future cash flow of $25,000 back to its current value using the given discount rate of 10%. The formula to calculate the present value is:

Present Value = Future Value / (1 + Discount Rate)ⁿ

Where:

Future Value is the amount to be received in the future ($25,000).

Discount Rate is the rate at which we discount the future cash flow (10%).

'n' is the number of periods or years until the future cash flow is received (9 periods in this case).

Let's plug in the values into the formula and calculate the present value:

Present Value = $25,000 / (1 + 0.10)⁹

Calculating the denominator:

(1 + 0.10)⁹ = 1.10⁹ ≈ 2.36

Present Value = $25,000 / 2.36 ≈ $10,593.22

(b) Present Value of $25,000 to be received at the end of each of 6 periods, discounted at 9%:

In this case, we have a cash flow of $25,000 to be received at the end of each of 6 periods, discounted at 9%. Let's calculate the present value:

Present Value = $25,000 / (1 + 0.09)¹ + $25,000 / (1 + 0.09)² + ... + $25,000 / (1 + 0.09)^6

Calculating each discount factor:

(1 + 0.09)¹ ≈ 1.09

(1 + 0.09)² ≈ 1.1881

(1 + 0.09)³ ≈ 1.2950

(1 + 0.09)⁴ ≈ 1.4116

(1 + 0.09)⁵ ≈ 1.5386

(1 + 0.09)⁶ ≈ 1.6765

Plugging in the values and summing them up:

Present Value = $25,000 / 1.09 + $25,000 / 1.1881 + $25,000 / 1.2950 + $25,000 / 1.4116 + $25,000 / 1.5386 + $25,000 / 1.6765

Present Value ≈ $22,935.35

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Answer:

-480

Step-by-step explanation:

(-5)(16)(-3)(-2) =

= (-80)(-3)(-2)

= (240)(-2)

= -480

Answer:

A ratio is basically how much of one thing there is compared to another thing. They can be showed using a colon like "3:1" or using the word "to" like "3 to 1" or lastly, they can also be shown as a fraction "3/1".

2 examples:

2:5

4 to 3

5/6

Answer:

muy bien ami si me funciono la pregunta

Answer:

eight and seventeen hundredths

Step-by-step explanation:

Answer:

Rational

Step-by-step explanation:

8.27 is rational

Answer:

Rational

Step-by-step explanation:

A rational number is a number with a decimal that doesn't go on forever.

An irrational number is a number with a decimal that goes on forever.

Since the decimal in 8.27 doesn't go on forever, it is rational.

Best of Luck!

The equivalent expression for the new price of the item is 0.57b. With b be the original price of the item.

The original price of the item is represented by "b". Paul received a coupon for "43 percent" off one item at a clothing store. This means that the new price of the item will be the "original price" minus the discount. The discount is calculated by multiplying the original price by the percentage discount.
So, the discount is:
43 percent of b = 0.43 * b

The new price of the item is the original price minus the discount:
b - 0.43 * b = b - 0.43b

This expression can be simplified by combining the like terms. The like terms in this expression are b and -0.43b.
To combine like terms, we add the coefficients of the like terms:
1b + (-0.43)b = 0.57b

So, the equivalent expression for the new price of the item is:
0.57b

This means that the new price of the item is 57% of the original price. Therefore, the equivalent expression for the new price of the item is 0.57b.

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Answer:

-10

Step-by-step explanation:

y-5y+2

=3-5 x 3+2

Using the rule of BODMAS

=3-15+2

=3-13

= -10

The value of the number √227 to the nearest integer is 15.

What is Rounding number?

To making a number simpler but keeping its value close to what it was, is called Rounding.

Given that;

The number is,

⇒ √227

Now,

Solve the number to the nearest integer as;

The value of the number is,

⇒ √227 = 15.0665

After rounded to the nearest integers, we get;

⇒ √227 = 15

Thus, The value of the number √227 to the nearest integer is 15.

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Answer:

Width x length

Step-by-step explanation:

Find the width or how wide it is

Then find the length or how long it is

multiply those

The graph of the function y = \(x^{2}\) does not intersect the given horizontal line y = -9.

What is a function?

A mathematical phrase, rule, or law that describes the relationship between an independent variable and a dependent variable is known as a function.

We are given a function as y = \(x^{2}\) and the horizontal line as y = -9.

We know that the function will lie in the first and the second quadrant as y will always be positive.

But, the line will lie in the third and the fourth quadrant as y is negative.

So, they will never intersect.

A graph depicting the relationship has been attached below.

Hence, the graph of the function y = \(x^{2}\) does not intersect the given horizontal line y = -9.

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Frank deposited $734 in the bank and let it sit for nine months, if the simple interest rate is 12%, the new balance after earning interest will be $1527.92.

To calculate the interest earned by Frank, we can use the simple interest formula:

Interest = Principal x Rate x Time

Given:

Principal (P) = $734

Rate (R) = 12% = 0.12

Time (T) = 9 months

Interest = $734 x 0.12 x 9 months

Interest = $793.92

Therefore, Frank will earn $793.92 in interest.

To find the new balance, we add the interest to the principal:

New Balance = Principal + Interest

New Balance = $734 + $793.92

New Balance = $1527.92

Therefore, the new balance after earning interest will be $1527.92.

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Answer:

t = -0.304 and 0.62 secs

the ball was thrown 0.62 secs later

Step-by-step explanation:

Given the quadratic equation

0=3+5t−16t^2

We are to factorize it using the formula;

The formula is expressed as

t = -b±√b²-4ac/2a

From the given expression

a = -16 b = 5 c = 3

Substitute

t = -5 ±√5²-4(-16)(3)/2(-16)

t = -5 ±√25+192/-32

t=  -5 ±√217/-32

t= -5 ±14.73/-32

t = -5+14.73/-32 and t = -5-14.73/-32

t = -9.73/32 and -19.73/-32

t = -0.304 and 0.62 secs

Hence the ball was thrown 0.62 secs later

The answer to Math.round(3.6) is D. 4.0. The Math.round() method is used to round a number to the nearest integer.

When we apply Math.round(3.6), it rounds off 3.6 to the nearest integer which is 4.

This method uses the following rules to round the given number:

1. If the fractional part of the number is less than 0.5, the number is rounded down to the nearest integer.

2. If the fractional part of the number is greater than or equal to 0.5, the number is rounded up to the nearest integer.

In the given question, the number 3.6 has a fractional part of 0.6 which is greater than or equal to 0.5, so it is rounded up to the nearest integer which is 4. Therefore, the correct answer to Math.round(3.6) is D. 4.0.

It is important to note that the Math.round() method only rounds off to the nearest integer and not to a specific number of decimal places.

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I may utilize the Cp Criterion, AICp, and SBCp to aid in choosing the optimal model. All of them impose sanctions for introducing predictions.

What is subset regression model?

Best subsets regression is a model-building regression analysis that is exploratory. It compares every model that might be built using a specified set of predictors.

There are Cp Criterion, AICp and SBCp that I can use to help select the best model. They all place penalties for adding predictors.

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