Use the binomial expansion of (p+q)ⁿ to calculate each binomial distribution.

n=6, p=0.9

The Fourier series coefficients are not even, as a0 and b1 are non-zero.

The given signal x(t) = -2.5 + 2sin(2.8t) - 4cos(2.8t) + 1.2cos(4.9t) is not periodic. Therefore, it does not have a fundamental period. The fundamental frequency, which corresponds to the least common multiple of all the given frequencies, is ω = 0.1π rad/s.

The Fourier series coefficients for the signal are a0 = 0, an = -1.55cos(0.1π) + 0.4sin(0.1π) for n = 1, and bn = 0 for n = 1. The associated harmonic frequencies are f0 = 0.05 Hz and f1 = 0.0159 Hz.

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The remote interior angles of ∠1 are ∠2 and ∠6.

Corresponding angles in a triangle are those angles which are contained by a congruent pair of sides of two similar (or congruent) triangles.

The remote interior angles of ∠1 is determined by applying the principle of corresponding angles as shown below;

∠1 = ∠2 ( vertical opposite angles are equal )

∠1 = 180 - ∠5 ( corresponding angles  are equal )

180 - ∠5  = ∠ 6 ( vertical opposite angles are equal )

So we can conclude that, ∠1 = ∠6.

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Answer:

56 drinks

Step-by-step explanation:

7 drinks = 1 coconut

x drinks = 8 coconut

cross multiply

x drinks = 7 × 8

x drinks = 56

so you can make 56 drinks with 8 coconuts

Answer:

One coconut = 7 drinks

Eight coconuts = X drinks

So set up the equation;

________   _________ = _________, solve for x:-

7/1 = x/8

*8     *8

56 = x, 56 drinks can be made with 8 coconuts.

The treasure hunter found an object at a depth greater than 1,000 feet below sea level.

When referring to elevation below sea level, negative values are used. Sea level is considered to be 0 feet, and any point below that is represented by negative values. In this case, the treasure hunter found an object at a depth greater than 1,000 feet below sea level, which means the elevation can be represented as -1,000 feet or any value below that. The negative sign indicates that the object is situated below sea level. The exact value of the elevation will depend on the specific measurement taken by the treasure hunter, but it is certain that the object was found at a significant depth beneath the surface of the sea.

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Answer:

if you round, its 99. if you ignore the decimal, its 98

Step-by-step explanation:

2/3 of 148 is 98.66

Answer:

Step-by-step explanation:

The number of years between 1996 to 2002 will be:

= 2002 - 1996

= 6 years

The relationship relating the value of the card y in dollars and the number of years x the player has been in retirement can be expressed as an equation in the form of:

y = 5.71 + 1.98x

where x = 6 years

y = 5.71 + 1.98(6)

y = 5.71 + 11.88

y = $17.59

The value of the card in 2002 ​is $17.59.

The relationship between x and y isn't proportional in this case.

Exercise needs to be consistent and done at regular times. The body can adjust more effectively and swiftly when there is consistency. Exercise should ideally be performed 3-5 times per week.

Exercise is any physical activity done to increase one's physical or mental fitness.

Exercise and physical activity not only aid to enhance physical health but also help to promote mental health.

A healthy mind follows from a healthy body.

By lowering body weight, frequent physical activity lowers the risk of developing serious conditions like heart attack, cardiovascular disease, diabetes, and high blood pressure. Regular exercise revitalizes the body and the mind.

Additionally, it raises energy levels, mood, and sleep quality.

Hence, Exercise must be performed consistently and at regular intervals. When there is consistency, the body can adjust more quickly and efficiently. The ideal number of times to exercise per week is three to five.

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∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel.

A pair of angles formed on each side of the transversal when it interacts with two parallel lines are known as consecutive angles. The angles in the same region (either interior or exterior) on each of the parallel lines form consecutive angles pairs and are supplementary.

Given that, in a race, all members of a rowing team should keep the oars parallel to produce maximum speed, and m∠1 = 6x + 18 and

m∠2 = 9x+12, and x = 10.

Putting the value of x, we get,

m∠1 = 6x + 18 = 6*10 + 18 = 78°

m∠2 = 9x+12 = 9*10 + 12 = 102°

m∠1 + m∠2 = 180°

Therefore, ∠1 and ∠2 are consecutive angles pairs.

We can prove that oars are parallel by converse of consecutive angles theorem.

Hence, ∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel

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Answer:

I IM NOT 100 PERCENT BUT IT MIGHT BE A

Step-by-step explanation:

i think it might be B

because first, u do slope formula y2-y1 and x2-x1 so 1-(-6) and 10-1

then u get 7/14 which is 2 and then plug in the numbers like -4=2(-6)+b

and then you add 12 to -4 and get 8=b I think after this u divide and get 4

Thus, the appropriate measure of variability found for the given data is 10.

The difference here between maximum and smallest values in a data set is known as the range. Utilizing the exact same units as the data, it measures variability. More variability is shown by larger values.

Given length of ribbons:

3, 6, 9, 11, 12, 13

Minimum value = 3

Maximum value = 13

Actually, the range, which is determined by deducting the lowest value from the greatest value in the dataset, would be the proper measure of variability for this data.

Range = Maximum value - Minimum value

Range = 13 - 3

Range = 10

Thus, the appropriate measure of variability found for the given data is 10.

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The intensity in the interference pattern of n identical slits is given by the formula:

I = I₀ [sin(nϕ/2) sin(ϕ/2)]²

Here's a step-by-step explanation of the terms in this formula:

1. I is the intensity at a point in the interference pattern.
2. I₀ is the maximum intensity at the center of the pattern (i.e., when ϕ = 0).
3. n is the number of identical slits.
4. ϕ is the phase difference between the waves from adjacent slits at the point being considered.

To find the intensity at a specific point in the interference pattern, you need to know the values of I₀, n, and ϕ. Then, you can simply plug these values into the formula and calculate the intensity I.

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In the figure of parallelogram attached the angle ABC is 145 degrees

Opposite angles of a parallelogram are equal (or congruent). Consecutive angles are supplementary angles to each other (that means they add up to 180 degrees)

hence < DAB + < ABC = 180 (consecutive angles)

35 + < ABC = 180

< ABC = 180 - 35

< ABC = 145 degrees

We can therefore say that angle ABC is 145 degrees.

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Answer:

5

Step-by-step explanation:

Answer:

10,260 in³

Step-by-step explanation:

Please find attached an image of the chest

The ice chest is shaped like a rectangle. Thus the formula for the volume of a cuboid can be used to determine the volume of the chest

volume of a cuboid = length x width x height

18 in x 19 in x 30 in = 10,260 in³

Answer: 30 fish

Step-by-step explanation:

A tank measuring 5 feet by 3 feet by 3 feet has a volume of 5*3*3 =45 cubic feet.

If there are 45 cubic feet of water in this tank, and each fish requires 1.5 cubic feet of water, the number of fish that can fit in the tank is 45/1.5 = 30.

Answer: -3

Step-by-step explanation: Hope I helped! :D

Answer:

\(A = 68.75 \text{ square inches}\)

Step-by-step explanation:

First, we need to identify the trapezoid's dimensions:

base 1 = 16

base 2 = 11.5

height = 5

Then, we can plug these values into the trapezoid area formula:

\(A = \dfrac{b_1+b_2}{2} \cdot h\)

\(A = \dfrac{16 + 11.5}{2} \cdot 5\)

\(A = \dfrac{27.5}{2} \cdot 5\)

\(A = \dfrac{137.5}{2}\)

\(\boxed{A = 68.75 \text{ square inches}}\)

The simple interest rate that is equivalent to the discount rate can be determined by multiplying the discount rate by (Time / 365).

i) To determine the maker of the note, we need to identify who issued the promissory note. Unfortunately, the information provided does not specify the name of the maker or issuer of the note. Without additional information, it is not possible to determine the maker of the note. ii) To calculate the face value of the note, we can use the formula for the maturity value of a promissory note: Maturity Value = Face Value + (Face Value * Interest Rate * Time). Given that the maturity value is RM7,266 and the note matured on 11 June 2022 (assuming a 365-day year), and Zafran held the note for 52 days, we can calculate the face value: 7,266 = Face Value + (Face Value * 0.09 * (52/365)). Solving this equation will give us the face value of the note.

iii) The discount date is the date on which the note was discounted at the bank. From the information provided, we know that Zafran discounted the note after holding it for 52 days. Therefore, the discount date would be 52 days after 10 January 2022. iv) The discount rate can be calculated using the formula: Discount Rate = (Maturity Value - Discounted Value) / Maturity Value * (365 / Time). Given that the discounted value is RM7,130.77 and the maturity value is RM7,266, and assuming a 365-day year, we can calculate the discount rate. v) The simple interest rate that is equivalent to the discount rate can be determined by multiplying the discount rate by (Time / 365). This will give us the annualized interest rate that is equivalent to the discount rate.

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Based on the annualized interest from the investments that Jill went into, the amount deposited in savings was $28,363.64 and the amount in the cd was $14,181.82.

Assuming that the amount invested in the cd was x, then the amount invested can be modeled as:

= 5%x

= 0.05x

The amount invested in savings was:

= 2 x 3% x

= 2 x 0.03x

= 0.06x

The amount invested in cd was:

0.06x + 0.05x = 1,560

0.11x = 1,560

x = 1,560 / 0.11

x = $14,181.82

The amount in the savings was:

= 14,181.82 x 2

= $28,363.64

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Answer:

Yes

Step-by-step explanation:

The left part is X and right part is Y

3(6)-4(5)=-2

18-20=-2

-2=-2

So yes

Answer:

yes

Step-by-step explanation:

if you put 3x-4y= -2 in y=mx+b form it is y= 3/4x+1/2 meaning the slope is 3/4 then you put it into y-y1=m(x-x1) form y-5=3/4(x-6) and if you solve it and it is the same as y=3/4x+1/2 then the ordered pair is a solution. when you solve it is y=3/4x+1/2 so (6,5) is a solution

Answer:

y= 3/4x + 1/4

Step-by-step explanation:

The height equal to the given rectangle couldn't be found due to the reason of more information is needed. Therefore the required answer for the question is Option D.

So, the Probability density function is portrayed graphically as a rectangle where   (b-a) is the base and 1/(b-a)  is the required height.

Probability density function refers to the method that helps to define the random variable's probability within a distinct range of values as opposed to taking one value.

then,

the height of the rectangle for a uniform probability distribution should be 1/(b-a)

The height equal to the given rectangle couldn't be found due to the reason of more information is needed. Thus the correct answer is Option D.  

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Answer:

C

Step-by-step explanation:

5 - 1 = 4

5 - 5 = 0

5 - -1 = 6

I hope this helps but the answer most likely is C

Answer:

I think it's letter C ..........

The total interest paid on each loan is different by about $34.75.

To calculate the total value of the loan with different compounding frequencies, we can use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)\)

Where:

A = Total value of the loan (including principal and interest)

P = Principal amount (initial loan)

r = Annual interest rate (as a decimal)

n = Number of times interest is compounded per year

t = Number of years

Part A: Semi-annually compounded interest,

Given:

Principal amount (P) = $20,000

Annual interest rate (r) = 3% = 0.03

Number of times compounded per year (n) = 2 (semi-annually)

Number of years (t) = 10

Using the formula, we can calculate the total value of the loan:

\(A = 20000(1 + 0.03/2)^{(2\times10)\)

\(A = 20000(1.015)^{20\)

A ≈ 20000(1.34812141)

A ≈ $26,962.43

Therefore, the total value of the loan with semi-annually compounded interest is approximately $26,962.43.

Part B: Monthly compounded interest

Given:

Principal amount (P) = $20,000

Annual interest rate (r) = 3% = 0.03

Number of times compounded per year (n) = 12 (monthly)

Number of years (t) = 10

Using the formula, we can calculate the total value of the loan:

\(A = 20000(1 + 0.03/12)^{(12\times10)\)

\(A = 20000(1.0025)^{120\)

A ≈ 20000(1.34985881)

A ≈ $26,997.18

Therefore, the total value of the loan with monthly compounded interest is approximately $26,997.18.

Part C: Difference in total interest accrued =

To find the difference in total interest accrued, we subtract the principal amount from the total value of the loan for each case:

For semi-annually compounded interest:

Total interest accrued = Total value of the loan - Principal amount

Total interest accrued = $26,962.43 - $20,000

Total interest accrued ≈ $6,962.43

For monthly compounded interest:

Total interest accrued = Total value of the loan - Principal amount

Total interest accrued = $26,997.18 - $20,000

Total interest accrued ≈ $6,997.18

The difference between the total interest accrued on each loan is approximately $34.75 ($6,997.18 - $6,962.43).

The loan with monthly compounded interest accrues slightly more interest over the 10-year period compared to the loan with semi-annually compounded interest.

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The factors of 54m³ - 32y³ are 2m³, 3 - 2y, and 9 + 6y + 4y². The expression can be written as 2m³(3 - 2y)(9 + 6y + 4y²) after factoring out the GCF and recognizing the expression inside the parentheses as a difference of cubes.

To factor 54m³ - 32y³, we can start by finding the greatest common factor (GCF) of the two terms. The GCF of 54m³ and 32y³ is 2m³, so we can write:

54m³ - 32y³ = 2m³(27 - 16y³)

Now we have factored out the GCF, and we can further simplify the expression inside the parentheses by recognizing that it is a difference of cubes. Specifically, we can use the formula:

a³ - b³ = (a - b)(a² + ab + b²)

If we let a = 3 and b = 2y, then we have:

27 - 16y³ = (3)³ - (2y)³ = (3 - 2y)(9 + 6y + 4y²)

Putting this back into our original expression, we get:

54m³ - 32y³ = 2m³(27 - 16y³) = 2m³(3 - 2y)(9 + 6y + 4y²)

Therefore, the factors of 54m³ - 32y³ are 2m³, 3 - 2y, and 9 + 6y + 4y².

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The probability of leaving it in any given class is 1/4, the probability of leaving it in the 5th class is 1/4, or\(0.250 (25.0%).\)

The probability that the student left her iClicker device in the 5th class is 0.250 (25.0%). This is because the probability of leaving it in any given class is 1/4, and as she attends 5 different classes,

there is 5/4 or 1.25 chances of her leaving it in the 5th class.

To explain further, the probability of an event can be calculated by dividing the number of ways the event can occur by the total number of possible outcomes. In this case, the event is leaving the iClicker device in the 5th class, and the total number of possible outcomes is 5 (for the 5 classes).

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