Find the radius of this sphere. Then, calculate the volume of a sphere.

Answer:

The central angle of the sector is 0.5 radian

Step-by-step explanation:

given;

radius of the circle, r = 80 mi

area of the sector, A = 1600 mi²

Area of sector is given by;

A = ¹/₂r²θ

where;

θ is the central angle (in radians) of the sector

\(\theta = \frac{2A}{r^2}\\\\\theta = \frac{2*1600}{80^2}\\\\ \theta = 0.5 \ radian\)

Therefore, the central angle of the sector is 0.5 radian

The central angle (in radians) of the sector is 28.66 degrees

The formula for calculating the area of a sector is expressed as:

\(A = \theta/360 \times \pi r^2\)

Given the following parameters

radius r = 80mi

Area of sector A = 1600mi²

Substitute the given parameters into the formula

1600 = Ф/360 * (3.14)(80)²

1600 * 360 = 20,096Ф

Ф = 576000/20,096

Ф =28.66 degrees

Hence the central angle (in radians) of the sector is 28.66 degrees

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Answer: 7.9

Step-by-step explanation:

\(P=2000, r=0.09, n=2\\\\4000=2000\left(1+\frac{0.09}{2} \right)^{2t}\\\\4000=2000(1.045)^{2t}\\\\2=1.045^{2t}\\\\\log_{1.045} 2=2t\\\\t=\frac{\log_{1.045} 2}{2}\\\\t \approx 7.9\)

Answer:

Area = 18

Step-by-step explanation:

Trapezoid formula is Area = (a + b) * h/2

Area = 5 + 7 * 3/2

Area  = 18

Answer:

A

Step-by-step explanation:

Two angles are complementary if their angles add up to 90

let x= angle b

35+x=90

x=55

Answer:

If the entire mass of the Milky Way was due to gas and stars, how would you expect the rotational speed of a star near the edge of the galaxy to compare to the rotational speed of a star near the center?

Step-by-step explanation:

Answer:

16 this is the real answer

Step-by-step explanation:

Hope this help

The Sample standard deviation would be 3.56 and the confidence interval is between72.74 to 78.60.

What is a confidence interval?

A confidence interval is a range of values that is estimated to contain the true value of a population parameter with a certain level of confidence. It is a measure of the uncertainty associated with an estimate of a population parameter, such as the mean, the proportion, or the variance.

a)

sample mean = 75.67

sample std. dev. = 3.56

b)

Given CI level is 90%, hence α = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 2.015

\(CI = (xbar - tc * s/\sqrt{n} , xbar + tc * s/\sqrt{n})\\\\CI = (75.67 - 2.015 * 3.56/\sqrt{6} , 75.67 + 2.015 * 3.56/\sqrt{6})\\\\\CI = (72.74 , 78.60)\)

Hence the Sample standard deviation would be 3.56 and the confidence interval is between72.74 to 78.60.

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The profit for 24 sales is $64.

The profit for 24 sales, we first need to calculate the revenue and then determine the profit based on the given information.

The revenue function is given as f(x) = 5x, where x represents the number of hamburgers sold.

To find the revenue for 24 sales, we substitute x = 24 into the revenue function:

Revenue = f(24)

= 5 × 24

= 120 dollars

Now, let's calculate the profit.

The profit is $20 less than 70% of the revenue.

We can express this mathematically as:

Profit = 0.7 × Revenue - $20

Substituting the value of Revenue we calculated earlier:

Profit = 0.7 × 120 - $20

= 84 - $20

= $64

We must first compute the revenue for 24 sales before calculating the profit based on the available data.

The revenue function is denoted by the formula f(x) = 5x, where x is the quantity of hamburgers sold.

We add x = 24 to the revenue function to get the revenue for 24 sales:

f(24) = 5 x 24 = 120 dollars is the revenue.

Let's now determine the profit.

The profit is $20 below the revenue's 70%.

This may be written mathematically as:

Revenue - $20 x Profit = 0.7

Substituting the earlier determined figure of Revenue:

Earnings = 0.7 x 120 - $20 = 84 - $20 = $64

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The type of association shown between the variables in this problem is given as follows:

Positive association.

There can either be a positive association between variables or a negative association between variables, as follows:

In the context of this problem, we have that an the homework hours increase, so does the GPA, hence there is a positive association between the variables.

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Answer:

$3.25

Step-by-step explanation:

In an ordinary deck of cards, we will notice that there are 52 cards.

However, we have 4 suits and 13 cards in each one making a total of 52, right?.

So, the probability that a person draws two cards and they will be of the same   suit is:

\(P(X) =\dfrac{ \bigg (^4_1 \bigg) \times \bigg ( ^{13}_{2}\bigg) }{ \bigg ( ^{52}_{2} \bigg)}\)

\(P(X) =\dfrac{ \dfrac{4!}{1!(4-1)!} \times \dfrac{13!}{2!(13-2)!} }{ \dfrac{52!}{2!(52-2)!} }\)

\(P(X) =\dfrac{4}{17}\)

Given that; A person bets 1 dollar to b dollars;

To make the bet fair is;

\(\dfrac{4}{17}b - \dfrac{13}{17}(1) = 0\)

\(= \dfrac{4}{17}b = \dfrac{13}{17}\)

multiply both sides by 17

4b = 13

b = 13/4

b = 3.25

Therefore, to make the fair, the value of b need to be $3.25

Using the expected value formular, the value of b such that the game is fair is 3.25

Total number of cards in a deck = 52

Number of cards per suit = 13

Number of suits = 4

Selection without replacement :

(C and C) or (H and H) or (S and S) or (D and D)

[(13/52 × 12/51) + (13/52 × 12/51) + (13/52 × 12/51) + (13/52 × 12/51)] = 0.2353

Probability of not selecting a card of the same suit :

For game to be fair :

X : ______ b _____ - 1

P(X): __ 0.2353__ 0.7647

[(0.2353b + (-1 × 0.7647)] = 0

0.2353b - 0.7647 = 0

0.2353b = 0.7647

Divide both sides by 0.2353

b = 0.7647 / 0.2353

b = 3.249

b = 3.25

Hence, the value of b is 3.25

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The transfοrmatiοn f(x)↦f(-x) , the graph οf f(x) reflects it acrοss the y-axis

Optiοn B

In mathematics, a functiοn is a rule that maps each element in οne set, called the dοmain, tο exactly οne element in anοther set, called the range. A functiοn can alsο be thοught οf as a set οf οrdered pairs, where the first element in each pair belοngs tο the dοmain, and the secοnd element belοngs tο the range.

Functiοns are cοmmοnly denοted by symbοls such as f(x), g(x), οr h(x), where x represents the input variable οr independent variable, and the functiοn prοduces an οutput value οr dependent variable, which is denοted by f(x), g(x), οr h(x), respectively.

Functiοns are impοrtant in many areas οf mathematics, science, and engineering, as they prοvide a way tο describe relatiοnships between variables and make predictiοns abοut the behaviοr οf systems. They are used tο mοdel physical phenοmena, analyze data, and sοlve equatiοns, amοng οther applicatiοns.

Given :

The transfοrmatiοn f(x) -> f(-x)

Fοr example , lets take a pοint οn f(x)

Let (x,y) be a pοint οn f(x)

given f(x)- > f(-x) it means x is replaced by -x

f(x) is nοt multiplied with -1  sο y value remains the same

(x,y) be a pοint οn f(x) .

After transfοrmatiοn f(x)-> f(-x) , the pοint (x,y) ---> (-x,y)

When x is multiplied by -1 then there is a reflectiοn acrοss the y axis

Sο, the graph οf f(x) reflects it acrοss the y axis.

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Complete Question:

What does the transformation f(x)↦f(-x) do to the graph of f(x)?

a) stretches it horizontally

b) reflects it across the y-axis

c) shrinks it horizontally

d) reflects it across the x-axis

e) Submit

The correct expression is  \($(150 \cdot 1.15)^7$\) (Choice A).

The problem states that the painting's value increases by a factor of 1.15 each year. This means that the value at the end of each year is 1.15 times the value at the beginning of the year. Therefore, after one year, the value of the painting is\($150 \cdot 1.15 = 172.50$\).

To find the value after 7 years, we need to multiply the value of the painting each year by 1.15 a total of 7 times. This can be represented mathematically as \($(150 \cdot 1.15)^7$\). This expression is equal to the starting value of the painting, 150, multiplied by 1.15$ raised to the 7th power, which represents the 7 years of appreciation.

If we were to choose expression B, it would give an incorrect result because it uses a value of 1.1 instead of 1.15 to represent the yearly increase in value.

Expressions C and D are also incorrect because they are not taking into account the compounding effect of the yearly increase. Expression C adds the initial value and the total years together, and expression D adds the initial value to the yearly increase multiplied by 7, neither of which correctly reflects the exponential growth of the painting's value.

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The product of (1 + 3i)(1 – 3i) is a real number.

Complex Numbers in Math. Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

We know that,

\(i^{2} = -1\)

case A) \((1+3i)(6i)\)

applying distributive property

\(6i+18i^{2}\)

\(6i-18\)

This is not a real number.

case B) (1+3i) (2-3i)

applying distributive property

\(2-3i+6i-9i^{2}\)

\(11+3i\)

This is also not a real number.

case C) \((1+3i) (1-3i)\)

applying difference of square

\(1-9i^{2}\)

1+9 = 10

This is a real number.

case D) \((1+3i) (3i)\)

applying distributive property

\(3i+9i^{2}\)

\(3i-9\)

This is not a real number.

Hence, The product of (1 + 3i)(1 – 3i) is a real number

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Using the lowest common factor of the shuttles' run times, they will depart again for the campus simultaneously at 10.25 A.M.

We can use the lowest common factor (LCM) of their run time to determine when they depart again for the campus.

The lowest common factor of 30 and 20 is 60 because both 30 and 20 can divide 60 evenly without a remainder, showing that it takes 60 minutes for the two shuttles to depart for the campus at the same time.

We can conclude that every 60 minutes or hour, the two shuttles simultaneously depart for the campus.  Every hour, the shuttle departing from Ball Hall completes 2 runs, while the shuttle departing from Lot A completes 3 runs.

Thus, using the lowest common factor, the next time both shuttles will depart for the campus at the same time is 10:25 A.M.

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The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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To answer this question we will use the following formula for compounded monthly interest:

where A₀ is the initial amount, r is the annual interest as a decimal number and 12 is the number of years.

Notice that:

Therefore, substituting t=42, r=0.02, and A₀=120000 we get:

Simplifying the above result we get:

Answer: $277,769.75.

Answer:

c=-9.75

Step-by-step explanation:

Answer:

c=-9.75

Step-by-step explanation:

-1.6(2c+12)=12

-3.2c - 19.2 = 12 <= using distributive property

-3.2c = 31.2

c = -9.75

The function can be defined as  price = 6x

It will cost $150 to buy 25 reams of paper.

The domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.

The range of the function is all non-negative real numbers, since the price cannot be negative.

Fir 25 items, price = 6(25) = $150

It will cost $150 to buy 25 reams of paper.

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Answer:

Diameter is Line D and Radius is Line R

Step-by-step explanation:

I don't really know how to explain it because I've known this for years now lol.

Answer:

the right half

Step-by-step explanation:

We know that cosine is a pair function.

This means that:

Cos(a) = Cos( -a)

We also know that:

Cos(pi) = 0

then:

Cos(-pi) = 0

pi and -pi are located in the y-axis, so from this we can know that the cosine function will be always positive on the right side, or in the left side, we can discard the other two options.

Now, we also know that cos(0) = 1.

And:

-pi < 0 < pi

So the two zeros are at the y-axis, and we know that cos(0) is positive (the angle 0 would be on the positive side of the x-axis, at the right), then all the right side must be positive.

Then the correct option is:

the right half

Answer:

C - The right half

Step-by-step explanation:

Just took the quiz on edge

Using the simplification, Manuel buy 15 stamps of 25 cents and 5 stamps of 30 cent.

In the given question,

Manuel wishes to purchase 25 cent and 30 cent stamps.

He decides to buy 10 fewer 30 cent stamps.

We have to find how many of each can he buy for no more than $19.00.

Let he buy x stamps of 25 cent.

He want to buy 10 fewer 30 cent stamps.

So he buy x−10 stamps of 30 cent.

But he have to buy total stamps of $19.

So the equation is

x+x−10 = 19

Simplifying

2x−10=19

Add 10 on both side

2x−10+10=19+10

2x=29

Divide by 2 on both side

2/2 x =29/2

x=14.5

x≈15

Hence, he buy 15 stamps of 25 cent.

Now finding the number of 30 cent.

he buy x−10 stamps of 30 cent.

So 15−10=5.

So he buy 5 stamps of 30 cent.

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Answer:

9

Step-by-step explanation:

12ⁿ⁻⁵ = 12⁴

n - 5 = 4

n = 9

Answer:

17

Step-by-step explanation:

-5 is 17 points away from 12.

\(a*b\) must contain all of the prime factors of n and the exponent of each factor must be less than or equal to the exponent of n. This means that a*b divides n.

Let n be an integer and a, b be relatively prime integers, each of which divides n. This means that a and b have no common factors other than 1. According to the Fundamental Theorem of Arithmetic, the prime factorization of n can be written as n = p1^k1 * p2^k2 * ... * pn^kn. Since a and b divide n, each of their prime factorizations must contain all of the prime factors of n, and the exponents must be less than or equal to the exponents of n. Therefore, a*b must contain all of the prime factors of n and the exponent of each factor must be less than or equal to the exponent of n. This means that a*b divides n.

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According to the information, it can be inferred that the total matches that would be played in total are 160,461.

A combination is a term to refer to an arrangement of elements in no particular order. For example:

When we put together a sandwich with salami, ham and turkey. The order in which the deli meats are placed does not matter as long as they are in a sandwich. There is only one way to stack the meat on the sandwich when the order doesn't matter.

To calculate how many matches will be played in total we have to perform the following procedure:

\(= ^{567} C_{2} \\= \frac{(567)!}{2!565!} \\= \frac{567 * 566 * (565)!}{2 * (565)!} \\= 567 * 283\\= 160,461\\\\\)

As we can see after the combination, the number of games that would be played in this tournament would be 160,461.

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The interest accumulated in the account after the first and second year indicates;

The amount Miguel originally put into the bank is about $728

An interest is a reward or cost of borrowing or lending money.

Let P represent the amount Miguel deposited in the bank, and let r represent the interest rate in percentage, therefore, we get;

The amount in the account after the first year is; P + r·p = P·(1 + r)

P·(1 + r) = $757.12...(1)

The amount in the account after the second year can be obtained using the following formula;

Principal at the start of the second year = P·(1 + r)

Therefore; Amount = P·(1 + r)  + P·(1 + r) × r = P·(1 + r) × (1 + r) = P·(1 + r)²

P·(1 + r)² = $787.40...(2)

Equation (1) indicates that we get; (1 + r) = 757.12/P

Therefore; P·(1 + r)² = P·(757.12/P)² = 787.40

757.12²/P = 787.40

P = 757.12²/787.40 ≈ 728

The amount Miguel deposited in the bank is about $728

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Answer:

a. k = 8

b. k = 95

c. k = 13.95

d. k = 40

Step-by-step explanation:

Answer:

a. K= \(\frac{8}{1}\)  b. K= \(\frac{95}{1}\) c. K= \(\frac{13.95}{1}\) d. \(\frac{40}{1}\)

Step-by-step explanation:

This is the constant of proportionality. The equation is  \(\frac{y}{x}\) which is the earliest form of a linear equation.

Answer:

Yes

Step-by-step explanation:

Integers are whole numbers that are positive and negative. Since -5 is an integer then is also a rational number because all integers are rational numbers

9514 1404 393

Answer:

  (a)  y = −50x + 250

Step-by-step explanation:

In case you don't realize that the graph starts at 250 and decreases by 50 for each increase of 1 in x, you can see if any of the equations match the given points. The only one that does is the first one:

  y = -50x +250

Answer:

(a)  y = −50x + 250

Step-by-step explanation:

The simplified equation is (π2 / 2) * ∫[0, ∞] (x(2x-1) * e(-x) / (Γ(x) * Γ(1 - x)) DX

a. To prove B(x+1, y) = x * B(x, y), proceed as follows.

Start with B(x+1, y) = [(x+1)! * y!] / ((x+y+2)!) (using the definition of B(x, y)).

Rewrite 1 / (x+1) to (x+y+2 - (y+1)) / (x+y+2) .

Using the formula above, express B(x+1, y) as (x+y+2) / (x+y+2) * [(x+1)! to rewrite. * y!] / ((x+y+2)!) - (y+1) / (x+y+2) * [(x+1)! * y!] / ((x+y+2) !).

Simplify the formula to (x+y+2) / (x+y+2) * B(x, y) - (y+1) / (x+y+2) * B(x, y) increase.

Simplify further to B(x, y) - (y+1) / (x+y+2) * B(x, y).

Note that B(x, y) can be expressed as (x / (x+y+1)) * B(x, y) .

Substitute this formula in the previous step to get,

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y).

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y)

= x * B(x, y)

You have now proved B(x+1, y) = x * B(x, y).

b. We wish to prove the identity Γ(2x) = ((2sin(πx))) * Γ(x) * Γ(x + 1/2).

Integrate ∫[0, ∞] (x(2x-1) * Start with dx.

Evaluating this integral using the permutation u = du is obtained.

Simplify the integral to (1/2) * Γ(x + 1/2).

Express sin(πx) as π / (Γ(x) * Γ(1 - x)).

Let the original integral be π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) * e(-x) * (1/sin( πx) Rewrite.)) DX.

Substituting the equations,

The integral, π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) *

We get * (π / (Γ(x) * Γ(1 - x)))) dx.

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