What is the volume of the cylinder? Show your work.

Answer: Let's plug in each value for n and compare the results:

a. n = 2

2 x 4/5 = 8/5 which is greater than 4/5.

b. n = 7/6

7/6 x 4/5 = 28/30 which simplifies to 14/15 which is greater than 4/5.

c. n = 5/8

5/8 x 4/5 = 20/40 which simplifies to 1/2 which is less than 4/5.

d. n = 5/4

5/4 x 4/5 = 20/20 which simplifies to 1 which is greater than 4/5.

e. n = 6/6

6/6 x 4/5 = 24/30 which simplifies to 4/5.

Therefore, the answer is (c) 5/8, which shows that Leo is incorrect. In this case, the product is less than 4/5.

Step-by-step explanation:

the perimeter is the sum of the lengths of all outside sides.

at the top is a triangle.

at the bottom is a rectangle.

the triangle looks like an isoceles triangle (both legs are equal), but the given measurement tells us otherwise.

if it were isoceles, the height would split the baseline into 2 equal halves (20/2 = 10ft).

per Pythagoras the 12 ft Hypotenuse would be

Hypotenuse² = 10² + 10² = 100 + 100 = 200

Hypotenuse = sqrt(200) = 14.14213562... and NOT 12 ft.

so, we need to calculate the actual part of the 20ft baseline (again Pythagoras) :

12² = 10² + part²

144 = 100 + part²

44 = part²

part = sqrt(44) = 6.633249581... ft

that means the 2nd part of the baseline is

20 - 6.633249581... = 13.36675042... ft

and we get the second leg of the large triangle again via Pythagoras :

leg² = 10² + 13.36675042...² = 100 + 178.6700168...

leg² = 278.6700168...

leg = sqrt(278.6700168...) = 16.69341238... ft

we need to sum up both legs of the triangle, 2 widths and one length of the rectangle, as the triangle base line and the second length of the rectangle cover each other up, and are not visible to the outside of the combined object.

P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈

≈ 64.69 ft

The formula for the normal approximation to the binomial with a correction for continuity is

P(X ≤ x) ≈ Φ(z), where z = (x + ½ - μ)/σ

In this case, μ is the expected number of left-handed people in the sample, which is 0.14*190 = 26.6

σ is the standard deviation of the sample, which is (0.14*(1-0.14))^0.5*190 = 5.58

x is the desired number of left-handed people in the sample, which is 24.5 (since fewer than 25)

Therefore, z = (24.5 + ½ - 26.6)/5.58 = -1.03

The probability that fewer than 25 people in the sample are left-handed is then Φ(-1.03) = 0.1545, to at least 3 decimal places.

The interest that is paid on the loan in 6 years will be $4,200.

The amount of interest that is saved is $2,100.

The simple interest is a linear function of the number of years of the loan, value of the loan and the duration of the loan. The higher either of these values are, the higher the simple interest.

Simple interest = loan x time x interest rate

Simple interest if the loan is paid off after 6 years: $12,500 x 6 x 0.056 = $4,200

Simple interest if the loan is paid off after 3 years: $12,500 x 3 x 0.056 = $2100

Interest saved = $4200 - $2100 = 2100

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A left the work after 3 days was solved by using work formula.

An algebraic equation is a mathematical statement that asserts that two expressions are equal. These expressions can contain variables, which are represented by letters, and the equation states that the values of the expressions are equal for some particular values of the variables.

The work formula is a mathematical concept used to determine how long it will take two or more workers to complete a job together. The formula is based on the idea that the amount of work done is directly proportional to the time spent working.

In the given question,

Let's assume that A worked for x days, and therefore he left the work unfinished for (15 - x) days. During this time, B finished the remaining work in 7 days.

According to the work formula, the amount of work done by A and B together in one day is:

1/15 + 1/18 = 11/90

This means that in one day, they can complete 11/90th of the work together.

During the x days when A worked, the amount of work he did is:

x * (11/90)

And during the remaining (15 - x) days, the amount of work left undone is:

(15 - x) * (11/90)

When A left, B completed the remaining work in 7 days, so we can set up an equation:

(11/90) * 7 = (15 - x) * (11/90)

Simplifying and solving for x, we get:

x = 3

Therefore, A left the work after 3 days.

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Answer:

5683200

Step-by-step explanation:

Move the decimal 4 places to the right because [tex]10^4[/tex] has 4 zeros.

Cindy paid the cashier a total of $6.90 for the three candy bars, including taxes.

What is expression ?

Expressions can be used to represent various mathematical concepts and relationships, and they are used extensively in algebra, calculus, and other branches of mathematics.

To calculate the total cost of the candy bars with taxes, we need to first find the cost of each candy bar and then add up all three costs.

The cost of the Giant Kit Kat is $3.59, but we need to add 9% tax to get the total cost:

$3.59 + 0.09($3.59) = $3.91 (rounded to the nearest cent)

The cost of the Mini Snickers is $0.75, but we need to add 9% tax to get the total cost:

$0.75 + 0.09($0.75) = $0.82 (rounded to the nearest cent)

The cost of the Twix TENDO is $1.99, but we need to add 9% tax to get the total cost:

$1.99 + 0.09($1.99) = $2.17 (rounded to the nearest cent)

Now we can add up the total cost:

$3.91 + $0.82 + $2.17 = $6.90

Therefore, Cindy paid the cashier a total of $6.90 for the three candy bars, including taxes.

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Answer: A 48 x 24/16 = r

Step-by-step explanation:

48 x 24 = the total number of drinks

Since there are 16 drinks in each row you want divide to get the number of rows in each drink.

Ex: 48 x 24= 1,152 (total drinks)

16 drinks in a row

1,152/16 = 72

72 rows

Answer:

x=-1/3

Step-by-step explanation:

3x-4+2x+6+x=0

6x+2=0

6x=-2

x=-2/6

x=-1/3

The nearest ten thousand of the digits  14509 is 14, 000.

The rule for rounding to the nearest ten thousand is to look at the last four digits.

If the last four digits of the number is greater than 5000, we have to round the value up but if the number is below 5000 we have to round below.

For example let's round up 27567 to the nearest ten thousands.

Therefore, 7567 is above 5000, Hence, we have to round up. The nearest ten thousand of 27567 is 30000.

Let's round 14509 to the nearest ten thousand.

The nearest ten thousand of 14509 is 14, 000

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Given the diagram above, which is a combination of three right triangles,

27) m∠DGE = 45°

28) m∠EDG = 85°

29) FD = 10

30) GD = 14

31) EG = 19.

27) m∠DGE = 45°

This is because m∠DGE is an alternate angle to m∠BAD which is = 45°. Recall that alternate angles are congruent.

28) m∠EDG = 85° because it is the vertical opposite of ∠ADC. Note that  ∠ADC = 180 - 45 - 50

= 85°

29)  and 30)

Given FG=10 and m∠DGE=45°,

FD = √DG² - FG²

Since we don't have FD

We use Cos Rule

GD = FG/cos(α)

GD = 10/Cos 45°

GD = 14.1421356237

GD [tex]\approx\[/tex] 14

Thus,

FD = √14.1421356237312 - 102

FD = √100

FD = 10

31)

EG = EF + 10

EF = √(GD² - FG²

EF = √(14² - 10²)

EF = √80.982478588641

EF =  8.99903

Hence,

EG = 8.99903 + 10

EG [tex]\approx[/tex]  19

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Answer: Answer is below <3

The quotient of three times a number and 7: 3n/7

The difference between 5 and a number is x:  5 - n = x

The product of 3 times a number and 7:  (3n)(7)

Two times the sum of a number and 9:  2 (n + 9)

The sum of twice a number and 9:  2n + 9

5 less than a number is x:  x = n - 5

Answer:

B: 9

Step-by-step explanation:

The prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and 23.

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.

Answer:

3x + 4 < 13

2y - 5 > 7

6n - 1 ≤ 23

8m + 2 ≥ 18

4a - 7 < 5a + 2

9b + 3 > 6b + 10

Step-by-step explanation:

I dunno if this is what you're asking for

Answer:

ok.....

x + 2 < 5

|x - 4| > 4

x + 7 [tex]\geq[/tex] 8

-x < -5

x - 5 < 9

5x + 18 > 2

|3x - 1| < 8

If James is sorting the numbers on his teddy bears from greatest to least, the number that would come next would depend on the numbers already sorted. For example, if the numbers he has sorted are 9, 5, and 3, then the next number would be 1.

Sort is a function used to rearrange items in a list in order of size, value or alphabetically. It is a computer algorithm that sorts a list, typically of numbers, words, or other items, into increasing or decreasing order. It is often used to arrange data so that it can be more easily analyzed or used in other applications. The simplest form of sorting is to take a list of items, compare each item to the items before it, and swap them if they are out of order. This process is repeated until all items are in the correct order. Sorting algorithms are used in many areas of computing, including data structures, artificial intelligence, databases, and programming languages.

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The numbers on teddy bears are sorted as 656, 666, 676, 686. The pattern rule is adding 10 so, the next number will be 696.

Sort is a function used to rearrange items in a list in order of size, value or alphabetically. It is often used to arrange data so that it can be more easily analyzed or used in other calculation. The simplest form of sorting is to take a list of items, compare each item to the items before it, and swap them if they are out of order. This process is repeated until all items are in the correct order.

If James is sorting the numbers on his teddy bears from greatest to least, the number that would come next would depend on the numbers already sorted.

The numbers on teddy bears are sorted as 656, 666, 676, 686.

Now, observe the pattern.

656 + 10 = 666

666 + 10 = 676

676 + 10 = 686

This indicates that the pattern rule is "adding 10", which means the next number in series is:

686 + 10 = 696

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The complete question is as follows:

The probability that at least one of the seven next births in the country is a girl is 0.992, or 99.2%.

The probability of a baby being a boy is 0.538, which means that the probability of a baby being a girl is:

P(girl) = 1 - P(boy) = 1 - 0.538 = 0.462

The probability of at least one of the seven next births being a girl is the complement of the probability that all seven are boys. The probability that a single birth is a boy is 0.538, so the probability that all seven births are boys is:

P(all boys) = (0.538)^7 = 0.008

Therefore, the probability of at least one of the seven next births being a girl is:

P(at least one girl) = 1 - P(all boys) = 1 - 0.008 = 0.992 (99.2%)

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Answer: Linear

Step-by-step explanation:

Since the difference between consecutive values of f(x) is constant, this suggests that the function could be linear. To confirm this, we can calculate the differences between consecutive values:f(1) - f(0) = -15 - (-18) = 3

f(2) - f(1) = -12 - (-15) = 3

f(3) - f(2) = -9 - (-12) = 3

f(4) - f(3) = -6 - (-9) = 3

Since the differences are constant and equal to 3, this confirms that the function is linear.

To find the equation of the linear function, we can use the slope-intercept form of a linear equation:

y = mx + bwhere m is the slope and b is the y-intercept.

We can use the first two points (0, -18) and (1, -15)  to find the slope:

m = (change in y) / (change in x) = (-15 - (-18)) / (1 - 0) = 3

Now we can use the slope and one of the points to find the y-intercept:

y = mx + b

-18 = 3(0) + b

b = -18

Therefore, the equation of the linear function is:

f(x) = 3x - 18

So the function type that could represent the values in the table is linear.

The value of x and y Iis, x = y = [tex]35^{0}[/tex]

Here O is the center of the circle.

According to the central angle theorem, the angle subtended by an arc is always half of its central angle.Understand the problem and draw a diagram: Read the problem statement carefully and try to understand the given information, what is asked and any given constraints. Then, draw a diagram of the circle and label any given variables, angles or lengths.

Identify the relevant circle properties: Recall the properties of circles such as the radius, diameter, circumference, and central angle. You may need to use these properties to solve the problem.

Use equations and formulas: Depending on the information given and what is asked, you may need to use equations and formulas to find the values of x and y. These formulas may include the Pythagorean theorem, trigonometric ratios, or circle equations such as the equation for the circumference or area of a circle.

Simplify and solve the equations: Simplify the equations and solve for the unknown variables, using algebraic techniques. Remember to show all steps of your working and check your answers for accuracy.

Verify your answer: Once you have found the values of x and y, check your solution to ensure that it satisfies any given constraints or conditions and makes sense in the context of the problem.

Let the Central angle of arc AB is [tex]70^{0}[/tex]

∠ACB and ∠ADB are subtended by the arc AB.

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The system is inconsistent and has no solution. Therefore, the answer is "inconsistent".Since the last row is of the form [0 0 0 | b], where b is nonzero (b=7

To determine whether the system of equations represented by the given matrix has a solution, we can use row operations to put the matrix into reduced row echelon form. If the resulting matrix has a row of the form [0 0 ... 0 | b], where b is nonzero, then the system is inconsistent and has no solution. If there are any free variables in the reduced row echelon form, then the system has infinitely many solutions and is dependent. If there are no free variables and no rows of the form [0 0 ... 0 | b], then the system has a unique solution and is independent.

Using row operations, we can put the given matrix into reduced row echelon form as follows:

[tex][1 -3 1 4 | 4] (R1)[3 2 1 | 3] (R2)[-6 -4 -2 | 1] (R3)[/tex]

([tex]R2 - 3*R1) - > R2:[/tex]

[tex][1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[-6 -4 -2 | 1] (R3)(R3 + 6*R1) - > R3:[1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[0 -22 4 | 25] (R3)(R3 + 2*R2) - > R3:[1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[0 0 0 | 7] (R3)[/tex]

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Answer:    32 and 43

Step-by-step explanation:

Gina finished making sugar cookies at 1:30 P.M.

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

To find out what time Gina finished making sugar cookies, we need to add the time it took her to make them to the starting time.

Starting time: 12:15 P.M.

Time it took to make cookies: 1 hour and 15 minutes

To add the time, we first convert 1 hour and 15 minutes to hours by dividing the minutes by 60:

1 hour and 15 minutes = 1 + 15/60 hours = 1.25 hours

Now we can add 1.25 hours to 12:15 P.M.:

12:15 P.M. + 1.25 hours = 1:30 P.M.

Hence, Gina finished making sugar cookies at 1:30 P.M.

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Complete question:

Gina started making sugar cookies for her friends at 12:15 P.M. It took her 1 hour and 15 minutes to make. By what time Gina finished making sugar cookies?

Answer:

C) Pi

Step-by-step explanation:

Pi is an irrational number, it cannot be written down as non-infinite decimal, basically meaning that in order for it to be a rational number you need an approximate value for Pi.

the value of variable x in the rhombus is Option (c) 25.

A parallelogram is a particular instance of a rhombus. opposite sides and angles of the rhombus are parallel and equal. The rhombus has equal-length sides on each side, and its diagonals meet at right angles to form its shape as square. The rhombus is sometimes called as a diamond or rhombus.

Let O be the intersection point of the line AC and the line BD in the rhombus.

This two lines intersect at a 90° angle in the center. ( Property of Rhombus)

∠AOD=90°

∠AOD+∠OAD+∠ODA=180° (triangle sum property)

90°+x+x+40°=180°

2x=180°-130°

x=25

Hence the value of x=25.

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Answer:

[tex]9 + 15 = 24 > 13[/tex]

[tex]9 + 13 = 22 > 15[/tex]

[tex]15 + 13 = 28 > 9[/tex]

So the lengths 13, 15, and 9 can form a triangle.

Hence the value of c = 4 in [3,5] for Rolles theorem.

Rolle's Principle

If a function f is defined in the closed interval [a, b] in a manner that meets the requirements listed below.

The interval [a, b] is closed and the function f is continuous.

ii) On the open interval, the function f can be differentiated (a, b)

iii) If f (a) = f (b), then at least one value of x exists; in this case, let's assume that this value is c, which is situated between a and b, i.e. (a c b), in such a way that f'(c) = 0.

There exists a point x = c in (a, b) such that f'(c) = 0 if a function is continuous on the closed interval [a, b] and differentiable on the open interval (a, b).

let f(x)=x²-8x+12 in [3,5]

i) f(x) is continuous in closed interval [3,5] because f(x) is algebraic function.

ii) f(x) is differentiable in the open interval (3,5) since the algebraic function is differentiable.

now f(3)=3²-8*3+12

f(3)= 9-24+12

f(3)= -3

f(5) = 25-40+12

f(5)= - 3

f(3) = f(5)

f'(x)= 2x-8

x=c ,c in [3,5]

f'(c)= 2c-8

2c-8=0

c=4

Hence the value of c = 4 in [3,5] for Rolles theorem.

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Hence, x has a value of 36 as the sum of the supplementary angles 3x and 2x must equal 180 degrees .

Angles in mathematics are used to quantify how much two intersecting surfaces or lines rotate relative to one another. Angles can be measured in degrees, radians, or various ways. Degrees, which divide a whole rotation into 360 equal parts, are the most popular unit of measurement for angles. Angles are a fundamental idea in geometry and trigonometry and have practical uses in a number of industries, including physics, engineering, and navigation.

given

The sum of the supplementary angles 3x and 2x must equal 180 degrees. Which is:

3x + 2x = 180

Putting similar phrases together on the left side, we get:

5x = 180

When we multiply both sides by 5, we get:

x = 36

Hence, x has a value of 36 as the sum of the complementary angles 3x and 2x must equal 180 degrees .

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Note that,
the encrypted message for "OK" is the pair of numbers (616, 2385).
and the final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).

To encrypt a message using RSA, we need to first represent the message as numbers using a suitable encoding scheme. For simplicity, we can use the ASCII code for each character, which is a standard encoding scheme for text.

a) To encrypt "OK", we first convert each letter to its corresponding ASCII code:

"O" = 79

"K" = 75

Next, we use the RSA encryption formula:

C ≡ [tex]M^{e}[/tex] (mod n)

For "O", we have C ≡ 79¹¹ (mod 2911) ≡ 616 (mod 2911)

For "K", we have C ≡ 75¹¹ (mod 2911) ≡ 2385 (mod 2911)

Therefore, the encrypted message for "OK" is the pair of numbers (616, 2385).

b) To encrypt "HELP", we break it up into two blocks:

Block 1: "HE"

Block 2: "LP"

For block 1, we have:

"H" = 72

"E" = 69

Using the RSA encryption formula, we get:

C1 ≡ 72¹¹ (mod 2911) ≡ 738 (mod 2911)

C2 ≡ 69¹¹ (mod 2911) ≡ 1277 (mod 2911)

Therefore, the encrypted message for "HE" is the pair of numbers (738, 1277).

For block 2, we have:

"L" = 76

"P" = 80

Using the RSA encryption formula, we get:

C3 ≡ 76¹¹ (mod 2911) ≡ 1479 (mod 2911)

C4 ≡ 80¹¹ (mod 2911) ≡ 2252 (mod 2911)

Therefore, the encrypted message for "LP" is the pair of numbers (1479, 2252).

The final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).

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After answering the prοvided questiοn, we can cοnclude that Sο, we can  equatiοn chοοse values οf a and b such that Cοv(X¯, μ) < (1 − a)/2 σ/n and MSE(θˆ) > MSE(θ), like a = 0.9 and b = 0.5.

An equatiοn in mathematics is a prοcedure that affects the equaIity οf equatiοns. Twο sides οf an equatiοn are cοnnected by the algebraic οperatοr (=). Fοr instance, the claim "2x + 3 = 9" asserts that the cοmment "2x + 3" means the value "9" in tοtal. The gοal οf sοlving equatiοns is tο identify the factοr(s) that will cause the equatiοn tο be true.

Equatiοns may be straightfοrward οr cοmplex, cοnstant οr nοn-linear, and cοntain οne οr mοre variables. Examples include raising the variable x tο the pοwer οf 2 in the equatiοn "x² + 2x - 3 = 0," fοr example. In mathematics, particularly in algebra, equatiοns, and geοmetry, lines are frequently used.

MSE(θˆ) = E[(θˆ − θ)²]

= E[((X1 + · · · + Xn)/n − μ²)²]

= E[((X1 − μ) + · · · + (Xn − μ))/n]²

= V[(X1 − μ)/n + · · · + (Xn − μ)/n]

= V[(X1 − μ)/n] + · · · + V[(Xn − μ)/n] (since the Xi's are independent)

Thus, MSE(θˆ) = σ²/n

b. Fοr MSE(θˆ) < MSE(θ), we want:

We can see that this is satisfied fοr any value οf a such that 0 < a < 1.

c. Fοr MSE(θˆ) > MSE(θ), we want:

σ/n > V[(1 − a)X¯ + aμ] = (1 − a)²Var(X¯) + aVar(μ) + 2a(1 − a)Cοv(X¯, μ)

σ²/n > (1 − a)(σ²/n) + 2a(1 − a)Cοv(X¯, μ)

Cοv(X¯, μ) < (1 − a)/2 σ²/n

Sο, we can chοοse values οf a and b such that Cοv(X¯, μ) < (1 − a)/2 σ/n and MSE(θˆ) > MSE(θ), such as a = 0.9 and b = 0.5.

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