Points D, B, and E are collinear. Find
the value of a so that points A, B, and
C are collinear.
A
(4x)
O
E
B
148°
D
C

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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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.

Answer:    32 and 43

Step-by-step explanation:

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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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

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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The solution to the system of equations 2x - 4y = 40 and -x + 2y = -20 is infinitely many solutions. The solution can be expressed as (x, y) = (2y + 20, y), where y can be any real number.

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:

the answer is 70%

Step-by-step explanation:

if all equals 100% and theres 10 pounds that means 7 pounds is eaqual to 70%

Answer:

To find 10.9% of $8.85 we can convert the percentage into a decimal:

10.9% = 0.109

0.109x8.85 = $0.964

=$0.96 (Rounded to 2 decimal places)

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.

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

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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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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The equation for the function is D(x) = 65 - 0.8x. Where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.

What is a linear function?

A linear function is a mathematical function that has a constant rate of change or slope between the independent variable (x) and the dependent variable (y). It is a function that can be graphically represented as a straight line.

We can use a linear function to approximate the depth of the water in the reservoir x months after the start of the study, since the depth is dropping at a constant rate of 0.8 meters per month. Let D(x) be the depth of the water in meters x months after the start of the study. Then we have:

D(x) = 65 - 0.8x

where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.

Therefore, the equation for the function is D(x) = 65 - 0.8x.

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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:  any shape with four sides

Step-by-step explanation:

Answer: 4 sides

Step-by-step explanation: The only qualification for a shape to be called a quadrilateral is that it has 4 sides

Hope this helps :)

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 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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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 volume of the cube of 7 inches when calculated is 343 cubic inches

A cube is a three-dimensional solid figure that has six faces, each of which is a square.

All the edges of a cube are of equal length. In this case, each edge of the cube measures 7 inches.

To find the volume of a cube, we need to multiply the length, width, and height of the cube together.

Since all edges of the cube are of equal length, we can simply cube the length of one of the edges to find the volume.

Therefore, the volume of this cube is calculated by multiplying the length of one edge by itself three times:

Volume = 7 x 7 x 7 = 343 cubic inches.

So, the volume is 343 cubic inches.

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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 function that expresses f(x) is f(x) = 1.99x + 3, and its graph is continuous.

A continuous function is one that doesn't have any sudden or unexpected changes in value. It means that if we make small enough changes to its input, the output will also change by a small amount.

We can express the total cost of an order as a function of the number of books sold, x, using the formula:

f(x) = 1.99x + 3

This function takes the number of books sold, multiplies it by the cost per book ($1.99), and adds a fixed fee of $3.

For example, if we sold 3 books, we can use the function to find the total cost:

f(3) = 1.99(3) + 3 = 9.97

This means that selling 3 books would cost $9.97 in total.

The graph of this function is continuous, which means that as we move along the x-axis, the y-values change smoothly and without any sudden jumps.

The term "continuous" refers to a function that can take on any value between two given points and can be broken down into infinitely many fractions and decimals.

In contrast, a discrete function can only take on specific values, usually whole numbers or integers.

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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:

x=-1/3

Step-by-step explanation:

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

6x+2=0

6x=-2

x=-2/6

x=-1/3

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:

5683200

Step-by-step explanation:

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

Frequency Distribution Table is down below.

Class Count Cumulative Frequency Table

160 - 180 3 3

181 - 201 5 8

202 - 222 14 22

223 - 243 14 36

244 - 264 10 46

265 - 285 2 48

286 - 306 1 49

307 - 327 1 50

Total 50     100

Here its peak is in between 202 to 243 frequency range. There are three extreme values that are 270, 295 and 325 pounds weight.

Median lies in the interval 223-243 and mean also lies in that interval. Maximum values lies in between 200 - 225 interval.

The distribution is left skewed.

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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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