can someone help me please.

step by step please
here is the picture

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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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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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 :)

why do we even need to know this stuff I think it's b

Answer:i think -81

Step-by-step explanation:3x (-3) = -9.        -9x(-3)=27.       27x(-3)= -81

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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Answer: $1,282.31 in the account after 8 years.

Step-by-step explanation:

To calculate the future value of the investment, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

where:

A = the future value of the investment

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, we have:

P = $1,000.00 (the initial deposit)

r = 3.44% = 0.0344 (the annual interest rate)

n = 12 (the number of times the interest is compounded per year, since it is compounded monthly)

t = 8 (the number of years)

So, plugging in the values:

A = $1,000.00 * (1 + 0.0344/12)^(12*8)

A = $1,000.00 * (1 + 0.0028666666666667)^96

A = $1,000.00 * 1.2823139327534472

A = $1,282.31 (rounded to the nearest cent)

Therefore, you will have approximately $1,282.31 in the account after 8 years.

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

Step-by-step explanation:

that the answerrrrrrrrr

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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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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The domain = {x ∈ R : x ≠ 2} and the range = {g ∈ R : g ≠ 5} In light οf this, g(x) has a h value οf 2 and a k value οf 5.

The difference between bοth the highest & lοwest values in statistics fοr a particular data cοllectiοn is called the range. Fοr instance, if the data set is 2, 5, 8, 10, 3, then the range is 10 - 2 = 8.

The definitiοn οf the functiοn g(x) is.

g(x) = 1/(x - 2) + 5

As the denοminatοr οf a fractiοn cannοt be zerο, the dοmain οf g(x) includes all real integers with the exceptiοn οf x = 2.

The range οf g(x) can be fοund by cοnsidering the behaviοr οf the functiοn as x apprοaches infinity οr negative infinity. As x apprοaches infinity οr negative infinity, the value οf g(x) apprοaches 5 (since the 1/(x - 2) term becοmes negligible cοmpared tο 5). Therefοre, the range οf g(x) is all real numbers except values very clοse tο 5.

It is pοssible tο rewrite the functiοn g(x) as fοllοws:

g(x) = (1/(x - 2)) + 5

This is in the fοrm:

g(x) = a/(x - h) + k

Where a = 1, h = 2, and k = 5.

Therefοre, the h value fοr g(x) is 2, and the k value fοr g(x) is 5.

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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)

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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Answer:

90

Step-by-step explanation:

it is a square

in a square all angles are equal to 90 degrees

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.

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%

Using simple interest his monthly installments are $1243.38

The amount on Simple interest is given by A = P(1 + rt) where

Now, since Justin purchased his dream car worth $18500 on a finance for 4 years. He was offered 6% interest rate. Assuming no other charges and no tax, we want to find his monthly installments.

His installments are his principal. so, making P subject of the formula, we have that

P = A/(1 + rt)

Given that

Substituting the vales of the variables into the equation, we have

P = A/(1 + rt)

P = $ 18500/(1 + 0.06 × 4)

P = $ 18500/(1 + 0.24)

P = $ 18500/1.24

P = $ 14919.35 per year

To find his monthly installments, we divide P by 12.

So, P' = P/12

= $ 14919.35/12

= $1243.38

So, his monthly installments are $1243.38

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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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Answer:

627422410000

hope it helps

Answer:

0.00005

Step-by-step explanation:

you move 5 decimal places left starting from 7 and right it as a decimal.

Ans=0.00007

Answer:    32 and 43

Step-by-step explanation:

Answer:

117

Step-by-step explanation:

If 30 out of 200 seventh-graders attend summer camp, we can estimate the proportion of seventh-graders who attend summer camp as 30/200 = 0.15.

To estimate how many seventh-graders out of the total of 780 are expected to attend summer camp, we can multiply this proportion by the total number of seventh-graders:

0.15 x 780 = 117

Therefore, we can estimate that about 117 seventh-graders are expected to attend summer camp.

The inequality that determines the maximum number of speakers, x, Michael can buy is: B. $46.00 + $483.33 < $1,045.69

To determine the maximum number of speakers, x, Michael can buy without spending more money than he has in his account, we need to use the following inequality:

Total amount spent on TV and speakers ≤ amount of money in the account

We know that Michael has $1,045.69 in his account, and he will spend $483.33 on a new television. Let x be the maximum number of speakers he can buy. Each speaker costs $46.00, so the total amount spent on the speakers will be $46.00x. Thus, we can write the inequality as:

$483.33 + $46.00x ≤ $1,045.69

Simplifying this inequality, we get:

$46.00x ≤ $1,045.69 - $483.33

$46.00x ≤ $562.36

x ≤ $562.36 ÷ $46.00

x ≤ 12.20 (rounded to two decimal places)

So the maximum number of speakers Michael can buy without spending more money than he has in his account is 12.20. However, since he cannot buy a fractional number of speakers, he can only buy a maximum of 12 speakers.

Therefore, the correct inequality that determines the maximum number of speakers, x, Michael can buy without spending more money than he has in his account is:

B. $46.00 + $483.33 < $1,045.69

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Answer:

The discount is $8.55, which is option C.

Step-by-step explanation:

To find the discount, we need to calculate 20% of the original price:

Discount = 20% x $42.75

Discount = $8.55

Therefore, the discount is $8.55, which is option C.

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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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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