Consider the function f(x) = x + 1/x . (a) Explain why the mean value theorem applies on the interval (1, 3). (b) Find the value(s) of c guaranteed to exist by MVT. (c) Give an interval where we can't apply the MVT to this function. How do you know MVT can't be applied on this interval

Answer:

Water gives in affect like this to a pencil in water as well. Refraction makes the object seem distorted or further away than you would expect.

Step-by-step explanation:

We can conclude that the dilated triangle abc is similar to the original triangle ABC with a dilation factor of 3,

Dilation is a transformation that performs a proportional resize of a figure. It changes the size of the figure while maintaining its shape and orientation. To dilate triangle ABC to create triangle abc, we can multiply the coordinates of each vertex of ABC by a dilation factor of 3.

The coordinates of the vertices of the original triangle ABC are A(-3,-3), B(3,3), and C(0,3). Multiplying each coordinate by 3 gives the coordinates of the vertices of the dilated triangle abc : A(-9,-9), B(9,9), and C(0,9).

We can compare the two triangles to see how the dilation has affected them. The size of triangle abc is three times larger than that of triangle ABC. The shape and orientation of triangle abc are the same as that of triangle ABC. The vertices of the dilated triangle, abc, are located at three times the distance from the origin as the corresponding vertices of triangle ABC. That is why the coordinates of all vertices of triangle abc are three times the coordinates of the corresponding vertices of triangle ABC. since the triangle was resized proportionally and has the same shape and orientation.

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Answer:

69 is the answer

Step-by-step explanation:

15% of 460 is 69

Answer:

I believe it to be D

Step-by-step explanation:

because thats the only one different out of those four.

Answer:

the answer is -120

Step-by-step explanation:

3x-2+3x²+6x

9x-2+3x²

3x²+9x-2

Answer:

I think the first one is 133 hours and 20 minutes to get 32,000 Dollars, and I think the second one is 66 hours and 50 minutes to get 16,000 dollars. I am probably wrong though.

The proof that shows that triangles PQR and TSR are similar by AA similarity theorem is explained below.

The AA similarity theorem proves that two triangles are similar if we can show that two of its corresponding angles are congruent to each other.

Therefore, for triangles PQR and TSR to be similar by the AA similarity theorem, they must have two corresponding congruent angles.

The proof below shows the triangles, ΔPQR ~ ΔTSR are similar to each other:

Statement                                             Reasons                                              

1. QR ⊥ PT                                             1. Given

2. ∠QRP and ∠SRT are right angles   2. Def. of perpendicular

3. ∠QRP ≅ ∠SRT                                  3. All right angles are ≅

4. ∠QPR ≅ ∠STR                                  4. Given

5. ΔPQR ~ ΔTSR                                   5. AA similarity theorem

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Answer:

126 square feet

Step-by-step explanation:

Lateral Surface Area :

Perimeter :

Height : 4.5 ft

Solving :

The appropriate limits of integration for finding the area between the functions defined by x = −1 and x = − y^3 − 3y^2 are y = -2 and y = 0.

To find the limits of integration, we need to determine the intersection points of the given functions. Equating x = −1 and x = − y^3 − 3y^2, we get:

−1 = − y^3 − 3y^2

Rearranging and simplifying, we get:

y^3 + 3y^2 - 1 = 0

We can solve this cubic equation to get the three roots, but we are only interested in the real root between y = -2 and y = 0. We can use numerical methods or a graphing calculator to find that the real root is approximately -1.7549.

Therefore, the appropriate limits of integration for finding the area between the given functions are y = -2 and y = 0. The integral to find the area is:

A = ∫^0_-2 [(− y^3 − 3y^2) + 1] dy

Simplifying and evaluating the integral, we get:

A = 49/12.

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The 95% confidence interval estimate of the population mean rating for Miami International Airport is approximately 5.50 to 6.74 (rounded to two decimal places).

To develop a 95% confidence interval estimate of the population mean rating for Miami International Airport, we can use the sample data provided. Here are the steps to calculate the confidence interval:

Step 1: Calculate the sample mean and sample standard deviation (s) from the given ratings.

Step 2: Determine the critical value (t*) for a 95% confidence level. Since the sample size is small (n = 50), we need to use the t-distribution. The degrees of freedom (df) will be n - 1 = 50 - 1 = 49.

Step 3: Calculate the standard error (SE) using the formula: SE = s / √n, where n is the sample size.

Step 4: Calculate the margin of error (ME) using the formula: ME = t* * SE.

Let's proceed with the calculations:

Step 1: Calculate the sample mean and sample standard deviation (s).

Sample ratings: 7 7 3 8 4 4 4 5 5 5 5 4 9 10 9 9 8 10 4 5 4 10 10 10 11 4 9 7 5 4 4 5 5 4 3 10 10 4 4 8 7 7 4 9 5 9 4 4 4 4

Sample size (n) = 50

Sample mean = (Sum of ratings) / n = (306) / 50 = 6.12

Sample standard deviation (s) = 2.18

Step 2: Determine the critical value (t*) for a 95% confidence level.

Using a t-distribution with 49 degrees of freedom and a 95% confidence level, the critical value (t*) is approximately 2.01.

Step 3: Calculate the standard error (SE).

SE = s / √n = 2.18 / √50 ≈ 0.308

Step 4: Calculate the margin of error (ME).

ME = t* * SE = 2.01 * 0.308 ≈ 0.619

Step 5: Construct the confidence interval.

Confidence Interval = 6.12 ± 0.619

Lower bound = 6.12 - 0.619 ≈ 5.501

Upper bound = 6.12 + 0.619 ≈ 6.739

The 95% confidence interval estimate of the population mean rating for Miami International Airport is approximately 5.50 to 6.74 (rounded to two decimal places).

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Answer:

-----------------------------

We see that triangles MNO and MPQ are similar.

Corresponding sides of similar triangles are proportional:

The percent change from 1994 to 1995 can be computed by which of the following methods.

The percent change from 1994 to 1995 would be computed by the following

Formula: Percent Change = ((New Value - Old Value) / Old Value) x 100Where,

Old Value = Annual caseloads in 1994 = 750

New Value = Annual caseloads in 1995 = 820

Let's put these values into the formula and calculate the percent change.

Percent Change = ((820 - 750) / 750) x 100

Percent Change = (70 / 750) x 100

Percent Change = 0.093 x 100

Percent Change = 9.3%

Therefore, the percent change from 1994 to 1995 would be 9.3%.

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Answer:

-2

Step-by-step explanation:

Note that slope-intercept form looks like: y = mx + b

In this case, isolate the y. Note the equal sign, what you do to one side, you do to the other. Subtract 2x from both sides:

2x (-2x) + y = 6 (-2x)

y = -2x + 6

Note in the slope-intercept form: y = mx + b

y = y

m = slope

x = x

b = y-intercept

In this case, your slope is -2. All lines parallel to the given equation will also have a slope of-2.

~

The triangle that has the coordinates as A(0,-4) B(0,-9) C(-2,-5) is; A scalene Triangle

The formula for the distance between two coordinates is;

D = √[(y₂ - y₁)² + (x₂ - x₁)²]

Thus;

Distance AB = √[(-9 + 4)² + (0 - 0)²]

Distance AB = √25

Distance AB = 5

Distance BC = √[(-5 + 9)² + (-2 - 0)²]

Distance BC = √20

Distance CA = √[(-4 + 5)² + (-2 - 0)²]

Distance CA = √5

Since the three sides all have different lengths, then they the triangle is said to be a scalene triangle.

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Answer:

148

Step-by-step explanation:

AP 200, 196, 192, ...

a14=?

---------

a1= 200

d= 196-200=192-196= -4

a14= a1+13d

a14= 200+13*(-4)= 200- 52= 148

Answer:

The novel has 2160 pages.

Step-by-step explanation:

The number of pages of the novel is x.

Mica has read 1/2 of the novel, so x/2 = 0.5x.

Denise has read 2/5 of the novel, so 2x/5 = 0.4x.

Mica has read 216 pages more than Denise

This means that:

0.5x - 0.4x = 216

0.1x = 216

x = 216/0.1

x = 2160

The novel has 2160 pages.

We can writey + dy = 2x1x2 / (x1+x2) + 2x1Δx2/ (x1+x2) + 2x2Δx1/(x1+x2)+ 2Δx1Δx2/ (x1+x2)On subtracting y from both sides, we getdy = 2x1Δx2/ (x1+x2) + 2x2Δx1/ (x1+x2) + 2Δx1Δx2/ (x1+x2)

Given y= x1/(x1+x2)  we need to find the total differential of y.It is given that, y= x1/(x1+x2)Let us assume, x1 = x1+Δx1, x2 = x2+Δx2. On substituting these values, we get + dy = (x1 + Δx1)/ (x1 + Δx1 + x2 + Δx2)We know that dy = y - (x1 + Δx1)/ (x1 + Δx1 + x2 + Δx2)

On further simplification, we get,dy = (Δx1(x2+Δx2))/(x1+Δx1+x2+Δx2)²-(Δx1x2)/((x1+Δx1+x2+Δx2)²)Since Δx1 and Δx2 are very small, we can neglect their squares and products, i.e., Δx1², Δx2², and Δx1.Δx2

Hence the total differential of y= x1/(x1+x2) is given by dy = (-x1x2/(x1+x2)²) dx1 + (x1²/(x1+x2)²) dx2. Note: x1 and x2 are independent variables.

Therefore, dx1 and dx2 are their differentials.Given y=2x1x2 /(x1+x2) Let us assume, x1 = x1+Δx1, x2 = x2+Δx2. On substituting these values, we gety + dy = 2(x1 + Δx1)(x2 + Δx2)/ (x1 + Δx1 + x2 + Δx2)On simplifying, we gety + dy = (2x1x2+2x1Δx2+2x2Δx1+2Δx1Δx2)/(x1+Δx1+x2+Δx2)

Since Δx1 and Δx2 are very small, we can neglect their squares and products, i.e., Δx1², Δx2², and Δx1.Δx2

Hence the total differential of y=2x1x2 /(x1+x2) is given by dy = (2x2/(x1+x2)²) dx1 + (2x1/(x1+x2)²) dx2.

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Answer:

The answer is (-3, 7) hope this helps

Step-by-step explanation:

Answer:If it's reflected,then it should be (-3.7).

Step-by-step explanation:

Ans:  B 63 degree

Step-by-step explanation:

Chord
to find the chord
1/2 or either 0.5

0.5 x 126 = 63
Mark me as Brainliest
Ty , hope it helped

Answer:

B

Step-by-step explanation:

is is correct 63 degrees , Hope this helps !!

Answer:

C. 21

Step-by-step explanation:

We use the Power of Point theorem, which states that for points A, B, C, D, and E oriented in the way shown in the attachment:

BC * AC = DC * EC

Here:

AC = AB + BC = (2x + 5) + 9 = 2x + 14

BC = 9

DC = 10

EC = KC = (1 + 2x) + 10 = 2x + 11

So plug all these in:

BC * AC = DC * EC

9 * (2x + 14) = 10 * (2x + 11)

18x + 126 = 20x + 110

2x = 126 - 110 = 16

x = 8

Put this back into the expression for AB:

AB = 2x + 5 = 2 * 8 + 5 = 16 + 5 = 21

The answer is thus C.

~ an aesthetics lover

Answer:

~ 3 1/2 days

Step-by-step explanation:

Mr.Tram travels at a constant speed of 60 km per hour, and travels for up to 8 hours per day (max). Multiply 8 with 60:

60 x 8 = 480

Next, divide 480 from 1620 to get the amount of days:

1620/480 = 3.375

~ 3 1/2 days is how long Mr.Tram will take to travel from Dallas, TX to Detroit, MI.

~

Answer:

4 days

Step-by-step explanation:

If he drives 60 km an hour and drives 8 hours a day, he can drive (60*8 = 480)

480 km in a day.

If the total distance is 1620 km and he drives 480 km a day (1620/480 = 3.375) it would take him four days to take his trip. You have to round up to 4 in this scenario. You can't round down because in three days he'd only have traveled (480*3 = 1440) 1440 km. If you even drive for a second on the fourth (3 < x < 4) day, then the trip "took" four days.  

Answer:

\(P(Not\ Star) =\frac{2}{3}\)

Step-by-step explanation:

Given

See attachment

Required

Theoretical probability that a roll will not land on a star

From the attachment, we have:

\(n = 12\) --- Total space

\(Star = 4\)

So, the theoretical probability that a roll will land on a star is:

\(P(Star) = \frac{n(Star)}{n}\)

\(P(Star) = \frac{4}{12}\)

\(P(Star) = \frac{1}{3}\)

Using the complement rule, the probability that it will not land on a star is:

\(P(Not\ Star) = 1 - P(Star)\)

\(P(Not\ Star) = 1 - \frac{1}{3}\)

Take LCM

\(P(Not\ Star) =\frac{3-1}{3}\)

\(P(Not\ Star) =\frac{2}{3}\)

Answer:

Look at the photo below

Step-by-step explanation:

The function g(x) = |x| + 2 is transformed by 2 units from f(x) = |x|. The graph is attached with the answer.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

In the function as the value of the independent variable varies the value of the dependent variable also varies.

Given that the function is f(x)=|x| and transformed to the function g(x) = |x| + 2.

The function is transformed by the 2 units up in the graph. The graph of the function is attached with the answer.

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To get the maximum profit, Kate should display as many cards from company B as possible, since she makes a higher profit from those cards.

Let x be the number of cards from company A and y be the number of cards from company B.

The constraints are:

The objective function is:

  P = 0.30x + 0.32y (the profit from selling the cards)

To maximize the profit, we need to maximize the value of y. Since the display rack can hold up to 90 cards, we can set y = 90 - x.

Substituting this into the objective function:

  P = 0.30x + 0.32(90 - x)
P = 0.30x + 28.8 - 0.32x
P = -0.02x + 28.8

To maximize P, we need to minimize x. Since x must be at least 40, we can set x = 40.

Substituting this back into the objective function:
P = -0.02(40) + 28.8
P = 28

So the maximum profit Kate can make is $28, by displaying 40 cards from company A and 50 cards from company B.

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a) This is a one-tailed test

b)  the decision rule is: Reject H0 when z > 1.645.

c) the value of the test statistic is approximately 2.21.

d) The test statistic is greater than the critical value, we reject the null hypothesis.

e) The p-value is approximately 0.0149.

a. This is a one-tailed test because the alternative hypothesis (H1) specifies a direction (µ > 23).

b. The decision rule depends on the chosen significance level (α) and the alternative hypothesis. Since the alternative hypothesis is µ > 23, we are interested in testing if the sample mean is significantly greater than 23. Therefore, we reject the null hypothesis (H0) when the test statistic (z) is greater than the critical value.

For a significance level of 0.05, the critical value can be obtained from the standard normal distribution table or calculator. In this case, since it is a one-tailed test with a significance level of 0.05, the critical value is 1.645.

So, the decision rule is: Reject H0 when z > 1.645.

c. The value of the test statistic (z) can be calculated using the formula:

z = (sample mean - population mean) / (population standard deviation / √sample size)

In this case:

sample mean = 24

population mean = 23

population standard deviation = 3

sample size = 44

z = (24 - 23) / (3 / √44) = 2.21

Therefore, the value of the test statistic is approximately 2.21.

d. To make a decision regarding H0, we compare the test statistic (2.21) with the critical value (1.645). Since the test statistic is greater than the critical value, we reject the null hypothesis.

e. The p-value is the probability of obtaining a test statistic as extreme as (or more extreme than) the observed value, assuming the null hypothesis is true. In this case, the p-value corresponds to the area under the standard normal distribution curve to the right of the test statistic (2.21).

Using a standard normal distribution table or calculator, we find that the area to the right of 2.21 is approximately 0.0149.

Therefore, the p-value is approximately 0.0149.

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Answer:

x = 2

Step-by-step explanation:

Here's your solution

=> we know that tangents from a point to a common circle are equal

=> so, ST = SU

=> 7x - 3 = 5x + 1

=> 7x - 5x = 1 + 3

=> 2x = 4

=> x = 4/2

=> x = 2

hope it helps

Answer:

X will be 2

Step-by-step explanation:

ST=SU

7x-3=5x+1

2x=3+1

2x=4

x=4/2

x=2

hope it helps....

have a great day!!!

Answer:

1714

Step-by-step explanation:

hope this helps have  a great day

The conditional probability of a randomly generated bit string of length five containing at least three consecutive 1s, given that the last bit is a 0, is 0.125.

To calculate the conditional probability, we need to consider the possible configurations of the bit string. For a bit string of length five ending in 0, the first four bits can take on any combination of 0s and 1s.

However, we need to exclude the cases where the bit string already contains three consecutive 1s.

The total number of possible bit strings ending in 0 is 2^4 = 16, as each of the four bits can take on two possible values (0 or 1).

Out of these 16 possible bit strings, we need to determine the number of bit strings that have at least three consecutive 1s.

Let's consider the favorable cases:

1110

1111

There are two favorable cases.

Therefore, the conditional probability is 2/16 = 1/8 = 0.125.

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