11.find the values of c that satisty the Mean Value Theorem. Show steps

The correct option for the given question is c) lim x→a¯ f(x) = f(a) when the function f(x) is said to have jump discontinuity at a point x=a.

Jump continuity is a concept in calculus that describes the behaviour of a function at a specific point where the function jumps from one value to another value without any intermediate values. In other words, a function is considered jump continuous at a point if the function approaches a finite limit from both the left and right sides of that point, but the function values on the left and right sides of the point are not equal.

According to the given information:

The correct notation for the left-hand limit as x approaches a from the left side is lim x→a¯, where the horizontal line above the "a" indicates approaching from the left side.

The statement "lim x→a¯ f(x) = f(a)" means that the limit of f(x) as x approaches a from the left side is equal to the value of f(a) at x = a. This indicates that the function f(x) has a jump discontinuity at x = a, where the function jumps from one value to another value at that specific point.

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Answer:

[tex]m = \frac{ - 5 - 2}{2 - 4} = \frac{ - 7}{ - 2} = \frac{7}{2} [/tex]

[tex]2 = \frac{7}{2} (4) + b[/tex]

[tex]2 = 14 + b[/tex]

[tex]b = - 12[/tex]

[tex]y = \frac{7}{2} x - 12[/tex]

Answer:

C

Step-by-step explanation:

if we have a number line that has fractions listed, it should be C, because if 6/2 makes 3, which would be D, 5/2 should be C.

Answer:

The answer is -3

Step-by-step explanation:

log(1/1000)=x

log 10(1/1000)=x

10^x=(1/1000)

10^x=10⁰/10³

10^x=10^-3

x= -3

Answer:

-3

Step-by-step explanation:

I did the test

Hope this helps :)

(PLS MARK BRAINLIEST)

Answer:

Area = length * width

Step-by-step explanation:

If all the sides of the room are equal, all you have to do is 20*20 = area

Answer:

x = 19.6

Step-by-step explanation:

The sum of the angles of a triangle is 180.

<A + <B+ < C = 180

x + 5x + 4x - 16 = 180

Combine like terms.

10x-16=180

Add 16 to each side.

10x-16+16 = 180+16

10x = 196

Divide each side by 10.

10x/10 = 196/10

x = 19.6

Answer :

Step-by-step explanation :

According to the question It is given that,

We will apply angle sum property in the question.

Angle sum property states that sum of all the angles of triangle is 180°

[tex]\: :\implies [/tex] ∠A + ∠B + ∠ C = 180

[tex]\: :\implies [/tex] x + 5x + 4x - 16 = 180

[tex]\: :\implies [/tex] 10x - 16 = 180

[tex]\: :\implies [/tex] 10x = 180 + 16

[tex]\: :\implies [/tex] 10x = 196

[tex]\: :\implies [/tex] x = 196/10

[tex]\: :\implies [/tex] x = 19.6

Therefore, The Measure of Angle A is 19.6°

Answer:

We have,

y - x^2 = 29 - (-5)^2

= 29 - 25

= 4

Therefore, y - x^2 = 4 when x = -5 and y = 29.

The probability that exactly 2 students prefer salad is 0.302

From the question, we have the following parameters that can be used in our computation:

n = 10

r = 2

p = 20%

The probability is then calculated as

P(x = 2) = nCr * p^x * (1 - p)^(n - x)

substitute the known values in the above equation, so, we have the following representation

P(x = 2) = 10C2 * (20%)^2 * (1 - 20%)^8

Evaluate

P(x = 2) = 0.302

Hence, the probability is 0.302

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The function N for d days of both rumors are N(d) = 2 + 5d and N(d) = 2(3)^d

Here, the number of students are the students that start the rumor i.e. Susanna and Liz

So, we have

For the Justin Beiber rumor, the rumor spreads at a linear rate of 5 per day

So, we have

JB day 2 = 2 + 5(2) = 7

For the Rihanna rumor, the rumor spreads at an exponential rate of 3

So, we have

Rihanna day 2 = 2 * (3)^2 = 18

Using the functions, we have

JB

2 + 5x = 32 students

5x = 30

x = 6 days

Rihanna

2(3)^x = 162 students

3^x = 81

x = ln(81)/ln(3)

x = 4 days

JB

N(d) = 2 + 5d

Rihanna

N(d) = 2(3)^d

So, we have

d          JB          Rihanna

0           2           2

1           7           6

2          12           18

3           17           54

4           22           162

5           27           486          

6           32           1458

7           37           4374

8           42           13122

9           47           39366

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The image coordinates of M′ are M′(0, 3).

What is translation?

A translation is a geometric transformation when each point in a figure, shape, or space is moved in a specific direction by the same amount. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Here, we have

Given: Polygon JKLM is drawn with vertices J(−2, −5), K(−4, 0), L(−1, 2), M (0, −1).

When the shape is moved up by k units, then replace y with y + k.

The translation is as follows:

Here, J(-2, -5) → (-2, -5+4) → J'(-2, -1)

K(-4, 0) → (-4, 0+4) → K'(-4, 4)

L(-1, 2) → (-1, 2+4) → (-1, 6)

M(0, -1) → (0, -1+4) → (0, 3)

Hence, the image coordinates of M′ are M′(0, 3).

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The set of all elements that are in either A or B is the union of A and B, which is 1, 2, 3, 4, 5, 6, 8, 9, 10. As a result, A u B = 1, 2, 3, 4, 5, 6, 8, 9, 10

Set operations are done on two or more sets to produce a combination of components based on the operation. There are three primary sorts of operations done on sets in a set theory, such as: Intersection of sets () Union of sets () Set difference (-).

¡) (A n B) u C:

The value of the intersection of A and B is 5, 8. As a result, (A n B) = 5, 8. The union of this set with C is thus 1, 2, 3, 4, 5, 6, 8. As a result, (A n B) u C = 5, 8 u 1, 2, 3, 4, 5, 6, 8 = 1, 2, 3, 4, 5, 6, 8.

¡¡) (A-B) u C:

A-B is the set of elements in A that are not in B, which is 3, 6. The union of this set with C is thus 1, 2, 3, 4, 5, 6, 8. As a result, (A-B) u C = 3, 6 u 1, 2, 3, 4, 5, 6, 8 = 1, 2, 3, 4, 5, 6, 8.

¡¡¡) (A u B):

The set of all elements that are in either A or B is the union of A and B, which is 1, 2, 3, 4, 5, 6, 8, 9, 10. As a result, A u B = 1, 2, 3, 4, 5, 6, 8, 9, 10.

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¡) (A ∩ B) ∪ C  = {1,2,3,4,5,6,8}.

¡¡) (A-B) ∪ C = {1,2,3,4,5,6,8,10}.

¡¡¡) (A ∪ B)' is the set of elements that are in U but not in {1,2,3,4,5,6,8,9,10}. This is simply the set {7}.

What is probability?

Probability is a measure of the likelihood of an event occurring.

Recall that:

A ∩ B denotes the intersection of sets A and B, i.e., the set of elements that are in both A and B.

A ∪ B denotes the union of sets A and B, i.e., the set of elements that are in either A or B or both.

A' denotes the complement of set A, i.e., the set of elements that are not in A.

Using these notations, we can solve each part of the question as follows:

¡) (A ∩ B) ∪ C

First, we need to find A ∩ B, which is the set of elements that are in both A and B. We can see that A={3,5,6,8,10} and B={1,2,4,5,8,9}. So, A ∩ B={5,8}.

Next, we take the union of (A ∩ B) and C. We have C={1,2,3,4,5,6,8}, so the final set is:

(A ∩ B) ∪ C = {5,8} ∪ {1,2,3,4,5,6,8} = {1,2,3,4,5,6,8}

Therefore, (A ∩ B) ∪ C = {1,2,3,4,5,6,8}.

¡¡) (A-B) ∪ C

First, we need to find A-B, which is the set of elements that are in A but not in B. We can see that A={3,5,6,8,10} and B={1,2,4,5,8,9}. So, A-B={3,6,10}.

Next, we take the union of (A-B) and C. We have C={1,2,3,4,5,6,8}, so the final set is:

(A-B) ∪ C = {3,6,10} ∪ {1,2,3,4,5,6,8} = {1,2,3,4,5,6,8,10}

Therefore, (A-B) ∪ C = {1,2,3,4,5,6,8,10}.

¡¡¡) (A ∪ B)'

Recall that A ∪ B denotes the union of sets A and B, i.e., the set of elements that are in either A or B or both. So, (A ∪ B)' denotes the complement of A ∪ B, i.e., the set of elements that are not in A or B.

We can see that A={3,5,6,8,10} and B={1,2,4,5,8,9}. So, A ∪ B={1,2,3,4,5,6,8,9,10}. Therefore, (A ∪ B)' is the set of elements that are not in {1,2,3,4,5,6,8,9,10}.

The universal set U={1,2,...,10}, so (A ∪ B)' is the set of elements that are in U but not in {1,2,3,4,5,6,8,9,10}. This is simply the set {7}.

Therefore, (A ∪ B)'={7}.

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Step-by-step explanation:

There are six sides...   3 pairs of equal sides

2 x ( 4x5  +  4x7   +  5x7)   = 166 cm^2

Answer:

166 cm²

Step-by-step explanation:

5x7=35

35x2=70

4x7=28

28x2=56

5x4=20

20x2=40

70+56+40= 166cm²

hope this helps!

Por lo tanto, el área del vidrio de la lupa es de aproximadamente 50.24 centímetros cuadrados.

What is el área?

"El área" is a Spanish phrase that translates to "the area" in English. "The area" is a mathematical term that refers to the measure of the size of a two-dimensional region, usually measured in square units such as square centimeters (cm²) or square meters (m²). The area of a figure can be calculated using various mathematical formulas, depending on the shape of the figure.

El área del vidrio de una lupa circular se puede calcular usando la fórmula del área del círculo, que es A = πr², donde "A" es el área, "π" es una constante aproximadamente igual a 3.14 y "r" es el radio de la lupa.

En este caso, el radio de la lupa es de 4 centímetros. Sustituyendo este valor en la fórmula, obtenemos:

A = πr²

A = 3.14 x 4²

A = 3.14 x 16

A = 50.24

Por lo tanto, el área del vidrio de la lupa es de aproximadamente 50.24 centímetros cuadrados.

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To cover the full football pitch, you will want 10 bags of fertiliser, rounded up to the nearest whole number.

The term "area" refers to the volume of space occupied by a two-dimensional (2D) form or surface.

It's represented by squares.

You must multiply the length by the breadth of the football pitch to determine its total area:

field size for football = length x width

field size for football = 360 feet x 160 feet

field size for football = 57,600 square feet

You must now calculate how many thousands of square feet the football pitch has in order to get the total amount of fertiliser required:

the size of a football pitch in square feet = the size of the football pitch overall / 1,000

the size of a football pitch in square feet = 57,600 / 1,000

the size of a football pitch in square feet = 57.6

You must spread 8 pounds of fertiliser per 1,000 square feet of the football pitch because it is 57.6 thousand square feet in size.

Total required fertiliser quantity = 8 pounds per 1,000 square feet x 57.6 thousand square feet

Total required fertiliser quantity = 460.8 pounds

Given that the fertiliser is sold in 50-pound bags, you will require:

number of fertiliser bags = Total amount of fertilizer needed / Weight of each bag

number of fertiliser bags = 460.8 pounds / 50 pounds/bag

number of fertiliser bags = 9.216 bags

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Answer:

apples per pound: 0.25

pears per pound: 0.33

Apples give him the best value per pound

Step-by-step explanation:

to find apple per pound: 4/16= 0.25

to find pears per pound: 7/21= 0.33

We have shown that dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = n!/x using Leibniz's theorem.

What is the Leibniz's theorem?

Leibniz's theorem, also known as the product rule for derivatives, is a rule for finding the nth derivative of a product of two functions. It states that if u(x) and v(x) are functions of x, then the nth derivative of their product

To apply Leibniz's theorem, we need to express the function in terms of a product of two functions: u and v.

Let u = xⁿ and v = ln(x)

Then, du/dx = n*xⁿ⁻¹ and dv/dx = 1/x

Using the formula,

d/dx(xⁿ ln(x)) = u(dv/dx) + v(du/dx)

= xⁿ * (1/x) + ln(x) * n * xⁿ⁻¹

= xⁿ⁻¹ + n*xⁿ⁻¹ ln(x)

To find the nth derivative, we differentiate n times using the product rule.

First, we need to find the first few derivatives:

f(x) = xⁿ⁻¹ + n*xⁿ⁻¹ ln(x)

[tex]f'(x) = nx^{(n-2)} + (n-1)*x^{(n-2)} ln(x)[/tex]

[tex]f''(x) = n(n-2)x^{(n-3)} + 2(n-1)x^{(n-3)} ln(x) - (n-1)x^{(n-3)}/(x^2)[/tex]

[tex]f'''(x) = n(n-2)(n-3)x^{(n-4)} + 3(n-1)(n-2)x^{(n-4)} ln(x) - 3(n-1)x^{(n-4)}/(x^2) - 2(n-1)x^{(n-4)} ln(x)/(x^2)[/tex]

and so on...

The pattern becomes apparent and the nth derivative can be expressed as:

[tex]f^{(n)}(x) = n!/(x^{(n+1)})[/tex]

So,

dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = [tex]f^{(n)}(x) = n!/(x^{(n+1)})[/tex]

Hence, we have shown that dⁿ⁺¹ / d xⁿ⁺¹ (xⁿ ln x) = n!/x using Leibniz's theorem.

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The right answers  outoff these options are: 3,5,6,8

Length is a measure of the size or distance of an object or space in one dimension, usually referring to the longest dimension of an object. It is typically measured in units such as inches, meters, or feet.

In geometry, a triangle is a closed two-dimensional shape that is formed by connecting three non-collinear points with straight line segments. The line segments are called sides, and the points where they meet are called vertices. A triangle has three angles, which are formed by the intersection of its sides.

To determine the possible length of the third side of a triangle, we need to apply the triangle inequality theorem which states that the sum of the lengths of any two sides is always greater than the third side.

Using this theorem, we can see that the possible lengths for the third side are:

- 3 inches

- 5 inches

- 6 inches

- 8 inches

Therefore, the correct answers are:

3,5,6,8.

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The inequality states that the sum of the number of conference rooms and ballrooms should be greater than the number of guests, so that all the guests can be accommodated. The correct answer is d. 30y + 139x>1640.

It is usually written using symbols such as “<”, “>”, “≤”, and “≥”, where one side of the expression is greater than, less than, or equal to the other side.

This is the appropriate inequality to determine how many of each type of room Amy will need to reserve because it expresses the total number of guests (1,640) that must be accounted for in the total number of conference rooms (30y) and ballrooms (139x).

To solve the inequality, Amy can start by assuming the number of conference rooms (y) she will need to reserve.

If she decides to reserve 10 conference rooms, the inequality will become 30(10) + 139x > 1640.

This can be simplified to 1390x > 1640 - 300, which reduces to x > 7.64. This means that Amy will need to reserve at least 8 ballrooms to accommodate all 1,640 guests.

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The Results:

a) Cost of the bouncy castle for 20 children = £149

b) Number of children who went to the party = 14.

a) To find the cost of the bouncy castle for 20 children, we can substitute the number of children, which is 20, into the formula provided:

Cost = £3.65 * number of children + £76

Cost = £3.65 * 20 + £76

Now we can estimate the cost:

Cost = £73 + £76

Cost = £149

Thus, the cost of the bouncy castle for 20 children = £149.

b) To find the number of children who went to the party based on the given cost of £127.10, we can rearrange the formula to solve for the number of children:

Cost = £3.65 * number of children + £76

£127.10 = £3.65 * number of children + £76

Subtracting £76 from both sides of the equation:

£127.10 - £76 = £3.65 * number of children

£51.10 = £3.65 * number of children

Now we can divide both sides of the equation by £3.65 to isolate the variable:

£51.10 / £3.65 = number of children

14 = number of children

Therefore, the number of children who went to the party = 14.

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The payment due is given as Rs 875.94

Interest rate Rs 730.50

The principal is Rs 145.44

The balance is Rs 145954.56

Given:

P = principal, the initial amount of the loan

I = the annual interest rate (from 1 to 100 percent)

L = length, the length (in years) of the loan, or at least the length over which the loan is amortized.

J = monthly interest in decimal form = I / (12 x 100)

N = number of months over which loan is amortized = L x 12

Okay now for the big monthly payment (M) formula, it is:

                             J

        M  =  P  x ------------------------

                     1  - ( 1 + J ) ^ -N

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The ordered pairs that represent points on the graph of y = 2x - 3 are (0,-3), (5,7), (-2,-7), (2,1), and (4,5).

An ordered pair is a pair of numbers written in a specific order (x,y) that represents a point in the coordinate plane.

A graph is a visual representation of data or a mathematical function that is plotted on a coordinate plane, usually with an x and y-axis. It is used to analyze trends and relationships between variables.

According to the given information:

To determine whether a given ordered pair represents a point on the graph of the equation y = 2x - 3, we need to substitute the values of x and y into the equation and see if the equation is true.

a) (3,-3):

y = 2x - 3

-3 = 2(3) - 3

-3 = 3

This is not true, so (3,-3) is not on the graph.

b) (0,-3):

y = 2x - 3

-3 = 2(0) - 3

-3 = -3

This is true, so (0,-3) is on the graph.

c) (5,7):

y = 2x - 3

7 = 2(5) - 3

7 = 7

This is true, so (5,7) is on the graph.

d) (-2,-7):

y = 2x - 3

-7 = 2(-2) - 3

-7 = -7

This is true, so (-2,-7) is on the graph.

e) (2,1):

y = 2x - 3

1 = 2(2) - 3

1 = 1

This is true, so (2,1) is on the graph.

f) (4,5):

y = 2x - 3

5 = 2(4) - 3

5 = 5

This is true, so (4,5) is on the graph.

Therefore, the ordered pairs that represent points on the graph of the equation y = 2x - 3 are: (0,-3), (5,7), (-2,-7), (2,1), and (4,5). Answer: b), c), d), e) and f).

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According to the information, the exact values of sin(2u), cos(2u) and tan(2u) are sin(2u) = -120/169, cos(2u) = -1, and tan(2u) = -120/119.

We can use the double-angle formulas to find the values of sin(2u), cos(2u), and tan(2u) in terms of sin(u) and cos(u).

First, we need to find cos(u) using the Pythagorean identity:

Since pi/2 < u < pi, we know that sin(u) is positive and cos(u) is negative. Therefore:

Now we can substitute sin(u) and cos(u) into the double-angle formulas:

Therefore, sin(2u) = -120/169, cos(2u) = -1, and tan(2u) = -120/119.

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The probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.

1. Let's calculate the probability of selecting a blue disk

We can select a blue disk with number 2, 6 or 8 out of a total of 8 disks, it means that the probability of selecting a blue disk is

3/8

2. Let's calculate the probability of selecting the blue disk labeled with number 2:

We can select the blue disk labeled with number 2 out of three blue disks, it means that the probability of selecting the blue disk labeled with number 2 is  1/3

3. These are dependent events because the fact that we select the disk labeled with number 2, depends on selecting a blue disk before, thus:

Probability of selecting a 2 given that a blue disk is selected =

3/8 * 1/3 = 3/24 = 1/8

So we can state that the probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.


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Full Question:

See the attached image.

The statement "color cannot work to bring together parts of a painting" is false. OB. False

what is proportionality ?

The interaction of two variables that changes as a single ratio or proportion is referred to as proportionality.

The use of a cohesive color palette can help to create a sense of unity throughout the painting, tying together disparate elements and creating a harmonious whole. Color can also be used to create visual connections between different parts of the painting, leading the viewer's eye from one area to another and creating a sense of flow and movement within the composition.

So, the statement "color cannot work to bring together parts of a painting" is false.

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The surface area of the triangular prism is 511 in²

An exponential equation is an expression that shows how numbers and variables using mathematical operators.

The surface area of the prism is gotten by summing the individual area of each surface of the prism.

The surface area = (0.5 * 11 in * 7 in) + (0.5 * 11 in * 7 in) + (11 in * 14 in) + (9 in * 14 in) + (8 in * 14 in) = 511 in²

The surface area is 511 in²

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HI THIS IS DREAM AND TO

An equation of the regression line is y = 5.98 + 0.39x.

The data has a pattern that is not a straight line.

In this scenario, the x-values (x) would be plotted on the x-axis of the scatter plot while the y-values (y) would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the relationship between the x-values (x) and y-values (y), the linear regression equation and the correlation coefficient are given by:

y = 5.98 + 0.39x

Correlation coefficient, r = 0.6021345002 ≈ 0.60

In conclusion, we can logically deduce that there is a moderate correlation between the data because the correlation coefficient (r) is is greater than 0.4 but less than 0.7;

0.4＜|r| ≤ 0.7   (strong correlation)

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Brainiest please.

Answer:

Draw three overlapping circles to represent the sets A, B, and C.

Label the regions inside each circle with the name of the corresponding set (i.e., A, B, and C).

Shade the region that represents the set A - B, which includes all the elements that belong to A but not to B.

Finally, shade the region that represents the intersection of (A - B) and C, which includes all the elements that belong to both (A - B) and C.

The resulting diagram should show three overlapping circles, with the region for A shaded but with a part removed (to represent the exclusion of elements in B from A), and the region for (A - B) n C shaded within that.