Determine whether Rolle’s Theorem can be
applied to on the closed interval If Rolle’s Theorem can
be applied, find all values of in the open interval such
that If Rolle’s Theorem cannot be applied, explain
why not

Answer:

x = 2

y = 14

Step-by-step explanation:

{y = 4x + 6;

{y = 7x;

.

Let's replace y in the second equation with the value given in the 1st equation:

4x + 6 = 7x

4x - 7x = -6

-3x = -6 / : (-3)

x = 2

x = 2y = 4 × 2 + 6 = 8 + 6 = 14

The average rate of change between t = 0 and t = 2 is 16 feet/second and the average rate of change between t = 1 and t = 2 is 8 feet/second.

The correct answer choice is option A and C respectively.

The average rate of change between t = 0 and t = 2

At t = 0

h(t) = -16t² + 40t + 6

= -16(0)² + 40(0) + 6

= 0 + 0 + 6

= 6 feet/second

At t = 2

h(t) = -16t² + 40t + 6

= -16(2)² + 40(2) + 6

= -16(4) + 80 + 6

= -64 + 80 + 6

= 22 feet/second

The average rate of change between t = 0 and t = 2 is

22 feet - 6 feet

= 16 feet/second

At t = 1

h(t) = -16t² + 40t + 6

= -16(1)² + 40(1) + 6

= -16 + 40 + 6

= 30 feet/second

Therefore,

The average rate of change between t = 1 and t = 2 is

30 feet - 22 feet

= 8 feet

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The total surface area of the square pyramid is 39 ft².

The total surface area of a square pyramid can be determined by adding the area of the lateral surfaces and the base together.  A square pyramid has four lateral sides and one base.  

Total surface area= area of the base + area of the lateral sides

Area of the base = area of a square = length² = 3² = 9 ft²

Area of the lateral sides = 2 x base x height

2 x 3 x 5 = 30 ft²

Total surface area = 30 + 9 = 39 ft²

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Colin have £ 1392 in his bank account after 7 years.

Step-by-step explanation:

Given, Principal = P = £ 980

Rate of interest = R = 6% =  = 0.06

Time = T = 7 years

Amount = A = P + S.I

Simple Interest = S. I = PRT = 980 x 0.06 x 7 = £ 411.6

Amount after 7 years = £ 980 + £ 411.6 = £ 1391.6 ≈ £ 1392

Hence, Colin have £ 1392 in his bank account after 7 years.

The total volume of Cubic Yards of Concrete needed to fill in the footer is approximately 225.19 cubic yards.

To calculate the total volume of Cubic Yards of Concrete needed to fill in the footer, we need to use the formula for the volume of a rectangular prism, which is length x width x height. In this case, the length and height are both 20 feet since that is the size of the enclosed frame in the left of the diagram.

The width of the footer needs to be 2 feet, which means we need to subtract 4 feet (2 feet on each side) from the total width of the frame to get the inside width of the trench, which is 16 feet.

The depth of the footer needs to be 1 foot, which means we need to subtract 1 foot from the height of the frame to get the height of the trench, which is 19 feet.

Using these measurements, we can calculate the volume of the trench by multiplying length (20 feet) x width (16 feet) x height (19 feet) which gives us a total volume of 6,080 cubic feet.

To convert cubic feet to cubic yards, we need to divide the total volume by 27 (since there are 27 cubic feet in a cubic yard). Therefore, the total volume of Cubic Yards of Concrete needed to fill in the footer is approximately 225.19 cubic yards.

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Note the full question is

1) Calculate the total volume of Cubic Yards of Concrete needed to fill in the footer. (That is the enclosed frame in the left of the diagram above) (the footer needs to be 2 ft wide and 1 ft deep. (remember there is a 2 ft difference between the outside and the inside of trench)

2) What is the square footage of the footer trench ?

3) If the footer trench is 2 ft deep, would 10 Cubic-yards of concrete overfill this trench? By how much. ?

The complete labels to the parts of the circle such as tangent, diameter, radius and secant are found in the attchment.

The various parts of a circle are:

Center: The point inside the circle that is equidistant from all points on the circumference.

Circumference: The distance around the circle.

Radius: A line segment from the center of the circle to any point on the circumference.

Diameter: A line segment that passes through the center of the circle and has its endpoints on the circumference.

Chord: A line segment with both endpoints on the circumference.

Tangent: A line that intersects the circle at only one point, called the point of tangency.

Secant: A line that intersects the circle at two points.

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Answer:

Step-by-step explanation:

use formula I = prt

I=Interest P=principal R=rate T=time so Interest is = to 750 x 5% or 0.05 x 4 which is 150 so after 4 years 150 interest is gained

To calculate the minimum amount of wrapping paper needed to wrap the gift, Naomi would be finding the Surface Area.

The Surface Area of a three-dimensional object is the sum of the areas of all its faces. In this case, the gift is a rectangular prism with dimensions of length 10 inches, height 2 inches, and depth 3 inches.

To wrap the gift, Naomi would need to cover all six faces of the rectangular prism with wrapping paper. The formula for the Surface Area of a rectangular prism is:

Surface Area = 2lw + 2lh + 2wh

where l, h, and w are the length, height, and width of the rectangular prism, respectively.

Substituting the values for the length, height, and depth of the gift, we get:

Surface Area = 2(10 x 2) + 2(10 x 3) + 2(2 x 3)

Surface Area = 20 + 60 + 12

Surface Area = 92 square inches

Therefore, Naomi would need at least 92 square inches of wrapping paper to cover the gift, which is the Surface Area of the rectangular prism.

Triangle (B) is a comparable number that you must drag into the table.

An angle is formed when two straight lines or beams meet at a singular endpoint.

The intersection of two locations is known as the vertex of an arc.

The word "angle" is derived from the Latin word "angulus," which means "corner."

But there are some basic viewpoints.

Combining different shots greatly expands your camera options.

The most confusing of the five angles involves taking a scene from straight overhead.

So, the following:

Using the provided figure, we obtain:

A 60-degree equilateral triangle is depicted in the image.

And as can be seen in figure B, we obtain an equilateral triangle with a 60-degree inclination on each side.

Therefore, triangle (B) is a comparable number that you must drag into the table.

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a) the probability that the consumer is 18-24 years of age, given that he/she dislikes Crunchicles, is 0.0889 or approximately 0.089.

b) the probability that the selected consumer dislikes Crunchicles is 0.35 or 35%.

c) the probability that the selected consumer dislikes Crunchicles is 0.35 or 35%.

d) the probability that the selected consumer is 35-55 years old or likes Crunchicles is 0.44 or 44%.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

To solve these problems, we need to use the information given in the table and apply the rules of conditional probability and total probability.

What is the probability that the consumer is 18-24 years of age, given that he/she dislikes Crunchicles?

We want to find P(18-24 | disliked). By Bayes' theorem, we have:

P(18-24 | disliked) = P(disliked | 18-24) * P(18-24) / P(disliked)

We know that P(disliked | 18-24) = 17/132, P(18-24) = 92/300, and P(disliked) = 150/300. Therefore,

P(18-24 | disliked) = (17/132) * (92/300) / (150/300) = 0.0889

So the probability that the consumer is 18-24 years of age, given that he/she dislikes Crunchicles, is 0.0889 or approximately 0.089.

What is the probability that the selected consumer dislikes Crunchicles?

We want to find P(disliked). We know that the total number of consumers surveyed is 300 and the number of consumers who disliked Crunchicles is 105. Therefore,

P(disliked) = 105/300 = 0.35

So the probability that the selected consumer dislikes Crunchicles is 0.35 or 35%.

What is the probability that the selected consumer is 35-55 years old or likes Crunchicles?

We want to find P(35-55 or likes). By the rule of total probability, we have:

P(35-55 or likes) = P(35-55) + P(likes)

We know that P(35-55) = 32/300 and P(likes) = 92/300. Therefore,

P(35-55 or likes) = 32/300 + 92/300 = 0.44

So the probability that the selected consumer is 35-55 years old or likes Crunchicles is 0.44 or 44%.

Hence, a) the probability that the consumer is 18-24 years of age, given that he/she dislikes Crunchicles, is 0.0889 or approximately 0.089.

b) the probability that the selected consumer dislikes Crunchicles is 0.35 or 35%.

c) the probability that the selected consumer dislikes Crunchicles is 0.35 or 35%.

d) the probability that the selected consumer is 35-55 years old or likes Crunchicles is 0.44 or 44%.

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To measure a straight angle, Shirley could use any combination of pattern blocks that adds up to 180 degrees.

What are the pattern block angle combinations Shirley could use to measure the angle?

As a result, the pattern block angle combinations that Shirley could use to measure the angle are:

Incomplete question provided, below is the complete question -
Shirley measures the straight angle using pattern blocks. Choose every possible combination of angle possibilities for pattern blocks Shirley could use to calculate the angle.

# The tan pattern block has six minor angles.

# On the red pattern block, there are two angles: one large and one small.

# On the red pattern block, there is one large angle and three small angles.

# The tan pattern block has four tiny angles, and the red pattern block has one tiny angle.

# The red pattern block has two sharp angles.

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Answer:

x = 7

Step-by-step explanation:

      4*(2x - 10) = 16

Use Distributive property,

     4*2x - 4*10 = 16

        8x - 40    = 16

Now, we have to isolate ' x'. To isolate 'x', first Add 40 to both sides,

                   8x = 16 + 40

                   8x = 56

Divide both sides by 8,

                    x = 56 ÷ 8

                    [tex]\boxed{\bf x = 7}[/tex]

Answer:

247700% I'm not sure

I'm not good I'm maths

The second piece of the function applies to x = 1, which is f(x) = -x².

Thus, f(1) = -(1)² = -1.  The correct answer is f(1) = -1.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

To find the value of f(1), we need to determine which piece of the function applies to x = 1.

Since 1 is greater than 0 and less than 2, the second piece of the function applies to x = 1, which is f(x) = -x².

Thus, f(1) = -(1)² = -1.

Therefore, the correct answer is f(1) = -1.

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Answer:

n = 15

Step-by-step explanation:

the equation for inverse variation is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

to find k use the point (5, 3 ) , that is y = 3 when x = 5 , then

3 = [tex]\frac{k}{5}[/tex] ( multiply both sides by 5 )

15 = k

y = [tex]\frac{15}{x}[/tex] ← equation of variation

substitute (1, n ), that is x = 1, y = n into the equation

n = [tex]\frac{15}{1}[/tex] = 15

The value of x in the right angled triangle above is 7√3.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle.

To calculate the value of x in the right angle triangle above, we use the formula below.

Formula:

Where:

Substitute these values into equation 1 and solve for x

Hence, the value of x is 7√3.

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(I THINK I USED THE RIGHT CALCULATOR)

Answer: V≈113.1

Step-by-step explanation:

V=πr2h=π·1.52·16≈113.09734

The equation of the rational function is F(x) = 1/(x-2)(x+1). Thus, the answer is B. F(x) = 1/(x-2)(x+1).

It is a type of function that can be expressed in the form f(x) = p(x) / q(x), where p(x) and q(x) are polynomials and q(x) is not equal to zero. Rational functions are used in various areas of mathematics, including calculus and algebra.

The graph of a rational function is the set of points which satisfy the equation of the rational function.

In this case, the equation of the rational function is F(x) = 1/(x-2)(x+1).

The graph of this function is a line which passes through the points (2, 0) and (-1, 0) and has a vertical asymptote at x = 0.

The graph of a rational function can be determined by finding the zeroes, vertical and horizontal asymptotes, and intercepts of the function.

The zeroes of F(x) = 1/(x-2)(x+1) are x = 2 and x = -1. The vertical asymptote is x = 0 and the horizontal asymptote is y = 0.

The intercepts are (2, 0) and (-1, 0).

The graph of F(x) = 1/(x-2)(x+1) is a line which passes through the points (2, 0) and (-1, 0) and has a vertical asymptote at x = 0.

This is different from the graph of F(x) = 1/X² which is a parabola and from the graph of F(x) = 1(x+2)(x-1) which is two lines intersecting at (2, 0) and (-1, 0).

Therefore, the correct answer is B. F(x) = 1/(x-2)(x+1).

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the principle square root of -27 is √5.196.

Answer:

19 degrees

Step-by-step explanation:

hope this helps

The standard form of the expression (7.2 × 10⁵) ÷ (3.4 × 10³) include the following: C. 2.12 x 10².

In Mathematics, an exponent refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the law of indices for powers of the same base number and division, we have the following:

(7.2 × 10⁵) ÷ (3.4 × 10³

(7.2/3.4) × 10⁵⁻³

2.12 x 10².

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Complete Question:

The standard form of (7.2 × 10⁵) ÷ (3.4 × 10³)

a) 2.14 x 10

b) 2.11 x 10

c. 2.12 x 10²

d) 2.12 x 10​

Therefore, Aditi's mother requires 342 yellow tiles and 57 red tiles for the floral design on the kitchen wall.

Proportion is a statement that two ratios are equal. A ratio is a comparison of two quantities and is written in the form of a fraction. A proportion can be written in the form of a:b = c:d, where a, b, c, and d are numbers. This means that the ratio of a to b is equal to the ratio of c to d. We can also write a proportion as a fraction, where the numerator is the product of the means (ad) and the denominator is the product of the extremes (bc). Proportions are commonly used in mathematics to solve problems involving ratios and rates.

Here,

Since the floral design is made up of yellow and red hexagonal tiles, we need to determine the proportion of yellow tiles and red tiles in the design. Let's assume that the design consists of x yellow tiles and y red tiles. Each flower in the design consists of 7 hexagonal tiles - 6 yellow tiles and 1 red tile. Therefore, the total number of tiles in the floral design is:

Total number of tiles = 57 flowers x 7 tiles per flower

Total number of tiles = 399 tiles

Since each flower consists of 6 yellow tiles and 1 red tile, the total number of yellow tiles in the design is:

Number of yellow tiles = 6 x Number of flowers

Number of yellow tiles = 6 x 57

Number of yellow tiles = 342

Similarly, the total number of red tiles in the design is:

Number of red tiles = 1 x Number of flowers

Number of red tiles = 1 x 57

Number of red tiles = 57

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Complete question:

Aditi's mother is renovating her kitchen. One of the walls of kitchen is entirely made up of tiles. She wants to have a row of floral designs made up of yellow and red hexagonal tiles in the middle of the wall as shown in the adjoining figure. If there are 57 flowers in a row, find out how many yellow-and red-coloured tiles she requires for that wall.

Answer: -2， 6

（-2）Because from 3a³ to (1)a³, it needs to subtract 2a³.

   (6)  Because from -5b³ to b³, it needs to add 6.

Answer:

24

Step-by-step explanation:

Total number of food = x

If ¾ of food = number of burgers bought

Then 3/4 times x = 3x/4

3x/4= 18

x = 24

Answer:

The dimensions of the t r including the path are 12+3+3 and 6+3+3 which is 18x12=216 m2

If we subtract the  tr area 12x6=72m2

216m2–72m2=144m2

Step-by-step explanation:

The characteristic polynomial of A is λ³ - 4λ² - 3λ + 14. The eigenvalues of A are 2, 1, and 7.

According to the rational root theorem, p is a factor of the constant term and q is a factor of the leading coefficient if a polynomial with integer coefficients has a rational root of p/q, where p and q are integers without any shared factors. As the leading coefficient is 1 and the constant term is 14, the only potential rational roots in this situation are 1, 2, 7, and 14.

The characteristic polynomial of a matrix is given as

det(A - λI)

Here, λ is the eigen value.

det (A - λI)

[tex]\left[\begin{array}{ccc}1 - \lambda&0&1\\2&3 -\lambda&-1\\0&6& \lambda\end{array}\right][/tex]

Taking the determinant we have:

det(A - λI) = (1-λ)[(3-λ)(-λ) - (-1)(6)] - 0[2(-λ) - (-1)(0)] + (-1)[2(6) - (3-λ)(0)]

det(A - λI) = (1-λ)(λ² - 3λ - 6) - (-1)(12) = λ³ - 4λ² - 3λ + 14

Hence, the characteristic polynomial of A is λ³ - 4λ² - 3λ + 14.

The eigen values is the solution of the polynomial.

Using the rational roots of polynomial we have:

λ³ - 4λ² - 3λ + 14. factors as (λ-2)(λ-1)(λ-7)

Hence, the eigenvalues of A are 2, 1, and 7.

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According to the graph, the value of the constant in the equation below is 2. The correct option is B.

A constant function in mathematics is one whose (output) value is constant regardless of the input value.

We are given the equation for the height.

On the graphic, height, and width are related. By choosing a point, we can find the value of the constant.

To find a constant in a graph, the width is multiplied by height.

(Height)(Width) = Constant.

Multiply any of the coordinate values shown, and you will see the constant is 2.

 3 × 1.5 = 2 × 1 = 8 × 4 = 7 × 3.5 =

we will take only one variable which is 2 x 1 = 2, so the constant is 2

Therefore, the correct option is B, 2.

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Rounded to the nearest tenth, the approximate duration for one swing of a pendulum with a length of 13.69 meters is 7.7 seconds.

We are given that the time, t, in seconds it takes for a pendulum to swing back and forth once is given by:

t = 2.01√L

where L is the length of the pendulum in meters.

We are asked to find the time it takes for a pendulum of length 13.69 meters to swing back and forth once. So we can substitute L = 13.69 into the equation above to get:

t = 2.01√(13.69) ≈ 2.01 × 3.7 ≈ 7.7

Therefore, the time it takes for a pendulum of length 13.69 meters to swing back and forth once is approximately 7.7 seconds (rounded to the nearest tenth).

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