Let f be the continuous function defined on [-4,3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. Let g be the function given by g(x) = integral^x_1, (t) dt. Find the values of g(2) and g(-2). For each of g'(-3) and g"(-3), find the value or state that it docs not exist. Find the x-coordinate of each point at which the graph of g has a horizontal tangent line. For each of these points, determine whether g has a relative minimum, relative maximum, or neither a minimum nor a maximum at the point. Justify your answers. For -4 < x < 3, find all values of v for which the graph of g has a point of inflection. Explain your reasoning.

Proved that, sin⁴x-cos⁴x/ sin²x-cos²x = 1​.

Here, we have,

given that,

the LHS is:

sin⁴x-cos⁴x/ sin²x-cos²x

now, we know that,

sin²x+cos²x = 1

and, we know that,

a² - b² = (a+b) (a-b)

so, we get,

sin⁴x-cos⁴x/ sin²x-cos²x

= (sin²x+cos²x) (sin²x-cos²x ) / sin²x-cos²x

=(sin²x+cos²x)

=1

= RHS

Hence, Proved that, sin⁴x-cos⁴x/ sin²x-cos²x = 1​

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The graph of the inequality y ≥ (x+2)^2 is added as an attachment

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

y is greater than or equal to (x+2)^2

Express the statement properly

So, we have

y ≥ (x+2)^2

The above expression is a an inequality of a quadratic function

Next, we plot the graph using a graphing tool

To plot the graph, we enter the expression in a graphing tool and attach the display

See attachment for the graph

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Answer:

B: rectangle JKLM ~ rectangle QRSP

Step-by-step explanation:

5/6=0.83

12.5=0.83

JK corresponds to QR

JM corresponds to PQ

rectangle JKLM ~ rectangle QRSP

The value of x is given as follows:

x = 24.

The measure of angle DFE is given as follows:

<DFE = 62º.

To obtain the measures, we consider that the sum of the measures of the internal angles of a triangle is of 180º.

The internal angle measures for this problem are given as follows:

Hence the value of x is obtained as follows:

180 - 5x + 14 + 44 + 3x - 10 = 180

228 - 2x = 180

2x = 48

x = 24.

The measure of angle DFE is obtained as follows:

<DFE = 3(24) - 10

<DFE = 72 - 10

<DFE = 62º.

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The area of the triangle with the given vertices is 11.5 square units.

The area of a triangle can be calculated using the coordinates of its vertices using the following formula.

To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:

A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2

Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:

A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2

A = (0 - 4 + 27)/2

A = 23/2

A = 11.5

Therefore, the area of the triangle with the given vertices is 11.5 square units.

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Answer:

n = 11

Step-by-step explanation:

Step 1: Write equation

2 = -9 + 22 - n

Step 2: Solve for n

Step 3: Check

Plug in n to verify it's a solution.

Complete Question

The option to the blank space are shown on the first uploaded image

Answer:

Neal's decision is to fail to reject the null hypothesis   (p 0.066). There is no sufficient evidence to prove the claim that the average electricity consumption of all  Ledee household is greater than , 854.28 kWh

Step-by-step explanation:

From the question we are told that

   The population mean is  \(\mu = 854.11\)

   The sample size is  \(n = 65\)

    The sample mean is  \(\= x = 879.28 \ kWh\)

    The standard deviation is  \(\sigma = 133.29 \ kWh\)

    The level of significance is  \(\alpha = 0.05\)

     The  null hypothesis is  \(H_o: \mu = 854.11\)

     The  alternative hypothesis is  \(H_a : \mu > 854.11\)

     The  t-statistics is  \(t = 1.522\)

      The  p-value is \(p-value = 0.066\)

Now from the given data we can see that

         \(p-value < \alpha\)

Generally when this is the case , we fail to reject the null hypothesis

   So

Neal's decision is to fail to reject the null hypothesis   (p 0.066). There is no sufficient evidence to prove the claim that the average electricity consumption of all  Ledee household is greater than , 854.28 kWh            

Answer:

diameter=12ft

radius=7 in

Step-by-step explanation:

A semicircle has been cut out of a rectangular paperboard that is 20 inches long and 12 inches broad, as seen below. After the semicircle is taken out, the paperboard's remaining perimeter is 34.58 inches.

The paperboard has a length of 20 inches and a width of 12 inches. A semicircle is cut out of it, which means we need to find the perimeter of the remaining part.

The diameter of the semicircle is equal to the width of the paperboard, which is 12 inches. So, the radius of the semicircle is half of the diameter, which is 6 inches.

The perimeter of the remaining part will be the sum of the length of the paperboard and the two straight sides of the semicircle.

The length of the paperboard is 20 inches, and the two straight sides of the semicircle are equal to the diameter of the semicircle, which is 12 inches. So, the perimeter of the remaining part is:

P = 20 + 12 + 12 = 44 inches

However, we also need to subtract the length of the curved part of the semicircle from the perimeter. The length of the semicircle can be found using the formula:

C = πr

where C is the circumference of the semicircle and r is the radius.

Since we have a semicircle, we need to divide the circumference by 2. So, the length of the curved part of the semicircle is:

C/2 = (π x 6) / 2 = 9.42 inches (rounded to two decimal places)

Therefore, the perimeter of the remaining part is:

P = 44 - 9.42 = 34.58 inches (rounded to two decimal places)

So, the perimeter of the remaining paperboard is 34.58 inches.

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Answer:

\(3x^{3} - 14x^{2} - 5x\)

Step-by-step explanation:

I'm assuming what you're looking for is the expansion, or simplification, of the right side of that equation: x(3x + 1)(x - 5). So, let's go ahead and do that; let me know if you're looking for something else.

First, let's distribute that "x" at the beginning of the expression onto that first parenthetical expression, (3x + 1).

\(x(3x + 1) = x(3x) + x(x) = 3x^{2} + x\)

Now we have something different to simplify, \((3x^{2} + x)(x - 5)\).

\((3x^{2} + x)(x - 5) = \\3x^{2}(x) + 3x^{2}(-5) + x(x) + x(-5) = \\3x^{3} - 15x^{2} + x^{2} - 5x = \\3x^{3} - 14x^{2} - 5x\)

And there's our answer. Hopefully that was helpful - again, if you have any more questions, please let me know. :)

The correct option regarding whether the relation is a function is:

B. The relation is a function. Each input value is paired with one output value.

A relation represent a function if each value of the input is paired with one value of the output.

In this problem, when the input - output mappings are given by:

{(–2, 3), (–1, 3), (0, 2), (1, 4), (5, 5)}.

Which means that yes, each input value is paired with one output value, hence the relation is a function and option B is correct.

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Answer and Step-by-step explanation:

To find x, we have to understand the information given by the figure.

We see that the lines:
DC = 4

CA = 7

BA = x + 12

EC = x

We need to check if the triangle follows the Triangle Proportionality Theorem, which states that if a line parallel to one side of a triangle intersects the other two sides at different points, it divides the sides into corresponding proportional segments.

The triangle doesn't appear to have symbols (> or ∥) indicating that the segments EC and BA are parallel to each other.

This means we can't use any proportionality theorems to find x.

The answer is B. Cannot be determined.

Have a great day!

Answer:

I think you mean this :

\( \sqrt{x - 5} = 6 \\ = > {( \sqrt{x - 5} })^{2} = {6}^{2} \\ = > x - 5 = 36 \\ = > x = 36 + 5 \\ = > x = 41\)

Or,

Square root of x-5=6 is :

\( \sqrt{x - 5} \:=\:\sqrt{6} \)

The value of probability P (A or B) is,

P (A or B) = 19/34

We have to given that,

From the Venn diagram, we can observe that there are two events A and event B

n(A ∪ B) = 17 + 2

n(A ∪ B) = 19

And, The sample space would be,

n(S) = 17 + 2 + 15

n(S) = 34

Hence, Using the definition of probability,

P(A) = n(A) / n(S)

P (A) = 17/34

P (A) = 1/2

P(B) = n(B)/n(S)

P(B) = 2/34

P(B) = 1/17

So, We get;

P (A or B) = P (A) + P (B)

P (A or B) = 1/2 + 1/17

P (A or B) = 19/34

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Answer:

B

Step-by-step explanation:

Answer: y=1.25

Step-by-step explanation:

First things first you have to find what is in the bracket things (i don’t know what it’s called) So 3 - 7 is -4y but since it’s absolute it’s going to be 4y.

So now you’ve got 4y - 10 = -5. Your going to want to eliminate 10 so, subtract 10 to both sides giving you 4y = -5

Lastly to get y by itself you need to divide it by its self so, 4y divided by 4. Do it to both sides. This gives you…

Y = 1.25

Answer:

the confidence interval for the true weight of the specimen is;

4.1593 ≤ μ ≤ 4.1611

Step-by-step explanation:

We are given;

Standard deviation; σ = 0.001

Sample size; n = 8

Average weight; x¯ = 4.1602

We are given a 99% confidence interval and the z-value at this interval is 2.576

Formula for confidence interval is;

CI = x¯ ± (zσ/√n)

Plugging in the relevant values, we have;

CI = 4.1602 ± (2.576 × 0.001/√8)

CI = 4.1602 ± 0.000911

CI = (4.1602 - 0.000911), (4.1602 + 0.000911)

CI ≈ (4.1593, 4.1611)

Thus, the confidence interval for the true weight will be expressed as;

4.1593 ≤ μ ≤ 4.1611

Where μ represents the true weight

Answer:

Step-by-step explanation:

Translate the given into two pairs of coordinates:

Work out the equation of the line passing through both of the points.

Find the slope:

Find the y-intercept:

The line is:

Find the value of y when x = 1500:

Answer:

rrir

Step-by-step explanation:

e8

Given:

\(m\angle ABC=60\)

To find:

The \(m\angle ADC\).

Solution:

In circle B, \(\angle ABC\) is central angle and \(\angle ADC\) is inscribed angle from two points A and C.

According to central angle theorem, central angle is always twice of inscribed angle.

\(m\angle ABC=2(m\angle ADC)\)         [Central angle theorem]

\(60=2(m\angle ADC)\)

Divide both sides by 2.

\(\dfrac{60}{2}=m\angle ADC\)

\(30=m\angle ADC\)

Therefore, \(m\angle ADC=30\).

Answer:

y = -8

Step-by-step explanation:

2(y-2)- 6y-28 = 0

2y - 4 -6y - 28 = 0

-4y = 32

y = -8

Answer: 6.8622 ; 8.1778

Step-by-step explanation:

Given the data:

2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9

6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9

7 10 7 9 9 9 9

Assume a confidence interval of 95%

Using calculator :

The mean of the distribution (m) = 7.52

Standard deviation (s) = 2.314

Sample size),

Obtaining the t score ;

Degree of freedom (df) = (n-1) = 50 - 1 = 49

t(1-α/2), 49 = t(0.025, 49) = 2.01 ( t distribution table)

Margin of Error :

2.01 * s/√n = 2.01 * 2.314/7.0710678

Margin of Error (E) = 0.6578

Confidence interval:

(Mean - E) ≤μ≤ (mean + E)

(7.52 - 0.6578) ≤μ≤ (7.52 + 0.6578)

6.8622 ≤μ≤ 8.1778

The area covered by the signal is 181.37 m²

Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m

The area of a circle of radius R is given by:

A = 3.14*R²

Then the area of a fourth of a circle is:

A = (3.14/4)*R²

Replacing the value of the radius in the formula we will get:

A =  (3.14/4)*(15.2m)² = 181.37 m²

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Answer:

1.Let the number be x

5x + 50 = 200 – x

2. Let the number be x

50 – 4x = 15 + x

4. Let the smaller number be x  

and the larger number be 5 – 2x

X + 5 – 2x = 70

X + 5 = 70

X = 70 -5

X = 65

1. Let the smallest consecutive number be x

The largest be x + 2

2x = 12 + x + 2

2x – x = 14

x = 14

The numbers are  

14, 15, 16

2. Let the smallest be x

The middle be x + 1

The largest be x+ 2

X + x+ 1 = 24 + x + 2

2x + 1 = 26 + x

2x – x = 26 -1

X = 25

The numbers are

25 , 26, 27

3. Let the first even number be x

Let the second even number be x + 2

Let the third even number be x+ 4

= x + 2 (x + 2) = 20 + x + 4

= x + 2x + 4 = 20 + x + 4

= 3x + 4 = 24 + x

= 3x – x = 24 -4

= 2x = 20

= x = 20/2

X = 10

The even numbers are

10. 12, 14

Answer:

a table of products of two factors especially the integers 1 to 12 have a nice day

Step-by-step explanation:

:)

Answer:

YOUR WELCOME

\(\:\)

y = 3x − 1

Using the slope-intercept form, the slope is 3.

m = 3

For the given confidence interval, the correct statement is Option C. The manager can be 99% confident that the constructed interval captures the true mean number of fish in saltwater tanks.

Confidence interval:

Confidence interval refers the mean of your estimate plus and minus the variation in that estimate.

Given,

Here we need to find which of the following correctly interprets the 99% confidence interval for the true mean number of fish in saltwater tanks.

While we looking into the given question,

We know that, it states that 99% confidence interval for the true mean number of fish in saltwater tanks,

Based on these fact the correct statement is the manager can be 99% confident that the constructed interval captures the true mean number of fish in saltwater tanks.

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Answer:

3/20  hope it is right

Step-by-step explanation:

Answer:

  x = 36

Step-by-step explanation:

Given a tangent segment of length 24, and a secant segment from the same point with an external length of 12 and a total length of (12+x), you want to find the value of x.

The product of lengths from the common point to the two intersections with the circle are the same for both segments. In the case of the tangent, the two intersections with the circle are the same point, so the square of the length is used.

  24² = 12(12 +x)

  2·24 = 12 +x . . . . . . . divide by 12

  36 = x . . . . . . . . . subtract 12

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