Given the triangle below, find the angle θ.


Give your answer in radians rounded to four decimal places.

The value of k, considering the numeric value of the derivative at x = 0, is given as follows:

b) k = -2 or k = 2.

The function in the context of this problem is defined as follows:

y = (x + k)³.

Applying the power of x rule followed by the chain rule, the derivative of the function is given as follows:

y' = 3(x + k)².

When x = 0, the numeric value of the derivative is of 12, hence the value of k is obtained as follows:

3k² = 12

k² = 4

k = -2 or k = 2.

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The area of the sector rounding to the nearest tenth is C. 8377.6 [tex]cm^2[/tex].

The law of cosines is a formula used to find the length of a side or the measure of an angle in a non-right triangle (a triangle that does not have a 90-degree angle).

According to given information:

To find the area of the windshield swept by the wiper blade, we can consider it as a sector of a circle with radius equal to the length of the segment swept by the wiper blade. The length of this segment can be found using the law of cosines:

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

where a and b are the lengths of the sides adjacent to the angle C, and c is the length of the side opposite to the angle C.

In this case, we have:

a = 80 cm (length of the wiper blade)

b = 90 cm (length of the swing arm)

C = 120 degrees (angle swept by the swing arm)

Substituting these values, we get:

[tex]c^2 = 80^2 + 90^2 - 2(80)(90)cos(120)[/tex]

[tex]c^2[/tex] ≈ [tex]20418[/tex]

[tex]c[/tex] ≈ [tex]142.8 cm[/tex]

So the radius of the circle is approximately 142.8 cm. The central angle of the sector is 120 degrees, so its measure in radians is 2π/3. Therefore, the area of the sector is:

A = (1/2) * [tex]r^2[/tex] * θ

A = (1/2) * [tex](142.8)^2[/tex] *[tex](2\pi /3)[/tex]

A ≈ 8377.6 [tex]cm^2[/tex]

Rounding to the nearest tenth, we get the answer as C. 8377.6 [tex]cm^2[/tex].

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The arc length of the each arc are 14π cm, 95π/6 ft, 7π cm, 39π/4 ft.

What is arc length of a circle?

The arc length formula for a circle is given by L = rθ, where L is the arc length, r is the radius, and θ is the central angle measured in radians.

9) Here angle= 315° and radius= 8cm.

First, we need to convert the angle to radians: 315° × (π/180°) = 7π/4.

Then we can use the arc length formula,

L = 8 × 7π/4 = 14π cm.

10) Here angle = 150° and radius= 19 ft.

First, we need to convert the angle to radians: 150° × (π/180°) = 5π/6.

Then we can use the arc length formula,

L = 19 × 5π/6 = 95π/6 ft

11) Here angle = π/2 and radius= 14 cm.

According to the arc length formula,

L = 14 × π/2 = 7π cm .

12) Here angle= 3π/4 and radius= 13 ft.

According to the arc length formula,

L = 13 × 3π/4 = 39π/4 ft.

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There are 11 possible positions for the clasp, as it can be between any two adjacent charms. If we want the clasp to be between the charms of June and July, we need to count how many of these positions satisfy this condition.

Since there are 12 charms in total, we can arrange them in 12! ways. However, since the order of the charms doesn't matter except for the position of the clasp, we need to divide by 12 to account for the different arrangements of the same set of charms.

Now, we can fix the charms of June and July in their correct positions, which leaves us with 10 remaining charms to arrange. There are 10! ways to do this. However, since we want the clasp to be between the charms of June and July, we need to treat them as a single block and arrange the 10 remaining charms and this block. There are 11 ways to do this.

Therefore, the total number of arrangements where the clasp is between the charms of June and July is 11 × 10!.

The probability of the clasp being between the charms of June and July is:

P = (number of favorable outcomes) / (total number of possible outcomes)

= (11 × 10!) / (12!)

= 11/66

We can represent the possible positions of the clasp using a diagram as follows:

Charm 1 - Charm 2 - Charm 3 - Charm 4 - Charm 5 - Charm 6 - Charm 7 - Charm 8 - Charm 9 - Charm 10 - Charm 11 - Charm 12

|---------------------|

To draw a scatter plot we will determine the plot's x and y axis. We can specify the scale for each axes and finally plot the points.

Data can be graphically represented using a scatter plot. The Coordinate axes are used in a straightforward scatter plot to plot the points according to their values.

To create a scatter plot, follow these three easy steps.

Determine the scatter plot's x- and y-axes in step one.

Specify the scale for each of the axes in STEP II.

Plot the points based on their values in Step 3.

Now here in the question,

We will draw a scatter plot using the data given in the table.

The graph is attached to the answer.

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Answer:

The answer is option C) 4.037 x 10^7.

Step-by-step explanation:

To find out how many more people live in California than in Vermont, we need to subtract the population of Vermont from the population of California.

The population of California is 4.1 x 10^7.

The population of Vermont is 6.3 x 10^5.

Therefore, the difference in population between California and Vermont is:

4.1 x 10^7 - 6.3 x 10^5

= 4.037 x 10^7

So, about 4.037 x 10^7 more people live in California than in Vermont.

The answer is option C) 4.037 x 10^7.

The number οf favοurs that Bertrand needs tο buy is 63

An algebraic equatiοn is a mathematical statement that uses οne οr mοre variables and mathematical οperatiοns tο describe a relatiοnship between thοse variables.

Algebraic equatiοns are cοmmοnly used in mathematics, science, engineering, and οther fields tο mοdel real-wοrld phenοmena, sοlve prοblems, and make predictiοns.

Here we have

Bertrand invites 21 peοple tο his party and wants tο give each guest 3 party favοrs.

If n is the tοtal number οf party favοrs he will need tο οrder,

The equatiοn that represents this situatiοn is: n/21 = 3

Where n is the tοtal number οf party favοrs Bertrand will need tο οrder, and 3 represents the number οf party favοrs each guest will receive.

On sοlving the equatiοn will get

=> n/21 = 3

Multiply with 21 οn bοth sides

=> 21(n/21) = 21 × 3

=> n = 63

Therefοre, The number οf favοrs that Bertrand needs tο buy is 63

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The cost for 100 shares at the 52-Week Low is $5228.  Therefore the correct option is option A.

We need to look at the table or chart that shows the data on stock prices at the 52-week low in order to respond to this question. The question alone does not provide the response.

After gaining access to the table, we may calculate the price for 100 shares by multiplying the price for 1 share at the 52-week low by 100.

Let's use $52.28 as an example of the price per share at the 52-week low. The price for 100 shares would be as follows:

$52.28 x 100 = $5,228

Thus, $5228 is the correct response (A).

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The correct answer is option C: Laura determines the four arithmetic means to be −7.2, 2.8, 12.6, and 22.2.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

To determine the arithmetic means between two numbers, we need to find the common difference between each pair of consecutive means. The common difference is given by:

Common difference = (larger number - smaller number) / (number of means + 1)

In this case, the larger number is 32 and the smaller number is -17. Laura wants to find four means, so the number of means is 4. Therefore, the common difference is:

Common difference = (32 - (-17)) / (4 + 1) = 49 / 5 = 9.8

To find the four arithmetic means, we start with the smaller number and add the common difference successively. Therefore, the four arithmetic means are:

-17 + 9.8 = -7.2

-7.2 + 9.8 = 2.6

2.6 + 9.8 = 12.4

12.4 + 9.8 = 22.2

Therefore, the correct answer is option C: Laura determines the four arithmetic means to be −7.2, 2.8, 12.6, and 22.2.

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Answer: 171

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

|x+8|=x+8

x+8=x+8

x^2+8=8

x^2=16

√x^2=√16

x=8

Part 4:  By the theorem of inscribed angle in the circle: arc RP  = 136°.

Part 5: From the central angle theorem: m∠LNM = 54°.

Part 4:

m∠QRP = 68°

By the theorem of inscribed angle in the circle:

Two chords with a shared termination point on the circle make up an inscribed angle in a circle. The vertex of a angle is this common terminal point.

arc RP  = 2 * m∠QRP

arc RP  = 2 * 68°

arc RP  = 136°

Part 5:

From the central angle theorem:

An inscribed angle's measurement is equal to half of an intercepted arc's measurement.

As a result, any two inscribed angles in a circle with identical intercepted arcs remain congruent.

m∠LNM = 1/2 m∠LNP

m∠LNM = 1/2 * 108°

m∠LNM = 54°

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Answer:

Step-by-step explanation:

Let's use a Venn diagram to help us visualize the information given in the problem. We can start with three overlapping circles representing Physics (P), Chemistry (C), and Biology (B), and then fill in the numbers given:

                  P

                /   \

               /     \

              /       \

             CP        BP

              \       /

               \     /

                \   /

                  B

We know that 6 students study pure Chemistry, so we can write this number in the circle for Chemistry (C). We also know that 10 students study pure Physics and 8 students study pure Biology, so we can write these numbers in the circles for Physics (P) and Biology (B), respectively:

                  P (10)

                /   \

               /     \

              /       \

        CP (18)       BP (21)

              \       /

               \     /

                \   /

                  B (8)

               C (6)

Now we can use the information given in the problem to fill in the remaining numbers:

22 students study Physics and Biology, so this number goes in the overlap between P and B: PB = 22

21 students study Chemistry and Biology, so this number goes in the overlap between C and B: CB = 21

We don't know the number of students who study Physics and Chemistry only, but we can use the fact that 6 students study pure Chemistry to figure it out. Since 18 students study Chemistry and Physics in total, and 6 of them study pure Chemistry, the remaining 18 - 6 = 12 students must study both Chemistry and Physics but not Biology. We can write this number in the overlap between C and P: CP = 12.

                  P (10)

                /   \

               /     \

              /       \

        CP (12)       BP (21)

              \       /

               \     /

                \   /

                  B (8)

               C (6)

Now we can find the total number of students by adding up all the numbers in the Venn diagram:

Total = P + C + B - (CP + CB + PB) + (CPB)

Total = 10 + 6 + 8 - (12 + 21 + 22) + 0

Total = 19

Therefore, the total number of students in the class is 19.

Answer:

  19.2

Step-by-step explanation:

You want the solution to 38.4 = 2x.

When you divide both sides of the equation by 2, you will have your answer.

  38.4/2 = (2x)/2

  19.2 = x

The solution to the equation is x = 19.2.

__

Additional comment

When you learned multiplication and division, you learned that each multiplication fact corresponds to two division facts:

  A = B×C . . . . . . . 6 = 2×3

  A/B = C . . . . . . . . 6/2 = 3

  A/C = B . . . . . . . . 6/3 = 2

We use that relationship here to find the value of one of the factors in the product:

  38.4 = 2·x

  38.4/2 = x

The other division fact is still true, but isn't useful here for finding the value of x.

  38.4/x = 2

Answer:

22 problems

Step-by-step explanation:

50% is half of 100, so if 100 divided by 2 is 50, then 11 x 2 is 22. 22 is the answer

The Volume of Silo is. V= 13886 ft cube

A grain Silo is cylindrical in shape.

Height  (h) = 49 ft.

Diameter (d) = 19 ft.

We need to find the Volume of silo.

We will first find the radius.

Radius can be given as half of the diameter.

hence Radius (r) = 9.5

Since Silo is in Cylindrical Shape we will find the volume of a cylinder.

Now We know that the Volume of a cylinder can be calculated by multiplying π with the square of the radius and height.

Volume of Cylinder = πr²h

            V= 3.14×9.5×9.5×49

            v=13885.865 ft cube

Rounding to the nearest whole number we get;

Hence, the Volume of the Silo is. V= 13886 ft cube

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Answer: The sum of all the data values divided by the number of data values is 7.

Answer:

A line graph would best show the average temperatures each month

Angular speed is approximately 1.36 rad/sec and the linear speed of a point on the rim of the rotating wheel is approximately 28.56 ft/sec.

How to calculate the angular speed and linear speed of a point on the rim of the rotating wheel?

The angular speed of the rotating wheel in rad/sec is given by:

angular speed = 2π × RPM / 60

where RPM is the revolutions per minute. we get:

angular speed = 2π × 13 / 60

≈ 1.36 rad/sec

The linear speed of a point on the rim of the rotating wheel in ft/sec is given by:

linear speed = radius × angular speed

where radius is the radius of the wheel. we get:

linear speed = 21 ft × 1.36 rad/sec

≈ 28.56 ft/sec

Therefore, the angular speed of the rotating wheel is approximately 1.36 rad/sec and the linear speed of a point on the rim of the rotating wheel is approximately 28.56 ft/sec.

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Answer:

Answer: A, C, D, and F are polyhedra.

Chain of thought reasoning:

A. Pyramid: A pyramid is a polyhedron because its base is a polygon with four or more sides and its associated faces are triangles. Therefore, Pyramid (A) is a polyhedron.

B. Sphere: A sphere is not a polyhedron because it is not composed of flat faces connected at straight edges, thus it does not form a shape with flat faces and straight edges. Therefore, Sphere (B) is not a polyhedron.

C. Pentagonal prism: A pentagonal prism is a polyhedron because its base is a polygon with five sides and its associated faces are also polygons, resulting in a shape with flat faces and straight edges. Therefore, Pentagonal Prism (C) is a polyhedron.

D. Cube: A cube is a polyhedron because both its bases and its associated faces are polygons with four sides, resulting in a shape with flat faces and straight edges. Therefore, Cube (D) is a polyhedron.

E. Cylinder: A cylinder is not a polyhedron because it is not composed of flat faces connected at straight edges, thus it does not form a shape with flat faces and straight edges. Therefore, Cylinder (E) is not a polyhedron.

F. Cone: A cone is a polyhedron because its base is a polygon with three or more sides and its associated faces are circles or triangle, resulting in a shape with flat faces and straight edges. Therefore, Cone (F) is a polyhedron.

Answer:

Step-by-step explanation:

the answer is c because all those numbers are even and less than 12 its not a because yes all the numbers are greater than two but that answer must include 3,4,5,6,7 and on and on is not d because some numbers are prime and it's not d because the only numbers less than three are 2,1 so that's why the answer is c

Answer:

He has 68.8% of his drink left

Step-by-step explanation:

do 32 oz - 10 oz = 22 oz to get how much of his drink is left

To get the percentage, just do what left divided by original amount

so 22/32 = 0.6875 and in percent, that is about 68.8%

Answer: The teacher is incorrect

Step-by-step explanation: 20x3=60 4x12=48 60+48=108 108/24=4.5

4.5 does not equal 6.    5 packs of battery's will be needed and there will be 12 battery's left over.

Graph the two inequalities,

The region shaded in black satisfies both inequalities

Answer: 5.625 Cubed

Step-by-step explanation: First you will times 3.75 and 1.5. Which should get you 5.625 squared. Next you will just times 5.625 squared by 1. Which will get you 5.625 cubed.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2100\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 2100\left(1+\frac{0.02}{1}\right)^{1\cdot 5}\implies A=2100(1.02)^5 \implies A \approx 2318.57[/tex]

The LCD of the given rational function is option B (x²-25)(6x + 30)(6x).

An equation containing one or more rational expressions is referred to as a rational equation. A fraction with polynomials as the numerator and denominator is known as a rational expression. A rational expression is, in other words, the ratio of two polynomials. Finding the LCD (Least Common Denominator) of the fractions, removing the denominators, and then simplifying the resultant equation can be used to solve rational equations. By resolving the resultant equation, which may require factoring, simplification, or the use of other algebraic strategies, the solutions of rational equations can be discovered. In order to simulate complicated systems and events, rational equations are frequently employed in physics, engineering, and other disciplines.

For the given rational equation the LCD will be the multiplication of all the denominators in the given rational equation.

Thus,

(x²-25)(6x + 30)(6x)

Hence, the LCD of the given rational function is option B (x²-25)(6x + 30)(6x).

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Answer:

[tex]p(x)=2(x-3)^2-1[/tex]

Step-by-step explanation:

The values are symmetric about [tex]x=3[/tex], meaning the equation is of the form [tex]p(x)=a(x-3)^2-1[/tex].

Since [tex]p(4)=1[/tex], it follows that:

[tex]1=a-1 \\ \\ a=2[/tex]

Therefore, [tex]p(x)=2(x-3)^2-1[/tex].

Answer:

your answer is the second one.