Write an equation in slope-intercept line form form for the line perpendicular to 2x-3y=12 that passes through the point (8,5)

The area of a regular decagon whose apothem is 14 mm is 560 square milli meter

A polygon is a plane figure made up of line segments connected to form a closed polygonal chain

We have to find the area of a regular decagon whose apothem is 14 mm and side length of 8m

Area of decagon = 1/2×Apothem×perimeter

Perimeter =Number of sides ×side length

=10×8

=80

Area of decagon = 1/2×14×80

=7×80

= 560 square mm

Hence, the area of a regular decagon whose apothem is 14 mm is 560 square milli meter

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The area of a regular decagon is approximately 605.5 mm².

Area of a regular decagon :

Area = (1/2) × Perimeter × Apothem

If we denote the side length by 's,' we can find it using the relationship between the number of sides, the side length, and the apothem:

The number of sides (n) is 10 because it is a decagon.

The formula for the side length of a regular polygon given its apothem (a) is:

[tex]s = 2a \times tan(\pi/n).[/tex]

Substitute n = 10 and a = 14 mm into the formula:

s = [tex]2 * 4 mm \times tan(\pi/10)[/tex]

   ≈ 8.65 mm.

Then, the perimeter (P) of the decagon is:

[tex]P = n \times s[/tex]

 = 10 *8.65 mm

≈ 86.5 mm.

Now, use the area formula:

Area = (1/2) × P × a

           = (1/2) × 86.5 mm × 14 mm

            ≈ 605.5 mm².

So, the area of the regular decagon is approximately 605.5 mm².

Answer:

300 cm

Step-by-step explanation:

1 meter is 100 centimetres, so 3 meters would result in 3 x 100, which equals 300.

Question:

1. The females worked less than the males, and the female median is close to Q1.

2. There is a high data value that causes the data set to be asymmetrical for the males.

3. There are significant outliers at the high ends of both the males and the females.

4. Both graphs have the required quartiles.

Answer:

The correct option is;

1. The females worked less than  the males, and the female median is close to Q1

Step-by-step explanation:

Based on the given data, we have;

For males

Minimum = 0

Q1 = 1

Median or Q2 = 20

Q3 = 25

Maximum = 50

For females;

Minimum = 0

Q1 = 5

Median or Q2 = 6

Q3 = 10

Maximum = 18

Therefore, the values of data that affect the statistical measures of spread and center are that

The females worked less than the males as such the statistical data for the females have less variability than the males in terms of interquartile range

Also the female median is very close to Q1, therefore it affects the definition of a measure of center.

Answer:

the answer is the second one

Step-by-step explanation:

Answer:

The product of

36√cis(π/8) and 25√cis(7π/6)

is

(225√2)√[√(2 + √2) + i√(2 - √2)][√(3(-1 + i))]

Step-by-step explanation:

First note that

cis(π/8) = cos(π/8) + isin(π/8)

cis(7π/6) = cos(7π/6) + isin(7π/6)

cos(π/8) = (1/2)√(2 + √2)

sin(π/8) = (1/2)√(2 - √2)

36√cis(π/8) = (36/√2)√[√(2 + √2) + i√(2 - √2)]

cos(7π/6) = -(1/2)√3

sin(7π/6) = (1/2)√3

25√cis(7π/6) = (25/2)√3(-1 + i)

The product,

36√cis(π/8) × 25√cis(7π/6)

= (36/√2)√[√(2 + √2) + i√(2 - √2)] × (25/2)√3(-1 + i)

= (225√2)√[√(2 + √2) + i√(2 - √2)][√(3(-1 + i))]

Answer:

32.86 cis ( 4.06 )

Step-by-step explanation:

TTT

Answer:

88

Step-by-step explanation:

Final answer:

Time's accuracy is crucial in sports, and a high school track coach's new stopwatch with an uncertainty of ±0.05 s may not be suitable for distinguishing very close race outcomes, such as those within a few hundredths of a second apart.

Explanation:

Time is a fundamental measurement in athletic competitions, particularly in track and swimming events, where even hundredths of a second can determine the outcome. The precision of time measurements has become increasingly important with the advancement of athletes' abilities, pushing the limits of human performance. In recent history, various advanced instruments have been developed to ensure the accuracy of timing in these competitions.

For instance, a high school track coach who has recently acquired a new stopwatch might find it incredibly useful or not depending on its precision. If the manual states the stopwatch has an uncertainty of ±0.05 s, this could affect the outcome of close races. Given that the top runners on the coach's team regularly clock 100-m sprints with times that may only differ by a few hundredths of a second, this level of uncertainty could be problematic in accurately distinguishing winning times.

Considering a scenario where the first-place sprinter came in at 12.04 s and the second-place sprinter at 12.07 s, the new stopwatch’s uncertainty range may not clearly differentiate between the two, since the difference in their times is within the margin of error of the stopwatch. This is relevant when comparing a sprinter's 100-meter sprint time of 12.04 seconds one week and 11.96 seconds the next week; due to the uncertainty of the stopwatch, we cannot conclusively say that this week's time was faster.faster.

Answer:

B. 2.3

Step-by-step explanation:

Answer:

If the distance is 4.6 centimeters, then the actual distance has to be 2.3 kilometers.

Step-by-step explanation:

[tex]\frac{2 cm}{1 km}[/tex]

[tex]\frac{2}{1} * \frac{4.6}{?}[/tex]

[tex]\frac{4.6}{2}[/tex]

2.3 km

So, you answer is letter choice 2.3 kilometers.

Answer:

i would like to say the answer is 17

Step-by-step explanation:

Answer:

[tex]\chi^2 =\frac{10-1}{0.0144} 0.0217 =13.54[/tex]

The degrees of freedom are:

[tex] df=n-1=10-1=9[/tex]

Now we can calculate the p value using the alternative hypothesis:

[tex]p_v =2*P(\chi^2 >13.54)=0.279[/tex]

Since the p value is higher than the signficance level assumed of 0.05 we have enough evidence to FAIL to reject the null hypothesis and there is no evidence to conclude that the true deviation differs from 0.12 ounces

Step-by-step explanation:

Assuming the following data:"12.14 12.05 12.27 11.89 12.06

12.14 12.05 12.38 11.92 12.14"

We can calculate the sample deviation with this formula:

[tex]s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

[tex]n=10[/tex] represent the sample size

[tex]\alpha=0.05[/tex] represent the confidence level  

[tex]s^2 =0.0217 [/tex] represent the sample variance

[tex]\sigma^2_0 =0.12^2= 0.0144[/tex] represent the value to verify

Null and alternative hypothesis

We want to determine whether the standard deviation differs from 0.12 ounce, so the system of hypothesis would be:

Null Hypothesis: [tex]\sigma^2 = 0.0144[/tex]

Alternative hypothesis: [tex]\sigma^2 \neq 0.0144[/tex]

The statistic can be calculated like this;

[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]

[tex]\chi^2 =\frac{10-1}{0.0144} 0.0217 =13.54[/tex]

The degrees of freedom are:

[tex] df=n-1=10-1=9[/tex]

Now we can calculate the p value using the alternative hypothesis:

[tex]p_v =2*P(\chi^2 >13.54)=0.279[/tex]

Since the p value is higher than the signficance level assumed of 0.05 we have enough evidence to FAIL to reject the null hypothesis and there is no evidence to conclude that the true deviation differs from 0.12 ounces

Answer:

B

Step-by-step explanation:

240+240=480

yes

Answer:

B. 480

Step-by-step explanation:

You can find the answer to this by finding the unit rate of Ross's travel. 240:4=60:1, meaning that he drives at 60 miles per hour. Multiplying this by 8 hours, you get 480 miles. Hope this helps!

Answer:

6

There are three people, so 3x2x1 is 6

Erik could stand in all three spots, Mina could stand in two of the available spots, and then there's only one left for Roger

Even if you flip the characters around, it's still 6

If it helps to draw it so you can visually see it, that would be a great idea

:)

Answer:

y = 4

y = 0

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 5y • (y - 4)  = 0  

Step  2  :

Theory - Roots of a product :

2.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

2.2      Solve  :    5y = 0  

Divide both sides of the equation by 5:

                    y = 0

Solving a Single Variable Equation :

2.3      Solve  :    y-4 = 0  

Add  4  to both sides of the equation :  

                     y = 4

Hope this helps

Answer:

Your question that I have solved:

y= 0,4

Step-by-step explanation:

Answer:

2441.95 years

Step-by-step explanation:

We can model this exponencial function as:

P = Po * (1+r)^(t/n)

Where P is the final value, Po is the inicial value, r is the rate, t is the time and n is the period of half-life.

In this case, we have that P/Po = 100% - 25.5% = 74.5% = 0.745, r = -0.5 and n = 5750, so we have that:

0.745 = (1 - 0.5)^(t/5750)

Step 1: log in both sides:

log(0.745) = (t/5750) * log(0.5)

Step 2: isolate t

t = 5750*log(0.745)/log(0.5) = 2441.95 years

Answer:

0        1/2   7/8   1      2    -2.75    -3  

Explanation:

(1. Absolute value is the distance a number is from zero. It can only be positive. For example, the absolute value of -8 is 8 because it is 8 units away from zero. More examples: The absolute value of 5 is 5 because it is 5 units away from zero. The absolute value of -6.75 is 6.75 because it is 6.75 units away from zero.

(2. Because we know this, we can put the order as 0, 1/2, 7/8, 1, 2, -2.75, and -3. -3 is 3 units away from zero which is more than the absolute value of -2.75 which is 2.75 units away from zero.

(3. The absolute value of a number is basically just making the number positive. If the number is already positive then the absolute value of that number is that number.

Hope you understand!

Answer:

29

Step-by-step explanation:

1/2+1+1+1+1/2=4

1/2+1+1+1+1+1/2=5

1/2+1+1+1+1+1/2=5

1/2+1+1+1+1+1+1+1/2=7

1+1+1+1+1+1+1+1=8

8+7+5+5+4=29

15+10+4=29

25+4=29

29=29

Answer:

A = 4 in^2

Step-by-step explanation:

The area is given by

A = l*w

A = 1in * 4 in

A = 4 in^2

Answer: C

Step-by-step explanation:

4 * 2=  8

4 *2 = 8

6 * 1 = 6/2 = 3

6 *1 = 6/2 =3

6* 2 = 12

12 + 3 +3 +8 +8 = 34

Answer:2

Step-by-step explanation:

In relation to the independent variable, one graph represents a linear relationship, as shown by the linear equation examples provided. The remaining graphs depict quadratic, inverse, and exponential relationships.

The question asks, 'When compared with the independent variable, how many of the graphs represent a linear relationship?' In the given examples, 'y = 6x + 8', '4y = 8', and 'y + 7 = 3x' are all linear equations. This means they represent a linear relationship between two variables, often plotted on horizontal and vertical axes of a graph. In such graphs, the independent variable is usually plotted on the horizontal (x) axis and the dependent variable on the vertical (y) axis.

If we look at the information regarding different types of relationships, the examples show a linear, quadratic, inverse, and exponential relationship graph. As the linear graph is the only one representing a linear relationship, the answer is that 1 out of 4 graphs, when compared with the independent variable, represents a linear relationship.

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Answer:

A

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x - 4)² + (y - 1)² = 34 ← is in standard form

with centre = (4, 1 ) and r² = 34 ⇒ r = [tex]\sqrt{34}[/tex] → A

Final answer:

The equation represents a circle with the center at (4,1) and a radius of 5.83 units.

Explanation:

The center of the circle is at (4,1) and the radius is 5.83 units.

To find the center of the circle, you simply take the opposite of the numbers inside the parentheses of (x - 4) and (y - 1), giving you the center (4, 1). The radius is the square root of the number on the right side of the equation, which is √34 = 5.83 units.

Answer: 75 degrees

Step-by-step explanation: supplementary means 180 so you do 180-105 which is 75

Answer:

The volume of the prototype is 200 cubic inches.

Step-by-step explanation:

Hi, to answer this question we have to calculate the volume of the pentagonal prism:

Volume (V)= base area x height of the rectangular face

Replacing with the values given and solving for V (volume)

V = 20 in2 x 10 in = 200 cubic inches

The volume of the prototype is 200 cubic inches.

Feel free to ask for more if needed or if you did not understand something.

The volume of the prototype is 200 cubic inches.

Since The designer uses pentagons with a base area of 20 in2 and rectangles with a length of 10 in

So, here the volume is

= 20(10)

= 200 cubic inches

Therefore, The volume of the prototype is 200 cubic inches.

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We have been given an image of a circle. We are asked to find the value of each variable.

We can see that angle b corresponds to diameter of circle. We know that the measure of an angle that is inscribed to the diameter of a circle is 90 degrees . Therefore, the value of b will be 90.

we can see that angle is an inscribed angle of arc 99 degrees. We know that measure of an inscribed angle is half the measure of inscribed arc.

[tex]a=\frac{1}{2}\cdot 99[/tex]

[tex]a=49.5[/tex]

Therefore, the value of a is 49.5 units.

We know that measure of all angles of a triangle is 180 degrees. The measure of 3rd angle will be half the measure of c, so we can set an equation as:

[tex]a+b+\frac{1}{2}c=180[/tex]

[tex]49.5+90+\frac{1}{2}c=180[/tex]

[tex]139.5+\frac{1}{2}c=180[/tex]

[tex]139.5-139.5+\frac{1}{2}c=180-139.5[/tex]

[tex]\frac{1}{2}c=40.5[/tex]

[tex]\frac{1}{2}c\cdot 2=40.5\cdot 2[/tex]

[tex]c=81[/tex]

Therefore, the value of c is 81.

Answer:

5

Step-by-step explanation:

That's all I could come up with

The solutions to the quadratic equation [tex]$x^2 = 25$[/tex] are x = 5 and x = -5. Thus, the correct options are 5 and -5.

To solve the quadratic equation [tex]\(x^2 = 25\)[/tex] by finding square roots, we take the square root of both sides.

Taking the square root of 25, we get [tex]\(x = \pm 5\)[/tex].

So, the solutions are [tex]\(x = \pm 5\)[/tex].

Therefore, the correct options are:

5

-5

Answer:

92

Step-by-step explanation:

The two angles add to make a straight line, so their sum is 180

88+x = 180

Subtract 88 from each side

88+x-88 = 180-88

x =92

Answer:

92

Step-by-step explanation:

Answer:

1 unit

Step-by-step explanation:

We have the following formula to find  the length of an arc that subtends an angle of radians is:

S = rΘ where:

Given the information in this question, we have:

=> the length of an arc in this question is:

1*1 = 1 unit

Hope it will find you well

Final answer:

The length of an arc in a circle with radius 1 that subtends an angle of a radians is a units.

Explanation:

The student's question asks for the length of an arc in a circle with a radius of 1 that subtends an angle of a radians. The formula to calculate the arc length (s) is derived from the fact that the circumference of a circle (S) with radius r is S = 2πr. A full revolution around a circle results in an angular rotation of θ = 2π radians.

The arc length for an angle a radians in a circle with radius r is therefore s = r × a. Since the radius of the circle in this question is 1, the arc length is simply equal to the angle a in radians. Thus, the length of the arc is a units.

Answer:

In the next two levels the tree we have 8 branches

Step-by-step explanation:

In mathematics, the Fibonacci numbers, commonly denoted Fₙ, form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones.

The Fibonacci numbers are given as 1,2, 3,5,8,13........n

The Second level according to the Fibonacci sequence indicates that the tree will have 8 branches

Answer:

21,34

Step-by-step explanation:

Answer:

(0,0)

Step-by-step explanation:

Answer:

2^2*4*5^2*9=900

Step-by-step explanation:

900= 100*9

100=20*5

20=5*4

4=2*2

2*2*4*5*5*9=900=

2^2*4*5^2*9=900

Hope this helps!

Answer:

2×2×3×3×5×5

2²×3²×5²

Step-by-step explanation:

Hope this helped (:

Answer:

B and c.

Step-by-step explanation:

Area is: L x W.

8 x 3 = 24

6 x 4 = 24

Feel free to let me know if you need more help. :)

Answer:

b. and c.

Step-by-step explanation:

Area of a rectangle is wl

8 x 3 = 24

6 x 4 = 24