Find an equation of the line passing through the given points. Use function notation to write the equation. ​(3​,8​) and ​(4​,13​)

it should be the radius

Answer:

384√3 in²

Step-by-step explanation:

Given in the question a regular 6 sided polygon

To find it's area you have to use the following formula

Perimeter = the sum of the lengths of all the sides

Suppose length of one side = x

Apothem = a segment that joins the polygon's centre to the midpoint of any side that is perpendicular to that side = 8√3

Since the polygon have 6 sides so

perimeter = 6x

x = 2(8)

x = 16

perimeter = 6(16) = 96 in

plug values in the formula of area

384√3 in²

Answer:

= 384√3 In²

Step-by-step explanation:

The polygon is a hexagon ; thus the angle subtended by each side at the center will be given by;

θ = 360/6

 = 60°

Therefore; we can calculate the length of each side;

Tan θ = opp/Adj

Tan θ = x /8√3

 Tan 30 = x /8√3

Therefore; 1/√3 =x /8√3

x = 8√3× 1/√3

   = 8

The length of each side is 8 × 2 = 16 In

The area of the polygon will be;

Area of one triangle multiplied by the number of a triangle;

= 1/2 × 16 × 8√3 ×6

Answer:

The correct answer option is 0.67.

Step-by-step explanation:

We are given that the probability that a child eats popcorn and cotton candy is 0.58, probability that a child eats popcorn is 0.69 and the probability that a child eats cotton candy is 0.87.

We are to find the probability that a child eats popcorn given that the child has already eaten cotton candy.

P (eats popcorn and has already eaten cotton candy) = [tex]\frac{0.58}{0.87}[/tex] = 0.67

Trigonometric ratios are vital in real-world applications such as construction for measuring building heights, in navigation or aviation for determining distances, and in physics for predictions and descriptions of natural phenomena.

Trigonometry and special right triangles are fundamental in various real-world scenarios, especially in fields such as engineering, astronomy, and construction. One example where trigonometric ratios are crucial is in construction when determining the height of a building using a measured baseline and the angles of elevation. If a surveyor knows the distance from his point of observation to the base of the building (the adjacent side in a right triangle) and the angle of elevation to the top of the building, they can use the tangent ratio (opposite over adjacent) to calculate the building's height.

Another scenario involves navigation or aviation, where knowing the distance between two locations is necessary. By measuring the angle from two different points to a third point, one can apply the basic problem of trigonometry to find the distance to the third point using a known baseline and the measured angles, a process often referred to as triangulation.

Lastly, in physics, the principles of special right triangles like the Pythagorean theorem are used to predict certain outcomes. Whether a calculation is made using trigonometry or some other physics principle, the predictions must agree and accurately describe natural phenomena. The Pythagorean theorem is always reliable as long as the algebra and arithmetic are correctly done, illustrating the logic and interconnectedness of mathematical postulates.

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Answer:

The horizontal distance from the plane to SCCA is [tex]32,708.5\ ft[/tex]

Step-by-step explanation:

Let

x-----> the horizontal distance from the plane to SCCA

we know that

see the attached figure to better understand the problem

[tex]tan(17\°)=\frac{10,000}{x}[/tex]

[tex]x=\frac{10,000}{tan(17\°)}[/tex]

[tex]x=32,708.5\ ft[/tex]

Answer:

The measure of the angle is [tex]30\°[/tex]

Step-by-step explanation:

Let

x-----> the measure of the angle in degrees

we know that

The measure of a complete circle is [tex]360\°[/tex]

so

by proportion

[tex]\frac{360}{1}\frac{degrees}{circle}=\frac{x}{(1/12)}\frac{degrees}{circle}[/tex]

[tex]x=\frac{1}{12}(360\°)[/tex]

[tex]x=\frac{360\°}{12}[/tex]

[tex]x=30\°[/tex]

An angle that represents 1/12 of a circle measures 30 degrees. We found this by understanding that a full circle is 360 degrees and then multiplied 1/12 by 360.

The question is asking for the measure in degrees of an angle that represents 1/12 of a circle. As we know, a circle consists of 360 degrees next we measure the angle just like when we are measuring the angle in the sky. To find the angle, we can use a simple proportion. Since the whole circle is 360 degrees, we know that 1/12 of the circle will be equal to 1/12 of 360 degrees.

So, the calculation will be like: 1/12 x 360 = 30 degrees. Therefore, an angle that represents 1/12 of a circle measures 30 degrees.

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In a parallelogram, adjacent angles sum to 180. Since the labeled angle is adjacent to the 124° angle, we have

[tex] 2z+16 +124 = 180 \iff 2z = 180-124-16 \iff 2z= 40 \iff z = 20[/tex]

Answer:

12 and 15     or

12 and 18    or

15 or 18

Step-by-step explanation:

The two numbers have to both be divisible by 3, since their greatest common factor is 3.  This only leaves..

12, 15, or 18     (no other numbers between 10 and 20 are divisible by 3)

The factors of 12 are: 2, 3, 4, 6, and 12

The factors of 15 are: 3, 5, and 15

The factors of 18 are: 2, 3, 6, 9, and 18

All three numbers have 3 as a greatest common factor, so we have 3 pairs of numbers they could be...

12 and 15     or

12 and 18    or

15 or 18

Answer:

15 and 18

Step-by-step explanation:

Because The number 3 is the greatest common factor of 15 and 18, and both numbers are between 10 and 20.

Answer:

False

Step-by-step explanation:

We have the serie:

[tex]\frac{1}{49}+ \frac{1}{64} + \frac{1}{81}+...[/tex]

To test whether the series converges or diverges first we must find the rule of the series

Note that:

[tex]7^2 = 49\\\\8^2 = 64\\\\9^2 = 81[/tex]

Then we can write the series as:

[tex]\frac{1}{7^2}+ \frac{1}{8^2} + \frac{1}{9^2}+...[/tex]

Then:

[tex]\frac{1}{7^2}+ \frac{1}{8^2} + \frac{1}{9^2}+... = \sum_{n=7}^{\infty}\frac{1}{n^2}\\\\\sum_{n=7}^{\infty}\frac{1}{n^2} = \sum_{n=1}^{\infty}\frac{1}{(n+6)^2}[/tex]

The series that have the form:

[tex]\sum_{n=1}^{\infty}\frac{1}{n^p}[/tex]

are known as "p-series". This type of series converges whenever [tex]p > 1[/tex].

In this case, [tex]p = 2[/tex] and [tex]2 > 1[/tex]. Then the series converges

Answer:

I am assuming it is the same table as mine. So it would be 0.56

Step-by-step explanation:

To find P(2.5≤X≤4), calculate the length of the interval between 2.5 and 4, and divide by the total length of the distribution's support.

For a uniform distribution U(0.5, 4), this would result in a probability of ¾ or 0.75.

To calculate the probability P(2.5≤X≤4) for a random variable X, given the graph of the probability distribution, you would typically integrate the probability density function (pdf) from 2.5 to 4 (in the case of a continuous distribution) or sum the probabilities for each whole number value of X between 2.5 and 4 (in the case of a discrete distribution).

For a uniform distribution U(0.5, 4), the probability is uniform (constant) across the interval.

Since the total area under the distribution is equal to 1, the probability of any interval can be found by calculating the length of the interval divided by the total length of the distribution's support (4 - 0.5).

For P(2.5≤X≤4), this would be ¾ or 0.75 since the interval length from 2.5 to 4 is 1.5 and the total length of distribution's support is 3.5 (4-0.5).

Answer:

  3/8

Step-by-step explanation:

You want the probability P(2.5 ≤ x ≤ 4), given X has a uniform distribution between 0 and 4.

The probability can be found by integrating the PDF over the interval [2.5, 4]:

  [tex]\displaystyle\int_{2.5}^4{\dfrac{1}{4}}\,dx=\dfrac{1}{4}(4-2.5)=\dfrac{1}{4}\cdot\dfrac{3}{2}=\dfrac{3}{8}[/tex]

The probability is 3/8.

Answer:

The radius is 98

Step-by-step explanation:

The circumference of a circle is the distance around the edge of the circle. To find the circumference, we use the formula C = 2πr. You have the circumference so substitute C = 615.44. Then solve for r.

C = 2πr

615.44 = 2πr

98 = r

Answer: 98 units

Step-by-step explanation:

Answer:

40 yes it is i got 100 on this

Step-by-step explanation:

There are 2.4 hours of infomercials in a 24-hour day if they account for 10% of the daily broadcast.

The question asks us to calculate the amount of time designated for infomercials in a 24-hour day if they make up 10% of the day's broadcast. To find the answer, we can use the basic percentage calculation.

To calculate 10% of a day, we need to know that a day has 24 hours. So 10% of 24 hours is calculated as follows:

(10/100) × 24 = 2.4

Therefore, there are 2.4 hours of infomercials in a 24-hour day.

To find the equation of the perpendicular bisector, find the midpoint of the line segment and determine the slope of the perpendicular line.

To find the equation of the perpendicular bisector of a given line segment, we need to find the midpoint of the segment and then determine the slope of the perpendicular line. Let's denote the coordinates of the endpoints of the line segment as (x1, y1) and (x2, y2). The midpoint of the segment can be found using the formula:

M = ((x1 + x2) / 2, (y1 + y2) / 2)

The slope of the perpendicular line can be found using the negative reciprocal of the slope of the given line segment:

Perpendicular slope = -1 / slope of given line segment

Once we have the midpoint and the slope of the perpendicular line, we can use the point-slope form of a linear equation to write the equation of the perpendicular bisector:

y - y1 = perpendicular slope * (x - x1)

The probability that a randomly selected person is 41-55 in age or prefers drinking Dr. Fizz is approximately 60%.

To find the probability that a randomly selected person is 41-55 in age or prefers drinking Dr. Fizz, we need to sum the frequencies for the 41-55 age group and the frequency for Dr. Fizz, and then divide by the total number of people.

From the table:

- Frequency of 41-55 age group = 30

- Frequency of Dr. Fizz preference = 30

Total number of people = 100

Therefore, the probability is:

[tex]\[ \text{Probability} = \frac{\text{Frequency of 41-55 age group} + \text{Frequency of Dr. Fizz}}{\text{Total number of people}} \][/tex]

[tex]\[ = \frac{30 + 30}{100} \][/tex]

[tex]\[ = \frac{60}{100} \][/tex]

[tex]\[ = 0.60 \][/tex]

Converting to a percentage, rounded to the nearest whole percent:

[tex]\[ \text{Probability} \approx 60\% \][/tex]

So, the correct answer is: 60%.

Answer:

Step-by-step explanation:

[tex]\text{The quadratic equation:}\ ax^2+bx+c=0.\\\\\text{We have}\ x^2-4x+2=0\\\\a=1,\ b=-4,\ c=2\\\\\text{Substitute to}\ b^2-4ac:\\\\b^2-4ac=(-4)^2-4(1)(2)=16-8=8[/tex]

Factor 3x^3−12x

3x^3−12x

=3x(x+2)(x−2)

Answer:

3x(x+2)(x−2)

3x^3 - 12x //Common factor: 3x

3x (x^2 - 4)

3x (x - 2) (x + 2)

Answer: C

//Hope this helps.

Answer:

it is A) No, there is not an overlap between the two data setsStep-by-step explanation:

i did it on usatestprep

Answer:

A-No, there is not an overlap between the two data sets.

Step-by-step explanation:

Multiply total sales by 11%

4265 x 0.11 = 469.15

His commission was $469.15

Final answer:

Wilson Green's commission is calculated by multiplying his total sales of $4265.00 by his commission rate of 11 percent, which equals $469.15.

Explanation:

Wilson Green earns an 11 percent commission on every home security system he sells. For the month, his total sales amounted to $4265.00. To calculate Wilson's commission, we need to find 11 percent of $4265.00.

The formula for calculating the commission is:

Commission = Total Sales × Commission Rate

By plugging in the numbers:

Commission = $4265.00 × 0.11

Now, let's do the math:

Commission = $469.15

Therefore, Wilson's commission for the month is $469.15

To find the sale price of a $384 skateboard with a 24% discount, convert the paid percentage to a decimal (76% to 0.76) and multiply with the original price, resulting in a sale price of $291.84.

To calculate the sale price of a skateboard originally priced at $384 with a 24% discount, we first need to determine what percentage of the original price will actually be paid. Since the discount is 24%, that means 76% of the original price will be paid (100% - 24% = 76%). To convert this percentage to a decimal, we divide by 100, getting 0.76.

Next, we find the sale price by multiplying the original price by the decimal form of the percentage paid:
$384 × 0.76 = $291.84 as the sale price of the skateboard.

Answer:

A

Step-by-step explanation:

Add up the votes for each person and order them greatest to least and pick the top 4.

Answer: the answer should be A= Parallel

Step-by-step explanation:

Answer:

C. Neither

Step-by-step explanation:

The first equation is [tex]y=2x+13[/tex]

This equation is already in the slope-intercept form; [tex]y=mx+c[/tex]

The slope of this equation is 2.

The second equation is [tex]y=-2x+2[/tex].

This equation is also already in the slope-intercept form.

The slope of this equation is [tex]-2[/tex].

Since the two slopes are not the same, the two lines are not parallel.

If these two lines are perpendicular, then the product of their slopes is -1.

But [tex]2\times -2=-4[/tex] which is not equal to -1.

Therefore the two lines are also not perpendicular.

The correct choice is C.

Answer:

p score = 0.031

Step-by-step explanation:

We will be running a hypothesis test to find the p-value.  See attached photo for the work needed and the running of the test.

Our hypothesis are:

H0: µ = 1500

HA: µ > 1500 (claim)

They say that the life of the light bulbs are more than 1,500 hours, so that is the alternate hypothesis since it's strictly more than, not equal to or greater.

we have a sample mean of: 1509.5

we have a sample standard deviation of: 24.27

We just need to find the p-value, we don't need to make a conclusion about the test results.

The p-value of the hypothesis test that the light bulbs last more than 1500 hours is estimated to be less than 0.05, supporting the company's claim. The calculation involved computing a t-statistic from the sample data and then finding the probability of getting a t-statistic larger than the computed value.

The question involves conducting a hypothesis test for the claim that the company's light bulbs last more than 1500 hours. The null hypothesis H0 for this test would indicate that the population mean longevity is less than or equal to 1500 hours (H0: μ ≤ 1500), while the alternative hypothesis H1 posits that the mean exceeds 1500 hours (H1: μ > 1500). The company collected a sample (n=25) and computed the sample mean ( = 1509.5 hours) and the sample standard deviation (s = 24.27 hours). To calculate the p-value for this test, we need to first calculate the test statistic (z or t) by using the given sample data and then find the area to the right of this test statistic in the relevant distribution.

Using the formula for calculating the test statistic in t-tests: t = ( - μ0)/(s / √n), where μ0 is the population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size. Here, t = (1509.5 - 1500)/(24.27 / √25) = approximately 1.96.

Since the alternative hypothesis is looking for values greater than 1500, we seek the probability that a test statistic is greater than what we observed (i.e., t > 1.96). This probability is equal to the p-value. To obtain it, we use the t-distribution with n-1 = 24 degrees of freedom. Since exact p-values can be challenging to retrieve without a statistical software or detailed tables, it's typically adhered to note if the p-value is less than or greater than the significance level, which is 0.05 in this case. Due to the calculated t-statistic, our p-value is approximately less than 0.05. Hence, this result supports rejecting the null hypothesis and lends credibility to the company's claim that its light bulbs typically last more than 1500 hours.

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Answer:

Option B. 36

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

The graph of the figure represent an inverse variation

so

In this problem

Constant=Height*Width

Take any point in the graph

example -----> the point (4,9)

Constant=4*9=36

Answer:

The value of x = -0.17

Step-by-step explanation:

∵ [tex]2e^{8x}=1-e^{4x}[/tex]

Let [tex]e^{4x}=y[/tex]

∴ [tex]e^{8x}=y^{2}[/tex]

∴ 2y² = 1 - y

∴ 2y² + y - 1 =0 ⇒ factorize

∴ (2y - 1)(y + 1) = 0

∴ 2y - 1 = 0 ⇒ 2y = 1 ⇒ y = 1/2

∴ y + 1 = 0 ⇒ y = -1

∵ [tex]y=e^{4x}[/tex]  

Note: [tex]e^{4x}=-1[/tex] ⇒ refused

         ([tex]e^{ax}[/tex] never gives -ve values)

∴ [tex]e^{4x}= 1/2[/tex] ⇒ insert ln in both sides

∵ [tex]ln(e)^{ax}=axln(e)=ax[/tex] ⇒ ln(e) = 1

∴ 4xln(e) = ln(1/2) ⇒ 4x = ln(1/2)

∴ x = [ln(1/2)]/4 = -0.17

Answer:

M = 4S

In three years

M + 3 = 3(S + 3)

So you put the 4S in to substitute for the M.

4S + 3 = 3(S + 3)

4S + 3 = 3S + 9

S = 6

If the son is 6, the father must be 24.

We can check this by adding three to both ages. Then, the son will be 9 and the father will be 27, which is three times 9.

Step-by-step explanation:

Step-by-step answer:

Angle ECF = 110 = angle of intercepted (minor) arc EF.

The inscribed angles (angles EDF and EHF) are equal to half the angle of the inscribed arc, namely 110/2 = 55 degrees.

For your information, an inscribed angle is an angle with its vertex on (circumference of) the circle, formed by two intersecting chords, with a base on the inscribed arc.

Answer:

Step-by-step explanation:

Look at the pictures.

(the picture 1)

Inscribed angle and central angle.

(the picture 2)

In a circle, central angle is two times larger than inscribed angle that intercept the same arc.

In a circle, inscribed angles that intercept the same arc are congruent.

We have the central angle C = 110°. The inscribed angle EHF is two times smaller than ∠C. Therefore m∠EHF = 110° : 2 = 55°.

The inscribed angles EHF and EDF that intercept the same arc. Therefore are congruent. m∠EHF = m∠EDF.

Answer:

28.26

Step-by-step explanation:

The circumference of a circle is the distance around the edge of the circle. To find the circumference, we use the formula C = 2πr. The area of the circle is the amount inside the circle and is found using A = πr². Substitute the relevant values in each situation into the formulas to find the circumference and/or area.

Substitute C = 18.84 and solve for r. Then substitute r into the area formula.

C = 2πr

18.84 = 2πr

3 = r

A = πr² = π(3)² = 28.26

Answer:

28.26

Step-by-step explanation: