If r= 6 and the intercepted arc length is 47, what is the measure of the central angle?

We have 98 % confidence that the true mean time a student sleeps per night is between 6.2928 hours and  7.1832 hours.

Mean = (8.6 + 8.3 + 7.6 + 6 + 7.1 + 5.6 + 5.1 + 6)/ 8 =  6.7875

Standard deviation = √Σ(x - mean)²/n

Σ(x - mean)² = (8.6 - 6.7875)^2 + (8.3 - 6.7875)^2 + (7.6 - 6.7875)^2 + (6 - 6.7875)^2 + (7.1 - 6.7875)^2 + (5.6 - 6.7875)^2 + (5.1 - 6.7875)^2 + (6 - 6.7875)^2

Standard deviation  : \(\sqrt{11.82875}/8\)

s = 0.42991

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

sample standard deviation

number of samples

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 8 - 1 = 7

Since confidence level = 98% = 0.98, α = 1 - CL = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01

the area to the right of z0.01 is 0.01 and the area to the left of z0.01 is 1 - 0.01 = 0.99

Looking at the t distribution table,

z = 2.998

Margin of error = 2.998 × 0.42/√8

                        = 0.4452

The lower limit of this confidence interval is

6.738 - 0.4452 = 6.2928

The upper limit of this confidence interval is

6.738 + 0.4452 = 7.1832

Learn more about Confidence Interval at:

https://brainly.com/question/24131141

#SPJ4

The airplane's groundspeed is approximately 242.25 km/h, and the resultant bearing is approximately 55.04° (relative to true north, measured clockwise).

How to solve for the airplane's groundspeed

To determine the resultant velocity of the airplane, we need to break down the airplane's velocity and the wind's velocity into their respective components and add them. Let's assume that the angles are measured clockwise from true north.

Let's denote:

Vp = airplane's speed = 250 km/h

θp = airplane's heading = 075 degrees

Vw = wind's speed = 85 km/h

θw = wind's heading = 300 degrees

We can then find the eastward (x) and northward (y) components of the velocities:

For the airplane:

Vpx = Vp * cos(θp) = 250 * cos(75 degrees) = 64.95 km/h

Vpy = Vp * sin(θp) = 250 * sin(75 degrees) = 241.92 km/h

For the wind:

Vwx = Vw * cos(θw) = 85 * cos(300 degrees) = 73.60 km/h

Vwy = Vw * sin(θw) = 85 * sin(300 degrees) = -42.50 km/h

We then sum the x and y components of the two velocities to find the resultant velocity components:

Vrx = Vpx + Vwx = 64.95 km/h + 73.60 km/h = 138.55 km/h

Vry = Vpy + Vwy = 241.92 km/h - 42.50 km/h = 199.42 km/h

The magnitude of the resultant velocity, which represents the groundspeed (Vr), is found using the Pythagorean theorem:

Vr = sqrt((Vrx)^2 + (Vry)^2) = sqrt((138.55)^2 + (199.42)^2) = 242.25 km/h

The bearing (θr) of the resultant velocity (relative to north) can be found using inverse tangent:

θr = atan2(Vry, Vrx) = atan2(199.42, 138.55) = 55.04 degrees

Therefore, the airplane's groundspeed is approximately 242.25 km/h, and the resultant bearing is approximately 55.04° (relative to true north, measured clockwise).

Read more on resultant velocity here https://brainly.com/question/4945130

#SPJ1

The inequality relation  -q > -7  can be represented in the form of q as q < 7

The numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be A

The value of A is - q > - 7

Now , multiplying by (-1) on both sides of the equation , we get

( -1 ) ( -q ) > ( -1 ) ( - 7 )

The inequality relation will change the sign from > to < and ,

q < 7

So , the value of the inequality relation A is q < 7

Now , all the values in the number line which satisfy the inequality equation q < 7 are given in set A

The numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

Hence , The inequality relation  -q > -7  can be represented in the form of q as q < 7 and numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ1

Answer:

3.45

Step-by-step explanation:

you have to do tihis then that

Answer:

A. Tossing 5 coins and getting 4 heads

Step-by-step explanation:

Compound events may be described as events whose occurence has more than one possible outcome, that is the number of possible events is more than one. From the options given above, Rolling 3 on a die, this event has only one possible outcome, which is rolling 3 ; tossing a coin and getting tails also has one obe possible outcome. Drawing 10 diamonds from a deck also focuses on one event which is drwinh diamonds. However, tossing 5 coins and getting 4 heads involves that the 5th toss will be tail. This has more than one event and thus a compound event.

Answer: A.

Step-by-step explanation:

Tossing five coins and getting four heads is a compound event as the coins and cards are different

Answer:

45

Step-by-step explanation:it gives you the answer chiices if you plug each number into x and then do the equation you will get 180

Answer:  45

Step-by-step explanation:

Did the test.

Answer:

16

Step-by-step explanation:

3^x +1 = f(X)

2x-4 = g(x)

find f(2)-g(-1)

we substitute in function f(X) by value (2), and in function g(X) by value (-1)

1. 3^x +1 becomes 3^2+1 =9+1=10

2. 2(-1)-4= -2-4=-6

then f(2)-g(-1)

= 10-(-6) =10+6=16

Answer:

2,4

Explanation:

Because a midpoint is the middle of the line

Answer:

\(mAB=(2,4)\)

Step-by-step explanation:

Step 1: Use the midpoint formula to solve

\(mAB=(\frac{x1 +x2}{2},\frac{y1+y2}{2} )\)

\(mAB=(\frac{0+4}{2},\frac{6+2}{2} )\)

\(mAB=(\frac{4}{2},\frac{8}{2} )\)

\(mAB=(2,4)\)

Therefore the midpoint on the line segment AB is (2,4)

Answer: s is \(> 118 \frac{2}{3}.\)

Step-by-step explanation:

The air balloon will have to fall more than 890 feet for it to reach an elevation below 300 feet. It falls at a rate of 7.5, so 890/7.5=118.6666666666, which is 118 and 2/3. The answer is positive because time can never be negative.

Answer:

Line ZL and line LZ.

Step-by-step explanation:

Since it is a line (because a line needs to have two or more points to be able to graph), it can be represented in two ways. The first being ZL, and the second being LZ.

Brainliest please.

Answer:

Step-by-step explanation

Oh

volumes of cone: V= TT ×R2 × H ÷ 3

Answer:

I believe for a cylinder the volume is the base times the height.

Step-by-step explanation:

this is just from my own head

The surface area of the cube given in the above diagram would be = 1922.46 in².

To calculate the surface area of the cube, the formula that should be used would be given below as follows:

Surface area of cube = 6(a)²

a = side length= 17.9

SA=6(17.9)²

= 6×320.41

= 1,922.46 in²

Learn more about area here;

https://brainly.com/question/28470545

#SPJ1

Answer:

x<-12 or x>16

Step-by-step explanation:

Answer:

|x - 2| + 3 > 17

|x - 2| > 14

x - 2 < -14 or x - 2 > 14

x < -12 or x > 16

Answer:

\(\frac{8}{x}\)

Step-by-step explanation:

what is the sum 3/x+9+5/x-9

\(\frac{3}{x} + 9 + \frac{5}{x} - 9 =\)     (add \(\frac{3}{x}\) and \(\frac{5}{x}\))

\(\frac{8}{x} + 9 - 9 =\)            (solve 9 - 9 = 0)

\(\frac{8}{x}\)                           ( your answer)

The forecast high represents the day's highest temperature, which is normally reached in late afternoon. It is anticipated that this heat will at minimum during night, probably around daybreak following morning.

The measurement of an entity's sexiness or coolness in relation to a reference value is called its temperature. The thermometer is the name of the device that monitors body temperature.

A little cup of water, for instance, possesses the same temperatures as a tank of water, but still the tub or water is hotter because it contains more moisture and hence has less heat energy overall. Joule is the SI unit for heat. Kelvin is the SI unit of temperature.

To know more about temperature visit:

https://brainly.com/question/14878207

#SPJ1

Answer:

Volume=355 cm³

Step-by-step explanation:

I assume it should be 10 cm, not 10 m.  If it is 10 m, everything will have to be adjusted.

Circumference = 2\(\pi\)r

10=2\(\pi\)r

10÷2\(\pi\)=r

1.59=r

V=\(\pi\)r²h

V=\(\pi\)(1.59)(71)

v=355

Answer: 700 ? Because it depends on speed or not

Step-by-step explanation:

Answer: 1,599,960

Step-by-step explanation:

Since the population of crawfish in a section of the Louisiana bayou increased from 900,000 to 1.2 million between 2010 and 2011. The percentage increase in population will be:

= (1.2 million - 900000) / 900000 × 100

= 300000/900000 × 100

= 33.33%

Since the population increases by the same percentage between 2011 and 2012, then the population in 2012 will be:

= (100% + 33.33%) × 1.2 million

= 133.33% × 1.2 million

= 1.3333 × 1.2 million

= 1,599,960

The population in 2012 is 1,599,960

Compound Interest Formula:

A = P(1 + r/n)^nt

Where:

A = amount (principal + interest)

P = principal

r = rate in decimal

n = number of compounding periods per unit of time

t = time in decimal years

So:

A = 15500x(1 + 0.04/4)^(4x4.25)

A = 18356.72

Interest = Amount - Principal

I = 18356.72 - 15500.00

I = 2856.72

Answer:$31,500

Step-by-step explanation:

To calculate the total amount Mario will pay, including the loan amount and interest, for the loan from First Bank of Trust, we need to calculate the interest and add it to the loan amount.

The formula to calculate simple interest is:

Interest = (Loan Amount) x (Interest Rate) x (Loan Length)

Let's plug in the values given:

Loan Amount = $25,000

Interest Rate = 6.5% (or 0.065 as a decimal)

Loan Length = 4 years

Interest = $25,000 x 0.065 x 4 = $6,500

Now, let's calculate the total amount Mario will pay:

Total Amount = Loan Amount + Interest = $25,000 + $6,500 = $31,500

Therefore, the total amount Mario will pay, including the loan amount and interest, for the First Bank of Trust loan is $31,500.

Using the length formula we know that the length of the given arc is 30.144 miles.

In mathematics, an arc is a portion of the boundary of a circle or curve. It is sometimes referred to as an open curve.

The measurement around a circle that determines its edge is called the circumference, often known as the perimeter.

So, the formula to find the length of the arc is:

Length of an Arc = θ × r

Now, insert values and calculate as follows:

Length of an Arc = θ × r

Length of an Arc = 4π/5 × 12

Length of an Arc = 4π/5 × 12

Length of an Arc = 12.56/5 * 12

Length of an Arc = 2.512 * 12

Length of an Arc =  30.144

Therefore, using the length formula we know that the length of the given arc is 30.144 miles.

Know more about an arc here:

https://brainly.com/question/2005046

#SPJ1

Answer:

(-2,5)

Step-by-step explanation:

The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

To learn more about line plot

https://brainly.com/question/16321364

#SPJ8

Answer:

80%

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer: (2, -1)

Explanation: Since one equation has a -5y and the other equation

has a +5y, when we add the equations together, the y's will cancel out.

So we have 5x = 10 and x = 2.

To find y, plug 2 back in for x in either of the two original equations.

I have chosen to plug 2 into the second equation to get (2) + 5y = -3.

Solving from here, y = -1.

So our final answer is the ordered pair (2, -1).

Now, check your answer.

Answer:

108

Step-by-step explanation:

The linear functions that define their distances are given as follows:

The number of hours after noon in which they will be the same distance away from the stadium is of:

8 hours.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

In the context of this problem, the meaning of each parameter is:

They will be the same distance away at the point of intersection of the graph given at the end of the answer, which is of 8 hours.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:

Is there names or how do you do this

Step-by-step explanation:

well we know its a boy and he players football and has 2 brothers and is in 7th grade but do we pair with a name or something