Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. The students kept track of many lifestyle variables including how many hours of sleep obtained on a typical day. Researchers found that visually impaired students averaged 8.77 hours of sleep, with a standard deviation of 2.18 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed.

value of the slope is 22.3 % per Kg

Charging a single, fixed price for a given service is known as flat rate pricing.

The U.S. Postal Service charges a $21.90 flat rate.

additional $4.90 per kilogram.

slope rate =[tex]\frac{4.90}{21.90} X 100 = 22.3 %[/tex] %

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The function g(t)=100(t-4)/84.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

g(0) = 4

g(1)= 4 + .84x

g(2)= 5.85

g(t) = mt+c

c = 4

g(t) = t-c/m = t-4/0.84 = 100(t-4)/84

Hence, the g(t)=100(t-4)/84.

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Answer:

25.749504 kilometers

Step-by-step explanation:

16miles  x 1.609(constant) = 25.749504

Answer:

12000 is the correct answer.

Step-by-step explanation:

Hope this helps you :)

Mark has brainiest please

On solving the equations y = (-1/2)x + [tex]4\frac{1}{2}[/tex] and 3x - 4y = 12 graphically , the solution is (6 , 3/2) .

In the question ,

it is given that

the equations are y = (-1/2)x + [tex]4\frac{1}{2}[/tex]  and 3x - 4y = 12

which can be written as y = (-1/2)x + 9/2  and 3x - 4y = 12

to plot the graph of the given equations , we need intercept .

For the equation y = (-1/2)x + 9/2

when x= 0  , y = (-1/2)(0) + 9/2 = 9/2

when y = 0 ,

0 = (-1/2)x + 9/2

(1/2)x = 9/2

x = 9

the points are (0 , 9/2) and (9 , 0)

For the equation 3x - 4y = 12

when x = 0 , 3(0) - 4y = 12

-4y = 12

y = -3

when y = 0 , 3x -4(0) = 12

3x = 12

x = 4

the points are (0,-3) and (4,0) .

after plotting the lines on the graph , we can see that the both the lines intersect at the point (6 , 3/2) ,

Therefore , On solving the equations y = (-1/2)x + [tex]4\frac{1}{2}[/tex] and 3x - 4y = 12 graphically , the solution is (6 , 3/2) .

The given question is incomplete , the complete question is

Consider this equation y = (-1/2)x +  [tex]4\frac{1}{2}[/tex]  and 3x - 4y = 12 .

Solve the system by graphing. label each graph.

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Answer:

See below

Step-by-step explanation:

In Q I    cos sin and thus tan are all positive

tan = sin / cos     so you need to find sin

TRIG identity:  

cos^2 + sin^2 =1

 16/27 + sin^2 =1

              sin^2 = 1 - 16/27 =  11/27

                  sin = sqrt (11/27)

tan = sqrt (11/27) / ( 4/sqrt27) =+ sqrt (11) /4

Yes, Timothy is correct because triangle AKLM was dilated by using a scale factor of 1.5 centered at the origin.

In Mathematics, dilation can be defined as a type of transformation that is typically used for enlarging or reducing the size of a geometric object but not its shape, based on the scale factor.

For the given coordinates of the preimage triangle KLM, the dilation with a scale factor of 1.5 from the origin (0, 0) would be calculated as follows:

Coordinate K (-1, 3) → Coordinate K' (-1 × 1.5, 3 × 1.5) = Coordinate K' (-1.5, 4.5).

Coordinate L (8, 4) → Coordinate L' (8 × 1.5, 4 × 1.5) = Coordinate L' (12, 6).

Coordinate M (10, -3) → Coordinate M' (10 × 1.5, -3 × 1.5) = Coordinate M' (15, -4.5).

In conclusion, the coordinates of the image triangle K'L'M after a dilation with a scale factor of 1.5 from the origin are (-1.5, 4.5), (12, 6), and (15, -4.5) as shown in the graph above, therefore, Timothy is correct.

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The probability that the customer would come in that time is  0.0007

The question puts the mean u = 7.3

We are required to get the probability of less than 1 customer in one hour. The poisson probability formula is what would be used to solve this problem

the formula is given as

[tex]P(X=x) = e^-^u*^u^x[/tex]/X!

where x = 1

p(X=x) = P(X = 0)

P(X < 1) = P(X = 0)

e⁻⁷.³ x 7.30 / 0!

=  0.0007

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Answer:

x = 16

y = 10

Step-by-step explanation:

x+5y =46 [1]

x-y =-14 [2]

x=-14+y [3]

put [3] into [1],

x+5y =46

-14+y+5y=46

6y = 60

y = 10

put y=10 into [1]

x+5(10)=46

x = 16

The correct answer to this question is A.

The point (0, 1) and (-2.5, 6) is the solution to y = 2x² + 3x + 1 and y = -2x + 1

From the information, we want to solve the system by graphing. y = 2x² + 3 x + 1 and y = - 2 x + 1.

An equation is an expression that is used to show the relationship between two or more numbers and variables.

Given the quadratic and linear equation, y = 2x² + 3x + 1 and y = -2x + 1, the solution is at the intersection of both equations. Here, the intersection point of the equations is the solution of the system i.e. (-2.5,6) and (0,1). Therefore, the point (0, 1) and (-2.5, 6) satisfies this equation.

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Answer:

x^(9/7)

Step-by-step explanation:

inverse function f(x) = (x^(1/9))^7 = x^(9/7)

Answer:

it is the answer number 1

Take a look at the attachments...

Hope this helps! :)

The table of values for the total cost is:

# of Rides, x    Total cost, y

0                             $8

1                              $11

2                               $14

3                               $17

4                                $20

5                                $23

The table of values create a linear function. This is because the table of value increases by a constant value.

The total cost is the sum of the amount the carnival charges, the number of rides and the cost per ride.

Total cost = cost to enter + (cost per ride x number of rides)

Total cost for 0 ride = $8 + ($3 x 0) = $8

Total cost for 1 ride = $8 + ($3 x 1) = $11

Total cost for 2 rides = $8 + ($3 x 2) = $14

Total cost for 3 rides = $8 + ($3 x 3) = $17

Total cost for 4 rides = $8 + ($3 x 4 ) = $20

Total cost for 5 rides = $8 + ($3 x 5) = $23

The table of values creates a linear function. This is because the total cost increases by a constant amount.

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The graph that represents the solution of the inequality is

What is a system of inequality?

An inequality is known as an expression in which two value do not have an equal sign. they have either >, <,≥,≤. And to compute the solution

We plot the inequality and find the common region between them.

We are given a system of inequalities

Which are

y > x-1 and y< -x-2

We plot the graphs of the inequalities

Now we have plotted the graph the red one represents inequality y> x-1

and blue one represents inequality y< -x-2

And the intersection of the two is known as the solution of the system of inequality

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Solving the system of linear inequalities, we get

-4x+3y<15 = (0,5),(-15/4,0)

-6x-4y<12 = (0,-3),(-2,0)

What is a system of linear inequalities?

At least two linear inequalities in the same variables make up a system of a linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

Here, we have

Given inequalities

-4x+3y<15 and -6x-4y<12

Now we solve  the system of linear inequalities

For, -4x+3y<15

When we put x= 0, we get

y = 5

and if we put y = 0 , we get

x = -15/4

For, -6x-4y<12

When we put x= 0, we get

y = -3

and if we put y = 0 , we get

x = -2

Hence,  Solving the system of linear inequalities, we get

-4x+3y<15 = (0,5),(-15/4,0)

-6x-4y<12 = (0,-3),(-2,0)

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The measure that best describes the change in the location of the drone is D. -26 1/10m

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the underwater drone is located 9 3/5 meters below sea level and the drone is moved to a location that is 15 1/2 meters below sea level

The change will be:

= - 9 3/5 - 15 1/2

= - 9 6/10 - 15 5/10

= - 25 1/10

The change is - 25 1/10m.

The options are incorrect.

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Answer:

6261

Step-by-step explanation:

it was 6261 because I have to do a i test at

Answer:

7

Step-by-step explanation:

First, we need to get rid of the square root. To do this, square both sides.

(x - 5)^2 = √((x - 3)^2)

x^2 - 10x + 25 = x - 3

Next, continue simplifying

x^2 - 10x + 25 - x + 3 = 0

x^2 - 11x + 28 = 0

(x - 7)(x - 4) = 0

x - 7 = 0         and        x - 4 = 0

x = 7              and        x = 4

Next, plug in these values into the equation

x = 7 ---> 7 - 5 = √(7 - 3)

              2 = √4

              2 = 2

x = 7 is a possible value

x = 4 ---> 4 - 5 = √(4 - 3)

               -1 = √1

x = 4 is an extraneous solution and not a possible value.              

Answer:

7 is the only solution

Step-by-step explanation:

x-5=square root x-3

7-5=square root 7-3

2=square root of 4

2=2

7 is a solution

4-5=square root 4-3

-1= square root of 1

-1=1

hopes this helps please mark brainliest

Answer:

$151.50 deducted

Step-by-step explanation:

Walter used his bank's ATM to withdraw $150. This was the sixth time he used the ATM in June. His bank does not charge for the first five ATM uses each month. After that, the fee is $1.50 for each use. What is the total he should subtract from his balance including fees?

1 charge of $1.50 + withdrawal of $150

= $151.50 deducted

The equation for temperature 67, gives the time as 4.8 hours.

What is amplitude?

A sound is a type of energy that is created when objects vibrate. For it to spread, a medium is needed. As a result, sound cannot travel in a vacuum because there is nothing for the sound waves to travel through. The object's back-and-forth movement creates the sound. Sound vibration is the name for this. Additionally called oscillatory motion. Oscillation describes the regular rhythmic back-and-forth movement.

We know that the general equation of a sine wave is:

[tex]$$y(t)=A \{Sin}(W(t-C))+D$$[/tex]

where,

A- Amplitude

D = Average of Max(y) and Min(y);

[tex]W=\frac{2 \pi}{\text { Period }}[/tex]

C - Phase shift on y(axis)

Part a)

Given Max T= 94 and Min T = 66

Hence,

D = (Max+Min)/2 = 80

A = Max - D = 94-80= 14

Since period is 24 hours, so W = 2\pi/24 = \pi/12

Thus the function till now is:

[tex]T(t)=14Sin(\frac{\pi}{12}(t-C))+80[/tex]

Given low temperature occurs at 3 AM so,

T(3)=66

Solving this we get C = 9

Hence,

[tex]T(t)=14Sin(\frac{\pi}{12}(t-9))+80[/tex]

Part b)

Given Max T= 58 and Average = 45

Hence,

D = 45

A = Max - D = 58-45= 13

Since the period is 24 hours, so W = [tex]2\pi/24 = \pi/12[/tex]

Thus the function till now is:

[tex]T(t)=13Sin(\frac{\pi}{12}(t-C))+45[/tex]

Given high temperature occurs at 5 PM so,

T(17)=58

Solving this we get C = 11

Hence,

[tex]T(t)=13Sin(\frac{\pi}{12}(t-11))+45[/tex]

The temperature at 4 AM is:

[tex]T(4)=13Sin(\frac{\pi}{12}(4-11))+45 = 32.44[/tex]

Part c)

Given Max T= 86 and Min T = 64

Hence,

D = (Max+Min)/2 = 75

A = Max - D = 86-75= 11

Since period is 24 hours, so W = 2\pi/24 = \pi/12

Thus the function till now is:

[tex]T(t)=11Sin(\frac{\pi}{12}(t-C))+75[/tex]

Given average temperature occurs at 8 AM so,

T(8)=75

Solving this we get C = 8

Hence,

[tex]T(t)=11Sin(\frac{\pi}{12}(t-8))+75[/tex]

Now,

We need to find t such that T(t) = 67.

[tex]67=11Sin(\frac{\pi}{12}(t-8))+75[/tex]

[tex]\Rightarrow t=4.88945 \approx 4.89 hours[/tex]

Hence, The equation for temperature 67, gives the time as 4.8 hours.

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Answer:

The slope of a line perpendicular to m=2 is m= 1.

Step-by-step explanation:

2x+2y=-12

2y=-2x-12

y= -x-6.

The equation is in slope-intercept form now, so it is easy to tell what the slope is.

The slope of y= -x-6 is m = -x. Technically, -x = -1x, so now make the -1 positive and find the reciprocal, which is still 1.

All you need to do to find the perpendicular slope of any line is simply to find the reciprocal of the number and make the positive/negative number the opposite. I hope this helps, have a good day/night! :)

Answer:

part A=3x-23=28

part B=17

Step-by-step explanation:

3x-23=28

3x=23+28

3x=51

x=17

Answer:

This is commutative property of supplements

The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9

The equation of the function is given as

f(x) = 3x²

Also, we have

Vertex = (5, 9)

The form of the equation is given as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

This means that

Vertex = (h, k) = (5, 9)

Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 5)² + 9

This also means that

f(x) = -3(x - 5)² + 9

The -3 is gotten from f(x) = -3x²

Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9

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Answer:

Step-by-step explanation:

$427,011.92