university dean wants to estimate the average number of hours per week that freshman spend studying, and so she plans to take a survey. she wants to be 99% confident that her survey average is within 0.5 hours of the true number of hours. the standard deviation from a previous study is 2.6 hours. how large of a sample should the dean take to ensure this is true?

Answer:

By counting, we see that the point travels down 3, over 6. This is a slope of -3/6. This then simplifies down to -1/2.

The slope is -1/2

Answer:

X= 1/2 y= -2/5. X+2y= -1/5.

The equation of the line passing through the point with coordinates (1/2, -2/5) and having slope -1/2 is:

y = -1/2x + b.

Substituting coordinates of the point in the equation, we get:

-2/5 = -1/2(1/2) + b => b = 1/5.

Therefore, the equation of the line is:

y = -1/2x + 1/5.

Step-by-step explanation:

Answer:

216, 343

Step-by-step explanation:

1, 8, 27, 64, 125 ← are perfect cubes , that is

1³ = 1 × 1 × 1 = 1

2³ = 2 × 2 × 2 = 8

3³ = 3 × 3 × 3 = 27

4³ = 4 × 4 × 4 = 64

5³ = 5 × 5 × 5 = 125

continuing the pattern for 6 and 7

6³ = 6 × 6 × 6 = 216

7³ = 7 × 7 × 7 = 343

thus the next 2 terms in the sequence are 216, 343

The value of y-coordinate of the solution of the system of equation

2x + 3y = 6 and 2x + y = -2 is y = 4.

Given, a system of equation

2x + 3y = 6 and 2x + y = -2

On subtracting both the equations, we get

3y - y = 6 - (-2)

2y = 6 + 2

2y = 8

On dividing both the sides by 2, we get

2y/2 = 8/2

y = 4

So, the value of y-coordinate of the solution is y = 4.

Hence, the value of y-coordinate of the solution of the system of equation 2x + 3y = 6 and 2x + y = -2 is y = 4.

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The value of b in the equation  4.2g+ 5 =2.2g + 11 is g = 3   .

In the question ,

it is given that ,

the equation is  4.2g+ 5 =2.2g + 11

on arranging like terms together , we get

4.2g - 2.2g = 11 - 5

2g = 6

g = 6/2

g = 3

the value of g is = 3 .

to check whether the value g = 3 is correct  ,

we substitute g = 3 , in the equation

4.2(3)+ 5 =2.2(3) + 11

12.6 + 5 = 6.6 + 11

17.6 = 17.6

So , the answer that g = 3 is correct .

Therefore , The value of b in the equation  4.2g+ 5 =2.2g + 11 is g = 3   .

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Answer: Answer: 1m = 60s, what is the equation?

Step-by-step explanation: 1 minute = 60 seconds so 60s = 1m

Answer:

5q+5q+5

Step-by-step explanation:

A parabola that have a focus of (7,3) and a directrix of y = 5 has these attributes

The parabola is a vertical parabola and facing down

the vertex of the parabular is v(7, 4)

p value of the parabola = -1

A parabola refers to  shape that traces equation of the form

ax² + bx + c

The directrix of a parabola refers to a vertical or horizontal line that never touches the parabola and at distance p to the vertex of the parabola., and 2p to the focus of the parabola.

when the directrix is on the y coordinate, the parabola formed is a vertical parabola.

If the value of the directrix is more than the corresponding focus or vertex there will be negative p and the parabola will face downward.

conversely, If the value of the directrix is less than the corresponding focus or vertex there will be positive p and the parabola will face up.

from definition of the directrix we calculate for p

2p = y coordinate of focus - equation of directrix

2p = 3 - 5

2p = -2

p = -1

vertex, v(h, k) compared with f(h, k + p)

h + p = 3

h = 4

therefore vertex is (7, 4)

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The axis of symmetry has the equation x=2, and the vertex is (2,4). The chart is displayed below.

For example,

Find the vertex of y = x^2 - 4x + 8 and sketch its graph.

Solution

Completing the square, we have

y  = x^2 - 4x + 8

= (x-2)^2+4 .

Hence the vertex is (2,4) and the axis of symmetry has equation x=2.

The graph is shown below.

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Camron (E) = 20h, she earns $300 for 15 hours.

acc to our question-

Hence,Camron (E) = 20h, she earns $300 for 15 hours.

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Answer: 0

Step-by-step explanation:

ƒ(x) = −x² – 10x – 9

Putting value of x as -1

the function is as followed:

ƒ(-1)  = -(-1)^2  - 10 (-1) - 9

ƒ(-1)  = -1 +10-9

ƒ(-1)  = 9-9

         = 0

23.

f(x) is just a function in terms of x.

where it says 4f(2) all that means is 4 times the function when x is 2.

To work it out, you just need to swap all xs with 2 and calculate what that is. That gives you f(2), then multiply that answer by 4 to get 4f(2)

Same thing for g(x). First step swap xs for 6 to get g(6) then multiply answer to get 6g(6). At that point, you should have 2 numbers with no x's and you can minus the f by g.

24. Is about compound interest which means that after each year a new amount is worked out rather than a flat amount for the whole 8 years.

2 ways to tackle it, you could work out 8% of each year but that would require you to work it out 8 times which is time consuming and possible to make errors.

2nd way is much easier in that regard.

Final Answer = Initial Amount * (1 + interest rate)^amount of years.

Answer = 5000*(1+0.08)^8

The volume of a cylinder in terms of r is √V/πh.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Given that, the volume of a cylinder = πr²h

Solving in terms of r,

r = √V/πh

Hence, The volume of a cylinder in terms of r is √V/πh.

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Answer:

-6

Step-by-step explanation:

3(-4)/-2+(-12)

=-12/-2+(-12)

=6-12

=-6

Answer:

The scale factor is 3

Step-by-step explanation:

The value of [tex]x_4[/tex] = 5.8284.

Given:

An iterative formula:

[tex]x_{n+1} = 19/x_n + 3[/tex]

and [tex]x_1[/tex] = 9

for x_2 n = 1 substitute

[tex]x_{1+1} = 19/x_1 + 3[/tex]

[tex]x_{2} = 19/9 + 3[/tex]

= 19 + 3*9 / 9

= 19+27 / 9

= 46/9

[tex]x_3 = 19/x_2 + 3\\[/tex]

= 19/46/9 + 3

= 19*9 / 46 + 3

= 171+138 / 46

= 309/46

[tex]x_4 = 19/x_3 + 3[/tex]

= 19/309/46 + 3

= 19*46+3*309 / 309

= 1801/309

= 5.8284

Therefore The value of [tex]x_4[/tex] = 5.8284.

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Answer:

  (d)  72.925°

Step-by-step explanation:

You have congruent angles P and Q in triangle PQR, where angle R measures 34.15°. You want to know the measure of angle P.

The angle sum theorem tells you the sum of angles in a triangle is 180°.

  P +Q +R = 180°

  P +P +34.15° = 180° . . . . . substitute equivalents

  2P = 145.85° . . . . . . . . . subtract 34.15°

  P = 72.925° . . . . . . . . divide by 2

The measure of ∠P is 72.925°.

Answer:

0.89

Step-by-step explanation:

31.95 is about 32

36.05 is about 36

32/36 is 0.888...

rounded is 0.89

Answer:

.89

Step-by-step explanation:

Answer:

Step-by-step explanation:

(4 + 15.6a) − (7 + 3.7a) =

4 + 15.6a - 7 + 3.7a =

19.3a - 3

Answer:

[tex] \sf \: 11.9a - 3 [/tex]

Step-by-step explanation:

Now we have to,

→ simplify the given expression.

The expression is,

→ (4 + 15.6a) - (7 + 3.7a)

Let's simplify the expression,

→ (4 + 15.6a) - (7 + 3.7a)

→ 4 + 15.6a - 7 - 3.7a

→ (15.6a - 3.7a) + (4 - 7)

→ (11.9a) + (-3)

→ 11.9a - 3

Hence, the answer is 11.9a - 3.

The multiple of I is the imaginary portion. It is customary to write z = a + bi, where a represents the real part and b represents the imaginary part, to represent complex numbers. where b is the imaginary part and a represents the real part. Sum of Real parts and sum of imaginary parts i is (1 + 3i) 

A and b are referred to as the "real component" and "imaginary part," respectively, of the complex number z=a+bi. If a=0, the complex number is "purely imaginary," and if b=0, it is a real number.

Real components add up to 1, while imaginary parts add up to 3i.

A complex number is stated in its standard form as z = x + iy, where x represents the real part and y represents the imaginary part because it is connected to the imaginary axis.

Considering the formula (3 - 5i) + (-2 + 8i).

Collect similar phrases into real and fictitious parts as follows: 

= (3 - 5i) + (-2 + 8i)

= (3 - 2 - 5i + 8i)

=(1 + 3i) 

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Evaluating the expression in x = -25 and y = 10 gives the value -25.

Here we have the expression:

x + y - 10

And we want to evaluate it in x = -25 and y = 10, this just means that we need to replace the variables in the expression by the correspondent numbers.

Doing that we get:

-25 + 10 - 10

Now we can just simplify this expression:

-25 + 10 - 10 = -25 + (10 - 10) = -25

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The answer would be...

R + 7

Step-by-step explanation:

collect like terms

10r - 2r - 7r + 4 - 3 =

= r + 1

Solutions for the given expression in the given interval will be {0, π/2, 3π/2}.

What are trigonometric expressions?

Trigonometric identities are, by definition, reciprocal. These formulas show the connections between the sine/cosine functions and tangents.

Refer to the attachment for the Question:

[tex]\sin^2{(\theta)}=2\sin^2{(\frac{\theta}{2})}[/tex]

[tex][2\sin{(\frac{\theta}{2})}\cos{(\frac{\theta}{2})}]^2=2\sin^2{(\frac{\theta}{2})}[/tex]

[tex][4\sin^2{(\frac{\theta}{2})}\cos^2{(\frac{\theta}{2})}]=2\sin^2{(\frac{\theta}{2})}[/tex]

[tex][4\sin^2{(\frac{\theta}{2})}\cos^2{(\frac{\theta}{2})}]-2\sin^2{(\frac{\theta}{2})}=0[/tex]

[tex]2\sin^2{(\frac{\theta}{2})}[2\cos^2{(\frac{\theta}{2})}-1]=0[/tex]

[tex]\sin{(\frac{\theta}{2})}=0[/tex]

[tex]{(\frac{\theta}{2})}=n\pi[/tex]

[tex]\theta=2n\pi[/tex] [Here, n = integer]

[tex]\theta=0,\pi,2\pi,....[/tex]

Therefore,[tex]\theta=0[/tex]  [Since,[tex]0\le \theta < 2\pi[/tex] ]

[tex][2\cos^2{(\frac{\theta}{2})}-1]=0[/tex]

[tex]\cos{\theta}=0[/tex]

[tex]x=\frac{\pi}{2}+\pi n[/tex]  [Here, n = integer]

Therefore,[tex]\theta=\frac{\pi}{2}, \frac{3\pi}{2}[/tex]  [Since, [tex]0\le \theta < 2\pi[/tex]]

Hence, solutions for the given expression will be  {0, π/2, 3π/2}.

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a) The first three terms of the sequence are 21, 24 and 29.

b) There are 6 terms in the sequence are less than 50.

What is Geometric sequence?

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The nth term of a sequence is,

⇒ n² + 20

Now,

Since, The nth term of a sequence is,

⇒ n² + 20

First term of the sequence is,

⇒ n² + 20

⇒ 1² + 20

⇒ 1 + 20

⇒ 21

Second term of the sequence is,

⇒ n² + 20

⇒ 2² + 20

⇒ 4 + 20

⇒ 24

Third term of the sequence is,

⇒ n² + 20

⇒ 3² + 20

⇒ 9 + 20

⇒ 29

Thus, The first three terms of the sequence are 21, 24 and 29.

And, The fourth term of the sequence is,

⇒ n² + 20

⇒ 4² + 20

⇒ 16 + 20

⇒ 36

And, The fifth term of the sequence is,

⇒ n² + 20

⇒ 5² + 20

⇒ 25 + 20

⇒ 45

The sixth term of the sequence is,

⇒ n² + 20

⇒ 6² + 20

⇒ 36 + 20

⇒ 56

So, There are 6 terms in the sequence are less than 50.

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According to the given coordinates, there are 4 set of points will appear on the Kelsey’s graph and the graph is attached below.

Coordinates.

Coordinates refers the locations of points on a grid known as the cartesian plane or coordinate plane.

Given,

Kelsey is going to graph the ordered pairs that are represented by this table on a coordinate plane.

Here we need to find the number of points should appear in Kelsey’s graph.

In order to find the number of points, first we have to plot the table vales on the graph.

Once we plotted the values on the graph then the graph is look like the following graph.

While we looking through the graph we have identified that the points are (-6,-4), (-4, -6), (3, -6) and (5, 0) are presented on the graph.

Therefore, there are 4 points are plotted on Kelsey’s graph.

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The van will travel 5 miles in 1/4 hours, if its speed is 20 miles/hour.

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Answer:

The factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000

&

The multiples of 2000 are 2000, 4000, 6000, 8000, 10000, 12000, 14000, 16000, 18000, 20000, ...

As per the slope intercept form, the value of r is 66.

Slope intercept form:

In order to find the slope intercept form, we have to use the formula,

y = mx + c

where

(x, y) refers the point

m refers the slope

c refers the y-intercept.

Given,

Here we have the pair of points (12, 10), (−2, r) and the value of slope which is m = -4.

Now, we need to find the value of r.

We know that the general form of the slope intercept form is

y = mx + c

First we have to use the slope and the point (12, 10), to find the intercept of the line,

So, we have to apply the value on the formula, then we get,

10 = -4(12) + c

10 = -48 + c

c = 58

So, the slope intercept form equation is

y = -4x + 58

In order to find the value of r, we have to apply the point (-2,r) on the equation, then we get,

r = -4(-2) + 58

r = 8 + 58

r = 66

Therefore, the value of r is 66.

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