Find g(2) and g(3).
g(x) = 6x2-x+ 2
g(2)
g(3)

Answer:

Mean 1.580666667 1.769333333

Standard Deviation 0.890741799 1.123161779

Step-by-step explanation:

When we run the commands in the R software we get the graphs as follows.

The commands were

qqnorm(c(0.32,0.52,0.77,0.81,0.96,1.2,1.31,1.43,1.62,1.87,1.95,2.1,2.48,3,3.37))

and

qqnorm(c(0.47,0.59,0.81,0.9,1.18,1.2,1.35,1.51,1.74,1.89,2.05,2.2,2.81,3.09,4.75))

We can plot the graphs in any other plotting software .

The results would be same .

We see there's a slight difference between the two graphs.

One curve goes above ( Minneapolis) for  0.4 and the other ( for St Paul) is below 0.4

Answer:

Yes it's a right triangle

Step-by-step explanation:

IF it's a right triangle

a² + b² will equal c²

-----------------------

25.5² = 650.25

12² + 22.5² = 650.25

Therefor this IS a right triangle

Answer:

2day I think might not be right

The number of days it will take him to reach his goal is 6.5 days.

Given that, Marty decided he wants to run a 5 km race.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of days be x.

He is starting by running [tex]1\frac{3}{4} =\frac{7}{4}[/tex] km and adding 1/2km each day.

Now, 7/4 +1/2 x= 5

⇒ 1/2 x= 5-7/4

⇒ 1/2 x=13/4

⇒ x=6.5 days

Therefore, the number of days it will take him to reach his goal is 6.5 days.

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Answer: x=9 is an extraneous solution

Step-by-step explanation:

Given

Function is [tex]f(x)=\sqrt{x-5}[/tex]

for function to exist

[tex]\Rightarrow x-5\geq 0\\\Rightarrow x\geq 5[/tex]

Therefore, 9 satisfies the  above equation. It is it's extraneous solution.

Answer:

[tex] \rm \displaystyle y _{ \rm tangent} = - \frac{8}{5} x - \frac{5}{2} a[/tex]

[tex] \rm \displaystyle y _{ \rm normal} = \frac{5}{8} x - \frac{765}{128} a[/tex]

Step-by-step explanation:

we are given a equation of parabola and we want to find the equation of tangent and normal lines of the Parabola

finding the tangent line

equation of a line given by:

[tex] \displaystyle y = mx + b[/tex]

where:

to find m take derivative In both sides of the equation of parabola

[tex] \displaystyle \frac{d}{dx} {y}^{2} = \frac{d}{dx} 16ax [/tex]

[tex] \displaystyle 2y\frac{dy}{dx}= 16a[/tex]

divide both sides by 2y:

[tex] \displaystyle \frac{dy}{dx}= \frac{16a}{2y}[/tex]

substitute the given value of y:

[tex] \displaystyle \frac{dy}{dx}= \frac{16a}{2( - 5a)}[/tex]

simplify:

[tex] \displaystyle \frac{dy}{dx}= - \frac{8}{5}[/tex]

therefore

[tex] \displaystyle m_{ \rm tangent} = - \frac{8}{5}[/tex]

now we need to figure out the x coordinate to do so we can use the Parabola equation

[tex] \displaystyle ( - 5a {)}^{2} = 16ax [/tex]

simplify:

[tex] \displaystyle x = \frac{25}{16} a[/tex]

we'll use point-slope form of linear equation to get the equation and to get so substitute what we got

[tex] \rm \displaystyle y - ( - 5a)= - \frac{8}{5} (x - \frac{25}{16} a)[/tex]

simplify which yields:

[tex] \rm \displaystyle y = - \frac{8}{5} x - \frac{5}{2} a[/tex]

finding the equation of the normal line

normal line has negative reciprocal slope of tangent line therefore

[tex] \displaystyle m_{ \rm normal} = \frac{5}{8}[/tex]

once again we'll use point-slope form of linear equation to get the equation and to get so substitute what we got

[tex] \rm \displaystyle y - ( - 5a)= \frac{5}{8} (x - \frac{25}{16} a)[/tex]

simplify which yields:

[tex] \rm \displaystyle y = \frac{5}{8} x - \frac{765}{128} a[/tex]

and we're done!

( please note that "a" can't be specified and for any value of "a" the equations fulfill the conditions)

Answer:

In attachment

Step-by-step explanation:

For answer refer to attachment .

Answer:

[tex]y(t) =10t[/tex]

Step-by-step explanation:

The summary of the given parameters are:

[tex]a = 0[/tex] --- initial savings

[tex]m = 10[/tex] --- monthly savings

[tex]t \to[/tex] months

Required

The linear function

The linear function is calculated using:

y(t) = Initial Savings + Monthly Savings * Months

So, we have:

[tex]y(t) =a + m*t[/tex]

[tex]y(t) =0 + 10*t[/tex]

[tex]y(t) =10t[/tex]

Answer:

Step-by-step explanation:

sin for < Θ is : 15/17

Answer:

D

Step-by-step explanation:

If you look at the centerand radius of a circle (those are the two most important things when defining a circle), you will see, they shrank by a factor of two, so since it affected both x and y, it had to be from the origin.

Answer:

90

Step-by-step explanation:

there is 6 sides of box

2 bigger and 4 smaller

area of bigger side is 5×5 = 25 this is the area of one side as we have 2 sides so are of both sides is 25 + 25 = 50

now come to the smaller sides ( we have 4 here)

are of one side is 2× 5 = 10

so are of all 4 sides is 10× 4 = 40

now we get area of 4 smaller sides and 2 bigger sides

total area of box is 40+ 50 = 90

hope you understand

Answer:

[tex]\pi (inches)[/tex]

Step-by-step explanation:

[tex]16 inch -pizza, radius=8 inch\\Circumference=2\pi r=2\pi \times8=16\pi \\LC=\frac{16\pi}{16} =\pi (inches)[/tex]

Answer:

Step-by-step explanation:

L : y = -4x + 3

with a slope of -4.

Any line perpendicular to L will have a slope m such that

m ( -4) = -1, or m = 1/4

Any line perpendicular to L passing through point (a,b) will therefore have the form

P : (y-b) = (x-a)/4

When (a,b) = (8,1) as given, then substitute in P to get

P : (y-1) = (x-8)/4

y=x/4 -2 + 1

y = x/4 -1

Answer:

75

Step-by-step explanation:

this problem statement tries to confuse us. there is no pi involved - also because there are no round surfaces and edges involved.

what do you think the surface area of such a 4-sided pyramid consists of ?

think !

there are the 4 walls or sides. and then there is the bottom too (if you lift the pyramid up, yes, the "floor" or bottom also belongs to the surface area).

each "wall" or side is actually a triangle.

and the bottom is a square.

what is the area of a triangle (At) ?

At = base length × height / 2 = 3×11/2 = 33/2 in²

what is the area of a square (As) ?

it is a special form of a rectangle, where length = width.

the area of a rectangle (Ar) = length × width.

and the area of a square (As), where length = width is

As = side length × side length = length² = 3² = 9 in²

our pyramid now has 4 "walls", all of the same size, so we need 4 times the area of such a single triangle.

and then add the bottom area.

=> the pyramid surface area (Ap) is

Ap = 4 × At + As = 4×33/2 + 9 = 132/2 + 9 = 66+9 = 75 in²

Answer:

[tex]x = \frac{13 - 9y}{2} [/tex]

Step-by-step explanation:

[tex]2x = 13 - 9y \\ x = \frac{13 - 9y}{2} [/tex]

It sounds like Joe calculated 5/400 = 0.0125

He divided in the wrong order. It should be 400/5 = 80 since we divide distance over time to get the speed (or rate).

-----------------

In terms of x and y, we basically are saying

slope = rise/run

slope = (change in y)/(change in x)

slope = (change in distance)/(change in time)

slope = (400 km)/(5 hrs)

slope = 80 km per hour is the speed

Answer:

C

Step-by-step explanation:

I found the slope which is 28-22 / 1.5-1 = 12

I plug in the hours to 12x+10 and it matched

Answer:

Step-by-step explanation:

[tex]A_{circle}=\pi r^2\\\\A=\pi r_{walkway}^2-\pi r_{fountain}^2\\\\A=\pi(20^2-16^2)=244\pi[/tex]

use a calculator fo find the value

Answer:

a = 452.16 ft²    area of walkway

a = -351.68 ft²   area of the walkway minus the area of the fountain

Step-by-step explanation:

Area fountain

a = π16²

a = 256π

Area fountain and walkway

a = π(16 + 4)²

a = π20²

a = 400π

Area Walkway

a =400π - 256π

a = 144π

a = 144 * 3.14

a = 452.16 ft²

------------------------------

I think the Area of the Walkway is what the question should be asking for, but it asked for

"the area of the walkway minus the area of the fountain"

a = 144π - 256π

a = -112π

a = -112 * 3.14

a = -351.68

Answer:  -47/36  

Step-by-step explanation:

3/2y-14/3x

as x=3 and y=6

3/2(6)-14/3(3)

3/12-14/9

1/4-14/9

9-56/36

-47/36

Answer:

- 5

Step-by-step explanation:

[tex]\frac{3}{2}y-\frac{14}{3}x[/tex]

[tex]\frac{3}{2}(6)-\frac{14}{3}(3)[/tex]

9 - 14

- 5

Answer:

B) 8 and 24.

Step-by-step explanation:

Just by looking at the answer choices, since one number must be three times the other, we can determine that the correct answer is B.

Regardless, let's work this out mathematically. Let the first number be a and the second number be b.

Their difference is 16. Hence:

[tex]a-b=16[/tex]

The first number is three times the second number. So:

[tex]a=3b[/tex]

Substitute:

[tex]3b-b=16[/tex]

Solve for b. Subtract:

[tex]2b=16[/tex]

And divide both sides by two:

[tex]b=8[/tex]

So, the second number is 8.

And since the first number is three times the second, the first number is 24.

Our answer is B as expected.

Answer:

52,047.96

Step-by-step explanation:

9514 1404 393

Answer:

  a) t18,10 + t18,11

  b) t24,15 + t24,16

  c) t13,6 +t13,7

Step-by-step explanation:

Each term of Pascal's triangle is the sum of the two terms above it in the triangle:

  tn,r = t(n-1),(r-1) +t(n-1),r

__

a) t19, 11 = t18,10 + t18,11

b) t25,16 = t24,15 + t24,16

c) t14,7 = t13,6 +t13,7

Answer:

I don't no answer sorry

Step-by-step explanation:

you follow me

Answer:

y=-1/2x+7

Step-by-step explanation:

I think its that

Answer:

y = (1/2) x + 3

Step-by-step explanation:

The equation of linear functions is y = m x + b

In this case, we know m = 1/2 , and have point (4,5). We only need to find our y-intercept or b value.

What we can do is substitute what we know into our formula which will give us variable b, or the y-intercept. That will look like:

5 = (1/2) * 4 + b

5 = 2 + b

3 = b

So, the equation is y = (1/2) x + 3 :)

Answer:

{A, B, C, D}

domain = {A, B, C, D}

Happy learning!

--Applepi101

Answer:

Step-by-step explanation:

[tex]7- \sqrt[3]{2-x} =12[/tex]

we have to just keep in mind to do the same operation to both sides of the equal sign

[tex]7-7- \sqrt[3]{2-x} =12-7[/tex] ; subtract 7 from both sides

[tex]- \sqrt[3]{2-x} = 5[/tex] ; multiply both sides by -1

[tex]\sqrt[3]{2-x} = -5[/tex] ; raise both sides to the power 3

2-x = (-5)³

2-x = -125 ; subtract 2 from both sides

-x = -125-2

-x =-127; multiply both sides by -1

x= 127

Answer:

A. (-6,0)

Step-by-step explanation:

The point on the y-axis lies on the line that passes through point C and is perpendicular to line AB is (-6, 0). Therefore, option C is the correct answer.

Given that, on a coordinate plane, line AB goes through (-2, 4) and (2, -8). Point C is at (6, 4).

The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of that line.

The slope is represented by the letter m, and is given by, m = tan θ = (y2 - y1)/(x2 - x1)

Now, slope of line AB with (x1, y1) = (-2, 4) and (x2, y2) = (2, -8) is

Slope = m = (-8-4)/(2(-2)

= -12/4

= -3

Slope perpendicular to AB = -1/m = -1/(-3)

=1/3

Put m=1/3 and C(6, 4) in y=mx+c, we get

4 = 1/3 (6) + c

⇒ c = 4-2

⇒ c = 2

Substitute m=1/3 and c = 2 in y = mx+c

That is, y = x/3 + 2

⇒ 3y = x+6

Point on the y-axis lies is 3(0) = x+6

⇒ x=-6

So, the coordinate is (-6, 0)

The point on the y-axis lies on the line that passes through point C and is perpendicular to line AB is (-6, 0). Therefore, option C is the correct answer.

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Answer: i dont understand

Step-by-step explanation:

9514 1404 393

Answer:

  136

Step-by-step explanation:

The x-value at one end of the beam will be where f(x) = 0.

  0 = -x²/272 +17

  x² = 17(272) = 4624

  x = ±√4624 = ±68

The beam extends from x=-68 to x=68, so has a width of ...

  68 -(-68) = 136

__

Note that the x in the equation for f(x) is not the same as the x in the picture corresponding to width.

Answer:

False

Step-by-step explanation:

There is 3 feet in every yard so if we multiply by 3, we get 9. This is more than 8 so it is NOT equal to 3 yards.

Best of Luck!

Answer:

it's answer is 4:1

Because length of small intestine is 6 m and length of large intestine is 1•5m

So 6/1•5 =4:1