The following data represent the chemistry grades for a random sample of 12 freshmen at a certain college along with their scores on an intelligence test administered while they were still seniors in high school.
Test Chemistry Student Score,
x Grade, y
1 2 3 4 5 6 7 8 9 10 11 12 65 50 55 65 55 70 65 70 55 70 50 55 85 74 76 90 85 87 94 98 81 91 76 74
Compute and interpret the sample correlation coefficient.

Step-by-step explanation:

Which is the first sincetist of world

Answer:

−2x^2+6x

Explanation:

You just have to distribute meaning you have to multiply -2x to the equation.

Option 1 - StartFraction n Over 2 EndFraction minus 6 + 10; when n = 8, the value is 8.

Step-by-step explanation:

Given : Expression "six less than the quotient of a number and two, increased by ten".

To find : What is the expression and value of expression when n = 8?

Solution :

Let the number be 'n'.

The quotient of a number and two i.e. \frac{n}{2}2n

Six less than the quotient of a number and two i.e. \frac{n}{2}-62n−6

Six less than the quotient of a number and two, increased by ten i.e. \frac{n}{2}-6+102n−6+10

The required expression is \frac{n}{2}-6+102n−6+10 .

Now, when n=8,

\frac{n}{2}-6+10=\frac{8}{2}-6+102n−6+10=28−6+10

\frac{n}{2}-6+10=4-6+102n−6+10=4−6+10

\frac{n}{2}-6+10=82n−6+10=8

The value of the expression is 8.

Therefore, option 1 is correct.

StartFraction n Over 2 EndFraction minus 6 + 10; when n = 8, the value is 8.

9514 1404 393

Answer:

  $11,715.65

Step-by-step explanation:

The applicable formula is ...

  FV = P(1 +r/n)^(nt)

where principal P earns interest at rate r compounded n times per year for t years.

  FV = $9500(1 +0.042/12)^(12·5) = $9500(1.0035^60) ≈ $11,715.65

The account will hold $11,715.65 after 5 years.

Step-by-step explanation:

there must be something wrong with your text.

what we can see is

3.8 × 105

and

1.9 × 1022

the true answer for these values has nothing to do with the 4 answer options.

maybe you meant

1.9 × 10.5 ?

because that answer would be 20.

but first working with the presented numbers :

3.8 × 105 = 399

1.9 × 1022 = 1941.8

so, the second number is actually much bigger than the first number.

but if it is

1.9 × 10.5 = 19.95

that works.

and we can either use the calculator to calculate

399 / 19.95 = 20

or we can simply look at the factor changes of the multiplication terms.

3.8 = 1.9 × 2

105 = 10.5 × 10

so, the multiplication product of the two larger numbers is then 2×10=20 times larger than the product of the 2 smaller numbers.

Answer:

The missing side length is of 5.

Step-by-step explanation:

The sides are proportional, which means that the missing side can be found using a rule of three.

x - 10

3 - 6

Applying cross multiplication:

[tex]6x = 30[/tex]

[tex]x = \frac{30}{6} = 5[/tex]

The missing side length is of 5.

Answer:

i think 3

Step-by-step explanation:

Answer: [A] 2

Step-by-step explanation:

100% on edge 2023

Answer:

AC+ CD = ACD

X+1 + 2X + 2 = 30

3X+3 =30

3X=30–3

3X=27

X= 27/ 3

X= 9

I'm not sure of the solution, but I solved it according to a straight line (Line segment) .

I hope I helped you^_^

Answer:

the last two answers are the only correct ones

Answer:

1/144

Step-by-step explanation:

(-1/12)^2

(-1/12)*(-1/12)

1/144

Answer:

Paul is 2 and Kennedy is 6

Step-by-step explanation:

6 × 1/3 = 2

2 + 4 =6

Answer:

8.75

Step-by-step explanation:

211/8 = 26.375

141/8 = 17.625

now,

211/8-141/8

26.375-17.625

8.75

Answer:

0.01

Step-by-step explanation:

6/7% = 6÷7÷100 = 0.0085714286 round to the nearest hundredth = 0.01

Answer:

[tex]7\frac{1}{2}[/tex]

Step-by-step explanation:

15/2=7.5

7.5 as a fraction is [tex]7\frac{1}{2}[/tex]

Step-by-step explanation:

7whole number 1/2

that's your answer

9514 1404 393

Answer:

  x = 45°

Step-by-step explanation:

The triangle interior angle at I will be the supplement of the angle marked 2x. The triangle interior angle at G will be equal to x, the alternate interior angle with respect to transversal GI crossing the parallel lines.

The angle marked 3x is the sum of these "remote" interior angles:

  3x = 180 -2x +x

  4x = 180 . . . . . . . . . add x; next, divide by 4

  x = 180/4 = 45 . . . . . degrees

  x = 45°

Answer:

Let r = amount of the 7% solution

y represent the amount of the 15 percent solution

r =7.5 L

y = 12.5 L

Step-by-step explanation:

Let r = amount of the 7% solution

y represent the amount of the 15 percent solution

.07r + .15 y = (r+y) .12

r+y = 20

y = 20-r

.07r + .15 (20-r) = (20) .12

0.07r+0.15(20-r)=2.4

.07r+ 3 - .15r = 2.4

-.08r = 2.4-3

-.08r = -.6

Divide by-.08

r =7.5

y = 20-7.5

y = 12.5

Answer:

a)  [tex]Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}[/tex]

b)  [tex]n=24[/tex]

Step-by-step explanation:

From the question we are told that:

Rate r=90 units per hour

Setup cost =20

Operating Cost =26

Units=40000

Generally the equation for Total cost is mathematically given by

[tex]Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}[/tex]

[tex]T_n=20n+\frac{11556}{n}\\\\T_n=\frac{20n^2+11556}{n}.....equ 1[/tex]

Differentiating

[tex]T_n'=\frac{n(40n)-(40n^2+11556)}{n_2}\\\\T_n'=\frac{20n^2-11556}{n^2}.....equ 2[/tex]

Equating equ 1 to zero

[tex]0=\frac{20n^2+11556}{n}[/tex]

[tex]n=24[/tex]

Therefore

Substituting n

For Equ 1

[tex]T_n=\frac{20(24)^2+11556}{24}[/tex]

F(n)>0  

For Equ 2

[tex]T_n'=\frac{20(24)^2-11556}{24^2}[/tex]

F(n)'<0

Answer:

77/306 or around 25.2%

Step-by-step explanation:

[tex]\frac{7}{18} *\frac{11}{17}[/tex] section 1/total * section 2/(total-1) since there is no replacement

just solve and you get 77/306

Answer:

A) Exponential growth

Step-by-step explanation:

I

2/5 of 2.5. = 2x2.5 / 5x1 = 5/5 = 1 pound

Answer:

c. y=2x−48

Explanation:

It is telling us that it costs $48 each morning to buy the day's supply of hot dogs, so we must subtract that from our pay, and it will be our y intercept

It also says he earns $2 per hot dog, so that will be our slope (rate of change)

Hope it helps! :]

y = 2x - 48 equation represents the profit earned by the x hot dog sold.

A linear equation is an algebraic expression in which highest power of the given variable is equals to one.

Given that, the profit earned by a hot dog stand is a linear function of the number of hot dogs sold.

It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold.

We need to establish an equation that represents the total profit,

According to the question,

x represents the number of hot dogs sold

y represents the total profit earned

Cost required for supply = $48

Profit on each hot dog sold = $2

As per the condition given, the required linear equation is =

y = 2x - 48

Hence, y = 2x - 48 equation represents the profit earned by the x hot dog sold.

Learn more about linear equation here :

brainly.com/question/11897796

#SPJ7

The sum of the interior angles is 1260°

Answer:

See Below.

Step-by-step explanation:

We are given the function:

[tex]\displaystyle y=\sqrt{\sin x}[/tex]

And we want to show that:

[tex]\displaystyle 4y^3\frac{d^2y}{dx^2}+y^4+1=0[/tex]

Find the first derivative of y using the chain rule:

[tex]\displaystyle \frac{dy}{dx} = \frac{1}{2\sqrt{\sin x}}\cdot \cos x = \frac{\cos x}{2\sqrt{\sin x}}[/tex]

And find the second derivative using the quotient and chain rules:

[tex]\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{1}{2}\left(\frac{(\cos x)'(\sqrt{\sin x})-(\cos x)(\sqrt{\sin x})'}{(\sqrt{\sin x})^2}\right) \\ \\ &=\frac{1}{2}\left(\frac{-\sin x\sqrt{\sin x} - \left(\cos x\right) \left (\dfrac{\cos x}{2\sqrt{\sin x}}\right)}{\sin x}\right) \\ \\ & = \frac{1}{2}\left(\frac{ -\sin x(2\sin x) -\cos x(\cos x) }{\sin x \left(2\sqrt{\sin x}\right) }\right) \\ \\ &= -\frac{1}{2} \left(\frac{2\sin^2 x + \cos^2 x}{2\sin^{{}^{3}\!/\! {}_{2}}x}\right)\end{aligned}[/tex]

Find y³:

[tex]\displaystyle y^3 = \left((\sin x)^{{}^{1}\!/\!{}_{2}}\right) ^3= \sin^{{}^{3}\! / \! {}_{2} }x[/tex]

And find y⁴:

[tex]\displaystyle y^4 = \left((\sin x)^{{}^{1}\!/\!{}_{2}}\right)^4 = \sin^2 x[/tex]

Substitute:

[tex]\displaystyle 4\left( \sin^{{}^{3}\! / \! {}_{2} }x\right)\left(-\frac{1}{2}\left(\frac{2\sin ^2x + \cos ^2 x}{2\sin^{{}^{3}\!/ \! {}_{2}}x}\right)\right)+\left(\sin ^2 x\right) + 1= 0[/tex]

Simplify:

[tex]-\left(2\sin^2 x + \cos^2 x\right) + \sin ^2 x + 1=0[/tex]

Distribute:

[tex]-2\sin ^2 x - \cos^2 x + \sin ^2 x + 1=0[/tex]

Simplify:

[tex]-\sin ^2 x - \cos^2 x + 1= 0[/tex]

Factor:

[tex]-(\sin ^2 x + \cos^2 x ) + 1=0[/tex]

Pythagorean Identity:

[tex]-(1)+1=0\stackrel{\checkmark}{=}0[/tex]

Q.E.D.

shaded area = area of outer figure - area of inner figure........

Step-by-step explanation:

Let [tex]f(x) = 4[/tex] and [tex]g(x) = \frac{1}{x^2}[/tex]. The area A of the region bounded by the given lines is

[tex]\displaystyle A = \int [f(x) - g(x)]dx[/tex]

Note that [tex]g(x) = \frac{1}{x^2}[/tex] intersects y = 4 at x = 1/2 so the limits of integration go from x = 1/2 to x = 5. The area integral can then be written as

[tex]\displaystyle A = \int_{\frac{1}{2}}^{5}\left(4 - \dfrac{1}{x^2}\right)dx[/tex]

[tex]\:\:\:\:= \left(4x + \dfrac{1}{x}\right)_{\frac{1}{2}}^5[/tex]

[tex]\:\:\:\:= (20 + \frac{1}{5}) - (2 + 2) = \dfrac{81}{5} = 16\frac{1}{5}[/tex]

Answer:

Step-by-step explanation:

We have the equations

4x + 3y = 18   where x = the side of the square and y = the side of the triangle

For the areas:

A = x^2 + √3y/2* y/2

A = x^2  + √3y^2/4

From the first equation x = (18 - 3y)/4

So substituting in the area equation:

A = [ (18 - 3y)/4]^2 + √3y^2/4

A = (18 - 3y)^2 / 16 + √3y^2/4

Now for maximum / minimum area the derivative = 0 so we have

A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0

-3/8 (18 - 3y) + √3 y /2 = 0

-27/4 + 9y/8 + √3y /2 = 0

-54 + 9y + 4√3y = 0

y = 54 / 15.93

= 3.39 metres

So x = (18-3(3.39) / 4 = 1.96.

This is a minimum value for x.

So the total length of wire the square  for minimum  total area is 4 * 1.96

= 7.84 m

There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.

The length of the square must be 4 m in order to maximize the total area.

When we put the differentiation of the given function as zero and find the value of the variable we get maxima and minima.

We have,

Length of the wire = 18 m

Let the length of the wire bent into a square = x.

The length of the wire bent into an equilateral triangle = (18 - x)

Now,

The perimeter of a square = 4 side

4 side = x

side = x/4

The perimeter of an equilateral triangle = 3 side

11 - x = 3 side

side = (18 - x)/3

Area of square = side²

Area of equilateral triangle = (√3/4) side²

Total area:

T = (x/4)² + √3/4 {(18 -x)/3}² _____(1)

Now,

To find the maximum we will differentiate (1)

dT/dx = 0

2x/4 + (√3/4) x 2(18 - x)/3 x -1 = 0

2x / 4 - (√3/4) x 2(18 - x)/3 = 0

2x/4 - (√3/6)(18 - x) = 0

2x / 4 = (√3/6)(18 - x)

√3x = 18 - x

√3x + x = 18

x (√3 + 1) = 18

x = 18 / (1.732 + 1)

x = 18/2.732

x = 6.58

x = 7

Thus,

The length of the square must be 7 m in order to maximize the total area.

Learn more about maxima and minima here:

https://brainly.com/question/13178975

#SPJ5

Answer:

7,0, -1 and -2

Step-by-step explanation:

Just substitute the values,

a. f(g(7))=f(-1) [g(7)=-1 given]

            =7 [f(-1)=7 given]

b.f(g(-1))=f(3)=0 [g(-1)=3 Given]

c.g(f(-1))=g(7)=-1 [f(-1)=7 given]

d.g(f(7))=g(5)=-2 [f(7)=g(5) given]

Answer:

12.6 mi

Step-by-step explanation:

Arc length = 2πr (Θ/360)

2π(12) (60/360)

= 12.6 mi

Answered by g a u t h m a t h