How do I solve this?

Integrate:

[tex]\displaystyle\int_{-2}^3((x+6)-x^2)\,\mathrm dx = \int_{-2}^3(6+x-x^2)\,\mathrm dx[/tex]

[tex]=\left(6x+\dfrac{x^2}2-\dfrac{x^3}3\right)\bigg|_{-2}^3[/tex]

[tex]=\left(18+\dfrac92-9\right) - \left(-12+2+\dfrac83\right)[/tex]

[tex]=\boxed{\dfrac{125}6}[/tex]

Answer:

Exposure to nicotine is the independent variable

Step-by-step explanation:

An independent variable is a factor that remains unchanged (by other factors in the experiment) throughout the course of an experiment. It can however be manipulated by the researcher. A dependent variable, on the other hand, is the factor being measured that relies on the independent variable. In the case above, exposure to 1 hr of nicotine intake forms the independent variable while the levels of hand steadiness, which will be measured, form the dependent variable.

Answer:

x = 80

Step-by-step explanation:

3x/2=120°

3x=240°

x=80°

Answered by GAUTHMATH

Answer: hello your question is incomplete below is the complete question

The Two vectors;  A = 5i + 6j +7k and B = 3i -8j +2k.

answer;

angle = 102°

Step-by-step explanation:

multiplying the vectors

A.B = |A| * |B|* cosθ

hence : Cosθ = (Ai*Bi )+ (Aj*Bj) + ( Ak*Bk/ (√A^2 *√B^2 )

                       = 15 - 48 + 14 /(√25+26+29) * (√9+64+4)

                      = -0.206448454

θ = cos^-1 ( -0.206448454) = 101.9° ≈ 102°

Answer:

4,569 units

Step-by-step explanation:

Given :

Measured value = 123,415 units

Expected value = 118,846 units

Residual is the difference between the measured and expected value :

Residual = Measured value - Expected value

Residual = 123,415 units - 118,846 units

Residual = 4,569 units

Answer:

C. 17 units

Step-by-step explanation:

Surface area of rectangular prism is given as:

A = 2lw + 2lh + 2wh

A = 930 square units

l = 12 units

h = 9 units

w = ? (We're to find the width)

Plug in the value into the formula

930 = 2*12*w + 2*12*9 + 2*w*9

930 = 24w + 216 + 18w

Add like terms

930 - 216 = 42w

714 = 42w

Divide both sides by 42

714/42 = 42w/42

17 = w

w = 17 units

The question is incomplete. The complete question is :

Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision.

[tex]$\{ x^5, x^5-1,3 \} \text{ on } (- \infty, \infty)$[/tex]

Solution :

Given :

Function : [tex]$\{ x^5, x^5-1,3 \} \text{ on } (- \infty, \infty)$[/tex]

We have to determine whether the given function is linear dependent or linearly independent for the interval [tex]$(-\infty, \infty)$[/tex].

The given function are linearly dependent because for the constants, [tex]c_1[/tex] and [tex]c_2[/tex], the equation is :

[tex]$c_1x^5 + c_23 = x^5-1$[/tex]  has the solution [tex]$c_1 = 1$[/tex] and [tex]$c_2 = -\frac{1}{3}$[/tex]

Therefore,

[tex]$1x^5 + \left(-\frac{1}{3}\right)3 = x^5-1$[/tex]

Answer:

hey there hope this answer helps you out

Step-by-step explanation:

we have two functions f(x) and g(x) such that

[tex]f(x) = \frac{1}{x} [/tex]

and

[tex]g(x) = {x}^{2} + 6x[/tex]

solving for f ° g, we'll substitute the x in f(x) by the value of g(x)

[tex]fog = \frac{1}{g(x)} [/tex]

[tex]fog \: = \frac{1}{ {x}^{2} + 6x } [/tex]

taking x common in denominator

[tex]fog = \frac{1}{x(x + 6)} [/tex]

for a function to exist it should not have 0 in its denominator

checking the values of x for which the denominator of f ° g becomes 0 :-

so the function doesn't exist at values x = 0, -6

[tex]\rightarrow\sf {5a}^{2} + {b(a}^{2} + 5) + {b}^{2} [/tex]

[tex]\rightarrow\sf {5a}^{2} + {b(a }^{2} + 5) + {b}^{2} \\ = \sf {5a}^{2} + {ba}^{2} + b \times 5 + {b}^{2} \\ = \large\boxed{\sf{\red{ {5a}^{2} + {ba}^{2} + 5b + {b}^{2} }}}[/tex]

[tex]\rightarrow\large\boxed{\sf{\red{ {5a}^{2} + {ba}^{2} + 5b + {b}^{2} }}}[/tex]

[tex]\color{red}{==========================}[/tex]

✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ

✍︎ꕥᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢꕥ

Answer:

10. CD + DE = CE

11. BC + CE = BE

Step-by-step explanation:

10. CD and DE lie on a straight line, therefore, CD + DE = CE based on the segment addition postulate.

11. BC and CE lie on a straight line, therefore, BC + CE = BE based on the segment addition postulate.

Answer:

71, 71, 75, 85, 98, 98, 104, 111, 114, 122, 164

The middle quartile is 98.

The lower quartile is 80

The upper quartile is 112.5

Answer:

7

Log(4) 5 + log (4) 7 =log(4) 35

Step-by-step explanation:

Answer:

(A - B) - C = { 1 , 4 , 6 , 7 }

Step-by-step explanation:

A = { 1 , 2 , 3 , 4 , 5 }

B = { 4 , 5 , 6 , 7 }

A - B = { 1 , 2, 3 ,6 , 7 }

C = { 2 , 3 , 4 }

(A - B) - C = { 1 , 4 , 6 , 7 }

Answer:

b= 5i square root of 3

b = -5i square root of 3

Step-by-step explanation:

4b^2+300=0

4b^2 = -300

b^2 = -75

b = square root of -75

b = -75^1/2

^1/2 means square root

b = 25^1/2 * 3^1/2 * i

b= 5i square root of 3

b = -5i square root of 3

Answer:

The first term is 6; the common difference in 0.8.

Step-by-step explanation:

The nth term is:

[tex] a_n = a_1 + (n - 1)d [/tex]

The sum of the first n terms is:

[tex] S_n = \dfrac{n(a_1 + a_n)}{2} [/tex]

[tex] a_{n} = a_1 + (n - 1)d [/tex]

[tex] a_{11} = a_1 + (11-1)d [/tex]

[tex] a_1 + 10d = 14 [/tex]        Equation 1

[tex] S_n = \dfrac{n(a_1 + a_n)}{2} [/tex]

[tex] S_{26} = \dfrac{26(a_1 + a_{26})}{2} [/tex]

[tex] \dfrac{26(a_1 + a_1 + 25d}{2} = 416 [/tex]

[tex] \dfrac{52a_1 + 650d)}{2} = 416 [/tex]

[tex] 26a_1 + 325d = 416 [/tex]        Equation 2

Equation 1 and Equation 2 form a system of equations in 2 unknowns.

To eliminate a_1, subtract 26 times Eq. 1 from Eq. 2.

[tex] 65d = 52 [/tex]

[tex] d = \dfrac{52}{65} [/tex]

[tex] d = \dfrac{4}{5} = 0.8 [/tex]

[tex] a_1 + 10d = 14 [/tex]

[tex] a_1 + 10 \times 0.8 = 14 [/tex]

[tex] a_1 + 8 = 14 [/tex]

[tex] a_1 = 6 [/tex]

Answer:

The first term is 6; the common difference in 0.8.

Answer:

32 miles per hour

Step-by-step explanation:

x+85+75=192 x+160=192 x=192-160 x=32..

Answer:

v = ir

2 times 10 = 20v

Step-by-step explanation:

i think it is the one

Answer:

volume =l×b×h

45cm×32cm×35cm=48,960cm³

Answer:

q=4

p=2

Step-by-step explanation:

3p+2q=14

10p+6q=44

10(3p+2q=14)

3(10p+6q=44)

30p+20q=140-

30p+18q=132

2q=8

2q/2=8/2

q=4

3p+2*4=14

3p+8=14

3p=14-8

3p/3=6/3

p=2

hope this helps

Answer:

[tex]p=2\\q=4[/tex]

Step-by-step explanation:

One is given the following system of equations,

[tex]3p + 4q = 22\\\\10p + 12q = 68[/tex]

The fastest method to solve a system of equations is the method of elimination. This process is manipulating one of the equations, by multiplying or diving it by a value, such that one of the coefficients variables in the equation is the additive inverse of the like term in the other equation. That way, when one adds the equations, one of the variables cancels out. Then one can solve for the other term. Finally, one can back sovle by substituting the value of the solved variable into one of the equations and simplifying to find the value of the other variable.

[tex]3p + 4q = 22\\\\10p + 12q = 68[/tex]

Manipulate the first equation so that the variable (q) cancels

[tex](3p + 4q = 22) *(-3)\\\\10p + 12q = 68[/tex]

[tex]-9p + -12q = -66\\\\10p + 12q = 68[/tex]

Add the equations,

[tex]-9p + -12q = -66\\\\10p + 12q = 68[/tex]

[tex](10p-9p)+(-12q+12q)=(-66+68)[/tex]

Simplify,

[tex](10p-9p)+(-12q+12q)=(-66+68)[/tex]

[tex]p=2[/tex]

Backsovle for the variable (p). Substitute the values of (p) into one of the original equations. Then simplify and use inverse operations to solve for the variable (q).

[tex]3p+4q=22[/tex]

Substitute,

[tex]3(2)+4q=22[/tex]

Simplify,

[tex]3(2)+4q=22[/tex]

[tex]6+4q=22[/tex]

Inverse operations,

[tex]6+4q=22[/tex]

[tex]4q=16\\q=4[/tex]

Answer:

Step-by-step explanation:

She needs 12 pizzas

x + y = 12

She also can't spend more than 180 dollars.

8x + 11y < 180 She can get all 12 pizzas and have the bill come to 132 dollars

11 * 12 = 132

She could really be kind to her pocket book and get all cheese pizzas

8*12 = 96 which saves her 36 dollars.

So any number of either kind will do.

(0,12) = 132

(1,11) = 8*1 + 11*11 = 129

and so on down the line

Answer:

Step-by-step explanation:

office at point A =(-7,-5)   ........................in the form (x1,y1)

supermarket and point B = (-2,-6)........in the form (x2,y2)

home Home at point C = (4,-6).............in the from (x3,y3)

find the total distance from A to B + B to C

ABdist= sqrt[ (x2-x1)^2 + (y2-y1)^2 ]

ABdist = sqrt[ (-2-(-7))^2 + (-6-(-5))^2 ]

ABdist = sqrt[ (-2 + 7)^2 + (-6 +5)^2]

ABdist = sqrt[ [tex]5^{2}[/tex] + [tex](-1)^{2}[/tex]]

ABdist = sqrt[ 25 + 1 }

ABdist = [tex]\sqrt{26}[/tex]

BCdist= sqrt[ (x3-x2)^2 + (y3-y2)^2 ]

BCdist = sqrt[ (4-(-2))^2 + (-6-(-6))^2]

BCdist = sqrt[ 4+2)^2  + -6+6)^2 ]

BCdist = sqrt [ [tex]6^{2}[/tex] + [tex]0^{2}[/tex] ]

BCdist = [tex]\sqrt{36}[/tex]

BCdist = 6

total distance = [tex]\sqrt{26}[/tex] +6

The first answer looks good

Answer:

79.5, 110.5, 141.5, 172.5, 203.5, 234.5

Step-by-step explanation:

Given

The attached distribution

Required

The lower class limits

To do this, we simply subtract 0.5 from the lower interval

From the attached distribution, the lower intervals are:

80.0, 111.0, 142.0, 173,0 .......

So, the lower class limits are:

[tex]80.0-0.5 = 79.5[/tex]

[tex]111.0-0.5 = 110.5[/tex]

[tex]142.0-0.5 = 141.5[/tex]

[tex]173.0-0.5 = 172.5[/tex]

[tex]204.0-0.5 = 203.5[/tex]

[tex]235.0-0.5 = 234.5[/tex]

9514 1404 393

Answer:

  (c)  5x and 3x, and 4 and 1

Step-by-step explanation:

Like terms have the same variable(s) to the same power(s).

The terms of this expression are ...

The like terms are {5x, -3x}, which have the x-variable to the first power, and {4, -1}, which have no variable.

Answer:

b

Step-by-step explanation:

thbte

Answer:

Correct option is

C

10

5

10P

5

Total ways in which one passenger can stop =10

Total ways in which 5 passengers can stop =10∗10∗10∗10∗10

=10

5

We will select 5 floors from 10 floors and assign each individual to each floor to keep everyone isolated from each other

No. of ways in which no two persons stop at the same floor =10C

5

∗5!

=10P

5

⇒P(E)=10P

5

/10

5

Answer:

Step-by-step B represents the $14 John earned in the 2 hours he worked.

explanation: