A woman passed gas silently. I said "it stinks", and she said "I apologize. Excuse me". Why did she say both of those things?

Solving the exponential function, it is found that it will take 43.5 years for the amount of pollutant to reach 7 parts per million.

It is given by, after t years:

[tex]A(t) = 14(2.71)^{-0.016t}[/tex]

It will reach an amount of 7 parts per million when A(t) = 7, hence:

[tex]A(t) = 14(2.71)^{-0.016t}[/tex]

[tex]7 = 14(2.71)^{-0.016t}[/tex]

[tex](2.71)^{-0.016t} = 0.5[/tex]

[tex]\log{(2.71)^{-0.016t}} = \log{0.5}[/tex]

[tex]-0.016t\log{(2.71)} = \log{0.5}[/tex]

[tex]t = -\frac{\log{0.5}}{0.016\log{2.71}}[/tex]

t = 43.5.

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Answer:

B

Step-by-step explanation:

Answer:

X equals 10.

8x - x = 70

Step-by-step explanation:

8 x 10 = 80

80 - 10 = 70

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: a = -1[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

For a function f(x) = y,

x represents the value ( x - coordinate ) at which the function has a value y.

[tex]\qquad \tt \rightarrow \: f(x) = a {x}^{2} + 2[/tex]

for point (-1 , 1) to satisfy the equation, we have to calculate the value of a

[tex]\qquad \tt \rightarrow \: f( - 1) = a( - 1) {}^{2} + 2[/tex]

[tex]\qquad \tt \rightarrow \: 1 = a + 2[/tex]

[tex]\qquad \tt \rightarrow \: a = 1 - 2[/tex]

[tex]\qquad \tt \rightarrow \: a = - 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Substitute -1 into x

Substitute 1 into y

f(x)= a (-1) ^2+2=1

       a=-1

The value of e³ = 20.079.

e is an irrational number , It is a numerical constant used in mathematical constant .

The value of e = 2.718

It is asked in the question to determine the value of e³

Therefore

e³ = ( 2.718)³

e³ = 20.079

Therefore the value of e³ = 20.079.

The image of the calculation is attached with the answer.

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Answer:

write three methods of writing set. Give one example of each methods.

[tex] \huge \tt \underline {\green{Answer}}[/tex]

If on March 8, 2017 , one U.S. dollar worth 66.79 Indian rupees

ie. $1 = Rs 66.79

$ 1 = 66.79 × 1

$ ? = 110.66

$ = New / old

$ = 110.66 / 66.79

$ = 1.65683485552

or

$1.66 = 110.66

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex] \texttt{ \:The absolute maxima of f is f(-8) = 6} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Absolute maxima is the maximum possible value for a given x, of a function.

and here, the maximum value is at -8, and the maximum value is 6.

[tex]\qquad \tt \rightarrow \: maximum - \: \: f( - 8) = 6[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

angle M = angle P ( 90°)

so MN is parallel to pq

MN makes 90° with UT so it is perpendicular

Answer:

0.9668 USD

Step-by-step explanation:

1 USD=1.0343 AUD 1AUD=0.9668 USD.

Answer:

x = -31/4  or x = 17/4

Step-by-step explanation:

|4x + 7| − 4 = 20

⇔ |4x + 7| − 4 + 4 = 20 + 4

⇔ |4x + 7| = 24

⇔ 4x + 7 = 24  or 4x + 7 = -24

⇔ 4x = 24 - 7 or 4x = -24 - 7

⇔ 4x = 17 or 4x = -31

⇔ x = 17/4 or x = -31/4

Answer:

x = [tex]\frac{17}{4}[/tex]    (17/4 = 4.25)

or x =  [tex]-\frac{31}{4}[/tex]  (-31/4 = -7.75)

Step-by-step explanation:

| | is notation for absolute value

absolute value - the distance that a number is from 0

> essentially, you can think of absolute value as the "positive version" of whatever is inside of the | |

if we have | x | = 20, we could really have (without the | | ) two versions of x

either | x | = 20  ; or | -x | = 20  {because a negative x inside of the | | has the same value as positive x}

we set this up as two equations:

x = 20        or         -x = 20

                                ^ {multiply by -1}

x = 20  or   x = -20

now, let's plug our understanding into the equation

|4x + 7| - 4 = 20

first, we should simplify our equation to:

|4x + 7| - 4 = 20

           + 4   + 4

 |4x + 7|   =   24

now, let's separate this absolute value equation into two separate equations:

4x + 7 = 24:

      - 7    - 7  {subtract 7 from both sides to isolate x}

4x = 17

÷4  ÷4        {divide both sides by 4 to get 1x}

x= [tex]\frac{17}{4}[/tex]

or,

4x + 7 = -24:

      - 7    -7   {subtract 7 from both sides to isolate x}

4x     =    -31

÷4           ÷4   {divide both sides by 4 to get 1x}

 x = [tex]-\frac{31}{4}[/tex]

so, we know that

x = [tex]\frac{17}{4}[/tex]    (17/4 = 4.25)

or x =  [tex]-\frac{31}{4}[/tex]  (-31/4 = -7.75)

hope this helps!!

Answer:

-3 - false

0 - true

1 - true

2 - false

4 - true

Step-by-step explanation:

the "zeros" of a function are its x-intercepts

(because that is when the function = zero [0])

So, we can look at the x-intercepts of the graph to find the zeros:

at 0, 1, and 4 the function = 0, meaning that those are zeros of the function

hope this helps!! have a lovely day :)

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

Answer:  [tex]\textsf{y = -1.75x - 11.75}[/tex]

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

Given:  [tex]\textsf{Goes through (-5, -3) and parallel to 7x + 4y = 10}[/tex]

Find:  [tex]\textsf{The equation in slope-intercept form}[/tex]

Solution: We need to first solve for y in the equation that was provided so we can determine the slope.  Then we plug in the values into the point-slope form, distribute, simplify, and solve for y to get our final equation.

Subtract 7x from both sides

Divide both sides by 4

Plug in the values

Simplify and distribute

Subtract 3 from both sides

Therefore, the final equation in slope-intercept form that follows the information that was provided is y = -1.75x - 11.75

Answer:

12x^18

Step-by-step explanation:

The complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number shown in the picture:

-7i(3 + 3i)

= -7i

In trigonometric form:

z = 7 (cos (90) + sin (90) i)

= 3 + 3i

z = 4.2426 (cos (45) + sin (45) i)

[tex]\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)[/tex]

[tex]\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)[/tex]

[tex]\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}[/tex]

[tex]\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}[/tex]

=21-21i

After converting into the exponential form:

[tex]\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}[/tex]

From part (b) and part (c) both results are the same.

Thus, the complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

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Answer:

The costco basmati rice

Step-by-step explanation:

Under the label it is given that the bag is 18.14 kg

When converted to lbs= 18.14*2.2~39.91

39.91lbs>10lbs, so it has more quantity of rice: Costco Basmati

Answer:

The Costco bag is a better deal as each pound is $0.65 cheaper

Step-by-step explanation:

Let make the weight of each bag in a common unit

18.14kg = about 40 pounds (formula: multiply the mass value by 2.205)

Now find how much it cost per pound for each bag,

Costco: 49.99 / 40 = $1.25 per pound

Bulkmarket: 18.99 / 10 = $1.90 per pound

1.25 < 1.90

Answer:

6=6

Step-by-step explanation:

This is because the exponent is multiplying it by one so technically you don't have to do anything but multiply 6*1

Hope this helps

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Fun fact: ANY number powered to the}\\\huge\textbf{1 it automatically that number(just }\\\huge\textbf{regular multiplication).}[/tex]

[tex]\mathsf{6^1}\\\\\\\mathsf{\approx 6\times1}\\\\\\\large\text{So, you're making it 6 ONE TIME}\\\\\mathsf{= \bf 6}\\\\\\\\\\\\\huge\text{Thus, your answer should be: \boxed{\mathsf{Option\ B.\ 6^1 = 6}}}\huge\checkmark[/tex]

[tex]\large\text{Random\ note\ for\ rest\ of\ equations:}\\\\\mathsf{6^0\rightarrow \bf 1}\\\\\mathsf{6^2\rightarrow 6\times 6 \rightarrow \bf 36}\\\\\mathsf{6^3\rightarrow 6\times6\times6\rightarrow 36\times6\rightarrow \bf 216}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer: 32x+4

Step-by-step explanation:

[tex]f(x) \cdot g(x)=(8x+1)(-5+9)=4(8x+1)=\boxed{32x+4}[/tex]

7.5 pounds of the $0.82 per lb candy must be used in the mixture.

First, let's define the variables:

We want to make 9 lb of mixture, then:

x + y = 9.

And the price of these 9 pounds must be $0.91, then we can write:

x*$0.82 + y*$1.36 = 9*$0.91 = $8.19

Then we have a system of equations:

x + y = 9.

x*$0.82 + y*$1.36 = $8.19

We can isolate y on the first equation so we get:

y = 9 - x

Now we can replace that on the other equation:

x*$0.82 + (9 - x)*$1.36 = $8.19

And now we can solve this for x.

x*($0.82 - $1.36) = $8.19 - 9*$1.36

-x*$0.54 = -$4.05

x = (4.05/0.54) = 7.5

So 7.5 pounds of the $0.82 per lb candy must be used in the mixture.

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Answer:

[tex]52\sqrt{3} ft^{2}[/tex]

Step-by-step explanation:

Please refer to the attached picture.

First we will find the area of rectangle BCDE.

Area of Rectangle = Length x Breadth = DE x CD

= 11 x [tex]4\sqrt{3}[/tex]

[tex]=44\sqrt{3} ft^{2}[/tex]

Next we will find Area of Triangle ABE.

Area of Triangle = 0.5 x Base x Height

[tex]0.5*4*4\sqrt{3} \\=8\sqrt{3} ft^{2}[/tex]

Area of Trapezoid = Area of Rectangle + Area of Triangle

[tex]=44\sqrt{3} +8\sqrt{3} \\=52\sqrt{3} ft^{2}[/tex]

Answer:

A = 52[tex]\sqrt{3}[/tex] ft² ≈ 90.1 ft²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height and b₁ , b₂ the parallel bases

here h = 4[tex]\sqrt{3}[/tex] , b₁ = 15 , b₂ = 11 , then

A = [tex]\frac{1}{2}[/tex] × 4[tex]\sqrt{3}[/tex] × (15 + 11)

   = 2[tex]\sqrt{3}[/tex] × 26

   = 52[tex]\sqrt{3}[/tex] ft²

   ≈ 90.1 ft² ( to the nearest tenth )

Substituting in y=15,

[tex]\frac{1}{5}x-\frac{2}[3}(15)=30\\\\\frac{1}{5}x-10=30\\\\\frac{1}{5}x=40\\\\x=\boxed{200}[/tex]

Answer: B=16 and m=6

Step-by-step explanation:

in y=mx+b the number next to x is always the m/slope and the number without a variable is always the b.

The value of A and B is 5 , 10 ;The average temperature for first ten hours is  -7.466 degree F ; an expression for the rate that the temperature is changing with respect to h ; dt/dh = +B sin ((pi*h)/12)

A function is a mathematical statement used to correlate two variables.

The function given is

T(h) = - A - B * cos((pi*h)/12)

T is the temperature in degrees Fahrenheit and

h is the number of hours from midnight (0 <= h <= 24)

a. The initial temperature at midnight was - 15 degrees * F and

at Noon of New Year's Day it was 5 degrees * F

At midnight h = 0

T(h) = -15 degrees F

-15 = -A-B* cos 0

-15 = -A-B

A+B = 15------------------- (1)

At noon , h = 12 , T(h)= 5

- A - B*  cos(pi) = 5

-A - B (-1) = 5

B -A = 5 ----------------------- (2)

Solving equation 1 and 2

2B = 20

B = 10

A = 5

The value of A and B is 5 , 10

The average temperature for first ten hours is  -7.466 degree F

Find an expression for the rate that the temperature is changing with respect to h

dt/dh = +B sin ((pi*h)/12)

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The correct answer is option B which is the graph that represents the equation y = (1/2)x will be the second option in the figure. At every value of y, the value of x is double.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The graph of the equation y =1/2x is represented in the answer below we can see in the graph that at every value of y the value of x is double for example if we put y = 1 then the value of x will be 2.

y = 1/2 x

at x = 2

y = 1/2 x 2

x = 1

Therefore the correct answer is option B which is the graph that represents the equation y = (1/2)x will be the second option in the figure. At every value of y, the value of x is double.

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The answers are as follows:

a) X denotes the number of the california residents that have adequate earthquake insurance

b)  x = 1 ,2 ,3 ......

c) P( X=x ) = 0.3(1-0.3) ^ (x-1)

d)  P( X=1) +  P( X=2)  + P( X=3) +  P( X=4)

e) 0.49

f)0.42

g)0.33

It is a branch of mathematics that deals with the occurrence of a random event.

The complete question is

It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies. a. In words, define the random variable X. b. List the values that Xmay take on. c. Give the distribution of X.X~ _____(_____,_____) d. WhatistheprobabilitythatwemustsurveyjustoneortworesidentsuntilwefindaCaliforniaresidentwhodoes not have adequate earthquake supplies? e. What is the probability that we must survey at least three California residents until we find a California resident who does not have adequate earthquake supplies? f. HowmanyCaliforniaresidentsdoyouexpecttoneedtosurveyuntilyoufindaCaliforniaresidentwhodoesnot have adequate earthquake supplies? g. How many California residents do you expect to need to survey until you find a California resident who does have adequate earthquake supplies?

given that 30% of California residents have adequate earthquake supplies.

a) variable X denotes the number of the california residents that have adequate earthquake insurance

b) x = 1 ,2 ,3 ......

c) p=0.3

P( X=x ) = 0.3(1-0.3) ^ (x-1)

d) P( X=1) +  P( X=2)  + P( X=3) +  P( X=4)

= 0.3(1-0.3) ^ 0 + 0.3(1-0.3) ^1 + 0.3(1-0.3)^ 2 +...

e) P( X≥ 3) = 1- P(X<3)

= 1- (P(X=1) + (X=2))

= 1- 0.051

= 0.49.

f) E(X)= 1/P

p is the resident who does not have adequate earthquake supplies

p= 1-0.3

p = 0.7

E(X) = 1/0.7

= 0.42

g) E(X) =  1/q

= 1/0.3

= 3.333

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Answer:

Let the cost price be X

A Sells to B

profit = 20%

= cost price + 20%

= X + 20/100 of X

= 6x/ 5

B sells to C

profit = 25%

= Cost price + + 25%

= cost price + 25%

= 6x/5 + 25/100*6x/5

= 6x/5.+ 3x/10.

= 3x/2

3x/2 = 225.

3x = 450

x = 150.

sp = C. p + profit

S. p - profit = C. p

X - X/5

4x/5

4(150)/5.

120