If f (x) = -9x - 9 and g (x) = Vx - 9, what is (f ° g) (10)?

Answer: [tex]S=0.087p[/tex] .

Step-by-step explanation:

Equation for direct proportion:

y=kx

, where x= independent variable ,

y=dependent variable.

k= proportionality constant

Here, State sales tax S  is directly proportional to retail price p.

Also, dependent variable= S,  independent variable =p

Required equation: S= kp

Put S= 12.32 and x= 142

[tex]S=12.32=k(142)\\\\\Rightarrow\ k=\dfrac{12.32}{142}\approx0.087[/tex]

Hence, the required equation is [tex]S=0.087p[/tex] .

Answer:

no tiene mas informaion?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Length the length and breadth of the rectangle be x and y.

Area of the rectangle A = Length * breadth

Perimeter P = 2(Length + Breadth)

A = xy and P = 2(x+y)

If the area of the rectangle is 512m², then 512 = xy

x = 512/y

Substituting x = 512/y into the formula for calculating the perimeter;

P = 2(512/y + y)

P = 1024/y + 2y

To get the value of y, we will set dP/dy to zero and solve.

dP/dy = -1024y⁻² + 2

-1024y⁻² + 2 = 0

-1024y⁻² = -2

512y⁻² = 1

y⁻² = 1/512

1/y² = 1/512

y²  = 512

y = √512 m

On testing for minimum, we must know that the perimeter is at the minimum when y = √512

From xy = 512

x(√512) = 512

x = 512/√512

On rationalizing, x = 512/√512 * √512 /√512

x = 512√512 /512

x = √512 m

Hence, the dimensions of a rectangle is √512 m  by √512 m

Answer:

B.77.4%

Step-by-step explanation:

Mean wage (μ) = $4.50

Standard deviation (σ) = $0.50

For nay given salary X, the z-score is given by:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

For X = $3.75, the z-score is:

[tex]z=\frac{3.75-4.50}{0.50}\\z=-1.5[/tex]

For X = $5.00, the z-score is:

[tex]z=\frac{5.00-4.50}{0.50}\\z=1[/tex]

A z-score of -1.5 corresponds to the 6.68th percentile, while a score of 1 corresponds to the 84.13th percentile. Therefore, the percentage of workers getting paid between $3.75 and $5.00 an hour is:

[tex]P=84.13-6.68\\P=77.45\%[/tex]

The answer is alternative B.77.4%

Answer:

Step-by-step explanation:

[tex]\frac{x-1}{2} =t\\\frac{y-2}{3} =t\\\frac{z-3}{4} =t\\so~eq.~of~line~L_{1}~is\\\frac{x-1}{2} =\frac{y-2}{3} =\frac{z-3}{4} \\its~d.r's~are~2,3,4\\again~\frac{x-2}{1} =s\\\frac{y-4}{2} =s\\\frac{z+1}{-4} =s\\so~eq. ~of~line~L_{2}~is\\\frac{x-2}{1} =\frac{y-4}{2} =\frac{z+1}{-4} \\its~d.r's ~are~1,2,-4\\let ~the ~d.r's~of~line~perpendicular~to~both~L_{1}~and~L_{2}~be~a,b,c,~then~\\2a+3b+4c=0\\1a+2b-4c=0\\solving\\\frac{a}{3*-4-4*2} =\frac{b}{4*1-2*-4} =\frac{c}{2*2-3*1} \\[/tex]

[tex]\frac{a}{-20} =\frac{b}{-4} =\frac{c}{1} \\d.r's~of ~reqd~line~is~-20,-4,1~or~20,4,-1[/tex]

now you find the point of intersection.

then calculate the angle.

Answer:

what do you need help with its not really clear

Answer

1. 48 2. 308

Step-by-step explanation:

Answer:

the dimensions that will minimize the cost of constructing the box is:

a = 5.8481  in ;   b = 5.848 in  ; c = 10.234 in

Step-by-step explanation:

From the information given :

Let a be the base if the rectangular box

b to be the height and c to be the  other side of the rectangular box.

Then ;

the area of the base is ac

area for the front of the box is ab

area for the remaining other sides   ab + 2cb

The base of the box is made from a material costing 8 ac

The front of the box must be decorated, and will cost 10 ab

The remainder of the sides will cost 4 (ab + 2cb)

Thus ; the total cost  C is:

C = 8 ac + 10 ab + 4(ab + 2cb)

C = 8 ac + 10 ab + 4ab + 8cb

C = 8 ac + 14 ab + 8cb   ---- (1)

However; the volume of the rectangular box is V = abc = 350 in³

If abc = 350

Then b = [tex]\dfrac{350}{ac}[/tex]

replacing the value for c in the above equation (1); we have :

[tex]C = 8 ac + 14 a(\dfrac{350}{ac}) + 8c(\dfrac{350}{ac})[/tex]

[tex]C = 8 ac + \dfrac{4900}{c}+\dfrac{2800}{a}[/tex]

Differentiating C with respect to a and c; we have:

[tex]C_a = 8c - \dfrac{2800}{a^2}[/tex]

[tex]C_c = 8a - \dfrac{4900}{c^2}[/tex]

[tex]8c - \dfrac{2800}{a^2}=0[/tex] --- (2)

[tex]8a - \dfrac{4900}{c^2}=0[/tex]   ---(3)

From (2)

[tex]8c =\dfrac{2800}{a^2}[/tex]

[tex]c =\dfrac{2800}{8a^2}[/tex] ----- (4)

From (3)

[tex]8a =\dfrac{4900}{c^2}[/tex]

[tex]a =\dfrac{4900}{8c^2}[/tex]   -----(5)

Replacing the value of a in 5 into equation (4)

[tex]c = \dfrac{2800}{8*(\dfrac{4900}{8c^2})^2} \\ \\ \\ c = \dfrac{2800}{\dfrac{8*24010000}{64c^4}} \\ \\ \\ c = \dfrac{2800}{\dfrac{24010000}{8c^4}} \\ \\ \\ c = \dfrac{2800*8c^4}{24010000} \\ \\ c = 0.000933c^4 \\ \\ \dfrac{c}{c^4}= 0.000933 \\ \\ \dfrac{1}{c^3} = 0.000933 \\ \\ \dfrac{1}{0.000933} = c^3 \\ \\ 1071.81 = c^3\\ \\ c= \sqrt[3]{1071.81} \\ \\ c = 10.234[/tex]

From (5)

[tex]a =\dfrac{4900}{8c^2}[/tex]   -----(5)

[tex]a =\dfrac{4900}{8* 10.234^2}[/tex]

a = 5.8481

Recall that :

b = [tex]\dfrac{350}{ac}[/tex]

b = [tex]\dfrac{350}{5.8481*10.234}[/tex]

b =5.848

Therefore ; the dimensions that will minimize the cost of constructing the box is:

a = 5.8481  in ;   b = 5.848 in  ; c = 10.234 in

The dimensions that will minimize the cost of constructing this box are: a = 5.8481 inches, b = 5.848 inches, and c = 10.234 inches and this can be determined by using the given data.

Given :

According to the given data the total cost is given by:

C = 8ac + 14ab + 8cb   --- (1)

The volume of the rectangular box is (V = abc = 350 inch cube). So, the value of b is given by:

[tex]\rm b = \dfrac{350}{ac}[/tex]

Now, substitute the value of 'b' in the equation (1).

[tex]\rm C = 8ac + \dfrac{4900}{c}+\dfrac{2800}{a}[/tex]

First differentiating the above equation with respect to c.

[tex]\rm C_c = 8a-\dfrac{4900}{c^2}[/tex]   --- (2)

Now, differentiating the above equation with respect to a.

[tex]\rm C_a = 8c-\dfrac{2800}{a^2}[/tex]    --- (3)

Now, equate equation (2) and equation (3) to zero.

From equation (2):  

[tex]\rm a=\dfrac{4900}{8c^2}[/tex]    ----- (4)

From equation (3):

[tex]\rm c=\dfrac{2800}{8a^2}[/tex]   ----- (5)

Now, from equations (4) and (5).

[tex]\rm c = \dfrac{2800}{8\left(\dfrac{4900}{8c^2}\right)^2}[/tex]

Now, simplifying the above expression in order to get the value of c.

c = 10.234

Now, put the value of 'c' in equation (5) in order to get the value of 'a'.

a = 5.8481

The value of 'b' is given by:

[tex]\rm b = \dfrac{350}{5.8481\times 10.234}[/tex]

b = 5.848

So, the dimensions that will minimize the cost of constructing this box are: a = 5.8481 inches, b = 5.848 inches, and c = 10.234 inches.

For more information, refer to the link given below:

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None of these options seem to be correct. You can check each result by differentiation:

[tex](e^x\sec^2x)'=e^x(\sec^2x+2\sec^2\tan x)=e^x\sec^2x(1+\tan x)[/tex]

[tex](e^x\sec x)'=e^x(\sec x+\sec x\tan x)=e^x\sec x(1+\tan x)[/tex]

[tex](e^x\tan^2x)'=e^x(\tan^2x+2\tan x\sec^2x)=e^x\tan x(\tan x+2\sec^2x)[/tex]

[tex](e^x\tan x)'=e^x(\tan x+\sec^2x)[/tex]

But none of these are equivalent to [tex]e^x(\sec x+\tan^2x)[/tex]...

Answer:

Mars

Step-by-step explanation:

America

Answer:

Option A is the correct option.

Step-by-step explanation:

[tex] \frac{3}{x } = \frac{6}{x - 4} [/tex]

Apply cross product property:

[tex]3(x - 4) = 6 \times x[/tex]

[tex]3(x - 4) = 6x[/tex]

Hope this helps...

Best regards!!

Answer:

3 * (x - 4) = 6 * x.

Step-by-step explanation:

3 / x = 6 / (x - 4)

3 * (x - 4) = 6 * x

3x - 12 = 6x

6x = 3x - 12

6x - 3x = -12

3x = -12

x = -4.

Hope this helps!

Answer:

y = 1110

Step-by-step explanation:

In the above question, we are given the cubic model

y=x³ +x² + x

We are to solve for y when x = 10

Hence,

y = 10³ + 10² + 10

y = 1000 + 100 + 10

y = 1110

Therefore, the value of y when x is 10 using the cubic model of ' y =x³ +x² + x' is 1110.

The linear equation defines the arithmetic sequence is an = -8 + 4(n - 1). The correct option is A.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that, the sequence is -8, -4, 0, 4, 8, ...

a = -8

d = +4

The expression for the nth term will be written as,

an = a + ( n - 1 ) d

= -8 + ( n - 1 ) 4

To know more about arithmetic progression follow

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Answer:

The 95% confidence interval for true average degree of polymerization is (431, 446).

Step-by-step explanation:

The data provided for the degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range is:

S = {418, 421, 422, 422, 425, 429, 431, 434, 437,  439, 446, 447, 449, 452, 457, 461, 465}

Compute the sample mean and sample standard deviation:

[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{7}\times 7455=438.5294\\\\s=\sqrt{\frac{1}{n-1}\sum (X-\bar x)^{2}}=\sqrt{\frac{1}{17-1}\times 3594.2353}=14.988[/tex]

As the population standard deviation is not provided use the t-statistic to compute the two-sided 95% confidence interval for true average degree of polymerization.

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\frac{s}{\sqrt{n}}[/tex]

The critical value of the t is:

[tex]t_{\alpha /2, (n-1)}=t_{0.05/2, (17-1)}=t_{0.025, 16}=2.12[/tex]

*Use a t-table.

Compute the 95% confidence interval for true average as follows:

[tex]CI=438.5294\pm 2.12\cdot\frac{14.988}{\sqrt{17}}[/tex]

     [tex]=438.5294\pm 7.7065\\=(430.8229, 446.2359)\\\approx (431, 446)[/tex]

Thus, the 95% confidence interval for true average degree of polymerization is (431, 446).

Answer:

a. (24 ln 2 − 7) / 9

b. x tan x + ln|cos x| + C

Step-by-step explanation:

a. ∫₁² x² ln x dx

Integrate by parts.

If u = ln x, then du = 1/x dx.

If dv = x² dx, then v = ⅓ x³.

∫ u dv = uv − ∫ v du

= (ln x) (⅓ x³) − ∫ (⅓ x³) (1/x dx)

= ⅓ x³ ln x − ∫ ⅓ x² dx

= ⅓ x³ ln x − ¹/₉ x³ + C

= ¹/₉ x³ (3 ln x − 1) + C

Evaluate between x=1 and x=2.

[¹/₉ 2³ (3 ln 2 − 1) + C] − [¹/₉ 1³ (3 ln 1 − 1) + C]

⁸/₉ (3 ln 2 − 1) + C + ¹/₉ − C

⁸/₉ (3 ln 2 − 1) + ¹/₉

⁸/₃ ln 2 − ⁸/₉ + ¹/₉

⁸/₃ ln 2 − ⁷/₉

(24 ln 2 − 7) / 9

b. ∫ x sec² x dx

Integrate by parts.

If u = x, then du = dx.

If dv = sec² x dx, then v = tan x.

∫ u dv = uv − ∫ v du

= x tan x − ∫ tan x dx

= x tan x + ∫ -sin x / cos x dx

= x tan x + ln|cos x| + C

The answer is A. Dilate circle A by a scale factor of 3

I took the test :)

Answer:

probability of getting both are unripe

= 0.15

probability of getting both are ripe

= 0.375

Probability of one ripe and one unripe

=0.234375

Probability of at least one unripe

=0.625

Step-by-step explanation:

50 mangoes 20 of which are unriped in the first basket .

Riped = 50-20= 30

Probability of unripe = 20/50

Probability of unripe= 0.4

Probability of ripe = 30/50

Probability of ripe = 0.6

40 mangoes of which 15 are unripe In the second basket

Number of riped= 40-15= 25

Probability of unriped= 15/40

Probability of unriped= 0.375

Probability of riped= 25/40

Probability of riped= 0.625

probability of getting both are unripe

= 0.4*0.375

probability of getting both are unripe

= 0.15

probability of getting both are ripe

= 0.6*0.625

= 0.375

Probability of one ripe and one unripe

= 0.625*0375

= 0.234375

Probability of at least one unripe

= 1- probability of no unripe

= 1 - probability of both ripe

= 1-0.375

= 0.625

Answer:

The correct option is (C).

Step-by-step explanation:

The exponential function representing decay is as follows:

[tex]y=y_{0}\cdot e^{kt};\ k<0[/tex]

Here,

y = final value  

y₀ = initial value  

k = growth rate  

t = time passed

The graph represents exponential decay is:

"On a coordinate plane, a graph approaches y = 0 in quadrant 1 and curves up into quadrant 2."

Thus, the correct option is (C).

Answer:

The answer is C

Step-by-step explanation:

I  just took the test on edge

Step-by-step explanation:

[tex]W^m=\underbrace{W\cdot W\cdot W\cdot...\cdot W}_{m}\\\\W^n=\underbrace{W\cdot W\cdot W\cdot...\cdot W}_{n}\\\\W^mW^n=\underbrace{(W\cdot W\cdot W\cdot...\cdot W)}_{m}\underbrace{(W\cdot W\cdot W\cdot...\cdot W)}_{n}\\\\=\underbrace{W\cdot W\cdot W\cdot...\cdot W}_{m+n}=W^{m+n}[/tex]

From the following given equation, the answer to W^mW^n = [tex]\mathbf{W^{m+n}}[/tex]

The laws of indices provide us with the rules and principles for simplifying mathematical computations or algebraic expressions that include powers of the same base.

The example of the question given can be solved by using the multiplication rule. The multiplication rule states that we sum up the power of the integers if they have the same base.

From the given information

W^mW^n = [tex]\mathbf{W^{m+n}}[/tex]

Learn more about indices here:

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Answer: 6

Step-by-step explanation:

If we call each team, A, B, C and D, each team has to play each other team once. Let's call each pairing between 2 teams the 2 teams' letters next to each other, e.g. AB is A playing against B. A has to play against B, C and D so we have AB, AC and AD. So we have 3 so far.

We have already counted that B is playing A but we haven't counted B playing C and D yet so we also have BC and BD. So we have 5 in total

Lastly, C needs to play D, we have already counted C playing B and C playing A so we have CD left. In total that gives 6.

Now we have already included D playing every other team so we don't include any other pairings.

In total, now every team has played every other team giving a total of 6.

(another way of solving this is doing "3!2 but if you haven't learnt factorials yet stick to the first method.

Answer:

6 games.

Step-by-step explanation:

The answer is the number of combinations of 2 from 4

= 4*3 / 2*1

= 6.

Answer:

try 3x=30 or 10

Step-by-step explanation:

Answer:

The domain of the graph is all real numbers less than or equal to 0.

Step-by-step explanation:

Hello,

We know that we cannot take square root of negative numbers, so we must have

[tex]-x\geq 0 \ \text{ ***multiply by -1, it changes the inequality, so*** } \\ \\\large \boxed{\sf \ \ x\leq0 \ \ }[/tex]

So the domain of the graph is all real numbers less than or equal to 0.

For information, I attached the graph so that we can verify it.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

h = -9

Step-by-step explanation:

5h+2(11-h)= -5

Distribute

5h +22 -2h = -5

Combine like terms

3h +22 = -5

Subtract 22 from each side

3h +22-22 = -5-22

3h = -27

Divide by 3

3h/3 = -27/3

h = -9

Hey there! I'm happy to help!

First of all, if one bill weighs on gram, a million would weigh one million grams. Let's divide this by 1,000 to see how many kilograms it is.

1,000,000/1,000=1,000

Now, we need to convert 1,000 kilograms into pounds. We see that 1 kilogram is equal to about 2.205 pounds, so we multiply 1,000 kilograms by 2.205 to get our pounds.

1,000*2.205=2205

Therefore, one million dollar bills weigh about 2205 pounds.

Have a wonderful day! :D

Answer:

Thickness of rectangle prism is 20 inches.

Step-by-step explanation:

Given:

Surface area of rectangular prism, A =  992 sq inches.

Height, h = 12 inches

Width, w = 8 inches

To find:

Thickness / length of prism, [tex]l[/tex] = ?

Solution:

First of all, let us learn the formula for surface area of a rectangular prism.

Formula for surface area of a prism is given as:

[tex]A=2(wl+hl+hw)[/tex]

As there are 6 faces, each face is a rectangle and area of all the faces is considered in the formula. It is just like a cuboid like structure.

Putting all the given values in the formula to find the value of [tex]l[/tex]:

[tex]992=2(8l+12l+8 \times 12)\\\Rightarrow 496 = 20l + 96\\\Rightarrow 20 l =496-96\\\Rightarrow 20 l =400\\\Rightarrow l = \dfrac{400}{20}\\\Rightarrow l = 20\ inches[/tex]

So, the answer is Thickness of rectangle prism is 20 inches.

Answer:

Step-by-step explanation:

when h(t)=0

-4.9 t²+19.6t=0

4.9t(-t+4)=0

either t=0 or t=4

so domain is 0≤t≤4

for range

h(t)=-4.9t²+19.6t

=-4.9(t²-4t+4-4)

=-4.9(t-2)²+19.6

so range is 0≤h≤19.6

Domain = 0<t<4, make sure to use less than or equal to signs not just less than signs.

Range = 0<h<19.6, again, use less than or equal to signs.

Answer:

I believe the interquarrile range is 5

Answer:

[tex]B(a)=\frac{a}{5} -7[/tex]

Step-by-step explanation:

The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.

y = height [tex]*[/tex] ( ( unknown base value ( b ) + 7 ) / 2 ),

y = 10 [tex]*[/tex] ( ( b + 7 ) / 2 )

Now switch the positions of y and b -

b = 10 [tex]*[/tex] ( ( y + 7 ) / 2 ) or [tex]b=\frac{\left(y+7\right)\cdot \:10}{2}[/tex] - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,

[tex]y+7=\frac{a}{5}[/tex],

[tex]y^{-1}=\frac{a}{5}-7 = B(a)[/tex]

Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7

Answer:

b = 4

Step-by-step explanation:

3 - b = 6 - 7

3 - b = -1

-b = -1 -3

-b = -4

b = 4

Answer:

complementary because 2 angles that add up to 90º is a complementary angle and x=9 :)

Step-by-step explanation:

90=46+5x-1

45=5x

x=9

Answer:

x = 9 Complementary

Step-by-step explanation:

The angles are compplementary cause the angle add up to 90°

Well to find x we need to make the following equation,

46 + (5x - 1) = 90

We need to simplify and combine like terms,

46 - 1 = 45

45 + 5x = 90

-45 to both sides

5x = 45

Divide 5 by both sides

x = 9

Thus,

x is 9.

Hope this helps :)