Use Theorem 2 to calculate g'(x) where g is the inverse of f. f(x) = Sqrt(3 –x) Let g be the inverse of f(x) = x^3 + 2x + 3. Calculate g(7) (without finding a formula for g(x)], and then calculate g’(7).

what are the statements?

Answer:

x is smaller than 10in so x<5

Step-by-step explanation:

To calculate the UIF (Unemployment Insurance Fund) deduction from Mrs. Mdluli's salary, we need to know her gross salary and the current UIF contribution rate.

The current UIF contribution rate is 1% of the employee's gross salary, subject to a maximum amount of R148.72 per month. This means that if an employee's gross salary is above a certain threshold, the maximum UIF deduction of R148.72 will be applied.

Once we have Mrs. Mdluli's gross salary, we can calculate her UIF deduction using the following formula:

UIF deduction = Gross salary x UIF contribution rate

If Mrs. Mdluli's gross salary is above the threshold amount, the UIF deduction will still be capped at R148.72 per month.

Therefore, to calculate the missing value of A that will reflect on Mrs. Mdluli's salary slip, we need to know her gross salary and the current UIF contribution rate. Once we have these values, we can use the above formula to calculate the UIF deduction that will be reflected on her salary slip.

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Answer:

x>1

Step-by-step explanation:

Make a line put number like

__________|____________________

-4 -3  -2  -1  0 1  2  3  4  5  6  7  8  9  10

The answer for the missing piece is to 'find' the variable.

The first step that we need to take before solving is to understand what the question is asking us to do and what is given to us to do that.  Looking at this problem, we are given the goal of this problem which is to solve for h and we are given an expression to do so.

The next step that we need to take is to distribute the -2 to the contents inside of the parenthesis.

Distribute

After we have distributed the -2 to the contents inside of the parenthesis we can move onto the next step to isolate h which is to subtract 12 from both sides which would just leave us with -2h.

Subtract 12 from both sides

The next step that we will take to finish the problem is to divide both sides by -2 which will isolate h.  Then we will simplify the expression and that will give us our final answer.

Divide both sides by -2

Simplify the expression

We have now completed solving for h for the expression that was provided in the problem statement and we were able to determine that h is equal to 10.

The amount he opened the investment account with, his principal = $8600

This principal = 100% of his investment

If after a year the amount in his account increased by 24.5%, the total percentage now = 100 + 24.5 = 124.5%

By ratio, we can find the increase thus

His increase = 10707 - 8600 = $2107

At the end of last year, he had $10707 in his account

Answer:

y=10/7x-1/7

Step-by-step explanation:

m=(-3-7)/(-2-5)

m=-10/-7

m=10/7

y-y1=m(x-x1)

y-7=10/7(x-5)

y=10/7x-50/7+7

y=10/7x-50/7+49/7

y=10/7x-1/7

Answer:

1/6

Step-by-step explanation:

There are six sides on the die, and there is only "1" side of the die. Take the total amount of sides, 6, and make that the denominator. Then take one "1" side and make that the numerator, therefore 1/6.

Answer:

Step-by-step explanation:

1 out of six because their are six possible sides to roll on and only one side has a one

If a train leaves a station heading east. after traveling east for 33 miles, the train leaves 56 miles south. The distance of the train from the station is C. 65.

Using Pythagoreans theorem formula to find the distance

d² =  a² + b²

Where:

d = distance =?

a= east for 33 miles

b = 56 miles south

Let plug in the formula

d = √33² + 56²

d = √ 1089 + 3136

d = √4225

d = 65 miles

Therefore the correct option is C.

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Let's first get to know what is given in the question. A tank contains 280 gallons of water and 20 oz of salt. Water containing a salt concentration of 19(1/16 sint) oz/gal numbers into the tank at a rate of 10 gal/min, and the mixture in the tank flows out at the same rate.

The long-time behavior of the solution is an oscillation about a certain constant level.The equation to find out the concentration of salt in the tank at any time 't' is given by dS/dt = (19/16) (10 - V(t))where S(t) is the amount of salt in the tank at time t, V(t) is the volume of liquid in the tank at time t.The long-term behavior of the solution is an oscillation about a certain constant level, which can be found out using the formula given below:∆S/∆V = 19/16=> ∆S = (19/16) ∆VWe know, Rate of inflow = rate of outflowSo, dV/dt = 10 - V(t).

By solving this differential equation, we get V(t) = 280 - 280e^(-t/10)Now we can find out the level of salt concentration using the below formula∆S = (19/16) ∆V= (19/16) * (280 - V(t))= (19/16) * (280 - 280e^(-t/10))= 266.5625 - 17.5e^(-t/10)Hence, the long-time behavior of the solution is an oscillation about a certain constant level and the level is 266.5625 oz.

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The probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 4% rate of defects is 0.9660

This problem can be solved by permutations and combinations. This can also be solved using binomial probability experiment.

Let, then we could reasonably assume that follows a binomial distribution.

Given P = 0.01 and n = 29

P(x) = nCx.px.(1-p)^(n-x)

nCx = n! [x!-(n-x)!]

P = P(X<=1).

X<=1, if X = 0 and X = 1,

P(0) + P(1)

P(0) = 1.(0.01)^(0).(0.99)^(29) = 0.74717

P(1) = 29C1.(0.01)^(1).(1-0.01)^(29-1)

P(1) = 0.21887

P = P(0) + P(1)

P = 0.74717+0.21887 = 0.9660

So, therefore the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 4% rate of defects is 0.9660

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Answer:

\( 48 - 20x = 9 \)

Step-by-step explanation:

\( 2 - \dfrac{5}{6}x = \dfrac{3}{8} \)

Multiply both sides by the LCD which is 24.

\( 24(2 - \dfrac{5}{6}x) = 24(\dfrac{3}{8}) \)

\( 48 - 20x = 9 \)

Answer:

im dumb im sorry but u can look it up

Step-by-step explanation:

Answer:

pH = 8

Step-by-step explanation:

Formular is given as;

pH = -log[H+]

A)baking soda:

[H+] = 10^-8

Upon inserting it into the formular;

pH = -log (10^-8)

pH = - ( -8)

pH = 8

Answer:

Divide 64 by 16 and we get that it has to have 4 sides which has 16m it means it has to be a square

Answer:

Your answer would be 17 because 171 divided by 9 is 19, so 323 divided by 19 would be 17.

Answer:

Step-by-step explanation:

Tom made $171 for 9 hours of work. At the same rate, how many hours would he have to work to make 323 ?

171 : 9 = 323 : x

x = 9 * 323 : 171

x = 2907 : 171

x = 17

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

check

171 : 9 = 323 : 17

19 = 19

Distance = 75 units between t=0 and t=5. To find how far the particle travels between t=0 and t=5, we need to calculate the total distance traveled by the particle.

The distance traveled is equal to the total displacement, which can be found by taking the absolute value of the difference between the initial and final positions.

The initial position of the particle at t=0 is:

S(0) = 0^3 - 3(0)^2 - 2 = -2

The final position of the particle at t=5 is:

S(5) = 5^3 - 3(5)^2 - 2 = 73

Therefore, the total displacement of the particle is:

ΔS = |73 - (-2)| = 75

So the particle travels a total distance of 75 units between t=0 and t=5.

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Child must be higher than 36 which means any number between or above 36 isn't  allowed . graph that.

1 ball and 3 board games can be chosen by Amanda in option E. 60 ways.

Here it is given that Amanda needs 1 ball and 3 board games.

The toy store only has 3 kinds of balls and 6 types of board games. Hence we will use combinations to determine the no. of ways she can choose the items

ⁿCₓ = n! / (n - r)! X r!

The ball can be chosen in

³C₁ ways

= 3! / 2! X 1!

= 6/2

= 3 ways

The board game can be chosen in  ⁶C₃ ways

= 6! / 3! X 3!

= 720 / 36

= 20 ways

Hence the total number of ways the items can be chosen is

3 X 20 ways

= E. 60 ways.

Complete Question

Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?

A. 9

B. 12

C. 14

D. 15

E. 60

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The value of 3/12 of 100 is 25 .

In the question ,

a fraction 3/12 is given ,

we have to find the value of 3/12 of 100 .

to find the value , we first convert both the numbers into fraction

So 100 in fraction form can be written as 100/1

So the value 3/12 of 100 means

= \(\frac{3}{12} *\frac{100}{1}\)

multiplying the numerator with numerator

and multiplying denominator with denominator .

we get = 300/12

on further  simplification ,

we have ,

= 75/3

= 25

So , 3/12 of 100 = 25

Therefore , The value of 3/12 of 100 is 25 .

The given question is incomplete , the complete question is

What is the value of 3/12 of 100 ?

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Answer:

22-6

Step-by-step explanation:

there isnt a variable so the answer is 16

Answer:

I am pretty sure you would just write 22-6

Step-by-step explanation:

Answer:

\(base = 18 m\\\\altura= 12 m\)

Step-by-step explanation:

Disclaimer: My Spanish is not great so I used a translation tool. Please let me know if it is understandable. I think the equations are understandable.

Area = 216 m²

Sea base = b m y altura = h m

\(Area = bh\)

So

\(bh = 216\)

base = 6 m mayor que la altura
\(b = h + 6\)

Así que sustituyendo b en la fórmula bh = 216 da
\(b h = 216\)

⇒   \((h + 6)h = 216\)

⇒    \(h^2 + 6h = 216\)

⇒   \(h^2 + 6h - 216 = 0\)  [1]

Esta es una ecuación cuadrática que se puede resolver usando fórmulas cuadráticas o factorizando. Aquí se nos pide que utilicemos la fórmula general

Para una ecuación cuadrática general de la forma
\(ax^2 + bx + c = 0\)

hay dos soluciones dadas por la fórmula cuadrática

\(x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\)

En este problema, comparando  \(ax^2 + bx + c = 0\)  a \(h^2 + 6h - 216 = 0\) :

\(a = 1\\b = 6\\c = -216\\\)

Reemplaza estos valores en las fórmulas cuadráticas y resuelve para h

\(h = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\)

\(h = \dfrac{ -6 \pm \sqrt{6^2 - 4(1)(-216)}}{ 2(1) }\)

\(h = \dfrac{ -6 \pm \sqrt{36 - -864}}{ 2 }\)

\(h = \dfrac{ -6 \pm \sqrt{900}}{ 2 }\)
\(h = \dfrac{ -6 \pm 30\, }{ 2 }\)

\(h = \dfrac{ 24 }{ 2 } \; \; \; h = -\dfrac{ 36 }{ 2 }\)

que se convierte

\(h = 12\)

\(h = -18\)

Como no podemos tener altura negativa, la solución es
\(h = 12\) m

Desde b = h + 6,
\(b = 12 + 6 = 18 m\)

The actual cost to see the game is $150, as that is the amount you paid for the ticket. The cost in this scenario can be considered an opportunity cost. By choosing to attend the game instead of selling the ticket for $400, you forgo the opportunity to earn that additional $400.

In this scenario, the cost of attending the game refers to the actual amount of money you spent on the ticket, which is $150. This is the out-of-pocket expense that directly affects your financial resources.

On the other hand, the opportunity cost is the potential benefit or value that you give up by choosing one option over another. In this case, if you had sold the ticket for $400, you would have received a higher amount of money, which represents the opportunity cost of attending the game. By deciding to go to the game, you forego the opportunity to earn that additional $400.

Opportunity cost is a concept in economics that emphasizes the value of the next best alternative forgone when making a decision. It helps assess the trade-offs involved in different choices and helps in evaluating the true cost of a decision beyond the immediate financial expenses.

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Answer:

B

Step-by-step explanation:

Parallel lines have equal slopes, thus

slope of red line = slope of green line = 5 → B

The density of a 240-g rock that displaces 89.0 cm³ of water can be calculated by dividing its mass by its volume. The density of the rock is approximately 2.70 g/cm³.

Density is defined as the mass of an object divided by its volume. In this case, the mass of the rock is given as 240 g and the volume of water displaced is given as 89.0 cm³. To find the density, we divide the mass by the volume:

Density = Mass / Volume

Density = 240 g / 89.0 cm³

Calculating this expression gives us the density of the rock as approximately 2.70 g/cm³. Therefore, the density of the 240-g rock that displaces 89.0 cm³ of water is approximately 2.70 g/cm³.


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value of function f(x) at coordinate x=1 is -3

In mathematics, a function is a relation between two sets, called the domain and the range, that associates each element of the domain with a unique element of the range.  

A mathematical function can be represented in various ways, including algebraic expressions, graphs, tables, or sets of ordered pairs. The most common notation for a function is f(x), where x is an element of the domain, and f(x) is the corresponding element of the range.

To find: f(1)

limit f(x) tends to 1⁺ is -3

limit f(x) tends to 1⁻ is -3

Hence, value of function f(x) at x=1 is -3.

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the expression is "2 + 8." To find the quotient of 12 and 6, divide 12 by 6. The result is 2.

Step 1: Add 8 to the quotient.

Now, add 8 to the quotient found. The expression is "quotient + 8."

Step 2: Write the final expression.

The final expression that represents "8 more than quotient of 12 and 6" is "quotient + 8."

So, the expression is "2 + 8."

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