If
f
(
x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
x
)
f(x) is divided by
x
−
1
x−1?

Answer:

Refer to step-by-step

Step-by-step explanation:

Prove the following, [tex]\lim_{x \to \ 2} 2^{x}=4[/tex], [tex]\lim_{z \to \ -1} 3^{x}=\frac{1}{3}[/tex], and [tex]\lim_{x \to \ 1} e^{x-1} = 1[/tex].

For part f:

Plug in the value of the limit, 2,

[tex](2)^{2} =4[/tex]

Thus we proved the limit.

For part g:

Plug in the value of the limit, -1,

[tex]3^{(-1)}[/tex]=>[tex]3^{-1}[/tex]=>[tex]\frac{1}{3^{1} }=\frac{1}{3}[/tex]

Thus we proved the limit.

For part h:

Plug in the value of the limit, 1,

[tex]e^{(1)-1}[/tex]=>[tex]e^{1-1}[/tex]=>[tex]e^{0}=1[/tex]

Thus we proved the limit.

Answer:

y=2x+2

Step-by-step explanation:

Just look at the bottom dot which is 0,2 and y=2x+2 is the only one that works:

2=(2×0)+2

2=2

but the other is:

2=(3×0)

2=3

which isn't true,

therefore it must be the first one.

Answer:

B

Step-by-step explanation:

The volume of a rectangular prism is found by multiplying its length, width, and height.

[tex]\large\tt\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:V=l\times w\times h[/tex]

Therefore, the volume of a rectangular prism is 216m³

Another formula can be used if the area of the base (B) is given.

[tex]\large\tt\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:V=B\times h[/tex]

Therefore, the volume of a rectangular prism is 216m³

Answer:

3/10

Step-by-step explanation:

6/20

Reduce

3/10

On solving the provided question, we can say that - by formula of simple interest we have SI = [tex]2200 X 2 X 4/100 = > 17600/100 = > 176[/tex]

Multiplying the principal by the interest rate, time, and other factors yields simple interest. Simple return equals principle times interest times hours is the marketed formula. It is easiest to compute interest using this formula. A percentage of the principle balance is how interest is most commonly computed. For instance, he will only pay his portion of the 100% interest if he borrows $100 from a buddy and promises to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you lend money, you must charge interest. Most of the time, interest is expressed as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.

here,

principal, p = 2200

rate, r = 2%

time, t = 4 rs,

so SI = P X R X T/100

SI -

[tex]2200 X 2 X 4/100\\17600/100\\176[/tex]

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Answer:

4.3 minutes per mile

Step-by-step explanation:

26 minutes divided by 6 miles is 4.333, so the answer should be 4.3 minutes per mile. Hope this helped :)

There are six sides to a die and only one side has a two, so the probability of rolling a 2 is 1/6.

There are two sides to a coin and only one side has a head, so the probability of its coming up heads is 1/2.

The two events (rolling a die and flipping a coin) are independent, so the probability of both events occurring is (1/6)(1/2) = 1/12

The answer is All

Step-by-step explanation:

It has been proven that all quadratic equations can be solved with the quadratic formula.

Answer:

The square root means that IF you square the square root, you will get the original number. Thus, 16 squared = 256 and y^2 squared = (y^2)(y^2) = y^4

Step-by-step explanation:

Answer:

The first table is correct

Step-by-step explanation:

x=Yellow   Prob

0               .5625

1                .375

2               .0625

The attached document shows a tree diagram with all 16 outcomes.  Each outcome has probability 1/16.

The numbers at the right show the numbe of yellows for each outcome.  There are 9 outcomes with 0 yellow (prob = 9/16).

There are 6 outcomes with 1 yellow (prob = 6/16)

There is 1 outcome with 2 yellow (prob = 1/16)

Sorry about the watermarks--distracting!

Based on the given set of values, we can note that the first table is correct

This refers to the calculations of the way an event is most likely to occur.

Hence, the table for  x=Yellow   Prob

0               .5625

1                .375

2               .0625

For each outcome, there is probability 1/16.

The numbers at the right show the number of yellows for each outcome. There are 9 outcomes with 0 yellow (prob = 9/16).

There are 6 outcomes with 1 yellow (prob = 6/16)

There is 1 outcome with 2 yellow (prob = 1/16)

Hence, because the calculated values are consistent with the values in the first table, then we can conclude that the first table is correct.

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Answer:

The square root is 1.90

Step-by-step explanation:

Given

[tex]x = \sqrt{3.6}[/tex]

Required

Find x

Express 3.6 as 36/10

So, we have:

[tex]x = \frac{\sqrt{36}}{\sqrt{10}}[/tex]

This gives

[tex]x = \frac{6}{\sqrt{10}}[/tex]

Rationalize

[tex]x = \frac{6}{\sqrt{10}}*\frac{\sqrt{10}}{\sqrt{10}}[/tex]

[tex]x = \frac{6\sqrt{10}}{10}[/tex]

Using a calculator

[tex]\sqrt{10} \approx 3.16[/tex]

So, we have:

[tex]x = \frac{6*3.16}{10}[/tex]

[tex]x = \frac{18.96}{10}[/tex]

[tex]x = 1.896[/tex]

Approximate

[tex]x = 1.90[/tex]

Answer:

I would say it's 126in

Step-by-step explanation:

sorry if I'm not right but I'm pretty sure :)

She need a interest rate of 5.56%

Your wealth increases more quickly due to compound interest. Due to the fact that you will receive returns on both the money you invest and returns at the conclusion of each compounding period, it causes a sum of money to increase more quickly than with simple interest. As a result, you won't need to save as much money to achieve your objectives.

We are aware that A = P(1+rt), where A represents the Final Investment Value, is the simple interest formula.

P denotes the principal amount to be invested, r the interest rate, and t the number of time periods.

The formula for this issue is t = 18 Years, p = £90,000.

A = £9000 *2 => £18000\sr = ?

Fill in the appropriate values in the formula above to find 18000 = 9000(1+18r).

18r = 2 - 1\sr = 1/18\sr = 0.0555555556

Extend 0.0556

Ratio conversion: r = 0.0556 * 100 = 5.56%

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She need a interest rate of 5.56% .Your wealth increases more quickly due to compound interest.

Formula for Monthly Compound Interest. 12 times a year are used to calculate interest that is compounded monthly.

Formula for Quarterly Compounding. Four times a year are used to calculate interest that is compounded quarterly.

Formula for Daily Compound Interest.

Formula for Annual Compound Interest.

We are aware that A = P(1+rt), where A represents the Final Investment Value, is the simple interest formula.

P denotes the principal amount to be invested, r the interest rate, and t the number of time periods.

The formula for this issue is t = 18 Years, p = £90,000.

A = £9000 *2 => £18000\sr =

Fill in the appropriate values in the formula above to find 18000 = 9000(1+18r).

18r = 2 - 1\sr = 1/18\sr

= 0.0555555556

Extend 0.0556

Ratio conversion: r = 0.0556 * 100 = 5.56%

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If the total length of the journey is 146 km and he maintain the same  speed, the longer time he will be using for driving  will be 65m.

The  total length of my journey is 146 km.

Then the remain of the journry to reach 146 km = 146- 48 = 98

Then the if the same speed is maintained the estimate of  longer time he will be using for driving  will be calculated as :

(32 * 98)/48

Then get the productor quotient = 196/3 = 65 minutes

Therefore, option E is correct.

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MISSING OPTIONS:

A. 32

B.40

C. 52

D. 60

E.65

Answer:

D. y = 3√x+3 +3

Step-by-step explanation:

The correct answer to your question is the fourth option, y = 3 square root x + 3 + 3.

Answer: D

Step-by-step explanation:

Answer:

The tree is 44 feet

Step-by-step explanation:

[tex]\frac{8}{6}[/tex] is equivalent to [tex]\frac{4}{3}[/tex] (divide the numerator and denominator by 2)

[tex]\frac{4}{3}[/tex] = [tex]\frac{x}{33}[/tex]

3 x 1  = 33, so 4 x 11 = 44

Answer:

15/17

Step-by-step explanation:

Sin=opposite/hypotenuse

SinD=BC/CD=15/17

Answer:

The other pairs are:

[tex](a)\ (2, \frac{5\pi}{6}) \to[/tex]  [tex](2, \frac{17\pi}{6})[/tex] and [tex](-2, \frac{23\pi}{6})[/tex]

[tex](b)\ (1, -\frac{2\pi}{3}) \to[/tex] [tex](1, \frac{4\pi}{3})[/tex] and [tex](-1, \frac{7\pi}{3})[/tex]

[tex](c)\ (-1, \frac{5\pi}{4}) \to[/tex] [tex](-1, \frac{3\pi}{4} )[/tex] and [tex](1, \frac{7\pi}{4})[/tex]

See attachment for plots

Step-by-step explanation:

Given

[tex](a)\ (2, \frac{5\pi}{6})[/tex]

[tex](b)\ (1, -\frac{2\pi}{3})[/tex]

[tex](c)\ (-1, \frac{5\pi}{4})[/tex]

Solving (a): Plot a, b and c

See attachment for plots

Solving (b): Find other pairs for [tex]r > 0[/tex] and [tex]r < 0[/tex]

The general rule is that:

The other points can be derived using

[tex](r, \theta) = (r, \theta + 2n\pi)[/tex]

and

[tex](r, \theta) = (-r, \theta + (2n + 1)\pi)[/tex]

Let [tex]n =1[/tex] ---- You can assume any value of n

So, we have:

[tex](r, \theta) = (r, \theta + 2n\pi)[/tex]

[tex](r, \theta) = (r, \theta + 2*1*\pi)[/tex]

[tex](r, \theta) = (r, \theta + 2\pi)[/tex]

[tex](r, \theta) = (-r, \theta + (2n + 1)\pi)[/tex]

[tex](r, \theta) = (-r, \theta + (2*1 + 1)\pi)[/tex]

[tex](r, \theta) = (-r, \theta + (2 + 1)\pi)[/tex]

[tex](r, \theta) = (-r, \theta + 3\pi)[/tex]

[tex](a)\ (2, \frac{5\pi}{6})[/tex]

[tex]r = 2\ \ \ \ \theta = \frac{5\pi}{6}[/tex]      

So, the pairs are:

[tex](r, \theta) = (r, \theta + 2\pi)[/tex]

[tex](2, \frac{5\pi}{6}) = (2, \frac{5\pi}{6} + 2\pi)[/tex]

Take LCM

[tex](2, \frac{5\pi}{6}) = (2, \frac{5\pi+12\pi}{6})[/tex]

[tex](2, \frac{5\pi}{6}) = (2, \frac{17\pi}{6})[/tex]

And

[tex](r, \theta) = (-r, \theta + 3\pi)[/tex]

[tex](2, \frac{5\pi}{6}) = (-2, \frac{5\pi}{6} + 3\pi)[/tex]

Take LCM

[tex](2, \frac{5\pi}{6}) = (-2, \frac{5\pi+18\pi}{6})[/tex]

[tex](2, \frac{5\pi}{6}) = (-2, \frac{23\pi}{6})[/tex]

The other pairs are:

[tex](2, \frac{17\pi}{6})[/tex] and [tex](-2, \frac{23\pi}{6})[/tex]

[tex](b)\ (1, -\frac{2\pi}{3})[/tex]

[tex]r = 1\ \ \ \theta = -\frac{2\pi}{3}[/tex]      

So, the pairs are:

[tex](r, \theta) = (r, \theta + 2\pi)[/tex]

[tex](1, -\frac{2\pi}{3}) = (1, -\frac{2\pi}{3} + 2\pi)[/tex]

Take LCM

[tex](1, -\frac{2\pi}{3}) = (1, \frac{-2\pi+6\pi}{3})[/tex]

[tex](1, -\frac{2\pi}{3}) = (1, \frac{4\pi}{3})[/tex]

And

[tex](r, \theta) = (-r, \theta + 3\pi)[/tex]

[tex](1, -\frac{2\pi}{3}) = (-1, -\frac{2\pi}{3} + 3\pi)[/tex]

Take LCM

[tex](1, -\frac{2\pi}{3}) = (-1, \frac{-2\pi+9\pi}{3})[/tex]

[tex](1, -\frac{2\pi}{3}) = (-1, \frac{7\pi}{3})[/tex]

The other pairs are:

[tex](1, \frac{4\pi}{3})[/tex] and [tex](-1, \frac{7\pi}{3})[/tex]

[tex](c)\ (-1, \frac{5\pi}{4})[/tex]

[tex]r = -1 \ \ \ \ \theta = \frac{-5\pi}{4}[/tex]

So, the pairs are

[tex](r, \theta) = (r, \theta + 2\pi)[/tex]

[tex](-1, \frac{-5\pi}{4}) = (-1, \frac{-5\pi}{4} + 2\pi)[/tex]

Take LCM

[tex](-1, \frac{-5\pi}{4}) = (-1, \frac{-5\pi+8\pi}{4} )[/tex]

[tex](-1, \frac{-5\pi}{4}) = (-1, \frac{3\pi}{4} )[/tex]

And

[tex](r, \theta) = (-r, \theta + 3\pi)[/tex]

[tex](-1, \frac{-5\pi}{4}) = (-(-1), \frac{-5\pi}{4}+ 3\pi)[/tex]

Take LCM

[tex](-1, \frac{-5\pi}{4}) = (1, \frac{-5\pi+12\pi}{4})[/tex]

[tex](-1, \frac{-5\pi}{4}) = (1, \frac{7\pi}{4})[/tex]

So, the other pairs are:

[tex](-1, \frac{3\pi}{4} )[/tex] and [tex](1, \frac{7\pi}{4})[/tex]

Answer:

72 .22 inches is the answer bro

Answer:

72.22 inches

Step-by-step explanation:

Formula for circumference given diameter is:

c = πd

If you use 3.14 for pi, you get 72.22 inches:

c = 3.14(23)

c = 72.22

Answer:

a. The time between customers entering a checkout lane at a retail store - Continuous

b. The weight of refuse on a truck arriving at a landfill - Discrete

c. The number of passengers in a passenger vehicle on a highway at rush hour - Continuous

d. The number of clerical errors on a medical chart - Continuous

e. The number of accident-free days in one month at a factory - Discrete

Step-by-step explanation:

A discrete variable is one whose value can be counted or it is a countable variable while continuous variable is not countable and hence it is measured.

a. The time between customers entering a checkout lane at a retail store - Continuous

b. The weight of refuse on a truck arriving at a landfill - Discrete

c. The number of passengers in a passenger vehicle on a highway at rush hour - Continuous

d. The number of clerical errors on a medical chart - Continuous

e. The number of accident-free days in one month at a factory - Discrete

Random variables map sample space elements to real numbers. The classification of these random variables is done as:

Random variables are rules relating the sample space's elements to real numbers.

Those random variables, who take only distinct values, are called discrete random variables.

Those random variables, who take any value from a given continuous interval of real numbers are called continuous variables.

For the given first and second cases, the time between customers entering a checkout lane, or the weight on a truck can be any value in an interval of real numbers. Its not assuming distinct values and it can be any value in a continuous real number interval. Thus, they are continuous random variable.

For the given cases, from case third to fifth, the number of errors, the number of clerical errors, and the number of days, all can only be integers and thus, they are distinct, non-continuous in any non-zero sized interval, thus, they are discrete random variables.

Thus,  the classification of these random variables is done as:

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Answer:

y=|x|+2

Step-by-step explanation:

Umm where’s the graph.

If the graph is up 2 units y=|x|+2

Answer:

Lower quartile is 2

Median is 5

Upper quartile is 7

Answer:

Lower quartile 2

median 6.5

upper quartile 7

Answer:

Rate of change= 1/3

Initial value = -4

Step-by-step explanation:

The rate of change is rise/run = 1/3.

the initial value is the y-intercept which is -4.

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-3}-\stackrel{y1}{(-6)}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-6)}}} \implies \cfrac{-3 +6}{3 +6} \implies \cfrac{ 3 }{ 9 } \implies \cfrac{1 }{ 3 }[/tex]

now as far as the "initial value", dunno what that means.

The start of the line? well, the line by definition goes to infinity both ways.

the y-intercept? well, just look at the graph, the graph intercepts the y-axis when x = 0 and y = -4, so at (0 , -4).

Therefore , the solution of the given problem of percentage comes out to be 4250 mg, or 4.25 g and the percentage increase is 50%.

A% is a number that can be expressed as a decimal or a fraction and indicates what proportion of 100 it is. Put 100 in the denominator and the percentage amount in the numerator to turn a percentage into a fraction.

Here,

This "Nutritional Facts" table indicates that 85 mg of potassium, or 2% of the daily recommended value, corresponds to the row "Potassium".

By using the unitary method, (85/2) mg of potassium will represent 1% of the daily required intake.

As a result, 4250 mg of potassium, or 100% of the daily allowance, will be required: (85/2 * 100).

The entire quantity of potassium that is advised for daily consumption is 4250 mg, or 4.25 g.

(New value) − (Initial value) / (Initial value) = percent change. * 100%.

Here,

Initial value: $1.50 (the 1995 fare).

New value equals $2.25 for the 2008 fare.

Therefore,

percentage variation

= [(2.25 - 1.50) / 1.50] .50] * 100%

= (0.75 / 1.50) * 100%

= 0.5 * 100%

= 50%.

Positive indications of the transition point to an increase in fare.

The percentage increase is therefore 50%.

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Answer:

[tex]p = 7[/tex]

Step-by-step explanation:

So the key is that a line has a measure of 180 degrees. Notice the square between the rays. That is a 90-degree angle. So let's add this up and see what's going on

[tex](5p + 2) + 90 + (7p + 4) = 180[/tex]

[tex]12p + 96 = 180[/tex]

[tex]12p = 84[/tex]

[tex]p = 7[/tex]

Answer:

p = 7

Step-by-step explanation:

From the diagram, we can see that all the angles given form a straight line, and therefore add up to 180°.

We can create an equation with what is given:

***The angle with the square marked is 90°.

5p° + 2° + 90° + 7p° + 4° = 180°

You can combine the like terms, getting:

12p° + 96° = 180°

Now, subtract 96° from both sides:

12p° = 84°

Now, divide by 12°, and get:

p = 7

The building in the drawing is 700 centimeters or 7 meters.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

Given 3 meters on real is equal to 7 centimeters on drawing

i.e. 3 meters=7 centimeters

or, 1 meter = 7/3 centimeters

We need to find reading for 300 meters so,

or, 300 meters=7/3*300 centimeters

                        =700 centimeters or 7  meters

Therefore the building in the drawing is 700 centimeters or 7 meters.

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