Determine all pairs of real numbers a and b so that the following function, f(x),
is differentiable at all real values, x.
f(x) =
x- x^2, if x ≤ 1
x^2 - 5x + 4/ square root ax, if 1 sin(x-4)/x+b, if x > 4

1.Using the Chain Rule, show that the following statements are always true:
(a) If f(x) is an odd function then f'(x) is an even function.
(b) If f(x) is an even function then f’(x) is an odd function.

Answer:

Step-by-step explanation:

first you sit on the tolit then think and you'll get your anwser

The expression  x2 − 2x − 2 can be transformed into the form (x − 1)2 +-3.

Completing the square is a technique used to convert a quadratic expression of the form ax^2 + bx + c into the form a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex of the quadratic function.

To complete the square, we need to add and subtract the square of half of the coefficient of x from the expression.

Starting with x2 − 2x − 2:

x2 − 2x − 2 = x2 - 2x + (-2)

We take half of the coefficient of x, which is -1, and square it to get 1.

x2 - 2x + 1 - 1 - 2 = (x - 1)2 - 3

Therefore, the expression x2 − 2x − 2 can be transformed into the form (x − 1)2 − 3, which is an option (B).

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Answer:

a) (720 - 12xp) p

b) (960 - 17xp) p

Step-by-step explanation:

240 pence = 1 pound

Eliot's change

= 240x3 - (x  ×  12p)

= 720 - (x  ×  12p)

= 720 - 12xp

Maya's change

= 240 x 4 - ( x × 17p)

= 960 - ( x × 17p )

= 960 - 17xp

Answer:

Step-by-step explanation:

A model that is shaded to represent a fraction that is equivalent to 9/12 is: A. model A.

In Mathematics, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In Mathematics, a fraction is typically composed of two (2) main parts and these include the following:

In order to determine a model that is correctly and appropriately shaded in order to represent a fraction that is equivalent to 9/12, we would have to simplify the fraction as follows;

Fraction = 9/12

By dividing by 3, we have:

Fraction = 3/4

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The measure of ∠U to the nearest degree using Cosine rule is 154⁰.

The Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The law of cosines states that:

c² = a² + b² - 2ab cos(C)

where a, b, and c are the lengths of the sides of the triangle, and C is the angle opposite to the side c.

According to our figure,

UW²=UV²+VW²-2(UV).(VW).Cos V

UW²=1²+2.8²-2(1)(2.8).Cos 17⁰

UW²=3.49

Taking square root on both sides, we get

UW=√3.49

UW=1.87

Now,

Cos U=(UW²+UV²-VW²)/2(UV)(UW)

Cos U=(1.87²+1²-2.8²)/2·(1)·(1.87)

Cos U=-3.34/3.74

Cos U=-0.89

Taking inverse, we get

U=Cos⁻¹(-0.89)

U≈152.37

Rounding to the nearest value in option, we get U=154⁰.

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Step-by-step explanation:

I hope it's help full for you

answer

.0056

explanation

1000 has 3 zeroes so

decimal has to

3 spaces to the left if

dividing

5.6 ÷ 1000 = .0056

Answer:

Let's use "x" to represent the number of animals in the shelter.

The fixed weekly expenses of the animal shelter are $750, and each animal costs an additional $6 per week. Therefore, the total weekly expenses of the animal shelter would be:

Total Weekly Expenses = Fixed Weekly Expenses + (Cost Per Animal * Number of Animals)

Total Weekly Expenses = 750 + 6x

We know that during the winter month, the weekly expenses are at most $900. So we can write the following inequality to represent this situation:

Total Weekly Expenses ≤ 900

Substituting the expression for the total weekly expenses, we get:

750 + 6x ≤ 900

Simplifying this inequality, we get:

6x ≤ 150

Dividing both sides by 6, we get:

x ≤ 25

Therefore, the inequality that represents the number of animals in the shelter for expenses to be at most $900 a week is:

x ≤ 25

This means that the shelter can have at most 25 animals during the winter month for the expenses to be within the limit of $900 a week.

A. The experimental probability of a randomly selected worker walking to work is approximately 0.144. B. We can predict that about 374 workers walk to work out of the 2600 workers at the company.

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

a. The experimental probability of a randomly selected worker walking to work can be calculated as:

Experimental probability = Number of workers who walk to work / Total number of workers surveyed

Experimental probability = 23/160

Experimental probability ≈ 0.144

Therefore, the experimental probability that a randomly selected worker at that company walks to work is approximately 0.144.

b. To predict how many of the 2600 workers at the company walk to work, we can use the experimental probability found in part (a) and multiply it by the total number of workers:

Number of workers who walk to work = Experimental probability x Total number of workers

Number of workers who walk to work = 0.144 x 2600

Number of workers who walk to work ≈ 374.4

Therefore, we can predict that about 374 workers walk to work out of the 2600 workers at the company.

Therefore,a. The experimental probability of a randomly selected worker walking to work is approximately 0.144.b. We can predict that about 374 workers walk to work out of the 2600 workers at the company.

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Answer:

8g + 11h + 14f

Step-by-step explanation:

To find the perimeter just add the value of all the sides

P =9f + g + 5f + 9h + 2h + 7g

Combine like terms

P = 8g + 11h + 14f

The value of x is 7.3

The six trigonometric functions of an angle in a right-angled triangle are related by a set of fundamental identities in trigonometry known as the Circle identities.

Given below figure; diameter AC = 33.4 and length AM = 13.8

So, radius OA = 33.4/2 = 16.7

Here the right angle triangle ΔAMO;

So, OA² = AM² + OM²

or, , OM² = OA² - AM²

By putting all values and find OM,

OM² = (16.7)² - (13.8)²

OM² = 278.89 - 190.44

OM = √88.45

OM = 9.40

here, ON = OA = 16.7   (both are radius of circle)

ON = OM + x    

x = ON - OM     (Put the values here and find x value)

x = 16.7 - 9.40 = 7.3

Therefore, the value of x is 7.3

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Answer:

Step-by-step explanation:

The correct definition of volume is: "the amount of space a 3-dimensional object takes up."

so the answer is d

Brianna left a tip οf 19% οn the entire bill, which includes the tax. Therefοre, the tοtal amοunt Brianna paid is 1.2495(xx), so the expressiοn in terms οf xx that represents the tοtal amοunt Brianna paid is 1.2495(xx).

Equivalent expressiοns are expressiοns that perfοrm the same functiοn despite their appearance. If twο algebraic expressiοns are equivalent, they have the same value when we use the same variable value.

The tax οn the bill is 5% οf xx, which can be expressed as 0.05(xx). Therefοre, the tοtal bill including tax is:

xx + 0.05(xx) = 1.05(xx)

Brianna left a tip οf 19% οn the entire bill, which includes the tax. Therefοre, the tοtal amοunt Brianna paid is:

1.05(xx) + 0.19(1.05(xx)) = 1.05(xx) + 0.1995(xx)

Simplifying the expressiοn, we get:

Tοtal amοunt Brianna paid = 1.2495(xx)

Therefοre, the expressiοn in terms οf xx that represents the tοtal amοunt Brianna paid is 1.2495(xx).

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The total of the numbers 2, 5, 8, 11, and 14 is thus 40 as the series contains 5 terms.

An arithmetic progression (AP) is a series of numbers where each term is created by multiplying the previous term by a fixed constant (also known as the common difference). In other words, an AP is a set of numbers whose any two consecutive terms' differences are always the same.  For instance, the mathematical progression 2, 5, 8, 11, and 14 has a common difference of 3. An algebraic progression generally takes the following form: "a," "a+d," "a+2," "a+3,"... where a denotes the sequence's first word, d is its common difference, and the ellipsis (...) denotes that the series is infinite. Mathematical progressions are crucial and are utilised in many disciplines, such as algebra, calculus, and number theory.

given

We can use the arithmetic sum formula to determine the sum of the mathematical series with initial term a=2 and common difference d=3:

Sn = (n-1)d/2(2a + n-1)a

where Sn is the sequence's initial n phrases added together.

The value of the nth term can be determined by substituting n into the arithmetic calculation, a = 3n - 1:

We can use the following words to get the value of n for the final term in the sequence:

a n = 14 = 3n - 1

3n = 15

n = 5

Hence, the series contains 5 terms. Now we can calculate the sum using the arithmetic sum formula:

S5 = 5/2(2(2) + (5-1)3)

S5 = 5/2(4 + 12)

S5 = 5/2(16) (16)

S5 = 40

The total of the numbers 2, 5, 8, 11, and 14 is thus 40 as the series contains 5 terms.

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The height of the telephone pole is approximately 12.5 ft.

And the ladder will reach approximately 6 ft up the building.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It focuses on the study of the functions of angles, such as sine, cosine, tangent, cosecant, secant, and cotangent, and how they are used to solve problems involving triangles.

Part 9:-To solve the problem, we can use trigonometry. Let's draw a right triangle where the height of the pole is the opposite side, the distance from the top of the pole to the attachment point of the guy wire is the adjacent side, and the guy wire itself is the hypotenuse. We know the length of the hypotenuse is 12 ft, and the length of the adjacent side is 9.5 ft. The angle between the hypotenuse and the ground is given as 51°.

Using the trigonometric function tangent, we can calculate the height of the pole as follows:

tan(51°) = height of pole / 9.5 ft

height of pole = tan(51°) × 9.5 ft

height of pole ≈ 12.5 ft

Therefore, the height of the telephone pole is approximately 12.5 ft.

Part 10:-Again, we can use trigonometry to solve the problem. Let's draw a right triangle where the height of the building is the opposite side, the distance from the base of the building to the ladder is the adjacent side, and the ladder itself is the hypotenuse. We know the length of the hypotenuse is 8 ft, and the angle between the hypotenuse and the ground is given as 46°.

Using the trigonometric function sine, we can calculate the height of the building as follows:

sin(46°) = height of building / 8 ft

height of building = sin(46°) × 8 ft

height of building ≈ 6 ft

Therefore, the ladder will reach approximately 6 ft up the building. Rounded to the nearest whole number, the answer is 6 ft.

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The prοbability that a persοn chοsen at randοm has nο credit cards is:

P(nο credit cards) = 8/20 = 0.4 οr 40%

Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, with 0 representing an impοssible event and 1 representing a certain event. The prοbability οf an event is calculated by dividing the number οf ways the event can οccur by the tοtal number οf pοssible οutcοmes.

Since we knοw the tοtal number οf credit cards and the number οf peοple whο οwn them, we can find the prοbability that a persοn chοsen at randοm has nο credit cards by dividing the number οf peοple with nο credit cards by the tοtal number οf peοple in the grοup:

Number οf peοple with nο credit cards: 8

Tοtal number οf peοple: 20

Therefοre, the prοbability that a persοn chοsen at randοm has nο credit cards is:

P(nο credit cards) = 8/20 = 0.4 οr 40%

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Complete Question:

Answer:

  31.25 weeks

Step-by-step explanation:

You want to know how many weeks it took to construct 93.75 km of road at the rate of 3 km/week.

The relation between time, rate, and quantity is ...

  time = quantity/rate

  time = (93.75 km)/(3 km/wk) = (93.75/3) wk = 31.25 wk

It took the crew 31.25 weeks to build 93.75 km of road.

The equation that relates C to R, given the number of cars that Latoya has to rent and the number of cars left after renting, is C = 23 - R.

The number of cars left after 8 cars have been rented is 15 cars.

To write an equation relating the number of cars left (C) to the number of cars rented (R), we can use the total number of cars available (23) and subtract the number of cars rented:

C = 23 - R

Now, to find the number of cars left after renting 8 of them, we can substitute R = 8 into the equation:

C = 23 - 8

C = 15

So, Latoya would have 15 cars left after renting 8 of them.

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Statistical inference is the process of using data from a sample to make generalizations or draw conclusions about a larger population.

Based on the sample data, assumptions are made about the fundamental traits of the population, and the uncertainty in those assumptions is quantified using statistical techniques.

Because it enables us to forecast the future and make judgements based on incomplete data, statistical inference is crucial. For instance, with a sample of data, it enables us to confidently estimate population parameters such as averages and proportions. This can be helpful in a variety of contexts, including marketing analysis, surveys of public opinion, clinical trials, and manufacturing quality control.

By comparing the results of several groups or treatments, statistical inference also enables us to assess the efficacy of interventions or treatments.This can inform decisions about which treatments are most effective or which interventions should be implemented.

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The balance of the loan after 2 monthly payments is $246,778 (rounded to the nearest dollar).

Compounding refers to the process of earning interest on both the principal amount and the interest earned on that principal over time. In other words, it is the process of reinvesting earnings so that those earnings can also earn money, creating a compounding effect.

Compound interest is calculated on the initial principal amount and also on the accumulated interest of previous periods. This means that the interest earned in each period is added to the principal, and the interest for the next period is calculated on the new total.

To find the balance of the loan after 2 monthly payments, we first need to calculate the total number of payments over the life of the loan. Since the loan is paid over 25 years with monthly payments, the total number of payments is:

25 years x 12 months/year = 300 months

Next, we can use the formula for the present value of an ordinary annuity to calculate the remaining balance after 2 monthly payments. The formula is:

PV = PMT x ((1 - (1 + r)⁻ⁿ) / r)

where PV is the present value or remaining balance, PMT is the monthly payment, r is the monthly interest rate, and n is the total number of payments.

The monthly interest rate is the annual interest rate divided by 12, so in this case, it is:

6% / 12 = 0.005

Plugging in the values, we get:

PV = $1,610.75 x ((1 - (1 + 0.005)⁻³⁰⁰) / 0.005)

PV = $240,902.43

This is the remaining balance after 2 monthly payments. To find the balance after the second monthly payment, we need to subtract two monthly payments from the original loan amount:

$250,000 - ($1,610.75 x 2) = $246,778.50

Therefore, the balance of the loan after 2 monthly payments is $246,778 (rounded to the nearest dollar).

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The value of function f(x) will be 2,-1/2,-1,5/2,4 when x is equal to 0,1,2,-1,-2 respectively.

The given function is f(x) = (-3/2)x + 2

We want to find the value of f(x) for all values of x, we simply substitute different values of x in the given function and evaluate it. For example:

If x = 0, then [tex]$f(0)=-{\frac{3}{2}}\times(0)+2=2$[/tex]

If x = 1, then  [tex]$f(1)=-{\frac{3}{2}}\times(1)+2=-{\frac{1}{2}}$[/tex]

If x = 2, then [tex]$f(2)={\frac{-3}{2}}\times(2)+2=-1$[/tex]

If x = -1, then [tex]$f(-1)=-{\frac{3}{2}}\times(-1)+2={\frac{5}{2}}$[/tex]

If x = -2, then [tex]$f(-2)=-{\frac{3}{2}}\times(-2)+2=4$[/tex]

So, the value of f(x) for all values of x is given by f(x) = (-3/2)x + 2

Similarly, we can find the value of f(x) for any value of x.

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The value of function f(x) will be 2,[tex]\frac{1}{2}[/tex],-1,[tex]\frac{7}{2}[/tex],5 when x is 0,1,2,-1,-2 respectively.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function of s domain and co domain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

In mathematics ,The list of numbers used to replace the variable is defined by the table of values. The   value of function at a solution is determined by the optimization problem of value function, which only depends on the problem's parameters.

The given function is f(x) =[tex]\frac{-3}{2} x[/tex] + 2

We find the value of f(x) ∀ x,

we substitute different values of x in the given function and evaluate it. For example:

If x = 0, then

f(x) =[tex]\frac{-3}{2} *0+2[/tex] ⇒f(x)=2

If x = 1, then  

f(x)

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

If x = 2, then f(x)=

[tex]=(\frac{-3}{2} *2)+2\\=\frac{-6}{2} +2\\=\frac{-6+4}{2}\\=\frac{-2}{2}\\=-1[/tex]

If x = -1, then

[tex]f(x)=(\frac{-3}{2} *(-1))+2\\=\frac{3}{2} +2\\=\frac{3+4}{2}\\=\frac{7}{2}\\[/tex]

If x = -2, then

[tex]f(x)=(\frac{-3}{2} *(-2))+2\\=\frac{6}{2} +2\\=\frac{6+4}{2}\\=\frac{10}{2}\\=5[/tex]

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a. Yes, she will make a profit of around $300.

b. It will take 4 years to earn back her initial investment.

According to the given data, there is a 20% chance that the new business will lose $10,000, a 40% chance it will break even, a 30% chance it will make $5,000 in profits, and a 10% chance it will make $8,000 in profits.

By calculating the expected value, we get an estimate of $300.

To find the expected value :

0.2 × (-10,000) + 0.4 × (0) + 0.3 × 5,000 + 0.1 × 8,000 = $300

a. Yes, Claire should invest in the company. she will make a profit of around  $300 in a year.

b. If Claire's expected value will be $300 and her initial investment $1200.

1200 ÷ 300 = 4 years

It will take around 4 years to earn back her initial investment.

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the probability of picking 3 red marbles if each marble is NOT returned to the bag before the next marble is picked is14/285.

Probability is a measure of the likelihood or chance that a particular event will occur, expressed as a number between 0 and 1. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain.

After the first red marble is drawn, there will be 19 marbles left in the bag, of which 7 are red.

So, the probability of picking a red marble on the second draw, given that the first marble was red and not returned to the bag, is 7/19.

Similarly, after the second red marble is drawn, there will be 18 marbles left in the bag, of which 6 are red.

So, the probability of picking a red marble on the third draw, given that the first two marbles were red and not returned to the bag, is 6/18 or 1/3.

Therefore, the probability of picking 3 red marbles in a row is:

(8/20) x (7/19) x (6/18) = 14/285

So, the answer is 14/285.

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40+6%+15%

=$ 42.55

I hope this helps!

The table of value of the function and it's graph are attached below

Here's the table of values for the function m(x) = 0.5x^2 with x ranging from -5 to 5

All we need to do is simply substitute the corresponding value of x into the function to get the value of y.

m(x) = 0.5x^2

m(-5) = 0.5(-5)^2

m(-5) = 12.5

Doing this for all other values, we will have our table below

x m(x)

-5 12.5

-4 8.0

-3 4.5

-2 2.0

-1 0.5

0 0.0

1 0.5

2 2.0

3 4.5

4 8.0

5 12.5

You can use this table to plot the function using a graphing calculator.

Kindly find the attached graph below;

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Answer:

I would say that it would be 1/3 because there are 3 parts

Answer:

3/7

Step-by-step explanation:

There are 4 small squares inside the figure.

The partial squares are all half squares, so each two triangles have the same are as 1 small square. There are 6 small triangles which add to 3 squares.

4 + 3 = 7

Total area = 7 squares

Shaded area = 2 squares + 2 half squares = 3 squares

Fraction of shaded area = 3/7

Answer:

t > 28.

Step-by-step explanation:

First, write it and collect like terms:

t / 4 > 7

t > 7 x 4

t > 28.

The terminal point of the unit circle of angle 270° is (0, -1). The correct answer is (C).

Unit Circle is a circle with a radius of one unit. In trigonometry, it is commonly used as a reference circle to understand the values of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for different angles.

From the unit circle question given above,

angle 0 = 360° represents the point (1,0) on the x-axis,

angle 90° represents the point (0,1) on the y-axis.

angle 180° represents the point (-1,0) on the negative x-axis,

angle 270° represents the point (0,-1) on the negative y-axis.

Therefore, if 0 = 270° in a unit circle, the terminal point would be (0,-1), which is option C.

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