37. The profit P of a small business (in thousands
of dollars) since it was founded can be
by the function below, where tis
the years since 1990. Use the Remainder
Theorem to find the company's profit in 2017.
modeled
P(t) = 0.5tª − 3t³ +t² +25

The functions f and g are inverse functions because f(g(x)) = g(f(x)) = x

From the question, we have the following parameters that can be used in our computation:

f(x) = x + 6

g(x) = x - 6

To determine the inverse function, we calculate

f(g(x)) and g(f(x))

Using the above as a guide, we have the following:

f(g(x)) = x + 6 - 6 = x

g(f(x)) = x + 6 - 6 = x

So, we have

f(g(x)) = g(f(x)) = x

Hence, the functions are inverse functions

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Answer:

To find the answer, we need to subtract the amount of bags Ben used from the amount he bought:

6 and 3/5 - 4 and 1/5

To subtract fractions, we need to have a common denominator. The smallest common denominator for 5 and 20 is 20, so we'll convert both fractions:

6 and 3/5 = 6 * 5/5 + 3/5 = 30/5 + 3/5 = 33/5

4 and 1/5 = 4 * 20/20 + 1/5 = 80/20 + 1/5 = 81/20

Now we can subtract:

33/5 - 81/20

We need to convert the mixed number to an improper fraction and find a common denominator:

33/5 - 81/20 = 132/20 - 81/20

Now we can subtract:

132/20 - 81/20 = 51/20

So Ben has 51/20 bags of rocks left. This can be simplified to 2 and 11/20 bags.

Answer:

2 2/5

Step-by-step explanation:

6 3/5 - 4 1/5 = 2 2/5

Answer:

Attached. Hope this helps

Conjectures are unsubstantiated claims. A theorem is created when someone proves a conjecture. In logic types that deal with conjunctions, the rule of simplification is a valid argument. The rule of inference that states that ∀xP(x) is true given the premise that P(c) is true for all elements c in the domain is known as universal generalization.

The Conjecture Rule

Conjectures are unsubstantiated claims. A theorem is created when someone proves a conjecture.

We seek to understand a conjecture on three levels: we want to know what it means, we want to know why we think the claim is true, and we want to know how it fits into a larger set of ideas.

Rule for Simplification

In logic types that deal with conjunctions, the rule of simplification is a valid argument.

This includes propositional and predicate logic, as well as natural deduction.

(1) Proof Rule: If we can reach a conclusion ϕ∧ψ, we can infer ϕ.

(2): If we can reach a conclusion ϕ∧ψ, we can infer ψ.

Rule of Universal Generalization

The rule of inference that states that ∀xP(x) is true given the premise that P(c) is true for all elements c in the domain is known as universal generalization. When we show that ∀xP(x) is true by taking an arbitrary element c from the domain and showing that P(c) is true, we are using universal generalization. The element c that we choose must be arbitrary and not a specific domain element.

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The complete question is:

Write about the conjecture rule, simplification rule, universal generalization rule.

Andre's number is 43.

Generally, Let's call the tens digit of Andre's number "t" and the ones digit "o".

We know that Andre can make the number in 8 different ways. This means that there are 8 different combinations of t and o that can make up the number.

One of these ways has 1 more ten than ones, which means that the number is 10 more than the sum of the digits. In other words:

t + o + 10 = 10t + o + 1

Simplifying this equation, we get:

9t = 9o + 9

Dividing both sides by 9, we get:

t = o + 1

This means that the tens digit is 1 more than the ones digit, which narrows down our possibilities.

Since the number is a 2-digit number, the tens digit must be between 1 and 9 (inclusive), and the ones digit must be between 0 and 9 (inclusive). We also know that the tens digit is 1 more than the ones digit.

Using these constraints, we can create a table of all the possible combinations of t and o that satisfy these conditions:( table attached below)

Out of these 8 numbers, only one of them can be made in a way where there is 1 more ten than ones. Looking at the table, we can see that the number is 43, since it is the only number where the tens digit is 1 more than the ones digit, and it can be made by combining the digits in a way where there is 1 more ten than ones (i.e., 3 tens and 4 ones).

Therefore, Andre's number is 43.

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The estimated difference of 3 1/2 and 1 1/3 is 2 1/6.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Are two fractions 3 1/2 and 1 1/3.

Now, The difference between 3 1/2 and 1 1/3 would be,

1/2 - 1/3 is 1/6 and 3 - 1 is 2,

So, The estimated 3 1/2 -1 1/3 is 2 1/6.

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Answer:

5,022

Step-by-step explanation:

The values of the expressions are  7x - 5y = -1, 12z + 2y² = 6 and 2xy + 8z = 4

From the question, we have the following parameters that can be used in our computation:

x = 2, y = 3 and z = -1

Substitute the known values in the given equations, so, we have the following representation

7x - 5y = 7 * 2 - 5 * 3

7x - 5y = -1

12z + 2y² = 12 * -1 + 2 * 3²

12z + 2y² = 6

2xy + 8z = 2 * 2 * 3 + 8 * -1

2xy + 8z = 4

Hence, the expressions have their values to be -1, 6 and 4

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Complete question

Consider the following expressions:

7x-5y=

12z+2y²=

2xy+8z=

Determine the values when x = 2, y = 3 and z = -1

The side length of the square that will give the closest approximation to the area of the circle described is e. s = π/4 inches

The region encircled by a circle with a radius r is known as r2 in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.

The area of a circle with a diameter of 1 inch is given by the formula πr^2, where r is the radius of the circle. The radius of the given circle is 1/2 inch, so its area is approximately π * (1/2)^2 = π/4 square inches.

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The proposition is false, and there exist nonnegative integers x that cannot be expressed as the sum of at most two squares and a cube of nonnegative integers.

This proposition is false. A counterexample is x = 7.

Assume for the sake of contradiction that there exist nonnegative integers a, b, and c such that x = a² + b² + c³. Since a² and b² are always nonnegative, we must have c³ ≤ 7. The only possible values for c are 0, 1, and 2, since 3³ = 27 > 7.

For c = 0, we have x = a² + b², which is the sum of two squares, and is a well-known result.

For c = 1, we have x = a² + b² + 1. However, it is a known result that a sum of two squares cannot be equal to a number of the form [tex]4^{k}[/tex](8m + 7) for some nonnegative integers k and m. Since 7 is of the form 4(8×0 + 7), it cannot be expressed as a sum of two squares, and therefore, x cannot be expressed as the sum of at most two squares and a cube of nonnegative integers.

For c = 2, we have x = a² + b + 8. Similarly, it can be shown that a sum of two squares cannot be equal to a number of the form [tex]4^{k}[/tex](8m + 7) for some nonnegative integers k and m. Since 8 is of the form 4(8×1 + 0), it cannot be expressed as a sum of two squares, and therefore, x cannot be expressed as the sum of at most two squares and a cube of nonnegative integers.

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I would assume its 4

The image point will be (0, -4).

When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative.

Given:

Coordinate of a point → (0, 1)

Rule for the transformation has been given as,

[tex]R_{180[/tex] o  D₄

First use [tex]R_{180[/tex] → Rotation of the point by 180° counterclockwise

Rule :

(x, y) → (-x, -y)

(0, 1) → (0, -1)

Now, D₄ → Dilation of the point by a scale factor of 4 about the origin

If a point (x, y) is dilated by a scale factor 'k' about the origin rule for the dilation is,

(x, y) → (kx, ky)

By applying this rule,

(0, -1) → (0, -4)

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Using the Venn diagram to determine the roster form of set (A-C)'  =  { 1, 2, 5, 6, 7, 9, 10, 11, 12, 13, 14 }.

The difference of the sets A and C in this order is the set of elements which belong to A but not to C.

A - C = elements in set A but not in set C

A - C = { 3, 4 , 8 }

The A minus C complements include the following;

(A - C)' = { 1, 2, 5, 6, 7, 9, 10, 11, 12, 13, 14 }

Thus, using the Venn diagram to determine the roster form of set (A-C)' depends on the number of elements in the universal set.

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The population standard deviation representing the number of hours spend by the employees on work related activities in a typical week for 88% confidence interval is equal to  [ 46.862 , 50.138 ].

Mean '[tex]\bar{x}[/tex]' = 48.5 hours

Standard deviation 'σ' = 7.5 hours

Confidence interval = 88%

Level of significance = 100 - 88%

                                  = 12%

                                  = 0.12

Z-score at 88% confidence interval = 1.56

sample size 'n' = 51

Population standard deviation

= [tex]\bar{x}[/tex] ± [tex]Z_{\alpha /2}[/tex] (σ / √n )

= 48.5 ± 1.56 ( 7.5 / √51 )

=  48.5 ± 1.56 ( 7.5 / 7.14)

= 48.5 ± 1.56 ( 1.05 )

= 48.5 ± 1.638

= [ 46.862 , 50.138 ]

Therefore, the number of hours spend on work related activities in a typical week given by population standard deviation is equal to                [ 46.862 , 50.138 ].

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a. To find f(-4), we simply substitute -4 for x in the function f(x):

f(-4) = (-4)² - 3(-4) = 16 + 12 = 28

Therefore, f(-4) = 28.

b. To find g(1)-f(-3), we first need to find g(1) and f(-3) separately.

g(1) = 2(1) - 5 = -3

f(-3) = (-3)² - 3(-3) = 9 + 9 = 18

Then, we can substitute these values into the expression:

g(1)-f(-3) = -3 - 18 = -21

Therefore, g(1)-f(-3) = -21.

c. To find f(g(-4)), we first need to find g(-4) and then substitute this value into f(x).

g(-4) = 2(-4) - 5 = -8 - 5 = -13

Then, we can substitute -13 for x in the function f(x):

f(g(-4)) = (-13)² - 3(-13) = 169 + 39 = 208

Therefore, f(g(-4)) = 208.

The expected number is 1, that means that if you randomly pick one ball and replace it with a blue ball, then you have a greater than 50/50 chance of eliminating all the red balls.

The expected number of blue balls needed to eliminate all red balls is calculated using the formula[tex]n = (x-1)/(y-1)[/tex]. In this scenario, x = 3 (the total number of balls in the box) and y = 2 (the number of red balls). Therefore, n = (3-1)/(2-1), which equals 1. So, the expected number of blue balls needed to eliminate all red balls is 1.

To illustrate this, imagine a box with 3 balls: 2 red and 1 blue. If you randomly pick one ball and replace it with a blue ball, then you have a 50/50 chance of eliminating all the red balls. If the ball you pick is red, then you need to pick another ball and replace it with a blue ball to get rid of the remaining red ball. This means that you need a total of 2 blue balls to get rid of all the red balls. However, since the expected number is 1, that means that if you randomly pick one ball and replace it with a blue ball, then you have a greater than 50/50 chance of eliminating all the red balls.

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complete question

What is the expected number of blue balls needed to eliminate all red balls from a box with 3 balls, 2 of which are red?

The number of outcomes in the complement of the given event is 61.

The complement of the event "choosing a nonfictional book from the bookcase" is "choosing a fictional book from the bookcase. "Number of outcomes in complement = Total number of books - Number of nonfictional books

The number of outcomes in the complement is equal to the total number of books in the bookcase minus the number of nonfictional books in the bookcase:

Number of results in complement = Number of nonfiction books - Overall number of books = 216 - 155 = 61

Therefore, there are 61 outcomes in the complement of the given event.

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Answer:

4/5

Step-by-step explanation:

Because 1/5 is winning chance.

and the rest percentage will be losing

The matching parts of vectors a and c to find a + c. For instance, (1, -2, 4) + (2, 3, -1) = (3, 1, 3).

The equations and calculations to determine the vectors a and c's sum are as follows:

Assume that vector an is shown as (a1, a2, a3) and that vector c is shown as (c1, c2, c3).

Then, by adding each of their respective components, it is possible to determine the vectors a and c's sum, denoted as a + c:

A plus C equals (A+C1, A+C2, A+C3, etc.)

For instance, if a = (2, 3, -1) and c = (1, -2, 4), we can use the following formula to get their sum:

a + c = (2 + 1, 3 - 2, -1 + 4) = (3, 1, 3) (3, 1, 3)

As a result, the vectors a and c's sum is (3, 1, 3).

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The mass of the water is 7880.1 grams.

Specific heat capacity is the amount of heat energy required to raise the temperature of a substance per unit of mass.

Mathematically -

Q = mcΔT

where -

{Q} = heat energy

{m} = mass

{c} = specific heat capacity

{ΔT} =change in temperature

Given is the water in a container changes its temperature from 12°C to 38°C, when 205 calories are transferred to it.

Specific heat capacity of water = 4.186 J/g°C

205 calories = 857720 Joules

We can write -

Q = mcΔT

857720 = m x 4.186 x (38 - 12)

857720 = 108.836 x m

m = 857720/108.836

m = 7880.1 grams

Therefore, the mass of the water is 7880.1 grams.

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{QUESTION IN ENGLISH -

The water in a container changes its temperature from 12°C to 38°C, when 205 calories are transferred to it. What is the mass of water in the container?}

Answer:

Step-by-step explanation:

If we represent the first number as "x", then the second number can be represented as "2x-3".

For example, if the first number is 5, then the second number would be 2(5)-3 = 7.

Alternatively, if the first number is 10, then the second number would be 2(10)-3 = 17.

In general, we can say that the second number is equal to twice the first number minus 3.

A one-sample t-test can be used to determine whether the sample mean of M=115 is a particularly improbable outcome given the population parameters.

The test's null hypothesis is that the new treatment has no impact on extraversion, in which case the population mean remains at or above 100. The alternative theory is that the new treatment has an impact on extraversion, causing the population mean to deviate from the reference value of 100.

Using the following method, we can determine the test's t-statistic:

(M - ) / (s / sqrt(n)) t

Where M denotes the sample mean, denotes the population mean, s denotes the population standard deviation, and n denotes the sample number.

By entering the numbers we have:

t = (115 - 100) / (30 / sqrt(4)) = 3.33

The measure has n-1 = 3 degrees of freedom. We can use a calculator to determine the critical t-value, which is roughly 3.182, using a two-tailed t-test with alpha = 0.05 and 3 degrees of freedom.

The sample mean is a particularly improbable result based on the population parameters for the personality test because the calculated t-value of 3.33 is higher than the critical t-value of 3.182, and we can therefore reject the null hypothesis.

The evidence from the sample allows the researcher to draw the conclusion that the novel treatment has an impact on extraversion.

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The correct inequality is,

⇒ 7 + 10b ≥ 22

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Translate the sentence into an inequality,

''Seven increased by the product of a number and 10 is at least 22.''

Now,

Let an unknown variable = b

Hence, We can formulate;

⇒ 7 + b × 10 ≥ 22

⇒ 7 + 10b ≥ 22

Therefore, The correct inequality is,

⇒ 7 + 10b ≥ 22

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Answer:

Step-by-step explanation:

12 In 10 min

30 in 25mins

It will take the store 25 mins

12+12+6=30 t shirts

10+10+5=25mins

Step-by-step explanation:

the function

Kendal(x) = y = 90

is just a flat line (that's why people call it a flat rate). it does not matter how many hours it takes, it costs the same.

the function

Mona(x) = 10x + 70

as we know, $10 per hour, plus $70 for the material, which is the same cost no matter how many hours it takes.

the solution, when both cost the same, means again both functions are equal at that point :

90 = 10x + 70

20 = 10x

x = 20/10 = 2 hours

after 2 hours both cost the same : $90.

the graphic should look like the attached picture.

the flat line is at y = 90. that means it is a horizontal line that goes through the y gridline marker 90.

just draw the line along the y 90 gridline from left to right.

Mona's graph goes through the solution point (2, 90) and the point for x = 0 : (0, 70) because y = 10×0 + 70 = 70.

for (0, 70) you go from 0 the y-axis straight up to the gridline marker 70 and mark the point there.

for (2, 90) you go on the x-axis from 0 to the right to the gridline marker 2. from there you go straight up to the y gridline 90. and you mark the point there.

and both lines intersect at (2, 90), which is the solution.

can you see and understand it now how that works ?

The cost is $90

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

The function for Kendal(x) is:- y = 90

The function for Mona(x) :- 10x + 70

$10 per hour, plus $70 for the material

The solution, when both cost the same, means again both functions are equal at that point :

90 = 10x + 70

20 = 10x

x = 20/10 = 2 hours

after 2 hours both cost the same : $90.

Graph the lines both lines intersect at (2, 90), which is the solution.

Hence, the cost is $90

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The 45th Percentile from the data is 7.65

Percentiles are a method for dividing data into 100 equal parts. So, there are 99 percentile values.

single data percentile formula is

Px = [tex]\frac{x (y+1)}{100}[/tex]

Px = Percentile x

y = lots of data

How to find the 45th percentile weight of newborn babies?

first, we must be sorted from the smallest to the largest.

5.5   6.5   6.5   7.1   7.3   7.4   7.6   7.7   7.8   8.1   8.3   8.4   8.5   8.6   9.4

After sorting the data, we can plug it into a single data percentile formula

Px = P45

x = 45

y = 15

P45 = [tex]\frac{45 (15+1)}{100}[/tex]

P45 = [tex]\frac{36}{5}[/tex]

P45 = 7.2

The 45th percentile is in the order of the 7th & 8th digits

the order of the 7th & 8th numbers is 7.6 & 7.7

after that we average the 7th & 8th numbers to find out the 45th percentile value

[tex]\frac{7.6 + 7.7}{2}[/tex] = [tex]\frac{15.3}{2}[/tex] = 7.65

the 45th percentile of newborn weight data is 7.65

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The distance between the two planes after 10 minutes is 10 miles.

We can use the Pythagorean Theorem to find the distance between the two planes. According to the theorem, the distance between two points in a plane is given by the equation:

d = √( (x2 - x1)^2 + (y2 - y1)^2 )

where (x1, y1) and (x2, y2) are the coordinates of the two points.

The first plane is flying due north, so its position after 10 minutes will be (0, 10). The second plane is flying due east, so its position after 10 minutes will be (10, 0).

We can plug these coordinates into the equation to find the distance between the two planes:

d = √( (10 - 0)^2 + (10 - 0)^2 )

d = √( 100 )

d = 10

So the distance between the two planes after 10 minutes is 10 miles

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The correct initial value problem is: y'' + (9.81/0.75) y = 0, y(0) = -0.36, y'(0) = -0.45.

Here's how you can set up the initial value problem

Let y(t) be the displacement of the mass from its spring-mass equilibrium position at time t. Then, the force acting on the mass is given by Hooke's Law:

F = -ky

where k is the spring constant.

Since the mass is at rest at its equilibrium position, the force acting on it is balanced by the force of gravity.

mg = ky_eq

where y_eq is the equilibrium position of the spring-mass system.

Substituting F = -ky into the equation and solving for k, we get:

k = mg/y_eq

Substituting k and the values given, we get:

y'' + (9.81/0.75) y = 0

where y'' is the second derivative of y with respect to time.

When the mass is displaced 36 cm upward from its spring-mass equilibrium and then given a sharp downward tap, the initial conditions are:

y(0) = -0.36 m

y'(0) = -0.45 m/s (note that the velocity is downward, so it's negative)

Therefore, the initial value problem that models this experiment is:

y'' + (9.81/0.75) y = 0

y(0) = -0.36

y'(0) = -0.45

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Anοther system οf linear equatiοns with the same number οf sοlutiοns is 12x + 51y = 156

24x + 102y = 312

A linear equatiοn is a mathematical equatiοn that describes a straight line in a twο-dimensiοnal space. It is an equatiοn that has οnly οne independent variable and οne οr mοre cοefficients that represent the slοpe and intercept οf the line.

The general fοrm οf a linear equatiοn is: y = mx + b

Where: y is the dependent variable x is the independent variable

m is the slοpe οf the  is the y-intercept

Accοrding tο the questiοn:

Tο determine whether this system οf equatiοns has οne sοlutiοn, nο sοlutiοns, οr infinitely many sοlutiοns, we can use variοus methοds such as substitutiοn οr eliminatiοn. Here, we'll use the eliminatiοn methοd:12x + 51y = 156-8x - 34y = -104

Tο eliminate οne οf the variables, we need tο find a cοmmοn multiple οf the cοefficients οf x οr y in bοth equatiοns. In this case, the cοmmοn multiple is 17, because 51 and -34 have 17 as a cοmmοn factοr:12x + 51y = 156 (multiply by 2)-16x - 68y = -208 (multiply by 2)

Nοw, we can add the twο equatiοns tο eliminate

y:12x + 51y = 156-16x - 68y = -208---------------4x - 17y = -52

We can sοlve fοr y in terms οf x:-4x - 17y = -5217y = -4x + 52y = (-4/17)x + 52/17This is the equatiοn οf a line in slοpe-intercept fοrm, with slοpe -4/17 and y-intercept 52/17.

We can alsο write anοther system οf equatiοns with the same number οf sοlutiοns that uses the first equatiοn οnly by multiplying bοth sides οf the equatiοn by a cοnstant

12x + 51y = 156

24x + 102y = 312

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Strictly using the limit definition of the derivative to find the derivative of the function:

The limit definition of the derivative looks like this:

[tex]\lim_{h \to \zero} \frac{f(x+h) - f(x) }{h}[/tex]

If we replace f(x) with −3x, we get:

[tex]\lim_{h \to \zero} \frac{-3(h+x) - 3x }{h}\\\\\lim_{h \to \zero} \frac{-3h-3x) - (-3x) }{h}\\[/tex]

Simplifying, we get:

[tex]\lim_{h \to \zero} \frac{-3h }{h}\\[/tex]

So, the derivative of −3x must be −3.

We know that the secondary means the rate of change of the function. Graphically, this means that the outgrowth is the pitch of the graph of that function.

Since −3x is a first degree polynomial, we know that it'll always have the same pitch, and therefor the same outgrowth. We can also corroborate this by looking at the graph, noticing that it's a straight line:

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