For the functions f(x)=−7x+3 and g(x)=3x2−4x−1, find (f⋅g)(x) and (f⋅g)(1).

The sequence, [tex]a_n =e ^{\frac{{-8}}{\sqrt{n}}}[/tex], is convergent sequence because the limit of an exists, that is as n approaches infinity, so the sequence an approaches 1 ( finite value).

The sequence can be convergent if the limit is zero, or if the limit is finite. The divergent sequence is one whose limit is not finite. The limit can be found suing the limit properties or by simplification method, as applicable. We have, an sequence, [tex]a_n =e ^{\frac{{-8}}{\sqrt{n}}}[/tex]. We have to check whether the sequence converges or diverges. Using limits, [tex]lim_ {n->\infty } a_n = lim_{n-> oo} e^{\frac{-8}{\sqrt{n}}} [/tex]

n approaches infinity, so square root of n approaches infinity,

= e⁻⁰

= 1/e⁰ = 1 ( finite )

Therefore, it is a convergent sequence.

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According to the Venn diagram the value of [tex]n(A ^ C \cap B ^ C) = {3}[/tex] so the number of elements in that set is 1.

What is Venn diagram ?

A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. It is usually represented as a rectangle or a circle for each set and the overlapping areas between them, showing the common elements that belong to more than one set. Venn diagrams are widely used in mathematics, logic, statistics, and computer science to visualize the relationships between different sets and help solve problems related to set theory.

According to the question:
To solve this problem, we first need to understand the notation used.

n(A) denotes the set A and the numbers within the braces {} indicate the elements in set A. For example, n(A)={7,4,3,9} means that the set A contains 7, 4, 3, and 9.

n(AnB) denotes the intersection of sets A and B, i.e., the elements that are common to both A and B. For example, n(AnB)={4,3} means that the sets A and B have 4 and 3 in common.

^ denotes intersection of sets

cap denotes the intersection of sets

Now, we need to find the elements that are common to sets A and C, and sets B and C. We can do this by taking the intersection of A and C, and the intersection of B and C, and then taking the intersection of the two resulting sets.

[tex]n(A ^ C) = n(A \cap C) = {3,9}[/tex]

[tex]n(B ^ C) = n(B\cap C) = {3,5}[/tex]

Now, we take the intersection of [tex]n(A ^ C)[/tex] and [tex]n(B ^ C)[/tex]:

[tex]n(A ^ C \cap B ^ C) = {3}[/tex]

Therefore, the answer is 1.

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Answer:

E

Step-by-step explanation:

Answer has to have a star, the object (star) needs to be on the right side, and the two colors cannot be the same as any of the rest in the set. So E?

Step-by-step explanation:

try this option, all the details are in the attachment.

The probability that the computer generates a number between 1 and 4 is 4/11.

Since X has a uniform distribution, the probability of generating any number between 0 and 10 is equally likely. Therefore, the probability of generating a number between 1 and 4 is the same as the probability of generating a number between 0 and 4 minus the probability of generating 0

P(1 ≤ X ≤ 4) = P(X ≤ 4) - P(X = 0)

Since X has a uniform distribution, the probability of generating any specific number is 1/11. Therefore

P(X ≤ 4) = (4 + 1)/11 = 5/11

and

P(X = 0) = 1/11

So,

P(1 ≤ X ≤ 4) = (5/11) - (1/11) = 4/11

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I have solved the question in general, as the given question is incomplete,

The complete question is:

A random number generator generates numbers between 0 and 10. Let random variable X be the number generated. Suppose X has a uniform distribution. What is the probability that the computer generates a number between 1 and 4?

Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

(a)

the experimental probability is just using the actual experience to predict any future results.

the total number of cases was 20, and the number of desired cases (yellow) was 12.

so, the experimental probability of landing on yellow is

12/20 = 3/5 = 0.600

(b)

the theoretical probability of a totally fair spinner landing on yellow is 2 out of 5 possibilities, so

2/5 = 0.4000

(c)

the correct statement is the first one.

with a more or less balanced (fair) spinner the experimental numbers should get closer and closer to the theoretical numbers, the more spins we make.

The common factors of sixteen and twenty are 1, 2, and 4.

The factors of sixteen are 1, 2, 4, 8, and 16. The factors of twenty are 1, 2, 4, 5, 10, and 20. The factors that are common to both numbers are 1, 2, and 4.

To calculate the factors of sixteen, we can start by dividing sixteen by two until we cannot divide any further. We can start with sixteen divided by two, which equals eight. Eight divided by two equals four. Four divided by two equals two. Two divided by two equals one. As we can see, the factors of sixteen are 1, 2, 4, 8, and 16

To calculate the factors of twenty, we can start by dividing twenty by two until we cannot divide any further. We can start with twenty divided by two, which equals ten. Ten divided by two equals five. Five divided by two equals two. Two divided by two equals one. As we can see, the factors of twenty are 1, 2, 4, 5, 10, and 20.The common factors of sixteen and twenty are 1, 2, and 4. This can be determined by comparing the two lists of factors. As we can see, 1, 2, and 4 are present in both lists.

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Complete question

What are the common factors of sixteen and twenty ?

To solve this problem, we can use Bayes' theorem. Let's define:

- A: two story home

- B: owning a computer

We want to find the probability of B given A, which we can write as P(B|A). Using Bayes' theorem, we have:

P(B|A) = P(A|B) * P(B) / P(A)

We know that 50% of two story homes own computers, so P(B) = 0.5. We also know that 75% of homes in Dawn's neighborhood are two story, so P(A) = 0.75.

To find P(A|B), we need to use the conditional probability formula:

P(A|B) = P(A and B) / P(B)

We don't have the probabilities for A and B happening together, but we know that:

P(A and B) = P(B|A) * P(A)

Substituting this into the conditional probability formula gives:

P(A|B) = (P(B|A) * P(A)) / P(B)

Putting all the values together, we get:

P(B|A) = (P(A|B) * P(B)) / P(A)

= ((P(B|A) * P(A)) / P(B)) * P(B) / P(A)

= (P(B and A) / P(B)) * P(B) / P(A)

= P(A and B) / P(B)

Substituting the values gives:

P(B|A) = (0.5 * 0.75) / 0.5

= 0.75

Therefore, the probability that a two story home in Dawn's neighborhood owns a computer is 0.75.

The rate at which electric charge flows through a circuit is used to quantify electrical current: I (t) equals dQ (t) / dt. The derivative of the electric charge by time yields the momentary current. I (t) is the amps of the transient current I at time t. (A).

The temporary electric charge, measured in coulombs, is Q(t) (C).

The time in seconds is t. (s).

I =ΔQ / Δt

ΔQ is the amount of electric current flowing at time Δt, measured in coulombs (C).

The time length in seconds is t. (s).

We know that I = dQ/dt by definition; thus, if Q = f(t), then I = f' (t). By stating this, we obtain the current's expression as follows:

I (t) = (d/dt) (Q(t)) = (d/dt) (6t + 2t2) = 6 + 4t:  I(t) = 4t + 6; t >= 0

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Step-by-step explanation:

try this option (see the attachment), answers are marked with red colour.

Answer:

  40.3%

Step-by-step explanation:

You want to know the percentage of a 62 gram allowance of fat is represented by a burger with 25 grams of fat.

The fraction can be converted to a percentage by multiplying by 100%.

  burger/allowance = (25 g)/(62 g) × 100% = 40.3%

King has 40.3% of his daily allowance for fat when he ate his burger.

a) Number of one-to-one functions are equal to the zero, because n< m.

b) Number of one-to-one functions are equal to the ⁵P₅ = 120.

c) Number of one-to-one functions are equal to the ⁶P₅ = 720.

c) Number of one-to-one functions are equal to the ⁷P₅ = 2250.

One to one function is a special form of function that defined from one set to another and maps every element of the range to exactly one element of its domain unique output. As we know a set A has m elements and set B has n elements, then

Now, we have a domain set with five elements, m = 5

a) Here, another set (co-domain) has 4 elements, n = 4. So, Number of one-to-one functions = 0 , n<m.

b) number of elements in another set,n= 5

So, Number of one-to-one functions = ⁵P₅ = 5!/(5 - 5 )! ( permutation formula)

= 5!/0! = 120

c) Number of elements in another set, n= 6

So, Number of one-to-one functions= ⁶P₅

= 6!/(6 - 5)!

= 6!/1! = 720

d) Number of elements in another set, n

= 7

So, Number of one-to-one functions

= ⁷P₅ = 7!(7 - 5)!

= 7!/2! = 2250

Hence, required value is 2250.

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Answer:

Where is the table?

Step-by-step explanation:

The length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.

Since the area of the soap carvings is 300 square inches, we want the top of the bookcase to have the same area. Let's assume the length of the top of the bookcase is "l" and the width is "b". Then we have:

Area of top of bookcase = lb

We want this area to be equal to 300 square inches. Therefore, we can write:

lb = 300

We are solving for "b", so we can rearrange this equation to solve for "b":

b = 300/l

Since we don't know the value of "l", we can't solve for "b" exactly. However, we can approximate it by assuming a value for "l". Let's say we assume that "l" is 20 inches. Then we can calculate "b" as follows:

b = 300/20 = 15

So if the length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.

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The answer is 4 5/6

Step-by-step explanation:

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to draw an angle that is 150}^{\circ}.[/tex]

[tex]\textsf{We will need a Protractor to draw this angle.}[/tex]

[tex]\large\underline{\textsf{To Draw an Angle with a Protractor;}}[/tex]

[tex]\textsf{First, notice a point at the bottom of the Protractor. This is where we will start.}[/tex]

[tex]\textsf{Draw a Straight Line from the point to the 0}^{\circ} \ \textsf{mark.}[/tex]

[tex]\textsf{Secondly, use a ruler to carefully draw a straight line towards the 150}^{\circ} \ \textsf{mark.}[/tex]

[tex]\textsf{Note that some Protractors may be different from others. Similar steps should apply.}[/tex]

[tex]\textsf{Refer to the picture. It represents what the angle should look like afterwards.}[/tex]

To do :-

Instruments required:-

Steps of construction:-

Hence angle ECB represents 150° .

Precaution:- do not change the arm length of the compass.

and we are done!

Answer:

Notice the change in sample size.

Answer:

1. The expected mean for a sample of 150 women is 168.5 pounds.

2. The standard deviation of the mean for a sample of 150 women is 6.8 pounds.

3. The probability of 150 women having a sample mean below 160 pounds is 0.0849.

4. The probability of 150 women having a sample mean above 175 pounds is 0.0305.

5. The probability of 200 women having a sample mean below 160 pounds is 0.0434.

6. The probability of 200 women having a sample mean above 175 pounds is 0.0153.

The solution is given below. Notice the change in sample size.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

given that,

In 2016, the CDC estimated the mean weight of U.S. women over the age of 20 years old was 168.5 pounds with a standard deviation of 68 pounds.

so. we get,

1. The expected mean for a sample of 150 women is 168.5 pounds.

2. The standard deviation of the mean for a sample of 150 women is 6.8 pounds.

3. The probability of 150 women having a sample mean below 160 pounds is 0.0849.

4. The probability of 150 women having a sample mean above 175 pounds is 0.0305.

5. The probability of 200 women having a sample mean below 160 pounds is 0.0434.

6. The probability of 200 women having a sample mean above 175 pounds is 0.0153.

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In equation 7(5x + 2) = -4(6 - 5x), Using the Distributive Property, we get 35x + 14 = -24 + 20x. So, the correct option is D).

To solve the equation 7(5x + 2) = -4(6 - 5x), a good first step is to use the Distributive Property to simplify both sides of the equation. Distributing the 7 and -4 on the left and right sides, respectively, we get

35x + 14 = -24 - 20x.

Next, we can combine like terms by adding 20x to both sides to get 55x + 14 = -24. Then, subtracting 14 from both sides, we get 55x = -38. Finally, we can solve for x by dividing both sides by 55, giving us x = -38/55. Therefore, the solution to the equation is x = -38/55.

The evaluation process involves performing arithmetic operations in a logical order to simplify the equation step-by-step until a solution is reached. So, the correct answer is D).

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Answer:

see step by step.

Step-by-step explanation:

The THEORETICALLY probability is 0.5000 (this is, 50% each one) since each one have equal chance of being in list A or List B, but this is still a random probability, so this is not the same that if you have 60 students, 30 of them are going to be in the list A and the other 30 in B.

The experimental result show:

[tex]P (ListA) = \frac{27}{60} =0.45[/tex]

[tex]P (ListB) = \frac{33}{60} =0.55[/tex]

This is 45% of being in list A and 55% of being in list B, notice these values are close the the experimental value (50%) but still are lightly higher or lower. Additionally notice if you add both of them you still have 100% (0.45+0.55=1.00)

Answer: -1/6

Step-by-step explanation:

Put the equation into y = mx + b (slope) form.

3x + 18y = -486

18y = -3x - 486

y = -1/6x - 27

If the line is parallel to this line, the slope must be the same.

Answer:

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

Given is the special right triangle.

It is a 45° isosceles right triangle. It has a property that the hypotenuse is √2 times the leg.

We have a hypotenuse of 28 units, so the leg is:

Answer:

14√2

Step-by-step explanation:

Here we need to find out the value of "x" in the given right angled triangle, here we can make use of trigonometric ratios to find out the value of x .

In a right angled triangle, sine is defined as the ratio of perpendicular and hypotenuse . With respect to angle 45° , x is the perpendicular and 28 is hypotenuse (side opposite to 90° ) .

So we have;

sin45° = x/28

1/√2 = x/28

x = 28*1/√2

x = 14 * (√2)² / √2

x = 14√2

Hence the value of x is 14√2 .

Answer:

16, 22, and 32.

Step-by-step explanation:

Set up a system of equations to represent the situation with 3 unknown.

x + y + z = 70

z = 2x

x = y - 6  →  y = x + 6

The second two equations are the y and z in terms of x, so substitute both into the first equation.

x + (x + 6) + 2x = 70

4x + 6 = 70

4x = 64

x = 16

Use this number to calculate the value of the other unknowns.

y = x + 6

y = 16 + 6

y = 22

Calculate z.

z = 2x

z = 2(16)

z = 32

So, the three numbers are 16, 22, and 32.

According to the question. A. No punctuation is missing.

Punctuation is the use of symbols to indicate the structure and organization of written language. It is used to help make the meaning of sentences clearer and to make them easier to read and understand. Punctuation marks can also be used to indicate pauses in speech, to create emphasis, and to indicate the speaker’s attitude. There are many different types of punctuation marks, each with its own purpose. The most commonly used punctuation marks are the period, comma, question mark, exclamation mark, quotation marks, and the apostrophe.

Quotation marks are used to enclose quoted material, while the apostrophe is used to indicate possession or to replace missing letters in a word or phrase. By using punctuation correctly, writers can ensure that their messages are correctly understood by their readers.

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The area of this composite figure made from placing a sector of a circle on a triangle is 95.55 square cm

The sector area

The area of the sector is calculated as

Area = x/360 * πr²

Where

r² = 8² + 6²

So, we have

r² = 100

This means that

Area = 82/360 * π * 100

Evaluate

Area = 71.55

The triangle area

This is calculated as

Area = 0.5bh

So, we have

Area = 0.5 * 8 * 6

Evaluate

Area = 24

So, the area of the figure is

Figure = 24 + 71.55

Figure = 95.55

Hence, the area is 95.55

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According to the solving the function the value of  h(-2) + g(-2) is 45.

function is a mathematical phrase, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions are used frequently in mathematics and are crucial for constructing physical links in the sciences.

To find h(-2) + g(-2), we need to evaluate h(r) and g(r) when r = -2, and then add the results:

h(-2) = 11(-2)² - 6 = 44

g(-2) = (-2)² + 8(-2) + 9 = 1

So, h(-2) + g(-2) = 44 + 1 = 45.

Therefore, h(-2) + g(-2) = 45.

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Therefore, Ashley's annual premium on the contents of her house is $127.80.

Percent is a term used to express a fraction or a ratio as a portion of 100. It is denoted by the symbol % (per cent or percent). Percentages are commonly used in many different contexts, such as finance, statistics, science, and everyday life. They are used to express changes, comparisons, rates, probabilities, and many other types of information. To calculate a percentage, we usually divide the part by the whole and multiply the result by 100.

Here,

Based on the provided table, we can calculate Ashley's annual premium on her house and the contents of her house as follows:

Annual premium on Ashley's house:

Since Ashley's house is made of brick and located in a rural area, we can use the values from the "Brick" and "Rural" columns of the table. The premium per $100 of coverage for a brick house in a rural area is $0.60 for the building and $0.69 for the contents.

To calculate the annual premium for the house, we first need to determine the coverage amount. The coverage amount is the value of the house divided by 100, so in this case, it is $85,000 / 100 = $850.

The annual premium for the house is then calculated by multiplying the coverage amount by the premium per $100 of coverage:

Annual premium on house = coverage amount * premium per $100 of coverage for brick house in rural area

= $850 * $0.60

= $510

Therefore, Ashley's annual premium on her house is $510.

Annual premium on Ashley's contents:

To calculate the annual premium for the contents of Ashley's house, we use the same method as above. The coverage amount is the value of the contents divided by 100, so in this case, it is $18,000 / 100 = $180.

The annual premium for the contents is then calculated by multiplying the coverage amount by the premium per $100 of coverage:

Annual premium on contents = coverage amount * premium per $100 of coverage for contents in rural area

= $180 * $0.71

= $127.80

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The graph repeats itself every 32 units hοrizοntally. [ The graph is attached belοw ]

An interactive widget in a graph is a tοοl that allοws the user tο manipulate different elements οf the graph using their mοuse οr tοuch screen.

Interactive widgets can be used tο explοre the behaviοr οf a functiοn οr dataset in a mοre dynamic and engaging way than a static graph.

Sοme cοmmοn examples οf interactive widgets in graphs include sliders, buttοns, checkbοxes, and drοpdοwn menus.

Here we have

y = -5 cοs (π/16 x) - 4    

Represents a periοdic functiοn with a cοsine wave shape that is shifted dοwnwards by 4 units.

The cοsine functiοn οscillates between -1 and 1, sο multiplying it by -5 stretches the wave vertically by a factοr οf 5 and reflects it acrοss the x-axis.

The cοefficient οf x, π/16, cοntrοls the periοd οf the functiοn, which is the distance between twο cοnsecutive peaks οr trοughs οf the wave.

Specifically, the periοd οf this functiοn is 32 units, since the cοsine functiοn has a periοd οf 2π and 2π/(π/16) = 32.

Therefοre,

The graph repeats itself every 32 units hοrizοntally. [ The graph is attached belοw ]

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The value of x is 30° as per below diagram.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.

We know that,

Draw a line segment BG is with CBG equal to 20° on line CE.

So that, (40 + x)  = 70, so that means x = 30°

Therefore, The value of x is 30°

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Complete question here-

Triangle: According to the question the value of x is 30° as per below diagram.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.

We know that,
All the angles in a triangle sum → 180°
An isosceles triangle: two equal angles → two equal sides.
Draw a line segment BG is with CBG equal to 20° on line CE.
So that, (40 + x)  = 70, so that means x = 30°
Therefore, The value of x is 30°

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Complete question:

Answer:

0.75

Step-by-step explanation:

0.4 = 0.40

Add 0.40 + 0.35 = 0.75

There is a $243,570 cap on the amount you may finance.

MentaI arithmetic, aIso known as "quick math," aIgebra, trigonometry, statistics, and probabiIity are some of the key mathematicaI concepts and abiIities needed in the financiaI sector. A fundamentaI knowIedge of these abiIities shouId be sufficient to quaIify you for the majority of finance occupations.

The highest home vaIue that may be financed is x.

$39,000 in avaiIabIe cash for a down payment

16% is the needed down payment percentage.

16% of the home's worth can be expressed as,

x × 16/100=$39,000

x=39,000/0.16

x=$243,570

We can then infer that the highest vaIue you couId finance is $243,570.

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