If f(x) = 2x² + 3 and g(x)=x2-7, find (f+ g)(x).

Let the random variable p represent a randomly selected prize amount the expected value of p is $3.90  by using probability.

Prize                $1          $5            $10            $20              $50

Probability     0.60      0.30         0.05           0.04              0.01

It is based on the possible chances of something to happen. The theoretical probability is mainly based on the reasoning behind probability. For example, if a coin is tossed, the theoretical probability of getting a head will be ½.

The expected value is defined as the the sum of each outcome is multiplied by its probability.

p=x1p1+x2p2+x3p3+x4p4

p=1.0.60+5.0.30+10.0.05+20.0.04

p=3.90

Therefore, the correct option is A, i.e. $ 3.90 is the expected value of P.

Three Types of Probability

Classical: (equally probable outcomes) Let S=sample space (set of all possible distinct outcomes).

Relative Frequency Definition.

Subjective Probability.

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An equation for the total cost, y, in terms of the number of kites purchased, x, is y = 2x + 20.

In order to write a linear equation to describe this situation, we would a assign variable to the number of kites purchased and the total cost respectively, and then translate the word problem into a linear equation as follows:

Since Wendy charges $2 per kite and a flat rate of $20 for shipping, a linear equation that models the total cost is given by:

y = 2x + 20

When x = 4, the total cost for Wendy kites is given by:

y = 2(4) + 20

y = $28.

When x = 7, the total cost for Wendy kites is given by:

y = 2(7) + 20

y = $34.

When x = 10, the total cost for Wendy kites is given by:

y = 2(10) + 20

y = $40.

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If twice Brittany's age is less than the age of Abraham Lincoln when he died, then the answers are;

2b < 56

n = b - 2

b = n + 2

b < 28

n = b - 2 < 26

Yes, Brittany could be 27 years old and Nate 26

Let Brittany's age = b

Twice Brittany's age = 2 × b = 2b

Lincoln's age = 56

Inequality to represent Brittany's age: 2b < 56

b < 56/2 = 28

Nate's age = n

in terms of Brittany's age: n = b - 2

Isolating b: b = n + 2

Substituting b: b < 28

Solving for b: b < 28 and n = b - 2 < 26

Could Brittany be 27 years old and Nate 26? Yes, Brittany could be 27 years old and Nate 26 as both are within the range defined by the inequality (b < 28 and n < 26).

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The complete question is:

Twice Brittany’s age is less than the age of Abraham Lincoln when he died. President Lincoln was 56 years old at the time of his death. Write an inequality to represent Brittany’s age, b. Brittany’s brother, Nate, is two years younger than Brittany. Write an equation for Nate’s age, n, in terms of Brittany’s age, b. Rewrite the expression from Part B to get the variable b alone on one side of the equation. (This is also called isolating b.) Substitute the value of b from Part C into the inequality you found in Part A. Solve the inequalities from parts A and D for the variables b and n, respectively. Could Brittany be 27 years old and Nate 26? Why or why not?

The value of x is equal to 16

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².

Given here: A right angle triangle

let the triangle be ABC with AC as the hypotenuse and AB is the perpendicular and BC is the base of the triangle. And D be a point on AC with AD=32 and DC=8 .Clearly the perpendicular using the pythagoras theorem

AB=[tex]\sqrt{x^2+32^2}[/tex]

Now in triangle BDC we have BC= [tex]\sqrt{x^2+64}[/tex]

Again a triangle ABC we have

AC²=BC²+AB²

[tex]40^2=x^2+64+x^2+32^2\\2x^2=40^2-32^2-64\\2x^2=512\\x^2=256\\x=16[/tex]

Thus x is equal to 16

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6. The costs are given as follows:

7. The linear function is defined as follows:

y = 20 + 2x.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, when x = 0, y = 20, hence the intercept b is given as follows:

b = 20.

When x increases by one, y increases by two, hence the slope m is given as follows:

m = 2.

Then the function giving the cost y of x kites is defined as follows:

y = 2x + 20.

The costs are given obtaining the numeric values, replacing the lone instance of x in the equation by the number of kites, thus:

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The first three triangles are similar triangles as their corresponding sides are in same proportion but the last triangle with side lengths 4, 6, and 8 does not belong to the first three.

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

The base lengths 12, 6, and 18 of the first three triangles corresponds in proportion but does not for the last triangle with 8.

The side 6, 3, and 9 corresponds in proportion but does not for the side 4 of the last triangle

And lastly, the side 8, 4, and 12 of the first three triangles corresponds in proportion but does not for the last triangle with side length 6.

Therefore, the first three triangles are similar triangles as their corresponding sides are in same proportion but the last triangle with side lengths 4, 6, and 8 does not belong to the first three.

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The value of {x} is equivalent to {x} = 4β - (y + z).

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that triangle and the square have equal perimeters.

Assume the lengths of the triangle are {x}, {y} and {z} respectively.

Let the side length of a square be β. We can write -

P{T} = P{S}

(x + y + z) = 4β

{x} = 4β - (y + z)

Therefore, the value of {x} is equivalent to {x} = 4β - (y + z).

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The standard deviation represents the variability or spread of the data when graphing the class average for the serial dilution experiment.

It shows how much the individual data points deviate from the mean, or average, of the class data. The standard deviation can be used to determine how much variation there is in the data and how much the data is spread out from the mean.

If the standard deviation is small, it means that the data points are very close to the mean, and if the standard deviation is large, it means that the data points are spread out over a larger range.

The standard deviation is important to consider when analyzing data in the serial dilution experiment, as it gives insight into the variability of the data and helps to determine if the data is accurately representing the experiment.

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Let x represent the number of chickens and y represent the number of sheep.There is no proper system equation so such farms does not exist as this equations contradict.

A system of equations is a set of multiple equations with multiple variables that are related to each other. It is a mathematical problem that requires a solution for each equation in the system.

The total number of legs on the farm is given as "4x + 2y". What's more, we are told that the total number of animals is "x + y".

4x + 2y means the total legs

x + y = the number of total of animals

We'll now use the Elimination method to identify x and y.

One method is to multiply the first equation by 2 and subtract it from the second:

(2) * legs = (4x + 2y)

2x + 2y = the total number of animals

Legs = (2x + 2y)

0 = number of legs - 2 * the amount of animals

When we solve for the number of animals we get:

animal count = legs / 2

So, if we connect this back into either equation, we can find x and y.

Let's look at the first equation:

4x + 2y means the total legs

legs / 2 = x + y

When we substitute legs / 2 in the second equation for "number of animals," we get:

legs / 2 = x + y

Now we'll use substitution to find x. In the first equation, we'll substitute x = legs / 2 - y:

4x + 2y means the total legs

legs = 4(legs / 2 - y) + 2y

legs = 2 * legs - 4y + 2y

2 times legs = legs

There are no solutions due to this contradiction, and no such farm exists under the given conditions.

As a result, the answer to the system of equations is that no such farm occurs under the given conditions.

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So y = 2x + 2 is the equation of a line parallel to line ef and includes point (0, 2).

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

Since line ef has a slope of 2, any line parallel to it will also have a slope of 2. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. To find an equation of a line parallel to line ef that contains point (0, 2), we need to find its y-intercept.

We can use the point-slope form of a line to find the equation of the line: y - y1 = m(x - x1)

Plugging in the point (0, 2) and the slope of 2, we get:

y - 2 = 2(x - 0)

y - 2 = 2x

y = 2x + 2

So, the equation of a line parallel to line ef and containing point (0, 2) is y = 2x + 2.

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If the area to the right of z, given that it is a standard normal random variable, is 0.1112, then the value of z is 1.22. The answer is C.

A standard normal random variable has a mean of 0 and a standard deviation of 1. The area to the right of a value for a standard normal random variable can be found using a standard normal table or a calculator with a normal cumulative distribution function (CDF).

Given that the area to the right of z is 0.1112, we can use a standard normal table or normal CDF calculator to find the value of z such that the area to its right is 0.1112. This value will be approximately equal to 1.22.

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a) 60 selection excluded Connie. b) 24 selections in which neither Ben nor Francisco is an officer. c) 24 selection in which both Ben and Francisco are officers. d) 36 selections in which Dolph is an officer or Francisco is not an officer. e) 20 and 60 in which Dolph either selected or not.  

A chairperson, secretary, and treasurer are to be chosen by a six-person committee made up of Alice, Ben, Connie, Dolph, Egbert, and Francisco. Their Calculations are a) 5 × 4 × 3 = 60. (b) 4 × 3 × 2 = 24 (c) 3 × 2 × 4 = 24 (Ben can choose from 3 slots, Francisco has 2 spots remaining to choose from, and there are 4 people available for the final position.)  (d) 3 × 4 × 3 = 36 (Dolph is eligible for three seats, after which there are four more members to pick from.) Part e will be the sum of 2 cases: Case 1 : Dolph is a chairperson. Number of ways = 1 × 5 × 4 = 20. Case 2: Dolph isn't elected. Number of ways for this = 5 × 4 × 3 = 60. Hence a total of 80 selection for part e.

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The population size after 5 hours is 28.2 million.

Exponential functions are functions where the independent variable, x is in the exponent.

Given that,

Constant relative growth rate, r = 0.4419

Initial population, A = 3.1 million

Time = 5 hours

P = A e^(rt)

P = 3.1 e^(0.4419 × 5)

  = 3.1 × 9.111

  = 28.245 million ≈ 28.2 million

Hence the population after 5 hours will be 28.2 million.

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The given expression 5 subtracted from three times any number is written as 3x - 5

Algebra is the system of computation using letters or other symbols to represent numbers.

5 subtracted from three times any number.

Let

the unknown number= x

(3 × x) - 5

= 3x - 5

Therefore, 3x - 5 is the algebraic representation of the expression.

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Answer:

Similar by AA/SAS

Step-by-step explanation:

20.8/8 = 23.4/9 = 2.6

So, the bottom of the smaller triangle is parallel the bottom of the larger one (Thales' theorem)

So, corresponding angles are equal and hence, they are similar by AA similarity.

Note: As sides are given, similarity can also be proven by SAS.

Answer:

Below

Step-by-step explanation:

Volume of a cylinder :    Find the area of the end....then multiply by height

Volume = pi r^2     *   h

                 3.14 (6)^2  mm)   *  6 mm = 678.24 mm^3

When firing a handgun , you should hold the handgun (d) at arm's length , from the body .

When firing a handgun, it is recommended to hold it at arm's length, from your body. This allows for proper control and aim of the firearm, as well as providing a buffer between you and the potential dangers of the discharge.

Holding the handgun too close to your body can also interfere with accuracy and control, as your arms may obstruct the movement of the gun. It's important to follow manufacturer guidelines and seek proper training and follow all safety procedures when handling handgun to ensure responsible and safe use.

The given question is incomplete , the complete question is

When firing a handgun, how far should you hold it from your body?

(a) 9 inches

(b) one foot

(c) eighteen inches  

(d) at arm's length

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The angle of elevation of the observer to the kite is around 30 degrees

The hypotenuse in the given question is 405 feet, while the height of the kite from the ground is 210 feet.

It is also stated that the kite's height from the ground does not change.

The tangent function may be used to calculate the angle of elevation.

tan(angle of elevation) = height of the kite / horizontal distance to the kite

Since the height of the kite is 210 feet and the horizontal distance (the length of the kite string) is 405 feet, we can calculate the angle of elevation:

Let Ф be the angle of elevation

tan(angle of elevation) = 210/405

Ф = tan-1(210/405)

Ф = tan-1(0.516)

Ф = roughly 30 degrees

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Yes, it is widely known that 100-200 high-frequency words account for about 50% of the words used in school texts. This highlights the importance of explicitly teaching these words to students in order to improve their reading fluency and comprehension.

Among these high-frequency words, almost 25% are permanently irregular, meaning that they do not follow standard spelling and pronunciation rules. This makes it even more important for students to learn these words through direct and systematic instruction, as they can greatly impact their reading and writing abilities. By focusing on these high-frequency words, educators can help students build a strong foundation of vocabulary knowledge, which can lead to improved reading outcomes and success in school.

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The value of x that makes ABC~ ADEF is 4

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

AABC~ ADEF.

So, we have the following equivalent ratio

6 : 2x = 24 : 32

So, we have

2x/6 = 32/24

Make x the subject

So, we have the following representation

x = 6 * 32/(24 * 2)

Evaluate the expression

x = 4

Hence, the value is 4

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The standard normal distribution is a normal distribution of standardized values called z-scores.

A z-score is measured in units of the standard deviation. If a random variable is normally distributed and follows the parameters mean (mu) and standard deviation (sigma), the z-score is calculated as the difference between the value of the random variable and the mean divided by the standard deviation . The cumulative distribution function (CDF) of a standard normal variable is used to find the fraction of scores that lies between two given values. To determine the fraction of scores, one can use the CDF to find the area under the standard normal distribution curve between the given values.

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Answer:

98

Step-by-step explanation:

180 means supplementary so we subtract that by 82 which gives us 98

Answer:

Below

Step-by-step explanation:

The two supplementary angles sum to 180 °

180 - 82 = other angle = 98°

Answer:

Step-by-step explanation:

15+.31x ≤ 93

Note that the PQ table are attached according. Note that Heather's mom's statement is written in symbolic form as: ~p -> ~q.

Note that in situation 1:
according to the P Q table, the statement ~p -> ~q is false because the row where p is false and q is true (which corresponds to Heather not putting money into the savings account each month but still being able to take a vacation) evaluates to false.

While in Situation 2:

From the P Q table, the statement ~p -> ~q is false because the row where p is false and q is true (which corresponds to Heather not putting money into the savings account each month but still being able to take a vacation) evaluates to false.

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The total distance covered while swimming and running for a total of 3 hours is 45 kilometers.

In mathematics, the term "total" refers to the sum of two or more values. It is used to describe the combined or complete amount of a quantity. The total can be calculated by adding together all the individual values in a set or series.

The distance x can be calculated by using the formula:

distance = rate * time

For swimming, the rate is 5 kilometers per hour, and the time is t₁. So, the distance covered while swimming is:

d₁ = 5 * t₁

For running, the rate is 20 kilometers per hour, and the time is t2. So, the distance covered while running is:

d₂ = 20 * t2

The total time for swimming and running is 3 hours, so:

t₁ + t₂ = 3

The total distance covered while swimming and running is x, so:

x = d₁ + d₂

Substituting the values of d₁ and d₂, we get:

x = 5 * t₁ + 20 * t₂

Now, substituting the value of t₁ + t₂ = 3, we get:

x = 5 * t₁ + 20 * (3 - t₁)

Expanding the equation, we get:

x = 5 * t₁ + 60 - 20 * t₁

Combining the like terms, we get:

x = -15 * t₁ + 60

Substituting the value of t₁ = 3 - t2, we get:

x = -15 * (3 - t2) + 60

Expanding the equation, we get:

x = 45 - 15 * t₂

Now, we have to find the value of t₂ such that x is maximum.

Taking the derivative of x with respect to t₂, we get:

dx/dt₂ = -15

So, t₂ is a decreasing function of x. Hence, when t₂ is maximum, x is also maximum.

As t₂ cannot be negative, the maximum value of t₂ is 0. Hence,

t₂ = 0

Substituting the value of t₂ = 0 in the equation x = 45 - 15 * t₂, we get:

x = 45

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Answer:

Hi Elm!

Step-by-step explanation:

In a polygon, the sum of the measures of the interior angles and the sum of the measures of the exterior angles of adjacent angles are related. Specifically, the sum of the measures of the interior angles of a polygon is equal to (n - 2) times 180 degrees, where n is the number of sides in the polygon. For a given interior angle and its adjacent exterior angle, the measure of the exterior angle is equal to the sum of the interior angle and 180 degrees.

Step-by-step explanation:

I hope this helps a bunch! Make sure to rephrase!

The youngest child is Jade.

The expression that represents Jane's age is 2n.

The oldest child is Jem.

Jade is 12 years old

The equation that represents the sum of ages is 5n - 5 = 55.

Jade's age = n

Jane's age = 2 x n = 2n

Jem's age = 2n - 5

Sum of the ages:

n + 2n + 2n - 5 = 55

5n - 5 = 55

Jade's age can be determined using the above equation:

5n = 55 + 5

5n = 60

n = 60 / 5

n = 12

To determine Jane and Jem's age, substitute for n in the equation that represents their ages.

Jane's age = 2 x 12 = 24

Jem's age = 2(12) - 5

= 24 - 5

= 19

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Zeke's average speed in mph for the first 20 minutes was 3 mph.

To find Zeke's average speed in mph for the first 20 minutes, divide the distance traveled by the time it took him to travel that distance:

1.0 mile / 20 minutes = 0.05 miles per minute

Since there are 60 minutes in an hour, to convert minutes per mile to miles per hour, multiply by 60:

0.05 miles per minute * 60 minutes per hour = 3 mph

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The simplified form of the expression is (x - 2) / (x - 3).

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given expression is (1 - [tex]\frac{2}{x}[/tex] ) / (1 - [tex]\frac{3}{x}[/tex] ).

Cross multiplying both the denominator and numerator of the expression,

1 - [tex]\frac{2}{x}[/tex] = (x - 2) / x and 1 - [tex]\frac{3}{x}[/tex] = (x - 3) / x

(1 - [tex]\frac{2}{x}[/tex] ) / (1 - [tex]\frac{3}{x}[/tex] ) = [(x - 2) / x] / [(x - 3) / x]

                      = (x - 2) / (x - 3)

Hence the expression can be simplified as (x - 2) / (x - 3).

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