For the functions f(x)=2x4+2x3−x2+2x+3 and g(x)=x+1 find (fg)(x) and (fg)(−4)

The answer is -4, -1, 1, 3, 3.9, 3.99, 3.999.

Given,

In the question:

To see the figure:

To select the values that makes the inequality  s ≤ 4 true.

Number table are given in figure.

To see the figure and analysis.

Now, According to the question;

To make the inequality s ≤ 4 true.

The selected value must be less than 4 {Properties of Inequality}

The values are sorted from small to large:

So, The answer is -4, -1, 1, 3, 3.9, 3.99, 3.999.

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 a) the constant of proportionality multiplies every actual linear    dimension

 b)  height of a can of fruit juice is 3.85 inches high

What is Proportionality?

The term proportionality describes any relationship that is always in the same ratio.

Explanation for answer:

Since the desire is to have students look twice as tall, we expect the constant of proportionality to be [tex]\frac{1}{2}[/tex].

Instead, we're told that the stage manager is using a height of 44 inches to represent an 80-inch door.

This means their constant of proportionality is [tex]\frac{40}{80} = 0.55[/tex]

a) Any new props can be scaled by this factor (0.55) to find their height on set.

b) A 7-inch can would be scaled to [tex]7\times 0.55 = 3.85\ inches[/tex]

Question: The school's theater club is building sets that will make ordinary students look like giants. The actors need a door, a table, and a stool that will make them look almost twice as tall!

DOOR: actual height is 80 inches and Height on Set is 44 inches

TABLE: actual height is 28 inches

STOOL: actual height is 18 inches

How can the stage manager use the constant of proportionality to find the dimensions of any new props the director requires?

What should the height of a can of fruit juice used as a prop be if its actual height is 7 inches? Show your work.

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The Z distribution also referred to as the standard normal distribution is the distribution that we would have to use here.

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.

By transforming the values of any normal distribution into z-scores, it is possible to standardize it. Z-scores indicate the number of standard deviations from the mean that each value falls within.

This is the z distribution given that the value of n is more than 30.

We have to make use of z when n which is the number of samples  is greater than 30.

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Answer:

kind423

Step-by-step explanation:

Answer: 2(1.9)+1.30x<10

Step-by-step explanation:

Orange= $1.30/lb

Pear= $1.90/lb

$1.30/lb = $y/2lb

y=1.30*2

y=$2.6 for 2lb of orange

So

She spent

2(1.30)+1.90x< $10

2.6+1.90x<10

1.90x<10-2.6

1.90x<7.4

x<7.4/1.90

x<3.89

According to 2(1.30)+1.90x< $10

2.6+1.90*3.89<10

9.991<10

Answer: 1/6

Step-by-step explanation:

To subtract fractions, you must have a common denominator. To do this, the common multiple of 3 and 2 is 6. So 2/3 is multiplied by 2/2 and 1/2 is multiplied by 3/3. The multiplication is valid since we multiplied by one, it didn't alter the value but rather it put it into an alternate, equivalent form.

The value of x in the rhombus is 24 units.

According to the question,

We have the following information:

LM = 2x - 9 and KN = x + 15 in rhombus KLMN.

Now, we know that in a rhombus opposite sides are equal. In this case, LM and KN are opposite sides.

So, we have the following expression:

2x-9 = x+15

Adding 9 to both sides of the equation:

2x = x+15+9

2x = x+24

Subtracting x from both sides of the equation:

2x-x = 24

x = 24

Hence, the value of x for the given rhombus is 24 units.

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Answer:

x=y , x-3y=4. x = y x = y , x − 3y = 4 x - 3 y = 4. Replace all occurrences of x x with y y in each equation. Tap for more steps... −2y = 4 - 2 y = 4. x = y x = y. Divide each term in −2y = 4 - 2 y = 4 by −2 - 2 and simplify. Tap for more steps... y = −2 y = - 2.

Step-by-step explanation:

Just smart

Answer:

C) 29

Step-by-step explanation:

1st equation - 2nd equation,

x+y - (x-3y) = 40-(-4)

x+y-x+3y = 40+4

4y = 44

y = 44÷4

y = 11

substituting y into the first equation,

x + 11 = 40

x = 40-11 = 29

answer is C

hope it helps. :)

Answer:

Step-by-step explanation: First since the cookies are 36.44 dollars and the total spent is 102.44, use 102.44-36.44= 66 dollars

66/11=6 cupcake boxes

6 cupcake boxes + 1 cookie box = 7 boxes in total

The 14th term of the geometric sequence will be -1220703125.

What is geometric sequence?

The sequence where each word is varied by another by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.

Geometric Progression (GP), a form of sequence in mathematics, is a series in which each subsequent term is created by multiplying each preceding term by a set integer, known as a common ratio. A geometric sequence of integers that follows a pattern is another name for this development.

[tex]1*(-5)^{13}[/tex]The terms are given, 1,-5,25

a = 1

r = -5/1 = -5

The 14th term will be= [tex]ar^{13}[/tex]

= [tex]1*(-5)^{13}[/tex]

= -1220703125

Hence, the 14th term of the geometric sequence will be -1220703125.

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The time that the three buses will next arrive at the station, given the time between their individual arrivals is 10 am.

Service A arrives every 15 minutes. Service B arrives every 20 minutes. Service C arrives every 30 minutes.

The goal is to find the time when all services arrive at the same time. This can be found by finding the LCM of all three times. This will show the shortest time till all services arrive.

The LCM of 15 minutes, 20 minutes, and 30 minutes is 60 minutes.

The three bus services will arrive at the same time in 60 minutes which is:

= 9 am + 60 minutes

= 10 am

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Using the t-distribution, it is found that:

a)

b)

The bounds of the confidence interval are given according to the rule presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are listed as follows:

The margin of error of the interval is:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

Then the interval can be interpreted as the sample mean plus/minus the margin of error.

For the confidence interval in this problem, using a calculator, the parameters are given as follows:

[tex]\mu = 1280.1111, s = 33.5799, n = 9[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 9 - 1 = 8 df, is t = 1.86.

Then the margin of error of the interval is:

M = 1.86 x 33.5799/sqrt(9) = 21.

Then the bounds of the interval are:

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Answer:

Step-by-step explanation:

I

Step-by-step explanation:

T2= -6

T5=750

ar=-6

ar4=750

both a's cancel each other

we have;

r=-6

r4=750

r4-1(The law of indices) =750

r3=750

r=3√750

r=9.1

Answer:

-4 is not a solution to the following equation.

Step-by-step explanation:

It you replace x with -4 on both sides of the equation you get -2=-12 and they are not equal to each other. Therefore, -4 is not a solution to the equation.

The distance (in ft) that the car will travel in the first 10 seconds is 16.8 feet.

Speed describes how accelerated something or somebody is moving. If you know the distance traveled and the time it took, you can calculate the average speed of an object.

The speed formula is speed = distance/time.

We have been given certain vehicles that can accelerate from a standing start to a speed of v(t) = −0.24t² + 12t feet per second after t seconds (for 0 ≤ t < 30).

Then the distance that it will travel from its starting point in the first t seconds is;

[tex]\int\limits^{30}_b {v(t) } \, dx \\\\\\\int\limits^{30}_b {-0.24t^2 + 12t } \, dt \\\\\\\int\limits^{30}_b {-0.48t + 12} \, dt \\\\-0.48(30) + 12\\\\14.4 + 12 = 26.4[/tex]

At zero it will be 12 feet.

b. the distance (in ft) that the car will travel in the first 10 seconds.

-0.48(10) + 12 = 16.8 feet.

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The possible cards can be made 6719448100.

What is permutation & combination?

Subsets of a set can be created in two separate ways combination and permutation. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.

We have,

Letters must only be consonants = 26 - 5.

So, the total number of consonants are 21.  

There are 21 choices for the first letter, 21 choices for the second letter,  21 choices for the thirds letter,  21 choices for the fourth letter. For each of these letters, therefore 21 × 21 × 21 × 21 = 194481 possible pairs of letters.

There are 10 possibilities for the first digit & 10 possibilities for the second. therefore there are 10 x 10 = 100 different numbers.

Combining these results, it follows that there are 67194481 x 100 =  6719448100 different cards.

Hence, The possible cards can be made 6719448100.

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12 ounces of water.

Total mass of the solution: 30 ounces.

Total mass of salt (solute): (30*0.07)= 2.1 ounces.

Total mass of water (solvent): (30*0.93) 27.9 ounces.

2. Find an equation that relates amount of water and percentage of salt.

Since we know that the amount of salt is 2.1 ounces, and it has to remain constant, we have to create a function such that the variable is the amount of water and it gives us the percentage of solution we are looking for. The function should look like this:

[tex]\frac{2.1}{x} =0.05[/tex]; where x is the mass of the water in the solution.

Side note: The number "0.05" is 5% converted into a decimal.

[tex]\frac{2.1}{x} =0.05\\ \\\frac{x}{2.1} =\frac{1}{0.05} \\ \\x=\frac{2.1}{0.05} \\ \\x=42[/tex]

42 would be the total amount of ounces the solution should have in order to be a 5% solution. Therefore, 12 ounces (42-30) have to be added.

12 ounces of water have to be added to this solution in order to make it a 5% solution, where 2.1 ounces is salt and 39.9 is water.

On average, Jaya drinks 0.46 ounces glasses of water does she drink in one hour.

Average:

Average refers the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Given,

On average, Jaya drinks of a 6-ounce glass of water in 13 hours.

Here we need to find the number of glasses of water does she drink in one hour.

Let x be the number of glasses of water does she drink in one hour.

We know that, Jaya drinks of a 6-ounce glass of water in 13 hours.

So, in order to find the average we have to divide the number of glasses by the time taken.

So, it can be written as,

=> 6/13

=> 0.46

Therefore, for one hour Jaya drinks 0.46 ounces of water.

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Answer:

d = 15

Step-by-step explanation:

(-5, 4), (4, -8)

(x₁, y₁)   (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(4 - (-5))² + (-8 - 4)²

d = √(4 + 5)² + (-12)²

d = √(9)² + (-12)²

d = √81 + 144

d = √225

d = 15

I hope this helps!

In  linear equation, option A,B,C are equal expect D .

What in mathematics is a linear equation?

The given equation is  3x -4y =21.

A.  (11, 3)

3(11) - 4(3) = 21

21 = 21 > equal

B.  (7, 0)

3(7) - 4(0) = 21

21 = 21 > equal

C.  (−1, −6)

3(-1) - 4(-6) = 21

21 = 21 > Equal

D.  (−3, 3)

3x – 4y = 21

3(-3) - 4(3) = 21

-21 = 21 > not equal

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The number of minute talk's, text message's and picture message's are 128, 72 and 15 respectively.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Enrique who has a pay-per-use plan on his cell phone. It costs $0.10 per minute talk, $0.20 per text message, and $0.25 per picture message. His total bill last month was $30.95. The total number of text and picture messages sent was 87. The cost for the use of minutes was $1.60 less than the cost of the text messages

Assume that [x], [y] and [z] represents the number of minute talk's, text message's and picture message's respectively. Then -

0.1x + 0.2y + 0.25z = 30.95         ..[1]

y + z = 87           ..[2]

0.1x = 0.2y - 1.6     ...[3]

We can write Eq[1] as -

0.2y - 1.6 + 0.2y + 0.25z = 30.95  

z = 87 - y

0.2y - 1.6 + 0.2y + 0.25(87 - y) = 30.95  

Solving, we get y = 72.

So z = 87 - 72 = 15

and

0.1x = 0.2 x 72 - 1.6

0.1x = 14.4 - 1.6

x = 128

Therefore, the number of minute talk's, text message's and picture message's are 128, 72 and 15 respectively.

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Answer:

40%

Step-by-step explanation:

Answer:

D. The denominator means three out of five are shaded

The total middle school enrollment is 889 for the given city.

According to the question,

We have the following information:

Three middle schools in a city had enrollments of 296,315 and 278.

Now, the total middle school enrollment can be easily found by adding the enrollments in three middle schools of the city.

So, we have the following expression:

Total middle school enrollment = 296+315+278

(We already know that the digits are first added from the right hand side and then we move to the left hand side.)

Total middle school enrollment = 889

Hence, the total middle school enrollment is 889 for the given city.

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Using the stem-and-leaf plot, the mean of the data is 3.85.

It means the average feet that the heavy ball was thrown is 3.85 feet, which is the typical number.

To find the mean of a data set that is represented by a stem-and-leaf plot, first, list out all the data values that are represented on the stem-and-leaf plot, add all the values and divide by the number of values that was represented on the stem-and-leaf plot.

Given the stem-and-leaf plot above, using the key, the data points represented are:

2.0, 2.1, 2.4, 3.1, 3.2, 3.6, 4.1, 4.3, 4.7, 5.1, 5.1, 6.5

Mean = [2.0 + 2.1 + 2.4 + 3.1 + 3.2 + 3.6 + 4.1 + 4.3 + 4.7 + 5.1 + 5.1 + 6.5]/12

Mean = 46.2/12

Mean = 3.85 feet

The mean of 3.85 feet means that the average distance that the heavy ball was thrown in feet is 3.85.

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The Answer is:

3.85 ft.
* *

-

Step-by-step explanation:

that means that

$37.45 = 107%

as the price was 100% base price + 7% tax.

1% = 107%/107

100% = 1% × 100 = 107% × 100 / 107

so, the basic price (the "original cost") is

37.45 × 100/107 = $35.00

Answer: first graph

Step-by-step explanation:

The number of voters that each volunteer call is 18.

It is important to note that voting is done to choose a particular person during elections.

In this case, the candidate for mayor is calling 882 registered voters to remind them about the upcoming election and the candidate has 49 volunteers.

Since they gave same number of voters, this will be:

= Number of voters / Number of volunteers

= 882 / 49

= 18

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If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.

What is a value function?

The value function represents the optimal payoff of the system over the interval [t, t1] when started at the time- t state variable x(t)=x.

What is a variable?

A quantity that could take on any of a number of different values. : a sign that denotes a variable. : anything has a range. : a variable that might alter in a scientific experiment.

Here, we have

x = -4 and y = 3

then by putting the value of a function in a given equation, we get

1/2*(-4) + 3*(-4)*(3)²

= -110

Hence, If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.

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Answer:

Line v:  y = x + 5

Step-by-step explanation:

Given two lines are perpendicular and the equation of one line, we use the following formula to find the slope of the other line where m1 is the slope of the line we're given and m2 is the slope of the line we want to find:

[tex]m_{2}=-\frac{1}{m_{1} }\\m_{2}=1[/tex]

The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept.  

Therefore we plug in our slope and the point (-3, 2) to find the y-intercept of line v:

[tex]2=1(-3)+b\\2=-3+b\\5=b[/tex]