For all real values of x if f((x)=(x-3)^2 and g(x)=(x+3)^2 what is f(x)-g(x)?

Answer:

Step-by-step explanation:

We know that:

Then 6 gallons is:

Add 3 quarts to get total:

Answer:

27 quarts

Step-by-step explanation:

Now we have to,

→ find how many quarts does 6 gallons 3 quarts of paint measure.

Formula we use,

→ 1 gallon = 4 quarts

Now the required solution will be,

→ (6 × 4) + 3

→ 24 + 3

→ 27 quarts

Hence, the answer is 27 quarts.

The equation for the representation of the given situation will be

y = x - 0.54x, and the graph of the equation should only be in the first quadrant because x and y is representing a price which can't be negative.

An equation is a statement that says that the value of two mathematical expressions is equal.

Given that, a cinema sends out a coupon for ​54% off the price of a ticket.

The equation for this situation will be y = x - 0.54x,

And the line of this equation will always lie in the first quadrant because values of x and y in the first quadrant are always positive, and here x and y are prices which can't be negative.

Hence,  the graph of the equation should only be in the first quadrant because x and y is representing a price which can't be negative and The equation for the representation of the given situation will be

y = x - 0.54x

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Answer: 4/5 or 0.8

Step-by-step explanation:

[tex]1\frac{1}{4}[/tex] * [tex]\frac{4}{5}[/tex] = [tex]\frac{1}{1}[/tex] = 1

[tex]1\frac{1}{4}[/tex] is also equal to 1.25.

1.25 * 0.8 = 1

Answer:

4/5

Step-by-step explanation:

because 4 is half of a half two fourths are a half and 4/4 are 1 whole

Using differentiation, 36 feet is the maximum height, in feet, that the object will reach.

In the given question,

An object is launched directly in the air at a speed of 32 feet per second from a platform located 20 feet above the ground.

The position of the object can be modeled using the function [tex]f(t)=-16t^2+32t+20[/tex], where t is the time in seconds and f(t) is the height, in feet, of the object.

We have to find the maximum height, in feet, that the object will reach.

The given function is [tex]f(t)=-16t^2+32t+20[/tex].

To find the maximum height we differentiate the function with respect to t

[tex]\frac{df}{dt}=-32t+32[/tex]

As we know that at the maximum point the slope of the tangent is zero.

So df/dt = 0

So -32t+32=0

Subtract 32 on both side

-32t+32-32=0-32

-32t=-32

Divide by -32 on both side

-32/-32 t = -32/-32

t=1

Therefore at t=1 the function have maximum value. So we put t=1 in the given equation.

[tex]f(1)=-16(1)^2+32\times1+20[/tex]

f(1)=(-16)×1+32×1+20

Simplifying

f(1)=-16+32+20

f(1)=36 feet.

Hence, 36 feet is the maximum height, in feet, that the object will reach.

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The probability of picking a shirt that is red or striped is 2/3.

Given, that a drawer of shirts contains 3 solid red, 2 striped red, 4 solid blue, and 3 striped green.

We have to find the probability of picking a shirt that is red or striped,

P(R ∪ S) = P(R) + P(S) - P(R∩S)

where, R be the event that the shirt is red.

and S be the even that the shirt is striped.

P(R) = 5/12 (as, there are 5 red shirts)

P(S) = 5/12 (as, there are 5 striped shirts)

P(R∩S) = 2/12 (as, there are 5 striped red shirts)

P(R ∪ S) = 5/12 + 5/12 - 2/12

P(R ∪ S) = 8/12

P(R ∪ S) = 2/3

The probability of picking a shirt that is red or striped is 2/3.

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Answer:

15 more appetizers

Step-by-step explanation:

A restaurant has 60 menu items. Of these menu items, main dishes outnumber appetizers by a ratio of 4:1. How many more appetizers would the restaurant have to add to the menu to bring the ratio to 2:1?

at a ratio of 4e:1a and having 60e: there are (60/4=15) 15 appetizers

at a ratio of 2e:1a and having 60e: there are (60/2=30) 30 appetizers

Because they already have 15 appetizers, they will need:

30 appetizers - 15 appetizers  = 15 more appetizers

Answer:

3

Step-by-step explanation:

Margin did the successful candidate win is 5375 - 4300 = 1075.

Given:

In an election for a corporation seat, there were two candidates. A total of 9,791 votes were polled.

116 votes were declared invalid. The successful candidate got 5 votes for every 4 votes his opponent had.

Number of valid votes = 9791 - 116 = 9675.

Let the number of votes of successful candidate = 5x

Let the number of votes of opponent = 4x

5x + 4x = 9675

9x = 9675

divide by 9 on both sides

x = 9675/9

x = 1075

Hence the votes for successful candidate = 5*1075 = 5375.

votes for opponent = 4*1075 = 4300.

Margin by which the successful candidate wins = 5375 - 4300 = 1075.

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Answer:

It is A

Step-by-step explanation:

I have brainly tutor and had that exact question

Eve's data is a random sampling since she picked the participants randomly.

A simple random sample is a subset of a population chosen at random. This sampling strategy gives each person of the population an exact equal chance of being chosen, reducing the likelihood of selection bias.

To be considered a truly random sample, every subject in your target demographic must have an equal chance of being chosen. Conducting a study to estimate the length of time college students workout at your campus each week is an example of breaking this assumption.

In this case, Eve needed to collect the eye color of 50 random people for a high school statistics project and she felt more comfortable collecting the data from 20 arbitrary classmates, 12 arbitrary neighbors, and 18 arbitrary members of her bible study group. In this case, she picked them randomly. In Adam's case, it doesn't necessarily have to be strangers.

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The surface area of the cone is  282.6 [tex]in^2[/tex].

What is surface area of cone?

  The region that a cone's surface occupies in three dimensions is known as the surface area of a cone. The whole area a cone's surface covers is known as the cone's surface area. The overall surface area will include the cone's lateral and base surfaces. A three-dimensional solid construction with a circular base is referred to as a cone. A cone can be thought of as a collection of irregularly shaped circular discs that have been stacked on top of one another while maintaining a constant ratio between the radii of the adjacent discs. It is the total of the cone's lateral area and base area.

Here the given ,

=> Height h= 12in

=> Radius r = 5 in

Using surface area of cone formula,

=> Surface area SA = [tex]\pi[/tex]r(r+ [tex]\sqrt{r^2+h^2}[/tex]) square unit.

=> surface area SA = 3.14*5(5+[tex]\sqrt{12^2+5^2}[/tex])

=> surface area SA = 15.7(5+[tex]\sqrt{144+25}[/tex])=15.7(5+13)

=> surface area SA = 15.7*18=282.6 [tex]in^2[/tex]

Therefore surface area of the cone 282.6 [tex]in^2[/tex].

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The solution set for the inequality is (-3, 3)

Here we have the absolute value inequality

|2x| - 6  < 0

To solve this, we need to isolate the variable, which in this case is x.

Adding 6 in both sides we get:

|2x| -6 + 6 < 0 + 6

|2x| < 6

This can be decomposed in the inequality:

-6 < 2x < 6

Now to competely solve the inequality, we will divide both sides by 2, so we get:

-6/2 < 2x/2 < 6/2

-3 < x < 3

So the solution set is (-3, 3)

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Abdiel's total if he uses a coupon for 12% off the subtotal and leaves a 25% tip before the discount is $27.46

The correct answer option is option B

Amount of total after discount = 12% × $24.30

= 0.12 ×24.30

= $2.916

Amount of abdiel's tip = 25% × $24.40

= 0.25 × 24.30

= $6.075

Abdiel's total after discount before tip = (Amount of abdiel's tip + Abdiel's subtotal) - Amount of total after discount

= (6.075 + 24.30) - $2.916

= $30.375 - $2.916

= $27.459

Approximately,

$27.46

Therefore, the total amount Abdiel paid after discount before tip is $27.46

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1/2 - 5i/4 is the simplified form of the expression ( 5 + 2i ) / 4i.

Given the expression in the question;

( 5 + 2i ) / 4i

To simplify, multiply the numerator and denominator by the conjugate of 4i

( 5 + 2i ) / 4i

( 5 + 2i ) × i / 4i × i

( 5 + 2i )i / 4ii

Apply distributive property

( 5i + 2ii ) / 4ii

Not that i × i = i² = -1

( 5i + 2i² ) / 4i²

( 5i + 2( -1 ) ) / 4( -1 )

( 5i - 2 ) / -4

( -2 + 5i ) / -4

Split the fraction

-2/-4 + 5i/-4

1/2 - 5i/4

Therefore, the simplified form is 1/2 - 5i/4.

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The five number from the box plot is presented as follows:

A box and whisker plot shows five things of a distribution, listed as follows:

The value that 75% of the measures are larger than is found in the first quartile, which is the median of the data set's lowest 50% of measurements.

The data set's maximum value.

These numbers, which make up the five number summary, are the values highlighted on the box plot from left to right, from the minimum value to the greatest value, passing through the first quartile, the median, and the third quartile.

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The equation to model the situation is given below. And the months will the populations of the towns be​ equal will be 12.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A town's populace is 43,200. Around 125 individuals move out of the town every month. Every month, 175 individuals on the normal move into town. A close by the town has a populace of 45,900. It has nobody moving in and a normal of 175 individuals moving away consistently.

Let y be the total population and x be the number of months. Then the equations are given as,

y = (175 - 125)x + 43200

y = 50x + 43200           ...1

y = -175x + 45900        ...2

From equations 1 and 2, then we have

50x + 43200 = - 175x + 45900

50x + 175x = 45900 - 43200

225x = 2700

x = 2700 / 225

x = 12

The months will the populations of the towns be​ equal will be 12.

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Answer:

7.8

Step-by-step explanation:

Switch 8 and 7, it round to 8 and end in tenths.

Answer:

7.8

Step-by-step explanation:

7.8 rounds to 8, because 8 is greater than 5, and then we end in the tenths place.

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

The sum of first 50 terms of the sequence a(n) = 3n + 2 is  3925

In this question, we have been given a sequence a(n) = 3n + 2

We need to find the sum of the first 50 terms of the sequence

a(1) = 3 + 2

      = 5

a(2) = 6 + 2

      = 8

a(3) = 9 + 2

      = 11

a(4) = 12 + 2

      = 14

...

Given sequence is arithmetic sequence with common difference d = 3 and the first term a = 5

Using the formula for the sum of first n terms of AP

Sum of n terms of A.P. = n/2[2a + (n - 1)d]

For n = 50

S(50) = (50/2) * [2(5) + (50 - 1)3]

S(50) = 25 * [10 + (49 * 3)]

S(50) = 25 * 157

S(50) = 3925

Therefore, the sum of first 50 terms of the sequence a(n) = 3n + 2 is  3925

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Answer: x < 3

Explanation: Once you reach step 3, you divide -2 on both sides. -2x cancels out, and -6 divided by -2 is 3

Answer: y = -x - 8

Step-by-step explanation:

    Slope-intercept form is given in y = mx + b where m is the slope and b is the y-intercept.

    We can see our b, the y-intercept, is -8 since the line intercepts the y-axis at (0, -8).

    For our slope, we can see that the line moves down one and right one for a slope of 1/1=1. Since it's moving downwards, the slope is -1.

    Now, we will write the full equation:

y = -x - 8

As per the proportional relationship, the constant of the proportionality is 1/3

Proportional relationship

A relationship is said to be proportional if each pair of data values are related in the same way, by multiplying by a factor.

The standard form of proportional relationship is written as.

y = k x

where k refers the constant of proportionality.

Given,

The table shows the proportional relationship between h and j.

Now, we need to find the constant of proportionality from h to j and we have to express the answer as a fraction in reduced terms.

We know that the standard form of the proportionality is written as,

y = k x

So, here y takes the value of j and x takes the values of h.

Then we have to take the points as (18, 6) and apply t on the standard form to get the value of k,

=> 6 = k (18)

Here we need the value of k, so move the number to the other side then we get,

=> k = 6/18

When we reduce this, then we get,

=> k = 1/3

Therefore, the constant of proportionality is 1/3.

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The probability that the second ball drawn is yellow is of:

0.2926 = 29.26%.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

In this problem, the possible outcomes to obtain a yellow ball on the second draw are:

Then the probability of an yellow ball on the second draw is given as follows:

p = (3/11) x (3/11) + (8/11) x (3/10) = 0.2926 = 29.26%.

The problem asks for the probability that the second ball drawn is yellow.

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The completion of the inventory table is as follows:

A = $48

B = $264

C = $420

D = $304.

The above inventory table is completed using some of the inventory methods including:

FIFO (First-in, First-out) assumes that the physical flow of goods sold follows the chronological order of acquisition.

LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.

The weighted-average method uses the average cost of goods to determine both the ending inventory and the cost of goods sold.

Specification Identification does not base allocating the costs of goods sold and ending inventory on any assumptions. Instead, it uses specific costs.

                                     Units    Unit Cost    Total Cost

Jan. 1      Beg. Inventory   8        $6.00            $48 ($6 x 8)

Apri. 11    Purchases        24       $11.00          $264 ($11 x 24)

May 17    Purchases        30      $14.00          $420 ($14 x 30)

Dec. 5    Purchases         19      $16.00          $304 ($16 x 19)

Total                                 81                         $1,036

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Using the Quotient Rule, the differentiate the function with respect to x is [tex]\frac{4x^3}{9x^8+24x^4+16}[/tex] .

In the given question,

We have to differentiate the given function with respect to x.

The given function is [tex]y=\frac{x^4+1}{3x^4+4}[/tex]

We have differentiate with respect to x.

The given function is in fraction format. So solving the given expression we use Quotient Rule

According to Quotient Rule

"A method for recognizing issues where one function is divided by another is the quotient rule."

The formula of Quotient Rule is

[tex]\frac{d}{dx}[\frac{f(x)}{g(x)}]=\frac{g(x)f'(x)-g'(x)f(x)}{(g(x))^2}[/tex]....................(1)

As we see in our function then f(x) = x[tex]^4+[/tex]1 and g(x) = 3x[tex]^4+[/tex]4

Before solving the function we find the value of f'(x), g'(x) and (g(x))[tex]^2.[/tex]

Now solving the f(x) for f'(x) with respect to x.

f(x) = x[tex]^4+[/tex]1

[tex]\frac{d}{dx}f(x)=\frac{d}{dx}(x^4+1)[/tex]

[tex]f'(x)=\frac{d}{dx}x^4+\frac{d}{dx}1[/tex]

We know that the differentiation of [tex]x^n=nx^{n-1}[/tex] and differentiation of constant value is zero.

So [tex]f'(x)=4x^{(4-1)}+0[/tex]

[tex]f'(x)=4x^3[/tex]

Now solving the g(x) for g'(x) with respect to x.

g(x) = 3x[tex]^4+[/tex]4

[tex]\frac{d}{dx}g(x)=\frac{d}{dx}(3x^4+4)[/tex]

[tex]g'(x)=3\frac{d}{dx}x^4+\frac{d}{dx}4[/tex]

We know that the differentiation of [tex]x^n=nx^{n-1}[/tex] and differentiation of constant value is zero.

[tex]g'(x)=3(4x^{(4-1)})+0[/tex]

[tex]g'(x)=3(4x^{3})[/tex]

[tex]g'(x)=12x^{3}[/tex]

Now finding the value of (g(x))[tex]^2.[/tex]

g(x) = 3x[tex]^4+[/tex]4

[tex](g(x))^4=(3x^4+4)^2[/tex]

Now using the formula of [tex](a+b)^2=a^2+2ab+b^2[/tex].

Now solving

[tex](g(x))^4=(3x^4)^2+2\times(3x^4)\times4+(4)^2[/tex]

Simplifying

[tex](g(x))^4=9x^8+24x^4+16[/tex]

Now putting the value of f'(x), g'(x) and (g(x))[tex]^2.[/tex] in the equation (1)

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(3x^4+4)(4x^3)-(12x^3)(x^4+1)}{9x^8+24x^4+16}[/tex]

Simplifying

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(3x^4(4x^3)+4(4x^3))-((12x^3)x^4+1(12x^3))}{9x^8+24x^4+16}[/tex]

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(12x^{(4+3)}+16x^3)-(12x^{(3+4)}+12x^3)}{9x^8+24x^4+16}[/tex]

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(12x^{7}+16x^3)-(12x^{7}+12x^3)}{9x^8+24x^4+16}[/tex]

Now solving the bracket

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{12x^{7}+16x^3-12x^{7}-12x^3}{9x^8+24x^4+16}[/tex]

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{16x^3-12x^3}{9x^8+24x^4+16}[/tex]

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{4x^3}{9x^8+24x^4+16}[/tex]

Hence, the differentiate the function with respect to x is [tex]\frac{4x^3}{9x^8+24x^4+16}[/tex] .

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The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,

Given that, [tex]\frac{d}{dx}(e^x) =e^x[/tex].

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

Differentiate using the Exponential Rule which states that [tex]\frac{d}{dx}(a^x)[/tex] is [tex]a^xln(a)[/tex] where [tex]a=e.e^x[/tex]

So, now [tex]\frac{d}{dx}(e^x) =e^x[/tex]

The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,

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Answer: 1) C- the survey participants should be randomly selected

2) C- how interested would you be in purchasing a blue car?
3) C- the stadiums front gate

Step-by-step explanation: I took the quick check.

Answer:

1. c

2. d

3. c

Step-by-step explanation:

The measure of side AC in the triangle is 2.7 m

From the question, we are to determine the measure of AC

From the given information, we have that ΔADC is similar to ΔCDB

Thus,

We can write that

|DC| / |DB| = |AC| / |CB|

From the diagram,

|DC| = 5.5 m

|DB| = 6.3 m

|AC| = h

|CB| = 3.1 m

Then,

5.5 / 6.3 = h / 3.1

∴ h = (5.5 × 3.1) / 6.3

h = 17.05 / 6.3

h = 2.70635 m

h ≈ 2.7 m

Hence,

The length of AC is 2.7 m

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Answer:

1/4

Step-by-step explanation:

rise/run                                          you can count it but it doesn't always work

If you want to know the mathematical way of doing it it's:

m(slope) = y2-y1/x2-x1                 Choose any two points I chose (-4,5) & (0,6)

m = 6-5/0-(-4)                               Then subtract 6 - 5 and 0-(-4)  

m = 1/4

The estimation of 719 x 26 is 14,000

Making a number simpler so that its value stays near to its original state is known as rounding. Although less exact, the outcome of rounding off a number is simpler to utilise.

Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.

Given:

Estimation of 719 x 26

Now, Round off nearest hundred for 719 which is 700

i.e., Round 719 = 700

Now, Round off nearest hundred for 26 which is 20

i.e., Round 26 = 20

Hence, the estimation is 700 x 20 = 14,000.

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