Given
f(x) = x2 + 5
and
(fg)(x) = 3x(x2 + 5),
what is
g(x)?

g(x) =

Answer:

Step-by-step explanation:

Since the probability of rain on any given day is 0.5, and the weather on each day is independent of the others, we can calculate the probability of it raining all three days by multiplying the probabilities of rain on each individual day:

P(rain on day 1) x P(rain on day 2) x P(rain on day 3) = 0.5 x 0.5 x 0.5 = 0.125

Therefore, the probability of it raining all three days of your trip to Seattle in October is 0.125, or 12.5%.

The data described, the numbers of cases of flu treated at a certain hospital in different years, are quantitative data.

Quantitative data is any data that can be measured or expressed in numerical terms. In this case, the data is expressed as the number of cases of flu treated at the hospital in different years. This type of data can be analyzed using mathematical and statistical methods to obtain insights and patterns.

The information provided, specifically the numbers of flu cases treated at a certain hospital in various years, is quantitative information because it is expressed numerically.

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The interpretation of the solution of the graph can be: the solution (6, 64) on the graph represents that after 6 minutes, there are 64 gallons of water.

The solution to a system that is plotted on a graph is the coordinates of the point interception of the graph.

Therefore, the solution (6, 64) represents a point on the graph of a relationship between time in minutes (represented by the x-axis) and water in gallons (represented by the y-axis).

The solution tells us that at 6 minutes, the water level is 64 gallons. In other words, (6, 64) on the graph, represents the amount of water in the tank over time.

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Answer:7 3/4

Step-by-step explanation:

(5*8+1)/8+(8*2+5)/8=41/8+21/8=62/8=7 6/8=7 3/4

Answer:

y=5

Step-by-step explanation:

i think it is ahhhh&hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

The correct statements regarding the function are given as follows:

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

To the left of x = 2, the graph of the function approaches x = 2 at y = 2, hence:

lim x-> 2^- f(x) = 2.

To the right of x = 2, the graph of the function approaches x = 2 at y = 1, hence:

lim x-> 2^+ f(x) = 1.

Due to the different lateral limits, the function is not continuous at x = 2, and the limit is not defined.

Due to the closed circle, the function is defined at x = 2, with a numeric value of y = 2.

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The equation of the line in point slope form is y + 6 = 3 (x + 3), and the line in slope intercept form is y = 3x + 3.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

We have the points on the line given.

(-3, -6) and (2, 9)

Slope of the line = (9 - -6) / (2 - -3) = 15/5 = 3

Equation of a line in point slope form is,

y - y₁ = m (x - x₁)

where (x₁, y₁) is a point on the line and m is the slope.

Substituting a point (-3, -6) and the slope = 3, we get,

y - -6 = 3 (x - -3)

y + 6 = 3 (x + 3), which is the point slope form.

Equation of a line in slope intercept form is,

y = mx + c

where m is the slope and c is the y intercept.

Substituting m = 3 and (x, y) = (2, 9),

9 = (3 × 2) + c

c = 9 - 6 = 3

Equation in slope intercept form becomes,

y = 3x + 3

Hence the point slope form and slope intercept form of the given line are y + 6 = 3 (x + 3) and y = 3x + 3 respectively.

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We would expect 306 people to go to see movies now, after the 32% decrease.

The expected value is calculated in statistics and probability analysis by multiplying each conceivable outcome by the likelihood that each outcome will occur, then adding up all of those values. By calculating anticipated values, investors can choose the scenario that is most likely to provide the desired outcome.

We must subtract 32% from the original number of persons in order to arrive at the anticipated number of people who would currently attend movies.

Let x represent the predicted proportion of moviegoers in the present. The following equation can be created:

x = 450 - 0.32*450

By condensing this equation, we obtain:

x = 450 - 144

x = 306

As a result, given the 32% decline, we would anticipate 306 individuals to attend movies this week.

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Answer:

B. 5

Step-by-step explanation:

The expression "4 to the power of 5" can be written as 4^5. Here, 4 is the base, and 5 is the exponent. So the exponent in the expression 4 to the power of 5 is option B, 5.

The height of the flagpole based on the information is 23 feet.

Let's start by converting the height of the person's shadow to feet, since the length of the flagpole's shadow is given in feet. There are 12 inches in a foot, so 54 inches is 54/12 = 4.5 feet.

Now we can set up a proportion to solve for the height of the flagpole:

(person's height) / (person's shadow length) = (flagpole height) / (flagpole shadow length)

Plugging in the values we know, we get:

5.75 / 4.5 = x / 18

5.75 * 18 = 4.5 * x

103.5 = 4.5x

Dividing both sides by 4.5, we get:

x = 103.5 / 4.5

x = 23

So the height of the flagpole is 23 feet.

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Answer:

Step-by-step explanation:

hashhshd

Answer:

≈ 7.8

Step-by-step explanation:

Specific gravity of steel = Density of steel / Density of water

Density of steel = 487 pounds per cubic foot

Density of water = 62.4 pounds per cubic foot

Specific gravity of steel = 487 / 62.4

Specific gravity of steel ≈ 7.8

Therefore, the specific gravity of steel is approximately 7.8.

The experimental probability that the next student to respond likes Hamlet best is 1/6 or 0.1667 as a decimal.

In this problem, we are given the results of a survey conducted in an English class to determine which Shakespeare play the students liked the best. The teacher recorded the number of students who liked each of the three plays: Hamlet, Twelfth Night, and A Midsummer Night's Dream.

To calculate the experimental probability, we first need to find the total number of students who have responded to the survey so far. From the information given, we know that 2 students liked Hamlet best, 8 students liked Twelfth Night best, and 2 students liked A Midsummer Night's Dream best. Therefore, the total number of students who have responded so far is: 2 + 8 + 2 = 12

Next, we need to determine how many of these 12 students liked Hamlet best. We know from the data given that 2 students liked Hamlet best, so the number of students who liked Hamlet best is: 2

Finally, we can calculate the experimental probability that the next student to respond likes Hamlet best. We do this by dividing the number of students who liked Hamlet best (2) by the total number of students who have responded so far (12): 2/12

Simplifying this fraction, we get: 1/6

Therefore, the experimental probability that the next student to respond likes Hamlet best is 1/6 or 0.1667 as a decimal. This means that if we were to randomly select a student from the class and ask them which Shakespeare play they liked the best, there is a 1 in 6 chance that they would choose Hamlet.

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h(-2) = 3

h(0) = 0

h(5) = 3/4

This can be solved by using the concept of function.

In arithmetic, a function from one set to another, X to Y, allocates precisely one element of Y to each element of X. Both of the set X and the set Y usually known as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.

A function with the name f is defined by the formula y=f(x). This is understood to mean "y is a function of x." The input value, also known as an independent variable, is represented by the letter X. The outcome value, or dependent variable, is denoted by the letter y, or f(x).

This is a piece wise-defined function:

For h(-2):

h(-2) = 3

For h (0):

h(0) = (x + 1)²- 1

h(0) = (0 + 1)² - 1

h(0) = 1 - 1

h(0) = 0

For h(5):

h(5) = -1/4 x + 2

h(5) = -1/4(5) + 2

h(5) = 3/4

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The equation Z-7x = 0 defines a plane in three-dimensional space, where Z is the vertical axis and x is one of the horizontal axes.

A coordinate is a set of values that specifies the position of a point or an object in a given space or system. In mathematics, the most common coordinate systems are the Cartesian coordinate system and the polar coordinate system. In the Cartesian coordinate system, a point in two-dimensional space is represented by an ordered pair (x,y), where x is the horizontal coordinate (also known as the abscissa) and y is the vertical coordinate (also known as the ordinate).

Here,

Specifically, this plane is parallel to the y-axis and intersects the Z-axis at (0,0,0) with a slope of 7.

None of the answer choices provided correctly describe this surface. The surface is a plane, not a cylinder or cone, and its trace in any plane parallel to the xy-plane is a line (not a square root or parabolic function). Therefore, the correct answer is not given among the choices provided.

Note that if we solve the equation Z-7x = 0 for Z, we get Z = 7x, which is a linear function with slope 7 that passes through the origin. This means that the surface defined by Z-7x = 0 is a plane that is parallel to the y-axis and intersects the three coordinate axes at (0,0,0), (1,7,0), and (0,0,7).

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Answer:

Ricky has 1204 hits and Pedro has 1481 hits.

Step-by-step explanation:

Answer: pedro had 1,200 and ricky had 1,485

Step-by-step explanation: all i did was 2685 - 285 which equals 2,400. then i did 2,400 divided by 2 which was 1,200, pedro had 1.200 hits.

1,200 add 285 equals 1,485. ricky has 1,485. to double check add 1,200 and 1,485 and you should get 2,685

Answer:

Step-by-step explanation:

We can represent the 5 consecutive odd integers as:

1. x

2. x + 2

3. x + 4

4. x + 6

5. x + 8

"...the sum of the first three integers", then, is

x + (x + 2) + (x + 4)

That is "the sum of the last two plus 7", which is

(x + 6) + (x + 8) + 7.

The connecting word "is" means there is an equals sign right there. Therefore,

x + (x + 2) + (x + 4) = (x + 6) + (x + 8) + 7 which simplifies down to

3x + 6 = 2x + 21 after we combine like terms.

x = 15. That means the first integer is 15, the next one is 17, the third one is 19, the fourth one is 21, and the fifth one is 23.

The proportion of items in each bin is given by the:

a. relative frequency.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The concept of probability was presented because it is the same concept of relative frequency, which gives the proportion of items in each bin.

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So, in response to the above question, we can state that The projected sum is $800, or around $780. Hence, equation  of Mr. Foreman's estimation is accurate.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

Nine touchdowns by the Tigers, each earning six points, for a total of nine times six or 54 points.

The Leopards scored 5 touchdowns for a total of 5 x 6 = 30 points, each of which was worth 6.

We may deduct the total points scored by the Leopards from the total points scored by the Tigers to see how many more points the Tigers scored than the Leopards:

Leopards' points minus Tigers' points equals 54 - 30 = 24.

As a result, the formula is p, where p = 24, where Tigers' points Equal Leopards' points.

Hence, the Tigers outscored the Leopards by 24 points.

$105 + $448 + $115 + $143 - $21 = $790

We have the following by rounding the numbers to the closest tens:

$110 + $450 + $120 + $140 - $20 = $800

The projected sum is $800, or around $780. Hence, Mr. Foreman's estimation is accurate.

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Answer:

5 3/5

Step-by-step explanation:

First, you write 4/5 x 7/1.

Next, you multiply 4x7 = 28.

Then, you multiply 5x1 = 5.

Now, you have an improper fraction--28/5.

You then divide 28/5 = 5 3/5.

No simplifying is needed.

Result: 5 3/5

Answer:

1. 4

2. [tex]cos^2(sin^2(0))tan^2(0)[/tex]

3. sec^2 theta

Hope it helped!

Answer: C) (1, -1)

Step-by-step explanation:

[tex]\boldsymbol{\sf{\underline{\diamond System \ of \ equations \ by \ the \ reduction \ method:} }}[/tex]

   [tex]\boldsymbol{\sf{We\:have\:the\:system\:of\:equations \ --\to \ \left \{ {{x+2y=1 \ } \atop {2x-3y=5 }} \right. }}[/tex]

Multiply the first equation by 2, and the second equation by -1, then both equations must be added.

             [tex]\boldsymbol{\sf{\star \ 2(x+2y=-1) }}\\ \boldsymbol{\sf{\star -1(2x-3y=5) }}[/tex]

We add these equations to eliminate x.

             [tex]\boldsymbol{\sf{\star \ 7y=-7 }}[/tex]

Then we solve 7y=-7 for y (divide by 7).

               [tex]\boldsymbol{\sf{\star \ \dfrac{7y}{7}=\dfrac{-7}{7} }}\\ \\ \boxed{\boldsymbol{\sf{\star \ y=-1}}}[/tex]

We place the found value of y, in one of the original equations y to solve for x.

                  [tex]\boldsymbol{\sf{\star \ x+2y=-1}} \\ \\ \boldsymbol{\sf{\star \ x+2(-1)=-1}}\\ \\ \boldsymbol{\sf{\star \ 0=-x+1 }}[/tex]

Simplify (We add x to both sides.)

                  [tex]\boldsymbol{\sf{\star \ 0+(x)=-x+1+(x) }}\\ \\ \boldsymbol{\sf{\star \ x=1}}\\ \\ \boldsymbol{\sf{\star -2=-1-x}}[/tex]

Add (2) to both sides.

                   [tex]\boldsymbol{\sf{\star \ -2+(2)=-x-1+(2) }}\\ \\ \boldsymbol{\sf{\star \ 0=-x+1 }}[/tex]

We divide by 1.

                      [tex]\boldsymbol{\sf{\star \ \dfrac{x}{1}=\dfrac{1}{1} }}\\ \\ \boxed{\boldsymbol{\sf{\star \ x=1}}}[/tex]

                                     [tex]\underline{\bf{ \ \ x,y \ answer\ \ \ \ }}\\\boxed{\boldsymbol{\sf{x=1,y=-1 }}}[/tex]

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To find the percent decrease, we first need to find the amount of the decrease, which is the difference between the regular price and the sale price:

$550 - $456.50 = $93.50

So the amount of the decrease is $93.50.

To find the percent decrease, we divide the amount of the decrease by the original price and then multiply by 100:

($93.50 / $550) x 100 ≈ 17.0%

Therefore, the percent decrease of the sale price from the regular price is approximately 17.0%.

Answer:

See My Attached Work For Answer. (POV THIS WAS HARD!!!)

Step-by-step explanation:

The completed function to model the data is:

[tex]y = 3.1cos(\frac{2\pi }{365} (x-15.3)) + 12.2[/tex]

A periodic variable's amplitude is a gauge of its change over a single period.

A non-periodic signal's magnitude in relation to a standard value is its amplitude. There are several ways to define amplitude, and they are all dependent on how much the extreme values of the variable deviate from one another.

To find the amplitude:

max - min/2=15.3-9.1/2

= 3.1

The wavelength is 365

The midpoint is 12.2

The max position is 15.3

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Por lo tanto, el precio original del abrigo era de 72€

Para resolver este problema, primero debemos determinar el precio original del abrigo antes de las rebajas.

Sea x el precio original del abrigo.

Después de aplicar la primera rebaja del 40%, el precio del abrigo sería:

x - 0.4x = 0.6x

Luego, tras la subida del 30%, elprecio se incrementaría al 130% del precio anterior:

1.3(0.6x) = 0.78x

Sabemos que este precio final es de 56,16€, por lo que podemos resolver la ecuación:

0.78x = 56.16

x = 72

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The discounted price per yard for ribbons and for fabrics is A. Ribbon costs $ 1. 50 per yard and fabric costs $ 5. 75 per yard.

You can find the discounted price by using the options and then multiplying the prices given, by the purchases of Gwen and Penelope to find out which price is right.

If the discounted price of ribbons were $ 1.50 per yard and the fabric was $ 5. 75 per yard, then the cost to Gwen would be:

= ( 1. 50 x 6 ) + ( 10 x 5. 75 )

= $ 66. 50

For Penelope :

= ( 1. 50 x 5 ) + ( 8 x 5. 75 )

= $ 53. 50

These are the amounts spent so these are the discounted prices.

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Answer:

33 inches

Step-by-step explanation:

Use triangle calculator online

The average rate of change of profit as x changes from 3 to 5 is $12 per item.

To find the average rate of change of profit as x changes from 3 to 5, we need to find the change in profit divided by the change in x over that interval:

Average rate of change = (P(5) - P(3)) / (5 - 3)

We can find P(5) and P(3) by plugging those values of x into the profit equation:

P(5) = 2(5)^2 - 4(5) + 6 = 36

P(3) = 2(3)^2 - 4(3) + 6 = 12

Substituting these values, we get:

Average rate of change = (36 - 12) / (5 - 3)

Average rate of change = 24 / 2

Average rate of change = 12

Hence, the average rate is $12 per item.

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Answer:picture is not clear on my side, please re-upload thx!

Step-by-step explanation: