Determine the domain of (g ∘ f)(x) if f (x) = x2 + 2x − 4 and g of x is equal to 1 over the quantity x plus 1 end quantity period

{x ∈ ℝ}
{x ∈ ℝ| x ≠ −1}
{x ∈ ℝ| x ≠ −3, 1}
{x ∈ ℝ| x ≠ −3, −1, 1}

The correct integers are;

For first diver, the elevation = - 36 feet

For second diver , the elevation = - 44 feet

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

One diver is 36 feet below the surface.

And, The other diver is 44 feet below the surface.

Now,

Since, One diver is 36 feet below the surface.

And, The other diver is 44 feet below the surface.

Hence, The correct integers to represent the surface are;

For first diver, the elevation = - 36 feet

For second diver , the elevation = - 44 feet

Thus, The correct integers are;

For first diver, the elevation = - 36 feet

For second diver , the elevation = - 44 feet

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Answer:

-60q+20

Step-by-step explanation:

The statement that best describes the changes in air pressure and wind speed is C. When a high- and a low-pressure air mass are far apart, air moves slowly from high to low pressure.

The weight of air molecules pressing down on the Earth is referred to as air pressure. As you ascend from sea level into the atmosphere, the pressure of the air molecules changes. The greatest pressure exists at sea level, where the density of air molecules is greatest.

Atmospheric pressure, also known as barometric pressure, is the pressure that exists within Earth's atmosphere. The region with low pressure will always get winds from the high pressure. This means that the region of low will attract winds from the high pressure and vice versa.

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Answer: 2m-6+4m

Step-by-step explanation:

The percentage increase in the population of the chilrden since past year is 11.96%.

What is Percentage ?

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.

According to the question, the town's population of children increased from 376 to 421 during the past year.

So, the increase in the population of the children is-

Increase =421-376

Increase =45

Now, the percentage increase in population of the children per year is calculated as-

Percentage Increase [tex]$=\frac{\text { Increase }}{376} \times 100 \%$[/tex]

Percentage Increase [tex]$=\frac{45}{376} \times 100 \%$[/tex]

Percentage Increase [tex]$=0.1196 \times 100 \%$[/tex]

Percentage Increase [tex]$=11.96 \%$[/tex]

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The evaluation of the function would be f(x) = 7.

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer:

32

Step-by-step explanation:

we have to find the side of the bigger triangle by making a ratio

5/8=7/x

cross multiply

5x=7(8)

5x=56

/5.  /5

x=11.2

now for the other side

5/8=8/x

5x=8(8)

5x=64

/5. /5

x=12.8

we know all three sides 11.2, 12.8 and 8 so we add them

11.2+12.8+8

24+8

32

hopes this helps

The largest number of matches she could have won before are 164 matches.

A ratio shows the relation between two amounts. For example, the ratio of apples to pears in a basket or the ratio of women to men in a town.

First represent the matches she had won, using n as a reference. This means:

[tex]\frac{n}{2n} = \frac{1}{2}[/tex]

Then, based on this let's add the current ratio:

[tex]\frac{n+3}{2n+4} = \frac{503}{1000}[/tex]

Based on this, let's solve this inequality to find out the number of matches the player won before. Follow these steps:

Based on the previous process, the number of matches the player could have won before the weekend began was 164 matches.

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Answer:

y = -4x-9

Step-by-step explanation:

The slope must stay the same for parallel lines, which is -4. Now we will plug the point into slope-intercept form(y=mx+b) where m is the slope and b is the y-intercept. Plugging in -4 for the slope and (-3, 3) for x and y, we get [tex]3=-4*13 + b[/tex], or [tex]3 = 12 + b[/tex]. Subtracting 12 from sides gives us that b = -9, which is the y-intercept! We know have both the slope and y-intercept, so we get that the equation is y = -4x - 9.

Hope this helps!

(a) The joint probability distribution of the two points will be 1/x, 0<x<1, 0<y<1

(b) The expectation of the product of the two points will be 1/6

(c) The marginal distribution of the point your friend picks will be (-1/2) lny^2

We have, X=(0,1)

Y | X=X=(0, X)

a) Let f(x,y) be the joint probability distribution of the two points will be:

f(X)=1

f(Y|X)=1/x

[tex]$$\begin{aligned}& f(x, y)=f(X) f(Y \mid X=x)=1 / x, 0 < x < 1,0 < y < x\end{aligned}$$[/tex]

b) Let E(XY) be the expectation of the product of the two points.

[tex]$$\begin{aligned}E(XY)=& \int_0^1 \int_0^x \frac{x y}{x} d y d x=\frac{1}{6} \quad \text { (Decimal : } 0.16667 \ldots \text { ) }\end{aligned}$$[/tex]

c) Let f(y) be the marginal distribution of the point your friend picks.

So, the value of f(y) will be:

[tex]$$\begin{aligned}& \mathrm{f}(\mathrm{y})= \\& \int_y^1 \frac{1}{x} d x=-\frac{1}{2} \ln \left(y^2\right)\end{aligned}$$[/tex]

d)for 0<y<1

[tex]$$\begin{aligned}& f(y) > =0 \\& \int_0^1-\frac{1}{2} \ln \left(y^2\right) d y=1\end{aligned}$$[/tex]

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Answer: A gym membership cost 3 dollars a month. There is an initial fee of $5. How many months would you need to be paying for the membership to have spent 20 dollars?

Step-by-step explanation:

3x+5=20

3x=15

x=5

5 Months

The solution set of the function based on the graph is (3, 1). Option D

We know that the solution set of a function would be obtained as the points where the graph cut the axes of the graph. The graph has to do with a system in which information is presented in the x, y coordinate system.

In this kind of system, the vertical axis is the y axis while the horizontal axis is the x axis, as such we would need to plot the data points of the graph and then try to obtain the points that would correspond to the solutions of the points on the graph.

We would now need to observe the graphs so as to be able to obtain the correct presentation of the data points that would serve as the solutions of the graph as we can see the function plotted completely here.

The line cut the y axis at y =1. If we trace this point to the point that it corresponds to in the x axis we have x = 3 and we have the required points as (3, 1).

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Answer: y= -2/3x + 0

Explanation: y= mx +b

Y-intercept at (o,o), so b is 0

Let's pick 2 points (-3,2) ( 0,0), so the slope is -2/3

So the equation is y=-2/3x + 0

Answer:

5

Step-by-step explanation:

12x - 3y

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

4x - z

Input the values provided:

12(3) - 3(1/3)

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

4(3) - 5

Start by simplifying the numerator and denominator expressions:

-numerator;

12(3) = 36

3(1/3) = 1

36 - 1 = 35

-denominator:

4(3) = 12

12 - 5 = 7

Then divide:

35

----

7

This will equal to 5, which is your final answer.

Hope this helps! :D

Answer: 13/15

Step-by-step explanation:

2/3 x 5 = 10/15

1/5 x 3 =3/15

3/15 + 10/15 =13/15

Answer:

13/15

Step-by-step explanation:

2/3 = 15/3 = 10 this is because 5 and three have common factors. So I now have 10/15.
1/5 = 3/15.

3/15 + 10/15 = 13/15.

Noah is using the 50/30/20 budgeting strategy because he is using 50% of his income for his basic needs, 30% for entertainment, and 20% for savings and debt repayment.

Money management in mathematics is the application of mathematical principles and techniques to the management of personal or corporate money. It entails the use of mathematical tools like equations, graphs, and statistics to analyse financial data and make educated decisions about budgeting, saving, investing, and spending. Mathematicians also use probability and risk analysis to manage money by estimating the likelihood of different financial events and making decisions based on the benefits and dangers of various financial options. Overall, mathematicians' understanding of money management enables people and organisations to better manage their financial resources and reach their financial objectives.

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Answer:

36

Step-by-step explanation:

[tex]m\angle TSU=36^{\circ}[/tex] using the definition of an isosceles triangle. By CPCTC, [tex]m\angle USR=36^{\circ}[/tex].

For the mileage of 80 miles company A will charge less than company B.

So, the inequality is m≤80.

A variety of notations are available to denote different kinds of inequalities. An inequality in mathematics is a relationship between two expressions or values that is not equal. To resolve an inequality, follow these steps: First, multiply each term by the total of the least common denominators of all the fractions to be subtracted. Step 2: Combine similar terms on both sides to simplify the inequality. Step 3: Calculate the unknown by adding or subtracting the amounts from the numbers on either side.

Charge for company A=$131

Charge for company B=$75+0.70m

75+0.70m≤131

0.70m≤56

m≤(56/0.7)

m≤80

Therefore, for the mileage of 80 miles company A will charge less than company B.

So, the inequality is m≤80.

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Therefore the solution of this question is the velocity of roller coaster  after 3 second is 22 m/s

The rate at which an object's position is changing as perceived from a given point of view and as described by a certain unit of time is known as its velocity.

Here,

The speed of  roller coaster is 4m/s

The acceleration of  roller coaster is 6m/s2

So,

we have to find the velocity after 3 second

thus we use the formula v=u + at

Putting values

=> v = 4 +6*3

=> v = 4 + 18

=> v = 22 m/s

Therefore the velocity of roller coaster  after 3 second is 22 m/s

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Answer:

x = 3

Step-by-step explanation:

CD is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, that is

[tex]\frac{BD}{AD}[/tex] = [tex]\frac{BC}{AC}[/tex] ( substitute values )

[tex]\frac{x}{2.25}[/tex] = [tex]\frac{4}{3}[/tex] ( cross- multiply )

3x = 4 × 2.25 = 9 ( divide both sides by 3 )

x = 3

The percentage of students who live off campus and do not have a part-time job is 25.2%

The correct answer option is option C

Students who live off campus and gets a part-time job = Percentage of students who live off campus and gets a part-time job × Percentage of students who live off campus × 100

= 58% of 60% × 100

= 0.58 × 0.60 × 100

= 0.348 × 100

= 34.8%

percentage of students who live off campus and do not have a part-time job = Percentage of students who live off campus - Students who live off campus and gets a part-time job

= 60% - 34.8%

= 25.2%

Consequently, 25.2% of students live off campus and do not have a part-time job.

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Hello,

I hope you and your family are doing well!

If the potatoes in the bag are split equally among 5 people, each person will get 25 potatoes / 5 people

= 25/5

=5 potatoes.

Therefore, each person will receive 5 potatoes.

----

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Happy Holidays!

line k and second line h are not parallel lines because the have different slopes.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Where x₁ - x coordinate

y₁ - y coordinate

m - slope

A line k passes through the points ​(−5​,−5​) and ​(1,37​).

Then Slope m = 37 + 5/ 1 + 5

m = 7

Now Write the equation as;

y + 5 = 7(x + 5)

y = 7x + 30

A second line h passes through the points ​(−3​,−33​) and ​(3​,9​).

Then Slope m = 9 + 3/ 3 + 33

m = 0.33

Now Write the equation as;

y + 33 = 0.33(x + 3)

Hence, line k and second line h are not parallel lines because the have different slopes.

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Anserw:

Say the averge water a person uses a day is 90 gallons 30% of the water is used outside a day. So that would mean around 27 gallons.

hope that helps :)

Step-by-step explanation:

Answer:

-3/14

Step-by-step explanation:

Step 1) Convert into -7/14 + 4/14

Step 2) -7/14 + 4/14= -3/14

The option that is not a polynomial is d 2/y

An equation made up of variables, exponents, and coefficients along with operations and the equal sign is known as a polynomial equation.

Sums of terms of the form kxⁿ, where k is any number and n is a positive integer, make up polynomials.

a. -4x + 3y this is a polynomial

k = -4 and 3

n = 1

b. p^2q - 3pq^2 this is a polynomial

k = 1 and 3

n = 2

c. 4 - x this is a polynomial

k = -1

n = 1

d 2/y this is not a polynomial

= 2y^-1

A polynomial does not have a variable in the denominator or have a negative exponents. Hence this is not a polynomial

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According to the given figure of triangle , f = 58 °

A linear pair of angles is formed when two lines intersect at a single point. The angles are said to be linear if they follow the point where the two lines intersect in a straight line.

The sum of the angles in a pair of linear equations is always 180°. These are also referred to as additional angles.

According to the given information

We are given that

a = 119°

Applying linear Pair of Angles

a + b = 180°

119° + b = 180°

b = 180° - 119°

b = 61 °

We know that

b = c = 61 °

According to Angle sum Property

b + c + f = 180°

61° + 61° + f = 180°

f = 180 - 61 -61

f = 58 °

According to the given figure of triangle , f = 58 °

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Answer:

Step-by-step explanation:

The normal distribution is defined by its mean and standard deviation, so if we know that the heights of the seedlings are normally distributed and we know certain percentiles of the distribution, we can find the mean and standard deviation.

We are given that 10% of the seedlings are taller than 15 cm, which means that 90% of the seedlings are shorter than or equal to 15 cm. This tells us that the 90th percentile of the distribution is 15 cm.

Similarly, we are given that 5% of the seedlings are shorter than 4 cm, which means that 95% of the seedlings are taller than or equal to 4 cm. This tells us that the 95th percentile of the distribution is 4 cm.

Since the normal distribution is symmetrical, the mean of the distribution is the value that separates the upper and lower halves of the distribution. In this case, the mean is the value that separates the lower 95% from the upper 5%, which means it is the value that is exactly halfway between the 95th and 90th percentiles.

To find the mean, we can add the 95th percentile (4 cm) and the 90th percentile (15 cm) and divide by 2:

mean = (4 + 15) / 2

= 19 / 2

= 9.5 cm

To find the standard deviation, we can use the fact that the normal distribution has the property that approximately 68% of the values fall within one standard deviation of the mean, approximately 95% fall within two standard deviations, and approximately 99.7% fall within three standard deviations.

Since we know that the 95th percentile (4 cm) is 2 standard deviations below the mean and the 90th percentile (15 cm) is 2 standard deviations above the mean, we can set up the equation:

4 cm = mean - 2 * standard deviation

15 cm = mean + 2 * standard deviation

Solving for standard deviation, we get:

standard deviation = (15 cm - 4 cm) / (2 * 2)

= 11 cm / 4

= 2.75 cm

So, the mean height of the seedlings is 9.5 cm and the standard deviation is 2.75 cm.

Answer:

There are many possible ranges, including  (−∞,15.051464)

 and  (15.051464,18.6844845)

 as well as  31.5±0.6270678

 (centered on the mean). Observe, in R:

> pnorm(15.051464, 31.5, 10) - pnorm(-Inf, 31.5, 10)

[1] 0.05

> pnorm(18.6844845, 31.5, 10) - pnorm(15.051464, 31.5, 10)

[1] 0.05

> pnorm(32.1270678, 31.5, 10) - pnorm(30.8729322, 31.5, 10)

[1] 0.05

In general, if you are given a small enough but otherwise arbitrary number  a∈R

 you can find a unique  b

 such that  b>a

 and

∫baϕ(x,31.5,10)dx=0.05,

where  ϕ

 is the normal density. For example, if  a=10

, then  b≈16.42

. Again in R:

> qnorm(pnorm(10, 31.5, 10) + 0.05, 31.5, 10)

[1] 16.42003

So your question doesn’t determine the answer uniquely: I’m free to choose the upper or lower bound of the interval or any particular point relative to those (e.g. the midpoint) arbitrarily.

If you had asked for a 95% interval, it would have been a reasonable assumption (but an assumption nonetheless) that you want an interval centered on the mode, median, or mean. But for a 5% interval, it’s not obvious that you want that — in practice it’s more likely that you want the upper tail or the lower tail.

That said, at a fundamental level, the answer is the same: use the cumulative distribution function and/or its inverse, as appropriate.

If ABCD is a parallelogram and  ∠D=57° then ∠BCD =123°

What is a parallelogram ?

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.

Using corresponding angle property int he parallelogram we can se that the ∠D is equal to exterior ∠C (57° ) because side AD and BC are parallel

and we know ∠C + exterior ∠C will be 180°

∠BCD=180° - 57°

∠BCD =123°

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Answer:

One possible decomposition of h(x) is:

h(x) = (1/x²) * (1/(1 + 3/x))

This decomposition can be obtained by applying the identity (a/b) * (1/c) = a/(b*c).

Another possible decomposition of h(x) is:

h(x) = 1/((x+3)*(x+3))

This decomposition can be obtained by applying the identity (a/b) * (c/d) = (ac)/(bd).

Note that these are just two possible decompositions of h(x) and there may be other ways to decompose the function as well. The choice of decomposition will depend on the specific context and the intended use of the function.

Step-by-step explanation: