The world population in 2030 will be of 9.0062 billion.
The exponential formula for population growth is given below:
P(t) = P (0)e^rt
Here, P(t) is the population in t years from now P (0) is the population in the current year and r(decimal) is the growth rate, e=2.7 is the Eular number.
If the world population is 7.0 billion in 2012.
2012 is the initial year, P (0) =7
P(t) will be measured in billions of people.
The growth rate is constant at 1 .4%.
So that, r = 0.014
Now, the population in 2030 will be :
2030-2012=18 years after 2012, so this is P(18).
P(t)= 7e^rt
P(18) = 7e^0.0014*18
= 9.0062
So, the world population in 2030 will be of 9.0062 billion.
To learn more about population formula:
https://brainly.com/question/2497167
The world population will be 9.0062 billion in 2030.
The population growth exponential formula is as follows:
P(0)ert = P(t)
P(t) denotes the population in t years. P (0) is the current year's population, r(decimal) is the growth rate, and e=2.7 is the Euler number.
If the world population in 2012 is 7.0 billion.
The first year is 2012, and P (0) = 7.
The magnitude of P(t) will be measured in billions of people.
The rate of growth remains constant at 1.4%.
As a result, r = 0.014.
Now, in 2030, the population will be:
2030-2012 = 18 years after 2012, so P (18).
P(t)= 7e^rt
P(18) = 7e^0.0014*18
= 9.0062
As a result, the world population in 2030 will be 9.0062 billion people.
Learn more about growth rate on:
https://brainly.com/question/25630111
Solve for c. c÷2 + 45 = 66
Answer:
c=42
Step-by-step explanation:
have a good day!
in the quadrilateral , angle JML = 78, JK=LM = 20 ft, and KL=JM=14 feet. Find angle JKL , angle KJM, angle KLM
angle JKL=
angle KJM=
angle KLM=
You have n random number generators, where the ith one draws a number uniformly at random from the interval [0, ti]. Here the ti's are arbitrary positive integers. Let Xi be the number drawn by the ith random number generator.(a) What is the expected value of the sum, S = X1 + ... + X.? (Your answer will be in terms of t1,.....tn)(b) What is the expected value of Y, which counts how many of the Xi's are ≤ 1? (Your answer will be in terms of t1,..., tn.)
As per the given random number, the expected value of Y which counts how many of the Xi's are ≤ 1 is tₐ.
The term called random number in math is defined as a number chosen by chance that is randomly from a set of numbers.
Here we know that let us consider that n random number generators, where the a th one draws a number uniformly at random from the interval [0, tₐ].
Here we have also know that tₐ's are arbitrary positive integers.
Let us consider that Xₐ be the number drawn by the ₐ th random number generator.
Then the the expected value of the sum is written as,
=> S = X1 + X2 + ... + Xₐ
Where it can be simply written as,
=> S = ∑Xₐ
Here we have also know that the expected value of Y, which counts how many of the Xi's are ≤ 1 is calculated as,
=> Y = ∑Xₐ where {0 < tₐ < a}.
To know more about random number here.
https://brainly.com/question/18534135
#SPJ4
How many numbers are in the form: ab554433221100 such that the number is divisible by 11? Please answer ASAP!!
There are 10 numbers of form ab554433221100 is divisible by 11.
What is divisibility Rule?To decide if a fraction has to be decreased, divisibility rules can be applied. The patterns that appear when we list the multiples of any number serve as the foundation for the rules.
Given:
Form: ab554433221100
If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.
Let us take value of a, b= 0, 1, 2, 3, ....9
So, the possible number divisible by 11.
00554433221100
11554433221100
22554433221100
33554433221100
44554433221100
55554433221100
66554433221100
77554433221100
88554433221100
99554433221100
Thus, we have 10 numbers.
Learn more about divisibility Rule here:
https://brainly.com/question/28281492
#SPJ1
what is the slope of the line whose equation is y=-3x+6
Answer:
slope = -3
Step-by-step explanation:
Note the slope-intercept form: y = mx + b , in which:
y = (x , y)
m = slope
x = (x , y)
b = y-intercept
~
In the case of the given line:
y = mx + b
y = (-3)x + (6)
Note what values and sign are in each given variable:
y = y
m = slope = -3
x = x
b = y-intercept = 6
∴ -3 is your answer for slope.
~
Learn more about solving for slope, here:
https://brainly.com/question/18905545
special right triangle
The numerical value of x and y in the right triangle are 8√5 and 8 respectively.
What is the value of x and y?The figure in the diagram is a right angle triangle.
Angle θ = 60°Opposite to angle θ is xAdjacent to angle θ is yHypotenuse = 16Using the trigonometric ratios;
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Next, we determine the value of x.
sin( θ ) = Opposite / Hypotenuse
sin( 60 ) = x / 16
x = sin( 60 ) × 16
x = 8√5
For y;
cos( θ ) = Adjacent / Hypotenuse
cos( 60 ) = y / 16
y = cos( 60 ) × 16
y = 8.
Therefore, the value of x is 8√5 and y is 8.
Learn more about trigonometric ratio here: https://brainly.com/question/28038732
#SPJ1
after friday's football game, karen and her friends go out for ice cream. they share the mega mountain sundae and finish the whole thing! when they pay for the sundae, karen evenly divides the total among 4 people. each person pays $4.25.which equation can you use to find the total cost c of the sundae?
As per the equation, we are able to calculate the total cost of sundae being $17.
To calculate,
Per person cost × number of people = cost of sundaes
4.25 × 4 = 17
One of the four fundamental operations of arithmetic, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction. Divide a rational expression by multiplying the first fraction by its reciprocal. We factor everything and search for common factors after rewriting the division as multiplication of the first expression by the reciprocal of the second. rational arguments are divided. A division problem has three main components: the dividend, the divisor, and the quotient. That which will be divided is the dividend. The number of "people" into which the number is divided is referred to as the divisor. The ratio is the response.
To learn more division: https://brainly.com/question/25289437
#SPJ4
a van starts off 189 miles directly south from the city of hartville. it travels due west at a speed of 30 miles per hour. after travelling 126 miles, how fast is the distance between the van and hartville changing? (do not include units in your answer, and round to the nearest hundredth.)
The distance between the van and Hartville is changing at a rate of 39.42 miles per hour.
This is because the van has traveled 126 miles due west at a rate of 30 miles per hour, meaning it is now 63 miles away from Hartville. If the van continues travelling due west at a rate of 30 miles per hour, then it will take another 2 hours to reach Hartville. Thus, the distance between the van and Hartville is changing at a rate of 63 miles divided by 2 hours, or 39.42 miles per hour.
The distance between the van and Hartville is changing as the van travels due west at a rate of 30 miles per hour. After travelling 126 miles, the van will be 63 miles away from Hartville. This means that the distance between the van and Hartville is decreasing at a rate of 63 miles divided by the amount of time it takes for the van to reach Hartville, which is 2 hours.
Learn more about distance :
https://brainly.com/question/26550516
#SPJ4
The Total number of cherries on a plate, in a cup, and in a bowl is 780. The plate contains 145 cherries. The number of cherries in the bowl is 4 times the total number of cherries on the plate and in the cup. How many cherries are in the cup?
Answer:
total number of cherries=780
number of cherries on the plate=145
number of cherries on the bowl is 4 times the number of cherry in the plate=145×4=580
number of cherry in the cup =580+145-780=45
How many boxes would Alan have to sell to earn less than $2050?
Answer: Alan would have to sell less than 540 boxes.
Step-by-step explanation:
which of the functions in memory is more likely to be the interrupt service routine (isr) for handling system calls?
The functions in memory is more likely to be the Interrupt Service Routine (ISR) for handling system calls are f4 and f8
What is Interrupt Service Routine?
A software function known as an interrupt service routine (ISR) is called upon by hardware in response to an interrupt. An interrupt is examined by ISR, which decides how to handle it, executes the handling, and then returns a logical interrupt value. The ISR alerts the kernel with a return value if no more handling is necessary.
Reason:
Sending a Unix signal to the process that developed a variant allows for the handling of several variations. The intended action is delayed until the process receives a signal, allowing the kernel to evaluate other requests swiftly.
This approach does not accommodate interruptions since they typically occur after the associated process has ceased and the wholly unrelated process is running, as in the case of a process seeking a data transfer. Sending a Unix signal to the active process is therefore improper.
The handling of disruptions relies on the nature of interruption. We will categorize the three basic types of interruption for our needs as follows:
I/O causes disruptions.
The relevant interference handle should ask the I/O device to determine the best course of action if it needs attention. This kind of interruption is covered in the recently updated section "I / O Disorder Management."
Time is of the essence.
The kernel is informed that the deadline has passed by a specified timer, either an APIC timer or an external timer, by use of this type of interference. The majority of these illnesses are addressed as I/O disorders.
Another CPU multiprocessor system is interrupted by an interprocessor when its CPU is uninstalled. In the recently published section "Interprocessor Interrupt Handling," we conceal such interruptions.
Managing I/O Disruption
The I/O interfering adapter should typically be adaptable enough to support many devices simultaneously. For instance, many devices might share an IRQ line in the PCI bus architecture. This indicates that the interference vector alone does not provide a complete picture. The identical vector 43 is equipped with a USB port and sound card in the example displayed in Table 4-3. However, when their IRQ line is shared with other devices, several hardware components prevalent in earlier PC systems (such ISA) do not operate consistently.
The following list discusses two distinct methods for obtaining the bothersome handle's flexibility.
shared IRQ
Multiple interference lines are produced by the intrusion (ISRs). Each ISR is a feature connected to a single shared IRQ line device. Each ISR is carried out to see if its device requires attention because it is impossible to know in advance which device to issue an IRQ for. If it does, the ISR completes all the tasks that must be completed when the device generates interference.
When a disruption occurs, not all activities should be executed immediately. In actuality, not every activity should be performed near the distraction handle. Because the signals on the relevant IRQ line are momentarily disregarded while the interfering host is active, long-term non-processing performance should be delayed. Most crucially, even if system suspension is disabled, the disruptive host's process must continue in TASK RUNNING state. As a result, interference managers are unable to carry out any blocking operations like I/O disk performance. Linux divides post-disruption activities into the following three groups:
Actions that are crucial, such admitting PIC interference, redistributing the PIC or device controller, or updating the device's data acquisition and processor. Because it must be completed as soon as possible, this can be done rapidly and extremely swiftly. Sensitive actions are carried out when hidden interference is disabled inside the immediate disruption holder.
Not attentive
modifying data structures that are solely visible to the processor, for example (for example, reading a scan code after a push-key keyboard). These acts are turned into a short remedy with enabled distractions because they can also be swiftly stopped.
It is not indirectly transferred.
similar as replicating the bar's content in the process space (for example, sending the keyboard line bar to the end management process). Since the interested process will constantly be waiting for the data, this can be postponed for a long period without having an impact on kernel performance. The various tasks covered in the next section, "Softirqs and Tasklets," are used to carry out the actions that can be responded arbitrarily.
The functions f4 and f8 that handle system calls are more likely to be Interrupt Service Routines (ISRs) in memory.
To learn more about Functions visit:
brainly.com/question/28278699
#SPJ4
List the common factors of 20 and 24 in order from least to greatest
motorcycle 1 and motorcycle 2 are heading straight toward each other. motorcycle 1 is traveling at 55 mph, and motorcycle 2 is traveling at 70 mph. If the two motorcycles are 500 miles apart, how many hours will it be before they meet?
The number of hours for both the motorcycles to meet is given by the equation T = 4 hours
What is Speed?Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the speed of the motorcycle 1 = 55 mph
Let the speed of the motorcycle 2 = 70 mph
Let the total distance between them be D = 500 miles
Now , the number of hours for them to meet be T
So , the distance traveled by motorcycle 1 d = 55T
The distance traveled by motorcycle 2 = ( 500 - d ) = 70T
Substituting the values in the equation , we get
( 500 - d ) = 70T
500 - 55T = 70T
Adding 55T on both sides of the equation , we get
500 = 125T
Divide by 125 on both sides of the equation , we get
T = 500/125
T = 4 hours
Hence , the number of hours is 4 hours
To learn more about speed click :
https://brainly.com/question/19930939
#SPJ1
determine the required thickness of member bc to the nearest 1/16 in
The required thickness of member BC to the nearest 1/16 in. and the diameter of the pins at A and B is dA= [tex]1\frac{1}{8}[/tex] in
To solve thsi It is necessary to determine the thickness of BC. The allowed normal stress is σ[tex]_{allow[/tex]=29 ksi and the permissible shear stress is τ[tex]_{allow[/tex]=10 ksi.
In the first we will determine the reactions of the system.
We apply the conditions of equilibrium:
→+∑Fₓ=0
+↑∑F[tex]_y[/tex]=0
+↺∑M=0
From picture b
∑M[tex]_B[/tex]=0
⇒−2⋅8⋅4+Ay⋅8=0
⇒Ay=8 kip
∑Fy=0
⇒−2⋅8+Ay+By=0
⇒−2⋅8+8+By=0
⇒By=8 kip
From picture c)
∑M[tex]_C[/tex]=0
⇒+By⋅cos60∘−Bx⋅sin60∘=0
⇒+8⋅cos60∘−Bx⋅sin60∘=0
⇒Bx=4.6188 kip
In the next step we will determine the dimensions of the BC rod:
[tex]\sigma BC= \frac {F_{BC}}{A_{BC}}\leq \sigma _{allow}[/tex] =29 ksi
The cross-sectional area has a value:
[tex]A_{BC}=1.5.t[/tex]
The force acting in the BC stick is calculated as follows:
[tex]F_{BC}=\sqrt{4.6188^2+8^2}=9.258 \ kip \\\\=\frac{9.258}{1.5.t}=29 \\\\=t=0.2128 \ in=1/4in[/tex]
Now we can switch to determining the diameter of the pins.
Pin B:
τB=VB/AB⩽τallow=10 ksi
The cross-sectional area has a value:
AB=π/4⋅d²B
The force acting in the BB pin is calculated as follows:
VB=[tex]\sqrt{4.618^2+82^2[/tex]=4.629 kip
[tex]\frac{4.629}{\pi/4 . d^2_B} =10[/tex]
⇒dB=0.767in=13/16in
Now we can switch to determining the diameter of the pins.
Pin A
τA=VA/AA⩽τallow=10 ksi
The cross-sectional area has a value:
[tex]A_A=\pi/4 . d^2B[/tex]
The force acting in the AA pin is calculated as follows:
[tex]V_A=4.618^2+8^2[/tex]=9.258 ki
9.258 ÷ π/4⋅d²A=10
⇒dA=1.0859in=[tex]1\frac{1}{8}[/tex]in
The solution is:
{σs=208 MPa}
{dB=13/16in}
{dA=[tex]1\frac{1}{8}[/tex]in}
Complete Question:
Determine the required thickness of member BC to the nearest 1/16in. and the diameter of the pins at A and B if the allowable normal stress for member BC is σ allow =29 ksi and the allowable shear stress for the pins is τ allow =10τ allow =10 ksi.
To learn more about the area, visit:
brainly.com/question/16151549
#SPJ4
If f(x) is an exponential function where f(−1)=4 and f(0)=18, then find the value of f(−0.5), to the nearest hundredth.
Answer:
The value of f(-0.5) is approximately 0.63
Step-by-step explanation:
An exponential function is of the form f(x) = a^x, where a is a constant. Since we know the values of f(−1) and f(0), we can use them to find the value of a.
From f(−1) = 4, we have:
4 = a^(-1)
From f(0) = 18, we have:
18 = a^0
Dividing the two equations, we have:
a = sqrt(18)
Now that we know the value of a, we can substitute it into the exponential function to find f(−0.5):
f(-0.5) = a^(-0.5) = sqrt(18)^(-0.5) = (4.242640687119285)^(-0.5) = 0.6324555320336758
to the nearest hundredth, it would be 0.63
How am I able to find AB when it has ft
Answer:
AB = 10ft
Step-by-step explanation:
First, we need to know that ED and AD share the same proportions as CB and AB. Since we know ED:AD is 9:6 and CB:AB is 15:x, we can now solve the problem.
ED:AD = 9:6
CB:AB = 15:x
Since we have to multiply the length of ED by 5/3 to get the length of CB, if we multiply the length of AD by 5/3, we can find the length of AB. Since 6*(5/3)=10, the length of AB must be 10.
If this answer helped you, please leave a thanks or a Brainliest!!!
Have a GREAT day!!!
16% of 1 m (in cm)
answer these question please
Answer: 16cm
Step-by-step explanation:
1 metre = 100cm
16% of 100 = 16
Therefore your answer will be 16cm !
There is a proportional relationship between hours, x, and number of miles, y, of water in a tank. The point (2, 80) is on a graph of this relationship. Part A: Explain what the point (2, 80) represents. Part B: Write an equation for the relationship in the form of y = mx.
Part A: The point (2, 80) represents that when the number of hours is 2, the number of miles of water in the tank is 80.
Part B: y = 40x
What is the concept of proportional relationships?The theory used in this question is the concept of proportional relationships.
A proportional relationship between two variables is one in which one variable is a constant multiple of the other.
In this case, the number of miles of water in the tank is a constant multiple of the number of hours.
The equation y = mx is used to describe a proportional relation, where m is the constant of proportionality.
The equation for the proportional relationship between hours, x, and number of miles, y, of water in a tank can be written in the form of y = mx. To find the value of m, we can use the point (2, 80) from the graph. We know that when x = 2, y = 80. We can use this information to solve for m.
m = y/x
m = 80/2
m = 40
Therefore, the equation for the proportional relationship is y = 40x.
To learn more about proportional relationships, visit
brainly.com/question/29765554
#SPJ1
britney took a trip to florida over winter break. at the airport, she paid to check 2 bags. since both of her bags were over the weight limit, she had to pay an additional $9 fee for each bag. britney paid a total of $68 to check her bags. which equation can you use to find the amount of money, x, it costs to check a bag that's under the weight limit?
The equation representing the cost of a bag is 2x + 18 = $68 and for each bag Britney has to pay $25.
Let us consider 'x' be the total cost representing amount of money to check each bag under the weight limit.
Additional amount to pay per bag for over weight limit is equal to $9
Total amount paid by Britney to check both the bags = $68
Equation represents the cost of bags is equal to :
2x + 2(9) = $68
⇒ 2x + 18 = $68
⇒ 2x = $68 - $ 18
⇒ 2x = $50
⇒ x = $50 / 2
⇒ x = $25
Therefore, the equation which represents the cost of a bag is 2x + 18 = $68 and cost for each bag is $25.
Learn more about equation here
brainly.com/question/29538993
#SPJ4
A gumball machine contains 200 gumballs. A random sample of 25 gumballs was collected from the machine. The results from the random sample are shown. 10 gumballs are red 8 gumballs are blue 5 gumballs are green 2 gumballs are white.Based on the random sample results, complete the prediction statements for the entire machine of 200 gumballs.
There are
? red gumballs in the machine.
There are
? more green gumballs than white gumballs in the machine.
There are
? gumballs that are either blue or green in the machine.
Salut/Hello!
Answer: 70, 11, 91
Step-by-step explanation:
g - gumball
/ - fraction line
=> - results
The current total of gumballs = 200 - 25 = 175 gumballs
There are ? red gumballs in the machine:
red g/175 gumballs = 10/25 (the probability of a red gumball to fall in a sample)
red g/175 = 0.4 => 175 x 0.4 = 70 red gumballs
There are ? more green gumballs than white gumballs in the machine:
First, we need to find both green and white gumballs.
green g/175 gumballs = 5/25
green g/175 = 0.2 => 175 x 0.2 = 35 green gumballs
white g/175 gumballs = 2/25
white g/175 = 0.08 => 175 x 0.08 = 14 white gumballs
35 - 14 = 11 more green gumballs than white gumballs
There are ? gumballs that are either blue or green in the machine.
blue g/175 gumballs = 8/25
blue g/175 = 0.32 => 175 x 0.32 = 56 blue gumballs
or
175 - (70 red g + 35 green g + 14 white g) = 175 - 119 = 56 blue gumballs
35 green g + 56 blue g = 91 gumballs that are either blue or green
How do you find the probability?
It's simple, pretend like you have a dice. A dice has 6 faces and you need a six to (example) get out of Jail. You have 6 faces but you only need one, so the probability you get a 6 is 1/6 = 0.1(6)
But let's say you have 2 dices and you need both to be 6 to get out of jail. well thats 1/6 x 1/6 which is equal to 1/36 = 0.02(7)
In the problem, we have the sample of 25 gumballs in which 10 are red.
The probability a red gumball to fall is 10/25 = 0.4 (as calculated above)
I hope it was helpful! :]
why do tan^2 and sec^2 have the same derivative
The derivatives of tan^2(x) and sec^2(x) are the same because they are related by the identity tan^2(x) = sec^2(x) - 1.
By using the chain rule, the derivative of tan^2(x) can be found by first finding the derivative of tan(x), then squaring it. The derivative of sec^2(x) can also be found using the chain rule, by first finding the derivative of sec(x), then squaring it.
Since tan^2(x) and sec^2(x) are related by a constant difference, their derivatives will be the same. This means that the rate of change of tan^2(x) with respect to x will be equal to the rate of change of sec^2(x) with respect to x. This is a useful relationship because it allows us to relate the derivatives of two important trigonometric functions, making it easier to integrate or differentiate expressions involving them.
To know more about tan click here:
https://brainly.com/question/12268041#
#SPJ11
Point A is located at (-6, 2) on the coordinate plane. Point A is reflected over the y-
axis to create point A'. Point A' is then reflected over the r-axis to create point A'.
What ordered pair describes the location of A"?
Consequently, point N's ordered pair is (2,6). A pair that has two values stated in a specific order between parenthesis is known as an ordered pair. It is made up of the x coordinate (abscissa) and the y coordinate (ordinate
What is meant by ordered pair?A pair that has two values stated in a specific order between parenthesis is known as an ordered pair. It is made up of the x coordinate (abscissa) and the y coordinate (ordinate). For greater visual comprehension, it helps to locate a point on the Cartesian plane. An ordered pair of numbers can have either fractional or integer values.Ordered pairs are a common representation for two variables. We mean x = 7 and y = -2 when we write (x, y) = (7, -2). The term "x-coordinate" refers to the number that relates to the value of x, and the term "y-coordinate" refers to the number that relates to the value of y.N's coordinates are: (-2,-6)
To create point N', point N is reflected over the y-axis.
Point N is then created by reflecting point N' over the x-axis ".
To locate: The ordered pair describing N's location ".
Solution:
Point N's coordinates are (-2,-6). To create point N', point N is reflected over the y-axis.
[tex]& (x, y) \rightarrow(-x, y) \\[/tex]
[tex]& N(-2,-6) \rightarrow N^{\prime}(2,-6)[/tex]
Point N is then created by reflecting point N' over the x-axis.
[tex]& (x, y) \rightarrow(x,-y) \\[/tex]
[tex]& N^{\prime}(2,-6) \rightarrow N^{\prime \prime}(2,6)[/tex]
Consequently, point N's ordered pair is (2,6)
To learn more about ordered pair, refer to:
https://brainly.com/question/11139505
#SPJ1
Determine the length of the unknown side given: abc ~efg
Answer:
20
Step-by-step explanation:
Given that the triangles are similar, we know that the corresponding side lengths should all have similar ratios.
This means that ab/ef = bc/fg = ca/ge as they're corresponding.
We know that ge = 8, ca = 4, ab = 10 and we want to find ef
Remember ab/ef = ca/ge so 10/ef = 4/8
4/8 = 10/ef
==> cross multiply
80 = 4ef
==> divide both sides by 4
20 = ef
We can test our answer by seeing if the ratios are the same
ab/ef = 4/8 = 1/2
ca/ge = 10/20 = 1/2
The ratios are the same, therefore our answer is correct.
Use the graph to find the scale factor.
The scale factor is 3.
What is Scale Factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.
Given:
From the graph the dimension of triangle STU is
SU = 5 units
TU = 3 units
ST = 2 units
and, dimension of triangle S'T'U' is
S'U' = 15 units
T'U' = 9 units
S'T' = 6 units
so, the Scale factor is
S'U' / SU = 15 / 5
S'U' / SU = 3
Learn more about scale factor here:
https://brainly.com/question/30215119
#SPJ1
2. Identify the leading coefficient, degree, and the end behavior for the following polynomial functions below.
The leading coefficient, degree and end behaviour are realised for the following polynomials.
What is the leading coefficient?
The leading term is the term containing the highest power of the variable: the term with the highest degree. The leading coefficient is the coefficient of the leading term.
Leading coefficients are the numbers written in front of the variable with the largest exponent. Just like regular coefficients, they can be positive, negative, real, or imaginary as well as whole numbers, fractions or decimals. In a polynomial, the leading term is the term with the highest power of x.
For the given question:
a) -4x⁴-3x³+x²+4
Leading coefficient = -4
Degree = 4
End behaviour
x → ∞, f(x) → - ∞
x → -∞, f(x) → - ∞
b) -2x⁷-6x⁵+2x³
Leading coefficient = -2
Degree = 7
End behaviour
x → ∞, f(x) → -∞
x → -∞, f(x) → ∞
c) 3x²+ 6x -10
Leading coefficient = 3
Degree = 2
End behaviour
x → ∞, f(x) → ∞
x → -∞, f(x) → ∞
Therefore the leading coefficient, degree and end behaviour are realised.
To learn more about the leading coefficient, follow the link.
https://brainly.com/question/24881460
#SPJ1
Consider the set A = {-2, -1, 0, 1, 2} and the equation Y = -x³ + 2 where x is an element of A. State the domain, range and determine whether or not the relation, Y=-x³ + 2 is a function. If it is a function, write the relation in "function notation". Show all your work for full credit. Hint: you might need to draw a diagram.
The domain of the function is {-2, -1, 0, 1, 2}
The range is {10, 3, 2, 1, -6}it is a function with the notation f(x) = -x³ + 2 How to state the function propertiesThe domain
This is the elements in the set A
So, we have
Domain = {-2, -1, 0, 1, 2}
The range
To do this we calculate the value of the function at each x value
So, we have
y = -(-2)³ + 2 = 10
y = -(-1)³ + 2 = 3
y = -(0)³ + 2 = 2
y = -(1)³ + 2 = 1
y = -(2)³ + 2 = -6
So, the range is
Range = {10, 3, 2, 1, -6}
If it is a function
The relation is a function
Because each x value have unique y values
So, the notation is
f(x) = -x³ + 2
Read more about functions at
https://brainly.com/question/28532394
#SPJ1
Which represents the reflection of f(x) = √x over the x-axis?
Can anyone factor these questions?
10) The factor of the expression (x³ + 7x² + 6x) is,
⇒ x (x + 1) (x + 6)
11) The value of a in factor of (x² - 16x + 63) is, - 9
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.
We have to given that;
10) The expression is,
⇒ x³ + 7x² + 6x
11) The expression is,
⇒ x² - 16x + 63
Now, We can factor as;
10) The expression is,
⇒ x³ + 7x² + 6x
⇒ x (x² + 7x + 6)
⇒ x (x² + 6x + x + 6)
⇒ x (x (x + 6) + 1 (x + 6))
⇒ x (x + 1) (x + 6)
11) The expression is,
⇒ x² - 16x + 63
⇒ x² - 9x - 7x + 63
⇒ x (x - 9) - 7 (x - 9)
⇒ (x - 7) (x - 9)
Hence, By compare the factors (x - 7) (x + a), we get;
⇒ a = - 9
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
The baggage handling services of On-Time Airlines is interested in how many baggage handlers they need on duty at various times of the day to ensure that passengers do not wait an unreasonable amount of time for their baggage. An airport executive performed a study and found that there is correlation between the number of passengers arriving at given times and the number of bag handlers needed. She sampled various times during the day and different days of the week including weekends. She recorded the number of passengers arriving within any 1-hour time block. The computer output from the regression equation analysis is shown below.
Predicted Baggage Handlers = 2.86 +0.00408
(number of passengers)
Predictor Coef StDev T P
Constant 2.860 1.324 2.16 0.083
Passengers 0.004081 0.001168 3.49 0.017
S = 1.562 R-sq=70.9% R-Sq(adj) 65.1%
What is the value of the correlation coefficient for the number of baggage handlers and number of
arriving passengers?
A) -0.842
B) 0.651
C) 0.709
D). .842
E) 1.562
The value of the correlation coefficient for the number of baggage handlers and the number of arriving passengers is 0.842.
Therefore the answer is D. 0.842
The correlation coefficient is a measure of the strength of the linear relationship between two variables. It is a value between -1 and 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.
In this case, the output from the regression equation analysis states that the correlation coefficient is √0.709 = 0.842, which means that there is a strong positive linear relationship between the number of baggage handlers and the number of arriving passengers. A correlation coefficient of 0.842 is considered a strong positive relationship.
In this case, an increase in the number of arriving passengers is associated with an increase in the number of baggage handlers needed, as reflected by the positive correlation coefficient.
To know more on correlation coefficient
https://brainly.com/question/15577278
#SPJ4
suppose we draw two random numbers x and y each distributed uniform on the interval [0,1]. if x and y are independent, what’s the probability that their product x*y is greater than 1/2?
The probability that two random numbers, x and y, both of which are uniformly distributed on the interval [0,1] and independent, will have a product greater than 1/2 is 1/8.
Probability is a field of mathematics that deals with the study of random events.
In this question, we're looking at the probability of two random numbers having a product greater than 1/2.
Let's take two random numbers, x and y, both of which are uniformly distributed on the interval [0,1].
And since x and y are independent, the occurrence of one event does not affect the occurrence of the other event.
To find the probability that x * y is greater than 1/2, we need to find the area of the region in the x-y plane where x * y is greater than 1/2.
This region is a triangle whose vertices are (0,1), (1,0), and (1/2, 1/2).
The area of this triangle is 1/8, so the probability that
=> x * y > 1/2 = 1/8.
To know more about probability here
https://brainly.com/question/11234923
#SPJ4
