The domain is [2,6] and the range is [-2,0].
What is the Domain and Range of a Function?The Domain is all the possible input values to the function, while the range is all the possible values a function can have as an output.
The parabola has endpoints of (2,-2) and (6,-2).
The vertex is (4,-6)
The domain is [2,6]
The range is [-2,0]
Therefore, the domain is [2,6] and the range is [-2,0].
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What is the equation of the graph below?
Answer:
A
Step-by-step explanation:
The population f(x), in millions, of State A of a country after x years is represented by the function shown below:
f(x) = 4(1.08)x
The graph shows the population g(x), in millions, of State B of the country after x years:
graph of exponential function g of x that curves up from left to right and goes through points 0 comma 2 and 9 comma 4
Which conclusion is correct about the populations of State A and State B?
Option 1 is correct. The correct solution about these functions is that The original population of State A was double of the original population of State B.
How to solve for the solutionThe function in the question is given as
For A:
[tex]F(x) = 4*(1.08)^x[/tex]
For B
[tex]g(x) = 2*(1.08)^x[/tex]
The exponential growth equation that is used to solve this is
[tex]h(x) = A(r)^x[/tex]
such that A is the initial and r is the rate of growth.
f(x) and g(x) are at the same rate but the exponential function is known to grow faster.
Hence the correct option is The original population of State A was double of the original population of State B.
Complete question:Which conclusion is correct about the population of State A and State B? 1. The original population of State A was double of the original population of State B.
2. The original population of State A was half of the original population of State B.
3. The original population of State B was one-fourth of the original population of State A.
4. The original population of State A was one-fourth of the original population of State B.
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Answer:
Step-by-step explanation:
honestly thats what it is
what is the probability of getting a number less than 5 and a head when rolling a die and tossing, help someone quickly
Which of the following shows the simplified form of sin x/1+cos x
O sin x- tan x
O sin x-cot x
O csc x-cot x
01
Answer:
csc x - cot x
Step-by-step explanation:
(sinx)/(1+cos x)
Multiplying the numerator and denominator by (1-cos x),
((sinx)(1-cos x))/(1-cos² x)
((sinx)(1-cosx))(sin²x)
(1-cosx)/(sinx)
cscx - cot x
Can someone help me with this step by step with explanation im confused need help
The construction is to draw a parallel line to a given line AB passing through point P. To fix the error, the 3rd arc must be reconstructed. Thus the correct option is D. The third arc should be drawn centered at F.
The given construction involves drawing a parallel line through a given point P to a given line AB.
From the construction shown, drawing a straight line through P and G would not be parallel to the given line AB. Thus there is an error in the construction of the 3rd arc. To draw the required corresponding angle, the 3rd arc has to be reconstructed.
Therefore to fix the error the correct step to follow is: Option D. The third arc should be drawn centered at F.
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Kindly contact a 1-on-1 tutor if more explanations are needed.
Question 1 of 10
The Quadratic Formula gives which roots for the equation 2x²+x-6=0?
Answer:
x=-3/2 or-2
Step-by-step explanation:
hope this helps
14. Find the value of X round the nearest degree 12 15
The measure of the angle x is 53.13 degrees after applying the sin ratio.
What is the trigonometric ratio?The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
Applying sin ratio:
sinx = 12/15
sinx = 0.8
x = 53.13 degrees
Thus, the measure of the angle x is 53.13 degrees after applying the sin ratio.
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mark: 3,2,0,1,9,12,3,5
if the pass mark is 5, how many students failed the text
Answer:
5
Step-by-step explanation:
Anything below 5 is a fail:
3, 2, 0, 1, 3
That's 5 students.
The average student loan debt for college graduates is $25,150.
Suppose that that distribution is normal and that the standard deviation
is $12,050. Let X = the student loan debt of a randomly selected college
graduate. Round all probabilities to 4 decimal places and all dollar
answers to the nearest dollar.
a. What is the distribution of X? X - N
b Find the probability that the college graduate has between $14,200
and $33,950 in student loan debt.
c. The middle 10% of college graduates' loan debt lies between what
two numbers?
Low: $
High: $
Using the normal distribution, it is found that:
a) [tex]X \approx N(25150, 12050)[/tex]
b) There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.
c) Low: $23,519.65, High: $26,580.35.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 25150, \sigma = 12050[/tex].
Hence the distribution of X can be described as follows:
[tex]X \approx N(25150, 12050)[/tex]
The probability that the college graduate has between $14,200 and $33,950 in student loan debt is the p-value of Z when X = 33950 subtracted by the p-value of Z when X = 14200, hence:
X = 33950:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33950 - 25150}{12050}[/tex]
Z = 0.73
Z = 0.73 has a p-value of 0.7673.
X = 14200:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14200 - 25150}{12050}[/tex]
Z = -0.91
Z = -0.91 has a p-value of 0.1814.
0.7673 - 0.1814 = 0.5859.
There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.
Considering the symmetry of the normal distribution, the middle 10% is between the 45th percentile(X when Z = -0.127) and the 55th percentile(X when Z = 0.127), hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.127 = \frac{X - 25150}{12050}[/tex]
X - 25150 = -0.127(12050)
X = $23,519.65.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.127 = \frac{X - 25150}{12050}[/tex]
X - 25150 = 0.127(12050)
X = $26,580.35.
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The actual length of the ship is 575 feet. The scale of the model is 1 inch: 25 feet. What will be the length of the model?
The length of the model as described in the task content would be; 23 inches.
What is the length of the model?According to the task content, it follows that for every 25 feet measure of the actual ship length, the representation is 1 inch on the model.
On this note, for 575 feet length of the actual ship, the length of the model is; 575/25 = 23 inch.
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Write the equation of a sine or cosine function to describe the graph.
Answer:
y = cos(3/2x)
Step-by-step explanation:
A general sine or cosine function will have parameters of amplitude, vertical and horizontal offset, and period. The values of these parameters can be determined from the given graph.
y = A·cos(2π(x -B)/P) +C
where A is the amplitude, B and C are the horizontal and vertical offsets, and P is the period.
AmplitudeFor sine and cosine functions, the amplitude of the function is half the difference between the maximum and minimum:
A = (3 -1)/2 = 1
Horizontal offsetA sine function has its first rising zero-crossing at x=0. A cosine has its first peak at x=0. The given graph has its first peak at x=0, so it is a cosine function with no horizontal offset.
B = 0
Vertical offsetFor sine and cosine functions, the vertical offset is the average of the maximum and minimum values:
C = (3 +1)/2 = 2
PeriodThe period is the difference in x-values between points where the function starts to repeat itself. Here, we can use the peaks to identify the period as 4π/3.
P = 4π/3
Function equationUsing the parameter values we determined, the function can be written as ...
y = cos(3/2x) +2
__
Additional comment
The argument of the cosine function is ...
[tex]\dfrac{2\pi(x-B)}{P}=\dfrac{2\pi(x-0)}{\dfrac{4\pi}{3}}=\dfrac{3(2\pi)}{4\pi}x=\dfrac{3}{2}x[/tex]
A body of mass 50 kg explodes and splits into three pieces. The first piece has a mass of 10 kg and a velocity of [-3,2] m/s, the second piece has a mass of 18 kg and a velocity of [5,-4]m/s. What is the velocity of the third piece?
Step-by-step explanation:
From the conversation of angular momentum
Initial momentum=final momentum
Here,
Since body is initially resting, it's momentum must be zero.
Let v be velocity of third piece. Then
0= 10(-3i+2j) + 18(5i-4j) + 22v
Solving this we get,
v= 4/22(15i+13j).
The velocity of third piece is 2/11(13 j - 15i)
What is velocity?Velocity defines the direction of the movement of the body or the object.
Given:
As the body is at rest so the initial momentum is zero.
Let v be velocity of third piece.
so,
0= 10(-3i+2j) + 18(5i-4j) + 22v
0= -30i + 20j + 90i -72j + 22 v
0= 60i - 52j + 22 v
-60i +52j = 22v
v= 2/11( 13j - 15 i)
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Solution
We are given two endpoints here
Point 1: (−1, Answer
)
Point 2: ( Answer
,4)
We know our rise between the two points is 1. So
12= Answer
And our run between the two points is 4. So
42= Answer
We now have rise2+run2=distance2, so we have
1+16=distance2
Answer
=distance2
So once we take the square root of both sides we have
distance=√ Answer
We could also use the actual distance formula we developed to get the same answer.
d=(4−3)2+(−5−(−1)2)−−−−−−−−−−−−−−−−−−−√
d=(12+(−4)2)−−−−−−−−−−√
d=(1+16)−−−−−−−√
d=√ Answer
The distance between the two points on the plane is √17
Distance between two pointsThe formula for calculating the distance between two points is expressed as;
D = √(x2-x1)²+(y2-y1)²
From the given plane, we have the following coordinates
(-5, 4) and (-1, 3)
Substitute
D = √(3-4)²+(-1-(-5))²
D = √(-1)²+(4)²
D= √1+16
D=√17
Hence the distance between the two points on the plane is √17
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A simple random sample of 50 items from a population with 7 resulted in a sample mean of 35.
The 90% , 99% confidence interval for the population mean is 32.145 < [tex]\rm \mu[/tex] < 35.855 and 31.093 < [tex]\rm \mu[/tex] < 36.907
What is Probability ?Probability is the study of likeliness of an event to happen.
It is given that
Total Population = 50
Mean = 35
The confidence interval is given by
[tex]\rm CI = \mu + z \dfrac{s}{\sqrt n}[/tex]
[tex]\rm \mu[/tex] is the mean
z is the confidence level value
s is the standard deviation
n is the population width
(a) The 90% confidence interval for the population mean
90% [tex]\rm \alpha / 2[/tex] = 0.05
Z = 1.64
34 [tex]\rm \pm[/tex] 1.64 * 8 / √50
34 [tex]\rm \pm[/tex] 1.855
32.145 < [tex]\rm \mu[/tex] < 35.855
(b) The 99% confidence interval for the population mean
99% [tex]\rm \alpha / 2[/tex] = 0.005
Z=2.57
34 [tex]\rm \pm[/tex] 2.57 * 8 / √50
34 [tex]\rm \pm[/tex] 2.907
31.093 < [tex]\rm \mu[/tex] < 36.907
Therefore the confidence interval for population mean has been determined.
The complete question is
A simple random sample of 50 items from a population width =7 resulted in a sample mean of 35. If required, round your answers to two decimal places.
a. Provide a 90% confidence interval for the population mean
b. Provide a 99% confidence interval for the population mean
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Write the number in numerical form-twenty-six thousandths
A Bus begins its trip with R occupants (including the driver).At each of the 20 stops three people get on and no one leaves if there are three times as many boss occupants at the end of the 20th stop as there are at the end of the fourth stop how many occupants did the bus have immediately after the 10th stop?Pls explain for brainlest
A.12
B.24
C.30
D.42
Answer
D.42
Step-by-step explanation:
It's pretty easy and hard at the same time just do not overthink it. Obviously, the bus leaves with R occupants including the driver but that still means that there are occupants, to begin with. Now remembering that 3 people get on each stop you can take it to multiply 3*10 (3 people, ten stops) you would get thirty. Would this be the answer? NO! Remember that you began with R occupants to begin with and either using the process of elimination or common sense you can conclude that 12,24 are improbable answers because they are lower than thirty, and what about thirty? No, because you had thirty people in addition to the original occupants so that eliminates thirty. What's left?
42
There Is Your Answer
Answer:
D. 42================
GivenThe bus has initially R occupants,At each stop the occupants increase by 3,After 20 stops there are 3 times more occupants than after 4 stops.To findThe number of occupants after 10 stopsSolutionLet's find out the how many occupants are there after 20 and 4 stops, then compare:
After 20 stops:
R + 3*20 = R + 60After 4 stops:
R + 3*4 = R + 12Compare and solve for R:
R + 60 = 3(R + 12)R + 60 = 3R + 363R - R = 60 - 362R = 24R = 12We found the number of initial occupants.
Use this to find the number of occupants after 10 stops:
12 + 3*10 = 12 + 30 = 42Correct answer choice is D.
In the video, the water level was 15 milliliters before adding the chain, and 20 milliliters after adding the chain. When I weighed the chain, its mass was 73.5 grams.
I believe the chain is solid metal (not gold plated), but is probably a blend of gold and other metals. I looked up that gold has a density of 19.3 g/ml, while the other metals like silver and copper usually blended with gold have a combined density of about 9.7 g/ml.
Determine what percentage of the chain is gold, by mass, to at least 1 decimal place?
%
Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is H=60 and from a second position L=30 farther along this path it is B=50 What is the height of the tree?
The height of the tree based on the information is 229.23.
How to calculate the height?Based on the information given,
tan 50 = h/x + 60
h = (x + 60)tan 50°
x tan 60 = (x + 60)tan 50°
x(tan 60° - ta 50°) = 60 ta 60
x = 132.34
Therefore, the height will be:
= x tan60°
= 132.34 × tan 60
= 229.23
Therefore, the height is 229.23.
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Please solve this❣️
Answer:
f⁻¹(1/5) = 2
Explanation:
If f(x) = (2x -3)/5
To find inverse of f(x), make x the subject.
[tex]f(x) = \dfrac{2x - 3}{5}[/tex]
[tex]5 f(x) = 2x - 3[/tex]
[tex]2x = 5 f(x) + 3[/tex]
[tex]x = \dfrac{5 f(x) + 3}{2}[/tex]
Then,
[tex]f^{-1}(x) = \dfrac{5x+3}{2}[/tex]
To find f⁻¹(1/5), simplify insert [x = 1/5 or 0.2]
[tex]f^{-1}(0.2) = \dfrac{5(0.2)+3}{2}[/tex]
which yields
[tex]f^{-1}(0.2) = 2[/tex]
what is the reminder when X³ +4X² - 2X + I is divided by X + 1 what is the reminder when X³ + 4X² - 2X + I is divided by X + 1
Answer:
6
Step-by-step explanation:
Which of these is an exponential parent function? OA. f(x)=2x-2 OB. f(x) = 2x C. f(x) = 2x + 3 OD. f(x) = 24x
The answer to this question is choice B
9. The measure of each exterior angle of a regular pentagon is
the measure of each exterior
angle of a regular nonagon.
Answer:
55,55
Step-by-step explanation:
hereakaigdidjuwjapwwjshd
Halfway through the season, a soccer player has made 12 penalty kicks in 18 attempts.
Based on her performance to date, what is the relative frequency probability that she will miss
her next penalty kick?
Answer:
21
Step-by-step explanation:
18÷6=3 attemps
13÷6=2 makes
she will probably missed I next 3rd pe alty kick
21st attempts
A 4-sided dice is rolled. The set of equally likely outcomes is {1,2,3,4}. Find the probability of rolling a number less than 14
The probability of rolling a number less than 14 is?
The probability of rolling a number less than 14 among {1,2,3,4} is 1.
Given The dice is 4 sided. Likely outcomes is {1,2,3,4} and we have to find the probability of rolling a number less than 4.
Probability is the likeliness of happening an event among all the events possible. The value of probability cannot be negative or greater than 1. It lies between 0 to 1. The formula of calculating probability is:
Probability= number of events/ total number of events.
Total likely outcomes=4 {1,2,3,4}
Numbers less than 14 = 4
Probability of rolling a number less than 14=1/4
=0.25 because all number less than 14 is present.
1,2,3,4 are all less than 14.
and because all numbers are included that's why the value of probability is 1.
Hence the probability of rolling a number less than 14 is 1.
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The sum of two numbers is 32. One number is 3 times the other. Find the numbers.
The numbers whose sum is 32 in which one number is 3 times the other is 8 and 24 respectively.
Equation of the unknownLet
x = one of the unknowns3x = second unknownx + 3x = 32
4x = 32
x = 32/4
x = 8
So,
3x = second unknown
= 3(8)
= 24
Check:
x + 3x = 32
8 + 24 = 32
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Whats the correct answer answer asap for brainlist
Answer:
option C: Asian
explanation:
Asian countries, such as China, produce goods like the European products, but for much cheaper prices.
The cleaning service requires $39 in variable costs for cleaning materials. The fixed costs of labor, the company's truck, and administrative support are $349,200 per year. Chimneysweep averages 200 service calls per month. What is the average cost per cleaning service call?
The average cost per cleaning service call charge by the company is $184.5.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the total cost for x number of service calls in a year. Hence:
y = 39x + 349200
For 200 service call, in a year, x = 200 * 12 = 2400
y = 39(2400) + 349200 = $442800
Average cost = $442800 / 2400 = 184.5
The average cost per cleaning service call charge by the company is $184.5.
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Simplify the following.
7² =
4⁰ =
6-¹=
Answer:
49
1
1/6
Step-by-step explanation:
7^2 is just 7 * 7 = 49
4^0 = 1, since anything to the power of 0, is 1.
[tex]6^{-1}[/tex] is equal to [tex]\frac{1}{6}[/tex] since [tex](\frac{a}{b})^{-x}=(\frac{b}{a})^x=\frac{b^x}{a^x}[/tex]. Whenever you have a negative exponent, you flip the fraction, in this case the fraction is 6/1 so it becomes 1/6. then distribute the exponent across the division and you get 1^1/6^1 which is just 1/6
Answer:
491Step-by-step explanation:
hey
please like my question
Mr. Parks begins to fill a large container with water for the dunk tank at the school
fair before asking Brian to finish the job. The container has 25 gallons of water in it
before Brian uses a hose to finish filling it up. The container fills at a rate of 10
gallons per minute. Suppose that y is the amount of water in the tank after x
minutes. Which equation could be graphed to help Brian find out how much water is
in the tank at any time?
y = 25x + 10
y= 10x + 25
y= 10x - 25
y = 10x
Answer:
The answer is B / y= 10x+25
Step-by-step explanation:
your welcome
ch circle shows AB that measures 60°?
O
60⁰ -0
A
60°
B
60°
.0
Mark this and return
B
B
Save and Exit
Next
Submit
Step-by-step explanation:
there are a lot of typos and missing info in your problem and answer option definition.
based on what I understood the answer should be
"the second answer option".
this is where A and B have an arc angle (or inner angle at the center of the circle) of 60°.
one could see the 3rd answer to be right too, as the angle between A and B at Y is also 60°.
but I don't think this is really the meaning of this question here.