Answer:
We conclude that the mean waiting time is less than 10 minutes.
Step-by-step explanation:
We are given that a public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes.
Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.8 minutes with a standard deviation of 2.5 minutes.
Let [tex]\mu[/tex] = mean waiting time for bus number 14.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 10 minutes {means that the mean waiting time is more than or equal to 10 minutes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 10 minutes {means that the mean waiting time is less than 10 minutes}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean waiting time = 7.8 minutes
s = sample standard deviation = 2.5 minutes
n = sample of different occasions = 18
So, test statistics = [tex]\frac{7.8-10}{\frac{2.5}{\sqrt{18} } }[/tex] ~ [tex]t_1_7[/tex]
= -3.734
The value of t test statistics is -3.734.
Now, at 0.01 significance level the t table gives critical value of -2.567 for left-tailed test.
Since our test statistic is less than the critical value of t as -3.734 < -2.567, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean waiting time is less than 10 minutes.
Using the t-distribution, it is found that since the test statistic is less than the critical value for the left-tailed test, it is found that there is enough evidence to support the claim that the mean is less than 10 minutes.
At the null hypothesis, it is tested if the mean is of at least 10 minutes, that is:
[tex]H_0: \mu \geq 10[/tex]
At the alternative hypothesis, it is tested if it is less than 10 minutes, that is:
[tex]H_1: \mu < 10[/tex]
We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are: [tex]\overline{x} = 7.8, \mu = 10, s = 2.5, n = 18[/tex]
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{7.8 - 10}{\frac{2.5}{\sqrt{18}}}[/tex]
[tex]t = -3.73[/tex]
The critical value for a left-tailed test, as we are testing if the mean is less than a value, with a 0.01 significance level and 18 - 1 = 17 df is of [tex]t^{\ast} = -2.57[/tex]
Since the test statistic is less than the critical value for the left-tailed test, it is found that there is enough evidence to support the claim that the mean is less than 10 minutes.
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8.98 to the nearest tenth
Answer:
9.0
Step-by-step explanation:
depends on the last digit of the number.If it's 5 or more it becomes 9.0.If it's less than 5, then it's 8.0.In this case it's greater so the answer is 9.0
Hope that was helpful.Thank you!!!
1.5d+3=-4.5 what does D equal
Answer:
d = − 5
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
-1.5
Step-by-step explanation:
subtract 3 from both sides.
5d=-7.5
divide by 5
d=-1.5
Ms. Davis schedules after-school group
activities for 18 girls and 24 boys. She wants
to make equal groups with the same number
of girls and the same number of boys in
each group. Ms. Davis says that the greatest
number of equal groups she can make is 3.
Answer:
Ms. Davis is wrong
Step-by-step explanation:
she can make equal groups of 6
What is 13/15 as a decimal rounded to the nearest tenth
Answer:
i think it would be rounded to a whole
Step-by-step explanation:
tell me if im wrong
Step-by-step explanation:
Convert
13/15
to a decimal.
0.8
¯
6
Find the number in the tenth place
8
and look one place to the right for the rounding digit
6
. Round up if this number is greater than or equal to
5
and round down if it is less than
5
.
0.9
Simplest Form...
Choose a fraction that is in the
simplest form. Make 15 new
equivalent fractions.
can someone help me please I don't know how to do that
Answer:
Pick any fraction that is already in its simplest form, for example:
[tex]\frac{1}{2}[/tex]
and do this;
[tex]\frac{1 \times x}{2 \times x}[/tex]
times the denominator and numerator with any number, but must be the same! and do it 15 times, like so;
[tex]\frac{1 \times 2}{ 2 \times 2} , \frac{1 \times 3}{2 \times 3}, \: \: continue...[/tex]
and u will get this:
[tex]\frac{1}{2} =\frac{2}{4}, \frac{3}{6}, \frac{4}{8}, \frac{5}{10}, \frac{6}{12}, \frac{7}{14}, \frac{8}{16}, \frac{9}{18}, \frac{10}{20}, \frac{11}{22}, \frac{13}{26}, \frac{14}{28}, \frac{15}{30}, \frac{16}{32}, \frac{17}{34}[/tex]
To create equivalent fractions, you choose a simple fraction like 1/2. You then multiply both the numerator and denominator of this fraction by the same number to get a new fraction. You can do this 15 times to get 15 different equivalent fractions.
Explanation:The subject is finding equivalent fractions. Let's start with a simple fraction like 1/2. Equivalent fractions are just multiples of this fraction. So, we multiply both the numerator (top number) and the denominator (bottom number) by the same number to get an equivalent fraction. Here are some examples:
1/2 x 2/2 = 2/4 1/2 x 3/3 = 3/6 1/2 x 4/4 = 4/8 And so on...
Following this method, you can create 15 different equivalent fractions for 1/2. Remember that the fractions should be in their simplest form, meaning that there's no number (except for 1) that could divide both the numerator and denominator evenly.
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Which is the simplified form of the expression?
Please help!
Answer:
A
Step-by-step explanation:
The graph of which function has an axis of symmetry at x = 3? Picture A, B, C, or D?
Answer:
The last graph f(x)=x^2-6x-1
Step-by-step explanation:
The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
The graph shown in picture D with equation f(x) = x²-6x-1 , has axis of symmetry at x = 3.
4 graphs are given in order to identify which of them contains axis of symmetry at x = 3
The axis of symmetry is the center axis of the curves where the curve is equally divided.
For Picture A
The axis of symmetry is x = 1.5 so it is not the correct option.
For picture B
The axis of symmetry is x = 1.3 so it is not the correct option.
For picture C
The axis of symmetry is x = -3. So it is not correct option
For picture D
The axis of symmetry is x = 3. it is the correct option.
The graph shown in picture D with equation f(x) = x²-6x-1 , has axis of symmetry at x = 3.
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Which description compares the domains of Function A and Function B correctly?
Function A: f(x)=−3x+2
Function B:
Half of a parabola graphed on a grid in Quadrant One with the x and y axis beginning at negative ten and increasing in increments of two until reaching ten. The parabola, labeled g of x, contains a filled in point at begin ordered pair zero comma zero end ordered pair, passes through begin ordered pair two comma two end ordered pair and begin ordered pair four comma eight end ordered pair, and as a smooth curve while extending to infinity.
The domain of both functions is the set of real numbers greater than or equal to 0.
The domain of both functions is the set of real numbers.
The domain of Function A is the set of real numbers.
The domain of Function B is the set of real numbers greater than 0.
The domain of Function A is the set of real numbers.
The domain of Function B is the set of real numbers greater than or equal to 0.
Answer:
The domain of Function A is the set of real numbers.
The domain of Function B is the set of real numbers greater than or equal to 0.
The domain of a function is the set of its possible inputs. it means that the set of input values for which the function is defined.
The domain of Function A is the set of real numbers.
The domain of Function B is the set of real numbers greater than or equal to zero.
Here, function A is given that, [tex]f(x)=-3x+2[/tex]
Since, above function can take any value as its input.
That is function is defined for every value of x.
Therefore, The domain of Function A is the set of real numbers.
Here, graph of function B is attached.
From graph of function B, it is observed that graph of function is right side of Y - axis and starting from x = 0. It means that function B can take any value greater than equal to zero.
Therefore, The domain of Function B is the set of real numbers greater than or equal to zero.
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What is the length of arc S shown below?
The angle in the figure is a central angle in radians.
Answer:
2
Step-by-step explanation:
Arc length = r × theta
Arc length = 5 × 0.4
= 2
what is x + y = 12 if x = 2y
Answer:
x=8
y =4
Step-by-step explanation:
x + y = 12 if x = 2y
Replace x with 2y in the first equation
2y+y = 12
Combine like terms
3y =12
Divide by 3
3y/3 =12/3
y = 4
Now we can find x
x=2y
x=2(4)
x = 8
Determine which graph represents a reflection across the x-axis of f(x) = 3(1.5)x.
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and then decreases in quadrant 4. It crosses the y-axis at (0, negative 0.5).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and then decreases in quadrant 4. It crosses the y-axis at (0, negative 3) and goes through (2, negative 7).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and then decreases in quadrant 4. It crosses the y-axis at (0, negative 3) and goes through (0.5, negative 7).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and then increases in quadrant 1. It crosses the y-axis at (0, 3).
Answer:
its b
Step-by-step explanation:
i just did it
Answer:
graph B on edg
Step-by-step explanation:
Flying saucers pizza charges $0.15 per square inch for circular pizzas. If a pizza is measured by the diameter, how much will flying saucers pizza charge for a 7 inch, 10 inch and 14 inch pizza?
The local skating rink pays Mary a fixed rate per pupil plus a base amount to work as a skating instructor. She earns $90 for
instructing 15 students on Monday afternoon. Last Friday, she earned $62 for working with 8 students. Lisa is also a skating
instructor. She receives half the base amount that Mary does, but she is paid twice as much per student. Who would eam
more money instructing a class of 20 students?
Lisa would earn $120 more than Mary.
Lisa would earn $65 more than Mary.
Mary would earn $15 more than Lisa.
Mary would earn $10 more than Lisa.
Mark this and return
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Who earns
Answer:The expressions for the payment made to Mary are,
(Monday) 90 = 15m + b
(Tuesday) 62 = 8m + b
where m and b are the fee per student and the base fee, respectively. Solving for m and b, the values are 4 and 30.
The equation that represents Mary's earning is
y = 4x + 30
For 20 students,
y = 4(20) + 30 = 110
For Lisa's earnings,
y = 8x + 15
Substituting 20,
y =8(20) + 15 = 175
Thus, Lisa would earn more than Mary by $65.
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Step-by-step explanation:
if an inscribed angle has a measure of 100°, what is the measure of the intercepted arc?
Answer:
w
hi ut ir8fue j de bi 8d
Step-by-step explanation:
qqq73838rufjei34748ri4oi4i
What is the sum? StartFraction 3 y Over y squared + 7 y + 10 EndFraction + StartFraction 2 Over y + 2 EndFraction
Answer:
[tex]\dfrac{5}{y+5}[/tex]
Step-by-step explanation:
Here, we have to find the sum of 2 fractions:
1st fraction: [tex]\dfrac{3y}{y^{2}+7y+10}[/tex]
2nd fraction: [tex]\dfrac{2}{y+2}[/tex]
Considering the denominator of 1st fraction:
[tex]y^{2}+7y+10[/tex]
Using factorization method:
[tex]7y[/tex] can be written as [tex](2y + 5y)[/tex].
[tex]\Rightarrow y^{2}+2y+5y+10[/tex]
Taking 5 common from [tex]5y+10[/tex] and y common from [tex]y^{2}+2y[/tex]: [tex]\Rightarrow y(y+2)+5(y+2)[/tex]
Now taking [tex](y+2)[/tex] common:
[tex]\Rightarrow (y+5)(y+2)[/tex]
[tex]\dfrac{3y}{y^{2}+7y+10}[/tex] can be written as [tex]\dfrac{3y}{(y+5)(y+2)}[/tex]
Now, calculating the sum:
[tex]\dfrac{2y}{(y+5)(y+2)} + \dfrac{2}{y+2}[/tex]
Taking LCM and solving:
[tex]\Rightarrow \dfrac{3y+2(y+5)}{(y+5)(y+2)}\\\Rightarrow \dfrac{5y+10}{(y+5)(y+2)}\\\Rightarrow \dfrac{5(y+2)}{(y+5)(y+2)}\\\Rightarrow \dfrac{5}{(y+5)}[/tex]
Hence, answer is [tex]\dfrac{5}{y+5}[/tex].
Answer:
its c
Step-by-step explanation:
i have takin da test
1. A baseball player hits a baseball into the air with an initial vertical velocity of 72 feet per second from a height of 3 feet. ( h = -16t2 +72t +s )
Answer:
You actually do not ask anything here, so i will find the equation for the height and i will use it to find something useful, like the maximum height of the baseball.
For any object in a vertical motion, the only force acting on it is the gravitational force, so the acceleration of the object will be equal to g.
a(t) = -g
where the minus sign is because the gravitational acceleration pulls down.
For the velocity we can integrate over time, and get:
v(t) = -g*t + v0
Where v0 is the initial velocity, in this case v0 = 72 ft/s
v(t) = -g*t + 72ft/s
with this equation we can find the time in wich the height is maximum, we need to find the time where the velocity is 0.
-g*t + 72 = 0
t = 72/g
for the height we can integrate over time again:
h(t) = (-g/2)*t^2 + 72ft/s*t + h0
where h0 is the initial height, in this case h0 = 3ft
here we can also replace the value of g = 32ft/s^2
h(t) = (-16ft/s^2)*t^2 + 72ft/s*t + 3ft
Now we can evaluate this in the time that we previously find, t = 72/g = 72/32 = 2.25s
h(2.25s) = -16*2.25^2 + 72*2.25 + 3 = 85.08 feet
Write a coordinate proof to prove that the segment that joins the vertex angle of an isosceles triangle to the midpoint of its base is perpendicular to the base
Answer:
Slope of the base segment line is zero, hence base segment is horizontal
Slope of the segment that joins the vertex angle to the midpoint of its base is undefined hence the line is vertical
Therefore, angle between base segment line and the segment line from the vertex angle to the midpoint is perpendicular
Therefore, the segment that joins the vertex angle to an isosceles triangle to the midpoint of its base is perpendicular to the base
Step-by-step explanation:
Here we prove the required relation as follows;
Let the isosceles be ABC
The coordinates of the points are
C = (0, 0) (Vertex)
A = (-a, b)
C = (a, b)
P = (0, b) (Midpoint of base)
Therefore, the gradient or slope of the base AC is presented as follows;
[tex]Slope, m \, of \. base, \, AC= \frac{dy}{dx} = \frac{b - b}{a - (-a)} = \frac{0}{2\cdot a} = 0[/tex]
Hence, segment AC is vertical
[tex]Slope, m \, of \, segment \ CP \, joining \, vertex, \, to \, midpoint, P, on \,AC = \frac{0 - b}{0 - 0} = \frac{-b}{0} = Undifined.[/tex]
Hence, segment CP is vertical
Therefore, the segment that joins the vertex angle to an isosceles triangle to the midpoint of its base is perpendicular to the base.
In an isosceles triangle with base BC, the segment from vertex A to the midpoint M of BC is vertical, whereas BC is horizontal. Since vertical and horizontal lines are perpendicular by definition, AM is perpendicular to BC.
Let's assign coordinates to the isosceles triangle ABC, where AB = AC and BC is the base. Assume the vertex A is at the origin (0, 0), the base endpoints B and C are at coordinates (-b, c) and (b, c) respectively.
First, find the midpoint M of BC. The coordinates of M will be the average of the x-coordinates and the y-coordinates of B and C. Thus, M = (0, c).Next, determine the slope of line AM (vertex to midpoint). Since A is at (0, 0) and M is at (0, c), the slope is:Fiona is trying to prove that a pair of expressions are equivalent by using substitution. Which pair of expressions has the same value if she substitutes y = 3?
Answer:
the answer is A i finished that test now im on another test and timed sorry for no explanation
Step-by-step explanation:
A
Answer:
A
Step-by-step explanation:
A because I did all on the question and A was the one
Maria is buying new carpet for her bedroom. Her bedroom is in the shape of a square
and the length of each side is 12 feet. Write and simplify an exponential expression to
find how much carpet she needs.
Answer:
(12 ft)^2 = 144 square feet
Step-by-step explanation:
How does the store sell carpet?
In square feet of carpet, right?
so
If the whole square bedroom needs to be covered with carpet, then the area to cover is A = x * x = 12 feet * 12 feet = 144 square feet
How can you find the area of a two-dimensional composite figure, or the surface area of a three-dimensional composite figure?
Step-by-step explanation:
a. the area of a two-dimensional composite figure
In this situation, we need to draw any necessary segments to view the figure as basic shapes, then:
Step 1: add basic shape areas belonging to the composite shape Step 2: subtract basic shape areas NOT belonging to the composite shapeb. the surface area of a three-dimensional composite figure
As we know (3D) composite objects are made of two or more objects put together. To find the surface area of a 3D composite object, we need:
Step 1: find the outside surface area of each object Step 2: add the surface areas togetherHope it will find you well
Final answer:
To find the area of composite figures, break them down into simpler shapes and sum up their areas. For three-dimensional figures, find individual surface areas and add them up.
Explanation:
Area can be determined by counting the number of squares inside a shape on 1 cm x 1 cm graph paper. For composite figures, break them down into simpler shapes, find their individual areas using appropriate formulas, then add them up. For three-dimensional composite figures, calculate surface area by finding the sum of individual surface areas of each component shape.
The number of calories in a muffin is directly proportional to the amount of sugar in the muffin. If a 200 calorie muffin has 500 grams of sugar. How many calories are in a muffin with 2,075 grams of sugar
Answer:
830 calories
Step-by-step explanation:
The number of calories in a muffin is directly proportional to the amount of sugar in the muffin.
Let the number of muffins be N and the amount of sugar in the muffin be A. This means that:
N α A
=> N = kA
where k = constant of proportionality
A 200 calorie muffin has 500 grams of sugar.
This implies that:
200 = k * 500
=> k = 200 / 500 = 2/5
The constant of proportionality is 2/5.
The number of calories in a muffin with 2075 grams of sugar is:
N = 2/5 * 2075
N = 830 calories
There are 830 calories.
Final answer:
A muffin with 2,075 grams of sugar contains 830 calories, calculated using a proportion based on a known ratio of calories to sugar grams.
Explanation:
The question asks: How many calories are in a muffin with 2,075 grams of sugar if we know a 200 calorie muffin has 500 grams of sugar? This is an example of a proportion problem.
First, let's establish the relationship between calories and grams of sugar. We know that 200 calories correspond to 500 grams of sugar. We can set this up as a ratio: 200 calories/500 grams = x calories/2,075 grams, where x is the number of calories in the muffin with 2,075 grams of sugar.
To find x, we cross-multiply and solve for x: (200 calories * 2,075 grams) / 500 grams = x calories
Thus, x = 830 calories.
Therefore, a muffin with 2,075 grams of sugar contains 830 calories.
1.In the diagram of circle M shown, various points are located on the circle as shown. a) List three segments that are radii of this circle. b) List a segment that is a diameter of this circle. c) List a chord of this circle that is not a diameter.
Answer:
(a)|MA|, |MB| and |MC|
(b) |BD|
(c) |BC|
Step-by-step explanation:
An adapted diagram of this question is attached. You can vary the labelled letters as required.
Definition
A radius is a line drawn from the center of a circle to its circumference.A segment is a line that connects two points.A diameter is a chord which passes through the center of the circle.A chord is any line joining two points on the circles' circumference.By these definitions:
(a)Segments that are radii of this circle.
We have: |MA|, |MB| and |MC|
(b)Segment that is a diameter of this circle.
|BD|
(c)A chord of this circle that is not a diameter.
|BC|
What is 2+2? I cant figure it out I took 4 hours
Answer:
4
Step-by-step explanation:
You have $73.59 you ear additional money by mowing lawns when you purchase a new pair of shoes for $99.99 and have 23.51 left how much money do you ear mowing lawns
Answer:
50.00$
Step-by-step explanation:
99.99 minus 73.50
Gives you 27.50 so then you add up what you have left so that gives you 50.00$
Ed lined up 10 guitar picks across his desk. Each pick weighs 12 mg wide. How many grams does his entire set of guitar picks weigh?
Answer:
120 milligrams because 12 mg *10 =120
Ed's entire set of guitar picks, with each pick weighing 12 mg and having 10 picks in total is 0.12 grams.
To calculate the total weight of the guitar picks in grams, we first need to know that there are 10 guitar picks and each pick weighs 12 mg.
Knowing that there are 1000 milligrams in a gram, we can convert the weight of one pick into grams:
Weight of one pick in grams = 12 mg / 1000 = 0.012 grams.
Next, we multiply this by the total number of picks to get the combined weight:
Total weight of 10 picks = 0.012 grams pick * 10 picks = 0.12 grams.
So, Ed's entire set of guitar picks weighs 0.12 grams.
A company that manufactures toy trains is making a new boxcar. To fit on the track, the smallest dimension of the toy boxcar must be 2 inches. What should be the length and height of the toy if the company wants the toy boxcar to be geometrically similar to an actual boxcar with the dimensions shown?
Answer:
Length = 12 inches, height = 3 inches
Step-by-step explanation:
First, you have to set up a proportion. 2/7, x/42.
Then, you cross multiply and get the setup of 84=7x
Finally, you divide 84 by 7 and get 12.
12 is the length, and there is no other answer that has 12 in the height. You could just do the same proportion to get 3, though.
Answer:
A: length = 12 inches, height = 3 inches.
Step-by-step explanation:
The company wants the boxcar to be geometrically similar to the original boxcar.
The first step to doing this is to create a ratio. They tell us the smallest dimension of the toy boxcar must be 2 inches.
The smallest dimension of the original boxcar is 7 feet. We can use these two numbers to create a ratio. A 7:2 ratio to be exact.
A 7:2 ratio can be represented as 7/2. 7/2 equals 3.5. All you have to do now is divide the dimensions in the original boxcar by
For example, the length of the original boxcar is 42 feet. If we put 42/3.5 into a calculator, you get 12 as your answer. The same thing is true for the height.
Find the product using the number line. 3(-6) = A number line going from negative 7 to positive 3. An arrow goes from negative 6 to negative 4, from negative 4 to negative 2, and from negative 2 to 0. What error(s) are shown here? Check all that apply. The arrows should be a length of 2. The arrows should be a length of 6. The arrows should be pointing in the positive direction. The arrows should start at zero. The arrows should point in the negative direction.
Answer:
B - The arrows should be length of 6.
D - The arrows should start at zero.
E - The arrows should point in the negative direction
Step-by-step
since it is asking us to find the product you will have to start at negative 6 and then you are going to jump 3 spaces 3(-6)
Answer:
B - The arrows should be length of 6.
D - The arrows should start at zero.
E - The arrows should point in the negative direction
Step-by-step explanation:
A gym charges $30 per month plus $4 extra to swim in the pool for an hour. Because a member has just $50 to spend at the gym each month, the member can swim at most 5 hours. Find the inequality
Answer:
[tex]50\geq $30 + $4[/tex]
Step-by-step explanation:
If a correlation coefficient of -0.898 is given for comparing two things, what does this number tell you about the correlation of the two things?
strong positive
strong negative
weak negative
no correlation
Answer: Strong negative
Step-by-step explanation:
Correlation coefficient tells about the strength ( Strong , moderate or weak ) and direction ( positive or negative) of the relationship between two quantities.
Strong correlation: The value of correlation coefficient lies between -1 to -0.5 or 0.5 to 1.Moderate correlation : The value of correlation coefficient lies between -0.5 to -0.3 or 0.3 to 0.5.Weak correlation : The value of correlation coefficient lies between -0.3 to -0.1 or 0.1 to 3.The given correlation coefficient :-0.898
Since, it lies between -1 and -0.5 and has negative sign, it means it indicates a strong negative between the two things.
Hence, the correct answer is "strong negative ".
Can somebody help me find the Domain, Range, Horizontal Asymptote, Y-Intercept, and End Behavior of the function f(x) = -2e^x + 4 ?
Answer:
Domain = R
Range = (-∞, 4)
Hor. asymp = y=4
Y intercept: f(0) = (0,2)
end behaviour:
x → -∞: f(x) → 4
x→ ∞: f(x) → -∞
Step-by-step explanation:
For the domain, it is R because e^x works for all values of x
For the range, y will never be above 4.
The hor. asymptote is found via [tex]\lim_{x \to -\infty} f(x)[/tex] there the e term will be zero, so what is left is y=4.
Y intercept, fill in f(0)
end behaviour: for small x, y goes to the asymptote, for large x, y goes to minus infinity.
Final answer:
Explained the Domain, Range, Horizontal Asymptote, Y-Intercept, and End Behavior of f(x) = -2e^x + 4
Explanation:
Domain and Range:
Domain: All Real Numbers
Range: f(x) ≤ 4
Horizontal Asymptote:
Horizontal Asymptote: y = 4
Y-Intercept:
Y-Intercept: (0, 2)
End Behavior:
End Behavior: As x → ∞, f(x) → 4; As x → -∞, f(x) → -∞