The 95% confidence interval for the variance in the pounds of impurities would be (3.829, 14.121).
In the given question, the quality-control manager of a chemical company randomly sampled twenty 100-pound bags of fertilizer to estimate the variance in the pounds of impurities.
The sample variance was found to be 6.62.
We have to find a 95% confidence interval for the population variance in the pounds of impurities.
From the question,
N=20,
s^2=6.62
So, the Standard Deviation(SD) = √s^2
SD = √6.62
SD = 2.573
The confidence interval for the population variance is given by the following formula:
[tex]\frac{(n-1)s^2}{ \chi_{\alpha/2}} \leq\sigma^2\leq \frac{(n-1)s^2}{ \chi_{1-\alpha/2}}[/tex]
On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.
The next step would be calculating the critical values. First we need to calculate the degrees of freedom given by:
df = n-1
df = 20-1
df = 19
Since the Confidence is 0.95 or 95%, the value of α=0.05 and α/2=0.025, and we can use excel, a calculator or a table to find the critical values.
The excel commands would be: "=CHISQ.INV(0.025,19)" "=CHISQ.INV(0.975,19)".
So for this case the critical values are:
[tex]\chi_{\alpha/2}[/tex] = 32.852
[tex]\chi_{1-\alpha/2}[/tex] = 8.907
Now putting the value in the formula:
[tex]\frac{19\times6.62}{32.852}\leq\sigma^2\leq\frac{19\times6.62}{8.907}[/tex]
3.829≤σ^2≤14.121
So the 95% confidence interval for the variance in the pounds of impurities would be (3.829, 14.121).
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our test statistic z is found by taking the observed difference (81%-72%) minus the expected difference divided by the se for the difference. what is the expected difference in this problem? in other words, what would we expect the difference to be under the null hypothesis?
The expected difference under null hypothesis can be understood by the following :
The required null and alternate hypothesis will be
Null hypothesis : H0 : μ=μ0
Alternate Hypothesis: H1 : μ<μ0
To determine whether there is a difference in the means of two populations, the z test formula compares the z statistic to the z critical value.
The z critical value in hypothesis testing divides the distribution graph into acceptance and rejection regions. The null hypothesis can be rejected if the test statistic falls within the rejection region; otherwise, it cannot be rejected.
The z test formula to set up the required hypothesis tests for a one sample and a two-sample z test is
z = (( x−μ) /σ/√n )x
x = sample mean, μ = population mean, σ = standard deviation and n = sample size.To learn more about null hypothesis
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(02.04 MC)
Write the equation of the line that passes through the points (3, 6) and (5, 18) using function
notation.
Of(x) = 2x + 12
O f(x) = 6x - 12
Oy= 2x + 12
O y = 6x-12
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{18}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{18}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{3}}} \implies \cfrac{ 12 }{ 2 } \implies 6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 6}(x-\stackrel{x_1}{3}) \\\\\\ y-6=6x-18\implies {\Large \begin{array}{llll} y=6x-12 \end{array}}[/tex]
. consider the following situation: janet is examining triangles in her geometry class. all of the triangles janet examined were isosceles. janet concludes that all triangles are isosceles triangles. the type of reasoning janet used in this situation was
The type of reasoning janet used in this situation was
Inductive reasonings .
What is reasoning ?In mathematics, reasoning involves drawing logical conclusions based on evidence or stated assumptions. Sense making may be considered as developing understanding of a situation, context, or concept by connecting it with existing knowledge or previous experience.
Why is reasoning in maths important?
Reasoning in maths is the ability to make logical links and connections which help you tackle a new maths problem. The skill of reasoning equips students not only with the ability to say how they will attempt to work out an answer, but why and how they can be sure it will work.
Inductive reasoning is a type of reasoning that draws general conclusions from specific observations .
In this case Janet examines only isosceles traingle ( specific ) and concluded that all triangles are isosceles ( generalised ).
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What is the indefinite integral of 1/xlnx?
In integration the bindefinite integral of 1/xlnx is
ln(|u|)+C=ln(|lnx|)+C with the aid of using parts, we've discovered whilst the specified formula.
The vital of the 2 capabilities are taken, with the aid of using thinking about the left time period as first feature and 2nd time period as the second one feature.
This technique is referred to as Ilate rule.The vital of xlnx is same to (x2/2) lnx - x2/4 + C, wherein C is the mixing constant. We can compare this vital the usage of the technique of integration with the aid of using parts.
We have the vital:
[tex]∫1xlnxdx
Use substitution. Let u=lnx so that du=1xdx . Note that each of those are presently gift withinside the vital.
∫1xlnxdx=∫(1lnx)1xdx=∫1udu
This is a not unusualplace vital:
∫1udu=ln(|u|)+C
Since u=lnx :
ln(|u|)+C=ln(|lnx|)+C[/tex]
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Anyone know how to solve this? You are supposed to find X Y and Z within the circle.
The measure of the unknown angles in the circle are
x° = 38°
y° = 90°
z° = 90°
Circle Geometry: Calculating the measure of angles in the circleFrom the question, we are to determine the measure of the unknown angles.
From one of circle theorems, we have that "the angle in a semicircle is a right-angle"
Thus,
y° = 90°
z° = 90°
To determine the measure of x°
Using the theorem,
"The angle subtended by an arc at the center of a circle is twice the angle subtended at the circumference"
Thus,
x° = 2 × 19°
x° = 38°
Hence, x° = 38°, y° = 90°, and z° = 90°
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true or false? in every instance of the stable matching problem, there is a stable matching containing a pair (m, w) such that m is ranked first on the preference list of w and w is ranked first on the preference list of m
The statement "in every instance of the stable matching problem, there is a stable matching containing a pair (m, w) such that m is ranked first on the preference list of w and w is ranked first on the preference list of m" is true.
Stable pairing is a way which guarantees that all elements from two sets (men and women, children and toys, people and vacation destinations, whatever) are paired with an element from the other set AND that pair is the "best available match".
According to the statement, men are free to create a list of women's according to their preferences. There will be order sequence of women and men places them in queue of their preference. The men proposes the women with highest ranking in the list then it is possible that all men gets their preferred choice.
The pairing is a best available match and therefore can be called as a stable matching problem. Hence the statement is true.
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Please help, giving thanks and brainliest:) (Please give an explanation if possible and please dont give a fake answer)
Please answer both what angle relationship it is and what x equals
By analyzing the geometric system presented in the figure, the angle x has a measure of 56°.
What is the measure of the missing angle within a pair of angles?
In this question we find a representation of pair of angles, that is, a geometric system with two adjacent angles. The sum of the measures of the two angles equals 98° and one of the angles has a measure of 42°:
42° + x = 98°
x = 98° - 42°
x = 56°
The missing angle x has a measure of 56°.
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What is the answer?
Please help
-------------------------------------------------------------------------------------------------------------
Answer: 105 frames
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Given: [tex]\textsf{25 frames per second, starts at 0 seconds already played 190 frames}[/tex]
Find: [tex]\textsf{Frame count already played when time = -3.4}[/tex]
Solution: In order to find the number of frames that have already played when the time was equal to -3.4 seconds, we must first figure out long the delay is. We can do this by dividing 25 frames per second from 190 frames which gives us that 7.6 seconds passed before we started counting at 0.
Therefore, if we want to look at -3.4 seconds out of -7.6 seconds that means that 4.2 seconds passes after the initial playing to get to -3.4 seconds. Now we can just multiply 4.2 seconds by 25 frames per second which gives us that about 105 frames have played when the time was equal to -3.4
bivariate regression can not demonstrate: question 19 options: a) when the two variables are linear. b) when the two variables are strongly inversely related. c) when the two variables are strongly positively related. d) when the two variables are causally related.
Bivariate regression can not demonstrate when the two variables are causally related.
The term variables in math means an alphabet or term that represents an unknown number or unknown value or unknown quantity.
Here we have to find the term that must not demonstrate the bivariate in math.
In order to find the resulting term, we must know the definition of bivariate regression.
The term bivariate regression in statistics is defined as the simple linear regression model which is used to predict one variable referred to as the outcome, criterion, or dependent variable from one other variable referred to as the predictor or independent variable.
Based on these definition we have identified that if the two variables are related then the regression process is not possible.
Therefore, option (d) is correct.
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what are the numbers for h?
Answer:
0,1
2,2
4,3
6,4
Step-by-step explanation:
Some Examples
4 = 1/2 (6) + 1
4 = 3 + 1
4=4
----------
2 = 1/2 (2) + 1
2 = 1 + 1
2 = 2
h
0
2
4
6
...................
In triangle LMN, m∠L = (6c + 35)°. If the exterior angle to ∠L measures 79°, determine the value of c. c = 24 c = 7 c = 44 c = 11
The value of c, if In triangle LMN, m ∠ L = (6c + 35)°. If the exterior angle to ∠ L measures 79° is 11, so option D is correct.
What is the triangle?Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.
Given:
In triangle LMN, m ∠ L = (6c + 35)°
∠ L = 79°
Calculate the angle as shown below,
m ∠ L = 180 - 79
m ∠ L = 101
101 = 6c + 35
6c = 101 - 35
c = 66 / 6
c = 11
Therefore, the value of c, if In triangle LMN, m ∠ L = (6c + 35)°. If the exterior angle to ∠ L measures 79° is 11.
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graph the line that has a slope of -3 and includes the point (1,5)
On solving the provided question, we got to know that - to plot the graph, required equation is 3x +y -8 = 0
What is an expression?a collection of numbers, symbols, and operators (like + and ) that represent a value. Examples - 2 + 3 is a formula and there is also the statement 3 x/2. The equals symbol does not appear in expressions. Actually, none of these = ≠ < > ≤ ≥
How do you write a mathematical expression?We frequently have to understand a written phrase in order to write an expression. For instance, the notation x + 6 can be used to represent the phrase "6 added to some number," where x stands for the unknown value.
To plot the graph,
we need to find the equation first.
and to find the equation -
[tex](y - y1) = m(x - x1)\\here,\\x1 = 1\\y1 = 5\\m- ( -3 )[/tex]
equation -
(-3)(x-1) = y-5
-3x + 3 = y-5
3x - 3 = 5-y
3x +y -8 = 0
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What is the answer please say
Answer:
c) ♣ + 25
Step-by-step explanation:
♦ + 20 = ♣
♦ + 45 = ♦ + (20+25)
=> ♦ + 45 = ♣ + 25
The solution of the equation is C
How to solve equations?The equations can be solved as follows:
let
x = the quadrilateral shape
y = flower shaped figure
Hence, let's replace it in the equation
x + 20 = y
Let's find x + 45
Therefore,
x + 20 = y
x = y - 20
Let's substitute the value of x in the second equation
x + 45
y - 20 + 45
y + 25
Recall y is the flowered shaped figure. Therefore, the answer is C.
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Solve for x. Finals are soon need for an assignment!! Please help!
Using the concept of similar triangle and rule for the proportionality of it's sides, The answer is x=2.
What is a triangle?A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees.
What is similar triangle?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
Triangle ADE and Triangle ABC are similar in nature.
using the rule of proportionality of sides of the similar triangle, We have,
[tex]\frac{2+x}{2} = \frac{2}{1}[/tex]
x+2=4
x=4-2
x=2
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What is 15% of Jasmine's number?
I am thinking of a number.
10% of my number is 64.
Answer:
96
Step-by-step explanation:
100% of her number is 64015% of 640 is 96A 18oz pepsi for 2.00 or a 25 oz for 2.30
Answer: 25 oz for 2.30
Step-by-step explanation:
18oz Pepsi for $2.00
Take 2 divided by 18 = $0.11
25 oz for $2.30
Take 2.3 divided by 25 = $0.09
So 25 oz for 2.30 is better!
g neptunium-239 has a half-life of 2.35 days. how many days must elapse for a sample of 239np to decay to 0.100% of its original quantity? 0.0427 days 1.491 days 2.04 days 23.4 days
23.5 days must elapse for a sample of 239np to decay to 0.100% of its original quantity.
Given is the equation for radioactive decay.
N equals N0exp(-λt). We have to determine the λ decay constant.
λ= -(lnN/N0)/t where t = Neptunium-239's half-life, 2.35 days,
and N/N0 = 1/2 where N = Amount of Neptunium-239 after half-life,
and N0 = Amount of Neptunium-239 at the beginning.
Consequently,
λ = (-ln(1/2))/2.35 = 0.294/day.
Neptunium-239 will now degrade to 0.100% of its original value.
N/N₀ × 100 % = 0.100%
N/N₀ = 0.100/100
N/N₀ = 0.001
We calculate the time it takes for Neptunium-239 to decay to this value using the equation for radioactive decay. Making t the formula's subject,
-(lnN/N0)/ = -(ln(0.001))/0.294/day.= 23.5 days
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Question
.Jeff and Lauryn are long-distance runners.
Jeff's race time, based on his average pace, is represented by the equation y=9x, where x is the number of miles and y is the number of minutes.
Lauryn's average pace is represented in this graph.
If Jeff and Lauryn run a 10k (a 6.2-mile race), who will win? Why?
Select two answers: one for the winner of the race and one for the reason they won.
Responses
Lauryn's pace is 9 minutes per mile, so Jeff is slower at 10 minutes per mile.
Lauryn's pace is 9 minutes per mile, so Jeff is slower at 10 minutes per mile.
Lauryn wins.
Lauryn wins.
Lauryn's pace is 10 miles per minute, so Jeff is slower at 9 miles per minute.
Lauryn's pace is 10 miles per minute, so Jeff is slower at 9 miles per minute.
Lauryn's pace is 10 minutes per mile, so Jeff is faste
Lauryn's race time equation is y = 10x. Thus, Lauryn's pace is 10 minutes per mile, so Jeff is faster. Jeff will win.
How to determine who will win the race between Jeff and Lauryn?Given that:
Jeff's race time is represented by the equation y=9x
You will find Lauryn's race time equation in the graph:
The equation of the line is of the form y = mx
where m is the slope
m = 20-0 / 2-0 = 20/2 = 10
Thus, Lauryn's race time equation is y = 10x
For a 10k, the race time for Jeff will be:
y = 9x
y = 9×10 = 90 minutes
For a 10k, the race time for Lauryn will be:
y = 10x
y = 10×10 = 100 minutes
Therefore, Lauryn's pace is 10 minutes per mile, so Jeff is faster. Jeff wins.
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how many numbers less than 2017 are both the sum of two consecutive positive integers, and the sum of five consecutive positive integers?
201 numbers are less than 2017
If and only if it is odd, a number is the sum of two successive integers.
Only if it is a multiple of 5 is a number considered to be the sum of 5 consecutive integers. If you have any doubts, remember that the product of five consecutive integers equals five times the integer in the middle (this remains true if instead of 5 you put in any odd positive integer).
Consequently, you are seeking odd multiples of 5 below 2017. There are 403 multiples of 5 immediately below 2017, or 2015/5. Of those, 202 are odd. It is necessary to eliminate the number 5 because it is not completely positive when expressed as the sum of its successive integers, which is (-1)+0+1+2+3.
There are 201 numbers left.
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simplify the expression: (3x10^8)(6x10^-4)
The answer is 18x10^4 using simple arithmetic calculations and exponential function.
What are arithmetic calculations?
Arithmetic calculations are mathematical operations that involve the addition, subtraction, multiplication, and division of real numbers. Arithmetic is used to solve problems and execute tasks in everyday life, and is an integral part of mathematics. It is also used to analyze data and solve equations. Arithmetic involves the use of numbers, symbols, and operations in order to solve problems. Examples of arithmetic operations include addition, subtraction, multiplication, division, and exponentiation. The order of operations is an important part of arithmetic, as it dictates which operations take precedence over others. Arithmetic is used in a variety of applications, such as in engineering, finance, education, and science. It can also be used to solve puzzles and games. Arithmetic calculations can be used to help people better understand the world around them, as well as to help them make better decisions in life.
Two exponential function having same base , then powers can be added or subtracted.
In given equation, base is of 10 and powers are 8 and -4.
now the power will be 4
and 3 and 6 get multiplied i.e. 18.
So, the answer is 18x10^4.
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I’m having issues with natural logs and logs, and this problem is on my pre-call homework. Can anyone help me out?
2^x+7 = 3
Answer:
Step-by-step explanation:
23
Answer:
Step-by-step explanation:
2^x + 7 = 3
2^x = -4 this cannot be solved
Maybe you meant
2^(x+7) = 3
LOG both sides to get
(x+7) LOG 2 = LOG 3
x+7 = log3/log2 subtract 7 from both sides to get
x = - 5.415
you have 3.35$ in quarters and nickels. If you have 31 coins how many each do you have?
a. Write a system for the problem
b. how many types of each coin do you have?
SOMEONE ANSWER PLSS IM DYING HERE
0.25Q+0.05N=3.25 and Q+N=31 is the required system of equation and nickels should be 22.5 and Quarters should be 8.5
What is Equation?Two or more expressions with an Equal sign is called as Equation.
From given,
3.35$ in quarters and nickels. If you have 31 coins
0.25Q+0.05N=3.25..(1)
Q+N=31
Q=31-N
Now substitute Q value in (1)
0.25(31-N)+0.05N=3.25
7.75-0.25N+0.05N=3.25
7.75-0.2N=3.25
Subtract 7.75 on both sides
-0.2N=3.25-7.75
-0.2N=-4.5
Divide both sides by 0.2
N=22.5
and Q+22.5=31
Q=31-22.5
Q=8.5
Hence, 0.25Q+0.05N=3.25 and Q+N=31 is the required system of equation and nickels should be 22.5 and Quarters should be 8.5
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The graph of a linear function passes through (-8,4) and (4,5).What is the equation of the function?
The linear function that passes through (-8,4) and (4,5) will be y = (1/12)x + 14/3.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear equation or function is given as ;
y = mx + b
The slope (m) associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope = (y₂ - y₁)/(x₂ - x₁)
The slope associated with (-8,4) and (4,5) will be as,
m = (5 - 4)/(4 + 8) = 1/12
Thus, y = (1/12)x + b
Put (4,5)
5 = (1/12)4 + b
b = 5 - 1/3
b = 14/3
Thus, y = (1/12)x + 14/3
Hence "The linear function that passes through (-8,4) and (4,5) will be y = (1/12)x + 14/3".
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while virtually all time series exhibit _______ a random component, not all time series exhibit other components.
In contrast to the fact that almost all time series contain a random component, certain time series do not.
A TIME SERIES IS WHAT?
A time series is a group of observations of clearly defined data points produced over time via repeated measurements. A time series would include, for instance, calculating the amount of retail sales for each month of the year. This is due to the well defined and regular measurement of sales income at uniformly spaced intervals. Time series data are not those that are irregularly or once collected.
Three parts can be separated out of a time series observation: the trend (long-term direction), the seasonal (systematic, calendar-related motions), and the irregular (unsystematic, short term fluctuations).
In mathematics, a time series is a collection of data points that have been indexed chronologically.
A time series is typically a sequence that was recorded at a number of evenly spaced points in time.
It is therefore a set of discrete-time data.
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An isosceles triangle has side lengths of 3x, (4x − 7), and (1/2x+9)
Write an expression in
simplest form to represent the perimeter of the triangle. (Show your work on another paper)
The perimeter of the isosceles triangle with side lengths 3·x, (4·x - 7), and (1/2·x + 9) is 51[tex]\frac{1}{14}[/tex]
What is an isosceles triangle?An isosceles triangle is a triangle that has a pair of congruent sides and according to the triangle inequality theorem, a pair of congruent angles.
The lengths of the sides of the isosceles triangle are;
3·x, 4·x - 7, and 1/2·x + 9
Let the sides, 3·x and 4·x - 7 represent the congruent sides of the triangle, we get;
3·x = 4·x - 7
4·x - 3·x = x = 7
x = 7
The length of the sides of the triangle, found by plugging in x = 7 in the specified expressions for the lengths of the sides of the triangle are therefore;
Length of the first side; 3·x = 3 × 7 = 21
The length of the second specified side; 4·x - 7 = 4 × 7 - 7 = 21
Length of the third specified side; (1/2×x) + 9 = (1/(2 × 7)) + 9 = 1/14 + 9
The perimeter of the triangle is the sum of the lengths of the sides of the triangle, therefore;
The perimeter of the triangle is; 21 + 21 + 1/14 + 9 = 51 [tex]\frac{1}{14}[/tex]
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The simple interest formula is I=Prt, where I is the interest, P is the principal, r is the interest rate, and t is the time.
What is the interest if the principal is $10,000, the interest rate is 2%, and the time is 8 years?
options:
$160
$200
$1600
$16,000
Answer:
1600$
Step-by-step explanation:
By using the SI formula,
[tex]SI={PXRXT}/{100} \\SI=10000X2X8/100\\SI = 1600$\\\\Hence, the interest is 1600$[/tex]$
Option C) 1600$ is correct
Mark me brainliest
2x2+89+765-78
i'm lesbian what you gonna say? thats what i thought
have a nice day
Answer: 780
Step-by-step explanation:
Two times 2 is 4
4 + 89 = 93
93 +765 = 858
858 - 78 = 780
Use the drawing tool(s) to form the correct answer on the provided graph.
A dilation by a scale factor of 2 centered at (2,-1) is performed on the triangle shown.
Draw the resulting triangle.
Drawing Tools
Select
Point
Line Segment
Click on a tool to begin drawing.
<+++
-10 -9 -8-7 -6 -5
-4
-2
10
9-
8-
7+
6
5-
4-
3-
2-
1
Delete
3
5
Undo
6
7
00
8
Reset
9 10 no
The resulting dilated triangle is as attached and it has the coordinates; (2, 4), (4, -2) and (-6, -2).
How to interpret Dilation Scale Factor?When a triangle is dilated, it means that each vertex of the figure has it's coordinates multiplied by the scale factor of the dilation. Now, due to the fact that multiplication operation is involved, it means that the original triangle and the dilated triangle are not congruent, as their side lengths are different.
The vertices of the triangle are given as follows:
(1, 2), (2, -1) and (-3, -1).
The dilation has a scale factor of 2, meaning that each coordinate of the vertices will be multiplied by 2 and as such, the coordinates of the dilated triangle are given as follows:
(2, 4), (4, -2) and (-6, -2).
The new triangle is as attached
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(1 point) a bit is a 0 or a 1. a bit string of length 8 is a sequence of 8 digits, all of which are either 0 and 1. (a) how many bit strings of length 8 are there? (b) how many bit strings of length 8 or less are there? (count the empty string of length zero also.)
a) N = 2^8 = 256
b)N = 2^8 + 2^7 +2^6 +2^5 +2^4 +2^3 +2^2 +2^1
Given;
String of length 8, with two options (0 or 1) each.
a) for the number of bits of strings of length 8.
Each digit of the 8 digit string has 2 options.
For 8 digit, we have
N = 2×2×2.... = 2^8 =256
b) for bit of strings of length 8 or less.
For n string = 2^n
For n < 8
The number of bit strings for length 8 or less are;
N = N8 +N7 + N6 + ... +N1
N = 2^8 + 2^7 +2^6 +2^5 +2^4 +2^3 +2^2 +2^1
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Maria was given this absolute value graph and needs to come up with the equation, domain, range and intercepts.
function is y = |x|..and from her knowledge with translations she knows that it has translated horizontally to the right 4 units.
So she says the new equation must be y = |x+4|. The domain is all values of x. The range is all values of y greater u
to zero. The y-intercept is (0,4). There isn't an x intercept, because it just sits at (4,0). can you find any errors in her solution?
Maria wrote incorrectly the function, it is:
y = |x - 4|
And:
Domain: all real numbers.Range: all real numbers equal to or larger than zero.y-intercept: (0, 4)x-intercept: (4, 0).There are errors in her solution?She started with the parent absolute value function:
y = |x|
And wrote a translation to the right as:
y = |x + 4|
That is her mistake, a translation to the right of N units is written as:
g(x)= f(x - N)
So for a translation to the right of 4 units, we need to subtract 4 to the input, the actual function that we can see on the graph is written as:
y = |x - 4|
Now, the y-intercept is what we get when we evaluate in x = 0:
y = |0 - 4| = 4
So the y-intercept is (0, 4).
The x-intercept is the value of x such that y = 0, so we need to solve:
|x - 4| = 0
x - 4 = 0
x = 4
The x-intercept is (4, 0).
Finally, the domain (like in all absolute value functions) is the set of all real numbers, and the range is the set of all real numbers equal to or larger than zero.
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