The domain and the range of the piecewise function for this problem are given as follows:
Domain D: All real values.Range R: [-2, ∞).How to find the domain and the range of a function?The domain of a function is the set that contains all the values assumed by the values of x of the function.The range of a function is the set that contains all the values assumed by the values of y of the function.For this problem, the piecewise function is defined for all values of x, hence the domain is all real values.
The range is obtained as follows:
Up to x = 3: Positive infinity to y = -2, which is the least value assumed at x = 3.From x = 3 to x = 5: values from y = 3 to y = 5, which are already in the range for the above interval.x = 5 and greater: constant at y = -1, which is already in the range.Hence the range is given as follows:
[-2, ∞).
More can be learned about domain and range of functions at https://brainly.com/question/30630079
#SPJ1
i need help with pleaseee
The points are plotted on the graph below.
What are the Coordinates?Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.
Given a coordinate plane.
We have to plot the points given.
(0, 1/2) is a point on the Y axis, since the x coordinate is zero. y coordinate will be in the middle of 0 and 1.
(1, 1 1/2) is a point at a distance of 1 to the right from the origin and at a distance of 1 1/2 to the up from the origin.
(2, 2 1/2) is a point at a distance of 2 to the right from the origin and at a distance of 2 1/2 to the up from the origin.
These points are plotted in the graph below.
Hence the graph is shown below.
Learn more about Coordinates here :
https://brainly.com/question/16634867
#SPJ1
Sam is paid $12.45 per hour for a 37.5 hour week plus 6% of sales for a week. What would Sam's sales have to be for him to earn $800 in a week?
Answer:
ok Let’s calculate the money Sam makes per week, not including sales (or Assuming $0 in sales):
Money per week =$6.45/hour×37.5 hours/week= $241.88/week
The money he Gains from sales must make up the difference, So
money from sales = $400−$241.88 = $158.12
This Money is only 6% or 0.06 of the total sales though, so
Total sales = $158.120.06 = $2635.33
of course, this is Assuming that the money per week is rounded up from $241.875 to $241.88 instead of down to $241.87, in which case Sam would Have to make $2635.50 in sales (about 17 cents more).
Step-by-step explanation:
have a nice day.
Solve the following system of inequalities graphically on the set of axes below. State
the coordinates of a point in the solution set.
Y >1/2x-1
Y ≥-3/4x-6
The solution to the inequality are the region in the shaded area
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
Y >1/2x-1
Y ≥-3/4x-6
Represent properly
y > 1/2x - 1
y ≥ -3/4x - 6
Next, we make a plot of the system to determine the solution
The shaded area in the plot represent the solution to the inequality
In this case, one of the coordinates in the shaded area has a coordinate of (-4, -3)
Read more about inequality at
brainly.com/question/25275758
#SPJ1
The equation ŷ = 67.34x - 128,933.4 predicts a rodent population in a town in year x.
According to the equation, what was the rodent population in 2005?
Enter your answer in the box. Round to the whole number.
The predicted rodent population in the town in 2005 was approximately 6083.
What was the rodent population in 2005?From the question, we have the following parameters that can be used in our computation:
ŷ = 67.34x - 128,933.4
To find the rodent population in 2005, we need to substitute x = 2005 into the equation and solve for ŷ:
ŷ = 67.34(2005) - 128,933.4
So, we have
ŷ = 135016.7 - 128,933.4
Evaluate
ŷ = 6083
Hence, the predicted rodent population was 6083.
Read more about linear regression at
https://brainly.com/question/10209928
#SPJ1
a sample from a refuse deposit near the strait of magellan had 60% of the carbon-14 found in a contemporary living sample. how old was the sample?
The sample is approximately 50,000 years old, as the amount of Carbon-14 in it is lower than that of a contemporary sample.
1) Calculate the ratio of Carbon-14 in the sample compared to a contemporary sample.
Ratio = (60/100) = 0.6
2) Calculate the number of half-lives since the sample was alive.
Number of half-lives = ln(0.6) / ln(0.5) = 0.69897
3) Calculate the age of the sample.
Age of sample = (0.69897 x 5730) = 4020 years
60% of the Carbon-14 identified in a sample taken from a waste site close to the Strait of Magellan was present in the sample from the trash deposit. We must first determine the sample's carbon-14 ratio in relation to a more recent sample in order to determine the sample's age. This ratio is equivalent to the sample's 60% carbon-14 content, or 0.6, when divided by 100. The number of half-lives since the sample has been alive may then be determined by taking the natural log of the ratio and dividing it by the natural log of 0.5, which is 0.69897. By dividing the quantity of half-lives by the 5730-year half-life of carbon-14, we may finally determine the sample's age.
Learn more about sample here
https://brainly.com/question/11045407
#SPJ4
What is the value of x?
2x
x +4
X+1
12
Answer:
x = 8
Step-by-step explanation:
AB/AC = BD/DC
2x/12 = x+4/x+1
12x + 4 = 2x² + 2x
2x² - 10x - 48 = 0
x² - 5x - 24 = 0
(x-8) (x+3) = 0
x = 8 (or) x= -3 (impossible)
x = 8
How many solutions does this system of equations have? y=-2x+2 and 2y+4x=4
The system of equations will have a unique solution.
What is a system of equations?A finite set of equations for which we searched for common solutions is referred to as a system of equations, also known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized.
Given that the equations are:-
y=-2x+2 and 2y+4x=4
Convert the equations into general form,
2x + y = 2
4x + 2y = 4
If the ratio of a₁ / a₂ is not equal to the ratio of b₁ / b₂ the equation will have a unique solution. And if are equal than the equation will have infinitely many solutions.
2 / 4 = 1 / 2 = 2 /4
1 /2 = 1/ 2 = 1/ 2
The equation will have many solutions.
To know more about the system of equations follow
https://brainly.com/question/28866068
#SPJ9
Solve for k:
k-
-
k =
I
96
Answer: look it up frfr
Step-by-step explanation:
Original Price Percent of Discount Sale Price
$
64% $72
The original price when 64% is applied to the item will be $200.
What is the percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentile in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value × 100
Let 'x' be the Original Price. Then the equation is given as,
(1 - 0.64) x = $72
0.36 x = $72
x = $200
The original price when 64% is applied to the item will be $200.
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ9
a student measures the mass of a rock three times using the same properly calibrated analog (not digital) balance and gets slightly different values: 22.46g, 22.42g, and 22.44g. what type of error may have occurred here (systematic and/or random)? how would the student minimize the impact of this error during data analysis?
The errors that may have occurred in the student's measurements are random errors. These types of errors can arise from various sources, such as slight variations in measurement techniques or environmental factors.
Since the measured values are slightly different, it suggests that random errors affected the measurements rather than systematic errors, which would result in consistently incorrect measurements.
To minimize the impact of random errors during data analysis, the student can calculate the average of the three measured values. The average value can serve as the best estimate of the true value of the mass of the rock. Additionally, the student can calculate the standard deviation of the measured values to determine the precision of the measurements. The smaller the standard deviation, the more precise the measurements.
The student can further minimize random errors by taking multiple measurements and averaging them to obtain a more accurate value. Additionally, using a digital balance instead of an analog one may reduce random errors as digital balances have greater precision and accuracy.
It is also important for the student to use proper measurement techniques such as ensuring that the balance is calibrated and zeroed correctly before each measurement. The student should also avoid applying excessive force on the balance and ensure that the rock is stable and level during measurement.
To know more about measurement techniques: https://brainly.com/question/29603089
#SPJ4
two numbers are in the ratio 5:4 if the smaller is 32 find the greater one.
Answer:
The greater number is 40.Step-by-step explanation:
Greetings!!!
The given two numbers ratio.
[tex] \frac{5}{4} [/tex]
The smaller number is 32
[tex] \frac{5}{4} \times 32[/tex]
convert elements into fraction
[tex] \frac{5}{4} \times \frac{32}{1} [/tex]
Apply fraction rule
[tex] \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} [/tex]
Multiply the numbers
[tex] \frac{5 \times 32}{4 \times 1} [/tex]
Divide the numbers
[tex] \frac{32}{8} = 8 \\ 8 \times 5 = 40[/tex]
Hope it helps!!!
The graph shown here is the graph of which of the following rational
functions?
The rational function on the graph is the one in options B.
f(x) = 1/(x - 1)
Which equation describes the graph?Here we can see that the we have the graph of a rational function.
Notice that we have an asymptote at x = 1.
That means that the denominator becomes zero when we evaluate the function in x = 1.
Then the denominator is something like:
x + a
And when x = 1 we get:
1 + a = 0
a = -1
Then the denominator is:
x - 1
And the rational function is:
f(x) = 1/(x - 1)
The correct option is B.
Learn more about rational functions at:
https://brainly.com/question/1851758
#SPJ1
A math teacher has a number cube with faces numbered 1 through 6. He will roll the number cube 400 times. Which of the following ranges contains the best prediction for the number of times the number cube will land with a 1 or a 4 on the top face?
What is the answer and the steps to this question?
Answer:
The probability of rolling a 1 or a 4 on a single roll of the number cube is 2/6, or 1/3. So the expected number of times the number cube will land with a 1 or a 4 on the top face after 400 rolls is 400 * 1/3 = 133.33.
The range that contains this expected value is roughly between 130 and 140, so a good prediction for the number of times the number cube will land with a 1 or a 4 on the top face is between 130 and 140.
Step-by-step explanation:
The accompanying histogram shows the life expectancies at birth for 190 countries as collected by an international health agency.
a) Which would you expect to be larger: the median or the mean? Explain briefly.
b) Which would you report: the median or the mean? Explain briefly.
The choice of whether to report the median or mean as a measure of central tendency depends on the shape of the data distribution and the purpose of the analysis.
a) Whether the median or mean would be larger depends on the shape of the distribution of the data. The median is the value that separates the lower half of the data from the upper half, and is a robust measure of central tendency, meaning that it is not greatly affected by outliers or extreme values. On the other hand, the mean is the sum of the data values divided by the number of values, and can be influenced by outliers or extreme values.
In the case of the life expectancies data, if the distribution is roughly symmetrical, with most of the values clustered around the center and relatively few outliers or extreme values, then the mean and median would likely be similar in value. However, if the distribution is skewed to one side, with many values concentrated on one end and relatively few values on the other end, then the mean would likely be larger than the median.
b) The best measure to report depends on the context and the purpose of the analysis. In general, the median is a more appropriate measure of central tendency for skewed distributions, since it is not greatly affected by outliers or extreme values. On the other hand, the mean is more appropriate for symmetrical distributions, since it provides a more accurate representation of the typical value of the data.
In the case of the life expectancies data, it may be useful to report both the median and the mean in order to provide a full picture of the central tendency of the data. However, if there are outliers or extreme values that could significantly affect the mean, it would be more appropriate to report the median as the primary measure of central tendency.
To learn more about central tendency please click on below link.
https://brainly.com/question/12896875
#SPJ4
consider the following regression model: which of the following is an algebraic property of ols estimates of this model and its associated statistics? group of answer choices the sum, and therefore the sample average of the ols residuals, is positive. the sum of the ols residuals is negative. the sample covariance between the regressors and the ols residuals is zero. ols sample regression line always passes through the sample average of x and sample average of y both a and b are correct both a and d are correct both c and d are correct none of the above
Option (c) is correct: the sample covariance between the regressors and the OLS residuals is zero. This is an important property because it implies that the OLS estimator is not biased and the estimated coefficients of the independent variables are consistent.
The algebraic property of OLS (Ordinary Least Squares) estimates is that the sample covariance between the regressors and the OLS residuals is zero. This means that the OLS estimates are unbiased and not correlated with the independent variables in the regression model.
Option (a) is incorrect: the sum, and therefore the sample average of the OLS residuals, can be either positive or negative depending on the distribution of the data and the fit of the model.
Option (b) is also incorrect: the sum of the OLS residuals can be either positive or negative depending on the distribution of the data and the fit of the model.
Option (d) is incorrect: the OLS sample regression line does not always pass through the sample average of x and the sample average of y. However, it does pass through the point of averages when the model includes a constant term (i.e., intercept).
Therefore, the correct answer is (c): the sample covariance between the regressors and the OLS residuals is zero.
For more such questions on OLS
https://brainly.com/question/30009450
#SPJ4
ASAP Select the correct answer.
What is the slope of the line that goes through the points (-4,2) and (8,5)?
A.-4
B.-1/4
C.1/4
D.4
If A, B, C, and D, are the only possible outcomes of an experiment, find the probability of D using the table below.
Answer:
D. 8/11
Step-by-step explanation:
why ?
the sum of the probabilities of all possible outcomes of an experiment must always be 1.
because there always has to be an outcome - one of the many possibilities.
the reality has to be part of this list of possibilities, and so, their total sum is 1 : the sure event.
the probability of A is 1/11.
of B is 1/11.
of C is 1/11.
A + B + C + D = 1
1/11 + 1/11 + 1/11 + D = 1
3/11 + D = 1
D = 1 - 3/11 = 11/11 - 3/11 = 8/11
How do I find the roots of a cubic equation?
Answer:First, we need to find which number when substituted into the equation will give the answer zero. Therefore is a factor. Factorise the quadratic until the expression is factorised fully. Therefore the roots occur when = -3, -2 and 1.
Step-by-step explanation:
Answer:
by reducing it into a quadratic equation and then solving
Step-by-step explanation:
someone help me pls :b
Answer:
13 months
Step-by-step explanation:
(b)
let C(x) = 431.5 and solve for x , that is
29x + 54.5 = 431.5 ( subtract 54.5 from both sides )
29x = 377 ( divide both sides by 29 )
x = 13
that is cable service for 13 months
Please help!!!
Match the new coordinates that define the figure after dilation with a center at the origin by the given scale factor.
1. (3.0) dilated by scale factor of 1/3 a (0, 6)
2. (3,4) dilated by scale factor of 1/3 scale factor b (1,0)
3. (0,4) after dilation with a scale factor of 1/3 c (0, 4/3)
4. (3,0) after dilation with a scale factor of 3/2 d (1, 4/40
5. (3,4) after dilation with scale factor of 3/2 e (9/2, 0)
6. (0,4) after dilation with a scale factor of 3/2 f (9/2, 6)
The required (0,4) after dilation with a scale factor of 1/3 is (0, 4/3). Option C is correct.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
here,
Since let the coordinate before dilation be (x, y),
Now when applying the scale factor to the coordinate, the transformation equation is given as,
(X, Y) = (sx , sy) where s is the scale factor,
Since matching the above equation with the option,
(3.0) dilated by a scale factor of 1/3 a (0, 6) (False)
(3,4) dilated by a scale factor of 1/3 scale factor b (1,0) (False)
(0,4) after dilation with a scale factor of 1/3 is (0, 4/3) (True)
Thus, the required (0,4) after dilation with a scale factor of 1/3 is (0, 4/3). Option C is correct.
Learn more about Scale factors here:
https://brainly.com/question/22312172
#SPJ1
Using a ruler and a pair of compasses, construct a right-angled triangle with a base of 6 cm and a hypotenuse of 11 cm.
How to construct the right-angled triangle with a base of 6 cm and a hypotenuse of 11 cm.
Constructing the TriangleGiven:
Base = EF = 6 cmHypotenuse = ED=11 cmThe angle between EF and ED= 90֯To find:
Construct a right-angle triangle DEF
1. Draw the line segment2. Then mark the center of the line segment.3. In the compass set its width to 6 cm.4. Keep the pointer of the compass on the midpoint C and marc arcs on both sides of C5. Mark points E and F where the arc crosses the line.6. Again set the width of the compass to the length of the hypotenuse, which is 11 cm.7. Keep the pointer of the compass in E and draw an arc above midpoint C.8. Repeat the above step keeping the pointer on F.9. Label the point as D where the arcs cross.10. Join the points DE and DF with the scale.11. Thus, we get the right-angled triangle DEF of necessary measurements
The constructed right-angle triangle DEF is given below:
Read more about triangles here:
https://brainly.com/question/1058720
#SPJ1
Please help!
The polygons in each pair are similar. Find the scale factor of the smaller figure to the larger figure.
Answer: 1.25 and 1.33
Step-by-step explanation:
question 3:
both sides of 24 became sides that measure 30.
24 times x = 30
therefore x, the scale factor, is 1.25
question 4:
3 increases to 4 and 15 increases to 20 (you have to rotate these shape before anything else to see the corresponding changes)
15 times x = 20
20 divided by 15 is 1.33 repeating, so 4/3
If u ever had a side getting smaller in the second shape, the scale factor would be less than 1.
If A = {3,5,9} and B
{2,4,5,6,9,12}, what is AU B?
For the given sets A = { 3, 5, 9 } and set B = { 2, 4, 5, 6, 9, 12 } then the value of AU B is equal to { 2, 3, 4, 5, 6, 9, 12 }.
Two different sets A and set B are equal to :
Set A = { 3, 5, 9 }
Set B = { 2, 4, 5, 6, 9, 12 }
Union of two different set A and B is defined as set having all the elements of set A and set B .
Union of two sets A and B is represented by AU B .
AU B
= { 3, 5, 9 } ∪ { 2, 4, 5, 6, 9, 12 }
= { 2, 3, 4, 5, 6, 9, 12 }
Therefore, the union of two given sets A and set B is given by :
AU B = { 2, 3, 4, 5, 6, 9, 12 }.
Learn more about sets here
brainly.com/question/18877365
#SPJ4
PLEASE help me understand the steps to solve this i feel like crying i dont understand
Answer:
4
Step-by-step explanation:
First:
(-2 1/2)*(-1 3/5) = 2.5*1.6
Second:
2.5*1.6=5/2*8/5
Third:
5/2*8/5=
4
An AP has first term 7 and common difference 4. If the sum of all it's terms is 900,how many term are there?
If an AP has first term 7 and common difference 4. If the sum of all it's terms is 900, then there are 3 terms.
Let's use the formula for the sum of an arithmetic progression to solve this problem:
S = n/2[2a + (n-1)d]
where S is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.
We know that a = 7 and d = 4, and we're given that S = 900. Substituting these values into the formula, we get:
900 = n/2[2(7) + (n-1)(4)]
Simplifying the expression inside the brackets:
900 = n/2[14 + 4n - 4]
900 = n/2[10 + 4n]
Multiplying both sides by 2 to eliminate the fraction:
1800 = n[10 + 4n]
Simplifying the right-hand side:
1800 = 4n^2 + 10n
Rearranging to get a quadratic equation in standard form:
4n^2 + 10n - 1800 = 0
We can solve for n using the quadratic formula:
n = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 4, b = 10, and c = -1800, so:
n = (-10 ± √(10^2 - 4(4)(-1800))) / 2(4)
n = (-10 ± √(100 + 28800)) / 8
n = (-10 ± √(28900)) / 8
n = (-10 ± 170) / 8
n = 20/8 or n = -180/8
n = 2.5 or n = -22.5
Since the number of terms must be a positive integer, we can discard the negative solution and conclude that there are 2.5 terms. However, this doesn't make sense because the number of terms in an arithmetic progression must be a whole number. Therefore, we need to round up to the nearest whole number, which gives us:
n = 3
Therefore, there are 3 terms in the arithmetic progression with first term 7 and common difference 4, and the sum of these terms is 900.
To learn more about arithmetic progression click on,
https://brainly.com/question/18233448
#SPJ4
how many sides does a regular polygon have if each interior angle measures 172
A regular polygon with an interior angle of 172 degrees has 20 sides.
The formula to find the measure of an interior angle of a regular polygon is:
Interior angle = (n-2) x 180 / n
where n is the number of sides of the polygon.
Setting the equation equal to 172 and solving for n, we get:
172 = (n-2) x 180 / n
172n = 180n - 360
8n = 360
n = 45
Therefore, the regular polygon has 45 sides, but since the question asks for a regular polygon, all sides must be equal and all interior angles must be congruent. The only regular polygon that satisfies these conditions with an interior angle of 172 degrees is a regular 20-sided polygon.
Learn more about polygon here: brainly.com/question/26583264
#SPJ4
If 10,000 is deposited into a savings account that pays 2. 3% annual interest, how much more would the
The account would contain 10,230.00 after 1 year.the amount in the account after 1 year, we can use the formula: [tex]P (1 + r/n)^nt[/tex]
To find the amount in the account after 1 year, we can use the formula:[tex]P (1 + r/n)^nt[/tex]
Where,
P = Principal Amount
r = Rate of Interest
n = Number of times the interest is compounded per year
t = Time in years
For this question,
P = 10,000
r = 2.3%
n = 1
t = 1
Therefore,
[tex]10,000 (1 + 0.023/1)^1*1\\10,000 (1.023)^1[/tex]
10,000 x 1.023
= 10,230.00
The complete question is:
If 10,000 is deposited into a savings account that pays 2.3% annual interest, how much more would the account contain after 1 year?
Learn more about amount here
https://brainly.com/question/8082054
#SPJ4
What is 100 x 2 - 100 ?
Answer:
100
Step-by-step explanation:
100x2=200
200-100=100!
Answer:
100
Step-by-step explanation:
First do 100 multiplied by 2 you will then get 200
Next step is to do 200 subtracted by 100 which will give you 100.
Pls help i’m desperate
Answer: 5/13
Step-by-step explanation: cos is adj/hyp giving us a 12 for adj and 13 for hyp. Tan is Opp/Adj confirming 12 is the adj and 5 being the Opp. Sin is Opp/Hyp giving us 5/13. Hope it helps
sean gets an average of 20 calls during his 8 hour work day. what is the probability that sean will get at most 9 calls in a 4 hour portion of his work day? round the final answer to three decimal places.
The probability that Sean will get at most 9 calls in a 4 hour portion of his work day is 0.037.
The probability that Sean will get at most 9 calls in a 4 hour portion of his work day can be calculated by using the Poisson distribution formula. The formula is [tex]P(x)=e^-μ(μ^x/x!)[/tex].
In this case, μ = 20/4 = 5.
Therefore, [tex]P(x=9) = e^-5(5^9/9!) = 0.037[/tex]
Rounding the answer to three decimal places, the probability that Sean will get at most 9 calls in a 4 hour portion of his work day is 0.037.
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ4