The expression that is the difference of two squares is [tex]9a^2 - 4b^6[/tex]
How to find the expression that is the difference of two squares?The difference of two squares is an algebraic expression of the form a² - b², which can be factored as (a + b)(a - b).
Using this rule, we can determine which of the given expressions is the difference of two squares.
[tex]9a^2 - 4b^6[/tex] is the difference of two squares because [tex]9a^2[/tex] is a perfect square [tex](3a)^2[/tex]and [tex]4b^6[/tex] is a perfect square[tex](2b^3)^2[/tex]. Therefore, we can write:
[tex]9a^2 - 4b^6 = (3a + 2b^3)(3a - 2b^3)[/tex]
So, the expressions that are the difference of two squares is [tex]9a^2 - 4b^6[/tex]
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a teacher wants to see if a new unit on factoring is helping students learn. she has five randomly selected students take a pre-test and a post test on the material. the scores are out of 20. has there been improvement? (pre-post) what value of t would you use for the 90% confidence interval? student 1 2 3 4 5 pre-test 12 14 11 12 13 post- test 15 17 15 20 13 group of answer choices 2.776 2.132 4.604 3.747 1.645
The paired t-test results suggest that there is no significant improvement in students' learning after the new unit on factoring, based on a 90% confidence level.
How to find the value of t?To determine if there has been an improvement in students' learning after a new unit on factoring, we can perform a paired t-test on the pre-test and post-test scores of the five randomly selected students.
The differences between the pre-test and post-test scores for each student are: 3, 3, 4, 8, 0.
The mean of the differences is 3.6, and the sample standard deviation is 2.39.
The t-value for a 90% confidence interval with 4 degrees of freedom is 2.776. Since the calculated t-value of 2.68 (calculated as the mean of the differences divided by the standard error of the mean of the differences) is less than the critical t-value of 2.776, we fail to reject the null hypothesis that there is no improvement in students' learning.
Therefore, there is not enough evidence to conclude that the new unit on factoring has helped students learn based on the sample data.
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The function y = f(x) is graphed below.
What is the average rate of change of the
function f(x) on the interval
-1 ≤ x ≤ 0?
Answer:
-2
Step-by-step explanation:
The explanation is in the picture
The function f(x) = -4(3)-4+3 represents the value of a savings account in dollars, x months after the individual opened
the account.
In how many months will be account have a balance of $0?
O 0.26 months
O 2.46 months
O 3.74 months
O 4.26 months
NEED HELP ASP
Answer: A
Explanation:
the inequality 4/5-1/2p>9/5 is givin. solve the inequality for p
Answer:
p < -2
Step-by-step explanation:
Answer:
The answer is -2
Step-by-step explanation:
4/5-1/2p>9/5
C.L.T
-1/2p>9/5-4/5
-1/2p>5/5
-1/2p=1
-p/2>1
-p=2
p= -2
The angle of elevation from point A to the top of a hill is 49°. If point A is 400 feet from the base of the hill, how high is the hill? Round to the nearest tenth.
1. 460.1 ft
2. 301.9 ft
3. 262.4 ft
4. 459.3 ft
Add. Express your answer in simplest form. 2/5 + 5/6
A. 1/3
B. 7/11
C. 7/30
D. 1 7/30
Answer:
d. 1 7/30...............
Answer:
D
Step-by-step explanation:
2/5 + 5/6
Make the denominator same
(2×6)/30 + (5×5)/30
12+25/30
37/30
1 7/30
Martin deposits $7,000 in an account at Victory Bank. Find the amount of interest
earned and the total value of his account after 36 months
$682.50
Step-by-step explanation:Simple interest only builds on the initial deposit.
Interest Formula
Unlike compound interest, the change per time period is constant for simple interest. This means that simple interest can be calculated through the formula:
I = PrtIn this formula, I represents the amount of interest earned. P is the principle, which is the initial deposit. r is the rate of interest expressed as a decimal. t is the time in years.
Solving For Interest
Now, we can use the information we were given to solve for the amount of interest earned. The question states that the principle is $7,000. From the table, we can tell that the rate is 0.0325. Finally, t is 3 years because 36 months = 3 years. Then, plug these values into the formula.
I = 7000 * 0.0325 * 3I = 682.5This means that the account at Victory Bank would earn $682.50 over the course of 3 years.
TIME SENSITIVE! please help !
Consider the word PENCIL. If all the letters are used, and the first letter can’t be N or L, how many ways can the letters be arranged?
A) 720
B) 480
C) 360
D) 96
The number of ways to arrange the letters of PENCIL when the first letter can't be N or L is option (B) 480.
The word PENCIL has 6 letters, here we have to use permutation method. If all the letters are used, there are 6! = 720 ways to arrange them. However, the first letter can’t be N or L. This means that there are only 4 choices for the first letter (P, E, C, or I). After choosing the first letter, there are 5 letters left to arrange,
So there are 5! = 120 ways to arrange them.
Therefore, the total number of ways to arrange the letters of PENCIL when the first letter can’t be N or L is
4 x 5! = 4 x 120 = 480
Therefore, the correct option is (B) 480.
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Graph y ≥ -x2 - 1.
Click on the graph until the correct graph appears.
Answer:
To graph this inequality, you can start by graphing the related function y = -x^2 - 1. This is a downward-facing parabola that opens downwards and has a vertex at (0, -1).
To graph the inequality y ≥ -x^2 - 1, you need to shade the region above the graph of the parabola. This is because any point above the parabola will have a y-coordinate that is greater than or equal to the corresponding y-coordinate on the parabola.
So, to graph the inequality, you can shade the region above the parabola. You can use a dotted line to represent the boundary of the inequality, since the inequality includes the possibility of equality (y = -x^2 - 1).
I hope this helps!
8.G.B.6
The better definition of squares is
A number multiplied by itself.
What is square?
In mathematics, a square is a number that is obtained by multiplying a number by itself. It is also a geometric shape with four equal sides and four right angles. The area of a square is calculated by multiplying the length of one of its sides by itself. The formula for calculating the area of a square is A = s^2, where A is the area and s is the length of one side.
Squares have many important applications in mathematics, including in algebra, geometry, trigonometry, and calculus. They are used in the Pythagorean theorem, which relates to the sides of a right triangle, and they are used to represent variables in algebraic equations. Squares are also important in geometry, where they are used to construct geometric shapes and to calculate their areas and perimeters.
The better definition of squares is:
A number multiplied by itself.
In mathematics, a square refers to the product of a number multiplied by itself. For example, the square of 4 is 16, because 4 multiplied by 4 equals 16. Squares have a variety of important applications in mathematics, including in geometry, algebra, and calculus.
While a result that has been proved to be true is sometimes referred to as a "square" in certain contexts, it is not the primary definition of the term. Similarly, a triangle with a right angle is referred to as a "right triangle" or a "right-angled triangle," but not a square.
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I need help with this please
The range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = (5/2)^x - 5, we need to find the minimum and maximum values of y that can be obtained by plugging in all possible x values.
Since (5/2)^x is always greater than 0 for any x, the minimum value of f(x) is -5.To find the maximum value of f(x), we can take the limit as x approaches infinity:
lim (x → ∞) (5/2)^x - 5 = ∞ - 5 = ∞Therefore, the range of f(x) is (-5, ∞).If a stock has a beta measure of 2.5, discuss what this means(be specific).
The means of a stock that has a beta measure of 2.5 is 2.5%.
A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.
This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.
The beta measure is a measure of the volatility of a stock relative to the market.
If the market goes down by 1%, the stock is expected to go down by 2.5%.
Therefore,
The stock is considered to be more risky than the average stock in the market.
A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.
This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.
Conversely, if the market goes down by 1%, the stock is expected to go down by 2.5%.
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what number is the greatest common factor of 90 and 315 divided by the least common multiple of 5 and 15?
The greatest common factor of 90 and 315 when divided by the least common multiple of 5 and 15 is 45.
When we multiply all the common prime factors, we get the greatest common factor of the numbers.
These prime factors should come from the prime factorization of the numbers given. These should be in all the unique combinations possible.
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Can anyone help me please
Answer:
25
Step-by-step explanation:
discuss possible sources of measurement error in this experiment. are these sources of error enough to account for the percent differences you calculated from your data? write out your answer in a clear and well supported paragraph.
The "possible-sources" of in the measurement error of an experiment are Instrument error, Human error, sampling error and environmental factors, these sources "may" or "may-not" be enough to account for the percent differences calculated from the data.
There are several possible sources of "measurement-error" in an experiment which affect the accuracy and precision of the results.
These sources include instrument error, human error, environmental factors, and sampling error.
(i) "Instrument-Error" : is defined as inaccuracies in the measuring instruments used in the experiment. This include issues such as calibration errors, sensitivity of the instruments.
(ii) "Human-Error" can arise from mistakes made by experimenters during data collection or analysis, such as misreading measurements or recording data incorrectly.
(iii) "Environmental-Factors", such as temperature, humidity, or electromagnetic interference, can also cause error into experiment if they affect performance of measuring instruments.
(iv) "Sampling-Error" occur when a subset of the population is used for the experiment, and the results are generalized to the entire population.
Depending on the magnitude of these sources of error, they may or may not be enough to account for the percent differences calculated from the data.
If the measurement errors are small and within an acceptable range for the experiment, they may not significantly impact the results.
If the errors are large or systematic, they can introduce significant bias into the data and affect the percent differences calculated.
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The given question is incomplete, the complete question is
Discuss the possible sources of measurement error in an experiment. Are these sources of error enough to account for the percent differences you calculated from your data? write out your answer in a clear and well supported paragraph.
The population of your town is about 30,000. This is about 1/10 the population of your friend’s town about what is the population of your friend’s town?
The population of your friend's town is 300,000 if the population of your town is about 30,000.
To solve this problem, we can use the fact that if one quantity is a fraction of another quantity, we can multiply or divide the given quantity by that fraction to find the other quantity. In this case, we know that the population of your town is 1/10th of your friend's town's population, so we can multiply your town's population by 10 to get your friend's town's population.
If the population of your town is about 30,000, and it's about 1/10 the population of your friend's town, we can calculate your friend's town's population by multiplying your town's population by 10.
So, the population of your friend's town is
30,000 x 10 = 300,000
Therefore, your friend's town has a population of about 300,000.
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Find the length of each segment.
12. AB and AC
Applying the Angle Bisector Theorem, the length of the segments are:
AB = 15; AC = 20.
What is the Angle Bisector Theorem?The Angle Bisector Theorem states that in a triangle, if a line segment bisects an angle of the triangle and intersects the opposite side, then it divides that side into two segments that are proportional to the lengths of the other two sides of the triangle.
Therefore, we would have the following equation based on the angle bisector theorem:
5y/8 = 4y - 1 / 6
Cross multiply:
8(4y - 1) = 6(5y)
32y - 8 = 30y
32y - 30y = 8
2y = 8
y = 4
AB = 4y - 1 = 4(4) - 1 = 15
AC = 5y = 5(4) = 20
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act scores have a mean of 21.4 and 15 percent of the scores are above 26 . the scores have a distribution that is approximately normal. find the standard deviation. round your answer to the nearest tenth, if necessary.
The standard deviation of the ACT scores is approximately 4.2.
What is Standard deviation?Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It indicates how much the data values deviate, on average, from the mean (or average) of the data set. A higher standard deviation indicates greater variability or spread in the data, while a lower standard deviation indicates less variability or spread.
According to the given information:
To find the standard deviation of ACT scores, we can use the given information about the mean and the percentage of scores above a certain threshold.
Given:
Mean (μ) = 21.4
Percentage of scores above 26 = 15%
Since the distribution is approximately normal, we can use the Z-score formula to find the Z-score corresponding to the given percentage. The Z-score is the number of standard deviations a particular value is from the mean in a normal distribution.
Z-score formula:
Z = (X - μ) / σ
Where:
Z = Z-score
X = Value (in this case, 26)
μ = Mean (21.4)
σ = Standard deviation (to be found)
We can rearrange the formula to solve for σ:
σ = (X - μ) / Z
Substituting the given values:
X = 26
μ = 21.4
Z = Z-score corresponding to 15% (which can be found using a standard normal distribution table or a Z-score calculator)
Assuming a standard normal distribution table or calculator gives us a Z-score of approximately 1.04 for a percentage of 15%, we can plug in the values:
σ = (26 - 21.4) / 1.04
σ = 4.4 / 1.04
σ ≈ 4.2 (rounded to the nearest tenth)
So, the standard deviation of the ACT scores is approximately 4.2.
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Zain's current credit card balance is $9,160.00 with a minimum payment of $325.00. Over the next month he spends $1,098.00. If the APR is 18.99% (billed monthly), what will the new balance be, including interest?
Answer: To find the new balance including interest, we need to take into account the interest charged on the current balance and the new purchase.
First, let's calculate the interest charged on the current balance. The monthly interest rate is 18.99% / 12 = 1.5825%.
The interest charged on the current balance is therefore:
interest on current balance = 0.015825 * 9160.00 = 144.98
So the total balance including interest for the current month is:
current balance including interest = 9160.00 + 144.98 = 9304.98
Next, let's calculate the interest charged on the new purchase of $1,098.00. The interest charged on the new purchase is:
interest on new purchase = 0.015825 * 1098.00 = 17.39
So the total balance including interest for the new purchase is:
new balance including interest = 1098.00 + 17.39 = 1115.39
Finally, we add the current balance including interest and the new balance including interest to get the total balance including interest:
total balance including interest = current balance including interest + new balance including interest
total balance including interest = 9304.98 + 1115.39
total balance including interest = 10420.37
Therefore, the new balance including interest is $10,420.37.
Step-by-step explanation:
Question # 5
Question # 6
Question # 7
Question # 8
Question # 9
Question # 10
Question # 11
Answer: question#7 is 7/12
question#8 is 1 3/8
question#5 is 1/2
question#6 is 12
question#9 is 1 1/6
question#10 is 31/40
question#11 is 3/4
Step-by-step explanation: give brainliest
Question #5: Option A, [tex]\frac{1}{2}[/tex]
Question #6: Option A, 12
Question #7: Option A, [tex]\frac{7}{12}[/tex]
Question #8: Option D, [tex]1\frac{3}{8}[/tex]
Question #9: Option D, [tex]1\frac{1}{6}[/tex]
Question #10: [tex]\frac{31}{40}[/tex]
Question #11: [tex]\frac{3}{4}[/tex]
Pls mark brainliest
bertha is stacking oranges in the form of a pyramid. the base is a rectangle that is four oranges by six oranges. each orange above the base rests on 4 oranges below it. how many oranges are used
The total number of oranges used in Bertha's pyramid is 24 + 6 + 2 + 1 = 33 oranges.
To calculate how many oranges are used in Bertha's pyramid, we first need to find out how many oranges are in each
layer of the pyramid. Since the base of the pyramid is a rectangle that is 4 oranges by 6 oranges, there are a total of 4 x 6 = 24 oranges in the base layer.
For the second layer of the pyramid, each orange rests on 4 oranges below it.
Since the base layer has 24 oranges, there will be 24 / 4 = 6 oranges in the second layer.
For the third layer, each orange again rests on 4 oranges below it.
So there will be 6 / 4 = 1.5 oranges in the third layer.
Since we cannot have half an orange, we round up to 2 oranges.
Finally, the top layer of the pyramid will consist of a single orange.
Therefore, the total number of oranges used in Bertha's pyramid is 24 + 6 + 2 + 1 = 33 oranges.
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T/F There exists a function f such that f(x) > 0, f'(x) < 0, and f"(x) > 0 for all x.
True, there exists a function f such that f(x) > 0, f'(x) < 0, and f"(x) > 0 for all x.
An example of such a function is[tex]f(x) = e^(-x)[/tex], where e is the base of the natural logarithm (approximately 2.718).
Let's verify the given conditions:
f(x) > 0:
Since e^(ax) is always positive for any real value of x and any constant a, [tex]e^(-x)[/tex]is also always positive for any real value of x.
f'(x) < 0:
To find the first derivative, apply the chain rule: [tex]f'(x) = -e^(-x). As e^(-x)[/tex] is always positive, the derivative
[tex]f'(x) = -e^(-x)[/tex] is always negative for all x.
f"(x) > 0:
To find the second derivative, apply the chain rule again:
[tex]f"(x) = e^(-x). As e^(-x)[/tex]is always positive, the second derivative[tex]f"(x) = e^(-x)[/tex] is always positive for all x.
Thus, it is true that there exists a function f with the given conditions.
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The function [tex]f(x) = e^(-x)[/tex] meets all the given conditions.
True. There exists a function f such that [tex]f(x) > 0, f'(x) < 0, and f"(x) > 0[/tex] for all x. One example of such a function is [tex]f(x) = e^(-x)[/tex].
True. There exists a function f(x) that satisfies the given conditions: f(x) > 0, f'(x) < 0, and f''(x) > 0 for all x.
Consider the function [tex]f(x) = e^(-x)[/tex]. This function has the following properties:
1. f(x) > 0 for all x because the exponential function is always positive.
2. [tex]f'(x) = -e^(-x)[/tex]which is always negative because e^(-x) is always positive, and the negative sign in front makes the derivative negative.
3. [tex]f''(x) = e^(-x)[/tex]which is always positive.
Thus, the function [tex]f(x) = e^(-x)[/tex]meets all the given conditions.
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Ten seventh graders and 15 eighth graders were selected for the elite choir ensemble.
a. Write the ratio of seventh graders to eighth graders who were selected for the
elite choir.
b. Write the ratio of seventh graders to total students who were selected for the
elite choir.
c. Write the ratio of eighth graders to total students who were selected for the elite
choir.
Answer:
Your answer should be A
Solve for X. I don’t know how to solve
The value of x is approximately 10.57 and the value of y is approximately 15.25.
Describe Chords?In mathematics, a chord is a straight line segment that connects two points on a curve. More specifically, a chord is a line segment that has its endpoints on the curve.
The term "chord" is most commonly used in the context of circle geometry, where a chord is a line segment that connects two points on the circumference of a circle. In this context, the length of a chord can be calculated using the Pythagorean theorem, given the lengths of the radii of the circle and the distance between the endpoints of the chord.
In a circle, if four chords are connected to form a quadrilateral, then opposite angles of the quadrilateral are supplementary. Using this property, we can set up the following equation:
105 + (7y + 1) + (7x + 1) + (4y + 14) = 180
Simplifying and solving for x and y, we get:
7x + 4y + 122 = 180
7x + 4y = 58 ......(1)
Also, we know that the opposite angles of a cyclic quadrilateral are supplementary. Therefore, we can set up the following equations:
105 + (4y + 14) = 180 ......(2)
(7y + 1) + (7x + 1) = 180 ......(3)
Simplifying and solving for y in equation (2), we get:
4y + 119 = 180
4y = 61
y = 15.25
Substituting this value of y in equation (3) and solving for x, we get:
(7x + 1) + (7*15.25 + 1) = 180
7x + 106 = 180
7x = 74
x = 10.57
Therefore, the value of x is approximately 10.57 and the value of y is approximately 15.25.
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x 3 + 3 x 2 − x + 2 x 2 + 6 x − 2
Answer: If you want me to evaluate its 18x - 2
Hope it helped :D
Rewrite in simplest terms: − 0. 4 ( − 6 g − 9 h ) − 2 h − 0. 2 ( − 5 h + 3 g ) −0. 4(−6g−9h)−2h−0. 2(−5h+3g)
The value of the given expression -0.4( -6g - 9h ) - 2h - 0.2( -5h + 3g ) in the simplest form is equal to 1.8g + 2.6h.
The expression is equal to,
-0.4( -6g - 9h ) - 2h - 0.2( -5h + 3g )
Apply distributive law multiplication over addition.
A ( B + C ) = A × B + A × C
Simplify the expression by first distributing the -0.4 and -0.2 coefficients to the terms inside the parentheses,
= (-0.4 × -6g + 0.4 × 9h ) -2h - ( 0.2 × -5h + 0.2 × 3g )
= 2.4g + 3.6h - 2h + h - 0.6g
Combine like terms,
= (2.4g - 0.6g) + (3.6h - 2h + h)
= 1.8g + 2.6h
Therefore, the simplest form of the expression is 1.8g + 2.6h.
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The above question is incomplete, the complete question is:
Rewrite in simplest terms:
− 0. 4 ( − 6 g − 9 h ) − 2 h − 0. 2 ( − 5 h + 3 g )
What is the sine ratio for angle A?
A. 5/4
B. 4/5
C. 3/4
D. 3/5
The sine ratio of for angle A is 4/5 and the right option is B. 4/5.
What is sine ratio?Sine ratio is the ratio of the length of the opposite side divided by the length of the hypotenuse.
The formula for the sine ratio of angle A is given in the formula below
Formula:
SinA = Opposite/Hypotenus................. Equation 1From the diagram.
Given:
Opposite = 4Hypotenus = 5Substitute these values into equation 1
SinA = 4/5Hence, the right option is B. 4/5.
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quiz 7the following table shows the individual measurements for five samples taken every 15 minutes starting at 10:00 am to be used in monitoring the quality of a process.10:00 am2.01.82.01.810:15 am2.02.02.02.010:30 am1.81.92.12.210:45 am2.12.11.91.911:00 am1.62.02.21.71. how many measurements are in each sample?2. suppose a mean control chart is being used with an upper limit of 2.2 and a lower limit of 1.8. using the data above, what would be the first point to plot on the control chart?
The first point to plot on the mean control chart would be at 1.9 at control chart with both limits.
1. There are four measurements in each sample, as shown in the table.
2. To plot the first point on the mean control chart, we need to calculate the mean of the first sample. Adding up the four measurements from the 10:00 am sample (2.0 + 1.8 + 2.0 + 1.8) gives a total of 7.6. Dividing by the number of measurements in the sample (4) gives a mean of 1.9. Since the mean is within the control limits of 1.8 and 2.2, the first point on the chart would be plotted at 1.9.
1. To determine how many measurements are in each sample, we simply count the number of measurements provided for each time.
10:00 am: 4 measurements (2.0, 1.8, 2.0, 1.8)
10:15 am: 4 measurements (2.0, 2.0, 2.0, 2.0)
10:30 am: 4 measurements (1.8, 1.9, 2.1, 2.2)
10:45 am: 4 measurements (2.1, 2.1, 1.9, 1.9)
11:00 am: 4 measurements (1.6, 2.0, 2.2, 1.7)
Each sample contains 4 measurements.
2. To plot the first point on a mean control chart, we need to calculate the mean of the first sample (10:00 am).
Mean = (2.0 + 1.8 + 2.0 + 1.8) / 4
Mean = 7.6 / 4
Mean = 1.9
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1. There are 4 measurements in each sample.
2. The first point to plot on the mean control chart would be 1.9, corresponding to the 10:00 am sample.
To determine the number of measurements in each sample, simply count the number of values for each time point.
10:00 am: 4 measurements (2.0, 1.8, 2.0, 1.8)
10:15 am: 4 measurements (2.0, 2.0, 2.0, 2.0)
10:30 am: 4 measurements (1.8, 1.9, 2.1, 2.2)
10:45 am: 4 measurements (2.1, 2.1, 1.9, 1.9)
11:00 am: 4 measurements (1.6, 2.0, 2.2, 1.7)
There are 4 measurements in each sample.
To plot the first point on the mean control chart, calculate the mean of the first sample (10:00 am).
Mean = (2.0 + 1.8 + 2.0 + 1.8) / 4 = 7.6 / 4 = 1.9.
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(15 POINTS) HELP ASAP TY!!
How are solving systems of two linear equations or inequalities and solving systems of two quadratic equations or inequalities alike? How are they different?
laptop: $199.99, 13% markup what is the markup
Answer:
≈ $26
Step-by-step explanation:
13% = 0.13
199.99 x 0.13 = $25.9987
So, 13% markup is ≈ $26