The common ratio of a geometric sequence is the ratio of any term to the previous term. The general nth term is given by an = n1 * r^(n-1), and the 10th term is a10 = n1 * r^9. The sum of the first 16 terms is S = (n1 * (1 - r^16)) / (1 - r).
Without the first term n1, we cannot find the common ratio r. However, we can still find the general nth term and the sum of the first 16 terms of the sequence.
(a) The common ratio r of a geometric sequence is the ratio of any term to the previous term. Let's assume that the first term of the sequence is n1. Then, the second term is n1r, the third term is n1r^2, and so on. Therefore, the common ratio is r = (n2 / n1) = (n3 / n2) = (n4 / n3) = ...
(b) The general nth term of a geometric sequence is given by an = n1 * r^(n-1).
(c) To find the 10th term of the sequence, we use the formula above with n = 10. Therefore, a10 = n1 * r^(10-1) = n1 * r^9.
(d) To find the sum of the first 16 terms of the sequence, we use the formula for the sum of a geometric series: S = (n1 * (1 - r^n)) / (1 - r), where n is the number of terms. In this case, n = 16. Thus, the sum of the first 16 terms is S = (n1 * (1 - r^16)) / (1 - r).
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The following data shows the number of times a class of 8th graders ate a sandwich over a 30-day period.
{6, 18, 23, 21, 14, 12, 24, 13, 19, 30, 25, 20, 23, 22, 27, 14, 20, 28, 24, 25}
Part A: Determine the best graphical representation to display the data. Explain why the type of graph you chose is an appropriate display for the data. (6 points)
Part B: Explain, in words, how to create the graphical display you chose in Part A. Be sure to include a title, axis label(s), scale for axis if needed, and a clear process of how to graph the data. (6 points)
Answer:
Step-by-step explanation:
Part A: A histogram would be the best type of graphic to use to depict the supplied data.
The distribution of quantitative data (in this case, the frequency of sandwich consumption) is presented by a histogram, which enables us to see the frequency of various values or ranges. When working with discrete data, as in this instance, it is quite helpful.
Part B: Making a histogram using the provided data
To divide the data set into appropriate intervals or bins, ascertain the range of values covered by the data set (from the least to the maximum value). In this instance, a minimum value of 6 and a maximum value of 30 are acceptable starting points. Based on the distribution of the data, pick an acceptable bin width, such as 5 or 10. Indicate "Number of times a sandwich was eaten" on the horizontal axis and "Frequency" (or "Count") on the vertical axis.
The height of each bar should represent the frequency of values falling within each interval or bin, and the bars should be created for each interval/bin on the horizontal axis.
The height of each bar should represent the frequency of values falling within each interval or bin, and the bars should be created for each interval/bin on the horizontal axis. Counting the number of data points in each bin will yield the frequency.
Due to the fact that each interval is continuous and the values are discrete, make sure the bars are next to one another without any gaps.
Give the histogram a suitable title, like "Frequency Distribution of Sandwich Consumption."
Include a scale on the vertical axis if necessary to make the frequency count obvious.
These instructions will help you generate a histogram that accurately depicts the provided data and shows how frequently sandwiches were consumed by eighth-graders over the course of a 30-day period.
If we find that the null hypothesis, H_0 : B_j = 0, cannot be rejected when testing the contribution of an individual regressor variable to the model, we usually should: 1. remove the variable from the model. 2. do nothing. 3. add a quadratic term in x; to the model. 4. do none of the above.
If we find that the null hypothesis, H_0 : B_j = 0, cannot be rejected when testing the contribution of an individual regressor variable to the model, we usually should 1. remove the variable from the model.
This is because if the variable is not contributing significantly to the model, it is not useful in predicting the outcome. Therefore, removing the variable will simplify the model and potentially improve its accuracy.
Options 2 and 3 (doing nothing or adding a quadratic term in x) would not be appropriate if the variable is not significant, as they would not address the issue of the variable's lack of contribution.
Option 4 is also incorrect because we do need to take action if a variable is not contributing significantly to the model.
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find the local maximums and minimums of f(x, y) = sin(x) sin(y) for 0 x ⇡ and 0 y ⇡
The local maximums of f(x,y) = sin(x)sin(y) occur at (nπ, mπ) and the local minimums occur at (nπ + π/2, mπ + π/2), where n and m are integers.
Where do the local maximums and minimums of f(x,y) = sin(x)sin(y) occur?The given function f(x,y) = sin(x)sin(y) is a product of two periodic functions, each with a period of 2π. Hence, the function f(x,y) also has a periodicity of 2π in both x and y directions. To find the local maximums and minimums of the function, we need to look for points where the partial derivatives with respect to x and y are equal to zero.
Taking the partial derivative of f(x,y) with respect to x, we get cos(x)sin(y), which is equal to zero at points (nπ, mπ), where n and m are integers. Similarly, taking the partial derivative of f(x,y) with respect to y, we get cos(y)sin(x), which is also equal to zero at points (nπ, mπ). Therefore, the local maximums of f(x,y) occur at these points.
On the other hand, taking the partial derivative of f(x,y) with respect to x, we get cos(x)sin(y), which is equal to π/2 at points (nπ + π/2, mπ), where n and m are integers. Similarly, taking the partial derivative of f(x,y) with respect to y, we get cos(y)sin(x), which is equal to π/2 at points (nπ, mπ + π/2). Therefore, the local minimums of f(x,y) occur at these points.
In summary, the local maximums of f(x,y) = sin(x)sin(y) occur at (nπ, mπ) and the local minimums occur at (nπ + π/2, mπ + π/2), where n and m are integers.
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7. What is the area of the given circle in terms of pi?
check down below for picture.
The area of the circle in terms of pi, with a diameter of 9.6 meters, is 23.04π square meters.
The diameter of a circle is twice the radius, so if the diameter is 9.6 meters, then the radius is half of that, or:
r = 9.6 / 2 = 4.8 meters
The area of a circle is given by the formula:
A = πr²
Substituting in the value of r, we get:
A = π(4.8)²
Simplifying the expression by squaring 4.8, we get:
A = π(23.04)
So the area of the circle is:
A = 23.04π square meters
Therefore, the area of the circle in terms of pi, with a diameter of 9.6 meters, is 23.04π square meters.
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7.
Here is a fair 6-sided spinner.
Liz is going to spin the spinner 120 times.
(b) Work out an estimate for the number of times the spinner will land on 7
An estimate of the number of times the 6 - sided spinner will land on 7 is 20 times
Probability is defined as the:
P (E) = number of times a favorable event occurs / number of events
For six-sided spinner:
Outcomes: 9, 1, 2, 3, 4, and 7
Number = 6
P(7)=1/6
If the event takes place 120 times then,
P (7)= number of times it will land on 7/120
1/6 = number of times it will land on 7/120
Number of times it will land on 7 = 20
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the complete question is
This six-sided spinner is decent.
Liz will complete 120 spins of the spinner.
(b) Calculate the likelihood that the spinner will land on 7 a certain number of times.
When the LM-curve is vertical, 1. the monetary policy multiplier is zero 2. monetary policy is at its weakest but fiscal policy has a maximum effect on income 3. monetary policy has a maximum effect, but fiscal policy has no effect on income 4. fiscal policy's impact on interest rates will not affect investment 5. monetary policy affects interest rates but no change in investment spending results
The correct option is option 5: monetary policy affects interest rates but no change in investment spending results when the LM-curve is vertical.
The LM curve represents the relationship between the interest rate and the level of income or output in an economy, assuming a fixed money supply. When the LM curve is vertical, it means that the central bank has fixed the money supply and is targeting a specific interest rate. In this case, changes in income or output do not affect the interest rate.
Option 1 is incorrect because the monetary policy multiplier can still be nonzero even when the LM curve is vertical. The multiplier refers to the effect of changes in monetary policy on income or output, and it depends on other factors such as the slope of the aggregate demand curve.
Option 2 is incorrect because when the LM curve is vertical, fiscal policy does not have a maximum effect on income. Fiscal policy refers to the use of government spending and taxation to influence the level of economic activity. In this case, changes in fiscal policy would not have a significant impact on income because the interest rate is fixed.
Option 3 is incorrect because when the LM curve is vertical, monetary policy has no effect on income. Fiscal policy would also have limited effectiveness since changes in government spending or taxation would not have a significant impact on interest rates.
Option 4 is incorrect because fiscal policy's impact on interest rates can still affect investment even when the LM curve is vertical. When fiscal policy influences interest rates, it can affect the cost of borrowing and, consequently, investment decisions.
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The heights, in feet, of the trees for sale at two nurseries are shown below.
Yard Works: 7, 9, 7, 12, 5
The Grow Station: 9, 11, 6, 12, 7
Which statements are true regarding the measures of center and variability of these data sets? Select three choices.
The mean of the tree heights at Yard Works is less than the mean of the tree heights at The Grow Station.
The median of the tree heights at Yard Works is greater than the median of the tree heights at The Grow Station.
The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station.
The mean absolute deviation of the tree heights at Yard Works is greater than the mean absolute deviation of the tree heights at The Grow Station.
The mean absolute deviation of the tree heights at Yard Works is equal to the mean absolute deviation of the tree heights at The Grow Station.
The true statements regarding the measures of center and variability of these data sets are: statements A, C and E.
How to Find the Measures of center and Variability of a Data Set?To analyze the statements regarding the measures of center and variability, let's calculate the required measures for each data set.
For Yard Works:
Tree heights: 7, 9, 7, 12, 5
Mean: (7 + 9 + 7 + 12 + 5) / 5 = 40 / 5 = 8
Median: 7, 7, 9, 12, 5 → Median = 7
Range: 12 - 5 = 7
Mean absolute deviation (MAD): Calculate the absolute difference of each value from the mean, then find the average of those differences.
|7 - 8| + |9 - 8| + |7 - 8| + |12 - 8| + |5 - 8| = 1 + 1 + 1 + 4 + 3 = 10 / 5 = 2
For The Grow Station:
Tree heights: 9, 11, 6, 12, 7
Mean: (9 + 11 + 6 + 12 + 7) / 5 = 45 / 5 = 9
Median: 6, 7, 9, 11, 12 → Median = 9
Range: 12 - 6 = 6
Mean absolute deviation (MAD):
|9 - 9| + |11 - 9| + |6 - 9| + |12 - 9| + |7 - 9| = 0 + 2 + 3 + 3 + 2 = 10 / 5 = 2
Analyzing the statements:
A. The mean of the tree heights at Yard Works is less than the mean of the tree heights at The Grow Station.
True. Mean Yard Works < Mean The Grow Station (8 < 9)
B. The median of the tree heights at Yard Works is greater than the median of the tree heights at The Grow Station.
False. Median Yard Works = Median The Grow Station (7 = 9)
C. The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station.
True. Range Yard Works > Range The Grow Station (7 > 6)
D. The mean absolute deviation of the tree heights at Yard Works is greater than the mean absolute deviation of the tree heights at The Grow Station.
False. MAD Yard Works = MAD The Grow Station (2 = 2)
E. The mean absolute deviation of the tree heights at Yard Works is equal to the mean absolute deviation of the tree heights at The Grow Station.
True. MAD Yard Works = MAD The Grow Station (2 = 2)
In summary, the true statements are: A, C, and E.
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From the attachment, what is the measure of Angle DBC?
According to the intersecting Secant Theorem, the measure of Angle DBC, in this case, is 96°. (Option A)
What is an angle?An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle.
The image below shows what occurs when tangents and secants intersect on a circle. You get inscribed angles and arcs.
Therefore, the measure of inscribed angle ABD is equal to one-half of the measure its intercepted arc BED. Likewise, the measure of inscribed angle BCD is equal to one-half its intercepted arc BC.
Since BED ≅ BD
Thus, BCD = 192/2 = 96° (Option A)
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find the curve that describes the level curve of value c of the surface z = f ( x , y ) = x 2 4 y 2 25 = c where c < 0 .
There is no curve that describes the level curve of value c for the given surface, as the condition c < 0 makes it impossible to find a real solution.
In two- or three-dimensional space, a curve is a mathematical object that symbolises a continuous, smooth path. Curves can be derived from geometric operations, parametric equations, or mathematical equations. They are commonly used to simulate real-world processes in physics, engineering, mathematics, and many other disciplines.
To find the level curve of value c for the given surface [tex]z = f(x, y) = (x^2/4) + (y^2/25) = c[/tex], where c < 0, follow these steps:
Step 1: Write down the equation of the surface.
[tex]z = f(x, y) = (x^2/4) + (y^2/25)[/tex]
Step 2: Replace z with the constant c.
[tex]c = (x^2/4) + (y^2/25)[/tex]
Step 3: Rearrange the equation to isolate [tex]y^2[/tex].
[tex]y^2 = 25(c - (x^2/4))[/tex]
However, note that we're given that c < 0. This means that the value inside the parentheses (c - ([tex]x^2/4[/tex])) must also be negative. Since y^2 can't be negative, there's no real solution for this equation.
In conclusion, there is no curve that describes the level curve of value c for the given surface, as the condition c < 0 makes it impossible to find a real solution.
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pedro took an exam in a class in which the mean was 68 with a standard deviation of 10. if his z-score was 3, what was his exam score?
To find Pedro's exam score, we can use the formula for calculating the z-score:
z = (x - μ) / σ,
where z is the z-score, x is the exam score, μ is the mean, and σ is the standard deviation.
Given that Pedro's z-score was 3, we can rearrange the formula to solve for x:
3 = (x - 68) / 10.
Multiplying both sides of the equation by 10, we get:
30 = x - 68.
Adding 68 to both sides, we find:
x = 30 + 68 = 98.
Therefore, Pedro's exam score was 98.
The z-score measures how many standard deviations an individual's score is above or below the mean. In this case, Pedro's z-score of 3 indicates that his exam score was 3 standard deviations above the mean of 68.
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a situation in which several independent variables are highly correlated with each other is defined as _____.
although studies continue to show smoking leads to significant health problems, 30% of adults in a country smoke. consider a group of 250 adults, and use the normal approximation of the binomial distribution to answer the questions below. (a) what is the expected number of adults who smoke?
Based on the 30% smoking rate, we can expect that approximately 75 adults out of the group of 250 will be smokers.
To determine the expected number of adults who smoke in a group of 250 adults, we need to consider the smoking rate of 30% in the country. The expected number can be calculated by multiplying the total number of adults by the smoking rate.
Expected number of adults who smoke = Total number of adults × Smoking rate
Given that there are 250 adults in the group, the expected number of adults who smoke can be calculated as follows:
Expected number of adults who smoke = 250 × 0.30 = 75
The expected number is derived by assuming that each adult's decision to smoke is independent of others in the group. While this calculation provides an estimate, it is important to note that individual smoking behavior can vary.
It's also worth considering that the expected number does not account for factors such as age, gender, or other demographic characteristics that could influence smoking rates.
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Which description best defines AB¯¯¯¯¯?
Responses
the set of all points that are the same distance from point A as point B
the set of all points that are the same distance from point , A, as point , B
the set containing point A and point B
the set containing point , A , and point , B
the set of point A and point B and all the points between point A and point B
the set of point , A, and point , B, and all the points between point , A, and point , B
the set of all points between point A and point B
The description that best defines AB¯¯¯¯¯ is:
"The set of points containing point A and point B."
AB¯¯¯¯¯ represents a line segment with endpoints A and B.
A line segment is a part of a line that connects two points, and it includes all the points that lie between the two endpoints.
Therefore, the set of all points between point A and point B is the most accurate description of AB¯¯¯¯¯.
The set of all points between point A and point B includes both endpoints A and B, as well as all the points that lie in between them. These points can be represented by the notation [A, B].
In other words, AB¯¯¯¯¯ is the line segment that starts at point A and ends at point B, and it includes all the points that lie between A and B.
This definition of AB¯¯¯¯¯ is important in geometry and other related fields. It is used in a variety of applications, including measuring the distance between two points and finding the slope of a line.
Additionally, it is an important concept in trigonometry and calculus, where it is used to define integrals and to calculate the arc length of a curve.
In summary, AB¯¯¯¯¯ is the set of all points between point A and point B, including both endpoints.
This definition is essential to many branches of mathematics and has important applications in geometry, trigonometry, and calculus.
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Mark invests $560 at a bank that offers a 3.73% rate of interest on deposits, compounded annually.
Select the explicit expression that represents the total value of the investment after a period of 19 years.
A. 560(1.373)19
B. 560(1.0373)19
C. 560(2.0373) 19
D. 560(0.0373)19
The explicit compound interest expression which represents the total value after 19 years is
[tex]560 {(1.0373)}^{19} [/tex]
Compound InterestCompound interest is obtained mathematically using the relation
[tex]A = {P(1 + r \div n)}^{nt} [/tex]
Here ;
A = total value of the investment after the specified period
P = principal amount
r = interest rate
n = number of compounding periods per year, and
t = number of years.
We are given the following parameters;
P = $560 (principal amount)
r = 3.73% = 0.0373
n = 1
t = 19
Plugging the values into the formula , we have
[tex]A = {560(1 + 0.0373)}^{19} [/tex]
Hence, the correct compounding interest expression is
[tex]{560(1 + 0.0373)}^{19} [/tex]
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A middle school mathematics class was interested in the amount of time it takes them to travel to school. They gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data. Which graphical representation would be best for their data? Circle graph Bar graph Line plot Box plot
A bar graph would be the most appropriate graphical representation for the middle school mathematics class's data on travel time to school.The correct answer is option B.
For the given scenario, the most appropriate graphical representation for the data collected from the random sample of 100 students would be a bar graph.
A bar graph is suitable for displaying categorical data, such as the time it takes students to travel to school. The x-axis can represent different categories or ranges of travel time (e.g., 0-5 minutes, 5-10 minutes, 10-15 minutes), while the y-axis represents the frequency or count of students falling within each category.
A circle graph (also known as a pie chart) is more appropriate for displaying proportional data, where the parts make up a whole. It is not suitable for showing individual travel times.
A line plot, also known as a dot plot, is useful for representing a distribution of data with numerical values along a number line. However, it may not be the best choice for displaying the travel times of 100 students, as it could become cluttered and difficult to interpret.
A box plot is typically used to display the distribution, variability, and outliers in a dataset. While it can provide useful insights into the spread of travel times, it may not be the most suitable choice for this particular scenario where the focus is on the frequencies or counts of different travel time categories.
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The probable question may be:
A middle school mathematics class was interested in the amount of time it takes them to travel to school. They gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data. Which graphical representation would be best for their data?
A. Circle graph
B. Bar graph
C. Line plot
D. Box plot
find the most general antiderivative of h(t)=−3sin(t)/cos^2(t), where −π2
The most general antiderivative of h(t)=-3sin(t)/cos^2(t) is F(t)=3sec(t)+C, where C is a constant of integration.
To find the antiderivative of h(t), we first recognize that -3sin(t)/cos^2(t) can be rewritten as -3cos^(-2)(t) * sin(t). We can then use the substitution u = cos(t), du = -sin(t) dt to obtain ∫ -3cos^(-2)(t) * sin(t) dt = ∫ -3/u^2 du. Integrating with respect to u, we get 3/u + C = 3sec(t) + C, where C is a constant of integration. Therefore, the most general antiderivative of h(t) is F(t) = 3sec(t) + C, where C is a constant of integration.
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what is the answer the this iready question?
Answer:
last option shown, 500 milliliters
Step-by-step explanation:
She has approx 3.5 liters of choc milk as shown in the pic.
3.5 liters x 1000 = 3500 milliliters total choc milk.
=3500/7 containers = 500 milliliters in each.
So pick the last option, 500 milliliters.
For each of the following assertions, state whether it is a legitimate statistical hypothesis and why. (a) H: σ> 110 Yes, this statement is an assertion about the value of a parameter Yes, this statement is an assertion about the value of a statistic No, e's not a parameter. O No, σ is not a statistic. There is not enough information to say
H: σ> 110 is a legitimate statistical hypothesis because it is an assertion about the value of a parameter, which is the population standard deviation (σ). Option A is correct.
In statistical hypothesis testing, hypotheses are statements made about the values of parameters, which are characteristics of the population being studied. The given statement H: σ > 110 is a valid statistical hypothesis because it asserts that the population standard deviation (σ) is greater than 110.
It addresses a parameter and not a statistic. Hypotheses about parameters are common in statistical analysis as they allow us to make inferences and draw conclusions about the population based on sample data. Thus, the statement H: σ > 110 is a legitimate statistical hypothesis.
Therefore, option A is correct.
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What is the length of CD in the figure below?
The value of length CD is 5
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are congruent i.e they are equal.
Also the the ratio of corresponding sides of similar triangles are equal.
Therefore;
25-2x/x = 24/8
25-2x/x = 3/1
25 -2x = 3x
25 = 3x+2x
25 = 5x
divide both sides by 5
x = 25/5
x = 5
therefore the value of CD is 5
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"Which of the following is not a step that must be conducted each time you use the p-value method?
Providing an interpretation
Marking the claim
Multiplying the test statistic by -1
Finding the test statis"
The step that is not necessary to conduct each time you use the p-value method is "Multiplying the test statistic by -1."
In hypothesis testing using the p-value method, the general steps include:
Formulating the null and alternative hypotheses.
Selecting an appropriate significance level (alpha).
Collecting and analyzing the data to obtain the test statistic.
Calculating the p-value, which is the probability of observing a test statistic as extreme as or more extreme than the one obtained, assuming the null hypothesis is true.
Comparing the p-value to the significance level.
Making a decision to reject or fail to reject the null hypothesis based on the comparison of the p-value and the significance level.
Providing an interpretation of the results in the context of the problem.
Multiplying the test statistic by -1 is not a standard step in the p-value method. The test statistic itself is calculated based on the data and the hypothesis being tested, and its sign is important in determining the direction of the effect being analyzed.
Multiplying it by -1 would invert the sign, which would change the interpretation and potentially lead to incorrect conclusions. Therefore, this step is not necessary in the p-value method.
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find the distance between u= [0 -5 2] z= [ -4 -1 8]
In this case, the distance between u and z is 2sqrt(14).
To find the distance between two vectors, we can use the formula: distance = ||u - z||
where || || denotes the norm (or magnitude) of the vector. In this case, we have:
u = [0, -5, 2]
z = [-4, -1, 8]
So, the difference between the two vectors is:
u - z = [0 - (-4), -5 - (-1), 2 - 8] = [4, -4, -6]
The norm of this vector is:
||u - z|| = sqrt(4^2 + (-4)^2 + (-6)^2) = sqrt(56) = 2sqrt(14)
Therefore, the distance between u and z is 2sqrt(14).
In summary, the distance between two vectors can be found by taking the norm of their difference vector. In this case, the distance between u and z is 2sqrt(14).
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Find the missing angle measure for each triangle, then classify each triangle as isosceles or not isosceles.
65°
isosceles
60⁰°
isosceles
60°
not isosceles
50°
60
70°
65°
65
60°
55°
60°
45°
isosceles
65°
not isosceles
45°
not isosceles
1) In first triangle, x = 65
So, It is isosceles triangle.
2) In second triangle, x = 60
So, It is not isosceles triangle.
3) In third triangle, x = 45
So, It is not isosceles triangle.
4) In fourth triangle, x = 65
So, It is not isosceles triangle.
In first triangle,
Let measure of third angle = x
Hence,
x + 50 + 65 = 180
x + 115 = 180
x = 180 - 115
x = 65
So, It is isosceles triangle.
In second triangle,
Let measure of third angle = x
Hence,
x + 60 + 60 = 180
x + 120 = 180
x = 180 - 120
x = 60
So, It is not isosceles triangle.
In third triangle,
Let measure of third angle = x
Hence,
x + 70 + 65 = 180
x + 135 = 180
x = 180 - 135
x = 45
So, It is not isosceles triangle.
In fourth triangle,
Let measure of third angle = x
Hence,
x + 55 + 60 = 180
x + 115 = 180
x = 180 - 115
x = 65
So, It is not isosceles triangle.
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Will give brainliest
Find the area of this shape, include units of measure in your answer
The area of the composite shape in this problem is given as follows:
18 inches squared.
How to obtain the area of a rectangle?To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:
Area = Length x Width.
The figure in this problem are composed by two rectangles, with dimensions given as follows:
2 inches and 3 inches.2 inches and 6 inches.Hence the area of the shape is given as follows:
A = 2 x 3 + 2 x 6
A = 6 + 12
A = 18 square inches.
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consider the function f(x) =xlnx.
let Tn be the nth degree Taylor approximation of f(2) about x=1. Find T1= T2= T3=
use 3 decimal places in your answer but make sure you carry all decimals when performing calculations
T3 is an over/under estimate of f(2)
If R3 is the remainder given by the Lagrange Remainder formula
R3<=
The first degree Taylor polynomial of f(x) = xlnx about x = 1 is given by T1(x) = f(1) + f'(1)(x-1) = 0 + 1(x-1) = x-1. Therefore, T1(2) = 2-1 = 1.
The second degree Taylor polynomial of f(x) = xlnx about x = 1 is given by T2(x) = T1(x) + f''(1)/2(x-1)^2. We have f''(x) = -1/x^2, so f''(1) = -1. Thus, T2(x) = x-1 - (1/2)(x-1)^2. Therefore, T2(2) = 2-1 - (1/2)(2-1)^2 = 1/2.
The third degree Taylor polynomial of f(x) = xlnx about x = 1 is given by T3(x) = T2(x) + f'''(c)/3!(x-1)^3, where c is some number between 1 and x. We have f'''(x) = 2/x^3, so f'''(c) = 2/c^3.
Thus, T3(x) = x-1 - (1/2)(x-1)^2 + (2/3!c^3)(x-1)^3. To find an upper bound for the error R3 = f(2) - T3(2), we need to find the maximum value of |f'''(x)| on the interval [1,2].
We have |f'''(x)| = 2/x^3, which is decreasing on the interval. Therefore, the maximum value occurs at x = 1, and we have R3 <= (2/3!)(2-1)^3/1^3 = 2/3.
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Which expression is equal to: 24 +14
A
6 ( 4 + 2)
B
2 ( 12 + 7 )
C
12 ( 2 +1 )
D
7 ( 3 + 2)
Answer:
B) 2x12=24 2x7=14
This equals to 24+14
The accompanying table shows the number of bacteria present in a certain culture
over a 5 hour period, where x is the time, in hours, and y is the number of bacteria.
Write an exponential regression equation for this set of data, rounding all coefficients
to the nearest thousandth. Using this equation, determine the number of bacteria
present after 10 hours, to the nearest whole number.
Hours (x) Bacteria (y)
0
1663
1
1821
2
2135
3
2467
4
2740
3179
10
5
The exponential regression equation for this set of data is y = [tex]14.129e^{(0.495x)[/tex] and the number of bacteria present after 10 hours is approximately 24684.
The exponential regression equation for this set of data can use a calculator or spreadsheet software.
The equation will have the form y = abˣ a is the initial number of bacteria and b is the growth rate.
Using the given data can create a table of values for the equation:
x y ln(y)
---------------------------------------
0 16 2.773
1 66 4.189
2 311 5.739
3 791 6.672
4 1553 7.349
5 2571 7.853
A regression tool can find that the equation is approximately y = [tex]14.129e^{(0.495x)[/tex] rounded to three decimal places.
The initial amount of bacteria is approximately a = 14.129 and the growth rate is approximately b = 1.649.
The number of bacteria present after 10 hours can plug x = 10 into the equation:
y = [tex]14.129e^{(0.495\times 10)[/tex]
= 24683.522
Rounding to the nearest whole number get that the number of bacteria present after 10 hours is approximately 24684.
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Find the following product, and write the product in rectangular form [4( cos 60° +i sin 60° )I7 (cos 210 i sin 2109)] [4(cos60° + i sin 60°)17( cos 210° + i sin 210°)-□
The product is 476(cos 540° + i sin 540°).
How to find the product of the given expressions?To find the product and write it in rectangular form, let's simplify the expression step by step.
First, let's simplify the expressions within each set of brackets separately:
Step 1: [4(cos 60° + i sin 60°)I7(cos 210° + i sin 210°)]
This expression involves multiplying two complex numbers using the polar form. When multiplying complex numbers, we multiply their magnitudes and add their angles.
The magnitude of 4 is 4, and the magnitude of I7 is 7. The angle of cos 60° + i sin 60° is 60°, and the angle of cos 210° + i sin 210° is 210°.
Therefore, the product of the first set of brackets is:
4 * 7 * (cos (60° + 210°) + i sin (60° + 210°))
= 28 * (cos 270° + i sin 270°)
= 28 * (-i)
= -28i
Step 2: [4(cos 60° + i sin 60°)17(cos 210° + i sin 210°)]
Similarly, we multiply the magnitudes and add the angles:
4 * 17 * (cos (60° + 210°) + i sin (60° + 210°))
= 68 * (cos 270° + i sin 270°)
= 68 * (-i)
= -68i
Now, we multiply the two results from the above steps:
(-28i) * (-68i)
= (-28 * -68) * (i * i)
= 1904 * (-1)
= -1904
So, the product of the given expression is -1904.
In rectangular form, a complex number is represented as a + bi, where a is the real part and b is the imaginary part.
Hence, the product in rectangular form is -1904 + 0i, or simply -1904.
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What method is best for solving for 9x^2-12x+12=0? Factor method,square root method or Quadratic formula method. And explain why.
The best method of solving for -9x^2-12x+12=0 is the factor method.
This is so because it is easier
How to determine the methodTo solve quadratic equations, there are different methods.
These methods are known as;
Factor methodSquare root methodQuadratic formula method.From the information given, we have that;
-9x²-12x+12=0
Using the factor method, we have that;
Find the pair factor of the product of 9 and 12 that would add up to given - 12, we have;
-9x² - 18x + 6x + 12 = 0
Group in pairs, we get;
(-9x² - 18x) + (6x + 12) = 0
Factorize
-9x(x + 2) + 6(x + 2) = 0
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The method that is best for solving for 9x^2-12x+12=0 is Quadratic formula method. because we are going to get a comlex roots.
How can the eequation be solved?
The quadratic formular can be written as;
x = -b ± √(b^2 - 4ac) / 2a
a = 3
b = -4
c = 4.
Then we can substitute as ;
x = -(-4) ± √(-4)^2 - 4(3)(4) /( 2*3)
x = 4 ±√(16 - 48) / 6
x = 4 ± √-32 / 6
x = 4 ± 4i√2 / 6
x = 2 ± 2i√2 / 3
x = 2 + 2i√2/3
x = 2 - 2i√2)/3
x=0.666667+0.942809i
x=0.666667−0.942809i
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a sportswriter wants to know how strongly columbus, ohio, residents support building a new stadium for the local minor league baseball team, the columbus clippers. she stands outside the stadium before a game and interviews the first 25 people who enter the stadium. the population for this survey is
The sample of 25 people interviewed by the sportswriter is not a Random sample. The correct answer is Option C. No, because not all residents of Columbus, Ohio have an equal chance of being selected.
In statistics, sampling is the process of selecting a subset of individuals or units from a larger population to estimate or infer information about the population.
A random sample is a subset of individuals or units from a larger population that is selected in a way that every member of the population has an equal chance of being selected. In other words, a random sample is unbiased and represents the population as a whole.
In the given scenario, the sportswriter interviews the first 25 people who enter the stadium before a game in Columbus, Ohio to determine how strongly Columbus residents support building a new stadium for the local minor league baseball team.
Now, the question is whether this sample is a random sample or not.
The answer is "No, because not all residents of Columbus, Ohio have an equal chance of being selected," which is option C.
The reason is that the sportswriter only interviews the first 25 people who enter the stadium before the game. This means that the sample is not selected randomly from the entire population of Columbus residents, but only from the people who happened to be at the stadium at that particular time.
Moreover, people who attend minor league baseball games may not be representative of the entire population of Columbus residents. For example, people who attend baseball games may be more likely to support building a new stadium than those who do not attend such games.
Therefore, the sample of 25 people interviewed by the sportswriter is not a random sample and may not be representative of the entire population of Columbus, Ohio. The results of the survey based on this sample may not accurately reflect the opinions of all Columbus residents.
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Complete Question
A sportswriter wants to know how strongly Columbus, Ohio residents support building a new stadium for the local minor league baseball team. She stands outside the stadium before a game and interviews the first 25 people who enter the stadium. Is this a random sample?
A. Yes, because it gives very accurate results.
B. Yes, because all fans had a chance to be asked.
C. No, because not all residents of Columbus, Ohio have an equal chance of being selected.
D. No, because the sample size is not right.
Which angle is coterminal with 5pi/3?
a. 2pi/3
b. 8pi/3
c. 11pi/3
d. -5pi/3
I already know that b is wrong
The coterminal angle of 5π/3
What are coterminal angles?Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side.
Examples of coterminal angles are 30°, -330, 390°. We can get the coterminal angles of a given angle by adding or subtracting 360 from the given angle.
5π/3
π is a symbol in radian that is equivalent to 180° in degrees.
therefore;
5 × 180/3
= 5× 60
= 300°
The coterminal angle of 300°
= 300+360
= 660°
converting it back to radian
= 660/180 = 66/18π
= 33/9 = 11/3π
Therefore the coterminal angle of 5π/3 is 11π/3
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