The possible coordinates of point A is: (-7, -4)
How to find the distance between two coordinates?The formula for the distance between two coordinates is:
D = √[(y₂ - y₁)² + (x₂ - x₁)²]
We are given:
(x₂, y₂) = (1, 2)
(x₁, y₁) = (-7, y₁)
Thus, if AB = 10, then we have:
√[(2 - y₁)² + (-7 - 1)²] = 10
(2 - y₁)² + 64 = 100
(2 - y₁)² = 100 - 64
(2 - y₁)² = 36
(2 - y₁) = √36
2 - y₁ = 6
2 - 6 = y₁
y₁ = -4
Thus, the coordinate of point A is: (-7, -4)
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Find the volume of the right cone below in terms of π.
The Volume of the right cone (V) that has a diameter of 6 units and a height of 11 units is calculated as: 33π units³.
What is the Volume of a Right Cone?The volume of a right cone can be determined by applying the following formula:
Volume of a right cone (V) = 1/3 * πr²h, where:
r represents the radius of the right cone
h represents the height of the right cone
Given the following:
radius (r) = 6/2 = 3 units
Height (h) = 11 units
Plug in the values:
Volume of the right cone (V) = 1/3 * π * 3² * 11
= 1/3 * π * 99
= π * 33
Volume of the right cone (V) = 33π units³
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suppose that we want to estimate what proportions of all drivers exceed the legal speed limit on a certain stretch of road. determine how large a sample we will need to be at least 99% confident that the resulting estimate, the sample proportion, is off by less than 0.04.
we need a sample size of at least 665 drivers to be 99% confident that the resulting estimate of the proportion of drivers who exceed the legal speed limit is off by less than 0.04.
To determine the sample size required to estimate a proportion with a given margin of error and confidence level, we can use the following formula:
n = (z^2 * p * q) / E^2
where:
n is the sample size
z is the z-score corresponding to the desired level of confidence. For 99% confidence, z = 2.576
p is the estimated proportion of drivers who exceed the legal speed limit (we can use a conservative estimate of 0.5 for p, which maximizes the sample size)
q = 1 - p
E is the maximum margin of error we allow in our estimate (0.04 in this case)
Substituting the values into the formula, we get:
n = (2.576^2 * 0.5 * 0.5) / 0.04^2
Simplifying, we get:
n = 664.33
Therefore, we need a sample size of at least 665 drivers to be 99% confident that the resulting estimate of the proportion of drivers who exceed the legal speed limit is off by less than 0.04.
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The circle passes through the point ( 3 , 6 ) What is its radius?
Answer: 5
Step-by-step explanation: The center of the circle will be (–3, 6), and the radius, which is the distance from (–3,6), will be 5. The standard form of a circle is given below: (x – h)2 + (y – k)2 = r2, where the center is located at (h, k) and r is the length of the radius. In this case, h will be –3, k will be 6, and r will be 5.
Find and interpret the mean absolute deviation of the data. Round your answer to the nearest tenth, if necessary.
The mean absolute deviation of the data is of:
1.25.
It represents the average by which the shoe sizes deviate from the mean shoe size.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the cardinality of the data-set, which is the number of observations in the data-set.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.The mean of the data-set in this problem is given as follows:
Mean = (6 + 8.5 + 6 + 9 + 10 + 7 + 8 + 9.5)/8
Mean = 8.
Then the deviations are given as follows:
|6 - 8| = 2.|8.5 - 8| = 0.5.|6 - 8| = 2.|9 - 8| = 1.|10 - 8| = 2.|7 - 8| = 1.|8 - 8| = 0.|9.5 - 8| = 1.5.Hence the MAD for the data-set is given as follows:
MAD = (2 + 0.5 + 2 + 1 + 2 + 1 + 0 + 1.5)/8
MAD = 1.25.
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Let R be the relation of the set of all differentiable functions defined f R g iff f and g have the same first derivative; that is f' = g'.
(a) Prove that R is an equivalence relation.
(b) Name three elements in the class 2x^3 + 5
(a) We must demonstrate that R satisfies the following criteria in order to establish that it is an equivalence relation:
1) Reflexivity: For any function f, f R f.
This is true since f' = f', so any function has the same first derivative as itself.
2) Symmetry: For any functions f and g, if f R g, then g R f.
This is true since if f' = g', then g' = f', so g and f have the same first derivative.
3) Transitivity: For any functions f, g, and h, if f R g and g R h, then f R h.
This is true since if f' = g' and g' = h', then f' = h', so f and h have the same first derivative.
R is an equivalence relation since it complies with each of the three requirements.
(b) To find three elements in the class of 2x³ + 5, we need to find all functions that have the same first derivative as 2x³ + 5. Since the derivative of 2x³ + 5 is 6x², any function of the form 2x³ + 5 + C, where C is a constant, will have the same first derivative. Consequently, the following three items belong to the 2x³ + 5 class:
1) 2x³+ 5
2) 2x³+ 5 + 1 = 2x³ + 6
3) 2x³ + 5 - 2 = 2x³+ 3
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Find the probabilities for the values of n
and \(p\_ when the conditions for the binomial distribution are met
The probability that two batteries used sequentially will remaining greater than 4 years is about 6.95%.
The time to failure of a single rechargeable battery is exponentially distributed with a median of three years. which means that the opportunity that a single battery will ultimate more than 4 years is given via:
P(X > 4) = e^(-4/3) ≈ 0.2636
Wherein X is the time to failure of a single battery.
Assuming that the two batteries are used sequentially and independently, the chance that each batteries will remaining more than four years is given by means of the made from their man or woman probabilities:
P(X1 > 4 and X2 > 4) = P(X1 > 4) * P(X2 > 4)
For the reason that two batteries are used successionally, the probability of the alternate battery lasting further than 4 times is analogous to the chance of the first battery lasting redundant than 4 years
P(X1 > 4 and X2 > 4) = P(X > 4)^2 ≈ 0.0695
Consequently, the probability that two batteries used sequentially will remaining greater than 4 years is about 0.0695 or 6.95%.
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
When comparing the data, the measure of center that should be used to determine which location typically has the cooler temperature is the median, because the histogram for Sunny Town is skewed.
A skewed histogram indicates that the distribution is not symmetric, and in this case, the histogram for Sunny Town is skewed to the right. This means that there are some unusually high temperatures that are pulling the mean towards the right, making it a less reliable measure of center. The median, on the other hand, is not affected as much by extreme values and gives a better representation of the typical temperature in Sunny Town.
In contrast, the histogram for Desert Landing is symmetric, which means that the mean and median are equal and either measure of center could be used to determine the typical temperature. However, the question specifically asks about the location with the cooler temperature, so we need to look at the histogram for Sunny Town, which is skewed and requires the use of the median.
Therefore, the correct answer is: Median, because Sunny Town is skewed.
solve:
cos theta = -0.37
give your answer to 1 decimal place
Answer: Not sure which one you need my guess would be RADIANS
Step-by-step explanation:
For COS THETA RADIANS = 1.9
For COS THETA DEGREES = 111.7
Sorry if its wrong
true or false:using an empirical (resampling) distribution includes sampling values outside the range of the actual data.
The given statement " using an empirical (resampling) distribution includes sampling values outside the range of the actual data. " is True because while resampling techniques may generate values outside the range of the original data, this is not necessarily a cause for concern.
Resampling techniques, such as bootstrapping or permutation tests, involve repeatedly sampling from the observed data to create an empirical distribution. This empirical distribution can then be used to make statistical inferences and hypothesis testing.
In some cases, resampling may generate values that are outside the range of the original data. This occurs because the resampling process is not constrained by the actual data values, but rather by the probability distribution of the observed data.
While sampling values outside the range of the actual data may seem counterintuitive, it is not necessarily a problem. In fact, resampling can be a powerful tool for testing statistical hypotheses and estimating uncertainty, particularly when the underlying population distribution is unknown or complex.
However, it is important to be aware of the limitations and assumptions of resampling techniques, particularly when making inferences or drawing conclusions. For example, if the original data is highly skewed or contains outliers, resampling may not accurately capture the underlying distribution.
Overall, while resampling techniques may generate values outside the range of the original data, this is not necessarily a cause for concern. Instead, it highlights the flexibility and power of empirical methods for statistical analysis.
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Painting A) The value was $12,050 in 2000 and steadily increased to $16,100 in 2020
Painting B) (Year, amount) (2000, 14200), (2005, 15075), (2010, 15950), (2015, 16825), (2020, 15950)
Answer choice what's true?
a) The value of painting B steadily increased from 2000 to 2020
b- In 2015, the value of painting A was greater than the value of painting B.
c- The graph that represents the value of painting B is nonlinear.
d- The value of painting B is always greater than value of painting A.
The value of painting B increases then decreases between 2000 and 2020, which indicates that the graph of the data is nonlinear
The option that is true is option C
C. The graph that represents the value of painting B is nonlinear
What is a linear graph?A linear graph is a graph that is a straight line.
The value of the painting A in the year 2000 = $12,050
The value in the year 2020 = $16,100
The variation of the value of painting B are;
Year [tex]{}[/tex] Amount
2000 [tex]{}[/tex] 14,200
2005 [tex]{}[/tex] 15075
2010 [tex]{}[/tex] 15950
2015 [tex]{}[/tex] 16,825
2020 [tex]{}[/tex] 15,950
Therefore, the value of painting B increases from 2000 to 2015 then decreases in 2020
Option (a) is incorrect
In 2015, the value of painting A = 12050 + 15 × (16100 - 12050)/(20) = 15, 087.5
The value of painting B in 2015 = 16,825 > 15,0875, therefore; option (b) is incorrect
The value of painting B increases and decreases as the number of years steadily increases, therefore, the graph that represents the value of painting B is nonlinear and option C is correct
The value of painting B in 2020, which is 15,950 is higher than the value of painting A in the same year (16,100), therefore, option d is incorrect
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Special Right Triangles
Answer:
w ≈ 137.6 feet
Step-by-step explanation:
using the tangent ratio in the right triangle formed
tan54° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{w}{100}[/tex] ( multiply both sides by 100 )
100 × tan54° = w , then
w ≈ 137.6 feet ( to the nearest tenth )
(Chapter 13) The binormal vector is B(t) = N(t) x T(t)
The binormal vector B(t) is then defined as the cross product of the unit tangent vector and the unit normal vector: B(t) = T(t) x N(t).
In the context of vector calculus, given a curve in three-dimensional space parameterized by the arc length parameter t, the unit tangent vector T(t) and the unit normal vector N(t) are defined as follows:
The unit tangent vector T(t) is a vector tangent to the curve at the point P(t), and its direction is the direction of the curve's motion at P(t). It is given by the first derivative of the position vector r(t) with respect to t, divided by its magnitude:
T(t) = r'(t) / |r'(t)|
The unit normal vector N(t) is a vector perpendicular to the curve at the point P(t), and its direction is toward the center of curvature of the curve at P(t). It is given by the second derivative of the position vector r(t) with respect to t, divided by its magnitude:
N(t) = r''(t) / |r''(t)|
The binormal vector is a vector perpendicular to both T(t) and N(t), and its direction is determined by the right-hand rule. It is used to complete the Frenet-Serret formulas, which describe the geometry of a curve in terms of its curvature and torsion.
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What is 1. 18 - 0. 88 show your working out
Answer: 0.3.
Step-by-step explanation:
1.18-0.88= 0.3
the ols estimator is derived by question content area bottom part 1 a. minimizing the sum of absolute residuals. b. connecting the yi corresponding to the lowest xi observation with the yi corresponding to the highest xi observation. c. minimizing the sum of squared residuals. d. making sure that the standard error of the regression equals the standard error of the slope estimator.
The OLS (Ordinary Least Squares) estimator is derived by: c. minimizing the sum of squared residuals. In a regression analysis, the OLS estimator aims to find the best-fitting line by minimizing the sum of the squared differences (or residuals) between the actual data points (yi) and the predicted values on the regression line.
The residuals represent the error between the actual and predicted values. Minimizing the sum of squared residuals ensures that the regression line fits the data as closely as possible, ultimately providing a reliable model for predicting future values based on the relationship between the independent variable (xi) and the dependent variable (yi).It is important to note that the standard error of the regression does not necessarily equal the standard error of the slope estimator, but they are related measures.
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Which sentence contains a remote reference?
After Tiara's lawn had been mowed, she cooled off in the swimming pool.
After her lawn had been mowed, Tiara cooled off in the swimming pool.
After Tiara mowed her lawn, she cooled off in the swimming pool.
The sentence "After Tiara's lawn had been mowed, she cooled off in the swimming pool." contains a remote reference because the pronoun "she" is ambiguous and could refer to either Tiara or someone else. The sentence "After her lawn had been mowed, Tiara cooled off in the swimming pool." would avoid the remote reference by explicitly stating who cooled off in the pool.
A_n=a_n-1+n and a_1=4 list the first four terms
For Aₙ = aₙ₋₁ + n and a₁ = 4, the first four terms will be 4, 6, 9, 13 respectively.
We will use the recursive formula aₙ = aₙ₋₁ + n for the recursive series to get the first four terms of the sequence, with a₁ set to 4 for the series.
a₁ = 4 (given),
a₂ = a₁+2
⇒ a₂ = 4+2
⇒ a₂ = 6,
a₃ = a₂+3
⇒ a₂ = 6+3
⇒ a₃ = 9,
a₄ = a₃+4
⇒ a₄ = 9+4
⇒ a₄ = 13,
As can be seen, one term is utilized to locate the next term in the sequence, which is why it is referred to as recursive. So the series' first four terms are 4, 6, 9, 13.
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The function a(b) relates the area of a trapezoid with a given height of 12 and
one base length of 9 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
a(b) = 12 +9
Which equation below represents the inverse function b(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
O A. b(a)=-6
OB. b(a) =
O c. b(a) =
OD. b(a) =
+6
-9
+ 9
Answer:
56
Step-by-step explanation:
because of its answee
What is the solution to this equation? In(x+6)-In(2x-1)=0
A. x = 5
B. x = -7
C. x = -5
D. x = 7
The solution to the equation ln(x+6)-In(2x-1)=0 is x = 7
What is the solution to the equation?From the question, we have the following parameters that can be used in our computation:
ln(x+6)-In(2x-1)=0
Rewrite as
ln(x+6) = In(2x-1)
When the equations are compared, we have
x + 6 = 2x - 1
Evaluate the like terms
x = 7
Hence, the solution is x = 7
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what are some other things a person making $40,000 would have to account for before determining their net pay?
Solve And Fill In The Boxes
The given angles are supplementary and the value of x is 86°.
Since both angles are composited above a straight line it makes the sum of angles 180°.
So, the given angles are supplementary.
As we know that supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.
As per the given figure,
∠x° + ∠(x+8)° = 180°
x + x + 8 = 180
2x = 180 - 8
x = 172/2
x = 86°
Thus, the given angles are supplementary and the value of x is 86°.
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can someone help me with this please explain it
Answer:
It's the last one :)))
Step-by-step explanation:
It starts with only 1 14, so look at the dots and see if they have one dot above 14. They all do.
Next look at 11. It is only counted once. look in between 10 and 12 for 1 plot of 11. The first one doesn't have 11 plotted once. That one is not it.
Then look at 4. It is counted 3 times. look at the last two options and see if 4 is plotted 3 times. The second one only has it once. So it has to be the last one.
That's what came off the top of my head. Hope this helps! :)))
The third dot plot best corresponds to the data set (14, 11, 4, 15, 12, 5, 17, 3, 6, 4, 6, 10, 4, 18, 5).
The given data set is (14, 11, 4, 15, 12, 5, 17, 3, 6, 4, 6, 10, 4, 18, 5)
We have to find the corresponding dot plot which matches the data set.
A dot plot is a graphical display of data using dots.
a simple form of data visualization that consists of data points plotted as dots on a graph with an x- and y-axis.
By observing the data set and plots the third dot plot matches the data set.
Hence, the third dot plot best corresponds to the data set (14, 11, 4, 15, 12, 5, 17, 3, 6, 4, 6, 10, 4, 18, 5).
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Through ten games of basketball this season, Mila has made 50% of her free-throws. Which word or phrase describes the probability that Mila will hit her next free throw?
Since Mila has made 50% of her free-throws. The word or phrase that describes the probability that Mila will hit her next free throw is uncertain or unknown.
What is the probability?To determine the likelihood of successful free throws, divide the number of successful attempts by the total number of attempts, and then multiply by 100.
A forecast of an probability distribution of uncertainty is passed by a probability distribution, and this term ought to be subject to modification only upon having additional knowledge.
Due to the fact that Mila has made 50% of her free throws in all, one cannot say or predict with accuracy if she will make her next free throw
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g a simple undirected graph has 17 edges, and each vertex is at least of degree 3. what is the largest number of vertices this graph can have? give the example of the graph with maximal number of vertices and prove that there is not such graph with larger amount of vertices.(10 pts)
Therefore, the graph with 11 vertices and 17 edges is the graph with the maximal number of vertices that satisfies the given conditions.
Let's denote the number of vertices in the graph as V. Since each vertex has a degree of at least 3, the sum of the degrees of all vertices must be at least 3V. But since each edge contributes to the degree of two vertices, the sum of the degrees of all vertices is also equal to 2E (where E is the number of edges in the graph). Therefore, we have:
3V ≤ 2E
3V ≤ 2(17)
3V ≤ 34
V ≤ 11.33
Since V is an integer, the largest possible value of V is 11. Therefore, the graph with 11 vertices and 17 edges is an example of a graph that satisfies the given conditions.
To show that there is no graph with a larger number of vertices that satisfies the given conditions, we can use the Handshaking Lemma, which states that the sum of the degrees of all vertices in a graph is equal to twice the number of edges. If we assume that there is a graph with more than 11 vertices and 17 edges, then at least one vertex must have a degree greater than 3 (since the sum of the degrees is equal to 2E). But if a vertex has a degree greater than 3, then there must be at least one vertex with degree less than 3 (since the sum of the degrees is equal to 2E). This contradicts the given condition that each vertex has a degree of at least 3. Therefore, there is no graph with a larger number of vertices that satisfies the given conditions.
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the european and mediterranean population over age 20 has a high percentage of overweight people who represent what percent of their population? group of answer choices 35% 55% 68% 80%
According to the World Health Organization (WHO), the European and Mediterranean populations over the age of 20 have a high percentage of overweight people. In fact, the WHO estimates that approximately 55% of the population in this region is overweight or obese.
This is a significant percentage, and it is important to note that being overweight or obese can increase the risk of numerous health problems, including cardiovascular disease, diabetes, and certain types of cancer.
There are a number of factors that contribute to the high prevalence of overweight and obesity in this region, including changes in diet, decreased physical activity levels, and cultural factors. For example, many people in these regions consume a diet that is high in calories, fat, and sugar, while also engaging in sedentary behaviors.
Overall, the high percentage of overweight and obese individuals in the European and Mediterranean populations over the age of 20 is a cause for concern. It highlights the need for effective public health interventions to promote healthy lifestyles and prevent chronic disease.
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The table summarizes results from pedestrian deaths that were caused by automobile accidents.
Driver
Intoxicated? Pedestrian Intoxicated?
Yes No
Yes 62 80
No 289 545
If one of the pedestrian deaths is randomly selected, find the probability that the driver was not intoxicated. (Please enter a decimal, and round your answer to 4 decimal places.)
Probability = _____
** Enter a decimal number, accurate to at least 4 decimal places.
the probability that the driver was not intoxicated is approximately 0.8545.
To find the probability that the driver was not intoxicated in a randomly selected pedestrian death, we first need to determine the total number of pedestrian deaths and the number of deaths where the driver was not intoxicated.
From the table:
- Driver Not Intoxicated & Pedestrian Intoxicated: 289
- Driver Not Intoxicated & Pedestrian Not Intoxicated: 545
Total pedestrian deaths = 62 + 80 + 289 + 545 = 976
Deaths with driver not intoxicated = 289 + 545 = 834
Now, we can calculate the probability:
Probability (Driver Not Intoxicated) = (Deaths with driver not intoxicated) / (Total pedestrian deaths) = 834 / 976 ≈ 0.8545
So, the probability that the driver was not intoxicated is approximately 0.8545.
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a survey of shopping habits found the percentage of respondents that use technology for shopping as shown in figure 5.30. for example, 17.39% only use online coupons; 21.74% use online coupons and check prices online before shopping, and so on. what is the probability that a shopper will check prices online before shopping? what is the probability that a shopper will use a smart phone to save money? what is the probability that a shopper will use online coupons? what is the probability that a shopper will not use any of these technologies? what is the probability that a shopper will check prices online and use online coupons but not use a smart phone? if a shopper checks prices online, what is the probability that he or she will use a smart phone? what is the probability that a shopper will check prices online but not use online coupons or a smart phone?
To answer these questions, we need to use the information provided in Figure 5.30. Let's first write down the given percentages for each technology:
Only use online coupons: 17.39%
Use online coupons and check prices online before shopping: 21.74%
Use a smart phone to save money: 15.22%
Don't use any of these technologies: 26.09%
Use online coupons and check prices online, but not a smart phone: 13.04%
Use a smart phone if they check prices online: 86.36%
Check prices online but not use online coupons or a smart phone: 4.35%
Now we can answer each question:
What is the probability that a shopper will check prices online before shopping?
This includes the percentage of shoppers who use online coupons and check prices online, plus the percentage of shoppers who only check prices online:
P(check prices online) = 21.74% + 4.35% = 26.09%
What is the probability that a shopper will use a smart phone to save money?
This is the percentage of shoppers who use a smart phone:
P(use a smart phone) = 15.22%
What is the probability that a shopper will use online coupons?
This includes the percentage of shoppers who only use online coupons, plus the percentage of shoppers who use online coupons and check prices online:
P(use online coupons) = 17.39% + 21.74% = 39.13%
What is the probability that a shopper will not use any of these technologies?
This is the percentage of shoppers who don't use any of the technologies:
P(not use any technology) = 26.09%
What is the probability that a shopper will check prices online and use online coupons but not use a smart phone?
This is the percentage of shoppers who use online coupons and check prices online, but not a smart phone:
P(check prices online and use online coupons but not a smart phone) = 13.04%
If a shopper checks prices online, what is the probability that he or she will use a smart phone?
This is the percentage of shoppers who use a smart phone if they check prices online:
P(use a smart phone | check prices online) = 86.36%
What is the probability that a shopper will check prices online but not use online coupons or a smart phone?
This is the percentage of shoppers who only check prices online:
P(check prices online only) = 4.35%
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Complete question:
A survey of shopping habits found the percentage of respondents that use technology for shopping as shown in figure 5.30. for example, 17.39% only use online coupons; 21.74% use online coupons and check prices online before shopping, and so on.
What is the probability that a shopper will check prices online before shopping?
What is the probability that a shopper will use a smart phone to save money?
What is the probability that a shopper will use online coupons?
What is the probability that a shopper will not use any of these technologies?
What is the probability that a shopper will check prices online and use online coupons but not use a smart phone?
If a shopper checks prices online, what is the probability that he or she will use a smart phone?
What is the probability that a shopper will check prices online but not use online coupons or a smart phone?
Please explain & answer, I will mark brainliest!
Complete the square for the expression. Also, identify the resulting expression as a binomial squared.
x^2 + 15x + ____
Answer:
A quadratic trinomial in x with coefficient of x^2 equal to 1 is a perfect-square trinomial if the constant term is the square of 1/2 the coefficient of x.
[tex] {x}^{2} + 15x + {( \frac{15}{2} )}^{2} [/tex]
[tex] {x}^{2} + 15x + \frac{225}{4} [/tex]
[tex] {(x + \frac{15}{2} )}^{2} [/tex]
Solving systems of equations by graphing
The solution is,
a) Option A
y = 2x + 10
Option B
y = 3x
b) Option A is represented with the red line and Option B is represented by the blue line.
Total Cost is presented on the y-axis and the Number of rides is presented on the x-axis.
The graph is presented below.
From this graph, we can see that the two lines cross at (10, 30)
So, the two options will have the same rides and the same total cost when
x = 10 rides
y = 30 dollars
Explanation:
There are two options to consider,
Let the amount to be paid be y
Let the number of rides be x
Option A
Each ride costs $2
x rides will cost 2x dollars
Activation fee = 10 dollars
Total cost = y
y = 2x + 10
Option B
Each ride costs $3
x rides will cost 3x dollars
Activation fee = 0
Total cost = y
y = 3x
So, we end up with a system of equation for when the number of rides and the total cost for both options become the same
y = 2x + 10
y = 3x
b) We are asked to solve this system of equations by graphing.
To do this, we will first plot the two lines for each equation, then the solution will be where the two lines cross each other.
We will use intercepts to plot the first line
y = 2x + 10
when x = 0,
y = 2x + 10
y = 2(0) + 10
y = 0 + 10
y = 10
First point on this line is (0, 10)
when y = 0
y = 2x + 10
0 =2x + 10
-2x = 10
Divide both sides by -2
(-2x/2) = (10/-2)
x = -5
Second point on the line is (-5, 0)
For the second option
y = 3x
when x = 0
y = 3x
y = 3(0)
y = 0
First point on this line is (0, 0)
when x = 1
y = 3x
y = 3(1) = 3
Second point on the line is (1, 3)
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The graph shown models the relationship between the distance a car travels and time. Distance (miles) (60. y) Time (minutes) What does the point (60, y) represent in this situation? A. The car travels for y minules. B. The car travels y miles per hour. C. The car travels 60 miles per hour. D. The car travels 60 miles every y minutes. 9/4
Answer:
the answer's letter D "The car travels 60 miles every y minutes"
Let the supply and demand equations for a certain commodity be the following.
demand: p=√√9-0.1q
supply: p=√0.1q+1 -2
a. Find the equilibrium demand.
b. Find the equilibrium price (in dollars).
a) the equilibrium demand is 122. b) the equilibrium price is $3.63.
How to calculate the equilibrium demand and equilibrium pricea) Equilibrium demand can be gotten by setting the demand equal to the supply:
√√9-0.1q = √0.1q+1 -2
Squaring both sides:
√9 - 0.1q = (0.1q + 1 - 2)²
9 - 0.1q = 0.01q² + 0.98q - 1
0.01q² + 1.08q - 8 = 0
Solving for q using the quadratic formula:
q = (-1.08 ± √(1.08² + 4(0.01)(8))) / (2(0.01))
q = (-1.08 ± 3.52) / 0.02
q = 122 or -130
Since we cannot have a negative quantity, the equilibrium demand is 122.
b) To find the equilibrium price, we can substitute q = 122 into either the demand or supply equation:
p = √√9-0.1q = √√9-0.1(122) ≈ $3.63
Therefore, the equilibrium price is approximately $3.63.
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