Write the transformation matrix and the resultant matrix that will translate the triangle, (-2, 4), given the triangles vertices are at A(-1, 3), B(0, -4) and C(3, 3).
Answers
The new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:
|-3 -2 1 |
| 7 0 7 |
| 1 1 1 |
Define translationIn mathematics, a translation refers to a geometric transformation that moves every point in a figure or a space by the same distance in a given direction. In other words, it involves sliding a figure or a point to a new location without changing its size, shape, or orientation.
To translate the triangle by a vector (x, y), we use the following transformation matrix:
|1 0 x|
|0 1 y|
|0 0 1|
For the given triangle with vertices at A(-1, 3), B(0, -4), and C(3, 3), let's assume we want to translate it by a vector (−2, 4). Then the transformation matrix for translation is:
|1 0 -2|
|0 1 4 |
|0 0 1 |
To apply this transformation matrix to each vertex of the triangle, we represent the vertices as column vectors and multiply them by the matrix:
| -1 | | 1 0 -2 | | -3 |
| 3 | -> | 0 1 4 | = | 7 |
| 1 | | 0 0 1 | | 1 |
| 0 | | 1 0 -2 | | -2 |
| -4 | -> | 0 1 4 | = | 0 |
| 1 | | 0 0 1 | | 1 |
| 3 | | 1 0 -2 | | 1 |
| 3 | -> | 0 1 4 | = | 7 |
| 1 | | 0 0 1 | | 1 |
So, the new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:
|-3 -2 1 |
| 7 0 7 |
| 1 1 1 |
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Related Questions
In the equation g−h=h−g, g and h are real numbers.
For what values does g−h=h−g?
Select ALL that apply.
Answers
In the given equation g - h = h - g, where g & h are real-numbers and LHS will be equal to RHS only when values of g & h are equal in magnitude & sign so that LHS & RHS becomes zero..
What are real-numbers?Natural numbers are used to count things or objects, whereas rational numbers can be used to represent or indicate fractions, irrational numbers are used to calculate or evaluate a number's square root, integers are used to measure temperature, and so on. Real numbers are a collection of several forms of numbers, such as whole, natural, integers, fractions, etc. Integers, both positive and negative, fractions, and irrational numbers are examples of rational numbers that are combined to form real numbers. R's symbol for or representation of the set of real numbers.
Given that g - h = h - g
On simplifying the equation we get:
g - h = h - g
g + g = h + h
2g = 2h
g = h
g & h can take any values, but both must be equal in order to satisfy the given condition.
For e.g, let g=h=12
g - h = h - g
12 - 12 = 12 - 12
0 = 0
Both LHS & RHS can only be zero.
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Explica por qué las siguientes expresiones representan el mismo valor.
a) 10 - (-2)
b) -10 +2
Answers
after calculating both the expressions we can conclude that both expressions represent the same value of 12.
what is expression ?Mathematical operations including multiplication, division, addition, and subtraction are possible. The construction of an expression looks like this: Expression, number, and mathematical operator Numbers, variables, and functions are the elements of a mathematical expression (such as addition, subtraction, multiplication, and division, etc.). Expressions and phrases can be contrasted. Expressions are any equations that comprise numbers, variables, and an arithmetic operation. They are occasionally referred to as algebraic expressions. For instance, the value of m in the computation of 4m + 5 is the same as the word m in the provided equation, which has been separated from the figures 4m and 5 by the mathematical symbol +.
given,
Since subtracting a negative integer is equivalent to adding its positive counterpart, the expressions "10 - (-2)" as well as "-10 + 2" have the same meaning.
To be more precise, "10 - (-2)" denotes starting with a value of 10 and then deducting a negative value of -2. The positive value of an amount that is negative may be subtracted without affecting it, and vice versa. Therefore, "10 - (-2)" equals "10 + 2," making 12 the result.
The expression "-10 + 2" on the opposite hand suggests that we start with an amount of -10 and subsequently add a value of 2.
A positive number is equal to its negative counterpart when added to a negative number. Because of this, "-10 + 2" equals "-10 - (-2)", which also equals 12.
Therefore, both expressions represent the same value of 12.
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The downside of using an interface for integration is that the data will not be as ________ as it would be if it were integrated more directly.
A) accurate
B) timely
C) economical
D) valuable
Answers
The downside of using an interface for integration is that the data will not be as accurate as it would be if it were integrated more directly.
When it comes to integrating data between different systems or applications, there are different approaches that can be taken.
One common method is to use an interface, which acts as a bridge between the two systems and facilitates the exchange of data.
However, while interfaces can be useful for integrating data, there are some downsides to this approach, including the potential for reduced accuracy.
The reason for this is that interfaces often require data to be transformed or mapped between the two systems, which can introduce errors or inconsistencies.
For example, if the data in one system is stored in a different format or with different data types than the other system, this may need to be converted before it can be transferred.
Similarly, if there are differences in the way that data is organized or labeled in the two systems, this can create challenges when integrating the data.
In contrast, more direct methods of integration, such as database replication or data synchronization, can be more accurate since they involve copying data directly from one system to another without the need for transformation or mapping.
However, these methods can also be more complex and costly to set up and maintain.
Ultimately, the choice of integration method will depend on the specific needs and constraints of the organization. While interfaces may have some drawbacks in terms of data accuracy, they can still be a useful tool for integrating data in many situations.
It is important to carefully consider the tradeoffs between different integration methods and choose the one that best meets the needs of the business.
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Make up two data sets. list all the values in each data set and write a story to describe where they come from. The data sets should meet the following conditions:
The data set should come from random samples from a population
The centers of the distribution should be similar
The variabilities of the distributions should be different
Answers
The two data sets that meet the given conditions for in centers, and variability is in the explanations.
What are the two datasets?Data Set 1 - Heights of Adults in a City:
Values in Data Set 1 (in inches): 64, 67, 65, 63, 66, 68, 62, 64, 67, 65, 63, 66, 68, 62
Story: The data set represents the heights of randomly sampled adults in a city. The city is known for having a relatively consistent height distribution, with the majority of adults falling within a similar height range. The heights in this data set range from 62 inches to 68 inches, with a center around 65 inches, which is the most common height among the sampled adults. The data set shows relatively low variability, with most heights clustering around the center, indicating that the population of adults in the city has a narrow height distribution.
Data Set 2 - Salaries of Employees in a Corporation:
Values in Data Set 2 (in thousands of dollars): 42, 45, 47, 48, 43, 50, 55, 44, 42, 45, 47, 48, 43, 50, 55
Story: The data set represents the salaries of randomly sampled employees in a large corporation. The corporation has a wide range of job positions, and as a result, the salaries of its employees show a higher variability compared to the heights of adults in the city. The salaries in this data set range from $42,000 to $55,000, with a center around $47,000, which is the most common salary among the sampled employees. The data set shows higher variability, with salaries spread out across a wider range, indicating that the population of employees in the corporation has a more diverse salary distribution. This could be due to differences in job roles, experience levels, and other factors that impact salaries within the corporation.
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Write a quadratic function f whose zeros are -2 and 12.
f(x) = 0
Answers
Answer:
[tex]f(x) = (x + 2)(x - 12)[/tex]
[tex]f(x) = {x}^{2} - 10x - 24[/tex]
PLSSSSSSSSSSSSSSSS HELP I WILL MARK YOU BRAINLYEST
Answers
2x0+2=2
2x1+2=4
2x2+2=6
2x3+2=8
A ball is dropped from a height of 12 feet and returns to a height that is one-half of the height from which it fell. How far will the ball have traveled when it hits the ground for the fourth time? A 24 B 34.5 C 1.5 D 12
Answers
In linear equation., 33 far will the ball have traveled when it hits the ground for the fourth time.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
in order to calculate the distance of the ball taht would have traveled when it hits the ground for the fourth time is to list the height everytime it bounces. We calculate as follows:
12+6+6+3+3+1.5+1.5 = 33 feet
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I have the GCF but I don't know the rest of the numbers.
Answers
Answer:
[tex]15 + 45 = 3(5 + 15)[/tex]
Carly spent $13.25 on supplies to make lemonade. At least how many glasses of lemonade must she sell at $0.20 per glass to make a profit?
Answers
Answer:
66.25
technically 67 glasses
Step-by-step explanation:
The value of houses in Livingston goes up by 7% each year. Ben owns a house in Livingston that is currently worth $281,320. How much will it be worth in 9 years?
Answers
Ben's house will be worth $490,523.96 in 9 years if the value continues to increase at a rate of 7% per year.
Formula for Compound InterestWe can use the formula for compound interest, which is:
A = P × (1 + r)ⁿ
Where:
A = final amount
P = principal (starting value)
r = annual interest rate (expressed as a decimal)
n = number of compounding periods
In this case, the principal is $281,320, the annual interest rate is 7% (or 0.07 as a decimal), and the number of compounding periods is 9 years. Plugging in these values, we get:
A = $281,320 × (1 + 0.07)⁹
A = $281,320 × 1.743
A = $490,523.96
Therefore, Ben's house will be worth approximately $490,523.96 in 9 years if the value continues to increase at a rate of 7% per year.
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One angle of a parallelogram measures 37°. What are the measures of the other three angles in the parallelogram?
Answers
The measures of the other two angles in the parallelogram are both 143 degrees.
what is a parallelogram?A parallelogram is a quadrilateral with two sides that are parallel to one another. A parallelogram has equal-length opposite sides and equal-length opposite angles. The internal angles that are extra to the transversal on the same side. A parallelogram's total interior angles add up to 360 degrees.
A parallelogram is formed by the junction of two parallel lines, and its opposite angles are equal.
Then, there are two 35 degree angles. Two further angles that are equivalent are noted: A parallelogram's angles add up to 360 degrees. Following that, x+x+37+37=360
2x=360-74
2x=286
x=143.
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A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces helmets transmit to wearers when subjected to a standard external force. The manufacturer desires the mean force transmitted by helmets to be 800 pounds (or less), well under the 1000-pound legal limit, and the standard deviation to be less than 40. A random sample of 31 helmets was tested and the sample mean and variance were found to be 825 pounds and 2350 pounds2, respectively. The manufacturer wants to know if the data provides sufficient evidence to indicate that the standard deviation is significantly less than 40.
Step 1 of 5: Calculate the test statistic for this problem. Round your answer to two decimal places.
Step 2 of 5: Determine the p-value for a lower one-sided alternative hypothesis (left-tail test). The alternative hypothesis for this problem is H1: Ï2 < 1600 lbs2.
Step 3 of 5: What is the rejection region at the 10% level of significance for the test on the variance for a left-tailed alternative hypothesis? The alternative hypothesis for this problem is H1: Ï2 < 1600 lbs2.
Step 4 of 5: State your conclusion using a significance level of 0.05. The alternative hypothesis for this problem is H1: Ï2 < 1600 lbs2.
Step 5 of 5: Calculate a 90% confidence interval for the variance of force on the helmets. Round your answers to four decimal places.
Answers
Step 1: The test statistic is 56.56.
Step 2: Using a chi-square distribution table with 30 degrees of freedom (n - 1), we find that the p-value is less than 0.0001.
Step 3: The rejection region for a left-tailed test with 30 degrees of freedom at the 10% level of significance is any test statistic less than 18.307.
Step 4: The test statistic of 56.56 is greater than the critical value of 18.307.
Step 5: The 90% confidence interval for the variance of force on the helmets is [1615.46, 4123.82]
What is Variance?In statistics, variance is a measure of the spread or dispersion of a set of data points. It is calculated as the average of the squared differences from the mean.
Step 1: To test whether the standard deviation is significantly less than 40, we can use a chi-square test with the null hypothesis H0: [tex]σ^{2}[/tex] ≥ 1600 lbs² and the alternative hypothesis H1: σ² < 1600 lb[tex]s^{2}[/tex]. The test statistic is:
chi-square = (n - 1) *[tex]s^{2}[/tex] / [tex]σ^{2}[/tex]
where n is the sample size, [tex]s^{2}[/tex] is the sample variance, and [tex]σ^{2}[/tex] is the population variance under the null hypothesis.
Substituting the given values, we have:
chi-square = (31 - 1) * 2350 / 1600 = 56.56
Rounding to two decimal places, the test statistic is 56.56.
Step 2: To determine the p-value for a left-tailed test, we need to find the area under the chi-square distribution to the left of the test statistic. Using a chi-square distribution table with 30 degrees of freedom (n - 1), we find that the p-value is less than 0.0001.
Step 3: The rejection region for a left-tailed test with 30 degrees of freedom at the 10% level of significance is any test statistic less than 18.307.
Step 4: Since the test statistic of 56.56 is greater than the critical value of 18.307, we reject the null hypothesis and conclude that there is sufficient evidence to indicate that the standard deviation is significantly less than 40 at the 5% level of significance.
Step 5: To calculate a 90% confidence interval for the variance of force on the helmets, we can use the formula:
[(n - 1) * [tex]s^{2}[/tex]/ chi-square upper, (n - 1) * [tex]s^{2}[/tex] / chi-square lower]
where chi-square upper and chi-square lower are the upper and lower critical values, respectively, from the chi-square distribution table for 30 degrees of freedom at the 5% level of significance. Substituting the given values, we have:
chi-square upper = 45.722
chi-square lower = 18.307
[(31 - 1) * 2350 / 45.722, (31 - 1) * 2350 / 18.307] = [1615.46, 4123.82]
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On a piece of paper, use a protractor and a ruler to construct two equilateral triangles: one with a side length of 4 inches and one with a side length of 5 inches.
Which statement is true about the two triangles?
Responses
The two triangles are the same size but not the same shape.
The two triangles are the same shape but not the same size.
It is impossible to construct equilateral triangles with these side lengths.
The two triangles are the same size and same shape.
Answers
The correct statement is "The two triangles are the same shape but not the same size."
How to determine Which statement is true about the two trianglesBoth triangles will have three congruent sides and three congruent angles, which means they will be equilateral and equiangular. However, since the side lengths are different, the triangles will be different in size. In other words, one triangle will be larger than the other.
To see why they cannot be the same size, imagine drawing a line from one vertex of each triangle to the opposite side. Since both triangles are equilateral, these lines will bisect the opposite side and form two congruent right triangles. The hypotenuse of the larger triangle (with side length 5) will be longer than the hypotenuse of the smaller triangle (with side length 4), which means the two triangles are not the same size.
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4. One of the players scored 13. 7 points per game with 4. 1 free throw attempts per game. How does this compare to what the model predicts for this player?
Answers
The model predicts that the player should score around 17.47 points per game based on their 4.1 free throw attempts per game. However, the player's observed score of 13.7 points per game suggests that they may be underperforming compared to what would be expected based on this relationship.
Let us assume that the model predicts a linear relationship between points per game and free throw attempts per game, we can calculate the predicted value of points per game for this player using the regression equation
points per game = slope * free throw attempts per game + intercept
From the given data, we know that the slope of the regression line is 2.6 and the intercept is 7.1. Plugging in the values for this player, we get:
points per game = 2.6 * 4.1 + 7.1 = 17.47
So the model predicts that this player should score approximately 17.47 points per game, which is higher than the observed value of 13.7 points per game. This suggests that this player may be underperforming compared to what would be expected based on their free throw attempts per game.
However, just one player and there may be other factors that could affect their performance beyond just free throw attempts per game.
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The interior angles formed by the sides of a regular octagon have measures that total 1080. What is the measure of each angel
Answers
Step-by-step explanation:
Welll.... there are EIGHT of them that total 1080
1080 / 8 = 135 degrees each
What is a measure of the differences of all observations from the mean, expressed as a single number
Answers
The measure of the differences of all observations from the mean, expressed as a single number is called the "standard deviation". It is a commonly used measure of the amount of variability or dispersion within a set of data.
The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences between each observation and the mean.
It is expressed in the same units as the data itself, and provides a way to understand how spread out the data is from the average or mean value.
A small standard deviation indicates that the data points tend to be close to the mean, while a large standard deviation indicates that the data points are more spread out.
The standard deviation can be used to compare the variability of different sets of data, and can also be used in statistical tests to determine if the difference between two sets of data is statistically significant.
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answer these questions please
Answers
The difference in the two figure's areas is 96 square units.
The height of the horse trough is 4 feet.
How to find the difference in the two figure's areas?No. 11
The area of Figure A is:
A = l * w = 12 * 8 = 96 square units
The area of Figure B is:
B = l * w = 16 * 12 = 192 square units
The difference in the two figure's areas is:
B - A = 192 - 96 = 96 square units
Therefore, the difference in the two figure's areas is 96 square units.
No. 12
We are given that the base area is 24 square feet, and the volume is 96 cubic feet.
Volume = base area * height
96 = 24 * height
height = 96/24
height = 4 feet
Therefore, the height of the horse trough is 4 feet.
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Answer:...............
Step-by-step explanation:
...................
Please help me I've been stumped on this problem
Answers
a. Angle 1 and angle 2 are equal because they are alternate to each other
b. since angle 1 and angle 2 are equal, arc AC and BD will be equal too
c. Parallel lines will intercept congruent arcs.
What is angle formed by parallel lines?When any two parallel lines are cut by a transversal, there are various pairs of angles that are formed.
These angles are corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.
Therefore , angle 1 and 2are alternate to each other, this means that they are equal.
Since the two angles are equal , the corresponding arc formed by the two angles are also equal.
This means parallel lines will intercept congruent arcs
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Students mesured different amounts of water into their beakers for an experiment. If the total amount of water is redistributed equally, how much water will be in the beaker?
1/4 x 6 + 3/4 x 2 + 1/2 + 1 1/4 + 1 1/2 + 1 3/4
Answers
However, each beaker would have the following if there were, say, five beakers: 2.5 units of water are equal to 8.5/5.
what is volume ?Typically, it is expressed in geometric units, which including cubic metres (m3), cubic centimetres (cm3), or cubic feet (ft3), depending on the length unit being used. A formula that is based on an object's shape can be used to determine its volume. The volume of such a rectangular prism, for instance, can be determined by utilizing the formula V = lwh, where l stands for length, w for width, and h for height. A cylinder's volume can be calculated using the formula V = r2h, where r denotes the circle of the base and h the height.
given
We can simply sum the numbers supplied to determine the total volume of water in all the beakers:
1/4 x 6 + 3/4 x 2 + 1/2 + 1 1/4 + 1 1/2 + 1 3/4
= 1.5 + 1.5 + 0.5 + 1.25 + 1.5 + 1.75 (converting mixed values to improper fractions)
= 8.5
8.5 units of water are therefore present in all of the beakers.
Each beaker will have 8.5 divided by the number of beakers if this water is distributed equally among them.
We are unable to provide a precise response since we are unsure of the number of beakers.
However, each beaker would have the following if there were, say, five beakers: 2.5 units of water are equal to 8.5/5.
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For what value of x must the quadrilateral be a parallelogram?
X=
(3x+28
work:
Answers
The value of x in the parallelogram is 9.3.
How to find the angle of a parallelogram?A parallelogram is a quadrilateral that has opposite sides equal to each other. Opposite sides of a parallelogram is also parallel to each other.
The opposite angle of a parallelogram are congruent while consecutive angles of a parallelogram are supplementary.
Therefore,
5x = 2x + 28
5x - 2x = 28
3x = 28
divide both sides of the equation by 3
x = 28 / 3
x = 9.333333
Therefore,
x = 9.3
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Dominique throws a softball from the outfield. After 1 second, the ball is 10 feet high. After 4 seconds, the ball reaches its maximum height of 46 feet. After 7 seconds, it returns to a height of 10 feet. What is the equation of the quadratic function that models the height of the ball h(t) at time t? a. h(t) = 4(t 4)2 + 46 b. h(t) = −4(t − 4)2 + 46 c. h(t) = 2(t + 3)2 + 46 d. h(t) = −2(t − 3)2 + 46
Answers
The equation of the quadratic function that models the height of the ball h(t) at time t is h(t) = -2(t-3)^2 + 46. So, correct option is D.
The height of the ball at time t can be modeled by a quadratic function in the form h(t) = at^2 + bt + c, where a, b, and c are constants that we need to find.
We know that after 1 second, the height of the ball is 10 feet. This gives us the point (1, 10), which we can substitute into the quadratic equation to get:
10 = a(1)^2 + b(1) + c
10 = a + b + c --------------- (1)
We also know that after 4 seconds, the ball reaches its maximum height of 46 feet. This gives us the point (4, 46), which we can substitute into the quadratic equation to get:
46 = a(4)^2 + b(4) + c
46 = 16a + 4b + c --------------- (2)
Finally, we know that after 7 seconds, the height of the ball is back to 10 feet. This gives us the point (7, 10), which we can substitute into the quadratic equation to get:
10 = a(7)^2 + b(7) + c
10 = 49a + 7b + c --------------- (3)
Now we have a system of three equations (equations 1, 2, and 3) with three unknowns (a, b, and c) that we can solve. Using algebraic manipulation or substitution, we can solve for a, b, and c to get:
a = -2, b = 12, and c = 28
Therefore, the equation of the quadratic function that models the height of the ball h(t) at time t is:
h(t) = -2t^2 + 12t + 28
The answer is not listed among the choices, but if we simplify the equation we can see that it matches with option D:
h(t) = -2(t-3)^2 + 46
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4) Hansen attaches his A+ test to the refrigerator with a circular magnet. Out of curiosity,
he measures the magnet and calculates that it has a diameter of 2 inches. What is the
magnet's area?
() Use 3.14 for л. If necessary, round your answer to the nearest hundredth.
square inches
Submit
Answers
The magnet's area is approximately 3.14 square inches.
What is circle?
Every point in a horizontal surface that is a certain distance above another point forms a circle (center).
The area of a circle is given by the formula:
[tex]A = \pi r^2[/tex]
where π is approximately equal to 3.14 and r is the radius of the circle. Since the diameter of the magnet is given as 2 inches, the radius is half of that, or 1 inch.
Plugging this value into the formula, we get:
[tex]A = 3.14 * 1^2[/tex]
A = 3.14 square inches
Therefore, the magnet's area is approximately 3.14 square inches.
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A rectangular prism has a length of 10 inches, a width of 4 inches, and a height of 3.7 inches. What is the volume of this rectangular prism?
Answers
Answer:
I believe it's 148.
Step-by-step explanation:
You must do L x W x H to find the volume of a rectangular prism or cube.
The set of values for x that satisfies a quadratic inequality is x < -0.5 or x > 1.5
Write down a possible quadratic inequality. Can u show me working it how to do this please. Thanks
Answers
Answer:
To write a possible quadratic inequality, we first need to determine which quadratic function has roots at x = -0.5 and x = 1.5.
We know that the solution to the quadratic inequality is x < -0.5 or x > 1.5, which means that the parabola associated with our quadratic function should not intersect the x-axis between x = -0.5 and x = 1.5.
One quadratic function with roots at x = -0.5 and x = 1.5 is:
(x + 0.5)(x - 1.5) ≤ 0
To see why this is the case, we can use a graphing calculator to graph the quadratic function y = (x + 0.5)(x - 1.5) and observe that the function is negative (i.e., has a y-value less than zero) when x is less than -0.5 or greater than 1.5.
Alternatively, we can use the fact that the product of two factors is less than or equal to zero if and only if one factor is positive and the other is negative.
Since (x + 0.5) is positive for x > -0.5 and negative for x < -0.5, and (x - 1.5) is positive for x > 1.5 and negative for x < 1.5, the inequality (x + 0.5)(x - 1.5) ≤ 0 is true for x < -0.5 or x > 1.5, but false for -0.5 < x < 1.5.
Therefore, a possible quadratic inequality that satisfies the given set of values for x is:
(x + 0.5)(x - 1.5) ≤ 0
obability and Sampling: End-of-Unit
Assessment (B)
Illustrative
iM
İM Mathema
Do not use a calculator. A standard number cube has the numbers 1 through 6 on its
faces.
1. Elena would like to know the average speed that people drive on her street. She
tracks the speed of 30 random cars that drive through with a speedometer. The
mean of Elena's sample is 30 miles per hour, and the MAD (mean absolute deviation)
is 3.
Select all the true statements.
A. Elena would be more likely to get an accurate estimate of the mean speed of
the population by sampling 60 cars instead of sampling 30 cars.
B. The median speed of the sample must be between 25 and 35 miles per hour.
C. Another random sample of 30 cars is likely to have a mean between 24 and 36
miles per hour.
D. The mean speed of these 30 cars is likely to be the same as the mean speed of a
second sample of 30 cars.
E. The mean speed of these random 30 cars is likely to be the same as the mean of
all cars that drive in a residential area.
Answers
The true statements are:
A. Elena would be more likely to get an accurate estimate of the mean speed of the population by sampling 60 cars instead of sampling 30 cars.
C. Another random sample of 30 cars is likely to have a mean between 24 and 36 miles per hour.
What is Mean Absolute Deviation (MAD)?Mean Absolute Deviation (MAD) is a measure of variability in a set of numerical data. It is calculated by finding the average absolute difference between each data point and the mean of the dataset.
Elena would be more likely to get an accurate estimate of the mean speed of the population by sampling 60 cars instead of sampling 30 cars. This statement is true. The larger the sample size, the more accurate the estimate of the population mean.Another random sample of 30 cars is likely to have a mean between 24 and 36 miles per hour. This statement is true. The mean of a random sample of 30 cars is likely to be within one MAD of the population mean.Learn about mean here https://brainly.com/question/1136789
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Solve for a. -3.7a 1.7 = -6.07
Answers
Answer:
a = 2.1
Step-by-step explanation:
-3.7a + 1.7 = -6.07
-3.7a = -7.77
a = 2.1
Max spent 3/5 of his money in a shop and 1/4 of the remainder in another shop. (a) What fraction of his money was left ?
Answers
3/10 of Max's money was left after he spent 3/5 of his money in the first shop and 1/4 of the remainder in the second shop.
Let's assume Max had $100 to start with (we can use any amount for this problem, but $100 is a convenient round number).
If Max spent 3/5 of his money in the first shop, he spent:
3/5 x $100 = $60
This means he had $40 remaining. If he then spent 1/4 of this remaining amount in the second shop, he spent:
1/4 x $40 = $10
So Max has spent a total of $60 + $10 = $70. Therefore, the amount of money Max has left is:
$100 - $70 = $30
So Max has $30 left out of his original $100. To express this as a fraction, we can write:
$30 / $100 = 3/10
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Solve the simultaneous equations:
y=x² + 3x - 18
x + 2y + 14 = 0
Answers
From the second equation, we have:
x + 2y + 14 = 0
Solving for x, we get:
x = -2y - 14
Substituting this expression into the first equation, we get:
y = (-2y - 14)^2 + 3(-2y - 14) - 18
Expanding and simplifying, we have:
y = 4y^2 + 56y + 196
Bringing all terms to one side, we have:
4y^2 + 55y + 196 = 0
We can solve for y using the quadratic formula:
y = (-55 ± sqrt(55^2 - 4(4)(196))) / (2(4))
y = (-55 ± sqrt(1081)) / 8
y ≈ -4.31 or y ≈ -11.44
Substituting each value of y into the expression we found for x earlier, we have:
x = -2(-4.31) - 14 ≈ 6.62
x = -2(-11.44) - 14 ≈ 18.89
Therefore, the solutions to the system of equations are approximately (6.62, -4.31) and (18.89, -11.44).
44 is less than or equal to x
Answers
Answer:
44 <= x
Step-by-step explanation:
Find the perimeter of the figure below.
Figure not drawn to scale
Answers
According to the given information, the perimeter of the given right-angle triangle is 30ft.
What is Pythagoras' Theorem?Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
According to the given information:We can use the Pythagorean theorem to find the length of the missing side of the right triangle, BC:
[tex]BC^2 = AB^2 - AC^2\\BC^2 = 13^2 - 12^2\\BC^2 = 169 - 144\\BC^2 = 25[/tex]
BC = 5
Now that we know all three sides of the triangle, we can find the perimeter by adding them together:
Perimeter = AB + AC + BC
Perimeter = 13 + 12 + 5
Perimeter = 30
Therefore, according to the given information, the perimeter of the given right-angle triangle is 30ft.
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