To determine whether the errors from the linear regression model are from a normal distribution, examine the normal quantile plot of the residuals.
Calculating the regression equation is the first step in a straightforward linear regression model. The link between the explanatory variable (x) and the response variable is modelled using this equation (y). A linear function of the explanatory variable, an intercept term, and an error term make up the regression equation. The errors or residuals (e), which indicate the difference between the observed and expected values of the response variable, are calculated as the following step. To evaluate the regression model's accuracy, the residuals are crucial. The residuals are then plotted using a normal quantile to see whether it is acceptable to believe that the errors are derived from a normal distribution. Because linear regression models presume that the errors are regularly distributed, this is significant. The residuals' normal quantile plot shows the distribution of the mistakes graphically, making it simpler to determine whether the errors follow a normal distribution. The linear regression model might not be the optimal one to employ if the errors do not follow a normal distribution.
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Factor completely.
28x³y7z² - 7xy4
Answer: 28xy(7x^2-1)
Step-by-step explanation:
28x^3yx7z^2-7x4xy
196x^3-28xy
In the U.S., shoe sizes are defined differently for men and women, but in Europe, both sexes use the same shoe size scale. The accompanying histogram shows the European shoe sizes of 269 male and female college students, converted from their reported U.S. shoe sizes. What might be the problem with either the mean or the median as a measure of center?
To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them.
The problem with either the mean or the median as a measure of center in this case is that the data is not separated by gender, and the shoe size distributions for men and women are likely to be different. Therefore, computing the mean or median shoe size across all students may not accurately represent the typical shoe size for men or women separately.
For example, if the men in the sample have, on average, larger shoe sizes than the women, then the mean shoe size across all students may be biased towards the larger sizes, even though the majority of the students are women. On the other hand, if there are a few male students with very large shoe sizes, then the median shoe size across all students may be biased towards the larger sizes as well, even if most of the students are women with smaller shoe sizes.
To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them. Alternatively, a better measure of center might be to report the mode, which represents the most common shoe size in the data.
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after conducting a one-sample z test, you arrived at a value of 0.2 for the z value. what is your conclusion?
The z value of 0.2 indicates the standardized difference between the sample mean and population mean
The z value is a standardized score that tells us how many standard deviations a sample mean is from the population mean. In other words, it helps us determine the likelihood that the difference between the two means is due to chance or some other factor.
Typically, we use a significance level (often denoted by alpha) to determine if the z value is significant or not. If the z value falls within the critical values for the chosen significance level, we reject the null hypothesis and conclude that there is a significant difference between the two means. If the z value falls outside the critical values, we fail to reject the null hypothesis and conclude that there is not a significant difference.
In your case, with a z value of 0.2, it is important to consider what significance level was used in the test. If the chosen significance level was 0.05. Since 0.2 falls within this range, we would fail to reject the null hypothesis and conclude that there is not a significant difference between the sample mean and population mean.
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morgan is analyzing her data and notices that the value of her mean is quite a bit smaller than the value of her median. she asks for your help in interpreting these results. what would you tell her?
We can interpret from the results that the distribution of data might be negatively skewed.
In the given question it is mentioned that while Morgan was analyzing her data, she notices that the value of her mean is quite a bit smaller than the value of her median.
As we know that, in statistics, when the mean is smaller than the median and mode, it indicates a negatively skewed distribution.
A negatively skewed distribution or left skewed distribution is a type of distribution in which more values are concentrated on the right side of the distribution graph while the left side of the graph is longer.
Hence, we can interpret from these information that the distribution of data of Morgan are negatively skewed.
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Leslie and Ben are designing a neighborhood. Drawing their designs out on a grid, they determined that the lot for the community mailboxes would be centered at (0,0). They created the first road to pass through lots centered at (3,1) and at (9,3). They want to make another road that intersects the first road at a 90-degree angle, and they want it to intersect the center of the lot at (3,1). Determine the equation for this second road.
The equation of the second road is y = -3x + 10
The location of the mail box = (0, 0)
The first road passes through the points (3, 1) and (9,3)
The slope of the line is the change in y coordinate with respect to the change in x coordinate
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
m = 3-1 / 9-3
m = 2/6
m = 1/3
The next road is 90 degrees to the first road
Then the slope of the second line will be
m1 = -1/m
= -1/(1/3)
= -3
The second road passing through the point (3, 1)
The equation of line
y = mx + b
Substitute the given values in the equation
1 = -3 × 3 + b
1 = -9 + b
b = 1 +9
b = 10
Therefore, the equation will be y = -3x + 10
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the same type of machines are used in two factories, a and b. with statistical data on 1000 machines operated in factory a, the reliability of the machine is estimated to be 0.99. statistics from factory b show that 5 machines failed out of 600 machines operated in factory b. based on the statistics from both factories, what is the reliability of the machine?
The reliability of the machine can be estimated to be 0.9833, calculated as (1000 - 1) / 1000 + (600 - 5) / 600. we can take the average of the two reliability estimates, giving us a reliability of 0.9833.
The reliability of a machine can be estimated by taking the ratio of machines that did not fail to the total number of machines operated in a given period. In this case, the reliability of the machine from Factory A can be estimated to be 0.99 (1000 - 1 / 1000). The reliability of the machine from Factory B can be estimated to be 0.9833 (600 - 5 / 600). To estimate the reliability of the machine based on both factories, we can take the average of the two reliability estimates, giving us a reliability of 0.9833.
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Solve the system for x and y:
Answer:
x = 6, y = -3
Step-by-step explanation:
[tex]\frac{x}{y + 1} = -3\\\frac{y}{x-3} = -1[/tex]
x = -3(y+1) - Isolate for x or y (I chose x)
x = -3y -3
Plug in x into y
[tex]\frac{y}{x-3} = -1\\\frac{y}{(-3y -3) - 3} = -1\\\frac{y}{-3y -6} = -1\\y = -1(-3y - 6)\\y = 3y + 6\\-2y = 6\\y = -3[/tex]
Plug y back into equation
[tex]\frac{x}{y+ 1} = -3\\\frac{x}{(-3)+ 1} = -3\\\frac{x}{-2} = -3\\x = -3(-2)\\x = 6[/tex]
Substitute -4 for a and 16 for b in the given equations. Which statements are true?
Select all that apply.
-The equation 2 (2x - 11) + 6 = ax + b has no solution.
-The equation 4x - 8 (x - 2) = ax + b has infinitely many solutions.
-The equation -5 (4x-6) 14 = ax + b has exactly one solution.
-The equation 10+ x + 2 - 6x = ax + b has no solution.
-The equation 9x +3 - 13x6 = ax + b has infinitely many solutions.
Answer:
After substituting -4 for "a" and 16 for "b", the equation can be simplified and solved.
-The equation 2 (2x - 11) + 6 = -4x + 16
Expanding the equation on the left-hand side, we get:
4x - 22 + 6 = -4x + 16
Simplifying, we get:
10 = -10x + 32
Subtracting 32 from both sides, we get:
-22 = -10x
Dividing both sides by -10, we get:
x = 2.2
This means that there is exactly one solution, which is x = 2.2. So, statement 3 is true.
-The equation 4x - 8 (x - 2) = -4x + 16
Expanding the equation on the left-hand side, we get:
4x - 8x + 16 = -4x + 16
Combining like terms, we get:
-4x + 16 = -4x + 16
This equation is true for all values of x, so there are infinitely many solutions. So, statement 2 is true.
-The equation 10 + x + 2 - 6x = -4x + 16
Expanding the equation on the left-hand side, we get:
10 + x + 2 - 6x = -4x + 16
Combining like terms, we get:
-5x + 12 = -4x + 16
Adding 4x to both sides, we get:
-x + 12 = 16
Adding x to both sides, we get:
12 = 16
This equation is not true for any values of x, so there are no solutions. So, statement 1 is true.
-The equation 9x +3 - 13x + 6 = -4x + 16
Expanding the equation on the left-hand side, we get:
9x + 3 - 13x + 6 = -4x + 16
Combining like terms, we get:
-4x + 9 = -4x + 16
Adding 4x to both sides, we get:
9 = 12
This equation is not true for any values of x, so there are no solutions. So, statement 1 is true.
Therefore, the true statements are:
-The equation 2 (2x - 11) + 6 = ax + b has no solution.
-The equation 4x - 8 (x - 2) = ax + b has infinitely many solutions.
-The equation -5 (4x-6) 14 = ax + b has exactly one solution.
A right rectangular prism measures 9in. x 4in. x 6in. What would be the dimensions of a cube with the same volume as the rectangular prism?
The rectangular prism's volume can be represented by a cube whose dimensions are 6 inches.
A right rectangular prism is what?
The right rectangular prism has two simultaneous end panels that are orthogonal to each of the bases, two adjacent lateral faces, and four rectangle-shaped lateral faces. The faces of an oblique prism, a non-right oblong prism, are parallelograms. Alternative name for a right rectangular prism is a cuboid.
To begin, determine the rectangular prism's volume. To calculate this, multiply the length by the breadth by the height, which equals 9 ×4 ×6. 216 cubic inches make up this.
The side length of a cube with a 216 cubic inch capacity must now be determined. The recipe for A cube's volume is equal to its side length raised to the third power (cubed). You are now attempting to determine where s³= 216 This can also be expressed as s = ∛216.
The only thing left to do is to discover the number that, when multiplied by itself three times, equals 216, or its cubic root. It is quite easy to determine that 6× 6× 6, sometimes known as 6 cubed, equals 216. This indicates that the cube's side length is 6 inches.
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Jake buys a membership to the YMCA pool. He pays a membership fee of $36 and $2 each visit. Jake has another option to pay $8 each visit and no membership fee. After how many visits will the two plans be equal in cost?
please help will give brainliest
Answer:
First option: 37°, 11°, 132°
Step-by-step explanation:
The sum of the three interior angles of a triangle must add up to 180°
Only the first option 37°, 11° and 132° add up to 180°
37 + 11 + 132 = 48 + 132 = 180°
You don't need to add up all the other sets of angles completely. Just look at the units place
Option 2, units sum = 4 + 6 + 1 =11; does not end in a 0, ends in 1
Option 3: units sum = 1 + 0 + 2; does not end in a 0, ends in 3
Option 4: units sum = 0 + 1 + 5 ends in a 6
The function,y=−16x2+32x+48, represents the height, in feet, of a firework x seconds after it is launched.
After how many seconds does the firework hit the ground?
Enter your answer in the blank.
x=□seconds
The number of seconds does the firework hit the ground is 3 seconds
How to determine the valueFrom the information given, we have the quadratic function;
y = -16x² + 32x + 48
To determine the value of x , let's reduce the expression, we get;
-2x² + 4x + 6
Now, let's factorize the terms
Multiply the coefficient by the constant and find the pair factors
-2x² + 6x - 2x + 6
Factorize in pairs, we get;
-2x(x -3) - 2(x -3)
Then, we have the expressions
-2x - 2 = 0
solve for x
x = -1
x - 3 = 0
x = 3
Hence, the value is 3 seconds
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Answer:
3
Step-by-step explanation:
i took the test
Write an expression to display a loss of 42 yards on the football field
Answer:
Step-by-step explanation:
An expression to display a loss of 42 yards on the football field would be: -42 yards.
The negative sign in front of the number 42 indicates a loss or a decrease in the yards, which represents a loss of 42 yards on the football field.
. A rectangle’s length is twice its width. Its perimeter is 156 meters. What is the rectangle’s length?
Answer:
Step-by-step explanation:
Perimeter is equal to 2 times length and 2 times the width.
This problem says the length is twice the width.
Let's use 2w for the length:
Here's the equation:
2L + 2W = 156
Substitute 2W for the length,
2(2W) + 2W = 156
4W + 2W = 156
6W = 156
6W/6 = 156/6
w = 26
so length is 2 times 26 = 56 Length = 56 m
9. When Maggie retires at age 70, she will deposit her savings into an annuity account which pays 6.2%
p.a. interest compounded monthly. She wants to withdraw $4,500 per month from the annuity account
until she's 90.
a. Calculate the amount Maggie will need in savings when she retires.
b. How much could her payment be if she had 1.2 million dollars in her account but her interest
dropped to 5.5%
The amount Maggie will need in savings when she retires is $1,204,519.62 and her payment be if she had 1.2 million is $4522.40
What is annuity?In investment, an annuity is a series of payments made at equal intervals
a) To calculate the amount Maggie will need in savings when she retires
Pm= {1 + r/j)pm - 1
Pm = (1+6.2%/12)4500 - 1
Pm (1+0.0052)4500 -1
Pm= (1.0052)4499
Simplifying to have
Pm = $4522.40
b) To calculate much could her payment be if she had 1.2 million dollars in her account but her interest dropped to 5.5
Pm= {1 + r/j)pm - 1 +d
Where d is the savings
Pm = (1+5.5%/12)4500 - 1 + 1.2m
Pm= (1+5.5%/12) 4499 + 1.2m
PM = (1.0046)4499 + 1,200,000
Pm = 1,204,519.62
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Given sin(-t) = 2/3, find csc (t).
Answer:
csc(t) = -3/2
Step-by-step explanation:
Given sin(-t) = 2/3, we can find the value of csc(t) as follows:
sin(-t) = 2/3
sin(t) = -2/3 (since the sine function is an odd function)
Since csc(t) = 1/sin(t), we have:
csc(t) = 1/sin(t) = 1/(-2/3) = -3/2
Answer:
[tex]\displaystyle \csc(t)=-\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]\displaystyle \sin(-t)=\frac{2}{3}\\\\\sin(t)=-\frac{2}{3}\\ \\\frac{1}{\sin(t)}=\frac{1}{-\frac{2}{3}}\\\\\\\csc(t)=-\frac{3}{2}[/tex]
The second step can be done because sin(-t) is an odd function.
Find the mode of each group of numbers:
62,63,67,66,66,63,62,68,69,65,67,63,64,68,65,62,69,63,61,60,63,65
The mode of the data set given is 63.
What is the Mode of a dataset?Statistics uses the terms mean, median, and mode to describe central tendency. They each provide information about what value in a data set is conventional or representative of the data set in their own unique ways.
The number that appears the most frequently in a piece of data is the mode. Count the occurrences of each number in the data collection. The figure with the largest total is the mode. More than one mode is acceptable. Additionally, there is no mode if all numbers appear exactly once.
Given that:
62,63,67,66,66,63,62,68,69,65,67,63,64,
By rearrangement, we have:
62, 62, 63, 63, 63, 64, 65, 66, 66, 67, 67, 68, 69
Therefore, the highest occurring number(mode) is 63.
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What is the value of x?
What is the value of y?
What is the value of z?
Answer:
X=63
Y=63
Z=72
Step-by-step explanation:
The value for angle X
X + 85 + 32 = 180°
X + 117 = 180°
X = 180° - 117°
X = 63°
Since <x and <y are vertically opposite
<X and <Y = 63°
Remember vertically opposite are the same.
The value for angle z
Z + 45 + Y = 180°
Z + 45 + 63 = 180°
Z° + 108° = 180° - 108°
Z = 72°
Therefore
Value for X = 63°
Value for Y = 63°
Value for Z = 72°
How many digits do you need to number all 178 buildings on a street?
You need 4 digits to number all 178 buildings on a street.
Explain Digits.In the decimal number system, digits are the symbols used to represent numbers. The 10 digits of the decimal numeral system are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. By utilizing them in various combinations and places, these digits are used to represent all possible decimal integers. A digit's value is also affected by its position in a number according to the place value system. For instance, the digits 1 and 2 in the number 123 each stand for one hundred, twenty, and three respectively. Digits are the fundamental components of numbers and are frequently used in daily life for calculations, measurement, and counting.
To find the number of digits in a number, you can take the logarithm of the number with base 10 and add 1. So, using the logarithm function, you can calculate:
log10(178) + 1 = 2.25 + 1 = 3.25
Therefore, you need 4 digits to number all 178 buildings on a street.
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Solve the system of linear equations by graphing.
y=-1/2x+2
y=1/2x-1
=negative 3 comma one half
=one half comma 3
=one half comma negative 3
=3 comma one half
From the graphs below, we can see that the solution of the given system of linear equations is (3,0.5).
What is meant by a system of linear equations?
A collection of one or more linear equations containing the same variables is known as a system of linear equations. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation is invariably a straight line equation. A group of diverse straight line equations make up a system of linear equations.
We are given two linear equations:
y = -1/2 x + 2
y = 1/2x - 1
As mentioned earlier, these are equations of two straight lines with slopes -1/2 and 1/2.
Now the solution of the equation is the intersecting point of these straight lines. We graph these equations and found the intersecting point.
Therefore, from the graphs below, the solution of the given system of linear equations is (3,0.5).
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3x^2-9x+2 in standard form
The standard form of 3x² - 9x + 2 is 3x² - 9x + 2.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
Given:
A quadratic function,
3x² - 9x + 2.
The standard form of the quadratic function is
ax² + bx + c.
The standard form of 3x² - 9x + 2 is 3x² - 9x + 2.
Therefore, 3x² - 9x + 2.
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Question 9 Multiple Choice Worth 2 points) (09.06 MC) Sara's kite flew 48 meters in the air. Tayjen's kite flew 5,860 centimeters in the air. How m 00.16 meters 016 meters O106 centimeters 1,060 centimeters
The difference in height between Sarah and Tayjen kite is 1060 cm (10.6 m)
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
1 m = 100 cm
Sara's kite flew 48 meters in the air. Hence:
Height of Sarah kite = 48 m = 48 m * 100 cm per m = 4800 cm
Tayjen's kite flew 5,860 centimeters in the air. Therefore:
Difference in height = 5860 - 4800 = 1060 cm = 1060 cm * 1 m per 100 cm = 10.6 m
The difference in height is 1060 cm (10.6 m)
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Mr. Taylor has been looking at buying a house, and he is even thinking about having a pool put into his backyard!
Your Task: Design a pool that will fit inside Mr. Taylor's backyard and find out how much water it will take to fill the pool.
Rules!
1. Your pool design must include at least two different solids that are connected
2. Your pool must fit inside Mr. Taylor's backyard and leave at least 3 feet of space on each side of it for construction purposes
3. Your pool must be accessible and realistic
*Look at the photo for the blueprint of the house.
*You must clearly describe the pool design. Write this in a word-written response
To design a pool that would fit inside Mr. Taylor's backyard, you would need to know the dimensions of the available space.
You would also need to take into account any landscaping, slopes, and other features of the backyard that could impact the design and construction of the pool.
Once you have the necessary information about the backyard, you can start designing a pool that would be accessible and realistic. Here are some tips and guidelines for designing a pool.
Choose a shape and size that fits the available space and is functional. Rectangular or oval shapes are typically the most common and practical, but other shapes can be used as well.
Consider the depth of the pool. For safety reasons, the depth should be at least 4 feet at the shallow end and 8 feet at the deep end. You may also want to consider adding a gradual slope in the pool to make it easier for people to enter and exit.
Choose the material for the pool. Concrete, fiberglass, and vinyl are common materials used for pools. Each material has its own advantages and disadvantages, so research the options and choose the one that is best for your design and budget.
Consider adding features such as a diving board, slide, or waterfall to make the pool more enjoyable and attractive.
Calculate the amount of water it will take to fill the pool. This will depend on the size and depth of the pool. To get an estimate, you can use online pool volume calculators or consult with a pool contractor.
Once you have a design for the pool and know how much water it will take to fill, you can determine if it is feasible and within Mr. Taylor's budget.
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3. There are two candy machines in a restaurant. One is filled with 200 gumballs and the other
is filled with 900 chocolate candies. The gumballs are dispensed 1 at a time and the chocolate
candies are dispensed 8 candies at a time. How many dispenses from each machine will make
the number of candies in the machines equal?
Answer:
100 dispenses
Step-by-step explanation:
To check the answer:
Gumballs: 200 - (1*100) = 100
Explanation: 200 gumballs - (1 gumball * 100 dispenses) = 100 gumballs left.
Chocolate Candies: 900 - (8*100) = 100
Explanation: 900 candies - (8 candies * 100 dispenses) = 100 candies left.
Answer:
100
Step-by-step explanation:
Given a candy machine with 200 gumballs dispensed 1 at a time, and another with 900 chocolates dispensed 8 at a time, you want to know how many dispenses from each will result in equal counts left in the machines.
GumballsThe number of remaining gumballs after d dispenses is ...
g = 200 -d
ChocolatesThe number of remaining chocolates after d dispenses is ...
c = 900 -8d
Equal numbersThe number remaining in each machine will be equal when ...
g = c
200 -d = 900 -8d . . . . . substitute the above expressions
7d = 700 . . . . . . . . . . add 8d -200
d = 100 . . . . . . . . . divide by 7
100 dispenses from each machine will make the number of candies in the machines equal.
In the U.S., shoe sizes are defined differently for men and women, but in Europe, both genders use the same shoe size scale. The accompanying histograrn shows the European shoe sizes of 269 male and female college students, converted from their reported U.S. shoe sizes. a) Describe the shape. b) How many modes does the histogram have? What might explain that? Click the icon to view the histogram of shoe sizes. a) The distribution is roughly symmetric and bimodal. b) Choose the correct answer below.
a) The distribution is roughly symmetric and bimodal. b) The histogram has two modes, which may be due to the different shoe size scales used for men and women in the U.S. but not in Europe.
The histogram of European shoe sizes of 269 male and female college students converted from their reported US shoe sizes is not visible based on the information provided, but the questions are clear.
a) The shape of the distribution is not visible, but it is mentioned that it is "roughly symmetric and bimodal".
b) There are two modes in the histogram. This could be because shoe sizes in the United States are defined differently for men and women, but not in Europe. As a result, the histogram of the distribution of European shoe sizes for both men and women may show two distinct peaks.
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A regulation basketball has a DIAMETER of about 9.2 inches.
What is the volume to the nearest tenths?
Rounding to the nearest tenth, the volume of the basketball is: V ≈ 381.7 cubic inches ≈ 381.8 cubic inches (rounded to the nearest tenth)
What is volume?
Volume is a measure of the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, or cubic inches.
For solid objects, volume refers to the amount of space the object occupies in three-dimensional space.
The diameter of a basketball is 9.2 inches, which means the radius is half of that, or:
r = 9.2 / 2 = 4.6 inches
The formula for the volume of a sphere is:
V = (4/3)πr³
Substituting the radius into the formula, we get:
V = (4/3)π(4.6)³
V ≈ 381.7 cubic inches
Therefore, Rounding to the nearest tenth, the volume of the basketball is: V ≈ 381.7 cubic inches ≈ 381.8 cubic inches (rounded to the nearest tenth)
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At the art store, Maria bought a poster board for $0.65, glitter for $3.29, and glue for $1.99. She told Carl that she paid $5.00 for everything. True or False?
Answer:
False
If we wanted to solve this equation, we can use this expression:
0.65 + 3.29 + 1.99 = 5.93Maria must have spent $5.93, making her statement false.
the length of the altitude drawn to the hypotenuse of right triangle t is 8. if the length of the hypotenuse of t is 20, what is the length of the shortest leg of t ?
The length of the shortest leg of T is approximately 18.33 units. We are given that the length of the altitude drawn to the hypotenuse (h) is 8, and the length of the hypotenuse (c) is 20.
We can start by using the area formula for a triangle:
Area = 1/2 * base * height
In this case, the base is the length of the hypotenuse (c), and the height is the length of the altitude (h). So we have:
Area = 1/2 * c * h
Substituting the given values, we get:
Area = 1/2 * 20 * 8 = 80
We also know that T is a right triangle, so we can use the Pythagorean theorem:
a^2 + b^2 = c^2
Substituting the given values, we get:
a^2 + b^2 = 20^2
a^2 + b^2 = 400
We can now solve for b by substituting a in terms of h (using the formula for the area of a triangle) and simplifying:
Area = 1/2 * base * height
80 = 1/2 * 20 * h
h = 8
a = (2 * Area) / c
a = (2 * 80) / 20
a = 8
Substituting a and h in the Pythagorean theorem equation, we get:
8^2 + b^2 = 20^2
64 + b^2 = 400
b^2 = 336
b = sqrt(336)
b ≈ 18.33
Therefore, the length of the shortest leg of T is approximately 18.33 units.
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what is the HCF of the expressions 3(x-y)^2 and 12x^2(x^2+y^2+2xy)
By factorizing the polynomials, the HCF of the expressions 3(x-y)^2 and 12x^2(x^2+y^2+2xy) is 3.
HCF or Highest Common Factor is the greatest number which divides each of the two or more numbers. HCF is also called the Greatest Common Measure (GCM) and Greatest Common Divisor(GCD).
To obtain the HCF of algebraic expression, take the common of all the prime factors of two polynomials.
We first factorize the given algebraic expressions:
3(x - y)^2 = 3 × (x - y) × (x - y)
12x^2(x^2+y^2+2xy) = 12x^2(x + y)^2
12x^2(x + y)^2 = 2 × 2 × 3 × x × x × (x + y) × (x + y)
so, the highest common factor between the both expressions is 3.
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round 224.91 to the nearest whole number
