Answer:
The farmer uses 221 pipes in total: 124 plastic pipes and 97 metal pipes.
Answer:
To find out how many pipes the farmer used in total, we simply add the number of plastic pipes to the number of metal pipes:
Total pipes = Plastic pipes + Metal pipes
Total pipes = 124 + 97
Total pipes = 221
Therefore, the farmer used a total of 221 pipes for the irrigation system.
Estimate the maximum fuel cell area that can be operated at 1 A/cmunder the condition from Example 5.2.Assume a stoichiometric number of 2.Assume that the fuel cell is made of a single straight flow channel. Discuss why channel flow in fuel cells is almost always considered to be laminar
The maximum fuel cell area that can be operated at 1 A/cm^2 under the given conditions can be estimated using the equation A = I/(2FJ), where A is the maximum cell area, I is the current density (1 A/cm^2), F is the Faraday constant, and J is the current density per unit area. Assuming a stoichiometric number of 2 and substituting the given values, we get A = 0.029 m^2 or 290 cm^2.
Channel flow in fuel cells is almost always considered to be laminar because turbulent flow can cause mixing of the reactants and products, reducing the efficiency of the fuel cell. Laminar flow allows for efficient mass transport of the reactants and products to and from the electrode surface. Additionally, laminar flow reduces the likelihood of damage to the fuel cell due to erosion or corrosion caused by turbulent flow. However, the design of fuel cell flow channels can also affect the degree of turbulence and mixing, and optimizing this balance is an ongoing area of research.
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State if the triangles in each pair are similar
Answer:
They are similar
Step-by-step explanation:
It's because 27/18 = 12/8
27/18 = 1.5
12/8 = 1.5
Just needing help here
Based on the graph given, the function is not continuous at x = 1.
What is function?In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. A function is typically represented using functional notation as f(x), which means that the output value of the function f corresponds to the input value x. Functions can take many forms and can be represented graphically or algebraically. They are used to describe many real-world phenomena, including physical systems, economic trends, and social behavior. Functions are important in mathematics because they provide a framework for understanding relationships between variables and for solving problems in various areas of mathematics, science, and engineering.
Here,
At x = 1, there is a "hole" or a point of discontinuity in the graph where the function is undefined. This is because the function has a removable discontinuity at x = 1, meaning that the limit of the function exists at x = 1 but the function is not defined at that point.
Therefore, the value of x at which the function is not continuous is: 1
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JJ fills in the grid of numbers below so that the sum of the first three numbers is 100, the sum of the middle three numbers is 200, and the sum of the last three numbers is 300. What is the filled in grid?
10 Fill in the three boxes 130
Answer:
Can you rephrase the question as it doesn't seem possible to solve. There may be a value missing.
When expressions of the form (x −r)(x − s) are multiplied out, a quadratic polynomial is obtained. For instance, (x −2)(x −(−7))= (x −2)(x + 7) = x2 + 5x − 14.
a. What can be said about the coefficients of the polynomial obtained by multiplying out (x −r)(x − s) when both r and s are odd integers? when both r and s are even integers? when one of r and s is even and the other is odd?
b. It follows from part (a) that x2 − 1253x + 255 cannot be written as a product of two polynomials with integer coefficients. Explain why this is so.
a.(1) When both r and s are odd integers, the quadratic polynomial obtained by multiplying out (x - r)(x - s) will have a coefficient of 1 for x^2 term, and both the coefficient of x term and constant term will be odd integers.
(2) When both r and s are even integers, the polynomial obtained by multiplying out (x - r)(x - s) will also have a coefficient of 1 for x^2 term, but the coefficient of x term and constant term will be even integers.
(3) When one of r and s is even and the other is odd, the polynomial obtained by multiplying out (x - r)(x - s) will have a coefficient of 1 for x^2 term, the coefficient of x term will be an odd integer, while the constant term will be an even integer.
b. x^2 - 1253x + 255 cannot be written as a product of two polynomials with integer coefficients.
a. When both r and s are odd integers, the product (x − r)(x − s) will have a coefficient of 1 for x^2 term, and both the coefficient of x term and constant term will be odd integers. This is because the sum of two odd integers and the product of two odd integers is also an odd integer.
When both r and s are even integers, the product (x − r)(x − s) will also have a coefficient of 1 for x^2 term, but the coefficient of x term and constant term will be even integers. This is because the sum of two even integers and the product of two even integers is also an even integer.
When one of r and s is even and the other is odd, the product (x − r)(x − s) will have a coefficient of 1 for x^2 term, and the coefficient of x term will be an odd integer, while the constant term will be an even integer. This is because the sum of an odd and even integer is an odd integer, and the product of an odd and even integer is an even integer.
b. If x^2 - 1253x + 255 can be written as a product of two polynomials with integer coefficients, then we can write it as (x - r)(x - s) where r and s are integers. From part (a), we know that both r and s cannot be odd integers since the coefficient of x term would be odd, but 1253 is an odd integer. Similarly, both r and s cannot be even integers since the constant term would be even, but 255 is an odd integer. Therefore, one of r and s must be odd and the other must be even. However, the difference between an odd integer and an even integer is always odd, so the coefficient of x term in the product (x - r)(x - s) would be odd, which is not equal to the coefficient of x term in x^2 - 1253x + 255. Hence, x^2 - 1253x + 255 cannot be written as a product of two polynomials with integer coefficients.
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What are inequalities?
Answer:
In mathematics, an inequality is a statement that compares two values, indicating that they are not equal, and specifies the relationship between them. In other words, an inequality expresses a relative difference between two values or quantities, rather than an exact equality.
There are different types of inequalities, but the most common ones involve comparisons between numerical values or algebraic expressions using inequality symbols, such as:
Greater than: x > y (read as "x is greater than y")
Less than: x < y (read as "x is less than y")
Greater than or equal to: x ≥ y (read as "x is greater than or equal to y")
Less than or equal to: x ≤ y (read as "x is less than or equal to y")
Inequalities can also involve multiple variables and can be used to describe ranges of values or conditions that must be satisfied. For example, x + y > 5 is an inequality that describes a region of the xy-plane where the sum of x and y is greater than 5.
Inequalities are used extensively in many areas of mathematics, including algebra, calculus, and optimization, and also have applications in other fields such as economics, physics, and engineering.
Step-by-step explanation:
i have a reed. i know not its length. i broke from it one cubit and it fit 60times along the length of my field. i restored to the reed what i had broken off and it fit 30 times alone the wifth of my Field. the area of my field is 375 square nindas. what was the original length of the reed? 1nandas:12cubits
The original length of the reed is 3.83 nindas which can be calculated by using the information given in the question.
What is area?Area is a two-dimensional measurement of a surface or space. It is a measure of how much space is occupied by a two-dimensional object or surface. The area of a shape is determined by multiplying the length and width of the shape together.
Firstly, we need to calculate the width of the field. As the reed fits 30 times along the width, this implies that the width of the field is 30 times the length of the reed. Therefore, the width of the field is 30 x length of the reed.
Now, we need to calculate the area of the field. As the area of the field is given as 375 nindas², this implies that the area of the field is equal to 375 nindas².
We can substitute the width of the field (30 x length of the reed) into the equation for the area of the field, to yield: 375 nindas² = (30 x length of the reed) x length of the reed.
Solving for length of the reed, we get: length of the reed = (375/30)1/2 = 3.83 nindas.
Therefore, the original length of the reed is 3.83 nindas.
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y varies inversely with x.
y = 15when x = 10
Find y when x = 5
Answer:
y=10
Step-by-step explanation:
Question 6
One gallon of water weighs 8.34 lb. How much weight is added to a fire truck when its tank is filled
with 750 gal of water?
Question 7
1
Answer
6255 pounds
8.34×750=6255lbs
what is the number of real solutions
X^2+6x=5
Answer options
1. No real solutions
2. Cannot be determined
3. Two real solutions
4. One real solution
In the given situation we know that the equation X²+6x=5 has (3) two real solutions.
What do we mean by real solutions?In algebra, a real solution is just an answer to an equation that is a real number.
Discriminant b² - 4ac has zero value in the case of a single actual solution.
One solution, x = -1, exists for the equation x² + 2x + 1 = 0.
The Determinant Calculator on Cuemath can be used to determine the determinant of a quadratic equation.
Use the formula: b²-4ac
Insert values:
b²-4ac
6²-4(1)(5)
36-20
16
We know that:
If b²-4ac is > o (Two real solutions)
Therefore, in the given situation we know that the equation X²+6x=5 has (3) two real solutions.
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I will mark you brainiest!
What is the length of EF?
A) 2.4
B) 3.8
C) 0.5
D) 1.2
Answer:
the answer is 2.4 for ef
pls mark me brainliest
How this app works? Why I can’t find any answers? I need pay for points when I ask questions? I subscribe this app and when I’m lucky to the answers almost the answers are wrong
please help fast!! brainliest!! Find the slope of a line perpendicular to the line whose equation is 4x − 6y = −24
Fully simplify your answer.
The slope of the sole sequence's perpendicular line is [tex]-\frac{3}{2}[/tex].
What is the perpendicular direction?As two lines meet at right angles, the word "perpendicular" refers to an angle. Every direction, including up and down, across, and side to side, can be faced by a pair of perpendicular lines.
Is a straight line considered to be perpendicular?A perpendicular is a straight line in mathematics that forms a correct angle (90 °) with another line. In other words, two lines are parallel to one another if they connect at a right angle.
[tex]y = mx + b[/tex], where [tex]m[/tex] is the slope:
[tex]4x - 6y = -24[/tex]
[tex]-6y = -4x - 24[/tex]
[tex]y = (4/6)x + 4[/tex]
[tex]y = (2/3)x + 4[/tex]
So the slope of the given line is [tex]2/3[/tex].
To find the slope of a line perpendicular to this line, we need to take the negative reciprocal of [tex]2/3[/tex]:
[tex]-1/(2/3) = -3/2[/tex]
Therefore, the slope of a line perpendicular to the given line is [tex]-\frac{3}{2}[/tex].
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Dish A had cells with a radius of 5.1 x10-10 cm. Dish B had cells that had a radius of 4.1 x 10-8 cm. What is the sum of the radii of the two types of cells, using scientific notation?
Answer:
Step-by-step explanation:
To find the sum of the radii of the two types of cells in scientific notation, we need to add the two radii together. However, the radii are given in different orders of magnitude (exponents), so we need to convert one of the radii to match the order of magnitude of the other radius.
The radius of dish A cells is 5.1 x 10^-10 cm.
The radius of dish B cells is 4.1 x 10^-8 cm.
We can convert the radius of dish A cells to match the order of magnitude of dish B cells by multiplying it by 100 (10^2), which gives us:
5.1 x 10^-10 cm x 10^2 = 5.1 x 10^-8 cm
Now that both radii have the same order of magnitude (10^-8), we can add them together to get the total sum of the radii:
5.1 x 10^-8 cm + 4.1 x 10^-8 cm = 9.2 x 10^-8 cm
Therefore, the sum of the radii of the two types of cells, in scientific notation, is 9.2 x 10^-8 cm.
Answer:9.2 x 10^-8 cm.
Step-by-step explanation:
given the following limit lim(x;y)!(0;0) infinty y infinity y , show that the function f (x; y) does not have a limit as (x; y) ! (0; 0).
The limit of f(x, y) as (x, y) approaches (0, 0) depends on the path taken, the limit does not exist, and we can conclude that the function f(x, y) do not have a limit as (x, y) → (0, 0).
To show that the function f(x, y) does not have a limit as (x, y) → (0, 0), we need to show that the limit does not exist, either because the limit is infinite or because the limit does not exist.
We are given that the limit of f(x, y) as (x, y) → (0, 0) when y → infinity is infinity. This means that as y approaches infinity, the function f(x, y) becomes arbitrarily large, regardless of the value of x. However, this does not imply that the limit of f(x, y) exists as (x, y) → (0, 0).
To see why, consider the sequence of points (x_n, y_n) = (1/n, n) as n approaches infinity. As y_n → infinity, we have
lim (x_n, y_n) → (0, 0) f(x_n, y_n) = infinity.
However, if we consider the sequence of points (x_n, y_n') = (1/n, n^2) instead, as n approaches infinity, we have
lim (x_n, y_n') → (0, 0) f(x_n, y_n') = 0.
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Daisy cream is sold in a bulk of 76 cups of cream. Kremlin cream is sold in a bulk of 4 1/2 gallons of cream. Mable cream is sold in a bulk of 40 pints. Which one has the most cream?
Answer:
Step-by-step explanation:
it is mable
find an equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 13xy.
The equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 13xy is y = e^(13x^2/2).
To find an equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 13xy, we can use the method of separation of variables. Let's start by separating the variables:
dy/dx = 13xy
We can then rewrite this equation as:
dy/y = 13x dx
Integrating both sides of the equation gives:
ln|y| = 13x^2/2 + C
where C is the constant of integration.
To find C, we can use the fact that the curve passes through the point (0, 1). Substituting x=0 and y=1 into the equation above, we get:
ln|1| = 0 + C
C = 0
Substituting this value of C back into the equation gives:
ln|y| = 13x^2/2
Solving for y gives:
|y| = e^(13x^2/2)
Since the curve passes through the point (0, 1), we can take the positive branch of the absolute value to get:
y = e^(13x^2/2)
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A convex, 11-sided polygon can have at most how many acute interior angles?
Note: Convex means that each interior angle measure is less than 180 degrees
Answer: At most 18 acute angles
Step-by-step explanation:
The sum of the interior angles of an n-sided polygon is (n-2) × 180 degrees. In a convex polygon, each interior angle is less than 180 degrees.
Let a₁, a₂, ..., a₁₁ be the interior angles of the 11-sided polygon. Then the sum of the interior angles is:
a₁ + a₂ + ... + a₁₁ = (11-2) × 180 = 1620 degrees
Since each angle is acute, we know that each angle is less than 90 degrees. Let A be the number of acute angles. Then the sum of the acute angles is at most:
A × 90
So we have:
a₁ + a₂ + ... + a₁₁ ≤ A × 90
Substituting the sum of the interior angles, we get:
1620 ≤ A × 90
Solving for A, we get:
A ≤ 18
Therefore, the polygon can have at most 18 acute angles.
Find the length of AD in the figure.
A. 34 units
B. 122 units
C. 130 units
D. 26 units
The length of quadrilateral ABCD of AD, which is closest to option A, is [tex]4*sqrt(13)[/tex] (34 units).
Is a triangle 90 degrees or 180?A triangle will always have an angle total of 180 degrees. A quadrilateral can be divided in half from corner to corner to form a triangle because the angle total of a quadrilateral is equal to 360°. A triangle is effectively half of a quadrilateral, therefore it makes sense that its angle measurements are also half. 180° is the half of 360°.
The Pythagorean theorem can be used to calculate the duration of AD.
The distance formula can be used to get the length of AB first:
[tex]AB = sqrt((4-(-4))2 + (6-(-2))2 = sqrt(8-(-8-8) + 8-(8) = 8*sqrt (2)[/tex]
The distance formula can then be used to get the length of AC:
[tex]Sqrt((12-(-4)) = AC^2 + (6-(-2))^2)= sqrt(16^2 + 8^2) = 8*sqrt(5) (5)\\[/tex]
Now, we can calculate the length of AD using the Pythagorean theorem:
[tex]AD^2 = AB^2 + BD^2AD^2 = (8sqrt(2))^2 + (4sqrt(5))^2AD^2 = 128 + 80AD^2 = 208AD = sqrt(208)[/tex]
Simplifying the radical, we get:
AD = sqrt(1613) = 4sqrt(13)
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The length of quadrilateral ABCD of AD, which is closest to option A, is (34 units). Thus, option A is correct.
What is the sum of the angles in a triangle?The sum of the angles in a triangle is always 180 degrees. Because a quadrilateral's total angles are 360°, it can be divided in half from a corner to create a triangle.
The distance formula can be used to get the length of AB first: [tex]AB = sqrt((4 — (-4))2+ (6— (-2))2 = sqrt(8 — (-8— 8)+8— (8) = 8* sqrt(2)[/tex] The distance formula can then be used to get the length of AC:
[tex]Sqrt((12 — (-4)) = AC2 + (6 — (-2))2) = sqrt(162 + 82) = 8* sqrt(5)(5)[/tex]
Now, we can calculate the length of AD using the Pythagorean theorem:
[tex]AD2 = AB2 + BD2AD2 = (8sqrt(2))2 + (4sqrt(5))2AD2 = 128 + 80AD2 = 208AD = sqrt(208)[/tex]
Simplifying the radical, we get: [tex]AD = sqrt(1613) = 4sqrt(13)[/tex]
Therefore, It makes obvious that since a triangle is functionally half of a quadrilateral, its angle measurements are also half. Half of a 360° circle is 180°.
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You deposit $100 in a savings account. The account earns 8% simple interest per year.
Answer:
124 and 125.97
Step-by-step explanation:
y
Homer's car weighs 4,000 pounds. How many tons does
Homer's car weigh?
Answer:2
Step-by-step explanation:
Answer:
2 Tons
Step-by-step explanation:
Homer’s car weighs 2 tons because there are 2,000 pounds in a ton and 4,000 divided by 2,000 equals 2
Chaz is a college student. He has a checking account balance of -$52.00. His roommate Will's
checking account balance is -$59.25. Chaz thinks that Will owes more to the bank than Chaz
does. Is Chaz correct? Explain your answer.
Answer: No, Chaz is not correct. Although their balances are both negative, we cannot compare them simply based on their numeric values. The magnitude of the balance does not indicate who owes more to the bank, as it depends on various factors such as account activity, fees, and interest rates. We would need to know more information about their accounts, such as the interest rates and any fees, in order to determine who owes more to the bank.
Excluding the bank fees Chaz would technically be correct.
No, Chaz is not correct.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
No, Chaz is not correct.
Although both Chaz and Will have negative checking account balances, we cannot determine who owes more to the bank based solely on the balance amount.
The balance amount only indicates how much money they owe to the bank, but it does not give any information about the amount they initially deposited or any other financial transactions they may have made.
To determine who owes more to the bank, we would need to know the initial deposit amount, the transaction history, and any fees or interest charges that have been applied to the accounts.
Without this additional information, we cannot accurately compare the two balances or determine who owes more to the bank.
Thus,
No, Chaz is not correct.
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Determine which points lie on the line L whose parametric or normal form is given. Circle all that afpjply: (c)L(x0,v) where x0 = 132 and v= −211 (5,1,0)(5,1,1)(1,3,2)
The points that lie on the line L with parametric form L(t) = (1, 3, 2) + t(-2, 1, -1) are (1, 3, 2), (-1, 4, 1), and (-3, 5, 0). So, the correct answer is C).
The parametric form of the line L can be written as:
L(t) = x0 + tv
where x0 = (1, 3, 2) and v = (-2, 1, -1)
To find which points lie on the line L, we can substitute different values of t into the parametric equation and see which points we get.
For t = 0, we have:
L(0) = x0 + 0v = (1, 3, 2) + 0(-2, 1, -1) = (1, 3, 2)
For t = 1, we have:
L(1) = x0 + 1v = (1, 3, 2) + (-2, 1, -1) = (-1, 4, 1)
For t = 2, we have:
L(2) = x0 + 2v = (1, 3, 2) + 2(-2, 1, -1) = (-3, 5, 0)
So the points that lie on the line L are (1, 3, 2), (-1, 4, 1), and (-3, 5, 0). So, the correct option is C).
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The Ford F-150 is the best selling truck in the United States.
The average gas tank for this vehicle is 23 gallons. On a long
highway trip, gas is used at a rate of about 3.2 gallons per hour.
The gallons of gas g in the vehicle's tank can be modeled by the
equation g(t)=23 -3.2t where t is the time (in hours).
a) Identify the domain and range of the function. Then graph
the function.
b) At the end of the trip there are 6.4 gallons left. How long
was the trip?
a) The domain of the function is [0, 7.1875], while the range is [0,23]. Considering the domain and the range, the graph of the function is given by the image presented at the end of the answer.
b) The trip had a duration of 5.1875 hours.
How to obtain the domain and the range of the function?The function for this problem is defined as follows:
g(t) = 23 - 3.2t.
The domain is the set of input values that can be assumed by the function. The time cannot have negative measures, hence the lower bound of the domain is of zero, while the gas cannot be negative, hence the upper bound of the domain is given as follows:
23 - 3.2t = 0
3.2t = 23
t = 23/3.2
t = 7.1875 hours.
The range is given by the set of all output values assumed the function, which are the values of the gas, hence it is [0,23].
The graph is a linear function between points (0, 23) and (7.1875, 0).
At the end of the trip there were 6.4 gallons left, hence the length of the trip is obtained as follows:
23 - 3.2t = 6.4
t = (23 - 6.4)/3.2
t = 5.1875 hours.
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Below is some output from the regression on the furniture factory data. What does the R-square value tell us?That we cannot reject the null hypothesis
That there is multicollinearity between the independent variables
That on average, 0.7059 more chairs are produced during weekday shifts than during weekend shifts.
That 71% of the variability in the number of chairs produced can be explained by whether the shift is in the morning or evening and whether it is a weekday shift or weekend shift.
The R-square value informs us that whether the shift is in the morning or the evening and whether it is a weekday shift or weekend shift may account for 71% of the variability in the number of chairs generated.
The R-square statistic measures how much of the variance in the dependent variable in a regression model is accounted for by the independent variables. A better fit of the model to the data is indicated by higher values, which range from 0 to 1.
A value of 0 indicates that no variation is explained by the independent variables, while a value of 1 indicates that all variation in the dependent variable is explained by the independent factors.
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If 20 is 20% of 20% of an integer, what is that integer?
F. 20
G. 50
H. 200
J. 500
K. 1000
Answer:
J. 500
Step-by-step explanation:
20 percent is 0.2 when multiplying.
0.2(0.2(x)) = 20
0.04(x) = 20
x = 500
A survey was given asking whether they watch movies at home from Netflix, Redbox, or a video store. Use the results to determine how many people use Redbox.
42 only use Netflix
44 only use Redbox
12 only use a video store
11 use only a video store and Redbox
42 use only Netflix and Redbox
33 use only a video store and Netflix
10 use all three
27 use none of these
How any people just use RedBox?
Answer:69
Step-by-step explanation: 32+420-90+09=69 pls mark it 5 stars
Find the area of the figure. (Sides meet at right angles.)
3 yd
8 yd
3 yd
5 yd
6 yd
The area οf the figure is 33 square yards.
What is rectangle?A rectangle is a clοsed 2-D shape, having 4 sides, 4 cοrners, and 4 right angles (90°).The οppοsite sides οf a rectangle are equal and parallel. Since, a rectangle is a 2-D shape, it is characterized by twο dimensiοns, length, and width. Length is the lοnger side οf the rectangle and width is the shοrter side.
A crοssed rectangle is a crοssed (self-intersecting) quadrilateral which cοnsists οf twο οppοsite sides οf a rectangle alοng with the twο diagοnals (therefοre οnly twο sides are parallel). It is a special case οf an antiparallelοgram, and its angles are nοt right angles and nοt all equal, thοugh οppοsite angles are equal. Other geοmetries, such as spherical, elliptic, and hyperbοlic, have sο-called rectangles with οppοsite sides equal in length and equal angles that are nοt right angles.
Tο find the area οf the figure, we first find the area οf the rectangle (8 yds by 6 yds) and subtract the area οf the smaller rectangle (3 yds by 5 yds). The area οf the figure is:
Area = (8 yd)(6 yd) - (3 yd)(5 yd)
[tex]= 48 yd^2 - 15 yd^2[/tex]
[tex]= 33 yd^2[/tex]
Therefοre, the area οf the figure is 33 square yards.
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Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows the frequency of each card drawn.
Card A 2 3 4 5 6 7 8 9 10 JQK
Frequency 4 7 5 6 7 6 8 10 7 10 8 12 10
Based on the table, what is the experimental probability that the card selected was a K or 6?
The experimental probability that the card selected was a K or 6 is 17/100 or 0.17.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In other words, it is the ratio of the number of desired outcomes to the total number of outcomes.
The frequency of card 6 is 7 and the frequency of card K is 12. However, the card K is also counted in the total count for JQK, so we need to subtract 2 from the frequency of K to get the actual count of K.
Actual count of K = 12 - 2 = 10
Total count of 6 and K = 7 + 10 = 17
The experimental probability of drawing a K or 6 is the frequency of drawing K or 6 divided by the total number of draws:
Experimental probability = (frequency of K or 6) / (total number of draws)
Experimental probability = 17 / 100
Therefore, the experimental probability that the card selected was a K or 6 is 17/100 or 0.17.
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Find the domains of the following functions:
f(x) = 2x + 7.
h(x) = (x-6)/(2x - 8)
The domain of the given function f(x) = 2x + 7 is -∞ < x < ∞.
What is a domain?The range of values that we are permitted to enter into our function is known as the domain of a function.
Consider the function y = f(x), which has the independent variable x and the dependent variable y.
A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
So, the given function is:
f(x) = 2x + 7
To find the domain:
There are no undefined places or domain restrictions in the function. As a result, -∞ < x < ∞ is the domain.
Therefore, the domain of the given function f(x) = 2x + 7 is -∞ < x < ∞.
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Correct question:
Find the domains of the following function: f(x) = 2x + 7