a) One possible basis for U is {(1/6,1,0,0,0), (0,0,1,-2,3)}.
b) A basis of C5 is {(1/6,1,0,0,0), (0,0,1,-2,3), (1,0,0,0,0), (0,0,1,0,0), (0,0,0,1,0)}.
c) The basis of W is {(1,0,0,0,0), (0,0,1,0,0), (0,0,0,1,0)}.
Linear Algebra Identificationa) To find a basis of U, we can use the two given equations to solve for two of the variables in terms of the others. From the first equation, we have z1 = z2/6. Substituting this into the second equation, we get z3 + 2z4 + 3z5 = 0. Therefore, one possible basis for U is {(1/6,1,0,0,0), (0,0,1,-2,3)}.
b) To extend this basis to a basis of C5, we need to add three more vectors that are not in the subspace U. These vectors can be any linearly independent vectors that are not in U. One possible set of additional vectors is {(1,0,0,0,0), (0,0,1,0,0), (0,0,0,1,0)}. Therefore, a basis of C5 is {(1/6,1,0,0,0), (0,0,1,-2,3), (1,0,0,0,0), (0,0,1,0,0), (0,0,0,1,0)}.
c) To find a subspace W of C5 such that C5 = U direct sum W, we can take the complement of U in C5. The complement of U is the set of all vectors in C5 that are not in U. Since we have already found a basis for C5, we can simply take the subset of basis vectors that are not in U to form a basis for W. In this case, the basis of W is {(1,0,0,0,0), (0,0,1,0,0), (0,0,0,1,0)}.
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To test if a regression coefficient is less than a critical value, C
, we conduct a one-sided test on the _________ tail of a ___________ distribution.
we conduct a one-sided test on the statistic one tail of a critical area of distribution.
The critical value for a two-tailed test of h0: β1 = 0 at α = .05 in a simple regression with 22 observations is 4.35.
What is a critical value?
A critical value can be calculated for different types of hypothesis tests. The critical value of a particular test can be interpreted from the distribution of the test statistic and the significance level.
Test of significance of linear regression between x and y.
Null hypothesis: There is no significant linear relationship between x and y.
Alternative hypothesis: There is a significant linear relationship between x and y.
Test statistic:
F0 = Mean square due to regression/ mean squared error ~ F(1, n-2)
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select the correct prefix to complete the equality. drag the appropriate labels to their respective targets. note: not all labels will be used.
The answers for the given units are 1 g = 0.001 kg; 1 m = 1000 mm; 1 cm = 10 mm; 1 dL = 100 mL; 1 kg = 1000 g; 1 pg = 1 × 10⁻¹² g; 1 g = 1 × 10¹² pg; and 1 mL = 1 cc.
A unit is a name given to a known quantity that is used to measure something. A gram is one-thousandth of a kilogram used to measure weight. This is written as 1 g = 0.001 kg or 10⁻³ kg and kg to g is written as 1 kg = 1000 g. In terms of their relationship, 1 m and 0.001 mm are equivalent. This is written as 1 m = 1000 mm or 10³ mm. The relationship between millimeters and centimeters is written as 1 cm = 10 mm.
Over a milliliter, a deciliter is greater. This is written as 1 dL = 100 mL. The relationship between picogram and gram is written as 1 pg = 1 × 10⁻¹² g
and 1 g = 1 × 10¹² pg. The relationship between a milliliter and a cubic centimeter is written as 1 mL = 1 cc.
The required answers are
1 g = 0.001 kg
1 m = 1000 mm
1 cm = 10 mm
1 dL = 100 mL
1 kg = 1000 g
1 pg = 1 × 10⁻¹² g
1 g = 1 × 10¹² pg
1 mL = 1 cc
The complete question is -
Select the correct prefix to complete the equality. Drag the appropriate labels to their respective targets. Note: not all labels will be used.
1 g = -----kg
1 m = -----mm
1 cm = ----- mm
1 dL = ----- mL
1 kg = ----- g
1 pg = ----- g
1 g = ----- pg
1 mL = ----- cc
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If f(-8) = 1, then the point ( ____ , ____ ) is on the graph of f.
If f(-8) = 1, then the point (-8, 1) is on the graph of f.
How to obtain the point on the graph of the function?The numeric value of the function at x = -8 is given as follows:
f(-8) = 1.
The format of each point on the coordinate plane is given as follows:
(x,y).
In which y is the numeric value of the function at x, meaning that the point can also be written as follows:
(x, f(x)).
Considering that when x = -8, f(x) = 1, the point is given as follows:
(-8,1).
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The mortgage is $158,750. Interest is 6.25% monthly payment is $1,168. How much will the principal be after the third payment?
How do I know what formula to use to figure the correct answer?
These are the choices:
A. $344.74
B. $342.95
C. $341.18
D. $826.82
Answer:
Step-by-step explanation:
B. $342.95 is your answer
baseball coach buys frozen treats for his team following their game.
The coach buys a total of 15 treats, which are either ice cream sandwiches or frozen juice pops
• An ice cream sandwich costs $2.00 and a juice pop costs $2.50.
• The coach spends a total of $33.00 on the treats (no tax is charged).
How many ice cream sandwiches does the coach buy? How much does the coach spend on juice pops? Use the drop-down menus to select the answers that make the statement true.
The coach buys ~ ice cream sandwiches and spends
~ on frozen juice pops.
According to the information, the coach will buy 9 ice cream sandwches and 6 frozen juice pops.
How to calculate how many sandwiches and frozen juices did the coach buy?To calculate how many sandwiches and frozen juices the coach bought we have to perform the following mathematical operation:
First we have to built a equation incluiding all the values of the problem.
I + J = 15 I = The number of ice cream sandwiches J = The number of juice pops15 = Treats were purchased in totalNow, we have to include the price of each product
$2 * I + 2.50 * J = 33.00
Then we have to solve the equation.
2 I + 2.5 ( 15 - I) = 3320 I + 25 ( 15 - I ) = 330 20 I + 375 - 25 I = 330 375 - 5 I = 330 - 5 I = 330 - 375 - 5 I = - 45 I = 9
According to the above the number of sanwiches is 9, and the number of juices is 6.
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I. Express each ratio 25 2 II. Express each num 1.
Each one of the given ratios should be expressed in its simplest form as follows:
50:150 = 1:3.25:40 = 5:8.33:99 = 1:3.What is a ratio?In Mathematics, a ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
In this exercise, you are required to express each of the given ratios in its simplest form. Therefore, we would divide both sides of the ratio by highest common factor (HCF) as follows;
50:150 = 50/150 = 1/5 = 1:5. (divide both sides by 50).
25:40 = 25/40 = 5:8. (divide both sides by 5).
33:99 = 1:3. (divide both sides by 33).
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Complete Question:
Express each one of the following ratios in its simplest form.
(i) 50: 150
(ii) 25:40
(iii) 33 : 99
Laura rents out small and large trucks. She has a total of 22 trucks. The number of large trucks is two more than triple the number of small trucks. how many of each type of truck does she have?
Answer:
see below
Step-by-step explanation:
S+L = 22
L=2+3S
so S+2+3S =22
4S=22-2 = 20
S =5
L =17
Answer:
Step-by-step explanation:
Find the distance of the line segment joining the two points: (2,0) (0,-2)
The distance of the line segment joining the two points is [tex]2\sqrt{2}[/tex].
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
Given;
The two points;
(2,0) (0,-2)
Now,
D=[tex]\sqrt{(0-2)^2+(-2-0)^2}[/tex]
=2[tex]\sqrt{2}[/tex]
Therefore, the distance between two points will be 2[tex]\sqrt{2}[/tex]
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How to find the area of the major sector
The area of the major sector in the given diagram is 115.5 sq.unit.
What is a Major sector?The region having a greater area is known as Major Sector while the one which has a smaller area is the minor sector.
A sector with a central angle greater than 180° is called a major sector and the formula is given below:
/360° ₓ r²
The radius is 7m and is 270°
Therefore 270/360 × 3.142 × 7² = 115.5sq.unit.
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8 times the sum of 2 and a number
The word problem "8 times the sum of 2 and a number" is equal to 8(2 + n).
What is an algebraic expression?In Mathematics, an algebraic expression simply refers to a mathematical equation that can be used for showing the relationship which exist between two (2) or more variables, numerical quantities, as well as in conjunction with different mathematical operations.
Assuming the variable n represents the unknown numerical value (number), we would translate the word problem into an algebraic expression as follows;
Algebraic expression = 8 × (2 + n)
Algebraic expression = 8(2 + n).
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Why is 5/100 not equal to 0.5
Answer: Because instead it equals 0.005
Step-by-step explanation:
The reason 5/100 is not equal to 0.5 is that they are written in different forms.
5/100 is written in the form of a fraction, where the numerator (5) represents the number of parts out of a whole, and the denominator (100) represents the total number of parts in the whole. So, 5/100 represents 5 parts out of 100 parts, which is equal to 0.05.
On the other hand, 0.5 is written in decimal form. It represents the number of parts out of 1, where the digits to the right of the decimal point represent the number of tenths, hundredths, thousandths and so on. So, 0.5 represents 5 tenths, or 5 parts out of 10 parts.
In conclusion, while they represent the same value, they are written in different forms and it's important to know how to read and convert them correctly.
What is the sequence of transformations that maps △ABC to △A′B′C′? Select from the drop-down menus to correctly identify each step. Step 1: Choose... Step 2: Choose... Two triangles on the coordinate plane. Triangle A B C has vertex A at negative 1 comma 2, vertex B at negative 2 comma 5, and vertex C at negative 5 comma 1. Triangle A prime B prime C prime has vertex A prime at 3 comma negative 2, vertex B prime at 4 comma negative 5, and vertex C prime at 7 comma negative 1.
The sequence of transformation which includes a reflection and a translation that maps triangle ΔABC to ΔA'B'C' are;
A reflection across the y-axisA translation of 2 units to the rightA reflection across the x-axisWhat is a reflection transformation?A reflection transformation is one in which the mirror image of the figure is produced, on the other side of a line known as the line of reflection.
The vertices of the triangle ΔABC are A(-1, 2), B(-2, 5), C(-5, 1), the vertices of triangle ΔA'B'C' are A'(3, -2), B'(4, -5), C'(7, -1)
A reflection of the triangle ΔABC across the y-axis, we get;
A''(1, 2), B''(2, 5), C''(5, 1)
A reflection of the triangle ΔA'B'C', across the x-axis produces;
A'''(3, 2), B'''(4, 5), C'''(7, 1)
The rule that maps the coordinates of the vertices of ΔA''B''C'' to the coordinates of the vertices of ΔA'''B'''C''' is a translation of triangle 2 units to the right,
Therefore, the sequence of transformation that maps ΔABC to ΔA'B'C' are;
A reflection across the y-axis, followed by ⇒A translation of two units to the right, then ⇒ A reflection across the x-axis.
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three students, a, b, and c are accused of creating a contradiction. three facts are known: if a is not guilty, then b and c are both guilty. either a is not guilty, or b is guilty. either b is not guilty, or c is not guilty. which one of the following statements correctly identifies the guilty students? [hint: review the end of the lecture for section 2.2.] group of answer choices either a or b is guilty, but not both, and c is guilty. neither a nor c is guilty, but b is guilty. only one of the three is not guilty and it is not a and not b. exactly two of the students are guilty.
Exactly two of the students are guilty. This can be deduced by looking at the facts given and understanding that if A is not guilty, then both B and C are guilty, while either B is not guilty or C is not guilty. This implies that exactly two of the students are guilty.
Given the three facts, we can determine that either A or B is guilty, but not both, and C is guilty. This means that exactly two of the students are guilty.
Since the statement either A is not guilty, or B is guilty, and the statement either B is not guilty, or C is not guilty, both cannot be true. This means that exactly two of the students are guilty.
Given the three facts, we can determine that either A or B is guilty, but not both, and C is guilty. This means that exactly two of the students are guilty. Since the statement either A is not guilty, or B is guilty, and the statement either B is not guilty, or C is not guilty, both cannot be true. This means that only one of the three is not guilty and it is not A or B. Therefore, exactly two of the students are guilty. This can be deduced by looking at the facts given and understanding that if A is not guilty, then both B and C are guilty, while either B is not guilty or C is not guilty. This implies that exactly two of the students are guilty.
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(50 POINTS AND BRAINLYEST)
The height of the cylinder is 30 units. What is the volume of the cylinder? Ignore the prism.
Answer:
9 234
Step-by-step explanation:
base area multiplied by height is volume
Question content area top Part 1 Think About the Process Use the algebra tiles to help you solve the equation 2x - 4 = 10. What is the first step in solving the equation using algebra tiles? What is the solution to the equation?
The solution to the equation is x = 7.
What is the linear equation in one variable?
A linear equation in one variable is an equation of the form ax + b = 0, where a and b are constants and x is the variable. The general form of a linear equation in one variable is ax + b = 0, where a and b are constants and x is the variable. The graph of a linear equation in one variable is a straight line.
The first step in solving the equation 2x - 4 = 10 using algebra tiles would be to add 4 to both sides of the equation to get 2x = 14. The next step would be to divide both sides of the equation by 2 to get x = 7.
Hence, the solution to the equation is x = 7.
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A scale drawn on the map shows that 1 inch represents 20 miles. If two cities
are 2.5 inches apart on the map, what is the distance between them in real
life?
OA. 40 miles
B. 30 miles
O C. 50 miles
OD. 20 miles
SUBMIT
Using the arithmetic operation of multiplication, two cities having a distance of 2.5 inches on map have an actual distance of 50 miles.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The value of 1 inch on scale = 20 miles.
The distance between two cities on map = 2.5 inches
To find the distance between two cities in actual use the arithmetic operation of multiplication.
Let the original distance value in miles be x.
The equation for distance will be -
x = 2.5 × 20
Solve the equation -
x = 2.5 × 20
x = 50
Therefore, the actual distance in miles is 50 miles.
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from a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed. how many different committees are possible if ross, sheldon. first course in probability, a (p. 16). pearson education. kindle edition.
There are 16128 ways to form the committee when 2 of the men refuse to serve together, 23040 ways to form the committee when 2 of the women refuse to serve together, and 5040 ways to form the committee when 1 man and 1 woman refuse to serve together.
(a) When two of the men refuse to serve together, there are 6 men to choose from for the first 3 positions, 4 for the next, and 2 for the last. So there are 6 × 4 × 2 = 48 ways to choose the 3 men.
There are 8 women to choose from for the first 3 positions, so there are 8 × 7 × 6 = 336 ways to choose the 3 women. Thus there are 48 × 336 = 16128 ways to form the committee when 2 of the men refuse to serve together.
(b) When two of the women refuse to serve together, there are 8 women to choose from for the first position, 6 for the next, and 4 for the last. So there are 8 × 6 × 4 = 192 ways to choose the 3 women.
There are 6 men to choose from for the first 3 positions, so there are 6 × 5 × 4 = 120 ways to choose the 3 men. Thus there are 192 × 120 = 23040 ways to form the committee when 2 of the women refuse to serve together.
(c) When 1 man and 1 woman refuse to serve together, there are 7 women to choose from for the first 3 positions and 6 men to choose from for the last 3 positions.
So there are 7 × 6 × 5 × 4 × 3 = 5040 ways to form the committee when 1 man and 1 woman refuse to serve together.
The answer to each of the questions is the number of different committees that can be formed under the given conditions.
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--The given question is incomplete; the complete question is
"From a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed. How many different committees are possible if (a) 2 of the men refuse to serve together? (b) 2 of the women refuse to serve together? (c) 1 man and 1 woman refuse to serve together?"--
A person in a car is driving at 60 km/h toward a ferry whose whistle is blowing at 400 Hz. (a) What frequency does she hear? (b) The ferry leaves the dock and heads directly away from the driver at 15 km/h, still blowing its whistle. What frequency does she hear now?
a. The frequency which she hears is 440Hz.
b. The person in the car would hear a frequency of 391.98 Hz when the ferry leaves the dock and heads directly away from the driver.
(a) The frequency that the person in the car hears is affected by the motion of the car and the sound source (the ferry). The effect is called the Doppler effect, which causes the perceived frequency of sound to change depending on the observer and the relative motion of the source.
If the car is moving toward the ferry, the frequency will be higher than the actual frequency of the sound. The perceived frequency is given by the formula:
f' = f (v + v_s) / (v + v_s)
where
f = the actual frequency of the sound (400 Hz)
v = the velocity of sound (approximately 340 m/s)
[tex]v_s[/tex] = the velocity of the car (60 km/h = 16.67 m/s)
So,
f' = 400(340 + 16.67) / (340 - 16.67) = 400(356.67) / 323.33 = 440 Hz
Hence, the frequency which she hears is 440Hz.
(b) The perceived frequency when the ferry leaves the dock and heads directly away from the driver is also affected by the Doppler effect.
f' = f (v - v_s) / (v - v_s)
where
f = the actual frequency of the sound (400 Hz)
v = the velocity of sound (approximately 340 m/s)
v_s = the velocity of the ferry (15 km/h = 4.17 m/s)
So,
f' = 400(340 - 4.17) / (340 + 4.17) = 400(335.83) / 344.17 = 391.98 Hz
The person in the car would hear a frequency of 391.98 Hz when the ferry leaves the dock and heads directly away from the driver.
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Two similar rectangular prisms. The smaller prism has a base length of 12 meters. The larger prism has a base length of 15 meters. The equations over the larger prism are the following.
Surface Area = 1575 square meters
Volume = 4050 cubic meters
Find the surface area and volume of the smaller similar solid
Answer:
Step-by-step explanation:
Solve the following equation for x. Round the answer to the nearest hundredth.
−1.5r = 4(c + 2.18)
A. 0.63
B. 3.49
C. -1.59
D. -0.40
The equation -1.5x = 4(x + 2.18) solved for x is -1.59. Option C
What are algebraic expression?Algebraic expressions are described as expressions that are mainly composed of variables, terms, constants, coefficients and factors.
These expressions are also composed of arithmetic operations, such as;
AdditionSubtractionDivisionMultiplicationParenthesesFloor divisionBracketFrom the information given, we have that;
-1.5x = 4(x + 2.18)
expand the bracket
-1. 5x = 4x + 8.72
Now, collect like terms, we get;
-1.5x - 4x = 8.72
subtract the like terms
-5.5x = 8.72
Divide both sides by the coefficient of x
x = -1.59
Hence, the correct option is Option C
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Complete question:
Solve the following equation for x. Round the answer to the nearest hundredth.
−1.5x= 4(x + 2.18)
A. 0.63
B. 3.49
C. -1.59
D. -0.40
a random sample of 1,175 people in a certain country were asked whether they thought climate change was a problem. the sample proportion of those who think climate change is a problem was calculated, and a 95 percent confidence interval was constructed as
The interpretation of the confidence interval is that "we can be 95% confident that the true population proportion of people who think climate change lies between 0.146 and 0.214".
Given :
A random sample of 1,175 people in a certain country was asked whether they thought climate change was a problem.
The sample proportion of those who think climate change is a problem was calculated, and a 95 percent confidence interval was constructed as (0.146, 0.214).
95% confidence interval means a person is 95% confident that true population lies in it.
95% confidence interval is given by (0.146,0.214).
So, the interpretation of the confidence interval is that "we can be 95% confident that the true population proportion of people who think climate change lies between 0.146 and 0.214".
Therefore, the correct option is C) We are 95 percent confident that the proportion of people in the sample who think climate change is a problem is between 0.146 and 0.214.
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4 (Simple Interest and Arithmetic Sequences MC)
After hip surgery, your physical therapist tells you to slowly return to walking. The therapist suggests walking for 5 minutes each day for the first week and increasing that time by 5 minutes per day each week thereafter. How many weeks will it be before you are up to 45 minutes of walking per day?
10
11
9
13
The number of weeks, it will take before it is up to 45 minutes of walking per day is, 9 weeks.
What is an arithmetic sequence?In the arithmetic sequence the common difference remains constant between any two consecutive terms. In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).
Formula for any nth term in AP,
T = a + nd
d = T₂-T₁
Where, a is first term , n is nth term and d is common difference
Given that,
The therapist suggests walking for 5 minutes each day for the first week
Increasing that time by 5 minutes per day each week
Number of weeks will it be before you are up to 45 minutes of walking per day = ?
At the end of first week, he will walk for 5 minute
in the beginning of second he started increasing time 5 minutes per day
So, before he reach up to 45 minutes weeks passed,
Before up to 45 minutes,
number of weeks = ?
45 = 5 + 5n
n = 8
Total number of weeks of walking = 1 + 8
= 9
Hence, the number of weeks is 9
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symbol for sample deviation is
The symbol for sample deviation or standard deviation is "σ"(sigma).
What is the standard deviation?The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. The standard deviation shows a "typical" variation from the mean. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.
Because it is the square root of the means of the squared deviations from the arithmetic mean, the standard deviation is often referred to as root-mean-square deviation or sample deviation, sample standard deviation.
the standard deviation of sample deviation is denoted by σ(sigma).
Hence the symbol is "σ"(sigma).
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If 15 workers can build a wall in 48 hours, how many workers will be
required to do the same work in 30 hours?
Answer:
24 workers
Step-by-step explanation:
solution
A wall can be built in 48 hrs by = 15 workers
A wall can be built in 1 hr by = 15× 48 workers
A wall can be built in 30 hrs by= 15 × 48/ 30 workers
= 24 workers
Bay City Balloons studied the demand in Bay City before opening a hot air balloon company. The owners expected to book 375 hot air balloon rides in their first ninety days of business. Instead, they booked 392 rides in that period. What is the percent error for the company's estimate?
+4.533 is the percent error for the company's estimate
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, Bay City Balloons studied the demand in Bay City before opening a hot air balloon company. The owners expected to book 375 hot air balloon rides in their first ninety days of business. Instead, they booked 392 rides in that period.
Since percentage error:
Percent error is the difference between the estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.
Thus in our case
Percentage error = ((392 - 375)/ 375) * 100
Percentage error = 4.533
therefore, the percent error for the company's estimate is +4.533.
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I do not get this at all please help
Answer:I think it is 6
Step-by-step explanation:
Answer:
h(2) = 6
Step-by-step explanation:
This function is called h.
In function notation, it is h(x).
h(2) means the value of the y-coordinate of the point whose x-coordinate is 2.
Look up 2 on the y axis.
Now go up until you get to the blue line of the function.
What y value does that correspond to? Go left horizontally until you get to the y-axis. You intersect the y-axis at 6. That means that
h(2) = 6
Given sin � = 21 29 sinA= 29 21 and that angle � A is in Quadrant I, find the exact value of cot � cotA in simplest radical form using a rational denominator.
The exact value of cot A is .20/21
What is rational denominator?The denominator means moving the radical term square root or cube root to the numerator such that a denominator is a whole number.
We have been given that sin( A ) = 21/29 and angle A is in quadrant 1. We are asked to find the exact value of cot (A) in simplest radical form.
We know that sine relates opposite side of right triangle with hypotenuse.
Since = opposite
hypotenuse
This means that opposite side is 21 units and hypotenuse is 29 units.
We know that cotangent relates adjacent side of right triangle with adjacent side.
Cot = Adjacent
opposite
Now we will find adjacent side using Pythagoras theorem as:
Adjacet² = hypotenuse² - opposite²
Adjacent² = 29² - 21²
Adjacent² = 841 - 441
Adjacent² =400
Let us take positive square root on both sides:
√Adjacent² = √400
Adjacent = 20
Therefore, adjacent side of angle A is 20 units.
Cot (A) = 20/21
The exact value of cot A is .20/21
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Find a function that represents the amount of air required to inflate the spherical balloon from a radius of r inches to a radius of r+1 inches.
A function that represents the amount of air that is f(r)=4/3π[3r²+3r+1]
Since a function is a rule that applies a specific output to a specific input, we can define a function in a variety of ways. This could involve a change in variables, for example, or defining a function that represents a rate of change.
The amount or volume of air required to inflate the spherical balloon from a radius of r inches to a radius of r+1 inches.
The formula for the volume of a sphere is V = 4/3 πr³
where V = volume and r = radius.
V= 4/3π[(r+1)³−r³]
V=4/3π[r³+3r²+3r+1−r³]
V =4/3π[3r²+3r+1]
For r in inches and V(r) in inches cubed,
f(r)=4/3π[3r²+3r+1].
To know more about the volume of a sphere:
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which pair of numbers does not have a least common multiple less than 100
select the correct answer. Which hyperbola has both vertices in the same quadrant?
Option (d) is the correct answer i.e. that hyperbola has both vertices in the same quadrant.
How does hyperbola work?A hyperbola is a conic section in analytical geometry that is formed when a plane intersects a double right circular cone at an angle that spans both cone halves.
Let's see each option one by one:
(a) We've a = 11 and b = 10
This hyperbola is centered at (-10,3) and has vertices as (1,3) and (-21,3).
So, both vertices are not in the same quadrant.
(b) We've a = 9 and b = 12
This hyperbola is centered at (-6,8) and has vertices as (-6,17) and (-6,-1).
So, both vertices are not in the same quadrant.
(c) We've a = 12 and b = 8
This hyperbola is centered at (1,11) and has vertices as (13,11) and (-11,11).
So, both vertices are not in the same quadrant.
(d) We've a = 9 and b = 11
This hyperbola is centered at (-1,10) and has vertices as (-1,19) and (-1,1).
So, both vertices in the same quadrant.
Hence, option (d) is the correct answer.
Learn more about hyperbola from the given link:
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