Solving the problem using basic algebra, the total number of hamburgers that were sold on Saturday can be obtained as 108 hamburgers.
The word problem that has been formulated in the question falls under the basic discipline of mathematics known as algebra.
Algebra is a branch of mathematics that deals with mathematical variables and the rules for manipulating these variables to solve diverse mathematical problems.
Let the total number of hamburgers sold be x.
In the question, it is given that the total number of cheeseburgers sold would be 3 times the number of hamburgers sold. Then the number of cheeseburgers sold would be 3x.
It is also given that the total number of hamburgers and cheeseburgers sold together is 432.
Using these data, the equation can be formulated as x + 3x = 432.
As x and 3x are variables of the same nature, which is x, they can be added to obtain the answer as 4x, hence the equation becomes
4x = 432. Solving for x, we get
x = 432 ÷ 4
x = 108.
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Let b ≠1 and consider the integral ∫(6x-9)dx where b is some real number.
a) What value of b will make this integral equal to 0?
If b ≠1 and integral [tex]\int\limits^b_1[/tex](6x-9)dx where b is some real number , then value of b that make this integral equal to 0 is b = 2 .
The integral is given as [tex]\int\limits^b_1[/tex](6x-9)dx ;
Since , at the value of (b) the given integral is 0.
So , evaluate the integral as :
⇒ [tex]\int\limits^b_1[/tex](6x-9)dx = 0 ;
⇒ [3x² - 9x]₁ᵇ = 0 ;
Simplifying further ,
we get ;
⇒ 3b² - 9b -3(1²) +9(1) = 0 ;
⇒ 3b² -9b +6 = 0 ;
⇒ b² - 3b +2 = 0 ;
On writing the above quadratic equation in factor form ,
we get ;
⇒ (b - 1)(b - 2) = 0 ;
that means b = 1 or b = 2 , but it given that b ≠ 1 ,
So , b = 2 .
Therefore , value of b = 2 , to make the integral 0 .
The given question is incomplete , the complete question is
Let b ≠1 and consider the integral [tex]\int\limits^b_1[/tex](6x-9)dx where b is some real number.
What value of b will make this integral equal to 0 ?
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You have a credit card that has a balance of $3,589.90 and has a credit limit of $5,000. How much is the balance over the acceptable debt ratio percentage?
Answer: You have a credit card that has a balance of $3,589.90 and a credit limit of $5,000. How much is the balance over the acceptable debt ratio percentage? $981.88.
Step-by-step explanation:
Answer:
Step-by-step explanation:
the acceptable debt rate would be 43%
7y+10x−8=0
2y−5x−18=0
Step-by-step explanation:
The system of linear equations can be solved using elimination method or substitution method.
Here's the solution using elimination method:
Add the two equations to eliminate the y variable:
(7y + 10x - 8) + (2y - 5x - 18) = 0 + 0
9y + 5x - 26 = 0
Solve for y:
9y = 26 - 5x
y = (26 - 5x) / 9
Substitute this expression back into either of the original equations to solve for x:
7y + 10x - 8 = 0
7((26 - 5x) / 9) + 10x - 8 = 0
26 - 5x + 70x - 56 = 0
65x - 32 = 0
Solve for x:
65x = 32
x = 32/65
Finally, substitute the value of x back into the expression for y to find the value of y:
y = (26 - 5x) / 9
y = (26 - 5(32/65)) / 9
y = (26 - 160/65) / 9
y = (26 - 8/3) / 9
y = (26 - 8/3) / 9
y = (26 - 8/3) / 9
y = 18/9 - 8/3
y = (18 - 24) / 9
y = -6/9
The solution to the system of linear equations is:
x = 32/65
y = -6/9
What is the linear function equation that best fits the data set? 15 14 13 + 12 + 11 + 10 9 ŷ = -x +9 o ŷ = 3x + 15 ŷ = -3x + 15 ŷ= - 4/3x + 10 8 7+ 6. 5+ 4+ 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
The equation ŷ = -3x + 15 best fits the given data sets.
The word linear function in mathematics refers to two separate but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
The linear function equation that best fits the data set is likely to be the one that minimizes the differences (or residuals) between the observed y-values (the data points) and the predicted y-values (calculated from the equation).
To find this equation, you can use the method of least squares, which involves finding the line that minimizes the sum of the squared residuals.
In this case, the equation ŷ = -3x + 15 minimizes the sum of the squared residuals and is therefore the best fit for the data set.
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Select all of the situations that could be represented by two numbers whose product is equal to
−
20
.
A.
The change in the balance of a checking account after a man spends
$
4
a day for five days.
B.
The miles traveled after a sailor makes two trips of
10
miles each.
C.
The total number of pages read if
8
students each read two and a half pages.
D.
The difference in altitude after a kite loses altitude four times by
5
feet each time.
E.
The amount of sugar in a recipe if it calls for
2
cups per pitcher and Martha is making
10
pitchers.
F.
The total charge created from twenty electrons each with a
(
−
1
)
charge.
The situations that could be represented by two numbers whose product is equal to 20 are options A, B, D, E and F
How to find the situation?Recall that the product of two numbers is the result you get when you multiply them together/
The Factors of 20 are: 1,2,4,5,10,20
From the analysis,
Option A: The change in the balance of a checking account after a man spends $4 a day for five days. = $4*5 = 20
Option B: The miles traveled after a sailor makes two trips of 10 miles each. = 2*10 = 20
Option D: The difference in altitude after a kite loses altitude four times by 5 feet each time.
⇒4*5 = 20
Option E: The amount of sugar in a recipe if it calls for 2 cups per pitcher and Martha is making 10 pitchers.
⇒2*10 = 20
Option F: The total charge created from twenty electrons each with a 1 charge
⇒1*20 = 20
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given the function f ( x ) = x − 4 x 2 − 7 x 12 . find the value(s) of x where the function is not continuous. if there is more than one answer, then list them separated by a comma.
There is point i.e., value of x where the function f(x) = x³ - 4x² - 7x +12 is not continuous.
Consider the polynomial function f(x) = x³ - 4x² - 7x +12
As we know if a function f be a function defined on an open interval containing point a where t a ∈ R be a constant, a function f is continuous at a if lim_(x→a) f(x) = f(a).
Here, the domain of polynomial function f(x) = x³ - 4x² - 7x +12 is set of all real numbers, as the function is well defined for all real values of x.
We know that every polynomial function is continuous in their domain.
This means, the polyomial function f(x) = x³ - 4x² - 7x +12 is continuous on set of all real numbers.
Therefore, there is no value of x where the polynomial function f(x) = x³ - 4x² - 7x +12 is not continuous.
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(after 2.2) find all values z1 and z2 such that (2, −1, 3), (1, 2, 2), and (−4, z1, z2) do not span r 3 .
The values of z1 and z2 that will satisfy this equation are z1 = −8 and z2 = 6 and the vectors (2, −1, 3), (1, 2, 2), and (−4, −8, 6) do not span R3.
To find these values, we need to understand that for any three vectors to span R3, they must be linearly independent.
This means that none of the vectors can be expressed as a linear combination of the other two vectors.
We can start by finding the determinant of the matrix formed by the three vectors. If the determinant is not equal to 0, then the vectors are linearly independent and span R3.
However, if the determinant is equal to 0, then the vectors are linearly dependent and do not span R3.
Let's consider the matrix formed by the three vectors:
[tex]= > \begin{bmatrix}2 & 1 & -4 \\-1 & 2 & z1 \\3 & 2 & z2\end{bmatrix}[/tex]
The determinant of this matrix is equal to:
=> 2 * (2 * z2 - 2 * z1) - (-1) * (1 * z2 - 2 * -4) + 3 * (1 * z1 - 2 * -4)
=> 2z2 - 2z1 + 7z1 + 24 - 2z2 + 8z1 - 24
=> 9z1 + 2z2 - 24
So, the vectors will not span R3 if 9z1 + 2z2 - 24 = 0.
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which two parent trigonometric functions have a period of π and a range that consists of the set of all real numbers? (select all that apply.)
a. sine
b. cosine
c. tangent
d. cosecant
e. secant
f. cotangent
The cosecant, secant, and cotangent functions are defined as the reciprocals of the sine, cosine, and tangent functions, respectively which have two parent trigonometric functions have a period of π and a range that consists of the set of all real numbers.
These functions also have a period of 2π and their ranges depend on the range of the corresponding parent function.
Therefore, correct answer will be a. sine, b. cosine and c. tangent.
The trigonometric functions are mathematical functions used to describe relationships involving lengths and angles of triangles. These functions include sine, cosine, tangent, cosecant, secant, and cotangent. Each of these functions has its own unique properties, including period and range.
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8. In physical education class, Mai takes 10 free throws and 10 jump shots. She earns 1
point for each free throw she makes and 2 points for each jump shot she makes. The
greatest number of points that she can earn is 30.
a. Write an inequality to describe the constraints. Specify what each variable
represents. 100-30
b. Name one solution to the inequality and explain what it represents in that
situation.
An inequality to describe the constraints is x + 2y ≤ 30
What is inequality?
A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than, or equal to, less than, or less than or equal to. Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations.
Here, we have
Assume that a free throw is represented by f and that a Juli throw is represented by j.
We can then write an inequality equation as
10f + 10j = 30
Where 30 is the total number of points earned
F is the free throws made, in which each gives or earns one point
J is the jump shots made, in which each gives or earns two points.
Hence, an inequality to describe the constraints is x + 2y ≤ 30
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(2n^4)^-2 simplify (positive exponents)
Step-by-step explanation:
The expression (2n^4)^-2 can be simplified as follows:
(2n^4)^-2 = 1 / (2n^4)^2
Using the rule that (a^b)^c = a^(bc), we can simplify further:
= 1 / (2^2 * n^4 * 2)
= 1 / (4 * n^4 * 2)
= 1 / (8 * n^4)
So (2n^4)^-2 = 1 / (8 * n^4) in simplified form using positive exponents.
A rare disease exists with which only 1 in 500 is affected. A test for the disease exists, but of course it is not infallible. A correct positive result (patient actually has the disease) occurs 95% of the time, while a false positive result (patient does not have the disease) occurs 1% of the time. If a randomly selected individual is tested and the result is positive, what is the probability that the individual has the disease?
Answer:
The probability that the individual has the disease is 1/500
Step-by-step explanation:
i found the fraction of 1 in 500 which is 1/500, hope this helps :)
Work out:
2 x 2.2 x 10^12 × 1.5 × 10^12/
2.2 x 10^12 - 1.5 x 1012
Give your answer in standard form correct to 3 significant figures.
The index forms is expressed as 9. 40 × 10¹²
What are index forms?Index forms are simply described as representation of a number in the form of an exponential expression or a single number that is raised to a number or variable.
Other names for index forms are standard form and scientific notation.
It also explains how many times a number contains itself.
From the information given, we have that;
2 x 2.2 x 10^12 × 1.5 × 10^12/2.2 x 10^12 - 1.5 x 1012
Represented as;
2(2.2) × 10¹² × 1.5 × 10¹²/ 2.2 × 10¹² - 1. 5 × 10¹²
We can add or subtract the index forms because they have the same exponential value, we have;
4.4(1.5)× 10²⁴/0.7 × 10¹²
Find the quotient
9. 4 × 10¹²
Hence, the value is 9. 4 × 10¹²
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A rectangular flag i 40 centimeter by 72 centimeter. What are the dimenion of a cale drawing of the flag uing the cale 1:8?
320 cm by 576 cm
5 cm by 9 cm
4 cm by 7. 2 cm
1. 8 cm by 11. 11 cm
The dimensions of a scale drawing of a rectangular flag that is 40 centimeters by 72 centimeters using the scale 1:8 is 4 cm by 7.2 cm. Option C.
This is because a 1:8 scale means that for every actual unit of length, the corresponding length on the scale drawing is 8 times smaller.
Therefore, in order to find the dimensions of the scaled drawing of the flag, we must divide the actual dimensions (40 cm by 72 cm) by 8. The result is 4 cm by 7.2 cm.
It is important to make sure that you use the correct scale when attempting to determine the dimensions of a scaled drawing. If you use a different scale than the one intended, your result will be incorrect.
For example, if you use a 1:4 scale instead of a 1:8 scale, you will end up with a scaled drawing that has dimensions of 20 cm by 36 cm, which is double the correct answer.
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Julia had a bag filled with gumballs. There were 1 lemon-lime, 2 watermelon, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?
Sample space = 1, 2, 3
Sample space = 1, 2, 3, 4, 5, 6
Sample space = lemon-lime, watermelon, grape
Sample space = lemon-lime, watermelon, watermelon, grape, grape, grape
the correct sample space for the gumball in her bag is option (D) Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape
What is sample space?The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment. In a random experiment, the outcomes, also known as sample points, are mutually exclusive
Given, Julia had a bag filled with gumballs. There were 1 lemon-lime, 2 watermelon, and 3 grape gumballs.
The number of lemon limes in the bag = 2 lemon-lime
Number of watermelons in the bag = 3 watermelon
Number of grape gumballs in the bag = 5 grape gumball
Sample space is the set of all the possible outcomes of the experiment
Here there are 2 lemon-lime, 3 watermelons, and 5 grape gumball
Hence, if Julia had a bag filled with gumballs and there were 2 lemon-lime, 3 watermelon, and 5 grape gumballs, then the correct sample space for the gumball in her bag is an option (D) Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape
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watermelon,lemon lime,lemon lime,grape,grape,grape
Can anyone solve 21x>5y+49x>2y>2-28x>2y for me?
A point in the solution of the system of inequalities is (2, 0.5)
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
21x>5y+49x>2y>2-28x>2y
Express properly
So, we have the following representation
21x > 5y+49
x > 2y
2 - 28x > 2y
Next, we plot the graphs of the inequality expressions on a plane
(See attachment for the graph)
The shaded region represent the solution
And a point in this region is (2, 0.5)
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Which of the following equations have infinitely many solutions? Choose all answers that apply: Choose all answers that apply: (Choice A) A 76 � + 76 = 76 � + 76 76x+76=76x+7676, x, plus, 76, equals, 76, x, plus, 76 (Choice B) B 76 � + 76 = − 76 � + 76 76x+76=−76x+7676, x, plus, 76, equals, minus, 76, x, plus, 76 (Choice C) C − 76 � + 76 = 76 � + 76 −76x+76=76x+76minus, 76, x, plus, 76, equals, 76, x, plus, 76 (Choice D) D − 76 � + 76 = − 76 � + 76 −76x+76=−76x+76
The equations have infinitely many solutions
-76x+76=-76x+76
76x + 76 = 76x +76
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
When certain requirements are met, an equation can have an unlimited number of solutions.
We have the equation
76x+ 76 = -76x+76
So, 152x = 0
x = 0
and, -76x+76=-76x+76
0= 0
and, 76x + 76 = 76x +76
0 = 0
and, -76x + 76x = 76x - 76
-152x = -152
x= 1
So, the equation with 0=0 shows infinite many solution which are
-76x+76=-76x+76
76x + 76 = 76x +76
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What does it mean if the graph is skewed to the right?
If the histogram is skewed to the right, the graph's peak will be to the left of the center.
What happens when the distribution is skewed to the right?The peak of the graph is located to the left of the center if the histogram is skewed to the right. The frequency of observations is less frequent on the right side of the graph than it is on the left.
The mean is typically higher than the median when the distribution is right-skewn. We anticipate that the mean and median will be roughly identical in value in symmetric distributions. There is a significant link between the distribution's form and how the mean and median are related.
A positively skewed distribution, sometimes referred to as a right-skewed distribution, is a type of distribution where the majority of values are concentrated around the left tail and the right tail is longer. The distribution that leans positively is the exact opposite of one that leans negatively.
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sarah is a marine biologist. of the coral she observes at a dive site, 30% is healthy, 40% is unhealthy, and 30% is dead. she estimates that 30% of the dead coral died in the past 12 months. what percentage of the coral that she observes is dead coral that died more than 12 months ago?
The percentage of the corals at the dive site that Sarah observes died more than 12 months ago is 21%.
What is a percentage?A percentage is a specification of the quantity of an item in a collection per 100 of all items in the collection.
The observations of the corals are;
The percentage of the corals that are healthy = 30%
Percentage of the corals that are unhealthy = 40%
Percentage of the corals that are dead = 30%
Percentage of the dead corals that died in the past 12 months = 30%
The percentage of corals Sarah observed died more than 12 months ago; required.
The 30% of the dead corals that died in the last 12 months, indicatesa that the percentage of the dead corals that died more than 12 months ago = 100% - 30% = 70%
The percentage of the dead corals that died more than 12 months ago = 70%
Therefore, the percentage of the population of corals at the dive site that died more than 12 months ago = 70% × 30% = 21%
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This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Below are two dot plots containing sample means from the same population
How many samples are represented in each plot?
There are __ samples in both plot A and plot B. Each dot represents one sample.
The number of samples for each dot plot is given as follows:
32.
What is shown by the dot plot?The dot plot shows the number of times that each measure appears in the data-set.
Hence the dot plot in this problem shows the number of samples that had means of 10, 20, 30, 40, 50, 60, 70, 80 and 90.
Hence, the total number of samples is obtained by the number of dots in each of the dot plots, which is of 32, hence the sentence is completed as follows:
There are 32 samples in both plot A and plot B. Each dot represents one sample.
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the multiplication rule is used to calculate what type of probability?
The multiplication rule is used to calculate joint probability.
Joint probability is the probability of two events happening simultaneously. The multiplication rule states that the probability of two independent events happening together is equal to the product of their individual probabilities.
The formula can be expressed as: P(A and B) = P(A) x P(B). For example, if the probability of event A is 0.3 and the probability of event B is 0.4, then the joint probability of both events happening together is 0.3 x 0.4 = 0.12. The multiplication rule is only applicable for independent events, meaning that the occurrence of one event does not affect the probability of the other event.
When events are dependent, the calculation of joint probability is more complicated and may involve conditional probability.
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What is the name of the relationship when a function of the form y = abx is
used to fit the data?
The formula for an exponential function is y = abx, where an is the value of y at x = 0 and b is the growth factor over each unit of time.
What relation also serves as a function?Consider the connection to be a function if each input value results in just one output value. Do not classify the relationship as a function if any input value results in two or more outputs.
When a function of the type y = a bX is used to fit the data, what is the name of the relationship?Simple linear regression uses the equation Y = a + bX to connect X and Y. Both quantify the link between two numerical variables, including its intensity and direction.
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Y = abx is the equation for an exponential function, where b is the growth factor per unit of time and an is the value of y at x = 0.
What is mathematical function?A mathematical function is a rule that assigns a dependent variable a value based on one or more independent variables having the specified values. Several formats, including a table, a formula, or a graph, can be used to express a function. An association between members of two sets that is made specifically by a relation is called a function. Formally, an object that has every being uniquely associated with an object is said to be a function from to. A function, then, is a many-to-one (or occasionally, a one-to-one) relation. A function is analogous to a machine. With that machine, you put something in, and it produces something. If f(2)=4, we can infer that the machine (f) will produce 4 if we enter 2 into it.To learn more about mathematical function, refer to:
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What is the volume of a triangular pyramid?
Answer:
1/2 Bh
Step-by-step explanation:
find the area of the base (B) by multiplying.5 xlengthxwidth. The take this answer, multiply by .5 and the height of the pyramid.
The volume of a triangular pyramid is 1/2 × area of the base× height.
What is a triangular pyramid?
A pyramid with a triangular base is referred to as a triangular pyramid. Vertices are essentially corners in geometry. Both regular and irregular triangular-based pyramids have four vertices. Pyramids with triangular bases have six edges, three of which run along the base and three of which rise above the base.
The volume of an object has defined as the space that is occupied by the object.
The volume of a triangular pyramid is 1/2 × B × h.
B = area of the base of the triangular pyramid.
h = Height of triangular pyramid
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S. The table below shows the relationship between the number of hours a student studied and their
grade on a certain test.
100
80
Test Grade
888
60
20
0246 8
Hours Studying
a) Find the line of best fit
b) Estimate the grade for a student that did not study at all:
a) The line of best fit is y = 10x + 60
b) the grade for a student that did not study at all is 0.
What is the slope?
The slope of a line represents the change in the dependent variable (y) for a unit change in the independent variable (x). In this case, the slope of the line of best fit represents the average change in the test grade for a one hour increase in studying. To find the slope, you can use the formula:
m = (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n)
a) The line of best fit is a line that best approximates the relationship between two variables. To find the line of best fit for this data, we can use the least squares method to minimize the sum of the squares of the differences between the observed data points and the line. The equation of the line of best fit is y = mx + b, where m is the slope and b is the y-intercept. The slope can be calculated as (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n), and the y-intercept as (Σy - m(Σx)) / n, where n is the number of data points.
(2, 60) and (5, 90)
The slope is
y2 - y1 = m(x2 - x1)
90 - 60 = m(5-2)
30 = 3m
m = 10
Slope line is
y - 60 = m(x - 2)
y = 10x - 20 + 80
y = 10x + 60
b) To estimate the grade for a student that did not study at all, we can use the line of best fit and plug in x=0 for the number of hours studying. The estimated grade for a student that did not study at all would be the y-intercept of the line,
which represents the expected test grade when
x = 0
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Complete question:
Help and write out the steps pls!???
f(x) = x + 4. q(x) = 12x1
F(g(x))
The composite result function of (f( g(x) ) in the given functions f(x) = x+4 and g(x) = 12x + 1 is 12x + 5.
What is the composite result function of f(g(x)) in the given function?A function is simply a relationship that maps one input to one output.
Given that;
f(x) = x + 4g(x) = 12x + 1f(g(x)) = ?First, we set up the composite result function f(g(x))
f(x) = x + 4
f( g(x) ) = g(x) + 4
f( 12x + 1 ) = ( 12x + 1 ) + 4
Simplify
f( 12x + 1 ) = 12x + 1 + 4
Add 1 and 4
f( 12x + 1 ) = 12x + 5
Therefore, the composite function f( 12x + 1 ) is 12x + 5.
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transform the polar equation to an equation in rectangular coordinates. identify and graph the equation. r sec /theta = 5
The transformation of polar coordinate into rectangular coordinate is r sec (theta) = 5 ⇒ x^2 - 5x + y^2.
What is rectangular coordinate?Two real number lines that intersect at a right angle make up the rectangular coordinate system. The x-axis refers to the horizontal number line, and the y-axis to the vertical number line. Each point on this plane is connected to an ordered pair of real numbers by means of these two number lines, which constitute a flat surface known as a plane (x, y). The x-coordinate is the first number, while the y-coordinate is the second number.
Given that the polar equation is r sec (theta) = 5.
We can write the equation as follows:
r = 5 cos(theta)
Multiply both the sides of the equation with r:
r^2 = 5 cos(theta) r
We know that the value of r^2 = x^2 + y^2 and the value of cos(theta) r = x.
Substituting the values we have:
x^2 + y^2 = 5x
x^2 - 5x + y^2
Hence, the transformation of polar coordinate into rectangular coordinate is r sec (theta) = 5 ⇒ x^2 - 5x + y^2.
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each of three people toss a coin. what is the probability of someone being the odd man out? this means that two of them obtain an identical outcome, while the odd man gets a different one.
The probability of someone being the odd man out is 0.667
What is Probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Given,
3 persons toss a coin to decide who will buy refreshments for the group.
So, total no. of outcomes = (outcomes per each person) total persons
Total no. of outcomes = [tex]2^{3}[/tex]
Total no. of outcomes = 9
The outcomes that one person gets tails and others do not are = (THHH) + (HTHH) + (HHTH)+ (HHHT).
Here T = person getting tails, H = person getting heads.
Number of times one individual receives tails while another does not = 4.
Now, we try to calculate the number of outcomes for one person getting heads and others getting tails, and the results are as follows:
The chances of one individual getting tails while others do not = (HTTT) + (THTT) + (TTHT)+ (TTTH).
The number of possibilities that one individual gets heads while others do not = 3
So, total no. of possibilities that we get a loser = 3+3
Total no. of possibilities that we get a loss = 6.
We know that probability is defined as probability= total no. of possibilities / total no. of outcomes
Now, we have a probability that there is a loser in any game.
So, required probability = 6/9
Required probability = 0.667
∴ The required probability is 0.667
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The probability of someone being the odd man out is 0.667
What is Probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Given,
3 people toss a coin to decide who will buy refreshments for the group.
So, total no. of outcomes = (outcomes per each person) total persons
Total no. of outcomes = 2*2*2
Total no. of outcomes = 8
The outcomes that one person gets tails and others do not are = (THHH) + (HTHH) + (HHTH)+ (HHHT).
Here T = person getting tails, H = person getting heads.
The number of times one individual receives tails while another does not = 4.
Now, we try to calculate the number of outcomes for one person getting heads and others getting tails, and the results are as follows:
The chances of one individual getting tails while others do not = (HTTT) + (THTT) + (TTHT)+ (TTTH).
The number of possibilities that one individual gets heads while others do not = 3
So, the total no. of possibilities that we get a loser = 3+3
Total no. of possibilities that we get a loss = 6.
We know that probability is defined as probability= total no. of possibilities / total no. of outcomes
Now, we have a probability that there is a loser in any game.
So, required probability = 6/9
Required probability = 0.667
∴ The required probability is 0.667
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Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given matrix. [2 -1 -4 2 6 -3] x = x_2 + X_3 (Type an integer or fraction for each matrix element.)
The solutions of Ax = 0 in parametric vector form, where A is a row equivalent to the given matrix are : x_1 = 2x_3 + 2x_2,x_2 = x_2 + x_3,x_3 = x_3,x_4 = 2x_3 + 6x_2,x_5 = -3x_3 - 6x_2,x_6 = -4x_3 - 2x_2
The given matrix is row equivalent, which means that it can be reduced to row echelon form using elementary row operations. To solve for the parametric vector, we start by performing the same operations to the identity matrix. First, we divide the first row by 2 to get the leading coefficient of 1 on the leftmost column. Then, we add the first row to the second row, and the third row to the fourth row to eliminate the elements below the leading coefficients.
Finally, we multiply the first row by -4 and add it to the third row to get the leading coefficient of 1 on the third column. After performing the same operations on the identity matrix, we get the parametric vector x_2 + x_3. This means that x_1 = 2x_3 + 2x_2, x_2 = x_2 + x_3, x_3 = x_3, x_4 = 2x_3 + 6x_2, x_5 = -3x_3 - 6x_2, and x_6 = -4x_3 - 2x_2. Essentially, the parametric vector is the sum of the two columns of the identity matrix that correspond to the two leading coefficients in the row echelon form of the original matrix.
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What is the interquartile range of the set of data this box-and-whisker plot represents
The interquartile range of the data represented in the box-and-whisker plot is given as follows:
IQR = 3.
How to obtain the interquartile range?The measures represented in the box-and-whisker plot are given as follows:
Minimum value of 12.First quartile of 15.Median of 16.Third quartile of 18.Maximum value of 20.The interquartile range is calculated as the difference between the third quartile and the first quartile.
Hence the correct value is given as follows:
IQR = 18 - 15
IQR = 3.
Meaning that the last option is the correct option.
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help please.........
The required quotient of the given expression -1/8 × 2/3 is given as -1/12.
What is simplification?The procedure in mathematics to work and crack the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
= -1/8 × 2/3
= -1/ [4×3]
= -1/12
Thus, the needed quotient of the given expression -1/8 × 2/3] is given as -1/12.
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How do you convert 140 Kilogram (kg) to Pound (lb)?
180 lb to 140 kg conversion. The base unit of weight in the metric system is the kilograms, sometimes known as the kilograms.
How do you convert 1b to kg?Convert 140 Kilograms to Pounds.
kg lb
140.00 308.65
140.01 308.67
140.02 308.69
140.03 308.71
Basically, to convert cost per kg to cost per lb, take the price for the kilogramme and divide it by 2.2046 to get the price for the pound. Fundamentally, 1 kilogramme equals 2.2046 pounds (there is a longer decimal position, but I shorten it to 2.2046).
Mathematical and technical fields frequently need to convert between kilogrammes and pounds; fortunately, this is a simple process. The majority of the time, all you have to do to convert is multiply the number of kilograms by 2.2 to get the number of pounds. Generally speaking, there are 2.2046 pounds in every kilograms.
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