The correct statement is Option - B →
The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false.
What is argument in mathematics?A mathematical argument is a sequence of statements and reasons given with the aim of demonstrating that a claim is true or false.
Given is that Bob is 13 feet tall. So, Bob is taller than most other people.
The correct statement is -
The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false.
Therefore, the correct statement is Option - B →
The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false.
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This is about Linear Equations, Please Help Me.
Option is Greater then, Less then and equal to
Answer:
Step-by-step explanation:
x inter for line a = 1
x inter for line B = -4
Line A is greater then Line B
Classify the triangle by its angles , x, 102, x a right,acute or obtuse triangle
The solution is, x = 39. Since we have a 102 degree angle it is a obtuse triangle.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
given that,
its angles , x, 102, x
now, we know,
The sum of the angles in a triangle add to 180
i.e.
x+ 102+x = 180
Combine like terms
so, we get,
102 + 2x = 180
Subtract 102 from each side
2x = 78
divide by 2, both sides,
x =39
Since we have a 102 degree angle it is a obtuse triangle.
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a student estimated their mass to be 82.0 kg. upon stepping on the scale at the doctor's office, the actual (accepted) mass of 83.8 kg was recorded. use the formula on page 4 of lab 3v to calculate the % error of the student's estimated mass. remember to take the absolute value in the numerator and to round off to the proper degree of certainty. the unit that should be reported is % (use the symbol, do not type out the word).
The percentage error of the student's estimated mass is 2.15%.
What is the percentage error?The percentage or percent error is the difference between the estimated value and the actual value divided by the actual value, multiplied by 100.
The estimated mass of the student = 82.0 kg
The actual mass of the student = 83.8 kg
Absolute error = Actual Value - Estimated Value
= 1.8 kg (83.8 - 82.0)
Percentage error = Actual Value - Estimated Value /Actual Value x 100
= 2.15% (1.8/83.8 x 100)
Thus, we can conclude that the student's estimate contains a 2.15% error.
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write the given function as the composition of two functions
y=-3/sqrt11+8x
The function [tex]y = -\sqrt[3]{11+8x}[/tex] can be written as the composition of functions f(x) = -∛x and g(x) = 11+8x.
What are functions?
The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.
A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Hence, a function is essentially applied to the output of another function. When two functions are combined, the output of the function inside the parentheses becomes the input of the function outside of the parenthesis.
Given a function as follows:
[tex]y = -\sqrt[3]{11+8x}[/tex]
Consider two functions, f(x) and g(x).
Let f(x) = -∛x
g(x) = 11+8x
Then f(g(x) = f(11+8x) = [tex]-\sqrt[3]{11+8x}[/tex]
Therefore the function [tex]y = -\sqrt[3]{11+8x}[/tex] can be written as the composition of functions f(x) = -∛x and g(x) = 11+8x.
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Adam is planning
a rectangular patio that will have an area of
16x2 1 20x square feet. The length of the patio
will be x 1 5 feet. Write an expression to
represent the width of the patio.
Answer:
The width of the patio is 15 feet
Step-by-step explanation:
We can start by using the formula for the area of a rectangle:
Area = length x width
In this case, we know that the area of the patio is given by:
16x^2 + 20x square feet
And we also know that the length of the patio is x + 5 feet. So we can substitute these values into the formula to get:
16x^2 + 20x = (x + 5) x width
Simplifying the right-hand side by multiplying x + 5 by width, we get:
16x^2 + 20x = width x^2 + 5x
To solve for the width, we can move all the terms with width to the left-hand side and all the other terms to the right-hand side:
width x^2 - 16x^2 + 20x - 5x = 0
Simplifying the left-hand side by combining like terms, we get:
width x^2 - 16x^2 + 15x = 0
Factoring out x, we get:
x (width x - 16x + 15) = 0
Now we can solve for the width by setting each factor equal to zero and solving for x:
x = 0 or width x - 16x + 15 = 0
Since the length and width of the patio must be positive values, we can disregard the solution x = 0. So we are left with:
width x - 16x + 15 = 0
We can factor this quadratic equation by finding two numbers whose product is 15 and whose sum is -16. These numbers are -1 and -15, so we can write:
(width x - 1)(x - 15) = 0
Setting each factor equal to zero and solving for x, we get:
width x - 1 = 0 or x - 15 = 0
width x = 1 or x = 15
Since the length of the patio is x + 5, which is 20 feet, we know that x = 15 is the correct solution. So we can substitute x = 15 into the expression for the width:
width x = 1, x = 15, so we choose x = 15
width x - 16x + 15 = (15) x - (16)(15) + 15 = 15 feet
Therefore, the width of the patio is 15 feet.
find the expected vaulue of the random variable with the following probability distribution 2 3 4 5 6 7 8 9 10 11 12 1/36 1/18 1/12 1/9 5/36 1/9 1/12 1/18 1/36
the expected value of the random variable with this probability distribution is 7.
Why it is?
To find the expected value of a discrete random variable with a probability distribution, you multiply each possible value of the random variable by its corresponding probability and then add up all of the products.
For example, for the probability distribution given:
X P(X)
2 1/36
3 1/18
4 1/12
5 1/9
6 5/36
7 1/9
8 1/12
9 1/18
10 1/36
The expected value, denoted by E(X), can be calculated as follows:
E(X) = (2)(1/36) + (3)(1/18) + (4)(1/12) + (5)(1/9) + (6)(5/36) + (7)(1/9) + (8)(1/12) + (9)(1/18) + (10)(1/36)
E(X) = 7
Therefore, the expected value of the random variable with this probability distribution is 7.
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Case 1. ABY is the accounting expert for a firm that has many small clients that need monthly accounting services. ABY has been asked by the partner in charge to analyze the asset section of firms’ statements of financial positions which follow below:
2017
2018
Cash
$2,500
$3,900
Accounts receivable, net
35,000
40,000
Inventory
85,000
122,000
Other current assets
3,400
4,110
Total current assets
125,900
170,010
Property, plant & equipment, net
180,000
230,000
Other assets
15,000
26,000
Total assets
$320,900
$426,010
Required:
Prepare a Horizontal analysis of the assets section of the project statement of financial position for 2017 & 2018.and interpret any significant change in assets values. Round all percentage answers to one decimal place.
The analysis shows that the company experienced significant growth in assets from 2017 to 2018, which could be a positive sign for investors and stakeholders.
What is the Horizontal analysis of the assets section?Horizontal analysis is used to examine a company's financial statements over time. It is typically represented as a percentage increase over the same line item in the base year. Horizontal analysis enables users of financial statements to quickly identify trends and growth patterns.
To perform a horizontal analysis, we need to compare the changes in the values of assets between two years (2017 and 2018) as a percentage of the base year (2017). The analysis is as follows:
Assets 2017 2018 Change % Change
Cash $2,500 $3,900 $1,400 56%
Accounts receivable, net $35,000 $40,000 $5,000 14%
Inventory $85,000 $122,000 $37,000 44%
Other current assets $3,400 $4,110 $710 21%
Total current assets $125,900 $170,010 $44,110 35%
PPE, net $180,000 $230,000 $50,000 28%
Other assets $15,000 $26,000 $11,000 73%
Total assets $320,900 $426,010 $105,110 33%
Interpretation
The analysis shows that the total assets of the company increased by 33% from 2017 to 2018. The most significant change occurred in the other assets category, which increased by 73%, followed by inventory, which increased by 44%. The increase in other assets could be due to investments made by the company or acquisitions of other companies. The increase in inventory could indicate an increase in sales or production. The increase in property, plant & equipment, net by 28% could indicate that the company invested in new equipment or facilities to increase productivity or efficiency.Read more about Horizontal analysis
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Number of strike outs after 20 hours
Answer:
According to the line of fit, after 20 hours of practice, the predicted number of strikeouts is 400.
Step-by-step explanation:
The equation given is:
y = 20x + 0
where y represents the number of strikeouts and x represents the number of hours of practice. To find the number of strikeouts after 20 hours of practice, we substitute x = 20 into the equation and solve for y:
y = 20(20) + 0
y = 400
Therefore, according to the line of fit, after 20 hours of practice, the predicted number of strikeouts is 400.
Solve and check the following equations. Show your solution.
18.) 19 - 3x = 14 + 2x
19.) 2(7 + 5y) - 3y = -35
20.) 14 + 4(x - 5) = 6 - 2x
Answer:
Step-by-step explanation:
18.) 19 - 3x = 14 + 2x
To solve for x, we can simplify the equation by moving all the x terms to one side and all the constant terms to the other side:
19 - 3x = 14 + 2x
19 - 14 = 2x + 3x
5 = 5x
x = 1
To check our solution, we can substitute x = 1 back into the original equation and see if it holds true:
19 - 3(1) = 14 + 2(1)
19 - 3 = 14 + 2
16 = 16
Since both sides of the equation are equal when x = 1, we have verified that x = 1 is the correct solution.
19.) 2(7 + 5y) - 3y = -35
We can start by simplifying the left-hand side of the equation by using the distributive property:
2(7 + 5y) - 3y = 14 + 10y - 3y = 14 + 7y
Now, we can solve for y by moving the constant term to the other side:
14 + 7y = -35
7y = -49
y = -7
To check our solution, we can substitute y = -7 back into the original equation and see if it holds true:
2(7 + 5(-7)) - 3(-7) = -35
2(7 - 35) + 21 = -35
-56 + 21 = -35
-35 = -35
Since both sides of the equation are equal when y = -7, we have verified that y = -7 is the correct solution
20.) 14 + 4(x - 5) = 6 - 2x
We can start by simplifying the left-hand side of the equation by using the distributive property:
14 + 4(x - 5) = 14 + 4x - 20 = 4x - 6
Now, we can solve for x by moving the constant term to the other side:
4x - 6 = 6 - 2x
6x = 12
x = 2
To check our solution, we can substitute x = 2 back into the original equation and see if it holds true:
14 + 4(2 - 5) = 6 - 2(2)
14 - 12 = 6 - 4
2 = 2
Since both sides of the equation are equal when x = 2, we have verified that x = 2 is the correct solution.
x=-2/3t find the value of t .if x=-1/6
Answer:t= 1/4
Step-by-step explanation:
Divide both sides by -2/3, and simplify which would leave u with 1/4.
Let triangle ABC be a right triangle, and let H be the point on side AB such that CH perp AB. Given that x = 3 and h = 4, find x + h, y + h, and a + b.
Inputting the values provided yields:
[tex](3^2 + y^2) + (4^2 + (5 - x)^2) = 5^2[/tex]
A + B = 5 - sqrt (34)after simplifying and solving for a + b.
As a result, we have established that a + b= 0.27.
Describe Right Angle Triangle.A right-angle triangle is a type of triangle that has one angle that measures exactly 90 degrees, which is called a right angle. The side opposite to the right angle is called the hypotenuse, and it is the longest side of the triangle. The other two sides are called legs or catheti. The legs can have different lengths and the Pythagorean theorem can be used to calculate the length of the missing side if the lengths of the other two sides are known. The sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. Right-angle triangles are used in many practical applications, such as in engineering, architecture, and trigonometry.
Since triangle ABC is a right triangle with CH perpendicular to AB, we can use the Pythagorean theorem to find the length of CH:
[tex]CH^2 = CB^2 - BH^2[/tex]
Since triangle ABC is a right triangle, we have CB = AC, and since CH is on AB, we have BH = x. Substituting these values, we get:
[tex]CH^2 = AC^2 - x^2[/tex]
We can also use the given values of x and h to find AC:
[tex]AC^2 = x^2 + h^2[/tex]
Substituting this into the equation for [tex]CH^2[/tex], we get:
[tex]CH^2 = AC^2 - x^2 = (x^2 + h^2) - x^2 = h^2[/tex]
Taking the square root of both sides, we get:
CH = h = 4
Therefore, we have found that CH = 4.
Now we can use the fact that CH is an altitude of triangle ABC to find the area of the triangle in two different ways:
Area = (1/2) * CH * AB
Area = (1/2) * AC * BC
Setting these two expressions equal to each other and substituting the given values, we get:
(1/2) * 4 * (x + 4) = (1/2) * (3 + y) * 5
Simplifying and solving for y, we get:
2x + 8 = 15 - 5/2 * y
2x + 13/2 = 5/2 * y
y = 2x + 13/5
Using the given value of x, we can find y:
y = 2(3) + 13/5 = 6.6
Therefore, we have found that y + h = 6.6 + 4 = 10.6.
Finally, to find a + b, we can use the Pythagorean theorem on triangle ABC:
[tex]AC^2 + BC^2 = AB^2[/tex]
Substituting the given values, we get:
[tex](3^2 + y^2) + (4^2 + (5 - x)^2) = 5^2[/tex]
Simplifying and solving for a + b, we get:
a + b = 5 - sqrt(34)
Therefore, we have found that a + b ≈ 0.27.
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En un trapecio isósceles la longitud de los lados iguales es un medio de la longitud de la base, mientras que la altura es un cuarto de la longitud de la base. Si el perímetro del trapecio es 45 cm.
The area of the isosceles trapezoid is 281.25 square cm.
How to solve for the area?Let's denote the length of the base of the trapezoid as "b".
According to the problem statement, the length of each of the equal sides is one-half the length of the base, which means each equal side has length b/2.
The height of the trapezoid is given as one-fourth the length of the base, so we can write it as h = b/4.
To find the perimeter of the trapezoid, we need to add up the lengths of all four sides.
The two parallel sides of length b each contribute b to the perimeter, while the other two sides of length b/2 contribute a total of b to the perimeter.
Therefore, we can write:
Perimeter = 2b + 2(b/2) = 3b
We know that the perimeter of the trapezoid is 45 cm, so we can set up an equation:
3b = 45
Solving for b, we get:
b = 15
Now we can use the formula for the area of a trapezoid to find the area of this isosceles trapezoid. The formula is:
Area = (1/2)h(b1 + b2)
where h is the height, b1 and b2 are the lengths of the two parallel sides. In this case, b1 and b2 are both equal to b (since it's an isosceles trapezoid), and h = b/4.
Substituting these values, we get:
Area = (1/2)(b/4)(b + b) = (1/2)(b/4)(2b) = b^2/8
Substituting b = 15, we get:
Area = 15^2/8 = 281.25 sq cm
Therefore, the area of the isosceles trapezoid is 281.25 square cm.
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In an isosceles trapezoid, the length of the equal sides is one-half the length of the base, while the height is one-fourth the length of the base. If the perimeter of the trapezoid is 45 cm.
Find the areae
Each year an organization raises money to offer Berkeley College students scholarships. They currently have raised $14,300. This represents 58% of the money they raise. Determine the amount of money the organization will raise in total.
I would really appreciate help, it's due very soon.
Answer:
Area = 380 square inch
Volume = 697 cubic inch
Step-by-step explanation:
Diameter = 11
=> radius = 11/2 = 5.5
A = 4πr^2 =4·π·(5.5^2) ≈ 380 square inch
V=4/3πr^3=4/3·π·(5.5^3) ≈ 697 cubic inch
PLEASE HURRY
A. Plot the circles x^2+y^2=4 and x^2+y^2=1 on the same coordinate plane.
B. Find the image of any point on x^2+y^2=4 under the transformation (x,y) to (1/2x,1/2y). The point (2,0) will go to the ordered pair___.
C. What do you notice about x^2+y^2=4 and x^2+y^2=1? The small circle is a __ of the larger one using the origin as a center and a scale factor of __.
PLEASE HURRY
Answer:
A. Image shows the two circles
B. he ordered point(2, 0) will go to the ordered pair [tex]\mbox{\large \left(\boxed{1}, \boxed{0}\right)}[/tex]'
C. The small circle is a [tex]\boxed{\textsf{copy}}[/tex] of the larger one using the origin as a center and a scale factor of [tex]\boxed{\dfrac{1}{2}}[/tex]
*** I am guessing what word goes into the first box. It should be something that is close to the word copy. The words replica or duplicate could be other choices If you are unable to come up with a choice, post the answer choices as a comment and I can be more specific ***
Step-by-step explanation:
A. Image shows the two circles
B. The larger circle x² + y² = 4 is dilated by a factor of 1/2
The ordered point(2, 0) will go to the ordered pair (2/2, 0/2) = (1,0)
C. What do you notice about the two circles?
They are concentric circles with origin(0, 0) as the center
The small circle is a copy of the larger one using the origin as a center and a scale factor of 1/2
* I do not know what your answer choices are. I have just filled in a term which indicates the relationship.
identify the parameters p and n in the following binomial distribution scenario. a basketball player has a 0.404 probability of making a free throw and a 0.596 probability of missing. if the player shoots 21 free throws, we want to know the probability that he makes no more than 6 of them. (consider made free throws as successes in the binomial distribution.)
Therefore, the parameters of the binomial distribution in this scenario are:
p = 0.404
n = 21
What is an example of a probability distribution?Probability, or the probability that an event will occur, is calculated by dividing the number of favourable outcomes by the total number of potential possibilities. Indeed, a coin flip is the most simple illustration. When you flip a coin, only one of two outcomes—heads or tails—is possible.
A binomial distribution with p and n parameters is present in this situation.
The likelihood of making a free throw, p (a success).
The quantity n represents the attempted free throws.
According to the given information:p = 0.404, which is the probability of making a free throw.
1 - p = 0.596, which is the probability of missing a free throw.
n = 21, which is the total number of free throws attempted.
the probability that the player makes no more than 6 of the 21 free throws. This can be represented as P(X ≤ 6), where X is the number of successful free throws (or made free throws).
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In the expression $c \cdot a^b - d$, the values of $a$, $b$, $c$, and $d$ are 0, 1, 2, and 3, although not necessarily in that order. What is the maximum possible value of the result?
The maximum possible value of the result is 8.
How to solve Linear Equations?
We are given the linear equation;
4x - x = 0
From the linear equation above, seeing that we have an x that is raised to the power of one-third, and we have a single x variable, the first step would be to add x to both sides to get;
The first step to solving the equation is to; C. add x to both sides
The second step to solving the equation is to; C. cube both sides
Solving the equation for x initially yields; C. two possible values
Checking the solutions shows that; D. none are valid solutions
4x - x + x = 0 + x
4x = x
Now, to remove the fraction root, what we will now do as the second step is to cube both sides to get;
(4x)³ = x³
4³x = x³
64x = x³
Divide both sides by x to get;
x² = 64
Take square root of both sides to get;
x = ±√64
x = ±8
Hence, The maximum possible value of the result is 8.
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Suppose that point P is on a circle with radius r, and ray OP is rotating with angular speed omega. Find each of the following for the given values of r, omega, and t. r = 16 cm, omega = pi/8 radian per sec, t = 8 sec (a) What is the angle generated by P in time t? theta = radian (Simplify your answer Type an exact answer using pi as needed. Use integers or fractions for any numbers in the expression. (b) What is the distance traveled by P along the circle in time t? s = Cm (Simplify your answer Type an exact answer using pi as needed. Use integers or fractions for any numbers in the expression (c) What is the linear speed of P? V cm per sec (Simplify your answer Type an exact answer using pi as needed. Use integers or fractions for any numbers in the expression.)
a. The angle generated by P in time t is pi radians.
b. The distance traveled by P along the circle in time t is 16pi cm.
c. The linear speed of P is 2pi cm/sec.
What is angular speed ?
Angular speed, also known as rotational speed, is a measure of how fast an object is rotating around a fixed point. It is typically measured in radians per second and is denoted by the symbol "ω" (omega).
Angular speed is calculated as the change in angle (measured in radians) divided by the time it takes to make that change. In other words, it is the rate at which the angle is changing over time.
Angular speed is an important concept in physics and engineering, as it is used to describe the motion of rotating objects such as wheels, gears, and turbines. It is also used to calculate other important parameters such as linear speed, centripetal force, and torque.
The problem involves finding the properties of a point P that is rotating around a circle with a given radius r and angular speed omega. The problem provides the values of r, omega, and t and asks to find the angle generated by P in time t, the distance traveled by P along the circle in time t, and the linear speed of P.
(a) To find the angle generated by P in time t, we use the formula for angular displacement:
theta = omega * t
Here, omega is given as pi/8 radians per second and t is given as 8 seconds. We substitute these values to get:
theta = (pi/8) * 8 = pi radians
Therefore, the angle generated by P in time t is pi radians.
(b) To find the distance traveled by P along the circle in time t, we use the formula for arc length:
s = r * theta
Here, r is given as 16 cm and theta is calculated in part (a) as pi radians. We substitute these values to get:
s = 16 * pi = 16pi cm
Therefore, the distance traveled by P along the circle in time t is 16pi cm.
(c) To find the linear speed of P, we use the formula for tangential velocity:
v = r * omega
Here, r is given as 16 cm and omega is given as pi/8 radians per second. We substitute these values to get:
v = 16 * (pi/8) = 2pi cm/sec
Therefore, the linear speed of P is 2pi cm/sec.
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.
What is the slop of the line that passes through (7,-4) and (11 -4)
Answer:
The slope of the line that passes through (7,-4) and (11 -4) is 0, since it is a horizontal line.
To find the slope when given two points, use the formula:
y2-y1/x2-x1=m(-4- -4)/(11-7)=0/4=0
So the slope is 0 because 0 is the numerator. If 0 is the denominator, the slope will be undefined.
Hope this helped!
How do we factorise 6x squared minus 4xy
I will rate your answer 5 stars if correct and a thanks
To factorize 6x²2 - 4xy, we can factor out the greatest common factor (GCF), which is 2x:
6x²2 - 4xy = 2x(3x - 2y)
What is factorization?
Factorization is the process of finding two or more expressions that, when multiplied together, produce a given expression. In other words, it is the process of breaking down a mathematical expression into simpler factors.
For example, consider the expression x²2 - 4x - 21. We can factorize it by finding two expressions that, when multiplied together, give us x²2 - 4x - 21. One way to do this is to factor the expression into (x - 7)(x + 3):
x²2 - 4x - 21 = (x - 7)(x + 3)
This is an example of factorization, where the expression on the left-hand side has been broken down into the simpler factors on the right-hand side.
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which is the standard equation of the hyperbola centered at the origin, with a vertical transverse axis and values of a
The standard equation of a hyperbola centered at the origin and a vertical transverse axis values of a=8 and b=9 is y²/64 - x²/81 = 1.
What is a hyperbola?In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
The standard equation of a hyperbola centered at the origin and a vertical transverse axis is given by
y²/a² - x²/b² = 1
We are given that;
a = 8
b = 9
Now, putting the values of the variables into the equation;
y²/a² - x²/b² = 1
y²/8² - x²/9² = 1
y²/64 - x²/81 = 1
Therefore, the standard equation will be y²/64 - x²/81 = 1.
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Given the equation y = 4x - 1/2, what is the y-intercept?
Answer: -1/2
Step-by-step explanation: The formula is y=mx+b where m is your slope and b is your y-intercept. Therefore, your b or y-intercept is -1/2
Answer:
[tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
In the equation [tex]y=mx+b[/tex], m is the slope and b is the y intercept. In this equation, we are given the slope is 4 and the y intercept as [tex]-\frac{1}{2}[/tex] because the equation can be simplified to [tex]y=4x+-\frac{1}{2}[/tex]
is 74.721 repeating rational or irrational
Answer:
Step-by-step explanation:
rational
Compare accounts a and b
Answer:
Account B will have the most after 10 years. It will be worth $21760
Step-by-step explanation:
Hope it helps! =D
two different points an a number line are bath 3 units from the point with coondinate .the solution to which of the following equations gives the coordinates of both points?
Answer: |x + 4| = 3
Step-by-step explanation:
−2⋅f(−6)−7⋅g(−7)=minus, 2, dot, f, left parenthesis, minus, 6, right parenthesis, minus, 7, dot, g, left parenthesis, minus, 7, right parenthesis, equals
Therefore, the value of the expression -2f(-6) - 7g(-7) is equal to -99.
What is function?In mathematics, a function is a rule that assigns a unique output value to each input value. Functions are often represented as equations or graphs that relate the input (also known as the independent variable) to the output (also known as the dependent variable). The input is usually denoted by the variable x, and the output is usually denoted by the variable y. Functions can be used to model relationships between different quantities, such as time and distance, or temperature and pressure. They are a fundamental concept in mathematics and are used in many fields, including physics, engineering, economics, and computer science.
Here,
Using the function notations given in the problem, the statement can be read as follows:
-2 times the value of the function f evaluated at x = -6, minus 7 times the value of the function g evaluated at x = -7, is equal to:
-2f(-6) - 7g(-7) =
Substituting the expressions for f(x) and g(x) given in the problem, we get:
-2*(3*(-6)+1) - 7*(-2*(-7)+5) =
Simplifying this expression, we get:
-2*(-17) - 7*(19) = 34 - 133 = -99
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The television show Pretty Betty has been successful for many years. That show recently had a share of 26, meaning that among the TV sets in use, 26% were tuned to Pretty Betty. Assume that an advertiser wants to verify that 26% share value by conducting its own survey, and a pilot survey begins with 14 households have TV sets in use at the time of a Pretty Betty broadcast.
Find the probability that none of the households are tuned to Pretty Betty.
P(none) = Find the probability that at least one household is tuned to Pretty Betty.
P(at least one) = Find the probability that at most one household is tuned to Pretty Betty. P(at most one) = If at most one household is tuned to Pretty Betty, does it appear that the 26% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Pretty Betty unusual?) yes, it is wrong no, it is not wrong
This means that if at most one household is tuned to Pretty Betty, it is not unusual and does not necessarily indicate that the 26% share value is wrong.
What is probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
This is a binomial distribution problem, where the probability of success (a household tuned to Pretty Betty) is p = 0.26 and the number of trials is n = 14.
The probability that none of the households are tuned to Pretty Betty is:
P(none) = (1 - p)ⁿ = (1 - 0.26)¹⁴≈ 0.031
The probability that at least one household is tuned to Pretty Betty is:
P(at least one) = 1 - P(none) = 1 - 0.031 ≈ 0.969
The probability that at most one household is tuned to Pretty Betty is:
P(at most one) = [tex]P(0) + P(1) = (1 - p)^n + np(1 - p)^{(n-1)[/tex] ≈ 0.500
However, if more than one household is tuned to Pretty Betty, it may indicate that the share value is inaccurate.
Therefore, This means that if at most one household is tuned to Pretty Betty, it is not unusual and does not necessarily indicate that the 26% share value is wrong.
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Jamal paints sceneries on canvas and sells them at art auctions. A large painting sells for $45.99 and a small one for $28.99. In six months he sold seven large paintings and four small ones. Calculate how much money Jamal made in six months.
Answer:
Step-by-step explanation: To calculate the total amount of money Jamal made in six months, we need to multiply the number of paintings sold by the price of each painting, and then add the results for the large and small paintings:
7 large paintings * $45.99/large painting = $321.93
4 small paintings * $28.99/small painting = $115.96
Total amount made = $321.93 + $115.96 = $437.89
Therefore, Jamal made $437.89 in six months by selling seven large paintings and four small ones.
The graph below shows the total amount, y, that an electrician charges for a service call that lasts x hours.
Which of the following is the rate of change in the total amount charged with respect to the time spent on the service call?
Question 5 options:
$25 per hour
$0.04 per hour
$65 per hour
$40 per hour
The rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.
What is the rate of change?The mathematical concept of rate of change describes how much one quantity changes in relation to another. It is calculated as the difference between the change in the output (the dependent variable) and the change in the input (independent variable).
The rate of change, in other words, informs us of how quickly or slowly something is changing through time or in relation to another variable. When tracking the distance an automobile travels over time, for instance, the rate of change would be the car's speed, which is calculated as the distance traveled divided by the time required.
Slope, which is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a graph, is a common way to depict the rate of change. The rate of change of the dependent variable with respect to the independent variable is depicted by the slope of a straight-line graph.
The rate of change in the total amount charged with respect to the time spent on the service call represents the slope of the graph. We can find the slope of the graph by taking any two points on the line and calculating the change in y (total amount) divided by the change in x (time spent on the service call).
Looking at the graph, we can choose two points: (2, 130) and (8, 370). The change in y is:
370 - 130 = 240
And the change in x is:
8 - 2 = 6
Therefore, the slope (rate of change) of the graph is:
240/6 = 40
So the rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.
Therefore, the correct option is $40 per hour.
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Fill in the blanks.
X =
P
S
m
m
(12x+3)
O
(7x-13)
R
The measures in the parallelogram are given as follows:
x = 10.m < R = 57º.m < Q = 123º.How to obtain the measures?In a parallelogram, consecutive angles are supplementary, meaning that the sum of their measures is of 180º.
The angles of 12x + 3 and 7x - 13 are consecutive, meaning that the value of x is given as follows:
12x + 3 + 7x - 13 = 180
19x = 190
x = 190/19
x = 10.
Then the angle measures are given as follows:
m < R = 7(10) - 13 = 57º.m < Q = 12(10) + 3 = 123º.More can be learned about angle measures at https://brainly.com/question/30749938
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