Answer:
Confidence Level z*-value
90% 1.645 (by convention)
95% 1.96
98% 2.33
99% 2.58
Step-by-step explanation:
the difference in sample means is 0.1, and the upper end of the confidence interval is 0.1 + 0.1085 = 0.2085 while the lower end is 0.1 – 0.1085 = –0.0085.
i don't know how to solve this. help please?
Answer:
51 74
Step-by-step explanation:
x = smaller
x +23 = larger
added together (x + x+23) equal to 28 less than 3x = 3x-28
x + x+23 = 3x-28 subtract 2x from both sides of the equation
23 = x -28 add 28 to both sides
51 = x then the larger = 51 + 23 = 74
Answer:
51 and 74
Step-by-step explanation:
Let the smaller of the two numbers be represented by x. The larger of the two numbers is 23 greater than the smaller, and therefore can be written as x + 23.
Set up an EquationFirst, we can write the sum of the two numbers in terms of the smaller number. "three times the smaller" is 3x, and "28 less" is 3x-28.
Therefore our equation is:
[tex]x+x+23=3x-28[/tex]
Solve the EquationStart by adding like terms
[tex]2x+23=3x-28[/tex]
Subtract 23 from both sides
[tex]2x=3x-51[/tex]
Subtract 3x from both sides
[tex]-x=-51[/tex]
Divide both sides by -1
[tex]x=51[/tex]
The larger term is: [tex]x+23\Rightarrow51+23\Rightarrow74[/tex]
Check[tex]51+74=125[/tex]
[tex]3(51)-28=153-28=125[/tex]
[tex]125=125[/tex]
The smaller number is 51 and the larger number is 74
Select the correct answer.
What is the approximate measure of exterior angle B in the polygon?
Answer:
C
Step-by-step explanation:
the sum of the exterior angles of a polygon = 360°
sum the 4 exterior angles and equate to 360
8x + 9x + 5 + 5x + 4 + 9x + 3 = 360 , that is
31x + 12 = 360 ( subtract 12 from both sides )
31x = 148 ( divide both sides by 31 )
x ≈ 11.23 ( to 2 dec. places )
then exterior angle at B is
9x + 3 = 9(11.23) + 3 ≈ 104° → C
The approximate measure of exterior angle B in the polygon is 104° option (C) is correct.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
It is given that:
A polygon is given in the picture with angle measures.
As we know,
The sum of the exterior angles of a polygon = 360°
8x + 9x + 5 + 5x + 4 + 9x + 3 = 360
31x + 12 = 360
31x = 148
x ≈ 11.23
= 9x + 3 = 9(11.23) + 3
≈ 104°
Thus, the approximate measure of exterior angle B in the polygon is 104° option (C) is correct.
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. The set of possible values of x is {-8, -3, 7}. If
5y = x-2, what is the set of possible values of y?
Answer:
{-2, -1, 1}
Step-by-step explanation:
Since we are given all the possible inputs {-8, -3, 7} we can use them one by one in the equation to find the outputs.
5y = x - 2 , if x is -8
5y = -8 - 2
5y = -10
y = -2
Next,
5y = x - 2, if x = -33
5y = -3 - 2
5y = -5
y = -1
Last,
5y = x - 2 when x =7
5y = 7 - 2
5y = 5
y = 1
So the set is {-2, -1, 1}
15 POINTS
Data Analysis and Probability
Constructing a box-and-whisker plot
The box and whisker plot for the data-set is given at the end of the question.
What is a box plot?It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.
The smallest value.The first quartile.The median.The third quartile.The highest value.For this problem, we have that:
The smallest value is of 50, hence the left dot has to be at 50 in your graph.The highest value is of 77, hence the right dot has to be at 50 in your graph.The data-set has an even cardinality, of 17, hence the median is the 9th element, which is of 65, which means that the middle vertical line should be at 65.The first quartile is the median of the first eight elements, hence the mean of the 4th and 5th elements, which are 55 and 57, hence the first quartile is of 56, which means that the left vertical line should be at 56.The third quartile is the median of the first eight elements, hence the mean of the 4th and 5th elements of the second half, which are both 71, hence the third quartile is of 71, which means that the right vertical line should be at 71.The graph at the end gives a vertical version of the box plot.
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Select the reason that best supports statement 2 in the given proof.
Answer:
Transitive property
The reason that best supports statement 2 in the given proof is division property of equality. Therefore, the correct answer is option D.
Given that, 3(m∠A)=90° and m∠B=m∠A.
We need to prove m∠B=30°.
According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0.
Here,
Statement: Reason:
1. 3(m∠A)=90° 1. Given
2. m∠A=30° 2. Division property of equality
3. m∠B=m∠A 3. Reflexive property
4. m∠B=30° 4. Transitive Property
Therefore, the correct answer is option D.
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Which geometry or geometries are common for complexes with a coordination number of 4?.
Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.
What is geometry?Geometry is a subfield of mathematics that examines the measurement and relationships of surfaces, solids, solid surfaces, angles, and points.Ge and metria, two Greek terms that signify "measuring," are the origin of the word geometry. The foundation of geometry has been the method of geometry devised by the Ancient Greeks for more than 2000 years.The calculation of a triangle's angles is a geometry example.Plane geometry, solid geometry, and spherical geometry are the three most popular types of geometry.Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.
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Question mode multiple choice question despite the large number of media options today, the average millennial still blank______ for an average of 10 hours every week.
A graph titled Population of Old Town has Time (years after 2000) on the x-axis, and number of people on the y-axis. A line goes through points (4, 7,000) and (6, 6,500). What is the slope for this scenario? -500 -250
The slope of the scenario is calculated as: -250.
How to Find the Slope Value?Slope (m) = change in y / change in x = (y2 - y1)/((x2 - x1).
Given the points:
(4, 7,000) = (x1, y1)
(6, 6,500) = (x2, y2)
Plug in the values
Slope (m) = (6,500 - 7,000) / (6 - 4)
Slope (m) = (-500) / (2)
Slope (m) = -250
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Kelley writes the expression n 2 to model the phrase "xander studied two more hours than nandini." which best explains the accuracy of kelley’s expression? it is accurate. in the phrase "two more hours than nandini," "two" is "2," "more" is " ," and nandini’s study time is unknown or "n," so 2 n or n 2 are correct translations. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more" is " ," and nandini’s study time is unknown or "n," so 2 n is the correct translation. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more than" is ">," and nandini’s study time is unknown or "n," so 2 greater-than n is the correct translation. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more than" is "<," and nandini’s study time is unknown or "n," so 2 less-than n is the correct translation.
It is accurate. In the phrase “two more hours than Nandini,” n + 2 are correct translations. Then the correct option is A.
What is Algebra?Algebra is used to analyze mathematical symbols, and logic is used to manipulate those symbols.
As an example, Kelley models the sentence "Xander studied two more hours than Nandini" using the equation n + 2.
Consequently, the following will describe Kelley's expression's accuracy the best:
It is precise. Since "two" is translated as "2," "more" as "+," and "Nandini's study time is unknown or "n," 2 + n or n + 2 are the appropriate translations for the sentence "two more hours than Nandini."
So, option A is the best choice.
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I understand that the question you are looking for is :
Kelley writes the expression n + 2 to model the phrase “Xander studied two more hours than Nandini.” Which best explains the accuracy of Kelley’s expression?
It is accurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more” is “+,” and Nandini’s study time is unknown or “n,” so 2 + n or n + 2 are correct translations.
It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more” is “+,” and Nandini’s study time is unknown or “n,” so 2 + n is the correct translation.
It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more than” is “>,” and Nandini’s study time is unknown or “n,” so 2 greater-than n is the correct translation.
It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more than” is “<,” and Nandini’s study time is unknown or “n,” so 2 less-than n is the correct translation.
The product of three consecutive integers is 210. What is their sum?
Answer:
3 consecutive no.s are
5×6×7=210
sum of them is= 5+6+7
=18
So, I hope. it helps !!
(50 POINTS PLEASE HELP!!!)
!!!THE QUESTION THAT I NEED TO BE ANSWERED IS THE PICTURE ATTACHED!!! BELOW IS JUST THE REQUIREMENTS AND EXAMPLE!!!
He has hired you as their new production manager. Your job is to look at four different figures and determine which would best suit the needs of the company for packaging the candy. You will choose one of the four options shown below. The candy is animal gummies. The package must hold between 80 and 100 cubic inches (roughly 5-7 cups of space). The cost of the plastic for the packaging is $0.004 per square inch. When finding cost you would multiply the Total Surface Area by $0.004.
For example:
Total Surface Area = 86 sq. in
Cost per sq in = $0.004
86 * .004 = .344 when rounded to nearest penny = $0.34
Your project should include the volume, total surface area, and materials cost for each figure given below, including the formulas you used and each step of your work. Be sure to find all measures for each figure, even if the figure does not meet the restraints that the company has given. Make sure to use the formulas given in your lessons, round your volume and area to the nearest hundredth, and round your cost to the nearest penny.
The figure in the question is a box with dimensions of 6 in. by 2 in. by 9 in., which gives;
Surface area of the packaging = 168 in.²Package volume = 108 in.³Cost of packaging = $0.672Which method can be used to provide the packaging estimates for the company?The dimensions of the box in the given figure are;
Length, L = 9 in.
Width, W = 2 in.
Height, H = 6 in.
The surface area, A, of a box is found using the following formula;
A = 2•L•W + 2•L•H + 2•H•W
Therefore;
A = 2×9×2 + 2×9×6 + 2×2×6 = 168
The surface area of the figure, A = 168 in.²The volume of a box, V, is calculated as follows;
V = L•W•HFor the given figure, therefore;
V = 9 × 2 × 6 = 108
The volume of the given figure, V = 108 in.³Cost of packaging per square inch, c = $0.004
Cost to package the figure, C, is therefore;
C = c × AWhich gives;
C = $0.004/in.² × 168 in.² = $0.672
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i do not know how to get what they are asking me too
Factorize completely 2xy -6mn - 3m + 4nx please help me solve it
First of all, your question should be: Factor completely 2xy – 6mn – 3my + 4nx, and not Factorize completely 2xy – 6mn – 3m + 4nx. This noted, we proceed to the solution, which is:
2xy – 6mn – 3my + 4nx
→ y(2x – 3m) + 2n(–3m + 2x)
→ (2x – 3m) (y + 2n)
.: Final answer: (2x – 3m) (y + 2n)
I hope this helps.(2x – 3m) (y + 2n) is the factorized form of 2xy -6mn - 3m + 4nx
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
The given expression is 2xy – 6mn – 3my + 4nx
Two times of xy minus six times of mn minus three times of m y plus four times of nx
2xy – 6mn – 3my + 4nx
By using commutative property arrange the terms
2xy –3my– 6mn+ 4nx
Take y as common from first two terms and 2n as common in last two terms
y(2x – 3m) + 2n(–3m + 2x)
(2x – 3m) (y + 2n)
Hence, (2x – 3m) (y + 2n) is the factorized form of 2xy -6mn - 3m + 4nx
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Factor the cubic polynomial 6x3 – 11x2 – 12x 5. use the rational root theorem and synthetic division
The factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:
6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])
For given question,
We have been given the cubic polynomial 6x³ - 11x² - 12x + 5
We need to factorize given cubic polynomial.
By the rational roots theorem, any rational zero of f(x) is expressible in the form ± [tex]\frac{p}{q}[/tex] for integers p, q with p a divisor of the constant term 5 and q a divisor of the coefficient 6 of the leading term.
Factors of p = 5: 1, 5
Factors of q = 6: 1, 2, 3, 6
That means that the only possible rational zeros are:
±{ [tex]\frac{1}{1} ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,\frac{5}{1} ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}[/tex] }
= ±{ [tex]1 ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,5 ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}[/tex] }
We need to find the exact zeros of given cubic polynomial.
For x = 1,
6(1)³ - 11(1)² - 12(1) + 5 = -12
This means, x = 1 is not a zero of given cubic polynomial.
For x = -1,
6(-1)³ - 11(-1)² - 12(-1) + 5 = 0
This means, x = -1 is a zero of given cubic polynomial and (x + 1) is a factor.
To factorize given cubic polynomial we use synthetic division.
The synthetic division (6x³ - 11x² - 12x + 5) ÷ (x + 1) is as shown in following image.
⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(6x² - 17x + 5)
The factors of above quadratic polynomial 6x² - 17x + 5 are:
⇒ 6x² - 17x + 5 = (x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])
So, the factors of given cubic polynomial are:
⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])
Therefore, the factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is: 6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])
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3. What kind of triangle is represented by the triangle shown below?
Isosceles
Right
O Equilateral
Scalene
Answer:
c
Step-by-step explanation:
In geometry, an equilateral triangle is a triangle in which all three sides have the same length.
Please help me solve this problem with work
Answer:
m∠B ≈ 51.5°
Step-by-step explanation:
A triangle solver can find this answer simply by entering the data. If you do this "by hand," you need to first find length BC using the Law of Cosines. Then angle B can be found using the Law of Sines.
Length BCThe Law of Cosines tells us ...
a² = b² +c² -2bc·cos(A)
a² = 21² +13² -2(21)(13)cos(91°) ≈ 619.529
a ≈ 24.8903
Angle BThe Law of Sines tells us ...
sin(B)/b = sin(A)/a
B = arcsin(sin(A)×b/a) = arcsin(sin(91°)×21/24.8903)
B ≈ 57.519°
The measure of angle B is about 57.5°.
A circle with center O. Two tangents to the circle from the point C meet the circle at points A, and B. Two lines O B, and O C forms an exterior angle of 250 degrees. Two lines B D, and A D are drawn from a point D on the circle.
In this figure, m∠BDA =
° and m∠BCA =
°.
Based on the calculations, the measure of m∠BDA and m∠BCA are 55° and 70° respectively.
What is a tangent?In geometry, a tangent is also referred to as a tangent line and it can be defined as a straight line that touches a plane curve at a specific point.
What is a circle?A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle simply refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
First of all, we would determine angle BOA:
∠BOA + ∠BOA = 360° (Angles at a point)
∠BOA + 250° = 360°
∠BOA = 360° - 250°
∠BOA = 110°
Next, we would determine angle BDA:
2 × m∠BDA = ∠BOA (Angle inscribed at the center is twice the angle at the circumference)
2 × m∠BDA = 110°
m∠BDA = 110°/2
m∠BDA = 55°.
What is the theorem of intersecting secants?The theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.
By applying the theorem of intersecting secants, angle BCA will be given by this formula:
m∠BCA = ½ × (m<AO - m<BO)
Substituting the given parameters into the formula, we have;
m∠BCA = ½ × (250 - 110)
m∠BCA = ½ × 140
m∠BCA = 70°.
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Answer:
70
Step-by-step explanation:
a section of a circle has both endpoints on the circle. what is the section of the circle called
Answer:
ChordStep-by-step explanation:
What is chord?A chord is a straight line that connects two points on a curve. An arrangement of three or more notes that blend harmoniously when played together.
A section of a circle has both endpoints on the circle. Chords are the sections of a circle.
Therefore, the final answer is "chords".
I hope this helps, let me know if you have any questions.
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!!!!!50 POINTS IF AND BRAINLEST IF ANSWERED CORRECTLY !!!!!!
By the end of the summer, Tammy and Keith had mowed the same number of lawns and raked the same
number of yards. Keith had met his goal of earning more than $180 but Tammy did not meet her goal of
earning more than $200.
B.) What is a possible combination of the number of lawns they could have each mowed and the
number of yards they could have raked? Explain how you chose the combination and why you
know that combination is correct.
1) The Inequalities for Tammy and Keith are respectively; For Tammy: 10x + 5y > 200 and for Keith: 12x + 3y > 180
2) The possible combination of the number of lawns they could have each mowed and the number of yards they could have raked are;
(11, 17), (14, 5), (16, 0), (18, 2)
How to create Inequalities?Tammy earns $10 for each lawn mowed.
Tammy earns $5 for each yard raked.
We are told that She wants to earn more than $200 from her part-time jobs. Thus, the inequality for Tammys would be;
10x + 5y > 200
Keith earns $12 for each lawn mowed
Keith earns $3 for each yard raked.
We are told that Keith wants to earn more than $180 for each part time job. Thus, the inequality is;
12x + 3y > 180
B) To know the possible combination of the number of lawns they could have each mowed and the number of yards they could have raked, i have drawn a graph of both inequalities and the possible points from there are;
(11, 17), (14, 5), (16, 0), (18, 2)
The complete question is;
Tammy and Keith each work two part-time jobs in the summer mowing lawns andraking yards . Tammy earns $10 for each lawn she mows and $5 for each yard sherakes . She wants to earn more than $200 from her part-time jobs . Keith earns $12 for each lawn he mows and $3 for each yard he rakes. He wants to earn more than $180 for each part time job.
A) Write a system of Inequalities to model the number of lawns they each mow (x) and the number of yards they each rake.
B.) What is a possible combination of the number of lawns they could have each mowed and the number of yards they could have raked? Explain how you chose the combination and why you know that combination is correct.
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What are angles <3 and <4 ?alternate interior angles
alternate exterior angles
vertical angles
corresponding angles
divide the polynomials:
x^2-3x+9/x-2
The value of dividing x^2-3x+9 by x-2 is x + 3
Ways of dividing polynomialsThere are several ways to divide polynomial functions; some of these ways include
By factorizationBy long divisionBy synthetic divisionBy using technology such as graphHow to divide the polynomials?The expression for the polynomial division is given as:
x^2-3x+9/x-2
To divide polynomial functions, we make use of the division by factorization method
Start by expanding the numerator of the polynomial division
x^2-3x+9/x-2 = x^2 + 3x - 6x + 9/x-2
Factorize the equation
x^2-3x+9/x-2 = x(x + 3) - 2(x + 3)/x - 2
Factor out x + 3 from the numerator
x^2-3x+9/x-2 = (x- 2)(x + 3)/x - 2
Cancel out the common factors
x^2-3x+9/x-2 = x + 3
Hence, the value of dividing x^2-3x+9 by x-2 is x + 3
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What are the steps to my answer?
Answer:
f[g(x)] = 4x²+6x-3Step-by-step explanation:
f[g(x)]=(2x)²+3(2x)-3...substitute the values of g(x) into the function f(x)f[g(x)]=4x²+6x-3...simplifiedWrite the standard equation for the circle center left parenthesis negative 6 comma 7 right parenthesis, r = 9.
A. left parenthesis x minus 6 right parenthesis squared plus left parenthesis y plus 7 right parenthesis squared equals 9
B. left parenthesis x minus 7 right parenthesis squared plus left parenthesis y plus 6 right parenthesis squared equals 81
C. left parenthesis x plus 6 right parenthesis squared plus left parenthesis y minus 7 right parenthesis squared equals 81
D. left parenthesis x plus 6 right parenthesis squared plus left parenthesis y minus 7 right parenthesis squared equals 9
Answer:
Step-by-step explanation:
The standard form equation for a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where h and k are the coordinates of the center. Our center is given as (-6,7) and the radius is given as 9, so that information fits into our standard form like this:
[tex](x-(-6))^2+(y-7)^2=9^2[/tex] and simplified, it looks like this:
[tex](x+6)^2+(y-7)^2=81[/tex]
That's choice C
What is the value of the expression when n = 3?
StartFraction 6 (n squared plus 2) Over n EndFraction
16
22
30
66
Answer:
B) 22
Step-by-step explanation:
The expression is:
[tex]\cfrac{6(n^2+2)}{n}[/tex]Find its value when n = 3, substitute n with 3 in the expression:
[tex]\cfrac{6(3^2+2)}{3} =\cfrac{6(9+2)}{3} =\cfrac{6(11)}{3}=2(11) = 22[/tex]The matching answer choice is B.
Verify that the intermediate value theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = x2 7x 1, [0, 9], f(c) = 19 c =
we verified the intermidiate value theorem applies to the function f(x) = x^2 + 7x + 1 . And the value of c is 2.
According to the given question.
We have a function.
f(x) = x^2 + 7x + 1
As, we know that "the Intermediate Value Theorem (IVT) states that if f is a continuous function on [a,b] and f(a)<M<f(b), there exists some c∈[a,b] such that f(c)=M".
Now, we will apply the theorem for the given function f(x).
So,
f(0) = 0^2 +7(0) + 1 = 1
And,
f(9)=9² + 7(9) + 1 = 81 + 63 + 1 = 145
Here, f(0) = 1< 19< 145 = f(9).
So, f is continous since it is a polynomial. Then the IVT applies, and such c exists.
To find, c,
We have to solve the quadratic equation f(c) =19.
This equation is
c² + 7c + 1 = 19.
Rearranging, c²+ 7c - 18=0.
Factor the expression to get
c² + 9c - 2c -18 = 0
⇒ c(c + 9) - 2( c + 9) = 0
⇒ (c - 2)(c + 9) = 0
⇒ c = 2 or -9
c = -9 is not possible beacuse it is not in the interval [0, 9].
So, the value of c is 2.
⇒ f(2) = 2^2 + 7(2) + 1 = 4 + 14 + 1 = 19
Hence, we verified the intermidiate value theorem applies to the function f(x) = x^2 + 7x + 1 . And the value of c is 2.
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Given the functions f(x) = –4ˣ + 5 and g(x) = x³ + x² – 4x + 5, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? (Consider domain, range, x-intercepts, and y-intercepts.)
Answer:
f(x) is an exponential functiong(x) is a polynomial function of degree 3Key common features: same domain, both have one x-intercept and one y-intercept.Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=-4^x+5\\g(x)=x^3+x^2-4x+5 \end{cases}[/tex]
Function f(x)This is an exponential function.
An exponential function includes a real number with an exponent containing a variable.
x-intercept (when y = 0):
[tex]\begin{aligned}f(x) & = 0\\\implies -4^x+5 & =0\\ 4^x &=5\\\ln 4^x &= \ln 5\\x \ln 4 &= \ln 5\\x&=\dfrac{ \ln 5}{\ln 4}\\x&=1.16\:\: \sf(2\:d.p.)\end{aligned}[/tex]
Therefore, the x-intercept of f(x) is (1.16, 0).
y-intercept (when x = 0):
[tex]\begin{aligned}f(0) & = -4^{0}+5\\& = 1+5\\& = 6\end{aligned}[/tex]
Therefore, the y-intercept of f(x) is (0, 6).
End behavior
[tex]\textsf{As }x \rightarrow \infty, \: f(x) \rightarrow \infty[/tex]
[tex]\textsf{As }x \rightarrow -\infty, \: f(x) \rightarrow 5[/tex]
Therefore, there is a horizontal asymptote at y = 5 which means the curve gets close to y = 5 but never touches it. Therefore:
Domain: (-∞, ∞)Range: (-∞, 5)Function g(x)This is a polynomial function of degree 3 (since the greatest exponent of the function is 3).
A polynomial function is made up of variables, constants and exponents that are combined using mathematical operations.
x-intercept (when y = 0):
There is only one x-intercept of function g(x). It can be found algebraically using the Newton Raphson numerical method, or by using a calculator.
From a calculator, the x-intercept of g(x) is (-2.94, 0) to 2 decimal places.
y-intercept (when x = 0):
[tex]\begin{aligned}g(0) & = (0)^3+(0)^2-4(0)+5\\& = 0+0+0+5\\& = 5 \end{aligned}[/tex]
Therefore, the y-intercept of g(x) is (0, 5).
End behavior
[tex]\textsf{As }x \rightarrow \infty, \: f(x) \rightarrow \infty[/tex]
[tex]\textsf{As }x \rightarrow -\infty, \: f(x) \rightarrow - \infty[/tex]
Therefore:
Domain: (-∞, ∞)Range: (-∞, ∞)Conclusion
Key features both functions have in common:
One x-intercept (though not the same)One y-intercept (though not the same)Same unrestricted domain: (-∞, ∞)Consider a situation where your sales have been quite stable in the month, but you have done exceptionally better in the past two days. what trendline is more sensitive to this change?
The trendline has a positive slope and 3-day moving average is the trendline that is more sensitive to this change.
In this question,
Trendlines are used to give traders a good idea of the direction an investment's value might move. In a healthy trend, it's ideal to enter your trades on a pullback (towards the moving average).
Understanding the direction of an underlying trend is one of the most basic ways to increase the probability of making a successful trade because it ensures that the general market forces are working in your favor.
A moving average is a technical indicator that investors and traders use to determine the trend direction of securities. It is one of the commonly used technical tools best known as trend following or lagging indicator, because it is based on past prices.
The sales have been quite stable in the month, but the sales was exceptionally better in the past two days. If the analyst draws a line between these price points, they have an upward trend and 3-day moving average is the trendline that is more sensitive to this change.
The options for this question are a) 3 days moving average, b) 7 days moving average, c) They are both equally sensitive, d) None of them is sensitive to this change.
Hence we can conclude that the trendline has a positive slope and option (A) 3-days moving average is the trendline that is more sensitive to this change is the correct answer.
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If point O represents the origin, PQ = 12 units, and P'Q' = 3 units, find the scale factor. (Note: point O represents the origin, what is the scale factor to dilate a shape on the other side of the origin?)
Answer:
1/4
Step-by-step explanation:
To transform PQR into P'Q'R, dilate the preimage by 1/4, or shrink it by a scale factor of 4 because 3/12 = 1/4
Use appropriate algebra and theorem 7. 2. 1 to find the given inverse laplace transform. (write your answer as a function of t. ) ℒ−1 1 s7
The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.
According to the statement
we have to find the inverse of the Laplace theorem with the help pf the given theorem in the statement.
So, For this purpose, we know that the
Laplace transformation is a transformation of a function f(x) into the function g(t) that is useful especially in reducing the solution of an ordinary linear differential equation with constant coefficients to the solution of a polynomial equation.
Now, We assume you want to find the inverse transform of [tex]s/(s^2 +3s -4).[/tex]
This can be written in partial fraction form as
[tex]\frac{(4/5)}{(s+4)} + \frac{(1/5)}{(s-1)}[/tex]
which can be found in a table of transforms to be the transform of
[tex]\frac{4}{5} e^{-4t} + \frac{1}{5} e^t[/tex]
There are a number of ways to determine the partial fractions. They all start with factoring the denominator.
[tex]s^2 +3x -4 = (s+4)(s-1)[/tex]
After that, you can postulate the final form and determine the values of the coefficients that make it so.
For example:
[tex]\frac{A}{(s+4)} + \frac{B}{s-1} = (A+B)s + \frac{(4B-A)}{(s^2 +3x -4)}[/tex]
This gives rise to two equations:
(A+B) = 1
(4B-A) = 0.
So, The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.
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Question:
Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) ℒ−1 s s2 + 3s − 4.
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PLEASE HELP!! i’ll give brainliest
A. ||
B.
C. neither they are skew lines
Answer:
I think it's A (parallel)
Answer:
A. its parallel
Step-by-step explanation:
all angles are equal... two sides are perpendicular and two are parallel
