The function is f(x) = [tex]x^3[/tex] + 2x is an odd function.
Given the function is :
f(x)=x^3-2x
To determine the function is Even , Odd , or Neither.
Let's Know :
What is an Odd function?
A function f is said to be an odd function if -f(x) = f(-x), for all value of x. In Mathematics, the functions even and odd are those that satisfy specific symmetry relations, with respect to considering additive inverses.
Now, Come to the question:
According to the question;
f(x) = [tex]x^{3}[/tex] - 2x
f(-x) = (-[tex]x^3[/tex]) - 2(-x)
f(-x) = -[tex]x^3[/tex] + 2x
Identify the relation between f(x) and f(-x)
f(x) ≠ f(-x)
Find -f(-x)
-f(-x) = -( -[tex]x^3[/tex] + 2x)
Remove the parentheses:
-f(-x) = [tex]x^3[/tex] + 2x
Identify the relation:
f(x) = -f(-x)
Hence, The function is f(x) = [tex]x^3[/tex] + 2x is an odd function.
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which equation shows the multiplication property of equality if n + 4 = 11
The equation D show the multiplication property of inequality if n+4 =11
What is inequality ?
inequality, When two numbers or algebraic expressions are stated to be greater than, greater than or equal to, less than, or less than or equal to each other in order. Inequalities can be stated as either statements of fact in the form of theorems, which are solved using methods similar to those used to solve equations, or as questions. For instance, the triangle inequality states that the length of the remaining side is greater than or equal to the sum of the lengths of any two sides of a triangle. Many of these inequalities, including the Cauchy-Schwarz inequality, are used in the proofs of many of mathematical analysis' most significant theorems.
Sol-
If n+4 =11
Then by applying the product rule -
(n+4)×2 =11×2
So the correct option is D.
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What has occurred if an increase in temperature accompanies a reaction?
Responses
Energy was released.
Energy was destroyed.
Energy was absorbed.
Energy was created.
The thing that has occurred if an increase in temperature accompanies a reaction is A. Energy was released.
How to illustrate the information?There are many other types of reactions in chemistry, but the exothermic reaction and the endothermic reaction are the two most common forms.
Respiratory reaction is an example of an exothermic reaction, which is one in which energy is released in the form of heat. Exothermic reactions transfer energy from the system to the environment, raising the ambient temperature.
An endothermic reaction is one in which energy is removed from the system during the process. An example of an endothermic reaction is photosynthesis, in which plants use solar energy to produce food.
Therefore, a chemical reaction is said to be exothermic when it releases energy and causes a change in the environment's temperature.
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5. Evaluate using a calculator (or desmos). Round to 2 decimal places: log 23.6
We get 1.37 when we evaluate log 23.6
Given,
log 23.6
We have to evaluate this using a calculator or desmos.
Desmos:
Desmos is a free math teaching and graphing application that is accessible on the web, iOS, and Android. There are classroom activities available to assist students in learning about a number of arithmetic concepts in addition to graphing equations.
Evaluation of logarithms:
You can use a calculator to assess logarithms by utilising the change of base formula, M = log a, M log a, and selecting either the common log or the natural log.
Lets evaluate log 23.6
log 23.6 = 1.372912003
Lets round to 2 decimal places:
log 23.6 = 1.37
That is,
We get 1.37 when we evaluate log 23.6
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Which equation shows direct variation?O y = 2xO y = x+2O y = 2x+2
In order to determine which equation shows direct variation, you take into account that a direct variation is a linear equation that can be written in the following form:
y= kx
here k is a constant fdifferent of zero. By comparing the given options you can notice that only the equation y = 2x
Hence, y = 2x shows a direct variation.
please help me out with this
Answer:
c
Step-by-step explanation:
1. Find the quotient of the averages prices of gold in 2010 and 1970. What
does the quotient mean?
Answer:
35.224137931
Step-by-step explanation:
2010: 1266.66
1970: 35.96
1266.66/35.96=35.224137931
Without the actual data for the average prices of gold in 2010 and 1970, I cannot provide the exact quotient. However, if we assume that we have the data, we can calculate the quotient by dividing the average price of gold in 2010 by the average price of gold in 1970. The resulting quotient would indicate how many times more expensive gold was in 2010 compared to 1970.
For example, if the average price of gold in 2010 was $1,500 per ounce and the average price in 1970 was $35 per ounce, then the quotient would be:
$1,500 / $35 = 42.86
This means that the average price of gold in 2010 was 42.86 times more expensive than the average price in 1970.
It is important to note that the actual quotient will depend on the actual data for the average prices of gold in 2010 and 1970.
divide550six by 50six
The quotient of 550six and 50six is obtained by the calculation to be 11 six
What is the quotient?We know that the result that we obtain after we have carried out a division operation is called a quotient. In this case, we have been required to carry out the operation of division in base six.
We could start by converting the both values to base 10 as follows;
(5 * 6^2) + (5 * 6^1) + (0 * 6^0) = 180 + 30 + 0 = 210 ten
(5 * 6^1) + (0 * 6^0) = 30 + 0 = 30 ten
Then we carry out the division in base ten; 210 ten/30 ten = 7 ten
We convert back to base six to obtain 11 six
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Nga buys three sports books. Each book costs £12, correct to the nearest pound. What is the maximum possible total price that Nga pays for the three books?
Answer:
The answer would be £36
Step-by-step explanation:
12+12+12=36
A math class consists of 21 female students and 16 male students. Two students are selected at random to participate in a probability experiment. Compute the following probabilities. Write your answers in decimal form. Round to the nearest thousandth as needed.a. A male is selected, then a female. b. A female is selected, then a male. c. Two males are selected. d. Two females are selected. e. No males are selected.
To solve this problem, we will use the conditional probability definition: Given events A,B such that P(B)>0 we have that
[tex]P(A|B)=\frac{P(\text{A}\cap B)}{P(B)}[/tex]Where P(A|B) means the probability of A given B occurred. This also leads to the following
[tex]P(A|B)\cdot P(B)=P(A\cap B)[/tex]Now, let us define two events. Let M1 be the event that we select a male first and let F2 be the event that we select a female second. We want to calculate the following probabilty
[tex]P(M_1\cap F_2)_{}[/tex]Using the definition of conditional probability, this is the same as
[tex]P(M_1\cap F_2)=P(F_2|M_1)\cdot P(M_1)[/tex]Now, we will calculate P(M1). At the beginning, when we have not picked anyone yet, we have 37 people (21 Female and 16 Male). So the probability of picking a male first is simply
[tex]P(M_1)=\frac{16}{37}[/tex]Now, we will calculate the second probability. Since we already picked one male, we have now 36 people (21 female and 15 male). Then the probability of picking a female is
[tex]P(F_2|M_1)=\frac{21}{36}[/tex]So,
[tex]P(M_1\cap F_2)=\frac{16}{37}\cdot\frac{21}{36}=\frac{28}{111}=0.252[/tex]Identify which is a function and which are not
Answer:(5,4) , (4,-2) , (-1,0) , (-2,-4)
Step-by-step explanation: Each input can only have one output
help pls ill give 50 points (well im putting in 50 points)
The common difference of each given sequence is:
a. -3
b. 3
c. -4
d. 5
What is an Arithmetic Sequence/Progression?An arithmetic sequence or progression is defined as a series of numbers whereby each term of the sequence is determined by adding a constant (known as the common difference) to the previous term to get the next term in the sequence.
What is the Common Difference of an Arithmetic Sequence?The common difference is the number that is added to each term of an arithmetic sequence to get the next term of the sequence.
How to Find the Common Difference of an Arithmetic Sequence?The common difference, d = difference between two consecutive terms in the sequence.
Subtract the first term from the second term or the second term from the third term to get the common difference of the sequence.
a. Common difference = 7 - 11 = 4 - 7 = 1 - 4 = -3.
b. 23 - 20 = 26 - 23 = 29 - 26 = 3.
c. 12 - 16 = 8 - 12 = 4 - 8 = -4.
d. 3 - (-2) = 8 - 3 = 13 - 8 = 5
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Answer:
a. -3
b. 3
c. -4
d. 5
Step-by-step explanation:
Have a good day!
Can someone please help me with this? I can’t understand it
Let us prepare an inequality statement to answer the question.
There is a one-time fee of $85 and a fee of $23 per guest. If x represents the number of guests, the amount spent will be:
[tex]85+23x[/tex]If the amount spent cannot exceed $1750, we have the inequality statement to be:
[tex]85+23x\leq1750[/tex]We can solve as follows:
[tex]\begin{gathered} 23x\leq1750-85 \\ 23x\leq1665 \\ x\leq\frac{1665}{23} \\ x\leq72.39 \end{gathered}[/tex]Since we cannot have a fraction of a person, the answer will be 72.
her maximum number of guests is 72.
a pound in lukes neighborhood has a depth of 81.6 inches. during the dry season the pond losses an average of 0.02 inches of water each day. luke wrote the function below to represent the depth of the pond in inches x days after the dry season begins. explain lukes error and rewrite the function correctly? f(x) = -0.02(x+81.6)
The correct function to represent the depth of the pond in inches x days after the dry season begins is f(x) = 81.6 - 0.02x
It is a question of functions.
Given that:-
Depth of pond in Luke's neighborhood = 81.6 inches.
Depth that pond loses everyday = 0.02 inches
Function written by Luke to represent the depth of the pond in inches x days after the dry season begins = f(x) = -0.02(x+81.6)
We have to find the error in Luke's function and then rewrite then correct function.
Let x be the number of days after the dry season begins.
We know that,
Depth of pond after x days = Initial depth of pond - (Depth that pond loses everyday)* (number of days after the dry season begins)
Hence, we can write,
f(x) = 81.6 - 0.02x
Luke has wrongly multiplied -0.02 with (x + 81.6) instead of only multiplying with x.
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Simplify by finding the product of the polynomials below. Then Identify the degree of your answer. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. (4t^2-5u)^2 This simplifies to: AnswerThe degree of our simplified answer is: Answer
The degree of our simplified answer is = 4
what is polynomials ?
Polynomials are sums of the terms of form k· x^ n, where k is any number and n is positive integers. polynomials are algebraic expression that consist of variable and coefficient. variables are also sometimes called Indeterminates
an example of polynomial with one variable is x^2+x-12.
so,
after expanding the identity (4t^2-5u)^2, it becomes:
16t^4+25u^2-40ut^2
as we know in case of polynomial highest degree from the polynomial is consider as the degree of that polynomial.
hence,
The degree of this equation is 4.
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Which expression is equivalent to the algebraic expression 8k5∙9k−2(6k2)2, where there are no variables in the denominator?
2k−181
2k81
2k−1
2k
The expression is equivalent to the 360[tex]k^2[/tex] - 48k
Given the Expression :
8k5∙9k−2(6k2)2
It means
(8k × 5) × 9k - 2(6k × 2) × 2
Now, Multiply the monomials
360[tex]k^2[/tex] - 2(6k × 2) × 2
Again, Multiply the monomials,
= 360[tex]k^2[/tex] - 48k
Hence, The expression is equivalent to the 360[tex]k^2[/tex] - 48k
What is Monomial ?
A monomial is a polynomial, which has only one term. A monomial is an algebraic expression with an single term but can have multiple variable and a higher degree too.
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The city is issuing bonds to raise money for a building project. You obtain a $6700 bond that pays 2% interest annually that matures in 5 years. How much interest will you earn?
The interest that will be earned when the city is issuing bonds to raise money for a building project is $670.
How to calculate the value?It should be noted that the formula for the calculation is the interest is given as:
Interest = Principal × Rate × Time / 100
where P = $6700
R = 2%
Time = 5 years
Interest = Principal × Rate × Time / 100
Interest = (6700 × 2 × 5) / 100
= 670
The interest is $670.
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(-4,-1) that is perpendicular to the line with the equation 4x+5y=5 how do I do this
To find the line that is perpendicular to the one we have, the first step is to rewrite the expression in the slope-intercept form.
[tex]\begin{gathered} 4x+5y=5 \\ 5y=5-4x \\ y=\frac{5-4x}{5} \\ y=-\frac{4}{5}x+1 \end{gathered}[/tex]The slope of this line is -4/5. The one that is perpendicular to it has a slope that is negative reciprocal to this one, which means that we need to invert the fraction and the signal.
[tex]\begin{gathered} m=-(\frac{1}{\frac{-4}{5}}) \\ m=-(\frac{-5}{4})_{} \\ m=\frac{5}{4} \end{gathered}[/tex]The equation for the perpendicular line so far is:
[tex]y=\frac{5}{4}x+b[/tex]To find "b" we need to replace the coordinates of (-4,-1) and solve for b.
[tex]\begin{gathered} -1=\frac{5}{4}\cdot(-4)+b \\ -1=-5+b \\ b=-1+5 \\ b=4 \end{gathered}[/tex]The full expression is:
[tex]y=\frac{5}{4}x+4[/tex]--- nerweter de 2 mm. em. 4 em 12 manam 2) Find the perimeter. Use 3.14 for it when needed. 20 m semicircle -2n trola To 31.1 10 m 2 2 P. = 314 = 77.4 D 31.141/2 + 2+2 P - Find area of figure. Round to the nearest hundredth if neces 41 in. 136 in. 45.5 in. 1 area of figure. Round to the nearest hundredth if ne 17 m 9 m n
The perimeter of the semicircle with different r values is:
(When r = 2) = 10.28 mm(When r = 4) = 20.56 mm(When r = 12) = 61.68 mmWhat is a semicircle?A circle is divided into exactly two parts in geometry to create a semicircle, a plane figure. Therefore, using the area and perimeter of a circle, we can calculate the area and perimeter of a semicircle. A semicircle is a one-dimensional locus of points in mathematics (and more specifically geometry) that makes up one-half of a circle. A semicircle's full arc (equivalent to π radians or a half-turn) is always 180° in length. It only has one symmetry line (reflection symmetry).So, the formula for the perimeter of the semicircle:
πr + 2rNow, insert values as follows:
(A) (When r = 2)
πr + 2r3.14 × 2 + 2 × 26.28 + 410.28 mm(B) (When r = 4)
πr + 2r3.14 × 4 + 2 × 412.56 + 820.56 mm(C) (When r = 12)
πr + 2r3.14 × 12 + 2 × 1237.68 + 2461.68 mmTherefore, the perimeter of the semicircle with different r values is:
(When r = 2) = 10.28 mm(When r = 4) = 20.56 mm(When r = 12) = 61.68 mmKnow more about semicircles here:
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The correct question is given below:
2 mm. em. 4 em 12 Manam. Find the perimeter of the semicircle. Use 3.14 for it when needed.
what is a triangle? can someone explain please (not serious, just couldn't figure out how to delete my previous question)
A brief definition of a triangle according to Euclidean geometry is shown below:
Closed figure consisting in three non-colinear, all of them coplanar, points named vertices and three line segments associated to each pair of points named sides.
What is a triangle?
To understand what a triangle is, we need to understand some basic concepts of the Euclidean geometry. There are three undefined terms, that is, fundamental elements that cannot be defined but are described in terms of its attributes. Those terms are point, line and plane. The atributes of each element are described below:
Point - Location, discrete, no dimensions. Line - Continuous, length, no width. Plane - Length, width, no depth.A line can be formed by knowing the location of two distinct points on a plane. Lines can be continuous lines (endless), line segments (lines with finite length) or semirrays (lines with only one endpoint).
Let suppose that we have three points not collinear to each other, then we construct line segments for each pair of collinear points. Then, we create a triangle, whose brief definition is shown below:
Closed figure consisting in three non-colinear, all of them coplanar, points named vertices and three line segments associated to each pair of points named sides.
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There is a 0.99967 probability that a randomly selected 30-year-old female lives through the year. An insurance company wants to offer her a one-year policy with a death benefit of $900,000. How much should the company charge for this policy if it wants an expected return of $400 from all similar policies?
Using probability we can calculate that the company must charge $697 for an expected return of 400 .
Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
The probability that a 30 year old female lives throughout the year
= 0.99967
Death benefit = $900,000
Expected amount the company would pay = probability that a person dies × insurance amount.
Expected amount = (1 - 0.99967) × 900000 = $297
Now Company wants a profit of $400
Cost charged by company =$( 297 + 400 ) = $ 697
Therefore using probability we can calculate that the company must charge $697 for an expected return of $400 .
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11. Convert the following dry measurements.
a. 11 bushels to quarts
b. 3 pecks to pints
c. 97 quarts to bushels
d. 1,120 quarts to pocks
The conversion of dry measurements are:
a. 352 quarts
b. 48 pints
c. 3.03 bushels
d. 140 pecks
a. 11 bushels to quarts
32 quarts make up one bushel, which is a unit of dry volume.
1 bushel = 32 quarts
11 bushels = (32 × 11) quarts = 352 quarts
b. 3 pecks to pints
A peck, which equals 16 dry pints in imperial and American usage, is a unit of dry volume.
1 peck = 16 pints
3 pecks = 3 × 16 = 48 pints
c. 97 quarts to bushels
As we know, 1 bushel = 32 quarts
1 quart = 1/32 bushel
97 quarts = 97/32 ≅ 3.03 bushels
d. 1,120 quarts to pecks
A peck is an imperial and American customary dry volume measurement unit that is equal to 8 dry quarts.
1 peck = 8 quarts
So, 1 quart = 1/8 peck
1120 quarts = 1120/8 pecks = 140 pecks
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the information given. When applicable, eraph the equations.2m =4y=2x-16aŭ= 28 b=_-16Equation of Line: 4y - 2x = 16Rewritten: ya2x-16Im =2x + m = -2I lineI line
From the given equation :
[tex]4y-2x=16[/tex]This can be written in the slope-intercept form :
[tex]y=mx+b[/tex]where m is the slope
and b is the y-intercept
Rewriting the equation :
[tex]\begin{gathered} 4y-2x=16 \\ 4y=2x+16 \\ y=\frac{2}{4}x+\frac{16}{4} \\ y=\frac{1}{2}x+4 \end{gathered}[/tex]The equation will be y = 1/2 x + 4
the slope is m = 1/2
nd the y-intercept is b = 4
Note that parallel lines have the same slope.
So the slope of parallel line is m = 1/2
Perpendicular lines have a slope of negative reciprocal with each other.
So the slope of perpendicular line to this line is m = -2
Equation of parallel line :
we have :
[tex]y=\frac{1}{2}x+b[/tex]Let's say the line passes at the origin (0, 0)
If a line passes thru the origin, the y-intercept is always b = 0
Therefore, the equation of parallel line is y = 1/2 x
quation of perpendicular line :
we have :
[tex]y=-2x+b[/tex]Let's also say that the line passes at the origin (0, 0)
and the y-intercept is also b = 0
he equation of the perpendicular line is yy = -2x
raphing these equations will be :
Original line (Blue)
Parallel line (Orange)
Perpendicular line (Pink)
y-intercepts :
(0, 0) and (0, 4)
1. Use complete sentences to explain how the special angles created by the Intersection of A and B by D can beused to solve for x.2. Solve for x, showing all of your work.3. Find the measure of <6.
According to the graph we have:
1. If the lines A and B cut by the secant D are parallel, then the collateral angles are supplementary, i.e. add up to 180°. In this case:
[tex](3x+7)+(4x+5)=180[/tex]2. Solve for x:
[tex]\begin{gathered} 3x+7+4x+5=180 \\ 7x+12=180 \\ 7x+12-12=180-12 \\ 7x=168 \\ \frac{7x}{7}=\frac{168}{7} \\ x=24 \end{gathered}[/tex]Answer: x = 24
3. Angle 6 corresponds to angle 3x + 7 so they are equal. So:
[tex]\angle6=3x+7[/tex]Where: x = 24
Substitute the value:
[tex]\angle6=3(24)+7=72+7=79[/tex]Answer: <6 = 79°
1. A survey of 36 students was conducted to find out how many students enjoy playing volleyball, and 17 said they did. If 648 students were surveyed, how many would say they enjoy playing volleyball?
The total number of students calculated with the method called simplification and who are playing volleyball is 206.
How simplification method work?
In mathematics, the simplification method is used for the equation formation for the problem statements. And it also convert the complicated expression into simpler one to make the calculation easy.
According to the question, the given survey data for the playing volleyball is written below and it is solved by the simplification method:
survey of students: 36
play volleyball: 17
As per question, the simplification expression for the given statement which state that, if the survey of 648 students how many students play volleyball?
Therefore, the required simplified expression can be written as:
Required expression: 648÷36= 18
Now, playing volleyball =18×17=206 students play volleyball
Hence, the total number of students calculated with the method called simplification who are playing volleyball is 206.
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The cost in dollars of making x items is given by ()=10+500. The fixed cost is
determined when zero items are produced. Find the fixed cost for this item. What
is the cost of making 25 items? Suppose the maximum cost allowed is $1500.
What are the domain and range of the cost function, C(x) ?
The answer is
(a) the fixed cost when zero items are produced is $500 .
(b) cost for making 25 items is $750 .
(c) the domain and range of cost function is [0,100] and [500,1500] respectively .
It the question ,
it is given that
the cost function is C(x)=10x+500
Part(a)
to determine the fixed cost when 0 items are produced
Since 0 items are produced , we substitute the value x=0 in the cost function , we get
C(0)=10(0)+500
= 500
the fixed cost is $500.
Part(b)
to find the cost of making 25 items , we substitute x=25
On substituting the x=25 , we get
C(25)=10(25)+500
= 250+500
=750
the cost for 25 items is $750.
Part(c)
to find the domain of the cost function C(x)
Given that the maximum cost allowed is 1500
So, 1500=10x+500
10x=1500-500
10x=1000
x=100
So minimum 0 items and maximum 100 items can be produced ,
hence the Domain is [0,100]
to find the range
substituting x=0, the cost = $500
on substituting x=100 , the cost = $1500
the Range is [500,1500]
Therefore , (a) the fixed cost when zero items are produced is $500 .
(b) cost for making 25 items is $750 .
(c) the domain and range of cost function is [0,100] and [500,1500] respectively .
The given question is incomplete , the complete question is
The cost in dollars of making x items is given by C(x)=10x+500. The fixed cost is determined when zero items are produced.
(a) Find the fixed cost for this item.
(b) What is the cost of making 25 items?
(c) Suppose the maximum cost allowed is $1500. What are the domain and range of the cost function, C(x) ?
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Question 1
Scientists are studying the growth of a particular virus in a large community.
The case count, C, in the community after d days can be modeled with the equation: C =
181(1.07)d
What type of model is the equation?
O Linear Growth
O Exponential Growth
O Exponential Decay
O Linear Decay
Linear Decay is the equation .
What is Linear Decay?
A line with a negative slope can be used to model linear decline. for instance, that James now withdraws $10 every month from her piggybank, which originally held $100. The remaining balance in the piggybank can then be predicted using. A = 100 - 10t.Is linear decay exponential?
A linear function reduces the original number by the same amount each time, but exponential decay reduces the original amount by a constant percentage over time. Exponential decay differs from linear decay in this way: the decay factor depends on a percentage of the original quantity.Scientists are studying the growth of a particular virus in a large community.
The case count, C, in the community after d days can be modeled with the equation: C = 181(1.07)d
This equation is showing Linear Decay .
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9 ft19 ftPlease refer to the rounding rules in the instructions.Circumference of the base = 59.5feetArea of the base = 254.3square feetSlant height = 19feetHeight = 16.7feetLateral area =536.9square feetSurface area = 791.2square feetVolume =cubic feetBlank 1: 59.5Blank 2: 254.3Blank 3: 19Blank 4: 16.7Blank 5: 536.9Blank 6: 791.2Blank 7:
The volume of a right cone is one-third of the product of the area of the base B and the
[tex]V=\frac{1}{3}Bh[/tex]Since the area of the base and the height is already given, substitute the values in to the equation and then simplify.
[tex]\begin{gathered} V=\frac{1}{3}(254.3)(16.7) \\ =\frac{1}{3}(4246.81) \\ \approx1415.603 \end{gathered}[/tex]We may also find the exact value by substituting the given values into the equation below.
[tex]V=\frac{\pi r^2h}{3}[/tex]where V is the volume, r is the radius, and h is the height.
To obtain the exact value of the height, we use the Pythagorean theorem.
[tex]\begin{gathered} a^2+b^2=c^2 \\ a^2=c^2-b^2 \\ a=\sqrt[]{c^2-b^2} \end{gathered}[/tex]where a and b are the legs of the formed right triangle while c is its hypothenuse.
From the figure, the slant height is the hypothenuse while the radius, 9 ft, serve as one of the legs. Thus, the other leg, which is the height of the cone can be solved as follows.
[tex]\begin{gathered} a=\sqrt[]{19^2-9^2} \\ =\sqrt[]{361-81} \\ =\sqrt[]{280} \end{gathered}[/tex]Therefore, the height of the cone is as stated above.
Substitute the obtained height and the radius into the second formula that was stated.
[tex]\begin{gathered} V=\frac{\pi r^2h}{3} \\ V=\frac{\pi(9^2)(\sqrt[]{280})}{3} \end{gathered}[/tex]Simplify the right side of the equation. Evaluate the exponential expression.
[tex]V=\frac{\pi(81)(\sqrt[]{280})}{3}[/tex]Multiply the numerator and then divide it by 3.
[tex]\begin{gathered} V=\frac{\pi(81)(\sqrt[]{280})}{3} \\ \approx\frac{(3.1416)(81)(16.7332)}{3} \\ \approx\frac{4258.0907}{3} \\ \approx1419.36 \end{gathered}[/tex]Note that the value that we obtain at first, 1415,603, is slightly different from the one that we obtained, which is 1419.36, since there are values that we already rounded off before substituting the values in the equation.
Therefore, to be more exact, it is best to indicate that the volume of the given cone is approximately 1419.36 ft³.
Hey can you solve #2 for me please, I’ve been having trouble figuring out what I’m doing wrong.Can you apply the dilation “D” to the polygon with the given vertices
New coordinate are P(0,0) ,Q(-4,2) ,R(6,6)
What is coordinate plane ?A coordinate plane is a two-dimensional surface made up of two number lines. It is produced when a horizontal line crosses the origin, which is the location where the X- and Y-axes meet. The numbers on a coordinate grid are used to find points. Using a coordinate plane, you may graph points, lines, and many other things. It functions as a map and gives precise driving instructions between two locations. The definition of a coordinate plane is as follows: A coordinate plane, also known as a rectangular coordinate plane grid, is made when the X-axis and Y-axis, two horizontal lines, cross.
Given that :P(0,0) , Q(-2,1) , R(3,3)
(x,y)→(2x,2y)
P(0,0)
Q(-4,2)
R(6,6)
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(-35) x 6 =? i need help!
Answer: -210 is your answer
Step-by-step explanation:
I took the test and worked it out
Answer: -210
Step-by-step explanation: remembered answering this question once and -210 was the right answer
Vertical analysis
The following income statement data for AT&T Inc. and Verizon Communications Inc. were taken from their recent annual reports (in millions):
AT&T Verizon
Revenues $132,447 $127,079
Cost of services (expense) 60,611 49,931
Selling and marketing expense 39,697 41,016
Depreciation and other expenses 20,393 16,533
Operating income $ 11,746 $ 19,599
Required:
Question Content Area
a. Prepare a vertical analysis of the income statement for AT&T. Round to one decimal place.
AT&T
Income Statement
Amount Percent
Revenues $fill in the blank 42f583fcffe2ffb_1
132,447
fill in the blank 42f583fcffe2ffb_2
100
%
Cost of services (expense) fill in the blank 42f583fcffe2ffb_3
60,611
fill in the blank 42f583fcffe2ffb_4
%
Selling and marketing expense fill in the blank 42f583fcffe2ffb_5
39,697
fill in the blank 42f583fcffe2ffb_6
%
Depreciation and other expenses fill in the blank 42f583fcffe2ffb_7
20,393
fill in the blank 42f583fcffe2ffb_8
%
Operating income $fill in the blank 42f583fcffe2ffb_9
11,746
fill in the blank 42f583fcffe2ffb_10
%
Question Content Area
b. Prepare a vertical analysis of the income statement for Verizon. Round to one decimal place.
Verizon
Income Statement
blank Amount Percent
Revenues $fill in the blank 9f21aef38fdffbf_1
fill in the blank 9f21aef38fdffbf_2
%
Cost of services (expense) fill in the blank 9f21aef38fdffbf_3
fill in the blank 9f21aef38fdffbf_4
%
Selling and marketing expense fill in the blank 9f21aef38fdffbf_5
fill in the blank 9f21aef38fdffbf_6
%
Depreciation and other expenses fill in the blank 9f21aef38fdffbf_7
fill in the blank 9f21aef38fdffbf_8
%
Operating income $fill in the blank 9f21aef38fdffbf_9
fill in the blank 9f21aef38fdffbf_10
%
a) A vertical analysis of the income statement for AT&T is as follows:
AT&T Percent
Revenue $132,447 100%
Cost of Services (Expenses) 60,611 45.8%
Selling & Marketing Expense 39,697 30.0%
Depreciation & other expenses 20,393 15.4%
Operating Income $11,746 8.9%
b) A vertical analysis of the income statement for Verizon is as follows:
Verizon Percent
Revenue $127,079 100%
Cost of Services (Expenses) 49,931 39.3%
Selling & Marketing Expense 41,016 32.3%
Depreciation & other expenses 16,533 13.0%
Operating Income $19,599 15.4%
What is a vertical analysis?A financial statement vertical analysis is a comparison of each line item on the financial statement as a percentage of the base figure.
For the income statement, the base figure is the revenue, which is set to 100%. For the balance sheet, the base figure is the total assets or total liabilities and equity, which are set to 100%.
The vertical analysis uses the following formula = Financial statement line item divided by the total base figure X 100.
AT&T Percent
Revenue $132,447 100% ($132,447/$132,447 x 100)
Cost of Services (Expenses) 60,611 45.8% ($60,611/$132,447 x 100)
Selling & Marketing Expense 39,697 30.0% ($39,697/$132,447 x 100)
Depreciation & other expenses 20,393 15.4% ($20,393/$132,447 x 100)
Operating Income $11,746 8.9% ($11,746/$132,447 x 100)
Verizon Percent
Revenue $127,079 100% ($127,079/$127,079 x 100)
Cost of Services (Expenses) 49,931 39.3% ($49,931/$127,079 x 100)
Selling & Marketing Expense 41,016 32.3% ($41,016/$127,079 x 100)
Depreciation & other expenses 16,533 13.0% ($16,533/$127,079 x 100)
Operating Income $19,599 15.4% ($19,599/$127,079 x 100)
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