For inequality –3(2x – 5) < 5(2 – x) the correct option is (–6x + 15 < 10 – 5x).
What is inequality?
An inequality is a mathematical statement that describes a relationship between two values or expressions, indicating that they are not equal.
To solve the inequality –3(2x – 5) < 5(2 – x), we need to simplify the expression first.
Starting with the left-hand side, we can distribute the –3 to get:
–3(2x – 5) = –6x + 15
For the right-hand side, we can distribute the 5 to get:
5(2 – x) = 10 – 5x
Substituting these back into the original inequality, we get:
–6x + 15 < 10 – 5x
To solve for x, we can first move all the x terms to one side by adding 5x to both sides:
–x + 15 < 10
Then, we can move the constant term to the other side by subtracting 15 from both sides:
–x < –5
Finally, we can divide both sides by –1 (remembering to flip the inequality sign since we're dividing by a negative number) to get:
x > 5
So the first correct representation of the inequality is x > 5.
To get the second correct representation, we can also start with the inequality –6x + 15 < 10 – 5x, and move all the x terms to one side:
–6x + 5x < 10 – 15
So second option (–6x + 15 < 10 – 5x) are correct representations of the inequality.
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1. Browse laptops from three retailers to get a rough idea of what laptops are being sold.
You can get a sense of what laptops are available, which brands are well-liked, and what specifications are shared by various models by looking through these three stores.
What is the browse laptops?Amazon:
Go to Amazon's homepage and hover over the “Electronics” category in the top menu bar.
Click on “Computers & Accessories” in the dropdown menu.
Under “Laptops,” you can browse through the different categories such as “
2-in-1 Laptops," "Traditional Laptops," and "Gaming Laptops."
You can also use the filtering options on the left-hand side of the page to narrow down your search by brand, price, screen size, and more.
Best Buy:
Go to Best Buy's homepage and click on "Laptops & Computers" in the top menu bar.
You can browse through the different categories such as "Laptops," "Gaming PCs," and “Chromebooks.”
You can also use the filtering options on the left-hand side of the page to narrow down your search by brand, price, screen size, and more.
Dell:
Go to Dell's homepage and click on “Laptops & 2-in-1 PCs" in the top menu bar.
You can browse through the different categories such as "Consumer Laptops," "Gaming Laptops," and "Mobile Workstations.”
You can also use the filtering options on the left-hand side of the page to narrow down your search by brand, price, screen size, and more.
Therefore, By browsing through these three retailers, you can get an idea of what laptops are available, what brands are popular, and what features and specs are common across different models.
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a classroom recorded all the heights, in inches, of their students and calculated the mean, median and mode. the heights are listed below: 38,38,39,39,40,40,40,40,40,40,40,41,42,42,43 after this project, a new student joined the class and wanted to be included in the data. the new student is much taller than the rest of the class at a height of 51 inches. what impact will this have on the statistics that were calculated?
The impact on the mode will be insignificant.
When a new student joined the classroom with a height of 51 inches, the statistics that were calculated will be
impacted in the following ways:
Mean: The mean is calculated by adding up all the heights and then dividing the total by the number of heights. Since
the new student is much taller than the rest of the class, the addition of 51 to the data set will increase the sum of the
data set by a significant amount. This will cause the mean to increase.
Median: The median is the middle number when the data set is ordered from lowest to highest. Since the data set has
an odd number of values, the median is 40. When a new student joins the class with a height of 51 inches, this will
cause the median to increase to 40.5.
Mode: The mode is the number that appears most often in the data set. Since the mode of the given data is 40, adding
a new student with a height of 51 will not change the mode. Therefore, the impact on the mode will be insignificant.
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Yolanda and her friends were asked to paint a mural on a wall at the park. Yolanda is making a scale drawing of the mural. If every 2 inches of her drawing represents 3 feet of the actual wall, what is the area in square feet of the actual mural?
If every 2 inches of Yolanda's drawing represents 3 feet of the actual wall, we can use the scale factor to convert the dimensions of the drawing to the dimensions of the actual wall.
Since we are dealing with area, we need to square the scale factor.
2 inches : 3 feet
(2 inches / 3 feet)^2 = (2/36)² = 1/324
This means that every square inch of Yolanda's drawing represents 1/324 square feet of the actual wall.
If the area of the mural in Yolanda's drawing is A square inches, then the area of the actual mural is:
A (square inches) x (1/324) (square feet per square inch) = A/324 square feet
Therefore, to find the area of the actual mural in square feet, we need to first find the area of the mural in Yolanda's drawing and then divide by 324.
If the area of the mural in Yolanda's drawing is, for example, 500 square inches, then the area of the actual mural is:
500 (square inches) / 324 = 1.54 square feet (rounded to two decimal places)
Therefore, the area of the actual mural is 1.54 square feet.
[tex] \: \: [/tex]
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Jake has 32 quarters on his desk and molly has q quarter in her purse
which algebraic expression represents the total number of quarters that Jake and molly have
According to given information, the algebraic expression that represents the total number of quarters that Jake and Molly have is: 32 + q.
What is algebraic expression?
An algebraic expression is a mathematical phrase that contains numbers, variables, and arithmetic operations, such as addition, subtraction, multiplication, and division. It can also include exponents, roots, and other mathematical symbols.
The algebraic expression that represents the total number of quarters that Jake and Molly have is:
32 + q
where 32 represents the number of quarters that Jake has on his desk and q represents the number of quarters that Molly has in her purse.
Adding these two quantities together gives the total number of quarters that Jake and Molly have.
Therefore, the algebraic expression that represents the total number of quarters that Jake and Molly have is:
32 + q
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Please help me out!
A telephone poll asked people whether they like playing golf. 3,360 people said they like playing golf and 3,640 people said they do not like playing golf. What percentage of the people polled like playing golf?
Write your answer using a percent sign.
48% of the people polled like playing golf.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.
The percentage of people polled who like playing golf can be calculated by dividing the number of people who like golf (3,360) by the total number of people polled (3,360 + 3,640 = 7,000) and then multiplying by 100 to express the answer as a percentage:
(3360 ÷ 7000) x 100% = 48%
Therefore, 48% of the people polled like playing golf.
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Adults leaving a library were surveyed about the possibility of an annual fee of $100
to support the library. Of those surveyed, 80% said they were in favor of the fee.
The survey takers concluded incorrectly that 80% of the adult residents of the city
are in favor of the fee.
What would be a better survey? What might be a more believable value for the
percent of adult residents of the city who are in favor of the fee?
The better survey would be when the possibility of adults in favour of fee and not in favour of fee is same that is 50% each.
Explain about the unbiased survey:Everything in surveys revolves around asking the appropriate questions in the right ways since they are meant to elicit feedback. Many polls purposefully and unintentionally ask one-sided questions.
An objective question attempts to avoid using leading language and is fact-based rather than judgmental.
Biased questionnaire items use word choice and sentence structure in a way that affects how respondents react. This is sometimes done on purpose. This usually happens as a result of inadequate survey planning and assessment.
Here are a few advices.
Check your questions to make sure they won't lead to bias in the responses.Make sure all potential responses are included in the answer choices.Ask as few and straightforward inquiries as you can.Don't ask participants to think more than is necessary.Given query:
When adults left a library, they were asked if they would be open to paying a $100 yearly fee to support it. 80% of those polled indicated their support for the fee.The survey respondents came to the false conclusion that the fee is supported by 80% of the city's adult residents.Thus, the better survey would be when the possibility of adults in favour of fee and not in favour of fee is same that is 50% each.
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Find the surface area of the sphere
The calculated value of the surface area of the sphere is 676π
Finding the surface area of the sphereGiven that
Radius, r = 13 inches
The formula for the surface area of a sphere is:
Surface area = 4πr^2
where r is the radius of the sphere
Substituting the given value of radius r = 13 inches, we get:
Surface area = 4π * 13^2
So, we have
Surface area = 676π
Hence, the surface area is 676π
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3. Helena wants to build a plant stand like the one
shown, and she wants to find its volume. Draw
line(s) to show how she might divide the stand
into two or more sections to make finding the
volume easier.
Find the volume of each section you identified.
Then find the total volume of the stand. Explain.
The total volume of the plant stand is given by the sum of these expressions: (x+1)³ + (x+1) * (x+1) * (x-1) + (2x+3) * (2x-2) * (x+1)
What is volume?Volume refers to the amount of space occupied by an object or substance. It is typically measured in cubic units (such as cubic centimeters, cubic inches, or liters) and is used to describe the size or capacity of an object or container. Volume can also refer to the loudness or intensity of a sound. In physics, volume is an important measurement in determining the properties and behavior of gases, liquids, and solids.
Here,
Let's calculate the volume of each section based on the given sides.
Cube with sides x+1:
The formula for the volume of a cube is V = side³, where side is the length of one of its sides. In this case, the side length of the cube is x+1, so the volume of this section would be:
V1 = (x+1)³
Cuboid with sides x+1, x+1, and x-1:
The formula for the volume of a cuboid is V = length * width * height. In this case, the length would be x+1, the width would be x+1, and the height would be x-1. So the volume of this section would be:
V2 = (x+1) * (x+1) * (x-1)
Cuboid with sides 2x+3, 2x-2, and x+1:
Similarly, using the formula for the volume of a cuboid, the volume of this section would be:
V3 = (2x+3) * (2x-2) * (x+1)
Now, to find the total volume of the plant stand, we can add up the volumes of all three sections:
Total volume = V1 + V2 + V3
= (x+1)³ + (x+1) * (x+1) * (x-1) + (2x+3) * (2x-2) * (x+1)
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amy, beth, and jo listen to four different songs and discuss which ones they like. no song is liked by all three. furthermore, for each of the three pairs of the girls, there is at least one song liked by those two girls but disliked by the third. in how many different ways is this possible? (2012amc10b problem 24 or 2012amc12b problem 16) (a) 108 (b) 132 (c) 671 (d) 846 (e) 1105
The number of different ways in which no song is liked by all three and there is at least one song liked by those two girls but disliked by the third is (b) 132 ways.
Let the song that is liked by Amy and Beth (but not Jo), Beth and Jo (but not Amy), and Amy and Jo (but not Beth), be denoted as : AB, BJ, and AJ.
Similarly, let the letters "A, B, J, and N" denote the song that is liked by only Amy, only Beth, only Jo, and none of them, respectively.
We know that there is at least 1 AB, BJ, and AJ, there must be 3 songs out of 4 songs which Amy, Beth, and Jo listened to.
The fourth song can be of any type : N, A, B, J, AB, BJ, and AJ (there is no ABJ because "no-song" is liked by all three),
So, we must find the number of ways to rearrange AB, BJ, AJ and a song from the set {N, A, B, J, AB, BJ, AJ}.
⇒ Case 1: Fourth song choices = N, A, B, J
All the four of choices for fourth song are different from the first 3 songs.
⇒ Number of ways to rearrange = 4! × 4 choices = 96.
⇒ Case 2: Fourth song choices = AB, BJ, AJ
All 3 of choices for fourth song repeat in the first three songs.
So, Number of ways to rearrange = (4!/2!) × 3 = 36,
So, total number of ways = 96 + 36 = 132.
Therefore, the required number of ways of arrangement is 132 ways, the correct option is (b).
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The given question is incomplete, the complete question is
Amy, Beth, and Jo listen to four different songs and discuss which ones they like. no song is liked by all three. furthermore, for each of the three pairs of the girls, there is at least one song liked by those two girls but disliked by the third. in how many different ways is this possible?
(a) 108
(b) 132
(c) 671
(d) 846
(e) 1105
Find the value of the variable in the equations given.
ANSWER: EQUATIONS:
a = ? a + 7 = 20
c = ? c - 12 = 29
b = ? 46 + 12 = 60
x = ? 5x + 2x = 35
z = ? 127 - 57 - 9 = 40
y = ? 5y + 3y + 4 = 68
x = ? 2(x + 4) = 24
q = ? 6(5g - 7) = 18
pls answer this plsplspls
I will solve each equation one by one to find the value of the variables:
The Math Solutionsa + 7 = 20
a = 20 - 7
a = 13
c - 12 = 29
c = 29 + 12
c = 41
46 + 12 = 60
b is not present in the equation. This equation cannot be used to find the value of b.
5x + 2x = 35
7x = 35
x = 35 / 7
x = 5
127 - 57 - 9 = 40
z is not present in the equation. This equation cannot be used to find the value of z.
5y + 3y + 4 = 68
8y = 68 - 4
8y = 64
y = 64 / 8
y = 8
2(x + 4) = 24
2x + 8 = 24
2x = 24 - 8
2x = 16
x = 16 / 2
x = 8
6(5g - 7) = 18
30g - 42 = 18
30g = 18 + 42
30g = 60
g = 60 / 30
g = 2
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a cannon ball is launched straight up into the air from a height of 8 feet above the ground and with a velocity of 420 feet per second
Write an equation to model the distance d, in feet the cannon ball is above the ground t, seconds after it was fired.
ow must the units be set up in order to get from the number of eggs used to make a certain number of cookies to the number of eggs needed to make some other number of cookies?
To get from the number of eggs used to make a certain number of cookies to the number of eggs needed to make some other number of cookies, you would use a proportional relationship.
Let's say x represents the number of eggs used to make a certain number of cookies, y represents the number of cookies made, and z represents the number of eggs needed to make some other number of cookies.
Then, we can set up the proportion:
x eggs / y cookies = z eggs / (some other number of cookies)
We can then solve for z by cross-multiplying:
z eggs = x eggs * (some other number of cookies) / y cookies
This formula tells us how many eggs are needed to make the specified number of cookies, based on the number of eggs used and the number of cookies originally made.
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Diagonals of a parallelogram bisect each other true or false
Can someone solve this please
The association on the line is a negative linear assosciation and other solutions are shown below
Calculating the slopeTo find the slope of the line passing through the given points, we use the slope formula
slope = (change in y) / (change in x)
Let's use the points (0, 90) and (8, 40) to find the slope:
slope = (40 - 90) / (8 - 0) = -50 / 8 = -6.25
Calculating the y-interceptThe y-intercept is 90 i,e, when x = 0
Calculating the equation of a lineThe equation is represented as
y = mx + c
Where
m = slope and c = y when x = 0
So, we have
y = -6.25x + 90
The association on the line is a negative linear assosciation
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A diameter of a circle has its endpoints at (-2,-1) & (4,7). What is the equation of the circle.
Check the picture below.
so the center of the circle is the midpoint of that diameter, and its radius is half its length.
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 4 -2}{2}~~~ ,~~~ \cfrac{ 7 -1}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 6 }{2} \right)\implies \stackrel{ center }{(1~~,~~3)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ r(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{ radius }{r}=\sqrt{(~~4 - (-2)~~)^2 + (~~7 - (-1)~~)^2} \implies r=\sqrt{(4 +2)^2 + (7 +1)^2} \\\\\\ r=\sqrt{( 6 )^2 + ( 8 )^2} \implies r=\sqrt{ 36 + 64 } \implies r=\sqrt{ 100 }\implies r=10 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{1}{h}~~,~~\underset{3}{k})}\qquad \stackrel{radius}{\underset{10}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 1 ~~ )^2 ~~ + ~~ ( ~~ y-3 ~~ )^2~~ = ~~10^2\implies {\large \begin{array}{llll} (x-1)^2+(y-3)=100 \end{array}}[/tex]
Jeremy rides his bike at a rate of 12 miles per hour. The table below
represents the number of hours and miles Kevin rides. Assume both bikers
ride at a constant rate.
Answer:
A) Jeremy has the greater speed.
B) y = 23x
C) See graph
D) The slope is 23. This means that Lauren can travel 23 miles in 1 hour.
Step-by-step explanation:
Part A:
Kevin's rate is 11.5 miles per hour.
Take two points, I used (2,23) and (4,46) to find the rate for Kevin.
Find the change in y over the change in x. The y values are 46 and 23. The x values are 4 and 2. You find the change by subtracting
[tex]\frac{46-23}{4-2}[/tex] = [tex]\frac{23}{2}[/tex] = 11.5
Part B:
If Kevin's rate is 11.5, then Lauren's rate is 23
Part C:
See graph
Part D :
The slope for C is 23. This means that Lauren can ride 23 miles in one hour.
Helping in the name of Jesus.
please please please please please please please please please please please help me out
Examine the following typical corporate bond listing: A 5-column table with 1 row. Column 1 is labeled Bonds with entry N Y Tel 7 and one-fourth 33. Column 2 is labeled current yield with entry 6.9. Column 3 is labeled Volume with entry 18. Column 4 is labeled Close with entry 101 and three-fourths. Column 5 is labeled net change with entry negative startFraction 1 Over 8 EndFraction. In the name column, NYTel is the abbreviated name of the company (New York Telephone) issuing the bond. What was the closing price of the bond? What was the dollar amount? a. 101Three-fourths; $101,750 b. 7One-fourth; $7250 c. 101Three-fourths; $1017.50 d. 107One-fourth; $1072.50
This bond has a Current yield of 6.9 percent, a volume of 18, and a net change of negative one-eighth. The correct answer is (a) 101Three-fourths; $101,750.
The bond listing provided is a typical example of how Corporate bonds are displayed. The table consists of 5 columns with 1 row, where each column provides specific information about the bond.
The first column displays the name of the bond, which in this case is NYTel 7 and one-fourth 33, indicating that it is a bond issued by New York Telephone.
The second column shows the current yield of the bond, which is 6.9 percent.
The third column displays the volume of the bond, which is 18.
The fourth column provides the closing price of the bond, which is 101 and three-fourths.
Finally, the fifth column shows the net change of the bond, which is negative one-eighth.
To answer the question, we need to determine the closing price and dollar amount of the bond. According to the bond listing, the closing price of the bond is 101 and three-fourths. To calculate the dollar amount, we need to multiply the closing price by the face value of the bond. Assuming that the face value of the bond is $1,000, the dollar amount of the bond would be $101,750 (101.75 x 1000).
Therefore, the correct answer is (a) 101Three-fourths; $101,750. This bond has a current yield of 6.9 percent, a volume of 18, and a net change of negative one-eighth. Understanding how to read and interpret bond listings is crucial for investors who want to make informed investment decisions.
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4÷2=
12÷2=
6÷3=
45÷9 =
Answer:
4÷2=2
12÷2=6
6÷3=3
45÷9 =5
Step-by-step explanation:
how large must be in order for to exceed 4? note: computer calculations show that for to exceed 20, and for to exceed 100, .
The value of the N must be in order of the 31 so that the value of the Sn will get exceeded by 4.
Only when the kind of sequence is known can the sum of n words in a sequence be calculated. Normally, while computing the sum of an n-number of terms, we take into account arithmetic progression.
The common distinction between each following phrase and each preceding term remains unchanged throughout this process. Natural numbers are an illustration of AP, where the common difference is 1. Hence, in order to determine the sum of all natural numbers, we must be aware of the formula.
[tex]S_N = \sum^N_{k=1} \frac{1}{k}[/tex]
= 1 + 1/2 + 1/3 + 1/4 + ..... 1/N
It is a harmonic series,
Therefore, by trial and error method we get N = 31 to exceed Sn = 4
There are some elimination methods,
ln N + 1/N < Sn < ln N+1
we want Sn > 4
ln N+1/N < 4
maximum value of N is ln N+1/N =4
4<ln N+1 → ln N > 3, N > e³
5<ln N+1 → ln 4, N > e⁴
For Sn to exceed it value maybe in between
e³ < N < e⁴.
20.08 < N < 54.5
As I said it is an approximation it won't give exact value.
By taking a value in that range and check for desired value.
for N = 31 Sn willl exceed '4'.
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Complete question:
How large must N be in order for
[tex]S_N = \sum^N_{k=1} \frac{1}{k}[/tex]
to exceed 100 to exceed 4? Note: Computer calculations show that for SN to exceed 20, N = 272, 400, 600 and for Sn to exceed 100, N = 1.5x10⁴³.
N = ?
How many solutions does the system of equations below have?
2x - 3y = 6
4x - 6y = 11
For any value of x and y, this equation cannot be true. As a result, the equation system has no solution.
0x + 0y = 1
The elimination approach can be used to resolve the system of equations below.
How does elimination work?
The elimination method is a method for algebraically resolving systems of linear equations. Using fundamental arithmetic operations, we can eliminate any one of the variables in the elimination technique, and then we can simplify the equation to determine the value of the remaining variable1.
The elimination procedure involves the following steps:
1. Choose one variable to leave out.
2. In order to make the coefficients of that variable opposite in sign, multiply or divide both equations by a non-zero constant.
3. Adjust the resulting equations such that the selected variable is removed.
4. Simplify and ascertain the other variable's value.
According to the question:
2x - 3y = 6
4x - 6y = 11
The result of multiplying the first equation by two is:
4x - 6y = 12
We can now take the second equation out of this equation:
4x - 6y = 12
(4x - 6y = 11)
—————————
0x + 0y = 1
For any value of x and y, this equation cannot be true.
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if it cost $15 to fill a gas tank in 1995, how much would it have cost to fill the same tank in 2015?
If the cost to fill a gas tank in 1995 is $15 then the cost to fill a gas tank in 2015 is equals to the $31.25.
Price Index is a effective method of comparing relative change in the price of a quantity with respect to its price in a reference year. This year which we use as a reference is called the base year and price index is ratio of the price of a product in a year to its price in the base year ( expressed in percentage ).
The cost to fill a gas tank in 1995 = $15
Price index in 1995 = 100.8%
price index in 2015 = 210.0%
In this case we want to determine the cost to fill a gas tank in 2015. Let the required cost value be x dolars. Using the formula, price index in 1995/price index in 2015 = reference value/ value in 2015
=> 100.8% /210% = 15/x
=> 2015 cost value, x =( 15 × 210 )/100.8
=> x = 3150/100.8
=> x = 31.25
Hence, required value is $31.25.
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Complete question:
If it cost $15 to fill a gas tank in 1995, how much would it cost to fill the same tank in 2015. 1995 index is 100.8%
2015 index is 210.0% round your answer nearest cent.
Find the first derivative of y=e^4x sin 4x
We use the product rule and the chain rule to find the derivative of y = e^4x sin 4x.
y = e^4x sin 4x
y' = (e^4x)(4sin 4x + cos 4x(4))
y' = 4e^4x(sin 4x + cos 4x)
Therefore, the first derivative of y=e^4x sin 4x is y' = 4e^4x(sin 4x + cos 4x).
Interpretation: The first derivative gives the instantaneous rate of change of the function at each point. In this case, the derivative represents the rate at which the amount of medicine remaining in a person's bloodstream changes with respect to time x. The function has a maximum or minimum when the first derivative is equal to zero.
What is the radius of a sphere with a volume of 12,348π cubic feet?
Answer:Radius = 21
Step-by-step explanation:
Volume of a sphere = 4/3 * pie * radius^3
12,348 pie = 4/3 * pie radius ^3
12,348 = 4/3 * radius^3
(12,348 * 3)/ 4 = radius^3
9261 = radius^3
radius = 21
write in fully simplified slope intercept form please
Answer:
Step-by-step explanation:
The measure of angle w is 100°, and the measure of angle z is 68°. a triangle has angles x, y, z. the exterior angle to angle x is w. what is the measure of angle y? 12° 32° 80° 168°
The measure of angle y is 32°.
To find the measure of angle y, follow these steps:
1. Since the exterior angle to angle x is w, and w measures 100°, we can use the fact that the sum of an interior angle and its corresponding exterior angle is 180°.
So, angle x = 180° - 100° = 80°.
2. Now we know that a triangle has angles x, y, and z.
The sum of angles in a triangle is always 180°.
We have x = 80° and z = 68°,
so we can find angle y as follows:
y = 180° - (80° + 68°)
= 180° - 148°
= 32°.
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Over a period of one week, the Dow Jones Industrial Average (DJIA) did the following: On Monday the DJIA went down by 3.2%, on Tuesday it went up by 11.2%, on Wednesday it went up by 0.7%, on Thursday it went down by 4.8%, and on Friday it went down by 9.4%. Find the percentage increase/decrease of the DJIA over the week. Round your answer to the nearest hundredth of a percentage.
The percentage increase/decrease of the DJIA over the week is a decrease of 6.53%.
What is percentage?Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%".
A decreased percentage refers to the amount or rate by which a quantity or value has decreased from its original or initial value, expressed as a percentage of the original value.
According to given information:
To find the percentage increase/decrease of the DJIA over the week, we need to calculate the overall change in the index and express it as a percentage of the initial value.
Let's assume that the DJIA started the week at a value of 100. Then, the following changes would occur:
On Monday, it went down by 3.2%, so its value decreased to 96.8.
On Tuesday, it went up by 11.2%, so its value increased by 11.2% of 96.8, or 10.82, to reach 107.62.
On Wednesday, it went up by 0.7%, so its value increased by 0.7% of 107.62, or 0.75, to reach 108.37.
On Thursday, it went down by 4.8%, so its value decreased by 4.8% of 108.37, or 5.20, to reach 103.17.
On Friday, it went down by 9.4%, so its value decreased by 9.4% of 103.17, or 9.70, to reach 93.47.
Therefore, over the week, the DJIA decreased by 6.53% (from 100 to 93.47).
Rounding this to the nearest hundredth of a percentage, we get a decrease of 6.53%.
So, the percentage increase/decrease of the DJIA over the week is a decrease of 6.53%.
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a manufacturer of a certain type of large ma- chine wishes to buy rivets from one of two manufac- turers. it is important that the breaking strength of each rivet exceed 10,000 psi. two manufacturers (a and b) offer this type of rivet and both have rivets whose breaking strength is normally distributed. the mean breaking strengths for manufacturers a and b are 14,000 psi and 13,000 psi, respectively. the stan- dard deviations are 2000 psi and 1000 psi, respectively. which manufacturer will produce, on the average, the fewest number of defective rivets?
The manufacturer B is calculated to produce, on the average, the fewest number of defective rivets amongst all the manufacturers.
To determine which manufacturer will produce, on average, the fewest number of defective rivets, we need to calculate the proportion of defective rivets for each manufacturer.
Let X be the breaking strength of a rivet from manufacturer A, and let Y be the breaking strength of a rivet from manufacturer B. Then:
P(X < 10000) = P((X - μ_A) / σ_A < (10000 - μ_A) / σ_A) = P(Z_A < -2.5) ≈ 0.0062
where Z_A is a standard normal random variable, and we use the given values μ_A = 14000 psi and σ_A = 2000 psi.
Similarly:
P(Y < 10000) = P(Z_B < -3) ≈ 0.0013
where Z_B is a standard normal random variable, and we use the given values μ_B = 13000 psi and σ_B = 1000 psi.
Therefore, the proportion of defective rivets for manufacturer A is approximately 0.0062, and the proportion of defective rivets for manufacturer B is approximately 0.0013.
Since manufacturer B has a lower proportion of defective rivets, on average, it will produce fewer defective rivets than manufacturer A. So the manufacturer that will produce, on average, the fewest number of defective rivets is manufacturer B.
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Krystal is catering a dinner for an organization. Dessert will be homemade ple and 1 cup of either chocolate or vanilla ice cream. The chocolate ice cream costs
$8 per gallon and the vanilla ice cream costs $6 for a 5-quart container. There are 4 cups in 1 quart and 4 quarts in 1 gallon; therefore, each container of
chocolate ice cream contains 16 servings and each container of vanilla ice cream contains 20 servings. Based on the budget, Krystal wants to spend no more
than $70 on ice cream, and she needs at least 150 servings of ice cream.
Let c represent the number of gallons of chocolate ice cream and v represent the number of 5-quart containers of vanilla ice cream.
Which system of inequalities can be used to determine the number of gallons of chocolate ice cream and the number of 5-quart containers of vanilla ice cream
that Krystal can buy for this dinner?
A
B
C
D
6c+8v ≤ 70
16c+20v > 150
8c + 6v 2 70
16c+20v ≤ 150
8c + 6v < 70
16c+20v < 150
8c + 6v ≤ 70
16c+20v2 150
Option A is the answer. The system of inequalities that can be used to determine the number of gallons of chocolate ice cream and the number of 5-quart containers of vanilla ice cream that Krystal can buy for this dinner is:
8c + 6v ≤ 70
8c + 6v ≤ 7016c + 20v ≥ 150
Step by step explanation of the inequalityThe cost of c gallons of chocolate ice cream is $8c, and the cost of v containers of vanilla ice cream is $6v. Krystal wants to spend no more than $70 on ice cream, so the inequality for the total cost of ice cream is:
8c + 6v ≤ 70
Krystal needs at least 150 servings of ice cream, and each gallon of chocolate ice cream provides 16 servings, while each container of vanilla ice cream provides 20 servings. The inequality for the total number of servings of ice cream is:
16c + 20v ≥ 150
Therefore, the system of inequalities that can be used to determine the number of gallons of chocolate ice cream and the number of 5-quart containers of vanilla ice cream that Krystal can buy for this dinner is:
8c + 6v ≤ 70
16c + 20v ≥ 150
Option A is the correct answer.
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