The current price index is mathematically given as,
$538.194
This is further explained below.
What is the current price index?The index value may be calculated by taking the ratio of the current value to the reference value and multiplying that ratio by 100.
In regard to this issue, we have that:
Current value = $3.10
Reference value: $0.576
Generally, the Index price for the is mathematically given as,
I = (3.10/0.576)*100
I= $538.194
The current price index number is 538.194
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A submarine at -20 feet descends 30 feet. What is the submarine's current location after the descent
The current location of the submarine would be -50 feet.
How to find the level of descent of the submarineThe questions says that the submarine was at -20 feet already.
Now it says that it descended 30 feet. Remember that the descent refers to a fall. Hence the way that it would be represented would be through the use of a negative sign.
This would be -30
The current location of the descent of the submarine would be
-20 - 30
= -50 feet
Therefore the current location of the submarine would be -50 feet.
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Given the function g(x) = -3x + 4,compare and contrast g(-2) and g(4).Choosr the statement that is true concerning these two values
D. The value of g(-2) is greater than the value of g as a result (4).
What is function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. Numbers, formulae, and related structures, shapes, and the spaces in which they are contained, as well as quantities and their variations, are all covered in the field of mathematics.
Given Data
function g(x) = -3x + 4,compare and contrast g(-2) and g(4)
We have provided that
g(x) = -3x + 4
g (-2) = -3 ( -2) + 4.
g (-2) = 6 + 4
g (-2) = 10 .
Now,
g (4) = -3 ( 4) + 4.
g (4) = -12 +4 .
g (4) = -8.
g (-2) > g (4)
10 > -8 .
D. The value of g(-2) is greater than the value of g as a result (4).
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let y=ln(x^2+y^2) determine y prime at the point -(e^4-16)^1/2
dy/dx = -2√e⁴ - 16/e⁴ - 8 is differential equation .
The meaning of a differential equation?
An equation involving one or more functions and their derivatives is referred to as a differential equation in mathematics. The rate of change of a function at a particular moment is determined by the function's derivatives. It is mostly employed in disciplines like biology, engineering, and physics.y = In( x² + y² )
now doing implicit differentiation
dy/dx = d/dx In( x² + y² )
dy/dx = 1/(x² + y² ) × d/dx ( x² + y² )
dy/dx = 1/x² + y² × ( 2x + 2y dy/dx)
(x² + y² )dy/dx = 2x + 2y dy/dx
dy/dx (x² + y² - 2y) = 2x
dy/dx = 2x/(x² + y² - 2y)
we need to calculate dy/dx at ( - √e⁴ - 16 , 4 )
dy/dx = [tex]\frac{2 * ( - \sqrt{e^{4} - 16} }{-\sqrt{(e^{4 - 16)^{2} }+ ( 4)^{2} - 2 * 4 } }[/tex]
dy/dx = - 2√e⁴ - 16/e⁴ - 16 + 16 - 8
dy/dx = -2√e⁴ - 16/e⁴ - 8
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2320 is what percent of 2000
Leroi is using coordinate geometry to prove this theorem.
Theorem: The diagonals of a parallelogram bisect one another.
Given: AD//BC; AB//CD; AC and BD intersect at M.
Prove: M bisects AC and BD.
Which of these is the BEST strategy for this proof?
A) Use the Midpoint Formula to find the coordinates of M, then use the Distance Formula to verify that AC= BD
B) Use the equations of line AC and line BD to find the coordinates of M, then use the Distance Formula to verify that AC= BD
C) Use the equations of line AC and line BD to find the coordinates of M, then use the midpoint Formula to verify that M is the midpoint of both AC and BD
D) Use the Distance Formula to find the coordinates of M, then use the Midpoint Formula to verify that M is the midpoint of both AC and BD
The BEST strategy for this proof is (A) Use the Midpoint Formula to find the coordinates of M, then use the Distance Formula to verify that AC= BD
How to determine the best strategy for the proof?The theorem is given as
Theorem: The diagonals of a parallelogram bisect one another.
Also, we have the following given parameters
AD//BC; AB//CD;
AC and BD intersect at M.
The above means that:
Lines AD and BC are parallel lines, and AB and CD are parallel lines
The statement AC and BD intersect at M implies that
AM = MC and BM = MD.
The above means that we need to calculate the lengths of the above segments, and then make comparison
The lengths of the segments can be calculated using the distance formula
Other than that, the coordinate of the point M needs to be calculated
The option that satisfies the above conditions is (a)
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HELP! 100 POINTS!!!
A baking company has developed two new cookie recipes, however, they only have the resources to add one item to their product line. They decide to randomly sample three groups of 100 people to determine which cookie recipe, A or B, is preferred. The results are shown in the following table.
Recipe A Recipe B
Sample #1 26 67
Sample #2 48 89
Sample #3 22 56
A. Based on the collected data, which recipe should the baking company add to their product line? How confident should the company be in their decision? Explain your reasoning using complete sentences.
B. Using the mean of the data for Recipe A, approximately what percentage of people would you expect to prefer Recipe A over Recipe B?
Answer:
Question A: They should add product B because it has a 69% rate of approval. They can be 69% confident that the addition of product B will be successful.
Question B: 31% of people would prefer cookie A over cookie B
Step-by-step explanation:
Evalúe the limit. Show steps
After evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow 2 }\frac{\sqrt{x-1} -1}{x-2}[/tex]as x approaches 2 is 0.5
What is limit?As an input or as an index approaches a specific value in mathematics, a limit is the value that the function, sequence, or index approaches. The definitions of continuity, derivatives, and integrals all require limits, which are fundamental to calculus and mathematical analysis.
In addition to having a connection to the category theory concepts of limit and direct limit, the idea of a limit of a sequence is further generalized to include the idea of a limit of a topological network.
A limit of a function is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]
To find the limit we will use L'Hôpital's Rule
Find the derivative
⇒ [tex]\lim_{x\rightarrow 2 }\frac{\sqrt{x-1} -1}{x-2}[/tex]
⇒ [tex]\lim_{x\rightarrow 2 } \frac{1/2(x-1)^{-1/2}}{1}[/tex]
⇒ [tex]\lim_{x\rightarrow 2 } \frac{1}{2\sqrt{x-1} }[/tex]
Evalúe 2 as x
⇒ [tex]\frac{1}{2\sqrt{(2)-1} }[/tex]
⇒ [tex]\frac{1}{2\sqrt{1} }[/tex]
⇒ [tex]\frac{1}{2}[/tex]
⇒ 0.5
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What is the sum of the first 7 terms for the geometric sequence with first term 3, seventh
term 46,875, and common ratio 5?
A. 58,593
B. 19,531
C. 35,154
The sum of the first 7 terms for the geometric sequence with first term 3, seventh term 46,875, and common ratio 5 is 58,583.
A geometric progression is a sequence where each and every succeeding term is formed by multiplying the preceding term by a constant number. That constant number is called common ratio.
The common ratio is provided to be 5. While the first term is 3.
The seventh term is 46875.
The formula for sum of n terms of a GP is,
Sn = a(rⁿ-1)/(r-1)
We have to find sum of seven terms,
Sn = a(r⁶.r - 1)/(r-1)
Putting,
a = 3
r = 5
n =6
Sn = 3(5⁶.5 - 1)/(5-1)
Sn = (3.5⁶.5 - 3)/4
Sn = (46875×5 - 3)/4
Sn = (234375-3)/4
Sn = 234372/4
Sn = 58593.
The sum is 58593.
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PLS HELP I WILL GIVE LOTS OF POINTS PLS HELP
Answer:
21 kilograms
Step-by-step explanation:
Every hour she produces 3 kilograms of dough. 9/3 = 3. So, in 7 hours, she can produce 21 kilograms of dough
Answer:
I want points
Step-by-step explanation:
e
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual
mean of 53.2 degrees.
Low Temperature (o F)
Frequency
40-44 45-49 50-54 55-59
1
6
9
6
The mean of the frequency distribution is
(Round to the nearest tenth as needed.)
degrees.
...
60-64
3
Answer:
7777777777777777777777770
Step-by-step explanation:
7777777777777777777777770
The numbers of trading cards owned by 9 middle-school students are given below.
(Note that these are already ordered from least to greatest.)
352, 409, 424, 471, 497, 503, 515, 525, 561
Send data to calculator
Suppose that the number 561 from this list changes to 768. Answer the following.
(a) What happens to the mean?
(b) What happens to the median?
OOO
It decreases by
It increases by
It stays the same.
It decreases by .
0.
It increases by 0.
It stays the same.
X
S
The mean increases by 23 and the median stays the same.
What are the mean and median?A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the middle value.
Given the data set: 352, 409, 424, 471, 497, 503, 515, 525, 561
(a) Mean = [tex]\frac{352+409+424+471+497+503+515+525+561}{9}[/tex]
Mean = [tex]\frac{4257}{9}[/tex]
= 473
The number 561 from this list changes to 768.
New mean = [tex]\frac{352+409+424+471+497+503+515+525+768}{9}[/tex]
= [tex]\frac{4464}{9}[/tex]
= 496
Thus, the mean increases by 496 - 473 = 23.
(b) Median = mid value
= 497
When the number 561 changes to 768, still the mid value will remain the same i.e. the median remains the same.
Therefore, the mean increases by 23 and the median stays the same.
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Rylie ate 12 of the 20 grapes that her mom packed in her lunch which decimal is equivalent to the fraction of grapes Riley ate?
Answer: 0.6
Step-by-step explanation: To find the decimal you seek, you put 12 over 20, 12/20. That means you divide it, so 12 divided by 20 is 0.6, or 60%.
a group of people are waiting in line for a movie premier. every 14th person in line will win a free movie ticket . every 10th person will receive a gift card of 30 dollars. which person is the first to win both prizes.if there are 200 people in line how many will receive both prizes?
In order to determine which person is the first to win both prizes, you have to find the least common multiple to both numbers 14 and 10.
To determine what is the least common multiple number you proceed as follow:
You list different multiples of each number 14 and 10.
For 14: 14 28 42 56 70 84 98 112
For 10: 10 20 30 40 50 60 70 80
The least common multiple is 70, becasue is the first common number in each list.
Hence the 70th person in the line will win both prizes.
Susan runs 4 miles in 30 minutes. At the same rate, how many minutes would she take to run 10 miles?
Answer:
It would take 75 minutes for Susan to run 10 miles.
Step-by-step explanation:
10 miles divided by 4 = 2.5
30 min. x 2.5 = 75 minutes
m=85kg, a=4.29m/s^write an expression for the magnitude of the force, F
The magnitude of force is 364.65 Kg / ( m/s²)
What is force?An influence that can change the motion of an object. A force can cause an object with mass to change its velocity, i.e., to accelerate.
given:
m = 85 Kg
a= 4.29 m/s²
We know
Force = mass x acceleration
F= 85 x 4.29
Force = 364. 65
Hence, the magnitude of force is 364.65 Kg / ( m/s²)
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Which complex number has an absolute value of 5?
I heard that I received a fourth rating from a customer on our customer service survey . What is my average monthly rating ?
Supervisor : “ you have been doing really well . You received ratings of 85, 90, 100 and 90 . What’s your monthly average ?
The average monthly rating is 91.25.
How to estimate averages?By adding a set of integers and then dividing by their count, the average, or arithmetic mean, is determined.Finding an average helps us determine a general pattern of behavior or trend.To compare different quantities of the same category, averages are utilized.In other words, the average is the proportion between the total number of observations and the sum of all observations presented.The common formula of average is:Average = Sum of the Observations/Number of Observations
Given:
The received ratings are 85, 90, 100, and 90.
Average monthly rating = Sum of ratings/ total number of ratings
= (85 + 90 + 100 + 90)/ 4
= 365/ 4
= 91.25
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please answer correctly 50 points
Answer:3
Step-by-step explanation:
To use the law of sines, which of the following statements must be true?
A. At least one side length and opposite angle pair must be known.
B. At least two angles must be known.
C. The triangle must be a right triangle.
D. All three side lengths must be known.
For the application of the law of sine the true statement is that at least one side length and opposite angle pair must be known.
How to use the law of sine to solve triangle?The law of sine is used to solve the sides and angles of a triangle.
Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other.
In other words, the law of sines is defined as the ratio of side length to the sine of the opposite angle.
It holds for all the three sides of a triangle respective of their sides and angles.
Therefore, the law of sine can be expressed as follows:
a / sin A = b / sin B = c / sine C
Hence, the statement that is true is at least one side length and opposite angle pair must be known.
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Select the correct answer from each drop-down menu.
In a city, Broadway, Main Street, and Water Street all intersect to form a triangle. Broadway is 2000 m from Main Street to Water Street, Main Street
is 1600 m from Broadway to Water Street, and Water Street is 1200 m from Main Street to Broadway.
Complete the statement below.
In the triangle formed by the three streets, the greatest angle is the one formed by the intersection of
smallest angle is the one formed by the intersection of
Reset
Next
The
Using the Law of Sines, it is found that:
The greatest angle is formed by the intersection of Main Street and Water Street.The smallest angle is formed by the intersection of Broadway and Main Street.What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A is given by a.The length of the side opposite to angle B is given by b.The length of the side opposite to angle C is given by c.The lengths and the sine of the angles are proportionally related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
From this relation, we have that:
The greatest angle is opposite the largest side.The smallest angle is opposite the smallest side.In this problem, we have that:
Broadway is the hypotenuse, hence the greatest angle is formed by the intersection of Main Street and Water Street.Due to the smaller distance, of 1200 m, compared to 1600 m and 2000 m, the smallest angle is formed by the intersection of Broadway and Main Street.More can be learned about the Law of Sines at https://brainly.com/question/27174058
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What is an equation in slope-intercept form for the line
perpendicular to y = 3x + 9 that
contains (-6, 3)?
An equation in slope-intercept form for the line perpendicular to y = 3x + 9 that contains (-6, 3) is 3 = -1/3(-6) + 1.
What is slope-intercept form?The most "popular" type of a straight line is one with a slope-intercept. Due to its simplicity, this is helpful to a lot of students. The slope and y-intercept of the straight line can be easily determined or read off from this form, making it possible to describe its properties without having access to the graph.
The equation for a line written in slope-intercept form
y = mx + b
Where,
m is the slope, and b is the y-intercept.
We know that the slope of a line perpendicular to given equation becomes reciprocal with opposite sign.
So, here slope is 3 and in perpendicular line it will become -1/3.
Now we will go with slope-intercept form and put the values (-6, 3) as x and y in y = mx + b
⇒ 3 = -1/3(-6) + b
Lets solve for b
⇒ b = 3 - ( -1/3(-6))
= 3 - (2)
= 1
Now we have the desired equation
3 = -1/3(-6) + 1
Thus, An equation in slope-intercept form for the line perpendicular to y = 3x + 9 that contains (-6, 3) is 3 = -1/3(-6) + 1.
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WILL GIVE BRAINLYEST 100 POINTS 3 QUESTIONS WILL GIVE EXTRA POINTS
Answer:
The answer to the first question is the first option
The answer to the second question is the third option
the answer to the third one is the second option
Step-by-step explanation:
*I'm not 100% sure about these but it's probably right*
Answer:
1. First one
2. Third one
3. Second on
Step-by-step explanation:
(★ ω ★)
What is the missing step in the sequence of transformations that will map figure 1 onto figure 2?
1.?
2. translation 3 units to the right
3. translation 4 units down
A. reflection across the x-axis
rotation 90° clockwise about the origin
rotation 270° clockwise about the origin
reflection across the origin
Answer: rotation 90° clockwise about the origin
The missing step is rotation 90° clockwise about the origin.
What is the translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
In the graph, triangle 1 is translated to triangle 2.
Triangle 1 has three transformations, rotation 90° clockwise, translation 3 units to the right and 4 units down.
Therefore, the missing step is rotation 90° clockwise about the origin.
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Evaluate -x + 3x¹ - 4 for x = 2.
Answer:
0
Step-by-step explanation:
[tex]x = 2 - x + 3x {}^{1} - 4 \\ [/tex]-2 +3.2' -4-2+3×2-4-2+6-40Make x the subject of m=n+x/p
mp=n+x the P on the right side cancels out now you want to shift the n to the left side by subtracting it from both sides x=mp-n so that leaves us with the solution. m=n+x/p first you want to move the P over to the left side by x P so that leaves us with the answer. ...
mp=n+X X=mp-n, where m=n+x/p multiplies p on both sides.
How can you change the formula so that x is the subject?
To change x to the subject:Identify the variable by:Arrange the terms in the equation so that they are all on the same side of the equal sign, or =.If more than one term contains x, factorization may be required. ...Make a change to ensure that there is only one x variable remaining to serve as the subject.To learn more about m=n+x/p refer to:
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x = mp - n ( x as the subject of m= n+ x/p)
How to make x the subject of m = n +x/p ?
[tex]m =\frac{n+x}{p} \\\\mp = n+ x\\\\mp - n = x\\\\x= mp -n[/tex]
What is making x the subject?
Making x the subject of a formula or equation requires rearranging the formula or equation such that we have a single x variable that is equal to the other variables in the formula.The equation should be rearranged so that each term containing x is on the same side of the equation.If more than one term contains x, factorization may be required.Only one x must be displayed at the end in order to make it the subject. A number or variable can have a positive or negative result when we square root it as an inverse operation.To learn more about making x the subject, refer:
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help meeeeeeeeeeeeeeeeeeeeeee
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]
Rectangle ABCD is shown with the dimensions given in units. The length of AB is greater than the length of AD which inequality represents this situation?
A: 9x-16<1.5+42
B: 9x-16>1.5x+42
C: 10.5x<26
D: 10.5x>26
Answer:
B
Step-by-step explanation:
it is simple.
because AB > AD, their size representations must have the same relationship.
therefore,
9x - 16 > 1.5x + 42
that could be simplified to
7.5x > 58
The inequality that represents AB > AD is B: 9x - 16 > 1.5x + 42.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, In Rectangle ABCD the length of AB is greater than the length of AD.
∴ The inequality that represents this is AB > AD which is,
9x - 16 > 1.5x + 42.
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A. Write the decimals in words.
Example: 32.76-thirty-two point seven six
1. 60.03 -
2. 209.11 -
Answer:
1. sixty point zero three OR sixty and 3 hundredths
2. two hundred and nine point one one OR two hundred nine and 11 hundredths
on a highway there are billboards located every 1 1/2 km there are 14 billboards in that highway how long is the highway
Answer:
1 1/2 = 3/2
3/2 x 14
= 42/2
=21
Step-by-step explanation:
go fast if you are smart.
see attachment beloww.
[tex]3x + x + (x + 12) = 152[/tex]
<AOD =<COB(VERTICAL OPPOSITE ANGLES)
[tex]3x + x + x = 152 - 12 \\ 5x = 140 \\ \frac{5x}{5} = \frac{140}{5} \\ x = 28[/tex]
x=28°
be reminded that <COB IS MADE OF ALOT OF BRANCH ANGLES THAT WE HAD TO ADD TO GET IT
i.e <COE,<EOF AND <FOB
Answer:x=28°
Step-by-step explanation:
152=3x+x+x+12
152=5x+12
140=5x
x=28