Step-by-step explanation:
We can model the annual consumption of iron by the equation
c = 900 million tons x [tex]1.025^n[/tex], where
n is the number of years after 1993 and
c is the consumption for that year.
An estimate for the total consumption of iron can now be obtained by integrating this equation with respect to a dummy variable, x from 0 to n.
[tex]C = 900*10^6* \int\limits^n_0 {1.025^x} \, dx[/tex]
This equation simplifies to
C = 900 million tons x (1.025^n - 1) / ln(1.025), where
x is a dummy variable and
C is the total consumption of iron n years after 1993.
Let R be the amount of iron remaining at n years after 1993, so
R = 480 billion tons - C
R = 480 billion tons - 900 million tons x (1.025^n - 1) / ln(1.025)
We need to find the value of n when R is 0, so
0 = 480 billion tons - 900 million tons x (1.025^n - 1) / ln(1.025)
Simplify this equation to obtain
n = 107.4
So the iron will run out in the year 1993 + 107 = 2100
HELP
Write an equation in slope-intercept form for a line with a slope of -2 and a 8 points
y-intercept of 7. *
Answer:
y=-2x+7
Step-by-step explanation:
slope intercept form is equal to y=mx+c
where y is the y value
x is the x value
m is the gradient
and c is the y intercept
so the equation for this set of values is equal to
y=-2x+7
slope will be the m
and b is the y intercept
y＝mx＋b
y＝-2x＋7
What is the surface area of a cylinder with a radius of 10 cm and a height of 30 cm
HELP ASAP PLSSSSSSSSSSSSSSS
Answer:
a. 5ab b. 11x+15y
Answer:
a. 5ab
b. 11x+5y
Step-by-step explanation:
12ab-7ab they have the same variables, so you can just subtract
19x+5y-8x just rearrange it to 19x-8x+5y and subtract 19x and 8x
PLEASE HELP TIMED
Do you want to install the updates
Understanding Expressions
Assignment
Active
Explaining Algebraic Expressions
o
Describe the parts of this algebraic expression using the
lesson's vocabulary.
-x+102-3x+y
Done
· 00000000
9 of 10
13) A Super Bowl Party Sub was cut into 3 equal pieces that were x inches long. Kevin took
6 inches of the sub for himself. There was still 30 inches of the sub when the game started.
How many inches was each of the pieces?
Answer:
12 inches
Step-by-step explanation:
now i am assuming kevin took 6 inches of the sub before the game because it says "there was still 30 inches of the sub when the game started". In that case, add 6 and 30 to get 36. Because the sub was cut into 3 equal pieces, divide 36 by 3 and get 12 inches as your final answer.
a local pet care center pays you $8 per hour to walk dogs. last summer you worked 36.75 hours a week. what was your total weekly straight time pay for one week?
Answer:
$294
Step-by-step explanation:
8(36.75) = $294
Answer:
294
Step-by-step explanation:
8(36.75)
= $294
Select all that may be correct
Answer:
Option (2) and Option (6)
Step-by-step explanation:
Expression representing the error can be given by,
Expected value = Original value ± percentage error
If original value of the ice cream filled in the container = 64 ounce
Percentage error to fill the ice cream in each container = 1.5%
So net error = ± 1.5% of 64
= [tex]64(\frac{1.5}{100})[/tex] ounce
= 64(0.015) ounce
Therefore, expression that can show the maximum maximum amount of ice cream in the container will be
= 64 + 64(0.015) Option (6)
= 64(1 + 0.015)
= 64(1.015) Option (2)
Therefore, Option (2) and Option (6) are the correct options.
find the length of side x in simplest radical form with a rational denominator
Answer:
x = (2√6)/3
Step-by-step explanation:
Reference angle = 30°
Hypotenuse = x
Adjacent = √2
Thus, applying trigonometric ratio, we have:
Cos(30) = adj/hyp = √2/x
x*cos(30) = √2
x = √2/cos(30)
x = √2/(√3/2) (cos 30 = √3/2)
x = √2 × 2/√3
x = (2√2)/√3
Rationalize
x = (2√2 × √3)/(√3 × √3)
x = (2√6)/3
Evaluate 2x + 9y -9, when x= 6 and y= 6
Answer:
57
Step-by-step explanation:
2x + 9y -9
2(6) + 9(6) - 9
12 + 54 - 9 = 57
good luck, i hope this helps :)
Answer:
57
Step-by-step explanation:
2*6+9*6-9=
12+54-9=
66-9=
57
Find the distance between the two points rounding to the nearest tenth (8,−9) and (2,−7)
Answer:
negative 7 is first then comes 2. negative 9 is first then comes 8.
Step-by-step explanation:
Answer:
6.3
Step-by-step explanation:
a boat travels 438 km in 8 hours with a constant speed, how far can it travel in 5 hours
Answer:
its the first one
Step-by-step explanation:
An internet survivor
game had 50,000
participants; however,
the game kicks off 20% of
the participants each day.
Which function models
this game?
Answer:
70,000
Step-by-step explanation:
5,000
20
70,000
the range for a list of numbers is 7. the smallest value is 4. what is the largest value in the list
Answer:
7
Step-by-step explanation:
The largest value in the list is 11.
What is list?A list is a structure consisting of an ordered set of numbers.
What is the range?"The range is the difference between the smallest and highest numbers in a list."
For given example,
The range for the given list is 7 and the smallest value is 4.
Let R be the range of the list.
⇒ R = 7
Let S be the smallest value in the list.
⇒ S = 4
Let the largest value in the list be L.
⇒ R = L - S
⇒ 7 = L - 4
⇒ L = 7 + 4
⇒ L = 11
Therefore, the largest value in the list is 11.
Learn more about the range of the list here:
https://brainly.com/question/14814262
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Forty percent of the students who enroll in a statistics course go to the statistics laboratory on a regular basis. Past data indicates that 55% of those students who use the lab on a regular basis make a grade of A in the course. On the other hand, only 15% of students who do not go to the lab on a regular basis make a grade of A. If a particular student made an A, determine the probability that she or he used the lab on a regular basis. (Round your answer to three decimal places.)
Answer:
0.71 = 71% probability that she or he used the lab on a regular basis.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Student got an A
Event B: Used the lab on a regular basis.
Probability of an student getting an A:
55% of 40%(go to the lab on a regular basis).
15% of 100 - 40 = 60%(do not go to the lab on a regular basis).
So
[tex]P(A) = 0.55*0.4 + 0.15*0.6 = 0.31[/tex]
Probability of getting an A and using the lab on a regular basis:
55% of 40%, so:
[tex]P(A \cap B) = 0.55*0.4 = 0.22[/tex]
Probability that she or he used the lab on a regular basis.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.22}{0.31} = 0.71[/tex]
0.71 = 71% probability that she or he used the lab on a regular basis.
A marching band has 80 members.
The ratio of members who play wind instruments to all others is 2 to 3.
How many members play wind instruments?
Answer:
30 members will play wind instruments
Answer:
30 would be the answer to the ?
can someone find what x please?
5x + 14 = 614
PLS HELP !!! I need this question done quick
Answer:
a. 17 b. 51
Step-by-step explanation:
Follow Order of Operations (PEMDAS):
Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
a. 9 + 4² - (4-2) • 4
9 + 4² - (4-2) • 4 –––Start with (4-2) = 2 (parentheses)
9 + 4² - 2 • 4 ––– 4² (exponents)
9 + 16 - 2 • 4 ––– 2 • 4 (multiplication)
9 + 16 - 8 ––– 9 + 16 (addition)
25 - 8 ––– 25 - 8 (subtraction)
17
b. 15 - 4 + 2(7-3) • 5
15 - 4 + 2(7-3) • 5 ––– Start with 2(7-3)
~ Note: this can be done using distributive property (2•7 - 2•3) OR solving the parentheses first and then multiplying 2(4). Both get 8 and same end result.
15 - 4 + 8 • 5 ––– 8 • 5 (multiplication)
15 - 4 + 40 ––– 15 - 4 (subtraction) *Note: Subtraction and addition are interchangeable in the order because you do it left to right*
11 + 40 ––– 11 + 40 (addition)
51
Answer:
(a. 7) (b. 51)
Step-by-step explanation:
A.
[tex]9 + 4^{2} - (4-2) * 4\\\\9 + 4^{2} - (2) * 4\\9 + 16 - 2 * 4\\9 + 16 - 8\\25 - 8\\17 \\[/tex]
B.
[tex]15 - 4 + 2 (7 - 3) * 5\\15 - 4 + 2 (4) * 5\\15-4+(2*4*5 )\\15-4+40\\11 + 40\\51[/tex]
(I don't know the numerical values)
Look at the formula for finding distance. Which of the following is the formula to find time? [picture included]
Answer:
A.
Step-by-step explanation:
Answer:
[tex] \huge \: \boxed { \boxed{ \red{ a)t = \frac{d}{r}}}}[/tex]Step-by-step explanation:
to understand thisyou need to know about:equationPEMDASgiven:[tex]d = rt[/tex]to find[tex]t[/tex]let's solve:[tex]step - 1 :define[/tex]
[tex]d = rt[/tex]
[tex]step - 2 : solve[/tex]
[tex]rewrite : \\ rt = d[/tex][tex]divide \: both \: sides \: by \: r : \\ \frac{rt}{r} = \frac{d}{r} [/tex][tex]simplify : \\ t = \frac{d}{r} [/tex][tex] \huge \: \boxed { \boxed{ \red{ \therefore t = \frac{d}{r}}}}[/tex]
PLEASE HELP ASAP DUE VERY SOON
Answer:
your answer will be A'B'/AB=3/1=3
Step-by-step explanation:
i hope this helps you
Answer:
3 is the correct answer......
1. Javier scored 78% on the test. Write this
percent as a fraction in simplest form and
as a decimal.
Answer:39/50
Step-by-step explanation:
Item 8 What is 31.5632 rounded to the nearest tenth?
Answer:
31.6
Step-by-step explanation:
Please help me!! Thank you!!
Answer:
[tex]Solution,\\PQ = \sqrt{(1-3)^2+(3-1)^2} = \sqrt{2^2+2^2} = \sqrt{8} = 2\sqrt{2} \\P'Q' = \sqrt{(3-9)^2+(9-3)^2} = \sqrt{6^2+6^2} = \sqrt{72} = 6\sqrt{2}\\Also,\\RQ = \sqrt{(1-3)^2+(1-1)^2} = \sqrt{2^2} = 2\\R'Q' = \sqrt{(3-9)^2+(3-3)^2} = \sqrt{6^2} =6\\Again,\\PR = \sqrt{(1-1)^2+(3-1)^2} = \sqrt{2^2}=2\\P'R' = \sqrt{(3-3)^2+(9-3)^2} = \sqrt{6^2} = 6\\Here, P'R' = 3PR, P'Q'=3PQ ~and~ Q'R'=3RQ~\\In~other~words~each~side~of~triangle~P'Q'R' ~is~three~times~the~length~of~triangle~PQR.\\[/tex][tex]So,~the~algebraic~rule~of~diliation(enlargement)~is~(x,y)----(3x,3y)[/tex]
If my answer did not help you, comment below but please don't delete it.
Amanda is researching her ancestry. She records names and birth dates for her parents, their parents and so on, in an online research tool. If she can locate all of the information, how many names will Amanda record in the generation that is 5 generations before her?
Answer:
Step-by-step explanation:
Amanda will record 32 names for the five previous generations.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that Amanda is researching her ancestry. She records names and birth dates for her parents, their parents and so on, in an online research tool.
We can write the series as -
Amanda
{M} {F}
{M} {F} {M} {F}
.
.
so on
We can write the sequence as -
2, 4, 8, ....
It is a geometric sequence. For n = 5, we can write -
a(5) = arⁿ⁻¹
a(5) = 2 x (2)⁴
a(5) = 2⁵
a(5) = 2 x 2 x 2 x 2 x 2
a(5) = 32
Therefore, she will record 32 names for the five previous generations.
To solve more questions on functions, expressions and polynomials, visit the link below -
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f(x) = 7x² + 21x - 70
factor
Answer:
Step-by-step explanation:
f(x)=7(x^2+3x-10)=7(x+2)(x-5)
Help pls !!! Answer u don’t have to explain
Answer:
B
Step-by-step explanation:
6 miles............
Which equation represents a line which is parallel to the line
6x + 7y = –49?
Answer: y= 7/6x-5
Step-by-step explanation:
The equations of parallel lines have the same slope or rates.
The equation of the line parallel to [tex]\mathbf{6x + 7y = -49}[/tex] is [tex]\mathbf{y = -\frac 67(x - x_1) + y_1}[/tex]
The equation is given as:
[tex]\mathbf{6x + 7y = -49}[/tex]
Make 7y the subject
[tex]\mathbf{7y = -6x-49}[/tex]
Make y the subject
[tex]\mathbf{y = -\frac{6}{7}x -7}[/tex]
A linear equation is represented as:
[tex]\mathbf{y =mx + b}[/tex]
Where m represents the slope.
So, we have:
[tex]\mathbf{m = -\frac 67}[/tex]
Parallel lines have the same slope.
So, the slope of the line is [tex]\mathbf{m = -\frac 67}[/tex]
The equation is then calculated as:
[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]
Substitute [tex]\mathbf{m = -\frac 67}[/tex]
[tex]\mathbf{y = -\frac 67(x - x_1) + y_1}[/tex]
Hence, the equation of the line parallel to [tex]\mathbf{6x + 7y = -49}[/tex] is [tex]\mathbf{y = -\frac 67(x - x_1) + y_1}[/tex]
Read more about parallel lines at:
https://brainly.com/question/402319
stella rewrites -2 1\2+3.7 as 3.7-2 1\2
Answer:
Step-by-step explanation:
Yes correct.
Commutative property upon integer addition/subtraction
-3 + 2 = 2 - 3
A store has a sale where every item has a scale price that is 20% less than the regular price . Write an Expression that represents the sale price of an items if the regular price is p dollars PLEASEEE HELP I HAVE TO MAKE PROGRESS
Answer:
0.80p
Step-by-step explanation:
sale price = p - (20% of p)
= p - 0.20p
= 0.80p
1 point
A boat in the ocean knows the nearest lighthouse has a light 220 feet
above the water. They look up at an angle of elevation of 25 degrees to see
the light. How far is the boat from the base of the lighthouse?*
93 feet
199 feet
472 feet
631 feet
Answer:
472 feet
Step-by-step explanation:
The 220 ft is the opposite leg.
The distance from the boat to the base of the lighthouse is the adjacent leg.
tan 25 = 220/x
x = 220/tan 25
x = 472
Answer 472 feet
Amy came up with a list of 28 good deeds she could perform around the house. She wants to do the same number of good deeds each day for the next 7 days to complete her list. How many good deeds will Amy do each day?
Answer: 4 deeds per day
Step-by-step explanation: 7 times 4 is 28