Answer:
I found thois from someone else asking this queetion so gope it helps.
Step-by-step explanation:
I'm sure you want your functions to appear as perfectly formed as possible so that others can help you. f(x) = 4(2)x should be written with the " ^ " sign to denote exponentation: f(x) = 4(2)^x
f(b) - f(a)
The formula for "average rate of change" is a.r.c. = --------------
b - a
change in function value
This is equivalent to ---------------------------------------
change in x value
For Section A: x changes from 1 to 2 and the function changes from 4(2)^1 to 4(2)^2: 8 to 16. Thus, "change in function value" is 8 for a 1-unit change in x from 1 to 2. Thus, in this Section, the a.r.c. is:
8
------ = 8 units (Section A)
1
Section B: x changes from 3 to 4, a net change of 1 unit: f(x) changes from
4(2)^3 to 4(2)^4, or 32 to 256, a net change of 224 units. Thus, the a.r.c. is
224 units
----------------- = 224 units (Section B)
1 unit
The a.r.c for Section B is 28 times greater than the a.r.c. for Section A.
This change in outcome is so great because the function f(x) is an exponential function; as x increases in unit steps, the function increases much faster (we say "exponentially").
A storage company designs a rectangular box with an open top that has a volume of 220 in3. Each box has a length that is three times its width. Calculate the minimum surface area of one of these boxes. Round your answer to three decimal places.
Answer:
191.016 in²
Step-by-step explanation:
Let the volume of the cube be V = lwh where l = length of box, w = width of box and h = height of box.
Now l = 3w.
So, V = lwh = (3w)wh = 3w²h
h = V/3w²
Since the rectangular box is open at the top, its total surface area is A = lw + 2lh + 2wh
substituting l = 3w, we have
= (3w)w + 2h(l + w)
= 3w + 2h(3w + w)
= 3w² + 2h(4w)
= 3w² + 8wh
substituting h = V/3w²
= 3w² + 8w(V/3w²)
A = 3w² + 8V/3w
Differentiating A with respect to w and equating it to zero, we have
dA/dw = d[3w² + 8V/3w]dw
dA/dw = d3w²/dw + d(8V/3w)/dw
dA/dw = 6w - 8V/3w²
dA/dw = 0
6w - 8V/3w² = 0
6w = 8V/3w²
6w³ = 8V/3
w³ = 8V/(3 × 6)
w³ = 4V/9
w = ∛(4V/9)
substituting V = 220 in³, we find the minimum value for the width
w = ∛(4 × 220 in³/9)
w = ∛97.7778
w = 4.607 in
To determine if this is a minimum value of width which gives minimum area, we take the second derivative of A. So,
d²A/dw² = d(6w - 8V/3w²)/dw
= 6 + 16V/3w³
substituting w³ = 4V/9, we have
d²A/dw² = 6 + 16V/3(4V/9)
= 6 + (16 × 9)/(3 × 4)
= 6 + 4 × 3
= 6 + 12
= 18
Since d²A/dw² = 18 > 0 , w = ∛(4V/9) = 4.607 in gives a minimum for the surface area.
So, we calculate this area by substituting w = 4.608 in. So,
A = 3w² + 8V/3w
= 3 × (4.607 in)² + (8 × 220 in³)/(3 × 4.607 in)
= 63.6733 in² + 1,760 in³/13.821 in
= 63.6733 in² + 127.3424 in²
= 191.0157 in²
≅ 191.016 in² to three decimal places.
Chang spent a total of $80 at the grocery store. Of this amount, he spent $36 on fruit. What percentage of the total did he spend on fruit?
Answer: 28 percent i believe
Step-by-step explanation:
Answer:
brandoncardona2007
Step-by-step explanation:
They are always right no matter what
I NEED HELP ... please help me.
Step-by-step explanation:
here = means the similar triangle plz don't confuse. And 1. is proved by SSS axiom or SAS axiom and 2. is proved through SAS axiom will be much more better.
Answer:
1. ∆STU- 75
2. ∆WVU-55
3. 65+ 50 =115 -180= 65
help pls- 10 points- algebra 1
solve for x
-8x+14 ≥ 60 OR − 4x+50 -2
D.) There are no solutions
Answer:
-8x+14 ≥ 60
Inequality Form:
x< -23/4
Interval Notation:
(−∞,−23/4)
A sweater originally priced at 80 dollars was marked down 25% what was the sale price of the sweater
Answer:
$60
Step-by-step explanation:
just is
You plan to run 2 miles, but you only make it \frac{3}{4}
4
3
of the way. How many miles did you run in total?
Answer:
1.5 miles
Step-by-step explanation:
is y=-2x proportional
Answer:
no
Step-by-step explanation:
Answer:
Yes, if you are referring to proportionality in general. No if you are referring to a direct proportionality.
Step-by-step explanation:
y = -2x is negatively proportional so it is not directly proportional because y or one quantity decreases when x or another quantity increases. In a directly proportional relationship, as one quantity increases another quantity must increase at the same rate, in other words both must increase thus be positive. When something is proportional it has a constant ratio, and relation.
Direct proportionality or variation is represented by y ∝ x, where ∝ is the symbol used to represent proportionality.
y = kx where k is the constant of proportionality.
Where k = y/x.
what is 9k + 1 = ─9 + 7k solved for the variable???
Answer:
k = -5
Step-by-step explanation:
The variable is k
9k + 1 = -9 + 7k
-7k -1
2k = -10
2k/2 -10/2
k = -5
:)
Is 518 decimal number
Answer:
no
Step-by-step explanation:
because there is supposed to be a decimal point for example 5.18 there needs to be a period
Answer:
what do you mean there is not decimal in the number you could make it a decimal tho
it would be 5.18 as a decimal
Step-by-step explanation:
HELP!!!!! will give brainliest to the right answer
Answer:
domain is x is an element of all real numbers, or {xer}, and the range is {3.5}
Step-by-step explanation:
since x stretches the whole way it is all real numbers, and y only touches one point on the graph so it has to be a single point
Get it right and ill paypal 25$ if ur fast
ight what do i gotta answer tho
The sum of two numbers is fifteen. One number is five more than the other. Find the numbers.
Note: List numbers with a comma separating them, e.g. 5,12.
Answer:
5,10
Step-by-step explanation:
10 is 5 more than 5 therefore
5+10=15
Answer:
5,2,2,2,2,2
Step-by-step explanation:
2+2+2+2+2=10
10+5=15
You have a budget of $1,900 per week for employees. Employees are pald $11 per hour and work 40 hours per week.
Ignoring overhead, how many employees can you hire ?
[tex]\boldsymbol{4}[/tex] employees were hired by the company.
Define unit method.Amount of total budget [tex]=\$1,900[/tex]
Amount paid to an employee per hour [tex]=\$11[/tex]
Number of hours for which an employee worked per week [tex]=40[/tex]
So,
Total amount paid to an employee [tex]=11\times 40[/tex]
[tex]=\$440[/tex]
Number of employees hired [tex]=4.3[/tex]
[tex]\approx 4[/tex]
So, [tex]\boldsymbol{4}[/tex] employees were hired by the company.
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Ignoring overhead, you can hire 4 employees.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
You have a budget of $1,900 per week for employees.
Employees are paid $11 per hour and work 40 hours per week.
That means,
11 x 40 = $440 per week.
The number of employees = 1900/440
= 4.3
≈ 4
Therefore, 4 number of employees.
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Two angles of a triangle have the same measure and the third one is 30 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.
Answer:
75 degrees
Step-by-step explanation:
Isosceles triangle with 3rd angle being 30 degrees:
2x + 30 = 180
2x = 150
X = 75
Help please here is a picture:
Answer:
2 1/3, 2 1/4, 2 3/7
Step-by-step explanation:
Mixed Fractions
Mixed fractions are made of an integer part followed by a proper fraction.
Some examples of mixed fractions are:
3 1/2, -4 5/8, 2 2/3
Between two consecutive integers a and a+1, there are infinitely many fractions. The centered number is a 1/2. Any number with its improper fraction part less than 1/2 is closer to a than to a+1.
In our problem, Jayne bought between 2 and 3 pounds of granola. We need to provide a mixed number that is closer to 2 pounds than to 3 pounds.
We can select any number with integer part 2 and a proper fraction less than 1/2.
Examples could be :
2 1/3, 2 1/4, 2 3/7
All of them are less than 2.5
Identify the method that will be used in solving for X
5+x=3/4
A• distributive property
B• multiplication property of equality
C• division property of equality
D• subtraction property of equality
Answer:D• subtraction property of equality
Step-by-step explanation:subtract 3/4 on both sides?????
using the arithmetic sequence 7 10 13 16 find the 6th term of the sequence
In how many ways can a president, vice president, and secretary be chosen from a class of 20 girls and 30 boys if the president must be a girl and the vice president a boy?
Given:
Number of girls = 20
Number of boys = 30
The president must be a girl and the vice president a boy
To find:
Number of ways to choose a president, vice president, and secretary.
Solution:
The president must be a girl and the vice president a boy. So, out of three students 1 is girl and 1 is boy. Third student can be a girl or a boy.
Total number of ways = Selecting 2 boys and 1 girl + Selecting 1 boy and 2 girls
[tex]=^{30}C_2\times ^{20}C_1+^{30}C_1\times ^{20}C_2[/tex]
[tex]=\dfrac{30!}{2!(30-2)!}\times \dfrac{20!}{1!(20-1)!}+\dfrac{30!}{1!(30-1)!}\times \dfrac{20!}{2!(20-2)!}[/tex]
[tex]=\dfrac{30\times 29\times 28!}{2\times 1\times 28!}\times \dfrac{20\times 19!}{19!}+\dfrac{30\times 29!}{29!}\times \dfrac{20\times 19\times 18!}{2\times 1\times 18!}[/tex]
[tex]=\dfrac{30\times 29}{2}\times 20+20\times \dfrac{20\times 19}{2}[/tex]
[tex]=8700+3800[/tex]
[tex]=12500[/tex]
Therefore, the required number of ways is 12500.
Largest prime factor of 35 x the smallest prime factor of 15
Answer:
7x3=21 ... i think
Step-by-step explanation:
the factor of 35 is 1,5,7 and 35 but 7 is the largest prime number like the factors of 15 is 1,3,5 and 15 but 3 is the smallest prime number according to the question the answer is 7x3+21
What percent of 78 is 16?
Answer:
78/16=
39/8=
19.5/4= 4.80805
16 is 20.51% of the number 78.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let x percent of 78 is 16.
So, x% of 78 = 16
x/100 (78)= 16
78x = 1600
x= 1600/78
x = 20.51%
Hence, 20.51 percent of 78 is 16.
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How do you do this please explain!
simply 8×4³+2×4⁴ giving you answer in the form of 4^b
Answer:
4^5
Step-by-step explanation:
8×4³+2×4⁴
4×2×4^3+2×4^4
4^4×2+2×4^4
4^4(2+2)
4^4×4
4^5
So answer is 4^5
Which equations are equivalent? Select all that apply.
2n + 4n + 3 = 51
3n + 4 + 5n = 52
3(2n + 6) = 36
8n + 4 = 52
4(2n + 1) = 52
Which statement is false? All points with an x-value of 3 are located in Quadrant I. There is only one point on the coordinate plane that is on both the x- and y-axes. All points with an x-value of 0 are located on the y-axis. There is only one point on the coordinate plane with an x-value of 2 and a y-value of 2.
Answer: Choice A) All points with an x-value of 3 are located in Quadrant I.
We can show it is false through the use of a counter example. For instance, the point (3, -5) is not in quadrant 1, but rather in quadrant 4.
We would need to say "all points with x value 3 and positive y value" to ensure the point is in quadrant 1.
The false statement:
All points with an x-value of 3 are located in Quadrant I.
What are coordinates?Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.
From the given choices:
Let the statement is true.
All points with an x-value of 3 are located in Quadrant I.
Let the coordinate point (3, -7)
This point lies in the fourth quadrant.
Which is contradiction.
Therefore, the statement is false.
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What is the equation for
7x - 4/y =10
in the form y = mx + b?
Answer:
Step-by-step explanation:
assume the equation is (7x-4)/y=10
10y= 7x-4 didvide both sides by 10
y= (7/10)*x - (2/5)
m=7/10
b=-2/5
The equation for 7x - 4/y =10 in the form y = mx + b . The equation in the form
[tex]\(y = mx + b\) is: \[y = \frac{4}{7x - 10}\][/tex]
To rewrite the equation in the form we need to [tex]\(y = mx + b\),[/tex] isolate the term involving y on one side of the equation. Here's the step-by-step process:
Step 1: Add [tex]\(\frac{4}{y}\)[/tex] to both sides of the equation to isolate the 7x term on the left side:
[tex]\[7x = 10 + \frac{4}{y}\][/tex]
Step 2: Get rid of the fraction by multiplying both sides of the equation by y:
[tex]\[7xy = 10y + 4\][/tex]
Step 3: Now, we want to express y alone on one side. To do this, subtract 10y from both sides:
[tex]\[7xy = 10y + 4\][/tex]
Step 4: Factor out y on the left side:
[tex]\[y(7x - 10) = 4\][/tex]
Step 5: Finally, divide both sides by to solve for [tex]\((7x - 10)\)[/tex]
[tex]\[y = \frac{4}{7x - 10}\][/tex]
Now, the equation is in the form where [tex]\(y = mx + b\), \(m\)[/tex] is the coefficient of x and b is the constant term. In this case,[tex]\(m = \frac{4}{7x - 10}\) and \(b\)[/tex] is equal to 0.
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u guys are very helpful <3
Answer:
x=35
Step-by-step explanation:
70+75is 145
and a triangle is equal to 180 degrees
so 180-145 gives you 35 :)
Wayne raked 30 bags of leaves in 3 hours. If he raked the same number of bags each hour, how many bags of leaves did he rake in 1 hour?
Answer:
he raked 10 bags each hour
30/3 = 10
daca stim cel mai mare divizor comun si cel mai mic multiplu comun,in ce mod aflam produsul? (raspunsuri troll iau raport) (troll answers will get reported)
Answer: i think this is romanian? so here is the answer in romanian
Pur și simplu, cel mai mare factor comun al lui a și b atunci când este înmulțit cu cel mai mic comun al lui a și b este egal cu produsul lui a și b ....
Puteți determina LCM de 12 și 16 folosind două metode
Step-by-step explanation:
CAN SOMEBODY PLEASE HELO ME!?!?!?
The radius of the unit circle is equal to_____.
•2π
•1
•2
•π
Answer:
r =1
Step-by-step explanation:
The radius of unit circle is 1
Answer:
1
Step-by-step explanation:
What value of y makes the equation below true?
2y – 25 = 19
44
A
B
22
C
с
-3
oo
D
-6
Please hurry
Answer:
b
Step-by-step explanation:
2*22 = 44
44-25 = 19