A 27 oz bottle of a new soda costs $2.25. What is the unit rate, rounded to the nearest tenth of a cent?
The unit rate is the cost per ounce of soda. By dividing the total cost by the total ounces, we get the price per ounce in dollars ($0.08333), and converting this to cents gives us $8.3 cents per ounce.
Explanation:The term unit rate refers to a rate in which the second term is 1. In this case, we want to find out how much 1 ounce of soda costs.
First, you want to divide the total cost of the bottle by the total ounces in the bottle. So you divide $2.25 by 27. The answer you get is the price of one ounce of soda in dollars. When calculating it, you get approximately $0.08333.
To get the rate in cents, convert the dollars to cents by multiplying by 100 (since 1 dollar is 100 cents). The answer ($8.33) is the cost of one ounce to the nearest tenth of a cent.
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In an x-y plot of an experiment what is usually plotted on the x axis?
a. the independent variable, which is the parameter that was manipulated.
b. th
a line that intersects the points (-23,-17) and (-13,-7), find the slope, now fill in the missing inputs to the slope-intercept formula -17=1(?)+b or (?)=(-13)+b
120 × a = 2889 what is the product
Lakeya makes cupcakes to sell at her friend's lemonade stand. She sold 24 cupcakes and sold them for $3 each. Write a number sentence using the variable m to represent the total amount of money she made.
How many times does 1/2 fit into 30
marissa sprinted for 48 yards. how many feet did she sprint.
What is the answer to this question ?
Ordering Least to greatest 2 9/11, 4/5, 2.91, 0.9
One side of a rectangle is 3 inches shorter than the other side, and the perimeter is 54 inches. Which of the following equations could be used to determine the dimensions of the rectangle
What is 164% of 25? I have no idea and im in the middle of a test XDDD
Multiple choice strategy: some students have suggested that if you have to guess on a multiple-choice question, you should always choose
c. carl, the student, wants to investigate this theory. he is able to get a sample of past tests and quizzes from various teachers. in this sample there are 110 multiple-choice questions with four options (a, b, c, d). the distribution of correct answers from this sample is given in the frequency table below. correct answer frequency a 22 b 26 c 38 d 24
HELP! solve for p p+10/p-7=8/9
Jeff invests an amount at 4% interest compounded annually. After 3 years, he has $1687.30. What was the original amount Jeff invested?
$1500
$1200
$1450
$750
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Rewrite as a square or a cube:
1 11/25
Answer:
1 11/25 = 36/25
= (6/5)^2
Step-by-step explanation:
How do i know that the variable x has a uniform distribution function?
Which of the following is rational
A. 3*pi
B. 2/3+9.26
C. sqrt of 45 + sqrt of 36
D.14.3... + 5.78765239...
Solve for x.
−5x−4(x−6)=−3
-5x -(4x-6) = -3
-5x -4x + 24 = -3
-9x = -27
x= 3
what is the solution of -8/2y-8=5/y+4 - 7y+8/y^2-16? y = –4 y = –2 y = 4 y = 6
Answer:
d. 6
Step-by-step explanation:
just took the pretest:) have such a fantastic day loves, you're doing AMAZING!
Simplify 6 - 23 + (-9 + 5) · 2
A. -10
B. -12
C. 6
D. -8
I've been told the answer is A. -10, but I need to know how to get that answer.
Thanks.
at least u tried to help but the answer is -10 bro
Two numbers total 53 and have a difference of 25. Find the two numbers.
lisha is making headbands using ribbon. she would like to make 12 head bands. Each one requires 15.5 inches of ribbon. She estimates that she will need to buy 160 inches of ribbon is her estimate reasonable? Explain your reasoning and lol I'm not in college i just did that
Help Algebra Question
You would like to join a fitness center. Fit-N-Trim charges $80 per month. Fit-For-Life charges a one tim e membership fee of $75 and $55 per month. The lines shown in the graph represent the cost y to attend each fitness center for x months. Are the lines parallel?
Hi, How do you find the first and second derivatives of the function.
y=(x^2-7/63x) (x^4+1/x^3)
I think for the first derivative dy/dx it's 2/63x-3/63x^-3+4/9x^-5 but I'm not sure, and I have no clue for the second derivative d^2y/dx^2.
The first hand derivative of the function is [tex]6x^5 - \frac{35}{63}x^4 - \frac{1}{x^2} - \frac{4}{63x^3}[/tex] and the second derivative is [tex]30x^4 - \frac{20}{9}x^3 + \frac{2}{x^3} - \frac{2}{3x^4} \\[/tex]. To find the first derivative, apply the product rule to the given function. Then, differentiate the first derivative to obtain the second derivative. Simplify each step carefully.
To find the first derivative of the given function [tex]y = \left( x^2 - \frac{7}{63}x \right) \left( x^4 + \frac{1}{x^3} \right)[/tex], we'll use the product rule, which states that if [tex]y = u(x) \cdot v(x)[/tex], then [tex]y' = u' \cdot v + u \cdot v'[/tex].
First, define u(x) and v(x) as following:
[tex]u(x) = x^2 - \frac{7}{63}x = x^2 - \frac{1}{9}x[/tex][tex]v(x) = x^4 + \frac{1}{x^3}[/tex]Compute u'(x):
[tex]u'(x) = 2x - \frac{1}{9}[/tex]Compute v'(x):
[tex]v'(x) = 4x^3 + (-3)x^{-4} = 4x^3 - \frac{3}{x^4}[/tex]Apply the product rule: [tex]y' = u' \cdot v + u \cdot v'[/tex]
Thus,
[tex]y' = \left(2x - \frac{1}{9}\right)\left( x^4 + \frac{1}{x^3} \right) + \left( x^2 - \frac{1}{9}x \right) \left( 4x^3 - \frac{3}{x^4} \right)[/tex]Simplify this expression step-by-step to find the first derivative.
[tex]y' = \left(2x - \frac{1}{9}\right)\left( x^4 + \frac{1}{x^3} \right) + \left( x^2 - \frac{1}{9}x \right) \left( 4x^3 - \frac{3}{x^4} \right)[/tex][tex]y'[/tex] [tex]&= \left(2x \cdot x^4 + 2x \cdot \frac{1}{x^3} - \frac{1}{9} \cdot x^4 - \frac{1}{9} \cdot \frac{1}{x^3} \right)[/tex][tex]&\quad + \ \left( x^2 \cdot 4x^3 - x^2 \cdot \frac{3}{x^4} - \frac{1}{9}x \cdot 4x^3 + \frac{1}{9}x \cdot \frac{3}{x^4} \right)[/tex][tex]y'[/tex] [tex]&= 2x^5 + \frac{2}{x^2} - \frac{1}{9}x^4 - \frac{1}{9x^3} \\[/tex] [tex]&\quad + \ 4x^5 - \frac{3}{x^2} - \frac{4}{9}x^4 + \frac{1}{3x^3}[/tex][tex]y'[/tex] [tex]&= 6x^5 - \frac{1}{x^2} - \frac{5}{9}x^4 + \frac{2}{9x^3}[/tex][tex]y'[/tex] [tex]&= 6x^5 - \frac{5}{9}x^4 - \frac{1}{x^2} + \frac{2}{9x^3}[/tex]To find the second derivative, differentiate the first derivative, carefully differentiating each term:
[tex]y'' &= \frac{d}{dx}\left( 6x^5 \right) - \frac{d}{dx}\left( \frac{5}{9}x^4 \right) - \frac{d}{dx}\left( \frac{1}{x^2} \right) + \frac{d}{dx}\left( \frac{2}{9x^3} \right) \\[/tex][tex]y''[/tex] [tex]&= 30x^4 - \frac{5}{9} \cdot 4x^3 - \left( -2x^{-3} \right) + \left( -\frac{2}{9} \cdot 3x^{-4} \right) \\[/tex][tex]y''[/tex] [tex]&= 30x^4 - \frac{20}{9}x^3 + \frac{2}{x^3} - \frac{2}{3x^4} \\[/tex]So, for the function [tex]y = \left( x^2 - \frac{7}{63}x \right) \left( x^4 + \frac{1}{x^3} \right)[/tex], we have:
First derivative [tex](y')[/tex] [tex]&= 6x^5 - \frac{5}{9}x^4 - \frac{1}{x^2} + \frac{2}{9x^3}[/tex]Second derivative [tex](y'')[/tex] [tex]&= 30x^4 - \frac{20}{9}x^3 + \frac{2}{x^3} - \frac{2}{3x^4} \\[/tex]A boat was sailing for 4 hours and covered 224 miles. A jet is ten times as fast as the boat. Find the jet’s speed.
You swim 121 out of 1,000 meters. How can you write this as a decimal
The number in decimal form will be 0.121 meters.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that you swim 121 out of 1,000 meters. The decimal for the number will be written by dividing the number by 1000.
Decinmal form = 121 / 1000
Decimal form = 0.121 meters
Therefore, the decimal form of the number will be 0.121 meters.
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John throws a rock straight down with speed 12 m/s from the top of a tower. the rock hits the ground after 2.37 s. what is the height of the tower? (air resistance is negligible)
Estimate instantaneous rate of change of the point indicated p(x) = 3x^2-5, x = 2
A college freshmen must take a science course, a humanities course and a mathematics course. If she may select any of 6 science courses, any of 4 humanities and any of 4 mathematics courses, how many ways can she arrange her program? Make a tree diagram and list the possibilities.