1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nastasia [14]
3 years ago
7

Select the objects that hold the same amount of liquid as a 98 fluid ounce jug

Mathematics
1 answer:
Tema [17]3 years ago
6 0
To answer this question, you need to know how many fluid ounces are in a pint and in a quart.  None of the choices reflect 98 fl oz, so I showed the ones that would hold 96 fluid ounces.

1 cup = 8 fl oz
2 cups = 16 fl oz
1 pint = 2 cups, so 1 pint also equals 16 fl oz.

2 pints equal 1 quart, so 16 x 2 = 32 oz (the number of fluid ounces in a quart)

1 pint - 16 fl oz
1 quart = 32 fl oz

Choice A: 3 quarts x 32 =96 fl oz.
Choice B: 2 quarts x 32 = 64 fl oz
Choice C: 2 quarts  x 32 + 2 pints x 16 = 64 + 32 (96 fl oz)
Choice D: 1 quart x 32 + 8 cups x 8 = 32 + 64 (96 fl oz)
Choice E: 2 cups x 8 + 2 pints x 16 = 16 + 32 (48 fl oz)
You might be interested in
<img src="https://tex.z-dn.net/?f=%5Clarge%20%5Crm%20%5Csum%20%5Climits_%7Bn%20%3D%200%7D%5E%20%5Cinfty%20%20%20%5Cfrac%7B%28%20
Fynjy0 [20]

The sum we want is

\displaystyle \sum_{n=0}^\infty \frac{(-1)^{T_n}}{(2n+1)^2} = 1 - \frac1{3^2} - \frac1{5^2} + \frac1{7^2} + \cdots

where T_n=\frac{n(n+1)}2 is the n-th triangular number, with a repeating sign pattern (+, -, -, +). We can rewrite this sum as

\displaystyle \sum_{k=0}^\infty \left(\frac1{(8k+1)^2} - \frac1{(8k+3)^2} - \frac1{(8k+7)^2} + \frac1{(8k+7)^2}\right)

For convenience, I'll use the abbreviations

S_m = \displaystyle \sum_{k=0}^\infty \frac1{(8k+m)^2}

{S_m}' = \displaystyle \sum_{k=0}^\infty \frac{(-1)^k}{(8k+m)^2}

for m ∈ {1, 2, 3, …, 7}, as well as the well-known series

\displaystyle \sum_{k=1}^\infty \frac{(-1)^k}{k^2} = -\frac{\pi^2}{12}

We want to find S_1-S_3-S_5+S_7.

Consider the periodic function f(x) = \left(x-\frac12\right)^2 on the interval [0, 1], which has the Fourier expansion

f(x) = \frac1{12} + \frac1{\pi^2} \sum_{n=1}^\infty \frac{\cos(2\pi nx)}{n^2}

That is, since f(x) is even,

f(x) = a_0 + \displaystyle \sum_{n=1}^\infty a_n \cos(2\pi nx)

where

a_0 = \displaystyle \int_0^1 f(x) \, dx = \frac1{12}

a_n = \displaystyle 2 \int_0^1 f(x) \cos(2\pi nx) \, dx = \frac1{n^2\pi^2}

(See attached for a plot of f(x) along with its Fourier expansion up to order n = 10.)

Expand the Fourier series to get sums resembling the S'-s :

\displaystyle f(x) = \frac1{12} + \frac1{\pi^2} \left(\sum_{k=0}^\infty \frac{\cos(2\pi(8k+1) x)}{(8k+1)^2} + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+2) x)}{(8k+2)^2} + \cdots \right. \\ \,\,\,\, \left. + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+7) x)}{(8k+7)^2} + \sum_{k=1}^\infty \frac{\cos(2\pi(8k) x)}{(8k)^2}\right)

which reduces to the identity

\pi^2\left(\left(x-\dfrac12\right)^2-\dfrac{21}{256}\right) = \\\\ \cos(2\pi x) {S_1}' + \cos(4\pi x) {S_2}' + \cos(6\pi x) {S_3}' + \cos(8\pi x) {S_4}'  \\\\ \,\,\,\, + \cos(10\pi x) {S_5}' + \cos(12\pi x) {S_6}' + \cos(14\pi x) {S_7}'

Evaluating both sides at x for x ∈ {1/8, 3/8, 5/8, 7/8} and solving the system of equations yields the dependent solution

\begin{cases}{S_4}' = \dfrac{\pi^2}{256} \\\\ {S_1}' - {S_3}' - {S_5}' + {S_7}' = \dfrac{\pi^2}{8\sqrt 2}\end{cases}

It turns out that

{S_1}' - {S_3}' - {S_5}' + {S_7}' = S_1 - S_3 - S_5 + S_7

so we're done, and the sum's value is \boxed{\dfrac{\pi^2}{8\sqrt2}}.

6 0
2 years ago
Subtract these polynomials
Sergio039 [100]

Answer:

simplify the equation into 6x^2-x+8-x^2-2, then subtract. the answer is B.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What is the value of a
dalvyx [7]
I hope this helps you

3 0
3 years ago
A computer store decides to increase the prices of all the items it sells by 15%. the store manager uses matrices to prepare the
Andrews [41]

The matrix exists as a set of numbers placed in rows and columns to create a rectangular array. The manager could achieve scalar multiplication on Matrix A, utilizing the scalar 1.15.

<h3>What is the matrix?</h3>

The matrix exists as a set of numbers placed in rows and columns to create a rectangular array. The numbers exist named the elements, or entries, of the matrix. Matrices contain wide applications in engineering, physics, economics, and statistics as well as in different branches of mathematics.

Increasing the price by 15% would mean we exist taking 100% of the value + another 15%

100 + 15 = 115%

115% = 115/100 = 1.15.

Multiplying every value in Matrix A by 1.15 will give the price raised by 15%.

Therefore, the correct answer is option c. by multiplying each entry of matrix a by 1.15.

To learn more about matrix refer to:

brainly.com/question/12567347

#SPJ4

7 0
2 years ago
Given f(x) = abx + c. How would increasing the value of a change the graph?
Helen [10]
Increasing the value of a would change the slope of the function specifically it would increase as well. Therefore, the line would be steeper than the original. The term ab represents the slope of the function and changing either one would result to the change of the steepness of the line.
4 0
3 years ago
Read 2 more answers
Other questions:
  • A sales representative must visit eight cities. There are direct air connections between each of the cities. Use the multiplicat
    9·1 answer
  • A rectangle's length is 6 units greater than its width. Write an equation expressing the rectangle's area, A, as a function of w
    14·1 answer
  • What is 119,000,003 in word form
    11·2 answers
  • Does anyone know the answer to the question below.
    14·1 answer
  • Solve and graph the inequality.<br><br> 8 + k &lt; 5
    12·2 answers
  • WILL GIVE BRAINLIEST. It is also worth 34 POINTS!!! PLEASE HELP!!!! Please respond in full sentences. I appreciate your help. Th
    12·1 answer
  • I WILL MARK AS BRAINLIEST PLEASE ANSWER FAST
    8·2 answers
  • I NEED THIS IN LESS THAN 7 MINS!! PLS​
    12·2 answers
  • Solve each system of equations or inequalities by graphing <br> 3x - 2y = 6<br> 2x + y = 4
    5·1 answer
  • Find the end time<br>start time: 3:46pm<br>elapsed: 2h 20min​
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!