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Lapatulllka [165]
2 years ago
15

B. To make salad dressing for the fruit salad, Mrs. Santos uses 2/4 cup oil, 1 cup orange juice, and 3/4 cup honey. How many cup

s of salad dressing does this make? Explain how you found your answer.
Mathematics
2 answers:
zalisa [80]2 years ago
8 0

Add all

\\ \rm\rightarrowtail \dfrac{2}{4}+\dfrac{3}{4}+\dfrac{4}{4}

\\ \rm\rightarrowtail \dfrac{2+3+4}{4}

\\ \rm\rightarrowtail \dfrac{9}{4}

\\ \rm\rightarrowtail 2\dfrac{1}{4}cups

Ket [755]2 years ago
5 0

Answer:

\sf 2 \frac14 \ cups

Step-by-step explanation:

Add the amounts together:

\sf \implies \dfrac24+1+\dfrac34

Convert the whole number 1 into a fraction with denominator 4:

\sf \implies \dfrac24+\dfrac44+\dfrac34

As all the denominators are the same, we can simply add the numerators:

\sf \implies \dfrac{2+4+3}4

\sf \implies \dfrac94

Finally, convert the improper fraction into a mixed number:

\sf \implies 2 \frac14 \ cups

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Step-by-step explanation:

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3 years ago
Jay has an album that holds 900 photos. Each page of the album holds 9 photos. If 64 % of the album is​ empty, how many pages ar
Butoxors [25]

well 9+10=21

Step-by-step explanation:

5 0
3 years ago
Round to the nearest tenth.
laila [671]

Answer:

8.2 units

Step-by-step explanation:

Given that the only information for our triangle are 2 sides and 1 angle, we must use the Law of Cosines to find side BC

<u />

<u>Recall the Law of Cosines</u>

<u />a^2=b^2+c^2-2bc\cdot cos(A)

<u>Identify angles and sides</u>

<u />m\angle A=23^\circ\\a=BC=?\\b=AC=14\\c=AB=6

<u>Solve for side "a"</u>

<u />a^2=b^2+c^2-2bc\cdot cos(A)\\\\a^2=14^2+6^2-2(14)(6)\cdot cos(23^\circ)\\\\a^2=196+36-168cos(23^\circ)\\\\a^2=222-168cos(23^\circ)\\\\a=\sqrt{222-168cos(23^\circ)}\\ \\a\approx8.2

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2 years ago
Find the derivative.
krek1111 [17]

Answer:

\displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}

General Formulas and Concepts:

<u>Algebra I</u>

Terms/Coefficients

  • Expanding/Factoring

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]:                                                                           \displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle f(x) = \frac{\sqrt{x}}{e^x}

<u>Step 2: Differentiate</u>

  1. Derivative Rule [Quotient Rule]:                                                                   \displaystyle f'(x) = \frac{(\sqrt{x})'e^x - \sqrt{x}(e^x)'}{(e^x)^2}
  2. Basic Power Rule:                                                                                         \displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}(e^x)'}{(e^x)^2}
  3. Exponential Differentiation:                                                                         \displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{(e^x)^2}
  4. Simplify:                                                                                                         \displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{e^{2x}}
  5. Rewrite:                                                                                                         \displaystyle f'(x) = \bigg( \frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x \bigg) e^{-2x}
  6. Factor:                                                                                                           \displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

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daser333 [38]
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