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stepladder [879]
3 years ago
8

Jason wants to bake 4 batches of peanut butter cookies. Each recipe requires 1 cup of peanut butter, 1/2 cup sugar and 2 eggs. H

ow much of each ingredient does he need to bake 4 batches? Use distributive property to set up problem then solve.
Mathematics
1 answer:
musickatia [10]3 years ago
6 0

Answer:

4 cups of peanut butter, 2 cups of sugar, and 8 eggs.

Step-by-step explanation:

(1x4=4 + 1/2x4= 2 + 4x2=8)

Hope this helps!

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Find e^cos(2+3i) as a complex number expressed in Cartesian form.
ozzi

Answer:

The complex number e^{\cos(2+31)} = \exp(\cos(2+3i)) has Cartesian form

\exp\left(\cosh 3\cos 2\right)\cos(\sinh 3\sin 2)-i\exp\left(\cosh 3\cos 2\right)\sin(\sinh 3\sin 2).

Step-by-step explanation:

First, we need to recall the definition of \cos z when z is a complex number:

\cos z = \cos(x+iy) = \frac{e^{iz}+e^{-iz}}{2}.

Then,

\cos(2+3i) = \frac{e^{i(2+31)} + e^{-i(2+31)}}{2} = \frac{e^{2i-3}+e^{-2i+3}}{2}. (I)

Now, recall the definition of the complex exponential:

e^{z}=e^{x+iy} = e^x(\cos y +i\sin y).

So,

e^{2i-3} = e^{-3}(\cos 2+i\sin 2)

e^{-2i+3} = e^{3}(\cos 2-i\sin 2) (we use that \sin(-y)=-\sin y).

Thus,

e^{2i-3}+e^{-2i+3} = e^{-3}\cos 2+ie^{-3}\sin 2 + e^{3}\cos 2-ie^{3}\sin 2)

Now we group conveniently in the above expression:

e^{2i-3}+e^{-2i+3} = (e^{-3}+e^{3})\cos 2 + i(e^{-3}-e^{3})\sin 2.

Now, substituting this equality in (I) we get

\cos(2+3i) = \frac{e^{-3}+e^{3}}{2}\cos 2 -i\frac{e^{3}-e^{-3}}{2}\sin 2 = \cosh 3\cos 2-i\sinh 3\sin 2.

Thus,

\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2-i\sinh 3\sin 2\right)

\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2\right)\left[ \cos(\sinh 3\sin 2)-i\sin(\sinh 3\sin 2)\right].

5 0
3 years ago
If Chris has 4 times as many nickels as quarters and they have a combined value of 180 cents, how many of each coin does he have
Oduvanchick [21]
82 to coins and quadrilateral
6 0
4 years ago
Read 2 more answers
Marta believes that the equation of the line of best fit for the scatterplot below is -
Alexus [3.1K]

Marta’s equation has a positive y-intercept, but the scatterplot shows a negative correlation.

<h3>What is a scatter plot?</h3>

The scatter plot is a manner in which data is presented as dots on a cartesian axes, The line of best fit is a description of the data that is presented in the scatter plot.

Hence, Marta is incorrect because Marta’s equation has a positive y-intercept, but the scatterplot shows a negative correlation.

Missing parts;

Marta believes that the equation of the line of best fit for the scatterplot below is y=-5/9x+23/9. Which statement best summarizes why Marta is likely incorrect?

Marta’s equation has a positive y-intercept, but the scatterplot suggests a negative y-intercept.

Marta’s equation has a positive y-intercept, but the scatterplot shows a negative correlation.

Marta’s equation has a negative slope, but the scatterplot suggests a negative y-intercept.

Marta’s equation has a negative slope, but the scatterplot shows a positive correlation.

Learn more about scatter plot:brainly.com/question/13984412

#SPJ1

7 0
2 years ago
In a class, 21 students have black hair, 11 students have blonde hair, 9 students have brown hair and 4 students have red hair.
tangare [24]
Total =45

Black hair=21*360/45=168
Blonde=11*360/45=88
Brown=9*360/45=72
Red=4*360/45=32
5 0
4 years ago
Plz help!
BlackZzzverrR [31]

Answer:

A. An altitude

Step-by-step explanation:

B/c B and C aren't used in graphs

4 0
3 years ago
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