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2 years ago

8

Shawna is making smoothies. The recipe calls for 2 parts yogurt to 3 parts blueberries. Shawna wants to make 10 cups of smoothie

mix. How many cups of yogurt and blueberries does shawna need?

1 answer:

vesna_86 [32]2 years ago

7 0

20 cups yogurt and 30 cups blueberry

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5. When looking at a map, a student realizes that Birmingham is nearly due west of Atlanta, and Nashville is nearly due north of

leonid [27]

Answer: 250 mi

Step-by-step explanation:

Here we can think in a triangle rectangle:

The distance from Birmingham to Atlanta is roughly 150 mi, and this is one of the cathetus.

And the distance from Birmingham to Nashville is roughly 200 mi, this is the other cathetus of the triangle.

Now, the distance from Atlanta to Nashville will be the hypotenuse of this triangle rectangle.

Now we can apply the Pythagorean's theorem:

A^2 + B^2 = H^2

Where A and B are the cathetus, and H is the hypotenuse:

Then:

H = √(A^2 + B^2)

H = √(150^2 + 200^2) mi = √(62,500) mi = 250 mi

Then the estimated distance from Atlanta to Nashville is 250 mi

6 0

2 years ago

Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant.

BlackZzzverrR [31]

This part of the plane is a triangle. Call it $\mathcal S$ . We can find the intercepts by setting two variables to 0 simultaneously; we'd find, for instance, that $y=z=0$ means $5x=20\implies x=4$ , so that (4, 0, 0) is one vertex of the triangle. Similarly, we'd find that (0, 5, 0) and (0, 0, 20) are the other two vertices.

Next, we can parameterize the surface by

$\mathbf s(u,v)=\langle4(1-u)(1-v),5u(1-v),20v\rangle$

so that the surface element is

$\mathrm dS=\|\mathbf s_u\times\mathbf s_v\|=20\sqrt{42}(1-v)\,\mathrm du\,\mathrm dv$

Then the area of $\mathcal S$ is given by the surface integral

$\displaystyle\iint_{\mathcal S}\mathrm dS=20\sqrt{42}\int_{u=0}^{u=1}\int_{v=0}^{v=1}(1-v)\,\mathrm dv\,\mathrm du$
$\displaystyle=20\sqrt{42}\int_{v=0}^{v=1}(1-v)\,\mathrm dv=10\sqrt{42}\approx64.8074$

3 0

2 years ago

Amy has a box containing 6 white, 4 red, and 8 black marbles. She picks a marble randomly. It is red. The second time, she picks

Alika [10]

8/15 or 11/15 would b the probabiltity of those

6 0

2 years ago

Determine the value of $a$. [asy] pair w=(0,4); pair x=(0,0); pair y=(4,0); pair z=y+7/sqrt(2)*(1,1); dot(w); dot(x); dot(y); do

grandymaker [24]

Answer:

a=7

Step-by-step explanation:

The image is rendered and attached below.

Triangle WXY is an Isosceles right triangle, since WX=XY.

First, we determine the length of WY using Pythagoras Theorem.

$WY=\sqrt{4^2+4^2}\\WY=\sqrt{32}$

Since triangle WXY is Isosceles, $\angle XYW=45^\circ$

$\angle XYZ=\angle XYW+\angle WYZ\\135^\circ=45^\circ+\angle WYZ\\\angle WYZ=135^\circ-45^\circ=90^\circ$

Therefore:

Triangle WYZ is a right triangle with WZ as the hypothenuse.

Applying Pythagoras Theorem

$WZ^2=WY^2+YZ^2\\9^2=(\sqrt{32})^2+a^2\\a^2=81-32\\a^2=49\\a^2=7^2\\$Therefore: a=7$

3 0

2 years ago

Determine whether each of these sets is finite, countably infinite, or uncountable. For those that are countably in- finite, exh

mrs_skeptik [129]

Answer:

a) the negative integers set A is countably infinite.

one-to-one correspondence with the set of positive integers:

f: Z+ → A, f(n) = -n

b) the even integers set A is countably infinite.

one-to-one correspondence with the set of positive integers:

f: Z+ → A, f(n) = 2n

c) the integers less than 100 set A is countably infinite.

one-to-one correspondence with the set of positive integers:

f: Z+ → A, f(n) = 100 - n

d) the real numbers between 0 and 12 set A is uncountable.

e) the positive integers less than 1,000,000,000 set A is finite.

f) the integers that are multiples of 7 set A is countably infinite.

one-to-one correspondence with the set of positive integers:

f: Z+ → A, f(n) = 7n

Step-by-step explanation:

A set is finite when its elements can be listed and this list has an end.

A set is countably infinite when you can exhibit a one-to-one correspondence between the set of positive integers and that set.

A set is uncountable when it is not finite or countably infinite.

8 0

2 years ago