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shtirl [24]
4 years ago
11

Amy and her sister are making lemonade for the school dance. Their recipe makes 2 quarts of lemonade. If they make 35 times the

recipe how many gallon
Mathematics
1 answer:
vichka [17]4 years ago
4 0

Answer:

Amy and her sister will have 17.5 gallons of lemonade for the school dance.

Step-by-step explanation:

The sister's recipe makes 2 quarts of lemonade. As they want to make 35 times more, so total number of quarts made will be =

quarts

Now, 4 quarts has 1 gallon.

So, total number of gallons in 70 quarts will be =

tex]\frac{70}{4} =17.5[/tex] gallons.

Hence, the answer is 17.5 gallons.

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Answer:

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Step-by-step explanation:

8 0
3 years ago
Round 56 to the nearest ten
motikmotik

60

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8 0
4 years ago
Suppose that A and B are nonsingular matrices. Then AB is also nonsingular. Furthermore, a theorem from linear algebra then stat
kherson [118]

Answer:

A) Verified

B) Proved

Step-by-step explanation:

a) Let's verify it for 2 x 2 matrix,

A=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] and B=\left[\begin{array}{ccc}e&f\\g&h\end{array}\right]

AB=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]\left[\begin{array}{ccc}e&f\\g&h\end{array}\right]=\left[\begin{array}{ccc}a.e+b.g&a.f+b.h\\c.e+d.g&c.f+d.h\end{array}\right]

(AB)^{-1}=\frac{1}{(a.e+b.g)(c.f+d.h)-(a.f+b.h)(c.e+d.g)}\left[\begin{array}{ccc}c.f+d.h&-(a.f+b.h)\\-(c.e+d.g)&a.e+b.g\end{array}\right]

A^{-1}=\frac{1}{a.d-b.c} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right]

B^{-1}=\frac{1}{e.h-f.g} \left[\begin{array}{ccc}h&-f\\-g&e\end{array}\right]

B^{-1}A^{-1}=\frac{1}{(a.e+b.g)(c.f+d.h)-(a.f+b.h)(c.e+d.g)}\left[\begin{array}{ccc}c.f+d.h&-(a.f+b.h)\\-(c.e+d.g)&a.e+b.g\end{array}\right]

So it is proved that the results are same.

b) Now, let's prove it for any n x n matrix.

(AB)(AB)^{-1}=I\\\\A^{-1}(AB)(AB)^{-1}=A^{-1}I\\\\IB(AB)^{=1}=A^{-1}I\\\\B(AB)^{=1}=A^{-1}\\\\B^{-1}B(AB)^{=1}=B^{-1}A^{-1}\\\\I(AB)^{=1}=B^{-1}A^{-1}\\\\(AB)^{=1}=B^{-1}A^{-1}

8 0
3 years ago
A window has the shape of a rectangle with a semi circle at the top. Find the approximate area of the window using the dimension
miv72 [106K]
First, let's find the area of the semi-circle.
Area of a circle = π*r²
Looking at the rectangle, the diameter for the circle is 2 ft. Since we need the radius though, divide the diameter by 2 to get the radius.
r = 1
A = π * 1²
A = π * 1
A = π

But since it's a semicircle, you need to divide that area by 2.
3.14/2 = 1.57

The area of the semi-circle is 1.57.

Area of a rectangle = lw
l = 2
w = 4
A = 2 * 4
A = 8

The area of the rectangle is 8.

Now add those together to get the area of the entire figure.

1.57 + 8 = 9.57

The figure is about 9.57 square feet.

8 0
3 years ago
Read 2 more answers
Faith owns an organic apple orchard. From her experience the last few seasons, she has developed the formula P=20x-0.01x^2 -240
Marta_Voda [28]

P=20x-0.01x^2-240

P=20(300)-0.01(300)^2-240

P=6000-0.01(90000)-240

P=6000-900-240

P=4860

Remember PEMDAS

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

EXPLANATION: first Is Parentheses, which would be 300, multiply that by 20, that would be 6000.

Next is Exponents, which would be the (^2) so you would Multiply the 300 by itself 2 times. which is 90000

Next is Multiplication, Multiply 0.01 by 90000, which would be 900.

There is nothing to divide or add so skip that.

Next is subtraction, subtract 6000-900-240 and the answer would be 4860.

so Faith's prediction profit for this season would be 4860 when her orchard produces 300 bushels of apples.

I hope that helped! Good Luck!

6 0
3 years ago
Read 2 more answers
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