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3 years ago

8

Kevin was having so much fun making cupcakes for his class. He made 2 dozen of them! But there are only 19 kids in his class. Lu

ckily everyone are one cupcake except for Emma. How many cupcakes are left over?

1 answer:

Evgesh-ka [11]3 years ago

5 0

6 cupcakes are left 2 dozen is 24 19 kids minus Emma is 18 24-18=6

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9) Lucy owes the bank $500. She has $100 and plans to save $25 each month to pay the bank back.

coldgirl [10]

Answer:

500$ she has 100$ and plans to save $25 each month

Step-by-step explanation:

she will have to save $25 for 16 months to pay the bank back there money

3 0

3 years ago

Find the area of the figure

yanalaym [24]

IT'S SImple just divid all them toghether 2x2x2x2x2x2x2x2x2=999,0000 and that is ur answer

8 0

3 years ago

Nina has prepared the following two-column proof below. She is given that ∠OLN ≅ ∠LNO and she is trying to prove that OL ≅ ON. S

Anit [1.1K]

Step number 3 should really be step number 7, it should be placed after step 4, 5, and 6. The reason is because we won't know that ∠LEO ≅ ∠NEO until after we learn that LE ≅ EN. Because of this, step 3 is in the wrong spot (mistake number one). The secod mistake is that step 7, triangle OLE ≅ triangle ONE is congruent by Angle-Side-Angle (ASA) Postulate, not Side-Angle-Side (SAS) Postulate. It is congruent by ASA because we know that both triangles have equal angles N and L. We also know that the perpendicular bisector creates a 90° angle. So m∠LEO = 90° and ∠NEO = 90°. Therefore, we already have 2 congruent angles in both of the triangles. We also learn that line LE ≅ EN based on the definition of a perpendicular bisector, so we have know one that one side of each triangle is congruent. It is ASA and not AAS, because the ASA Postulate states that two angles and one included side of one triangle are congruent to two angles and one included side of another triangle.

7 0

4 years ago

Which of the following is the value of x?<br><br> A. 2<br><br> B.11<br><br> C. 20 <br><br> D. 29

Lunna [17]

Answer:

c

Step-by-step explanation:

180= 45+ (5x+35)

-45 -45

135 = 5x + 35

-35 -35

100 = 5x

/5 /5

x=20

5 0

3 years ago

You have asked to design a rectangle box with a square base and an open top. The volume of the box must be620 cm to the 3rd powe

hammer [34]

Answer:

$69.21

Step-by-step explanation:

Since the box has a square base the length and breadth of the box will be equal. Let it be $x$

Let h be the height of the box

V = Volume of the box = $620\ \text{cm}^3$

$x^2h=620\\\Rightarrow h=\dfrac{620}{x^2}$

Now surface area of the box with an open top is given

$s=x^2+4xh\\\Rightarrow s=x^2+4x\dfrac{620}{x^2}\\\Rightarrow s=x^2+\dfrac{2480}{x}$

Differentiating with respect to x we get

$\dfrac{ds}{dx}=2x-\dfrac{2480}{x^2}$

Equating with zero

$0=2x-\dfrac{2480}{x^2}\\\Rightarrow 2x^3-2480=0\\\Rightarrow x^3=\dfrac{2480}{2}\\\Rightarrow x=(1240)^{\dfrac{1}{3}}\\\Rightarrow x=10.74$

Double derivative of the function

$\dfrac{d^2s}{ds^2}=2+\dfrac{4960}{x^3}=2+\dfrac{4960}{1240}\\\Rightarrow \dfrac{d^2s}{ds^2}=6>0$

So, x at 10.74 is the minimum value of the function.

$h=\dfrac{620}{x^2}\\\Rightarrow h=\dfrac{620}{10.74^2}\\\Rightarrow h=5.37$

So, minimum length and breadth of the box is 10.74 cm while the height of the box is 5.37 cm.

The total area of the sides is $4xh=4\times 10.74\times 5.37=230.7\ \text{cm}^2$

The area of the base is $x^2=10.74^2=115.35\ \text{cm}^2$

Cost of the base is $0.40 per square cm

Cost of the side is $0.10 per square cm

Minimum cost would be

$230.7\times 0.1+0.4\times 115.34=\$69.21$

The minimum cost of the box is 69.21 dollars.

8 0

3 years ago