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Ivanshal [37]
2 years ago
10

Ginger has 12 plastic bead containers. The containers measure 1 inch on each side. How many rectangular prisms, each with a diff

erent-sized base, could Ginger make by stacking all of the bead containers?
Mathematics
1 answer:
denis23 [38]2 years ago
8 0
Number of different bases for each one:
1 1 12 --->1 1 12, 1 12, 1 ----- 2 of them
1 2 6 ---> 1 2 6, 1 6, 2, 2 6 1 --- 3 of them
1 3 4 ---> 1 3 4, 1 4 3, 3 4 1 --- 3 of them
2 2 3 ---> 2 2 3, 2 3 2 ----- 2 of them
Answer-10 different prisms
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HELP MEEEEEEEEEE Package A contains 3 birthday cards and 2 thank-you notes and costs $9.60. Package B contains 8 birthday cards
hodyreva [135]

Answer:

Each birthday card costs $2.2 ⇒ answer c

Step-by-step explanation:

* Lets explain how to solve the problem

- Package A contains 3 birthday cards and 2 thank-you notes

- It costs $9.60

- Package B contains 8 birthday cards and 6 thank-you notes

- It costs $26.60

- x represents the cost of birthday card and y represents the cost of

 thank-you note

* Lets change these information to two equations

∵ x represents the cost of each birthday cards

∵ y represents the cost of each thank-you notes

∵ Bag A contains 3 birthday cards and 2 thank-you notes

∵ Bag A costs $9.60

∴ 3x + 2y = 9.60 ⇒ (1)

∵ Bag B contains 8 birthday cards and 6 thank-you notes

∵ Bag B costs $26.60

∴ 8x + 6y = 26.60 ⇒ (2)

* Lets solve this system of equations to find x and y

- Multiply equation (1) by -3 to eliminate y

∵ -3(3x) + -3(2y) = -3(9.60)

∴ -9x - 6y = -28.8 ⇒ (3)

- Add equations (2) and (3)

∴ -x = -2.2

- Multiply both sides by -1

∴ x = 2.2

∵ x represents the cost of each birthday cards

∴ The cost of each birthday card is $2.2

* Each birthday card costs $2.2

6 0
2 years ago
Read 2 more answers
What is the exact volume of the cone? 80π ft³ 4003π ft³ 400π ft³ 418710π ft³ Outline of cone with a dotted line rising from midd
rodikova [14]
Volume of cone = 1/3 x pi x r^2 x h
where r = 5 ft and h = 16ft

Volume = 1/3 x pi x 5^2 x 16 = 400/3 π ft^3
6 0
2 years ago
Read 2 more answers
In the figure below, what is the value of angle Z?
Hoochie [10]

Answer:

=2.83 the second option

Step-by-step explanation:

Using the trigonometric ratios we can find the sides of the triangle with the acute angles.

In the triangle provided we will use COSINE

Cos ∅=adjacent/hypotenuse

Let us substitute with the values in the question into the formula.

Tan 45 =2/x

x=2/Cos 45

=2.83 units

3 0
2 years ago
Read 2 more answers
a lunch stand makes a $.75 profit on each chef's salad and $1.20 profit on each caesar salad. On a typical weekday, it sells bet
tangare [24]

Answer:

<em>50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.</em>

Step-by-step explanation:

Suppose, the number of Chef's salad is x and the number of Caesar salad is y

On a typical weekday, it sells between 40 and 60 Chefs salads and between 35 and 50 Caesar salads.

So, the two constraints are:  40\leq x\leq 60 and  35\leq y\leq 50

The total number sold has never exceed 100 salads. So, another constraint will be:   x+y\leq 100

According to the graph of the constraints, the vertices of the common shaded region are:  (40,35), (60,35), (60,40), (50,50) and (40,50)   <em>(Refer to the attached image for the graph)</em>

The lunch stand makes a $.75 profit on each Chef's salad and $1.20 profit on each Caesar salad. So, the profit function will be:  P=0.75x+1.20y

For  (40, 35) ,   P=0.75(40)+1.20(35)=72

For  (60, 35) ,   P=0.75(60)+1.20(35)=87

For  (60, 40) ,   P=0.75(60)+1.20(40)=93

For  (50, 50) ,   P=0.75(50)+1.20(50)=97.5 <u><em>(Maximum)</em></u>

For  (40, 50) ,   P=0.75(40)+1.20(50)=90

Profit will be maximum when x=50 and y=50

Thus, 50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.

6 0
2 years ago
Suppose that the universal set is U={1,2,3,4,5,6,7,8,9,10}. Express each of the following subsets with bit strings (of length 10
Vladimir [108]

Answer:

0011100000

1010010001

0111001110

Step-by-step explanation:

As the question is not complete, Here is the complete question.

Suppose that the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Express each of these sets with bit strings where the ith bit in the string is 1 if i is in the set and 0 otherwise.

a) {3, 4, 5}

b) {1, 3, 6, 10}

c) {2, 3, 4, 7, 8, 9}.

So, we need to express a) b) and c) into bit strings.

Firstly, number of elements in the universal set represent the number of bits in the bit string.

Secondly, 1 = yes element is present in both universal set as well as in sub set.

0 = No, element is not present in sub set but present in universal set.

Hence, we have:

a) Sub set {3,4,5} = 0011100000  (As there are 3 1's which means only 3,4,5 are present in both universal set and subset.

Similarly,

b) Sub set {1, 3, 6, 10} = 1010010001

c) Sub set {2, 3, 4, 7, 8, 9} = 0111001110

5 0
2 years ago
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