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pickupchik [31]
3 years ago
5

Caroline is making some table decorations.

Mathematics
2 answers:
ollegr [7]3 years ago
6 0
She buys 3 candle packs and 5 holder packs, she will be able to make 90 decorations
lara [203]3 years ago
3 0

Answer:

(i) 30 packs of candles and18 packs of candle holders

(ii) 540 table decorations

Step-by-step explanation:

(i) In order to obtain an equal amount of candle to candle holders Caroline has to buy enough packs to obtain a 1:1 ratio.

Therefore to obtain a 1:1 ratio:

=30 candles/18 candle holders * (18/30)

Therefore she needs to buy 18 packs of candles and 30 packs of candle holders to have exactly the same number of candles and holders

(ii) Caroline can make = 30*18 = 540 table decorations

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You roll a 4-sided die repeatedly. On your odd-numbered rolls (1st,3rd,5th, etc.) you are victorious if you get a 4. On your eve
Sunny_sXe [5.5K]

Answer:

E (Y) = 3

Step-by-step explanation:

If a 4-sided die is being rolled repeatedly; and the odd-numbered rolls (1st 3rd,5th, etc.)

The probability of odd number roll will be, p(T) = \frac{1}{2}

However, on your even-numbered rolls, you are victorious if you get a 3 or 4. Also, the  probability of even number roll, p(U) = \frac{1}{2}

In order to  calculate: E (Y); We can say Y to be the number of times you roll.

We know that;

E (Y) = E ( Y|T ) p(T) + E ( Y|U ) p(U)

Let us calculate E ( Y|T ) and E ( Y|U )

Y|T ≅ geometric = \frac{1}{4}

Y|U ≅ geometric = \frac{1}{2}

also; x ≅ geometric (p)

∴ E (x) = \frac{1}{p}

⇒ \frac{Y}{T} = 4 ; also \frac{Y}{U} = 2

E (Y) = 4 × \frac{1}{2} + 2 ×

        = 2+1

E (Y) = 3

7 0
3 years ago
A coin is tossed twice. What is the probability of getting a tail in the first toss and a tail in the second toss?
skelet666 [1.2K]

Answer:

<h2>1/4 Chances</h2><h2>25% Chances</h2><h2>0.25 Chances (out of 1)</h2>

Step-by-step explanation:

Two methods to answer the question.

Here are presented to show the advantage in using the product rule given above.

<h2>Method 1:Using the sample space</h2>

The sample space S of the experiment of tossing a coin twice is given by the tree diagram shown below

The first toss gives two possible outcomes: T or H ( in blue)

The second toss gives two possible outcomes: T or H (in red)

From the three diagrams, we can deduce the sample space S set as follows

          S={(H,H),(H,T),(T,H),(T,T)}

with n(S)=4 where n(S) is the number of elements in the set S

tree diagram in tossing a coin twice

The event E : " tossing a coin twice and getting two tails " as a set is given by

          E={(T,T)}

with n(E)=1 where n(E) is the number of elements in the set E

Use the classical probability formula to find P(E) as:

          P(E)=n(E)n(S)=14

<h2>Method 2: Use the product rule of two independent event</h2>

Event E " tossing a coin twice and getting a tail in each toss " may be considered as two events

Event A " toss a coin once and get a tail " and event B "toss the coin a second time and get a tail "

with the probabilities of each event A and B given by

          P(A)=12 and P(B)=12

Event E occurring may now be considered as events A and B occurring. Events A and B are independent and therefore the product rule may be used as follows

        P(E)=P(A and B)=P(A∩B)=P(A)⋅P(B)=12⋅12=14

NOTE If you toss a coin a large number of times, the sample space will have a large number of elements and therefore method 2 is much more practical to use than method 1 where you have a large number of outcomes.

We now present more examples and questions on how the product rule of independent events is used to solve probability questions.

8 0
2 years ago
Read 2 more answers
State which theorem you can use to show that the quadrilateral is a parallelogram.​
tekilochka [14]

Answer:

If one pair of opposite sides in a four sided figure are both opposite and parallel, then the figure is a parallelogram.

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
An apartment building produces $4,000 per quarter in gross rents. The maintenance expenses run $350 per month. Property taxes ar
S_A_V [24]

Answer:

0.16%

Step-by-step explanation:

Cost of rent per quarter = $4000

Cost of rent per year = 4×$4000

= $16,000

This means that the apartment building produces $12,000 per year in gross rents.

Yearly Expenses are as follows;

Maintenance expenses per year = 12×$350 = $4200

Property taxes per year = $1,750

Mortgage payment per year = 12×$650 = $7800

Total expenses per year = sum of all the yearly expenses

= $4200+$1,750+$7800

= $13750

Yearly revenue generated = Cost of rent per year - total yearly expenses

= $16,000-$13750

= $2250 (net operating income)

Capitalization rate is given as the ratio of the net operating income to the market value of the building.

Capitalization rate = net operating income/market value of building

Since the building with $83750, that will be its market value

Cap rate = $13750/$83750

Cap rate = 0.16%

5 0
3 years ago
(2a-5)/6 = 5/12 what is the answer?
USPshnik [31]

Answer:

a = 15/4.

Step-by-step explanation:

(2a-5)/6 = 5/12

Cross multiply:

12(2a - 5) = 5*6

24a - 60 = 30

24a = 90

a = 90/24

a = 15/4.

3 0
3 years ago
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