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Ket [755]
3 years ago
8

Your bedroom ceiling is 10 feet high and is 2/3 as high as the living room ceiling. Write and solve and solve an equation to fin

d the height h of th living room ceiling
Mathematics
2 answers:
vfiekz [6]3 years ago
3 0
H=10+(10 1/3) is a correct equation. The answer should be h=13.33
Alisiya [41]3 years ago
3 0

\text{Let the height of the living room ceiling is h feet.}\\
\\
\text{Given that the bedroom ceiling is 10 feet high and this height is }\frac{2}{3}\\
\text{as high as the living room ceiling.}\\
\\
\text{So the equation that represents this situation can be set as:}\\
\\
\frac{2}{3}\ \text{of the height of the living room = Height of ceiling of bedroom}

\Rightarrow \frac{2}{3}(h)=10\\
\\
\Rightarrow \frac{2h}{3}=10\\
\\
\text{now to solve it, first we multiply both sides by 3. so we get}\\
\\
2h=30\\
\\
\text{now divide both sides by 2 to get}\\
\\
h=15

Hence the height of the living room ceiling is: 15 feet

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A coin is to be tossed as many times as necessary to turn up one head. Thus the elements c of the sample space C are H, TH, TTH,
slavikrds [6]

Answer:

Step-by-step explanation:

As stated in the question, the probability to toss a coin and turn up heads in the first try is \frac{1}{2}, in the second is \frac{1}{4}, in the third is \frac{1}{8} and so on. Then, P(C) is given by the next sum:

P(C)=\sum^{\infty}_{n=1}(\frac{1}{2} )^{n}=1

This is a geometric series with factor \frac{1}{2}. Then is convergent to \frac{1}{1-\frac{1}{2}}-1=1.. With this we have proved that P(C)=1.

Now, observe that

P(H)=\frac{1}{2}, P(TH)=\frac{1}{4},P(TTH)=\frac{1}{8},P(TTTH)=\frac{1}{16},P(TTTTH)=\frac{1}{32},P(TTTTTH)=\frac{1}{64}.

Then

P(C1)=P(H)+P(TH)+P(TTH)+P(TTTH)+P(TTTTH)=\frac{1}{2} +\frac{1}{4} +\frac{1}{8} +\frac{1}{16} +\frac{1}{32} =\frac{31}{32}

P(C2)=P(TTTTH)+P(TTTTTH)=\frac{1}{32}+\frac{1}{64} =\frac{3}{64}

P(C1\cap C2)=P(TTTTH)=\frac{1}{32}

and

P(C1\cup C2)=P(H)+P(TH)+P(TTH)+P(TTTH)+P(TTTTH)+P(TTTTTH)=\frac{1}{2} +\frac{1}{4} +\frac{1}{8} +\frac{1}{16} +\frac{1}{32} +\frac{1}{64}=\frac{63}{64}

5 0
2 years ago
A jar contains 6 red marbles numbered 1 to 6 and 4 blue marbles numbered 1 through 4. A marble is drawn at random from the jar.
ale4655 [162]
A Can you help me with these questions
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3 years ago
How much money has to be invested at 5.9% interest compounded continuously to have $15,000 after 12 years?
scoray [572]

The amount of $7389.43 has to be invested at 5.9% interested continuously to have $15,000 after 12 years.

Step-by-step explanation:

The given is,

                Future value, F  = $15,000

                           Interest, i = 5.9%

              ( compounded continuously )

                            Period, t = 12 years

Step:1

           Formula to calculate the present with compounded continuously,

                                       F=Pe^{(i)(t)}...............(1)

           Substitute the values in equation (1) to find the P value,

                                  15000=Pe^{(0.059)(12)}          ( ∵ i = \frac{5.9}{100}=0.059 )

                                  15000=Pe^{0.708}

                                  15000=P(2.0299)             ( ∵ e^{o.708} =2.0299 )

            We change the P (Present value) into the left side,

                                        P=\frac{15000}{2.0299}

                                            =7389.427

                                            ≅ 7389.43

                                         P = $ 7389.43

Result:

           The amount of $7389.43 has to be invested at 5.9% interested continuously to have $15,000 after 12 years.  

                       

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There are twenty cards labeled from 1 to 20 in a bag. A card is randomly selected from the bag.
AveGali [126]
If you are asking for the probability of getting a certain card you have a 1/ 20th  chance

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3 years ago
Is 1/2(12x + 24) and -6 (-x- 2)
ikadub [295]
I hope this helps you



12x/2+24/2



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-6 ( -x-2)
6 0
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