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2 years ago

Another one! Thanks for your help:)

Mathematics

2 answers:

PolarNik [594]2 years ago

6 0

Answer:

its the top right

Step-by-step explanation:

1/3 times 5/6 = 5/18

amid [387]2 years ago

4 0

1/3 divided by 5/6 = 2/5

1/3 x 6/5 = 6/15 = 2/5

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The figure shows the layout of a symmetrical pool in a water park. What is the area of this pool rounded to the tens place? Use

k0ka [10]

Answer:

$2489ft^{2}$

Step-by-step explanation:

The pool are is divided into 4 separated shapes: 2 circular sections and 2 isosceles triangles. Basically, to calculate the whole area, we need to find the area of each section. Due to its symmetry, both triangles are equal, and both circular sections are also the same, so it would be enough to calculate 1 circular section and 1 triangle, then multiply it by 2.

<h3>Area of each triangle:</h3>

From the figure, we know that <em>b = 20ft </em>and <em>h = 25ft. </em>So, the area would be:

$A_{t}=\frac{b.h}{2}=\frac{(20ft)(25ft)}{2}=250ft^{2}$

<h3>Area of each circular section:</h3>

From the figure, we know that $\alpha =2.21 radians$ and the radius is $R=30ft$ . So, the are would be calculated with this formula:

$A_{cs}=\frac{\pi R^{2}\alpha}{360\°}$

Replacing all values:

$A_{cs}=\frac{(3.14)(30ft)^{2}(2.21radians)}{6.28radians}$

Remember that $360\°=6.28radians$

Therefore, $A_{cs}=994.5ft^{2}$

Now, the total are of the figure is:

$A_{total}=2A_{t}+2A{cs}=2(250ft^{2} )+2(994.5ft^{2})\\A_{total}=500ft^{2} + 1989ft^{2}=2489ft^{2}$

Therefore the area of the symmetrical pool is $2489ft^{2}$

3 0

2 years ago

The sum of three consecutive is 267. What is the largest integer

Oliga [24]

Consecutive means in order. So let's call the first integer x. The next number in line would be x+1 and the largest integer would be x+2. Let's prove that so you're not confused. If x is 3, then x+1 is 4 (next in line), and x+2 is 5 next after that. See? So if we add all those together we set them equal to 267 and solve for x: x + x+1 + x+2 = 267. Combining like terms gives us 3x + 3 = 267 and 3x = 264. Now dividing both sides by 3 we get that x = 88. That's the smallest integer; the largest is found by adding 88 + 2 which is 90. So that means that the numbers are 88, 89, 90, and that adding them up = 267. Let's check that now: 88+89+90=267 so we're good.

4 0

2 years ago

3 to the 2nd power plus 2 to the 3rd power

Amanda [17]

Answer:

Step-by-step explanation:

$3^2=3\cdot3=9\\\\2^3=2\cdot2\cdot2=8\\\\3^2+2^3=9+8=17$

8 0

1 year ago

Read 2 more answers

A research team at Cornell University conducted a study showing that approximately 10% of all businessmen who wear ties wear the

LenKa [72]

Answer:

a) The probability that at least 5 ties are too tight is P=0.0432.

b) The probability that at most 12 ties are too tight is P=1.

Step-by-step explanation:

In this problem, we could represent the proabilities of this events with the Binomial distirbution, with parameter p=0.1 and sample size n=20.

a) We can express the probability that at least 5 ties are too tight as:

$P(x\geq5)=1-\sum\limits^4_{k=0} {\frac{n!}{k!(n-k)!} p^k(1-p)^{n-k}}\\\\P(x\geq5)=1-(0.1216+0.2702+0.2852+0.1901+0.0898)\\\\P(x\geq5)=1-0.9568=0.0432$

The probability that at least 5 ties are too tight is P=0.0432.

a) We can express the probability that at most 12 ties are too tight as:

$P(x\leq 12)=\sum\limits^{12}_{k=0} {\frac{n!}{k!(n-k)!} p^k(1-p)^{n-k}}\\\\P(x\leq 12)=0.1216+0.2702+0.2852+0.1901+0.0898+0.0319+0.0089+0.0020+0.0004+0.0001+0.0000+0.0000+0.0000\\\\P(x\leq 12)=1$

The probability that at most 12 ties are too tight is P=1.

5 0

2 years ago

Identify the examples as primary sources or secondary sources.

algol13

Answer:

Primary : letters, artifacts, contracts

Secondary : documentaries, encyclopedias, biographies

Step-by-step explanation:

(I'm not too sure about contracts, so you might want to check yourself for that one)

5 0

3 years ago