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Irina18 [472]
3 years ago
8

At a clothing store, Ted bought 4 shirts and 2 ties for a total price of $95. At the same store, Stephen bought 3 shirts and 3 t

ies for a total price of $84. how much does each shirt cost

Mathematics
1 answer:
zepelin [54]3 years ago
4 0

Answer:

$19.50

Step-by-step explanation:

We can turn these into equations by making the shirts 's' and the ties 't'.  

4s+2t=95 and 3s+3t=84

Now we can solve the system of equations with substitution.

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Slope = 75
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8 0
3 years ago
In which quadrant of the coordinate plane would the point (6, −8) fall?
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Answer:

Step-by-step explanation:

8 0
2 years ago
According to a study done by a university​ student, the probability a randomly selected individual will not cover his or her mou
VikaD [51]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

 P(X = 8) =  0.0037

b

 P(X <  5) =  0.805

c

 P(X > 6) =  0.0206

I would be surprised because the value is very small , less the 0.05

Step-by-step explanation:

From the question we are told that

The probability a randomly selected individual will not cover his or her mouth when sneezing is p = 0.267

Generally data collected from this study follows  binomial  distribution because the number of trials is  finite , there are only two outcomes, (covering  , and  not covering mouth when sneezing ) , the trial are independent

Hence for a randomly selected variable  X we have that  

   X \ \ \~ \ \ { B ( p , n )}

The probability distribution function for binomial  distribution is  

    P(X = x ) =  ^nC_x *  p^x *  (1 -p) ^{n-x}

Considering question a

Generally the  the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when​ sneezing is mathematically represented as

     P(X = 8) =  ^{12} C_8 *  (0.267)^8 *  (1- 0.267)^{12-8}

Here C denotes  combination

So

     P(X = 8) =  495  *  0.000025828 * 0.28867947

    P(X = 8) =  0.0037

Considering question b

Generally the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when​ sneezing is mathematically represented as

     P(X <  5 ) =[P(X = 0 ) + \cdots + P(X = 4)]

=>   P(X <  5 ) =[ ^{12} C_0 *  (0.267)^0 *  (1- 0.267)^{12-0} + \cdots +  ^{12} C_4 *  (0.267)^4 *  (1- 0.267)^{12-4} ]

=> P(X <  5 )  =  0.02406 +  0.10516 + 0.21067 + 0.25580 + 0.20964

=>  P(X <  5) =  0.805

Considering question c

Generally the probability that fewer than half(6) covered their mouth when​ sneezing(i.e the probability the greater than half do not cover their mouth when sneezing) is mathematically represented as

      P(X > 6) =  1 - p(X \le  6)

=>    P(X > 6) = 1 - [P(X = 0) + \cdots + P(X =6)]

=>    P(X > 6)=1 - [^{12} C_0 *  (0.267)^0 *  (1- 0.267)^{12-0}+ \cdots + ^{12} C_4 *  (0.267)^6 *  (1- 0.267)^{12-6} ]

=>    P(X > 6)= 1 - [0.02406 + \cdots + 0.0519 ]  

=>    P(X > 6) =  0.0206

I would be surprised because the value is very small , less the 0.05

8 0
3 years ago
Simplify the expression 2k+10k-(2k+3)+13
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12k - 2k +16 you add the 2 and 10 on the first half and the 3 and 13 on the other half
6 0
3 years ago
Read 2 more answers
Evelyn's made a cake in the shape of a circus tent the cake consisted of a cylinder and a cone .The height of the cone is half t
Lera25 [3.4K]
The volume of the cake is 1470 in³. 
volume of a cylinder = πr² x height
(Think about how a cylinder is basically a bunch of circles stacked on top of each other. To find the volume, first you need the area of the circle (πr², then you multiply by how many circles you are stacking on top of each other (height)) 

we know the diameter of the cylinder is 12 in. and the radius is half of the diameter. 
half of 12 is 6, therefore the radius is 6 in. or r = 6 
Assuming pi is 3.14, solve for the height of the cylinder
1470 = (3.14)(6²)(height)
1470 = 3.14 x 36 x height
1470 = 113.04 x height
height ≈ 13 in

Now that we know the height of the cylinder is about 13 in., we know the height of the cone, because the problem says that the height of the cone is half the height of the cylinder. 
half of 13 is 6.5, therefore the height of the cone is 6.5 
the radius of the cone is the same as that of the cylinder, 6 in. 

volume of a cone = πr² × (height ÷ 3)

volume of the cone = (3.14)(6²)(6.5 ÷ 3)
volume of the cone = (3.14)(36)(2.16666)
volume of the cone = 244.92 in³

Now all that's left to find the volume of the whole cake is to add the volume of the cylinder to the volume of the cone. 

1470 + 244.92 = 1714.92 in³



6 0
3 years ago
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