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atroni [7]
3 years ago
12

a man travels from town X to town Y at an average rate of 50 miles an hour and returns at an average rate of 40 miles an hour he

takes a half hour longer than he would take if he made round trip at an average 45 miles an hour what is the distance from town X to town y​
Mathematics
1 answer:
Luba_88 [7]3 years ago
6 0

Answer:

18 + 22.5 = 40 + .5; confirms out solution

Step-by-step explanation:

A man travels from Town X to Town Y at an average rate of 50 mph and returns at an average rate of 40 mph. He takes a 1/2 hour longer than he would take if he made the round trip at an average of 45 mph. What is the distance from Town X to Town Y

:

Let d = distance from x to y

:

Write a time equation; time = distance%2Fspeed

Different speed roundtrip time = 1 speed roundtrip time + half/hour

d%2F50 + d%2F40 = 2d%2F45 + 1%2F2

Multiply equation by 1800 to get rid of the denominators:

1800*d%2F50 + 1800*d%2F40 = 1800*2d%2F45 + 1800*1%2F2

Cancel the denominators and you have:

:

36d + 45d = 40(2d) + 900

:

81d = 80d + 900

:

81d - 80d = 900

:

d = 900 miles from x to y

:

:

Check solution in: d%2F50 + d%2F40 = 2d%2F45 + 1%2F2

900%2F50 + 900%2F40 = 1800%2F45 + 1%2F2

18 + 22.5 = 40 + .5; confirms out solution

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Panel of judges was asked to judge the quality of different kinds of potato chips. The scatterplot and regression line below sho
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Answer:

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Step-by-step explanation:

the slope begins at $1

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3 years ago
Francisco has a savings account balance of $2033.88. The interest rate on the account is 2.9% compounded monthly. If he opened t
artcher [175]
The equation for this is:

F = P(1+i)ⁿ
where
F is the present accounts balance
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i is the interest rate
n is the number of months

The interest rate is nominal which is 2.9% per year compounded monthly. Since there are 12 months in a year, that is equal to an effective interest rate of 0.24167% per month compounded monthly (i = 0.0024167). In 9 years, there are a total of 108 months, so n=108.

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3 0
3 years ago
The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 26
hjlf

Answer:

Probability that next week's show will have between 30 and 37 million viewers is 0.2248.

Step-by-step explanation:

We are given that the distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 26 million with a standard deviation of 8 million.

<em>Let X = number of viewers for the American Idol television show</em>

So, X ~ N(\mu=26,\sigma^{2}=8^{2})

Now, the z score probability distribution is given by;

          Z = \frac{X-\mu}{\sigma} ~ N(0,1)

where, \mu = population mean = 26 million

            \sigma = standard deviation = 8 million

So, probability that next week's show will have between 30 and 37 million viewers is given by = P(30 < X < 37) = P(X < 37) - P(X \leq 30)

    P(X < 37) = P( \frac{X-\mu}{\sigma} < \frac{37-26}{8} ) = P(Z < 1.38) = 0.91621

    P(X \leq 30) = P( \frac{X-\mu}{\sigma} \leq \frac{30-26}{8} ) = P(Z \leq 0.50) = 0.69146

<em>Therefore, P(30 < X < 37) = 0.91621 - 0.69146 = 0.2248</em>

Hence, probability that next week's show will have between 30 and 37 million viewers is 0.2248.

4 0
3 years ago
There are 21 juice bottles out of which 7 bottles are full. 7 are half-full and the remaining 7 are empty to divided amongst 3 f
kozerog [31]

answer:

each friend would have 3 and 1/2 bottles of juice meaning each friend would have 3 fully empty bottles.

4 0
2 years ago
All of the edges of a regular triangular pyramid have length 12. A frustum of the pyramid has height half of that of the pyramid
vlada-n [284]

Answer:

1) The volume of the frustum is 27·(√3)·h

2) The surface area the frustum is 24·h + 54·√3

Step-by-step explanation:

1) A frustum of the regular triangular prism is a portion of the triangular prism

The length of the edge of the triangle prism = 12

The area of the triangular face, A = (√3/4)·a²

∴ A = (√3/4)·12² = 36·√3

When

The volume of the triangular prism, V = A·h = (36·√3)·h

By triangle proportionality theorem, the cross sectional area of the top half of the triangular prism =  (√3/4)·6² = 9·(√3)

The volume of the top half, V₂ = 9·(√3)·h

The volume of the frustum = V - V₂ = (36·√3)·h - 9·(√3)·h = 27·(√3)·h

The volume of the frustum = 27·(√3)·h

2) The surface area of the triangular side of the frustum is given as follows;

A = 36·√3- 9·(√3) = 27·(√3)

The surface area the frustum, F_A = 2×27·(√3) + 2 ×6 ×h + 12×h = 24·h + 54·√3

The surface area the frustum = 24·h + 54·√3

4 0
3 years ago
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