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Alexandra [31]
4 years ago
13

If four times the brother's age is subtracted from three times the sister's age, the difference is 8. Give an equation that repr

esents this statement using b as the age of the brother and s as the age of the sister.
Mathematics
1 answer:
hjlf4 years ago
7 0

Answer:

3s-4b=8

Step-by-step explanation:

Let b is the age of the brother and s as the age of the sister.

It is given that if four times the brother's age is subtracted from three times the sister's age, the difference is 8.

We need to find an equation for the given statement.

Four times the brother's age = 4×b = 4b

Three times the sister's age = 3×s = 3s

Four times the brother's age is subtracted from three times the sister's age.

3s-4b

The difference is 8.

3s-4b=8

Therefore, the required equation is 3s-4b=8.

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A train covered the distance of 400 km between A and B at a certain speed. On the way back it covered 2/5 of the distance at tha
padilas [110]

Answer:

s - 20 = 60 km/hr

Step-by-step explanation:

The distances are the same going there and coming back.

So

Givens

d = 400

2/5 * d = 2/5 * 400 = 160

The rest of the trip back = 400 - 160 = 240

Equation

400/(s) + 160/s + 240/(s - 20) = 11 hours.

Solution

distance / speed = time or

d/s = time

Multiply through by s*(s - 20)

400*(s - 20) + 160*(s - 20) + 240s = 11*s*(s - 20)       Remove the brackets.

400s - 8000 + 160s - 3200 + 240s= 11(s^2 - 20s)   Collect like terms on the left.

560s - 11200 + 240s = 11(s^2 - 20s)                          Remove the brackets on the rt.

800s - 11200 = 11s^2 - 220s                                   Switch and add 220s

11s^2 - 220s + 220s = 800s +220s - 11200          Combine

11s^2 = 1020s - 11200                                            Put everything on the left.

11s^2 - 1020s + 11200 = 0

this quadratic factors into

(11s - 140 )(s - 80) = 0

You have 2 solutions

11s - 140 = 0

11s = 140

s = 140/11

s = 12.727272... This solution won't work because the speed has no room to drop down 20 km / hour

===========

s - 80 = 0

s = 80 km hour

But that is not the answer

=======

The answer you want is s - 20 which is 60 km/hr.

7 0
3 years ago
A jar contains 5 blue marbles, 8 red marbles, 4 white marbles, and 3 purple marbles. Suppose you pick a marble at random without
andreyandreev [35.5K]
P(purple)=3/20
P(white)=4/20=1/5
P(not blue)=15/20=3/4
5 0
3 years ago
I have 15a but I need 15b and 14
Naily [24]
14. For a prism, the volume is given by
.. V = Bh . . . . . . . . where B is the area of the base, and h is the height of the prism

For a pyramid, the volume is given by
.. V = (1/3)*Bh . . . . where B is the area of the base, and h is the height of the pyramid

The volume is proportional to the area of the base. If the dimensions of the base decrease linearly to zero at the height of the geometry as they do for pyramids and cones, then the volume formula includes a factor of 1/3.


15b. The volume of a pyramid is 1/3 that of a prism with the same base area and height.
8 0
3 years ago
In a sample of 100 steel canisters, the mean wall thickness was 8.1 mm with a standard deviation of 0.5 mm. Someone says that th
Travka [436]

Answer:

This statement can be made with a level of confidence of 97.72%.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 8.1 mm

Standard Deviation, σ = 0.5 mm

Sample size, n = 100

We are given that the distribution of thickness is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

Standard error due to sampling:

=\dfrac{\sigma}{\sqrt{n}} = \dfrac{0.5}{\sqrt{100}} = 0.05

P(mean thickness is less than 8.2 mm)

P(x < 8.2)

P( x < 8.2)\\\\ = P( z < \displaystyle\frac{8.2 - 8.1}{0.05})\\\\ = P(z < 2)

Calculation the value from standard normal z table, we have,  

P(x < 8.2) =0.9772 = 97.72\%

This statement can be made with a level of confidence of 97.72%.

8 0
4 years ago
A small craft in lake Ontario sends out a distances signal. The coordinates of the boat in trouble are (57,64). One rescue boat
KatRina [158]

Answer:

The coast guard craft will get to the distressed boat the fastest.

Step-by-step explanation:

The coordinates of boat are (57,64).

The coordinates of rescue boat are (67,83).

The  coordinates of coast guard craft are (65,46).

Both rescue crafts travel at the same rate. One of them will get to the distressed boat the faster, whose distance from the boat is least.

Distance formula:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

The distance between boat and rescue boat is

d_1=\sqrt{(67-57)^2+(83-64)^2}=21.4709105536\approx 21.47

The distance between boat and coast guard craft is

d_2=\sqrt{(65-57)^2+(46-64)^2}=19.6977156036\approx 19.70

Since the distance between boat and coast guard craft is least, therefore coast guard craft will get to the distressed boat the fastest.

6 0
3 years ago
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