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3 years ago

A number is chosen at random from 1 to 50. Find the probability of selecting either a multiple of 4 or a multiple of 5.

Mathematics

2 answers:

anygoal [31]3 years ago

6 0

A multiple of 4 is a 12/50 chance and a multiple of 5 is a 10/50 chance or simplified 1/5 chance

kykrilka [37]3 years ago

6 0

A mulitiple of 4 is 12/50

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Doug hits a baseball straight towards a 15 ft high fence that is 400 ft from home plate. The ball is hit 2.5ft above the ground

Scorpion4ik [409]

Answer:

$125.4\ \text{m/s}$

Step-by-step explanation:

u = Initial velocity of baseball

$\theta$ = Angle of hit = $30^{\circ}$

x = Displacement in x direction = 400 ft

y = Displacement in y direction = 15 ft

$y_0$ = Height of hit = 2.5 ft

$a_y$ = g = Acceleration due to gravity = $32.2\ \text{ft/s}^2$

t = Time taken

Displacement in x direction

$x=u_xt\\\Rightarrow x=u\cos\theta t\\\Rightarrow t=\dfrac{x}{u\cos\theta}\\\Rightarrow t=\dfrac{400}{u\cos30^{\circ}}\\\Rightarrow t=\dfrac{400}{u\dfrac{\sqrt{3}}{2}}\\\Rightarrow t=\dfrac{800}{u\sqrt{3}}$

Displacement in y direction

$y=y_0+u_yt+\dfrac{1}{2}a_yt^2\\\Rightarrow y=y_0+u\sin\theta t+\dfrac{1}{2}a_yt^2\\\Rightarrow 15=2.5+u\sin30^{\circ}(\dfrac{800}{u\sqrt{3}})+\dfrac{1}{2}\times -32.2\times (\dfrac{800}{u\sqrt{3}})^2\\\Rightarrow \dfrac{400}{\sqrt{3}}-\dfrac{10304000}{3u^2}-12.5=0\\\Rightarrow 218.44=\dfrac{10304000}{3u^2}\\\Rightarrow u=\sqrt{\dfrac{10304000}{3\times218.44}}\\\Rightarrow u=125.4\ \text{m/s}$

The minimum initial velocity needed for the ball to clear the fence is $125.4\ \text{m/s}$

5 0

3 years ago

Write the number that has 4 thousands,6 humdred thousands,5 ten thousands, 3 tens, and 5 ones

anyanavicka [17]

654,035 654,035 654,035 654,035 654,035 654,035 654,035

7 0

3 years ago

In order to remove water from a flooded basement, two pumps, each rated at 40 gallons per minute, are used. After half an hour,

Scrat [10]

Answer:

3600 gallons of water was removed from the basement.

Step-by-step explanation:

Given:

Rate of each pump = 40 gallons/min

We need to find find the number of gallons of water removed from the basement.

Solution:

Now Given:

After half an hour, the one pump burns out.

Now we know that;

1 hour = 60 mins

$\frac12$ hour = $\frac{60}{2}=30\ mins$

Now for 30 mins both the pumps were working and removing the water.

So we can say that;

Water remove for first 30 mins = $40\times2\times30=2400\ gallons$

Also Given:

the second pump finishes removing the water half an hour later.

So we can say that;

Water removed for next 30 mins = $40\times 30\times1 =1200\ gallons$

Now we can say that;

Total water removed from the basement is equal to sum of Water remove for first 30 mins and Water removed for next 30 mins .

framing in equation form we get;

Total water removed from the basement = $2400+1200=3600\ gallons.$

Hence 3600 gallons of water was removed from the basement.

6 0

3 years ago

Which pair of equations represents two perpendicular lines? <br>answers shown in picture.

kolezko [41]

Answer:

y =1/2x+6

y = -2x+2

Step-by-step explanation:

Perpendicular line have slopes that multiply to -1

The slopes are negative reciprocals

-4*4 = 16 not perpendicular

1/2 * -2 = -1 perpendicular

1/5 *5 = 1 not perpendicular

2/3 * 2/3 = 4/9 not perpendicular

3 0

3 years ago

Please help <3

Aleksandr [31]

Answer:

x =3

Step-by-step explanation:

3(4x + 4) = 2(5x+9) - 12

First step is to open the brackets by multiplying. It becomes

3×4x + 3×4 = 2×5x + 2×9 -12

12x + 12 = 10x + 18 - 12

Collecting like terms on the right hand side and left hand side of the equation, it becomes

12x -10x = 18 -12 -12

2x = -6

Negative sign on the right hand side of the equation overwhelms the positive sign on left hand side of the equation. It becomes

2x = -6

x = -6/2 = -3

Checking

3(4×-3 + 4) = 2(5×-3+9) - 12

-24 = -12-12= -24

So x = -3

3 0

3 years ago