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2 years ago

12

A Statue cast a shadow 25 feet long a boy standing next to the statues 4.5 feet tall and casts a shadow that is 3.6 feet long ho

w tall is the statue

1 answer:

tester [92]2 years ago

8 0

Set up a proportion. Let h = the statue height. h/statue shadow = boy height/boy shadow.

h/25 = 4.5/3.6

Cross multiply and solve for h.

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a train of length 100 m is moving at speed of 50km/ hr. a horse is running alongside the train at a speed of 56km/h. How long wi

scoray [572]

Distance = 100 m = 100/1000 = 0.1 km speed of train = 50 km/hr speed of horse = 56 km/hr resultant speed = (56 – 50) 6 km/hr time = distance/speed time = 0.1/6 = 1/60 hr = 1 min

6 0

2 years ago

Find the lateral area for the pyramid with the equilateral base

likoan [24]

<h3>The lateral area for the pyramid with the equilateral base is 144 square units</h3>

<em><u>Solution:</u></em>

The given pyramid has 3 lateral triangular side

The figure is attached below

Base of triangle = 12 unit

<em><u>Find the perpendicular</u></em>

By Pythagoras theorem

$hypotenuse^2 = opposite^2 + adjacent^2$

Therefore,

$opposite^2 = 10^2 - 6^2\\\\opposite^2 = 100 - 36\\\\opposite^2 = 64\\\\opposite = 8$

<em><u>Find the lateral surface area of 1 triangle</u></em>

$\text{ Area of 1 lateral triangle } = \frac{1}{2} \times opposite \times base$

$\text{ Area of 1 lateral triangle } = \frac{1}{2} \times 8 \times 12\\\\\text{ Area of 1 lateral triangle } = 48$

<em><u>Thus, lateral surface area of 3 triangle is:</u></em>

3 x 48 = 144

Thus lateral area for the pyramid with the equilateral base is 144 square units

5 0

2 years ago

When four fifths 4 5 of a number is subtracted from 1414, the result is 22. find the number?

galben [10]

If we say:
x = the number we want to find
Then, we can formulate an equation using the information given:
1414 - 4x/5 = 4
Now, we just solve for x:
4x/5 + 4 = 1414
4x/5 = 1410
4x = 7050
x = 1762.5

8 0

2 years ago

Solve for x: 2+3 (x+2x) = -2x(2-4) +1

Ronch [10]

Answer:

x = -1/5

Step-by-step explanation:

2+3 (x+2x) = -2x(2-4) +1

Combine like terms

2+3(3x) = -2x (-2) +1

Distribute

2+9x = 4x +1

Subtract 4x from each side

2+9x-4x = 4x+1-4x

2+5x = 1

Subtract 2 from each sdie

5x = 1-2

5x = -1

Divide by 5

5x/5 = -1/5

x = -1/5

7 0

3 years ago

There are 52 cards in a deck, and 13 of them are hearts. Four cards are dealt, one at a time, off the top of a well-shuffled dec

irga5000 [103]

Answer:

10.97%

Step-by-step explanation:

There are 52 cards.

13 of them, are hearts.

Then

52 - 13 = 39 cards are not hearts.

4 cards are drawn, we want to find the percent chance that the fourth card is a heart card, but no before.

So the first card can't be a heart card.

because the deck is well-shuffled, all the cards have the same probability of being drawn.

Then the probability of not getting a heart card, is equal to the quotient between the number of non-heart cards (39) and the total number of cards (52), then the probability is:

p₁ = 39/52

The second card also can't be a heart card, the probability is calculated in the same way than above, but now there are 38 non-heart cards and a total of 51 cards (because one card was already drawn) then the probability here is:

p₂ = 38/51

For the third card the reasoning is similar to the two above cases, here the probability is:

p₃ = 37/50

The fourth card should be a hearts card, the probability is computed in the same way than above, as the quotient between the number of heart cards in the deck (13) and the total number of cards in the deck (now there are 49 cards)

then the probability is:

p₄ = 13/49

The joint probability (the probability of these 4 events happening together) is equal to the product between the individual probabilities:

P = p₁*p₂*p₃*p₄

P = (39/52)*(38/51)*(37/50)*(13/49) = 0.1097

The percent chance is the above number times 100%

Percent = 0.1097*100% = 10.97%

3 0

2 years ago