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professor190 [17]
3 years ago
15

Help

Mathematics
2 answers:
Vedmedyk [2.9K]3 years ago
8 0
By pythagoreans' theorem,

Longer edge
= √(2² + 6²)
= √40

∴ The length of the longer edge is the square root of 40 feet.

Shorter edge
= √(1² + 3²)
= √10

Area = L × B
= √40 × √10
= 20 feet²
Montano1993 [528]3 years ago
5 0
A(2, 3); B(4, 9); C(7, 8); D(5, 2)

1. <span>How long is the longer edge of the table?
</span>AB= \sqrt{(x_b-x_a)^2+(y_b-y_a)^2} = \sqrt{(4-2)^2+(9-3)^2}= \\ = \sqrt{2^2+6^2}= \sqrt{4+36}= \sqrt{40} \  \text{feet}
<span>
2. </span><span>What is the area of the tabletop?
</span>BC= \sqrt{(x_c-x_b)^2+(y_c-y_b)^2} = \sqrt{(7-4)^2+(8-9)^2}= \\ = \sqrt{3^2+(-1)^2}= \sqrt{9+1}= \sqrt{10}  \ \text{feet}  \\  \\ Area=AB*BC= \sqrt{40}* \sqrt{10}= \sqrt{400}=   20 \ \text{square feet}
<span>
Answer: </span>√40; 20.

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A chemist has two alloys, one of which is 15% gold and 20% lead and the other which is 30% gold and 50% lead. How many grams of
vlabodo [156]

Answer: 490 grams of the first alloy should be used.

30 grams of the second alloy should be used.

Step-by-step explanation:

Let x represent the weight of the first alloy in grams that should be used.

Let y represent the weight of the second alloy in grams that should be used.

A chemist has two alloys, one of which is 15% gold and 20% lead. This means that the amount of gold and lead in the first alloy is

0.15x and 0.2x

The second alloy contains 30% gold and 50% lead. This means that the amount of gold and lead in the second alloy is

0.3y and 0.5y

If the alloy to be made contains 82.5 g of gold, it means that

0.15x + 0.3y = 82.5 - - - - - - - - - - - -1

The second alloy would also contain 113 g of lead. This means that

0.2x + 0.5y = 113 - - - - - - - - - - - - -2

Multiplying equation 1 by 0.2 and equation 2 by 0.15, it becomes

0.03x + 0.06y = 16.5

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Subtracting, it becomes

- 0.015y = - 0.45

y = - 0.45/- 0.015

y = 30

Substituting y = 30 into equation 1, it becomes

0.15x + 0.3 × 30 = 82.5

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6 0
3 years ago
A researcher wishes to estimate the number of households with two cars. How large a sample is needed in order to be 99% confiden
solmaris [256]

Answer:

Sample size n = 1382

so correct option is D) 1382

Step-by-step explanation:

given data

confidence level = 99 %

margin of error = 3%

probability = 25 %

to find out

How large a sample size needed

solution

we know here P = 25 %

so 1 - P = 1 - 0.25

1 - P  = 0.75

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α = 1 - 99%   = 1 - 0.99

α  = 0.01

and  \frac{\alpha}{2} = \frac{0.01}{2}

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Z_(\frac{\alpha}{2}) = 2.576

so

sample size will be

Sample size n =  (\frac{(Z_(\frac{\alpha}{2})}{E})^2 * P * (1-P)

put here value

Sample size n = (\frac{2.576}{0.03})^2 * 0.25 * 0.75

Sample size n = 1382

so correct option is D) 1382

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Answer:

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Step-by-step explanation:

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