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kykrilka [37]
3 years ago
15

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is

40 % salt and Solution B is 90 % salt. She wants to obtain 50 ounces of a mixture that is 80 % salt. How many ounces of each solution should she use?
Mathematics
1 answer:
krok68 [10]3 years ago
8 0

Answer:

The scientist must use 10 ounces of Solution A and 40 ounces of Solution B.

Step-by-step explanation:

Since a scientist has two solutions, which she has labeled Solution A and Solution B, each containing salt, and she knows that Solution A is 40% salt and Solution B is 90% salt, and she wants to obtain 50 ounces of a mixture that is 80% salt, to determine how many ounces of each solution should she use the following calculation must be performed:

100 x 0.9 + 0 x 0.4 = 90

90 x 0.9 + 10 x 0.4 = 85

80 x 0.9 + 20 x 0.4 = 80

50 x 0.8 = 40

Therefore, the scientist must use 10 ounces of Solution A and 40 ounces of Solution B.

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Verify the Cauchy-Schwarz Inequality and the triangle inequality for the given vectors and inner product.
lions [1.4K]

Answer:

To verify the Cauchy-Bunyakovsky-Schwarz Inequality, (p,q) must be less than (or equal to) ||p|| • ||q||

(1,1,1) is not equal to (-10,5)

Step-by-step explanation:

a°b° + a^1b^1 + a^2b^2 < 5x (-2x^2 + 1)

Any algebra raised to the power of zero is equal to 1.

a°b° = 1 × 1 = 1

1 + ab + a^2b^2 < -10x^3 + 5x

The vectors:

(1,1,1) < (-10,5)

This verifies the Cauchy-Schwarz Inequality

Triangle Inequality states that for any triangle, the sum of the lengths of two sides must be greater than or equal to the length of the third side.

5 0
3 years ago
Write the equation of a line that is parallel to y = -5/4x+ + 7 and that passes through the point (-4,1).
k0ka [10]

Answer: y- 1 = -5/4(x+4)\\

Step-by-step explanation:

y = mx + b, where m is the slope, and in the equation, the slope is -5/4.

For two-line that are parallel, the slope is the same, -5/4.

y - y_{1}= m( x - x_{1})\\y- 1 = -5/4(x-(-4))\\y- 1 = -5/4(x+4)\\

5 0
3 years ago
Which expression is equal to 5^4 x 5^8 ? <br><br> A: 5^12<br> B: 5^4<br> C: 5^2<br> D: 5^−4
mrs_skeptik [129]
A is the correct answer when you multip the same numbers you just summe the exp 4+8 = 12
4 0
4 years ago
Read 2 more answers
Abdul and his wife are each starting a saving Plan. Abdul Will initially set aside $50 and then add $50.85 every week to the sav
slamgirl [31]

Answer:T(n)=126.5n+50

Explanation: We are adding two linear functions: A the original function describing Abdul's deposits, and B the deposits made by his wife.

A(n) = 50.85n+50\\B(n)=75.65n\\T(n)=A(n)+B(n) = 50.85n+50 + 75.65n= (50.85+ 75.65)n+50=126.5n+50\\T(n)=126.5n+50

The resulting function is a larger slope due to the added deposit rate.


6 0
4 years ago
A company has two large computers. The slower computer can send all the company's email in minutes. The faster computer can comp
postnew [5]

Both the computers will take 18 minutes to do the job together.

The slower computer sends all the company's email in 45 minutes.

The faster computer completes the same job in 30 minutes.

Let's take minutes t  to complete the task together.

As they complete one job, we get the following equation:

\frac{t}{45}+\frac{t}{30}=1

LCM of 45 and 30 is:

45 = 3 x 3 x 5

30 = 2 x 3 x 5

LCM = 2 x 3 x 3 x 5 = 90

Now, solving for t;

⇒\frac{2t+3t}{90} = 1\\\frac{5t}{90} =1\\5t=90\\

Dividing both sides by 5;

\frac{5t}{5}=\frac{90}{5}

We get t = 18

Hence, it will take both the computers 18 minutes to do the job together.

A company has two large computers. The slower computer can send all the company's emails in 45 minutes. The faster computer can complete the same job in 30 minutes. If both computers are working together, how long will it take them to do the job?

Learn more about work and time here brainly.com/question/13086625

#SPJ4

6 0
2 years ago
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