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TEA [102]
2 years ago
13

What weight of dry substance is in 150g of a 3% substance solution? What weight of an 8% solution can we have with the same weig

ht of dry substance?
Answer:

g of dry substance and
g of an 8% solution.
Mathematics
1 answer:
Pavlova-9 [17]2 years ago
5 0
The answers are: 4.5 g and 56.25 g respectively.

Since the first type of measurement in this question is weight or mass, I'll suppose that the percentage concentration is % mass/mass. For that type of concentration measurement, just multiply the percentage by the total mass to get the mass of the wanted material.
So 150 g * 3% = 150 g * 0.03 = 4.5g

For the 8% solution with the same amount of dry substance, use the ratio of percentages, multiplied by the mass of the first solution to get the wanted amount of new solution:
3/8 * 150 g = 56.35 g
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Paul [167]

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8 0
2 years ago
Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software,
grandymaker [24]

Solution:

There is no saddle point (DNE). However, there is local maximum at (1, 1/2) for the given function.

Explanation:

we have function of two variables f(x,y)= 9-2x+4y-x^2-4y^2

we will find the values by partial derivative with respect to x,y,xy

f_{x}= -2 -2x

f_{y}= 4 -8y

to find the saddle point we should first find the critical points so equate

-2 -2x=0 and   4 -8y=0

we get x= 1  and y =1/2 so, critical points are (1,1/2)

to find local maximum or minimum we have to find f_{xx},  f_{yy} and f_{xy}

formula is f_{xx} *f_{yy} - f^{2_{xy} } =0

f_{xx} = -2

f_{yy} = -8

f^{2_{xy} } =0

putting values in formula

(-2)*(-8) -0 =16 > 0, and f_{xx}< 0  and f_{yy}<0

so, here we have local maximum

we have no saddle point for this function by using the same formula we used to find extrema.



4 0
2 years ago
Read 2 more answers
The mini muffins company bakes 1872 muffins the large mini muffin boxes hold a dozen muffins how many large boxes are needed to
lilavasa [31]

Answer:

To pack 1872 muffins the mini muffins company needs 156 large boxes.

Step-by-step explanation:

Number of muffins baked by the mini muffins company  = 1872.

the large mini muffin boxes hold a dozen muffins that is the large box contains 12 muffins.( 1 Dozen = 12 )

We have to find the number of large boxes needed to pack 1872 muffins.

Using unitary method,

12 muffins is contained in 1 large box.

1 muffin is contained in \frac{1}{12} large box.

1872 muffins contained in \frac{1}{12} \times 1872=156 large boxes.

Hence, To pack 1872 muffins the mini muffins company needs 156 large boxes.



6 0
2 years ago
Suppose the time required for an auto shop to do a tune-up is normally distributed, with a mean of 102 minutes and a standard de
hammer [34]

Answer:

Step-by-step explanation:

Suppose the time required for an auto shop to do a tune-up is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = points scored by students

u = mean time

s = standard deviation

From the information given,

u = 102 minutes

s = 18 minutes

1) We want to find the probability that a tune-up will take more than 2hrs. It is expressed as

P(x > 120 minutes) = 1 - P(x ≤ 120)

For x = 120

z = (120 - 102)/18 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.8413

P(x > 120) = 1 - 0.8413 = 0.1587

2) We want to find the probability that a tune-up will take lesser than 66 minutes. It is expressed as

P(x < 66 minutes)

For x = 66

z = (66 - 102)/18 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.02275

P(x < 66 minutes) = 0.02275

4 0
2 years ago
An aluminum ladder holds 220 lb. A 152-lb person, a 15-lb weight, and a box are on the ladder without breaking it. Write and sol
jolli1 [7]

Let x lb be the weight of a box. Since 152-lb person, a 15-lb weight, and a box are on the ladder without breaking it and the  ladder holds 220 lb, then

152+15+x≤220.

Solve this inequality:

167+x≤220,

x≤220-167,

x≤53 lb.

The maximum weight of the box can be 53 lb.

6 0
2 years ago
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