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antoniya [11.8K]
2 years ago
5

do you want to make a sodium carbonate solution with a concentration of 2.5%. You have 50 mL of a 1% solution about how many mil

liliters of a 6% solution should you add
Mathematics
1 answer:
Evgesh-ka [11]2 years ago
6 0

9514 1404 393

Answer:

  21 3/7 mL ≈ 21.43 mL

Step-by-step explanation:

Let x represent the amount of 6% solution that should be added. The the total volume of sodium carbonate in the mix is ...

  1%(50) +6%(x) = 2.5%(50 +x)

  50 +6x = 125 +2.5x . . . . . multiply by 100, eliminate parentheses

  3.5x = 75 . . . . . . . . . . . . . subtract 2.5x+50

  x = 21 3/7 . . . . . . . . . . . . . divide by 3.5

21 3/7 mL, about 21.43 mL, of 6% solution should be added to make a 2.5% solution.

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Solve the formula s=4pi r^2 for r
andrew11 [14]

Answer:

The formula to find the surface area of a sphere is to take the radius of the sphere and square it and multiply that amount by pi and then multiply that by 4. This is written algebraically as S=4πr2, where S is the surface area, r is the radius, and the value of π is 3.14.

7 0
3 years ago
Service calls arriving at an electric company follow a Poisson distribution with an average arrival rate of 5656 per hour. Find
liberstina [14]

Answer:

The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given interval. The variance is the same as the mean.

Average rate of 56 calls per hour:

This means that \mu = 56n, in which n is the number of hours.

Find the average and standard deviation of the number of service calls in a 15-minute period.

15 minute is one fourth of a hour, which means that n = \frac{1}{4}. So

\mu = 56n = \frac{56}{4} = 14

The variance is also 14, which means that the standard deviation is \sqrt{14} = 3.74

The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.

4 0
2 years ago
Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = 5 over 5 and 59 hundredths.
Vikentia [17]

The relationship between Traingle XYZ and ACB is that they are similar triangles. tanX = tanA = 5 over 2 and 5 tenths, where

  • AC = 2 x  XY
  • CB = 2 x  YZ

<h3>What is the dilation about?</h3>

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB, hence XYZ and ACB are similar triangles.

Angles Y and C are said to measure 90 degrees, and angles A and X are known to be congruent. Thus:

tanX = tanA = 5 over 2 and 5 tenths

AC = 2 x  XY

CB = 2 x  YZ

Another way to solve for it is by:

Note that Dilation of the triangle ΔXYZ was by a factor of "2".

Since m∠Y = m∠C = 90º   - given

ΔXYZ and ΔACB are said to be right triangles.

Since ∠X ≅ ∠A   - given

Then ∠X and ∠Z are  said to becomplementary angles

Since m∠Z = 90° - m∠X   -- given

Then ∠A and ∠B are said to be complementary angles

Since m∠B = 90° - m∠A  --- given

Then, ∠Z ≅ ∠B

Therefore ΔXYZ ∼ ΔACB are  similar triangles because it has its corresponding sides to be proportional and its corresponding angles to be congruent.

Note:

sin ∠X = 5/5.59

sin ∠X = YZ/XY

YZ = 5  seen in ΔXYZ

XZ = 5.59 seen in hypotenuse of ΔXYZ

Then one need to Calculate the length of one aspect of XY:

XY = √((5.59)2 - 52)

= 2.4996

Note CB/YZ = 2

CD = 2*YZ = 2 x 5

= 10

AC/XY = 2

AC = 2* XY

= 2 x 2.4996

= 4.999

Learn more about dilation from:

brainly.com/question/27517432

#SPJ1

7 0
2 years ago
The water is filling a swimming pool at a rate of 1000 gallons every 15 minutes. At this rate, how long will it take to fill a s
allochka39001 [22]

Answer:

2 hours and 30 minutes to fill it up

Step-by-step explanation:

3 0
2 years ago
The graphs of the equation y = 4x + 1 and y - kx = 10 are perpendicular when k = _______?
Ann [662]

Answer:

k=-\frac{1}{4}

Step-by-step explanation:

we have

Line 1

y=4x+1

Equation in slope intercept form

The slope is equal to

m_1=4

Line 2

y-kx=10

y=kx+10

Equation in slope intercept form

The slope is equal to

m_2=k

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

so

m_1*m_2=-1

substitute

(4)(k)=-1

k=-\frac{1}{4}

3 0
3 years ago
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