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3 years ago

Question

Mathematics

1 answer:

puteri [66]3 years ago

3 0

Answer:

The salt concentration of the mixed solution = 10%

Step-by-step explanation:

First assuming that the concentration of salt given is on a vol% basis.

First solution has 0.7 gallon of 5% salt

Amount of salt in this solution = 5% × 0.7 = 0.035 gallon

Second solution has 0.3 gallon of 22% salt

Amount of salt in this solution = 22% × 0.3 = 0.066 gallon

Total amount of salt in the resulting solution = 0.035 + 0.066 = 0.101 gallon

Total volume of the resulting solution = 0.7 + 0.3 = 1.00 gallon

Concentration of the mixture of salt = (0.101/1) = 0.101 = 10.1% = 10% to the nearest percent

Hope this Helps!!!

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The distance from the center of a round horse corral to the fence is 25 yards. What is the area of the horse corral?

Ksivusya [100]

Answer:

625 pi (no approximation)or 1962.5(approximation)

Step-by-step explanation:

You do pi times radius squared.

7 0

3 years ago

Translate the sentence into an equation Twice the difference of a number and 9 is equal to 5use the variable w for the unknown n

TEA [102]

Let w the unknown number. Then, you have

$\begin{gathered} 2(w-9)\rightarrow\text{ Twice the difference of a number and 9} \\ 2(w-9)=5\rightarrow\text{Twice the difference of a number and 9 is equal to 5} \end{gathered}$

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1 year ago

bonnie runs 1 2/3 times as far as john each day if bonnie runs 5 miles on monday 3 1/2 miles on tuesday and 5 3/4 miles on wedne

nignag [31]

Answer:

3 miles on Monday

2¹/₁₀ miles on Tuesday

3⁹/₂₀ miles on Wednesday

Step-by-step explanation:

We are told that Bonnie runs 1⅔ (⁵/₃) times as far as John each day

This means that John runs ³/₅ times as far as Bonnie.

MONDAY:

Bonnie runs 5 miles on Monday, therefore, John runs:

³/₅ * 5 = 3 miles

TUESDAY:

Bonnie runs 3½ (⁷/₂) miles on Tuesday, therefore, John runs:

³/₅ * ⁷/₂ = ²¹/₁₀ = 2¹/₁₀ miles

WEDNESDAY:

Bonnie runs 5³/₄ (²³/₄) miles on Wednesday, therefore, John runs:

³/₅ * ²³/₄ = ⁶⁹/₂₀ = 3⁹/₂₀ miles

6 0

2 years ago

4. Find the standard from of the equation of a hyperbola whose foci are (-1,2), (5,2) and its vertices are end points of the dia

Ad libitum [116K]

The standard form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

<h3>How to find the standard equation of a hyperbola</h3>

In this problem we must determine the equation of the hyperbola in its standard form from the coordinates of the foci and a general equation of a circle. Based on the location of the foci, we see that the axis of symmetry of the hyperbola is parallel to the x-axis. Besides, the center of the hyperbola is the midpoint of the line segment with the foci as endpoints:

(h, k) = 0.5 · (- 1, 2) + 0.5 · (5, 2)

(h, k) = (2, 2)

To determine whether it is possible that the vertices are endpoints of the diameter of the circle, we proceed to modify the general equation of the circle into its standard form.

If the vertices of the hyperbola are endpoints of the diameter of the circle, then the center of the circle must be the midpoint of the line segment. By algebra we find that:

x² + y² - 4 · x - 4 · y + 4= 0

(x² - 4 · x + 4) + (y² - 4 · y + 4) = 4

(x - 2)² + (y - 2)² = 2²

The center of the circle is the midpoint of the line segment. Now we proceed to determine the vertices of the hyperbola:

V₁(x, y) = (0, 2), V₂(x, y) = (4, 2)

And the distance from the center to any of the vertices is 2 (semi-major distance, a) and the semi-minor distance is:

b = √(c² - a²)

b = √(3² - 2²)

b = √5

Therefore, the standard form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

To learn more on hyperbolae: brainly.com/question/27799190

#SPJ1

5 0

1 year ago

a pile of sand has a weight of 90kg The sand is put into a small bag, a medium bag and a large bag in the ratio of 2 : 3 : 7 Wor

just olya [345]

Hi there!

To split 90 kilos in the ratio of 2 : 3 : 7 we must first realise that we have a total of 2 + 3 + 7 = 12 parts, in which we must split the total 90 kilos.

12 parts equal 90 kilo, and therefore
1 part equals 90 / 12 = 7.5 kilos.

1 part equals 90 / 12 = 7.5 kilos, and therefore
2 parts equal 7.5 × 2 = 15 kilos.

1 part equals 90 / 12 = 7.5 kilos, and therefore
3 parts equal 7.5 × 3 = 22.5 kilos.

1 part equals 90 / 12 = 7.5 kilos, and therefore
7 parts equal 7.5 × 7 = 52.5 kilos.

Hence, 90 kilos in the ratio of 2 : 3 : 7
gives 15 kg, 22.5 kg and 52.5 kg.

~ Hope this helps you!

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3 years ago