Two solutions of different concentrations of acid are mixed creating 40 mL of a solution that is 32% acid. One-quarter of the solution is made up of a 20% acid solution. The remaining three-quarters is made up of a solution of unknown concentration, c. Which equation can be used to determine c, the unknown concentration? 30c 10(0. 2) = 40(0. 32) StartFraction 3 Over 4 EndFraction left-parenthesis c right parenthesis plus left-parenthesis StartFraction 1 Over 4 EndFraction left-parenthesis 0. 2 right-parenthesis right-parenthesis equals 40 times 0. 32. (c) StartFraction 1 Over 4 EndFraction cup. (0. 2) = 40(0. 32) (c)( (0. 2)) = 40(0. 32) 30(c)(10(0. 2)) = 40(0. 32).

Linear expressions are expressions in which the highest power of the variable is 1.

Linear expressions 3x - 2 and 2x - 3 have a difference of 3x - 2

The given parameter is:

\(\mathbf{difference = x + 1}\)

Let one of the linear expressions be 2x - 3, and the other expression be y.

So, the difference would become

\(\mathbf{y -(2x -3) = x + 1}\)

Open bracket

\(\mathbf{y -2x +3 = x + 1}\)

Collect like terms

\(\mathbf{y = 2x + x + 1 - 3}\)

Evaluate like terms

\(\mathbf{y = 3x - 2}\)

Hence, 3x - 2 and 2x - 3 have a difference of 3x - 2

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Answer:

2/35

Step-by-step explanation:

If you convert 17 1/2 to a improper fraction, it becomes 35/2. Then to find the reciprocal, flip the numerator and denominator. So, 2/35

Hope this helps!

Answer:

\(y = -2x + 10\)

Step-by-step explanation:

Slope: \(m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}}\)

Slope-Intercept Form: \(y=mx+b\)

\(m=\frac{8-0}{1-5}\)

\(m = -2\)

\(y = -2x + b\)

\(0 = -2 (5)+b\)

\(0=(-10)+b\)

\(b = 10\)

\(y = -2x + 10\)

The expected value of the random variable x, based on the given probability distribution, is calculated to be 5.1.


To calculate the expected value of x, we multiply each value of x by its corresponding probability and sum them up. The calculation is as follows: (3.65 * 0.15) + (15 * 0.3) + (3.5 * 0.25) + (0.25 * 0.3) = 0.5475 + 4.5 + 0.875 + 0.075 = 5.9975.

Rounded to one decimal place, the expected value of x is 5.1. This means that, on average, if the experiment is repeated many times, the expected value of the random variable x would be close to 5.1. It represents the center or average value of the distribution.

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We have that the area of a triangle using two sides and the angle between those sides can be determined using the following expression:

Now, we replace and operate:

So, the area of the triangle is approximately 28.2 squared centimeters.

5 km = 5000 meters

66 minutes = 3960 seconds

Meters per second = 5000/3960 = 1.26

The answer is A.1.26

Answer:

A

Step-by-step explanation:

-4x+5y=10. -4x+5y=10. -4x+5y=10

The distance between the ground and the kite is approximately 62.53 feet. Rounded to the nearest foot, the distance is 63 feet.

To find the distance between the ground and the kite, we can use trigonometry and the given information about the angle of elevation and the length of the kite string.

First, let's draw a diagram to represent the situation. We have a right triangle formed by the ground, the kite string, and the distance between the ground and the kite. The angle of elevation (the angle between the ground and the kite string) is 44°.

In the triangle, we can assign the following variables:

- Let x represent the distance between the ground and the kite (the side opposite to the angle of elevation).

- Let 90 feet represent the length of the kite string (the hypotenuse of the triangle).

- Let 44° represent the angle of elevation (the angle formed between the ground and the kite string).

Using the trigonometric ratio for the sine function, we have:

sin(44°) = opposite/hypotenuse

Substituting the values we assigned, we get:

sin(44°) = x/90

To solve for x, we can rearrange the equation:

x = sin(44°) * 90

Now we can calculate the value of x:

x = sin(44°) * 90

x ≈ 0.6947 * 90

x ≈ 62.53 feet

Therefore, the distance between the ground and the kite is approximately 62.53 feet. Rounded to the nearest foot, the distance is 63 feet.

By using trigonometry and the given angle of elevation and length of the kite string, we were able to find the distance between the ground and the kite.

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Answer:472.5

Step-by-step explanation:

Answer:

After 1 year = $2548

Step-by-step explanation:

Answer:

41 is your answer

Step-by-step explanation:

m<EFG = 1/2 (121-39)

M<EFG= 1/2 (82)

M<EFG= 41

hope this helps u have a great day ^_^

Answer:

m∠EFG= 41°

Step-by-step explanation:

\(c=\frac{a-b}{2}\)

\(\frac{121-39}{2}\)

\(= \frac{82}{2}\)

so, m∠EFG=41°

\(----------\)

hope it helps...

have a great day!!

You should only use a closed dot for the symbols ≤ and ≥.

There are two types of dots used when graphing inequalities, closed and open.

So, for exampe in:

x > 3.

We would put an open dot at 3, because the value x = 3 is not a solution, but all the values at the right of the 3 are solutions.

In the other hand, for:

x ≥ 3

Now 3 is in fact a solution, so here we should use a closed dot.

Then, answering the question.

"When you graph an inequality, you used a closed dot when you use which symbols?"

The ≤ and ≥ symbols.

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Option B) If the sum of the squares of the two short sides equals the square of the longest side

Answer:

300

Step-by-step explanation:

375 divided by 5=75

Each “1”=75

4x75=300

There are 300 boys.

Hope this makes sense

Answer:

300 boys

Step-by-step explanation:

Let the number of boys = x

Girls: 375

boys : girls = 4 : 5

total in the ratio is 9

girls are 5/9 of total, and are 375

boys are 4/9 of total

5/9 x = 375

x = 375 × 9/5

x = 675

Boys are 4/9 of total.

4/9 × 675 = 300

To find the total number of students Mrs. Martinez teaches, we need to add the number of students in both of her classes. We are given that there are 12 women and 14 men in her first class, and 11 women and 17 men in her second class.

Therefore, we can add the number of women and the number of men in each class separately and then add the totals to get the final answer.Number of women in the first class = 12 Number of men in the first class = 14 Number of women in the second class = 11 Number of men in the second class = 17 To find the total number of students in the first class, we add the number of women and men:

Total number of students in the first class = 12 + 14 = 26 Similarly, to find the total number of students in the second class, we add the number of women and men:Total number of students in the second class = 11 + 17 = 28 To find the total number of students that Mrs. Martinez teaches, we add the number of students in both of her classes: Total number of students = 26 + 28 = 54

Therefore, Mrs. Martinez teaches 54 students altogether.

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The Triangle Midsegment Theorem states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side.

Given: In triangle DEF, DG ≅ GE and FH ≅ HE

To Prove: GH || DF and GH = 1/2 DF:

1. Draw triangle DEF and mark the midpoints of sides DE and EF as G and H, respectively.

2. Draw lines through G and H that are parallel to side DF and mark their intersection as point I.

3. By the definition of midpoint, we know that DG = GE and FH = HE.

4. Since G and H are midpoints, we know that GH is half the length of DE and EF, respectively. Thus, GH = 1/2(DE) and GH = 1/2(EF).

5. By the transitive property of equality, we can set these two expressions equal to each other:

1/2(DE) = 1/2(EF)

6. Multiplying both sides of the equation by 2 yields:

DE = EF

7. Therefore, triangle DEF is an isosceles triangle, and its base angles are congruent.

8. Using alternate interior angles and the fact that GH is parallel to DF, we can conclude that angle GHI is congruent to angle DEF.

9. Similarly, angle HIJ is congruent to angle EDF.

10. Therefore, angle GHI and angle HIJ are congruent, so triangle GHI is an isosceles triangle, and GH = GI.

11. Using the same alternate interior angles and parallel lines, we can also conclude that angle GIJ is congruent to angle EDF.

12. Therefore, triangle GIJ is an isosceles triangle, and GI = GJ.

13. Combining these two results, we get GH = GI = GJ.

14. Therefore, GH is parallel to DF, and GH = 1/2 DF, as required.

Thus, the triangle midsegment theorem is proved.

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Step-by-step explanation:

I know it not all but this is what I have

Answer:

supplementary angles

Step-by-step explanation:

Answer:

h = 15 ft

Step-by-step explanation:

using the 2 similar triangles in the diagram then the ratios of corresponding sides are in proportion.

let h be the height of the tree

\(\frac{h}{5}\) = \(\frac{24}{8}\) = 3 ( multiply both sides by 5 )

h = 15 ft

Answer:

m = 6

Step-by-step explanation:

We have the proportion:

12/m = 18/9

To solve for m, we can cross-multiply the terms in the proportion:

12 × 9 = 18 × m

Simplifying both sides of the equation, we get:

108 = 18m

Dividing both sides by 18, we get:m = 6

Therefore, the solution to the proportion 12/m = 18/9 is m = 6.

Answer: m = 6

Step-by-step explanation:

First, we will rewrite this proportion:

     \(\displaystyle \frac{12}{m} =\frac{18}{9}\)

Next, we will cross-multiply:

     12 * 9 = 18 * m

     108 = 18m

Lastly, we will divide both sides of the equation by 18:

     m = 6

We can also solve this proportion another way.

     We know that 18/9 = 2, so 12/m must equal 2 as well.

     12/6 = 2, so m = 6.

The statement is true. Trigonometry is indeed highly useful in navigation, and the term "bearing" is commonly used to describe direction in navigation.

In navigation, a bearing refers to the direction of an object or a point relative to a reference point. It is typically measured in degrees clockwise from the north direction. Trigonometric concepts such as angles, triangles, and trigonometric functions (sine, cosine, tangent) are used to determine and calculate bearings.

Bearing can be expressed in two ways:

a. True Bearing: True bearing refers to the direction of an object relative to true north. It is measured with respect to the Earth's geographic north pole.

b. Magnetic Bearing: Magnetic bearing refers to the direction of an object relative to magnetic north. It takes into account the magnetic declination, which is the difference between true north and magnetic north at a specific location.

Trigonometry plays a crucial role in converting between true bearing and magnetic bearing, as well as in various navigation techniques such as triangulation, dead reckoning, and celestial navigation.

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Athletes who test negative for steroids should not be automatically assumed innocent because the probability of a false negative can vary depending on the accuracy of the test.

The probability that an athlete who tests negative for steroids is using them depends on the type of test conducted. For example, a more accurate test such as a gas chromatography-mass spectrometry (GC-MS) test, can detect steroids with a higher degree of accuracy.

On the other hand, a less accurate test, such as a urine test, has a lower probability of detecting the presence of steroids. Generally speaking, if an athlete is tested negative for steroids, there is a relatively low probability that he/she is using them. However, this is not always the case, as even the most accurate tests can produce false negatives.

It is important to note that using steroids is a form of cheating in sport and is strictly prohibited. Furthermore, athletes may attempt to use methods such as masking agents or diuretics to conceal the presence of the steroids.

Consequently, athletes who test negative for steroids may still be using them and thus should not be considered innocent.

In conclusion, the probability that an athlete who tests negative for steroids is using them varies depending on the type of test conducted. Generally, it is low, but it is possible that even with an accurate test, false negatives can occur. As such, athletes who test negative should not be considered innocent.

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Answer:

Solution Given:

let pitcher which is small be S medium be M and large be L and barrel be B.

By question

6S+3M+1L= 1B...... eq. 1

2S+1M+3L=1B.......eq. 2

The difference in 2L from the first to the second is 4S and 2M

Therefore, each L=2S+M

In equation 2

2S+1M+3L=1B

replacing 2S +1M by L,we get

L+3L=1B

4L=1B

Therefore, 4 large pitcher is required

Answer:

4 large pitchers

Step-by-step explanation:

Define the variables:

Create two equations with the given information and the defined variables.

Equation 1

If the barrel can be filled with 6 small pitchers, 3 medium pitchers and 1 large pitchers:

⇒ 6x + 3y + z = b

Equation 2

If the barrel can be filled with 2 small pitchers, 1 medium pitcher and 3 large pitchers:

⇒ 2x + y + 3z = b

Substitute Equation 2 into Equation 1

⇒ 6x + 3y + z = 2x + y + 3z

Subtract 6x from both sides:

⇒ 3y + z = -4x + y + 3z

Subtract y from both sides:

⇒ 2y + z = -4x + 3z

Subtract z from both sides:

⇒ 2y = -4x + 2z

Divide both sides by 2:

⇒ y = -2x + z

Substitute the found expression for y into Equation 1:

⇒ 6x + 3(-2x + z) + z = b

⇒ 6x - 6x + 3z + z = b

⇒ 4z = b

Therefore, 4 large pitchers are needed to fill the barrel.

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Answer:

4

Step-by-step explanation:

Danielle viewed 7 movies on demand, thus you must divide her 35 dollars among them. So the monthly charge for Danielle's cable bill is $5.

Danielle pays a monthly charge of $69 for her cable bill.

She also pays a fee every time she watches a movie on demand.

Last month Danielle watched 7 movies on demand, and her total monthly bill was $104.

We have to find the monthly charge for Danielle's cable bill to choose.

Remove the monthly fee of 69 dollars for cable service from the total of 104 dollars, then check the statement to see that there is still a mystifying 35 dollars on it.

Danielle viewed 7 movies on demand, thus you must divide her 35 dollars among them, giving you the result of $5 per on-demand movie.

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The selling price is $36.25 and the markup amount is $11.25.

Given, Original cost of the bracelet, C = $25

Markup is 45% on the selling price

We need to calculate the selling price and the amount of the markup.

a) Selling price

We can find the selling price using the following formula:

Selling price = (1 + Markup%) × CostPrice = C × (1 + Markup%)

Putting the given values in the formula, we get:

Selling price = $25 × (1 + 45/100) = $25 × 1.45 = $36.25

Selling price of the bracelet is $36.25

b) Markup amount

The markup amount can be found using the following formula: Markup amount = Selling price - Cost price

Markup amount = $36.25 - $25 = $11.25

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Answer:

x < \(\frac{33}{4}\)

Step-by-step explanation:

Given

- 4x + 35 > 2 ( subtract 35 from both sides )

- 4x > - 33

Divide both sides by - 4, reversing the symbol as a result of dividing by a negative quantity.

x < \(\frac{33}{4}\)

Answer:

  y = (7/2)x -20

Step-by-step explanation:

The given line is in slope-intercept form, so you can read its slope from the equation.

  y = mx + b . . . . . m is the slope; b is the y-intercept

  y = -(2/7)x + 9 . . . . . . has slope -2/7

The perpendicular line will have a slope that is the negative reciprocal of this, so will be ...

  m = -1/(-2/7) = 7/2

We can use this and the given point to write the equation in point-slope form.

  y = m(x -h) +k . . . . . . line with slope m through point (h, k)

We have m = 7/2, (h, k) = (4, -6) so the equation is ...

  y = (7/2)(x -4) -6

  y = (7/2)x -20