how many liters of a 24% glucose solution must be added to 2 liters of a 9% glucose solution to obtain a 12% glucose solution?

Answer:

Choose f(x) = 11x + 1

Step-by-step explanation:

Note that we will simply plug the value of 2 into the equation for February:

f(2) = 11(2) + 1 = 23

And plug the value of 6 into the equation for June:

f(6) = 11(6) + 1 = 67

Note how the points on the graph seem to match up with these values.  If we evaluate following the same style for each:

f(3) = 11(3) + 1 = 34

f(4) = 11(4) + 1 = 45

f(5) = 11(5) + 1 = 56

Note, these values seems to be very close in approximation to the graph points for each month.

The other three functions return values that are just to far away from what are represented in the graph.

Cheers.

Answer:

Step-by-step explanation:

I got 408.33. dont know how to help you out

The 98% confidence interval for the population mean is (87.77, 96.23).

The parameters needed to calculate a confidence interval at the 98% confidence level are:

The sample mean (x) = 92 points

The population standard deviation (σ) = 6 points

The sample size (n) = 22

The critical value of the standard normal distribution corresponding to a 1 - α/2 = 0.98 level of confidence, which is Zα/2

= Z0.01

= 2.326.

Using the formula for the confidence interval for the population mean with known standard deviation, we have:

\(CI = x \pm Z\alpha /2 * (\sigma / \sqrt{(n)} )\)

Substituting the values, we get:

\(CI = 92 \pm 2.326 * (6 / \sqrt{(22)} )\)

= (87.77, 96.23).

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To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.



To find the equation of a line parallel or perpendicular to a given line through a specific point, follow these steps:

1. Determine the slope of the given line. If the given line is in the form y = mx + b, the slope (m) will be the coefficient of x.

2. Parallel Line: A parallel line will have the same slope as the given line. Using the slope-intercept form (y = mx + b), substitute the slope and the coordinates of the given point into the equation to find the new y-intercept (b). This will give you the equation of the parallel line.

3. Perpendicular Line: A perpendicular line will have a slope that is the negative reciprocal of the given line's slope. Calculate the negative reciprocal of the given slope, and again use the slope-intercept form to substitute the new slope and the coordinates of the given point. Solve for the new y-intercept (b) to obtain the equation of the perpendicular line.

Remember that the final equations will be in the form y = mx + b, where m is the slope and b is the y-intercept.Therefore, To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.

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When f(x) = 20

Then

5x + 10 = 20

Therefore

5x=20-10=10

x = 10 / 5 = 2

x= 2

Answer:

x=-1/25

Step-by-step explanation:

-3/5x=15

-3/5x(5x)=15(5x)

-3=75x

75x=-3

x=-3÷75

=-3/75

=-1/25

Probability of choosing a face card for the second card drawn, if the first card, drawn without replacement, was a jack is 11/51

What do you mean by conditional probability?

The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability.

Total number of face cards = 12

4 kings , 4 queens and 4 jacks

If first card drawn was Jack then remaining cards = 51

Remaimng face cards = 21 - 1 = 11

P( choosing a face card for the second card drawn, if the first card, drawn without replacement, was a jack ) = 11/51

Therefore, Probability of choosing a face card for the second card drawn, if the first card, drawn without replacement, was a jack is 11/51

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Answer:

348 feet

Step-by-step explanation:

Answer:

-348

or 348 feet under the oceans surface

Step-by-step explanation:

since your already 100 feet below the surface, if you go down(descends) another 248 feet. You subtract 248 from -100, you get -348.

So your 348 feet below sea level.

hope this helps!

Answer:

56 feet

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer:

8

Step-by-step explanation:

Reverse the steps and reverse the operations (divide to multiply, add to subtract)

Multiply 6 by 2 to get 12 and subtract 4 to get 8

Step-by-step explanation:

-12 = v + 8

v + 8 = -12

v = -12 - 8

v = -20

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In one minute it makes :

So, in 2 minutes it will make :

Step-by-step explanation:

If in one minute it makes

\( \\ \bf = 5 \frac{2}{9} \: \: rotations\)

\( \\ \bf = \frac{47}{9} \: \: rotations\)

Then, in two minutes it'll make

\( \\ \bf = \frac{47}{9} \times 2\)

\( \\ \bf = \frac{94}{9} \)

\( \\ \bf = 10\frac{4}{9} \: \: rotations\)

Answer:

x=-4

Step-by-step explanation:

(a) The expression for a Riemann sum of a function f on an interval [a, b] is Δx = (b-a)/n

(b) If f(x)⩾ 0, then the geometric interpretation of a Riemann sum is infinity

(c) If f(x) takes on both positive and negative values, then the geometric interpretation of a Riemann sum is infinity

Riemann sums are an important tool in calculus for approximating the area under a curve. They are used to estimate the value of a definite integral, which represents the area bounded by the curve and the x-axis on a given interval. In this explanation, we will discuss the expression for a Riemann sum, its notation, and its geometric interpretation.

(a) Expression for a Riemann sum:

A Riemann sum is an approximation of the area under a curve using rectangles. We divide the interval [a, b] into n subintervals, each of length Δx=(b−a)/n. The notation used to represent this is:

Δx = (b-a)/n

(b) Geometric interpretation of a Riemann sum when f(x)⩾ 0:

If f(x) is always non-negative, the Riemann sum represents an approximation of the area between the curve and the x-axis on the interval [a, b].

Each rectangle has a positive area, which contributes to the overall area under the curve. The sum of the areas of the rectangles approaches the true area under the curve as the number of subintervals n approaches infinity.

(c) Geometric interpretation of a Riemann sum when f(x) takes on both positive and negative values:

When f(x) takes on both positive and negative values, the Riemann sum represents the net area between the curve and the x-axis on the interval [a, b].

Each rectangle may have a positive or negative area, depending on the sign of f(xi).

The positive areas represent regions where the curve is above the x-axis, and the negative areas represent regions where the curve is below the x-axis.

In conclusion, Riemann sums are used to approximate the area under a curve on an interval [a, b]. The expression for a Riemann sum involves dividing the interval into n subintervals and approximating the area under the curve using rectangles.

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The value of f(-4) is -20

The equation of the function is given as:

f(x) = 5x

Substitute -4 for x

f(-4) = 5(-4)

Express as product

f(-4) = 5 * -4

Rewrite as:

f(-4) = -5 * 4

Evaluate the product

f(-4) = -20

Hence, the value of f(-4) is -20

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There are 16 possible 2-letter code words letters can be repeated. There are 12 possible 2-letter code words adjacent letters must be different.

If letters can be repeated, the number of possible 2-letter code words that can be formed from the given letters is determined by the formula:

Number of possibilities = (number of choices for the first letter) * (number of choices for the second letter)

Since we have 4 letters available (W, C, M, J), and we can repeat letters, the number of choices for each letter is 4.

Therefore, the number of possible 2-letter code words with repeated letters is:

4 * 4 = 16

If adjacent letters must be different, the number of possible 2-letter code words is determined as follows:

Number of possibilities = (number of choices for the first letter) * (number of choices for the second letter, excluding the previously chosen letter)

For the first letter, we have 4 choices. For the second letter, we have 3 choices because we need to choose a letter different from the first letter.

Therefore, the number of possible 2-letter code words with adjacent letters different is:

4 * 3 = 12

To summarize:

The number of possible 2-letter code words with repeated letters is 16.

The number of possible 2-letter code words with adjacent letters different is 12.

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Your current monthly income, before the effect of inflation, is approximately $2,129.63.

To determine your current monthly income, we need to account for the effect of inflation on the purchasing power of your income. Given that the inflation rate is eight percent, we can calculate the original income before the inflation adjustment.

Let's denote your current monthly income as "X."

The purchasing power after accounting for eight percent inflation is $2,300. This means that your original income, before the inflation adjustment, would have had a higher value. We need to find this original income.

Inflation reduces the purchasing power of your income, so we need to increase the current purchasing power by the inflation rate to find the original income. In this case, we'll increase $2,300 by eight percent:

Original Income = $2,300 / (1 + 0.08)

Original Income = $2,300 / 1.08

Original Income ≈ $2,129.63

Therefore, your current monthly income, before the effect of inflation, is approximately $2,129.63.

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The price per T-shirt should be at least $15 to achieve a profit of $250.

To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.

Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.

Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.

Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.

Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.

By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.

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Answer:

Step-by-step explanation:

Answer:

Vertical Reflection Apply a reflection over the line y=-1 The procedure to determine the coordinate points of the image is the same as that of the previous example with minor differences in that the change will be applied to the y-value and the x-value stays the same.

Step-by-step explanation:

Answer:

\(y=-x-3\)

Step-by-step explanation:

From the graph, we observe that the y-intercept of the line is c=-3.

So, the equation of the line is, where m is the slope:

\(y=mx+c= > y=mx-3---(1)\)

Since the line contains the point (x,y)=(-3,0), substitute x=-3 and y=0 into (1):

\(0=m(-3)-3\\0=-3m-3\\3m=-3\\m=-\frac{3}{3}= > m=-1---(2)\)

Substitute (2) into (1), and we get:

\(y=-x-3\)

The scale factor of the drawing is 2000.

In order to determine the scale factor of the drawing, we need to compare the length of the living room in real life to its length in the drawing. The living room is 4 meters long in real life and 2 millimeters long in the drawing.

To find the scale factor, we divide the length in real life by the length in the drawing.

Scale factor = Length in real life / Length in the drawing

Scale factor = 4 meters / 0.002 meters

Scale factor = 2000

Therefore, the scale factor of the drawing is 2000. This means that every unit in the drawing represents 2000 units in real life.

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Jared bought 7 cans of paint. Let the number of red paint cans that Jared bought be x. The number of black paint cans he bought would be 7 - x. A can of red paint costs $3.75 and a can of black paint costs $2.75.

He spent $22 in all. Therefore we can write:3.75x + 2.75(7 - x) = 22 Multiplying out the second term and collecting like terms gives:0.5x + 19.25 = 22Subtracting 19.25 from both sides:0.5x = 2.75Dividing by 0.5:x = 5.5Since Jared can't buy half a can of paint, we should round the answer to the nearest integer. Hence, he bought 5 cans of red paint and 2 cans of black paint. The total cost of the 5 cans of red paint would be 5 x $3.75 = $18.75.The total cost of the 2 cans of black paint would be 2 x $2.75 = $5.50.The total cost of all 7 cans of paint would be $18.75 + $5.50 = $24.25.We spent more than Jared's budget. The value of $24.25 exceeds Jared's budget of $22. Hence, there is a problem with this problem statement.

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Answer:

y= - 1/4x - 3

Step-by-step explanation:

The answer is x = 3 1/2. To solve, you must multiply both sides of the equation by the denominator of the fraction on the left side, which is 3. This will cancel out the fraction and you will be left with 4 1/3 - x = -3, which can then be solved by adding x to both sides.

4 1/4 - 1/3x

= (12/3) - (1/3)x

= 4 1/3 - x

= 4 1/3 - x -3

= x - 3

= x + 3

= 3 1/2

To solve the equation 4 1/4 − 1/3x = −3/4, you must first multiply both sides of the equation by the denominator of the fraction on the left side, which is 3. This will cancel out the fraction and you will be left with 4 1/3 - x = -3. Then you can add x to both sides of the equation to get 4 1/3 = x - 3. Then you can add 3 to both sides of the equation to get x = 3 1/2. So the answer is x = 3 1/2. This process is necessary because fractions need to be canceled out before you can solve the equation. If you do not cancel out the fractions first, then you will not be able to solve the equation correctly. It is important to remember that when you are solving equations with fractions, you must cancel out the fractions before you solve the equation.

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Answer:

There's no expressions.

Out of those who took the exam, 3/5 passed. So, 100 * 3/5 = 60 is the number of students passed the exam. Therefore, the correct answer is: c ) 60.

To solve this problem, we'll follow these steps:

Step 1: Determine the number of nursing students who were required to take the exam.

Since 1/2 of the nursing students were required to take the exam, we calculate: (1/2) * 200 = 100.

Step 2: Determine the number of students who took the exam.

Since all of the students who were required to take the exam actually took it, the number of students who took the exam is also 100.

Step 3: Determine the number of students who passed the exam.

Since 3/5 of those who took the exam passed, we calculate: (3/5) * 100 = 60.

University X required 1/2 of the 200 nursing students to take the exam, which means 200 * 1/2 = 100 students took the exam.

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A shape's perimeter is calculated by adding the lengths of all of its sides and edges. The V's direction is \((-5, -12)\)  .

The complete length of a shape's boundary is referred to as the perimeter in geometry. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

We need to know the lengths of all the sides of Fard ZH in order to calculate its perimeter. We can see from the diagram that  \(ZF = ZD + DF = 24 + 28 = 52\)  and \(FH = ZG = 30 and ZH = 36.\)

As a result, Fard ZH's perimeter is as follows:

perimeter = \(= ZF + FH + ZH + ZG\)

perimeter  \(= 52 + 30 + 36 + 30\)

perimeter  \(= 148\)

So the perimeter of Fard ZH is \(148\)  .

(3) The vector that connects points A and B must be identified in order to determine the direction of V, and it can be written as follows:

\(V = (xB - xA, yB - yA)\)

Where xA and yA represent point A's x and y coordinates, and xB and yB represent point B's x and y coordinates.

Plugging in the given values, we get:

\(V = (5 - 10, 2 - 14)\)

\(V = (-5, -12)\)

Therefore, The V's direction is \((-5, -12)\) .

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The rate of change of the volume of the sphere is 100,530.96 mm^3/s

How to calculate rate of change of the volume of the sphere?

Given,

radius = r = 80 / 2 = 40 mm

rate of change radius = \(\frac{dr}{dt}\) = 5 mm/s

Formula to calculate volume of the sphere is

\(V = \frac{4}{3}\pi r^{3}\)

Differentiating the volume formula and we get new formula to calculate rate of change of the volume.

\(\frac{dV}{dt} = \frac{4}{3}\pi 3r^{2}\frac{dr}{dt}\)

Simplify to

\(\frac{dV}{dt} = 4\pi r^{2}\frac{dr}{dt}\)

Now, we put the given value to formula and calculate it

\(\frac{dV}{dt} = 4\pi (40)^{2}(5)\)

\(\frac{dV}{dt} = 100,530.96\) mm^3/s

Thus, the rate of change of the volume of the sphere is 100,530.96 mm^3/s

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