How many mL of 14% medication solution is needed to make a final solution that is a 8% medication

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

300

Step-by-step explanation:

Neptune is approximately 33 times farther from the sun that earth.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Distance of Earth from the Sun  = 9 × 10⁷

Distance of Neptune from the Sun = 3 × 10⁹

Now,

Since, Distance of Earth from the Sun  = 9 × 10⁷

Distance of Neptune from the Sun = 3 × 10⁹

Hence, The times of distance between the Earth and Sun from Neptune; = 9 /3 × 10⁷×10²

=  100/3  × 9× 10^7        

=  100/3   times of distance between Earth & Sun

Hence, Neptune is approximately 33 times farther from the sun that earth.

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The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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Answer:

26 points

Step-by-step explanation:

Find the mean number of points by adding up all of the points and dividing it by 5

(21 + 25 + 36 + 16 + 32) / 5

130 / 5

= 26

So, the mean number of points is 26 points

Jody's team scored 21, 25, 36, 16 and 32 points at the last five football games. What is the mean number of points Jody's team scored ?

To find the mean, first of all we have to add up all the given points and then divide by how many number of points there are. So, there are total 5 points. Hence, we have to divide all the given points by 5.

So, Mean = \( \bf \frac{21 \: + \: 25 \: + \: 36 \: + \: 16 \: + \: 32}{5} \)

Mean = \( \bf \frac{130}{5} \)

Mean = \( \bf 26 \)

The ways to elect the candidates from the total is 462

From the question, we have

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 11 and r = 6

Substitute the known values in the above equation

Total = ¹¹C₆

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 11!/5!6!

Evaluate

Total = 462

Hence, the number of ways is 462

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Answer:

the perimeter of the rectangle is 26 meters.

Step-by-step explanation:

To find the perimeter of the rectangle, we need to know its width. We can find the width by dividing the area by the length:

width = area / length = 36 / 9 = 4 meters

Now we can use the formula for the perimeter of a rectangle:

perimeter = 2(length + width)

Substituting the given values, we get:

perimeter = 2(9 + 4) = 2(13) = 26 meters

Therefore, the perimeter of the rectangle is 26 meters.

Answer:

286.97

Step-by-step explanation:

find the area of the rectangle first

14*15=210

Next

Find the area of a circle

πr^2=a

the radius of the circle is half the height of the rectangle

π*(7*7)=a

a=153.94

Now

Divide the area by two

153.94/2=76.97

Now add the two areas

76.97+210

Answer:

Area of the figure= area of the rectangle+ area of the semicircle

=(15×14)+(1/2)π(7)²=210+77=287 square unit

287 square unit is the right answer.

Remember:--- area of the rectangle

=(length×breadth)

and area of the semicircle=π(radius)²/2

Velocity is not constant over time and can be influenced by a variety of factors. Changes in velocity can have implications for the relationship between changes in the money supply and the price level, highlighting the complexity of monetary dynamics in an economy.

According to the quantity equation (MV = PQ), changes in the money supply (M) will lead directly to changes in the price level (P) if velocity (V) and real GDP (Q) remain constant. However, velocity is not necessarily constant over time and can be influenced by various factors.

Velocity represents the rate at which money circulates in the economy, indicating how quickly money is used to facilitate transactions. It is influenced by factors such as changes in consumer and business behavior, technological advancements, financial innovation, and shifts in confidence and trust in the economy.

Changes in velocity can occur due to several reasons. For example:

Changes in Transaction Patterns: Shifts in consumer preferences or business practices can alter the frequency and speed of transactions, affecting how money circulates and influencing velocity.

Financial Innovation: Advancements in payment systems, such as the rise of electronic transactions, online banking, or mobile payments, can potentially impact the velocity of money by facilitating faster and more efficient transactions.

Confidence and Economic Stability: Changes in economic conditions, inflation expectations, or financial stability can influence people's willingness to hold money, affecting velocity.

Monetary and Fiscal Policies: Changes in monetary policy, such as interest rate adjustments or changes in the money supply, can indirectly affect velocity by influencing borrowing and spending behavior.

While changes in velocity can occur independently of changes in the money supply, they can also be related. For instance, if the money supply increases without a corresponding increase in the demand for money (velocity decreases), it can put upward pressure on prices. On the other hand, if velocity increases due to changes in transaction patterns or increased economic activity, it can offset the impact of changes in the money supply on prices.

Overall, velocity is not constant over time and can be influenced by a variety of factors. Changes in velocity can have implications for the relationship between changes in the money supply and the price level, highlighting the complexity of monetary dynamics in an economy.

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Answer:

Step-by-step explanation:

first work what's in the brackets { 4 x 2 -10}^3

{4 x 2-1000}

4 x -998

The proportion of Arts majors who have not found a job is 8%, rounded off to two decimal places.

To find the proportion of Arts majors who have not found a job, we first need to calculate the total number of students who have not found a job.

The total number of students who have not found a job would be 1500 - 1380 = 120.

To calculate the proportion of students who have not found a job, we can divide the number of students who have not found a job by the total sample size:

The proportion of students who have not found a job = 120 / 1500 = 0.08 or 8%.

Therefore, the proportion of Arts majors who have not found a job is 8%, rounded off to two decimal places. This suggests that a majority of the graduating Arts majors from the University of Western Cape have found employment before their graduation.

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Step-by-step explanation:Answer:

D: The exponential function grows faster than the quadratic function over two intervals

Step-by-step explanation:

From the table

The value of y is same for both functions

For first graph y=4x^2

When x= 3, y = 36

when x= 4 , y = 64

for second graph y = 4^x

When x= 3, y = 64

when x= 4 , y = 256

we can see that second graph increases faster over intervals 2 to 3  and 3  to 4

Second graph is exponential function

So, The exponential function grows faster than the quadratic function over two intervals

The maximum home value that can be financed is approximately $35,365.85.

Let's represent the maximum home value that can be financed by H.

If the minimum down payment is 18%, the amount financed is 100% - 18% = 82%.

Therefore, we have:

H × 82% = $29,000

Multiplying both sides by (1/82%), we get:

H = $29,000 / 82%

= $35,365.85

Hence, the maximum home value that can be financed is approximately $35,365.85.

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Answer:

\(y = -\frac{20-x}{7}\)

Step-by-step explanation:

To solve x - 7y = 20 for y:

Subtract x from both sides:

x - x - 7y = 20 - x

-7y = 20 - x

Divide both sides by -7 to isolate y:

\(\frac{-7y}{-7} = \frac{20-x}{-7}\)

\(y = -\frac{20-x}{7}\)

Answer:

y=1/7x-20/7

Step-by-step explanation:

x-7y=20

7y=x-20

y=1/7x-20/7

Answer: 81.64 feet

Step-by-step explanation:

Circumference of a circle = pi * diameter

Circumference of a circle = 3.14 * 26 feet

Circumference of a circle = 81.64 feet

Answer:

A 500 mg bag of prepackage seeds costing $3.95

Step-by-step explanation:

First, you need to know the amoun of grams in 1/2 kg to find the cost of the sunflower seeds:

1 kg→1000 grams

1/2 kg→ x

x=(1000*(1/2))/1

x= 1000/2

x= 500 grams

Second, you have to find the cost of 500 grams of sunflower seeds:

100 grams → $0.70

500 grams→    x

x=(500 *0.70)/100

x= 3.5

According to this, 1/2 kg of of bulk sunflower seeds cost $3.5 which is cheaper than the 500 mg bag of prepackage seeds that cost $3.95 and this means that the better value is 1/2 kg of bulk sunflower seeds as the amount is also higher as 500 mg is equal to 0.5 grams.

The ordered numbers in this problem are given as follows:

-|-12|, -7, -|5|, -|-4|, |-12|, |-21|

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 2.

Then the numbers for this problem have their actual value given as follows:

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Answer:

2

Step-by-step explanation:

on Edge

Answer: 2

Step-by-step explanation:

have a great day!

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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The probability of a prime number or a number greater than 3 coming up is given as follows:

5/6.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

When a dice is thrown, there are six possible outcomes, ranging from 1 to 6, and the desired outcomes are given as follows:

Hence the probability is given as follows:

5/6.

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Complete question is;

Peter drew two rays, AC and AP with A as a common endpoint. Which of the following statements

might describe Peter's drawing?

I. AC and AP are parallel.

II. PAC is an angle

III. AC and AP are perpendicular

A. I and II

B. II and III

C. I and 111

D. I, II, and III

Answer:

Option B: II & III

Step-by-step explanation:

We are told that Peter drew two rays which are AC and AP.

We are told that A is a common endpoint.

If A is a common endpoint, it means the 2 rays interaction point at A is at an angle.

The angle could also be 90° which means it's possible that the rays AC and AP are perpendicular.

Thus, the correct statements that describe his drawing are: II & III

Answer:

Step-by-step explanation:

In the given 30-60-90 triangle the value of x is calculated after rationalizing and simplifying to be equal to 2√3.

The hypotenuse of a right triangle is the longest side that is opposite the right angle. It is the side that is opposite to the right angle and is also the side that is opposite to the 90-degree angle in the triangle.

In a right triangle, the hypotenuse is always opposite to the right angle and is also the side that connects the two legs of the triangle. The hypotenuse is also the side that has the largest length among the three sides of a right triangle.

In a 30-60-90 triangle, the ratio of the sides opposite to the angles 30 degrees, 60 degrees, and 90 degrees are x: x√3 : 2x.

Therefore, in this triangle, the length of the hypotenuse (opposite to the 90-degree angle) is 2x.

The length of the perpendicular (opposite to the 60 degree angle) is 6.

So, we have:

tan (60 degrees) = perpendicular / base

√3 = 6 / x

Multiplying both sides by x, we get:

x√3 = 6

Dividing both sides by √3, we get:

x = 6 / √3

Rationalizing the denominator by multiplying both of the numerator and denominator by √3, we receive:

x = 6√3 / 3

Simplifying further, we get:

x = 2√3

Therefore, the value of x is 2√3.

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Let's simplify each expression

The circled portion in the confidence interval formula p ± z represents the Margin of Error, which plays a crucial role in interpreting the range of plausible values for the population parameter.

In the confidence interval formula p ± z, the circled portion represents the Margin of Error.

The Margin of Error is a critical component of a confidence interval and quantifies the level of uncertainty in the estimate.

It indicates the range within which the true population parameter is likely to fall based on the sample data.

The Margin of Error is calculated by multiplying the critical value (z) by the standard deviation of the sampling distribution.

The critical value is determined based on the desired level of confidence, often denoted as (1 - α), where α is the significance level or the probability of making a Type I error.

The Margin of Error accounts for the variability in the sample and provides a measure of the precision of the estimate.

It reflects the trade-off between the desired level of confidence and the width of the interval.

A larger Margin of Error indicates a wider confidence interval, implying less precision and more uncertainty in the estimate.

Conversely, a smaller Margin of Error leads to a narrower confidence interval, indicating higher precision and greater certainty in the estimate.

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Answer:

a

  \(S.E = 0.05\)

b

 \(P(P > 0.75) = 0.0013499\)

Step-by-step explanation:

From the question we are told that

      The population  \(p = 0.60\)

       The  sample size is  \(n = 96\)

       The  sample proportion is  \(\r p = 0.75\)

Generally the standard error is mathematically represented as

      \(S.E = \sqrt{ \frac{p(1-p)}{n } }\)

substituting values    

       \(S.E = \sqrt{ \frac{0.60 (1-0.60 )}{96 } }\)

       \(S.E = 0.05\)

The  probability that  more  than  75% of consumers will indicate they like the drink is mathematically represented as

       \(P(P > 0.75) = P(\frac{\r P - p }{\sqrt{\frac{p(1-p)}{n} } } > \frac{\r p - p }{\sqrt{\frac{p(1-p)}{n} } } )\)

 The  z-score is  evaluated as

              \(z = \frac{\r p - p }{\sqrt{\frac{p(1-p)}{n} } }\)

So  

         \(P(P > 0.75) = P(Z > \frac{0.75 - 0.60 }{0.05} )\)

         \(P(P > 0.75) = P(Z > 3)\)

         \(P(P > 0.75) = 0.0013499\)

This value above is obtained from the z-table  

The required  sum of the first n odd numbers is equal to n².

The first few odd numbers are 1, 3, 5, 7, 9, 11, and so on. When we add up the first few of these numbers, we get the following sums:

1 = 1

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

1 + 3 + 5 + 7 + 9 = 25

We can see that the nth odd number is equal to 2n - 1. And the sum of the first n odd numbers is equal to n². This can be verified geometrically by considering a square with sides of length n.

The sum of the first n odd numbers can be thought of as the sum of the diagonal elements of the square, which forms a square of length n.

Thus, the sum of the first n odd numbers is equal to n².

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Answer:

x = 5.7 years after 2000

Step-by-step explanation:

So the year when both the amount of users were the same can be found by using the both equations to solve for x  (since y is the same)

48x + y = 729

we will take the value of y from this equation and use it in the other equation

y = 729 - 48x

135x - 2y = -140

135x - 2(729 - 48x) = -140

135x -1458 + 98x = -140

231x = 1318

x = 1318/231

x = 5.7 years after 2000

The probability of selecting a name that begins with a vowel is 1/3.

The probability of selecting a name that begins with a vowel is the number of names that begin with a vowel divided by the total number of names.

In this case, there is one names that begin with a vowel:

Analise

And the total numner of names is 3

So the probability of selecting a name that begins with a vowel is 2/3.

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Complete question

A hat contains three slips of paper. One of the following names is written on each slip of paper: Analise, Benjamin, and Cora.

Determine the probability of selecting a name that begins with a vowel

The properties of angle bisector of triangle are as follows:

Angle Bisector:-

The angle bisector of an angle in a triangle is a straight line that divides the angle into two equal or congruent angles. Every triangle has three angle bisector. The point in a triangle where these three angle bisectors intersect is known as its incenter.

Angle Bisector's Properties:-

Thus, these are the properties of angle bisector of a triangle.

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