ACT/SAT A passenger in a hot-air balloon spots a small fire on the ground. The angle of depression to the fire is 30°, and the height of the hot-air balloon is 150 feet. To the nearest foot, what is the horizontal distance from the hot-air balloon to the fire?

Answer:

Step-by-step explanation:

ear

Given a solution containing 30 mg of medication per 3 mL, you need to determine how many mL makeup 15 mg of medication. By setting up a proportion, it can be calculated that 1.5 mL should be administered per dose.

To solve this problem, we need to determine how many milliliters correspond to the required dose of medication (15 mg). Given that the pharmacy dispensed a solution containing 30 mg of medication per 3 mL, we can construct a proportion to find the needed milliliter amount.

30 mg/3 ml = 15 mg/x ml

To solve this equation for 'x', multiply both sides by 'x' and then divide by 30 mg to isolate 'x':

x = (15 mg * 3 ml) / 30 mg

Upon completing this calculation, you find that x equals 1.5 ml. Therefore, you would administer 1.5 mL of the medication per dose.

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To administer 15 mg of a liquid oral medication given a concentration of 30 mg/3 mL, you will need to administer 1.5 mL per dose.

To calculate the mL of the liquid oral medication to administer, we need to determine the amount of medication in each mL. In this case, the pharmacy has dispensed a concentration of 30 mg/3 mL, which means there is 10 mg of medication in each mL. Given that the doctor's order is for 15 mg, we can calculate the mL to administer by setting up a proportion:

10 mg/1 mL = 15 mg/x mL

Cross-multiplying, we get:

10x = 15

x = 1.5

Therefore, you will need to administer 1.5 mL per dose.

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Answer:

There are about 12 people with genetic mutation.

Step-by-step explanation:

If you write out the equation, it should look like this:

600*0.02 = 12

Therefore, the answer is that there are about 12 people with genetic mutation.

Answer:

≈41,4∘

Step-by-step explanation:

I added a photo of my solution

Answer:

45∘

Step-by-step explanation:

∠2 = 180∘ - 135∘ = 45∘

∠2 = ∠1 = 45∘

∠1 = ∠4 = 45∘

The derivative of the function is determined as 6πx^(π - 1) + 54.15x^(4.7).

To find the derivative of f(x), we need to apply the power rule and the constant multiple rule.

Using the power rule for f(x) = 6x^π+ 9.5x^5.7 + π^5.7, we have:

f'(x) = 6πx^(π - 1) + 9.5(5.7)x^(5.7 - 1)

Next, applying the constant multiple rule, we get:

f'(x) = 6πx^(π - 1) + 54.15x^(4.7)

So the derivative of f(x) is:

f'(x) = 6πx^(π - 1) + 54.15x^(4.7)

Thus, the derivative of the function is determined by applying the power rule as shown above.

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Answer:

25%

Step-by-step explanation:

None explains the use of 0.5 for the most conservative sample size. Thus E is the correct one.

A confidence interval is a range of values that is likely to contain the true population parameter, and a wider confidence interval allows for a greater chance of accurately capturing the true population parameter.

The use of 0.5 as an estimate of the sample proportion is most conservative because it produces the widest confidence interval.

A larger sample size is generally used when the confidence interval is wider, as it improves the precision of the estimate.

Using 0.5 as the estimated proportion will produce the widest confidence interval and thus, a larger sample size.

This is why 0.5 is used to calculate the most conservative sample size.

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The statements that are true with regards to the graph of the functions and the sprinter that wins and lead the race are;

The true statements are; A, B, and C

The graph of a function visually represents the rule of the function showing how the output values of the function changes as the input value varies.

The distance the two sprinter's will run = 80 meters

The speed of sprinter A = 9 meters per second

The speed of sprinter B = 9 meters per second

The head start of sprinter B = 14 meter

The analysis of the statements are as follows

A. The graph of the functions representing the speeds of the sprinters have the same slope of 9 which is the rate of change of distance with time, therefore, the graphs are parallel and will never intersect.

The statement is therefore; True

B. Sprinter B will win the race. - True

Sprinter B has a head start of 14 meters and both sprinters have the same speed, therefore, sprinter B will reach the finish line first and win the race.

C. Sprinter B is leading the race at the 4 seconds mark;- True

Sprinter A will cover a distance of 9 m/s × 4 s = 36 m at the 4 seconds mark, while sprinter B will cover a distance in the 80 m race of 9 m/s × 4 s + 14 m = 50 m at the 4 second mark, therefore, sprinter B will be leading at the 4 second mark

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Minimum and maximum recommended width of the space between 6-inch by 6-inch tiles = 13/6 inches.

An inch is a unit of length in the Imperial system of units, which is primarily used in the United States, Canada, and the United Kingdom. One inch is equal to 1/12 of a foot or 2.54 centimeters. It is commonly used to measure the length or width of objects, such as a piece of paper, a television screen, or a piece of fabric. In the Imperial system, larger units of length, such as feet, yards, and miles, are based on inches.

by the question.

To simplify the expressions for the minimum and maximum recommended widths of the space between 6-inch by 6-inch floor tiles, we can convert the mixed numbers to improper fractions and then find the least common multiple (LCM) of the denominators.

First, let's simplify the minimum recommended width of the space:

[tex]2-2 inch = 2 + 2/12 = 2 + 1/6 = (2*6 + 1)/6 = 13/6 inches[/tex]

Next, let's simplify the maximum recommended width of the space:

[tex]2-1 inch = 2 + 1/12 = 2 + 2/24 = (2*12 + 2)/24 = 26/12 = 13/6 inches[/tex]

We can see that the minimum and maximum recommended widths of the space between the 6-inch by 6-inch tiles are the same, which is 13/6 inches. Therefore, we can simplify the expressions for both.

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Using expressions, we can get the following:

a. If W (6.5) =75, H (6.5) = 85

b. If W (2) = 60, H (2) = 70

c. W (x) + 10

Expressions are statements in mathematics that include variables, numbers, or both, as well as at least two terms connected by an operator. Addition, subtraction, multiplication, and division are examples of mathematical operations.

The equation x + y, which combines the terms x and y with an addition operator, serves as an illustration. Expressions can be classified into two categories in mathematics: algebraic expressions, which also contain variables, and numerical expressions, which only contain numbers.

W(x) gives the temperature W in the apartment x hours after midnight.

H(x) gives the temperature H x hours after midnight when it is hot outside.

When it is hot outside, the owner changes the settings to be exactly 10 degrees warmer than W.

So,

H (x) = W(x) + 10

If W (6.5) =75, then

H (6.5) =W (6.5) + 10

= 75+10

= 85

If W (2) = 60, then

H (2) = W (2) + 10

= 60+ 10

= 70

The expression of H in terms of W:

W (x) +10

Hence the equation:

H(x) = w(x) + 10

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Thus, infants are deemed preterm if they arrive on or before 240 days (rounded to the next integer).

The study of chance and uncertainty is covered in the mathematical field of probability. It is a way to gauge how likely something is to happen. Probability can be expressed as a number between 0 and 1, with 0 indicating that an occurrence is impossible, and 1 indicating that an event is certain. Probability is frequently employed in real-world situations to forecast the results of random occurrences like tossing a coin, rolling a die, or drawing cards from a deck. The probability of an occurrence is estimated by dividing the number of possible outcomes by the number of possible ways the event could occur.

given

a. We need to locate the region to the right of 307 under the normal distribution curve in order to determine the likelihood that a pregnancy would last 307 days or longer.

By standardizing the value of 307, we may make use of the standard normal distribution:

(X - mu) / sigma = z

z = (307 - 268) / 15\sz = 2.6

A basic normal distribution table or calculator can be used to determine that a z-score larger than 2.6 has a probability of about 0.0047.

Thus, the likelihood of a pregnancy lasting at least 307 days is roughly 0.0047, or 0.47%.

b. We must determine the gestational period that sets the lowest 3% of pregnancies apart from the others. The value with a cumulative probability of 0.03 to its left is this one.

The z-score for a cumulative probability of 0.03 can be calculated using a conventional normal distribution table or calculator. It is roughly -1.88.

To determine the corresponding length of pregnancy, we can apply the z-score formula:

z = (x - mu)/sigma -1.88 = (x - 268)/15 -28.2 = x - 268 x = 239.8

Thus, infants are deemed preterm if they arrive on or before 240 days (rounded to the next integer).

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The size of the sample required to be representative depends on the variability of the population and the level of precision required in the analysis.

What is Inductive logic ?

Inductive logic, also known as induction, is a type of reasoning that involves drawing general conclusions based on specific observations or examples.

In inductive logic, a sample is considered representative of the population from which it is taken if it possesses the following two characteristics:

Randomness: The sample should be selected randomly from the population. This means that every individual in the population should have an equal chance of being selected for the sample. A random sample helps to reduce the potential for bias in the selection process.

Size: The sample size should be large enough to accurately represent the population. A larger sample size helps to reduce the impact of chance variation and provides a more accurate estimate of the characteristics of the population.

Therefore, The size of the sample required to be representative depends on the variability of the population and the level of precision required in the analysis.

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Answer: congruent

Step-by-step explanation:

they look like the same shape

Answer: 4

Step-by-step explanation:

If there are two students in the first row and two students sit behind each of those students in the second row, then there are a total of 2 x 2 = 4 students in the second row.

The value of x = 2.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign. When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

According to our question-

y= -5x

6x+y=2

6x-5x=2

x=2

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Answer:

Step-by-step explanation:

you need to show us what circle x looks like

Answer: Let x be the number of gallons of the first brand (30% pure antifreeze) that needs to be mixed, and let y be the number of gallons of the second brand (80% pure antifreeze) that needs to be mixed. We want to find the values of x and y that satisfy the following conditions:

The total amount of antifreeze mixed is 150 gallons: x + y = 150

The resulting mixture is 40% pure antifreeze: 0.3x + 0.8y = 0.4(150)

We have two equations with two unknowns, so we can solve for x and y. We'll use the first equation to solve for y in terms of x:

y = 150 - x

Substituting this expression into the second equation gives:

0.3x + 0.8(150 - x) = 60

Simplifying and solving for x:

0.3x + 120 - 0.8x = 60

-0.5x = -60

x = 120

Substituting this value back into y = 150 - x gives:

y = 150 - 120 = 30

Therefore, we need to mix 120 gallons of the first brand and 30 gallons of the second brand to obtain 150 gallons of a mixture that contains 40% pure antifreeze.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: We can solve this system of equations by substituting the expression for y in terms of x from the second equation into the first equation, and then solving for x.

First, we substitute y = 2 + x from the second equation into the first equation, giving:

2x - 3(2 + x) = -5

Simplifying this expression by distributing the -3, we get:

2x - 6 - 3x = -5

Combining like terms, we get:

-x - 6 = -5

Adding 6 to both sides, we get:

-x = 1

Multiplying both sides by -1, we get:

x = -1

Therefore, the value of x in the system of equations is -1.

Step-by-step explanation:

After answering the presented question, we can conclude that Yet, we equation cannot make final decisions based just on the median.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Whether data is sorted in ascending or descending order, the median is the midway value. In this situation, the median sales amount for Company A is $7,000, which suggests that half of the sales are greater than $7,000 and half are less. The median sales amount for Business B is $6,000, which means that half of the sales are greater than $6,000 and half are less.

The median can be a useful approach to summaries a data set's core tendency. For example, we can see that Company A has a greater median sales amount than Company B, implying that Company A generates more money each sale on average. Yet, we cannot make final decisions based just on the median.

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The price for product A is Ksh 55,000 and the price for product B is Ksh 32,000.

What is the selling price?

The price you will pay to purchase a share or any other commodity is known as the "buy" or "bid" price. The price you will receive when you sell that share or commodity is the "sell" or "ask" price.

Here, we have

Given: Tom and John are engaged in buying and selling certain products A and B. Tom buys 5 of product A but sells twice as much of product B. John on the other hand sells three times what Tom bought of product A and buys 13 of product B. At the end of the business day, John banks Ksh 110,000/- while Tom banks Ksh 230,000.

Let's assume that the cost price for both products A and B is "x", and the selling price for both products A and B is "y". We can use this information to set up two equations, one for Tom and one for John, that relate the costs and profits for the two products:

Tom: 5x - 2(5y) = P₁

John: 3(5x) - 13x = P₂

where  P₁ and P₂ are the profits made by Tom and John, respectively.

We know that at the end of the business day, John banks Ksh 110,000/- while Tom banks Ksh

230,000. So we can write:

P₁ = 230,000 - 5x

 P₂ = 110,000 - 18x

Substituting these values into the equations for Tom and John, we get:

5x - 2(5y) = 230.000 - 5x

Simplifying these equations, we get:

10x - 10y = 230,000

2x = 110,000

x = 55,000

Substituting this value back into the first equation, we can solve for y:

10(55,000) - 10y = 230,000

Simplifying this equation, we get:

y = 32,000

Hence, the price for product A is Ksh 55,000 and the price for product B is Ksh 32,000.

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Answer:

C. 180° (since x and y are supplementary angles).

The factorised form of the given expression as required to be determined in the task content is; p ( p + 1 ) - q (q - 1).

It follows from the task content that the factored form of the given expression is to be determined.

As evident from the task content; the given expression is; p² - q² + p - q.

On this note, by first collecting like terms; we have;

p² + p - q² - q

By factorisation; we have that;

p ( p + 1 ) - q (q - 1)

Ultimately, the factored form of the given expression is; p ( p + 1 ) - q (q - 1).

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To rank the libraries from 1 having the greatest total number of comic books to 5 having the least total number of comic books, we need to first calculate the total number of books in each library.

Let's start by using the information given to find the total number of books in each library:

For Library A, we know that 30 comic books are 2% of its total books. So, we can set up the following equation:

 30 = 0.02x

where x is the total number of books in Library A. Solving for x, we get:

 x = 1500

Therefore, Library A has a total of 1500 books.

For Library B, we know that 45 comic books are 5% of its total books. So, we can set up the following equation:

 45 = 0.05x

where x is the total number of books in Library B. Solving for x, we get:

 x = 900

Therefore, Library B has a total of 900 books.

For Library C, we know that 65 comic books are 2% of its total books. So, we can set up the following equation:

 65 = 0.02x

where x is the total number of books in Library C. Solving for x, we get:

 x = 3250

Therefore, Library C has a total of 3250 books.

For Library D, we know that 75 comic books are 10% of its total books. So, we can set up the following equation:

 75 = 0.1x

where x is the total number of books in Library D. Solving for x, we get:

 x = 750

Therefore, Library D has a total of 750 books.

For Library E, we know that 90 comic books are 3% of its total books. So, we can set up the following equation:

 90 = 0.03x

where x is the total number of books in Library E. Solving for x, we get:

 x = 3000

Therefore, Library E has a total of 3000 books.

Now that we have the total number of books in each library, we can rank them based on the number of comic books they have:

Library C: 65 comic books

Library E: 90 comic books

Library B: 45 comic books

Library A: 30 comic books

Library D: 75 comic books

Therefore, the libraries ranked from 1 having the greatest total number of comic books to 5 having the least total number of comic books are: C, E, B, A, D.

The solution of the given problem of percentage comes out to be  $19,000 in 12 years, they should deposit $170.89 at the conclusion of each quarter.

The abbreviation "a%" is used to indicate a value or number in statistics that is expressed as a percentage of 100. Versions with "pct," "pct," or "pc" as the initials are also rare. However, the most popular method to do this is to use the percentage symbol ("%"). Additionally, both hints nor a constant ratio of every element to the overall amount exist. Since numbers commonly add up to 100, they are essentially integers.

Here,

=>  [tex]FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n)[/tex].

By entering these numbers, we obtain:

[tex]= > 19000 = PMT * [(1 + 0.07/4)^(4*12) - 1] / (0.07/4)[/tex]

Upon solving for PMT, we obtain:

[tex]= > PMT = 19000 * (0.07/4) / [(1 + 0.07/4)^(4*12) - 1][/tex]

=> PMT = $174.58 (rounded to the nearest cent)

In order to have $19,000 in 12 years, the investor needs to deposit $174.58 at the conclusion of each quarter at a rate of 7% compounded quarterly.

(b) Using the same procedures as in (a), but with an interest rate of 7.2%, we arrive at:

[tex]= > 19000 = PMT * [(1 + 0.072/4)^(4*12) - 1] / (0.072/4)[/tex]

Upon solving for PMT, we obtain:

[tex]= > PMT = 19000 * (0.072/4) / [(1 + 0.072/4)^(4*12) - 1][/tex]

=>  PMT = $170.89 (rounded to the nearest cent)

In order to have $19,000 in 12 years, they should deposit $170.89 at the conclusion of each quarter.

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Yolanda will spend a total of 3 hours / 9 tables,

or **1/3 hour per table**, if she spends an equal amount of time at each table.

Yolana can serve a total of 36 people if she has to serve 9 tables, each of which can hold 4 guests, and she must serve a total of 4 guests per table.

How long does each visitor spend on average?

We need to know the entire length of time Yolana will spend serving all 36 guests in order to calculate the average time spent per guest.

If the entire time is divided by the number of guests,we get:

36 people in 3 hours equals 5 minutes each person.

Thus, each visitor spends 5 minutes on average.

What is the average time?

A measurement of a set of time values' central tendency is the average time. It is determined by multiplying the total number of values in the set by the sum of all the time values.

As an illustration, if you have a series of times of 5, 10, and 15, you would add them all up to reach 30 minutes, divide that number by 3, and get an average time of 10 minutes.

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The value of the product  7 × 3 1/4 is 22 3/4

It is important to note that fractions are defined as the part of a whole variable, element or number.

There are different types of fractions, such as;

From the information given, we have;

7 = A whole number

3 1/4 = a mixed fraction

Let's convert it to an improper fraction by multiplying the denominator by the whole number, then adding the numerator

13/4

Multiply the values

7 × 13/4

91/4

Divide the values

22 3/4

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