The length of a rectangular frame is represented by the expression 3x + 8, and the width of the rectangular frame is represented by the expression 3x + 6. Write an equation to solve for the width of a rectangular frame that has a total area of 168 square inches.
9x2 + 42x − 120 = 0
9x2 + 42x + 48 = 0
3x2 + 42x − 120 = 0
x2 + 14x + 48 = 0

On a fair 8-sided die, the probability of rolling a 3 is 1/8, or 0.125, which is equivalent to 12.5% in percentage terms.

The possibility or likelihood that an event will occur is measured by probability.

A number between 0 and 1, where 0 indicates that the occurrence is hypothetical and 1, meaning it is inevitable, is used to express it.

To put it another way, probability is the ratio of likely outcomes to real outcomes that pertain to a particular occurrence.

Every result (rolling any number from 1 to 8) is equally likely since the die is fair.

There are only two ways to roll a 3, and there are a total of eight outcomes.

As a result, the probability of rolling a 3 is:

P(rolling a 3) = 1/8

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A scaled version of any object is the object that has undergone a form of increment/enlargement or reduction has been made to the object. in the case of 3:5 scaled version, it tells you the ratio of increment or reduction that has happened to the object in comparison to the original object.

In the height of an object has a 30cm height and perhaps a 12 cm width. Using a scaled version ratio provided which is 3:5. The scaled version f the object would be

3/5 x 30 = 18cm

3/5 x 12 = 7.2cm

A second example is if a rectangular room with dimensions 10 feet by 15 feet and you want to scaled version of  3:5, it becomes  = 10 x (3/5) = 6 feet and 15 x (3/5) = 9 feet

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Answer:

The motorist's rate is:

rate = distance / time

where distance is measured in kilometers and time is measured in hours.

We are given that the motorist travels 228 kilometers in 6 hours, so we can use this information to find the rate:

rate = distance / time = 228 km / 6 hours = 38 km/hour

To find how long it will take the motorist to travel an additional 247 kilometers at this rate, we can use the same formula and solve for time:

time = distance / rate = 247 km / 38 km/hour ≈ 6.5 hours

Therefore, it will take the motorist approximately 6.5 hours to travel an additional 247 kilometers at the same rate of 38 km/hour.

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

A compound in chemistry is a material comprised of two or more separate chemical elements mixed together in a certain proportion. Chemical connections that are challenging to break are created when the elements interact with one another.

Compound A:Compound B ratio in the medication is 3:5. In other words, there are 3 millilitres of compound A and 5 millilitres of compound B for every 3+5=8 millilitres of the medicine.

We may set up a percentage using the ratio of compound A to the total volume of the medicine to determine how much compound A is required to make 728 millilitres of the drug:

3 ml x 3 ml x 3 ml

-------- = ----------

728 ml total, 8 ml overall

If we cross-multiply, we obtain:

8(x) = 3(728)

To find x, we use the formula x = 3(728)/8 = 273

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

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273 milliliters of compound A are needed to make 728 milliliters of the drug.

What are proportions?

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:

a/b = c/d

To determine the amount of compound A needed to make 728 milliliters of the drug, we need to use the given ratio of 3 milliliters of compound A to 5 milliliters of compound B.

Let's start by finding the ratio of compound A to the total amount of ingredients (A+B) in the drug:

3 : (3+5) or 3:8

This means that for every 8 milliliters of the drug, 3 milliliters of compound A are used.

To find out how many milliliters of compound A are needed for 728 milliliters of the drug, we can set up a proportion:

3/8 = x/728

where x represents the amount of compound A needed.

To solve for x, we can cross-multiply:

8x = 3*728

8x = 2184

x = 273

Therefore, 273 milliliters of compound A are needed to make 728 milliliters of the drug.

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It is proved that [tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex]

How to prove [tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex]?

To prove that [tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex] , we need to express the convolution sum of

[tex]x[n-n_1] \: and \: h[n-n_2][/tex], and then simplify it to obtain [tex]y[n-n_1-n_2][/tex]

Let's start by expressing the convolution sum of [tex]x[n-n_1] \: and \: h[n-n_2][/tex]

:[tex]x[n-n_1] ×h[n-n_2] = ∑ x[k-n_1] × h[n-n_2-k][/tex] where the summation is over all possible values of k.

Now, we can replace k with [tex]n - n_1 - m[/tex], which gives:

[tex]x[n-n_1] × h[n-n_2] = ∑ x[n-n_1-m] × h[n-n_2-n+n_1+m][/tex]

Next, we can rearrange the terms inside the summation to obtain:

[tex]x[n-n_1] × h[n-n_2] = ∑ x[n-m] × h[n-n_1-n_2+m][/tex]

Notice that the expression inside the summation is identical to the definition of y[n], so we can replace it with y[n] and simplify:

[tex]x[n-n_1] × h[n-n_2] = ∑ x[n-m] × h[n-n_1-n_2+m] = ∑ y[n-m] [/tex]

The last expression is the convolution sum of x[n] and h[n], which we know equals y[n]. Therefore:

[tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex]

And we have proven that [tex]x[n-n_1] × h[n-n_2] = y[n-n_1-n_2][/tex]

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Accordingly, utilising name-brand microwave popcorn rather than store-brand microwave popcorn is anticipated to yield a higher percentage of popped kernels based on the results of this study.

A test statistic is a numerical summary of a sample used in statistics to evaluate the strength of the evidence presented by the data in support of a certain conjecture about the population from which the sample was taken. A test statistic determines how many standard errors the observed data deviates from the predicted value by comparing it to what would be expected under the null hypothesis. To ascertain if an observed effect or difference between groups is the result of chance or if it is statistically significant, test statistics are employed in hypothesis testing.

Here,

We can compare the mean percentage of popped kernels between the two groups using a hypothesis test to see if using name-brand microwave popcorn yields a higher proportion of popped kernels than store-brand microwave popcorn.

Let μ1 be the mean percentage of popped kernels for name-brand microwave popcorn and μ2 be the mean percentage of popped kernels for store-brand microwave popcorn.

The null hypothesis states that there is no distinction between store-brand and name-brand microwave popcorn in terms of the mean percentage of popped kernels:

H0: μ1 - μ2 = 0

The alternate theory is that name-brand microwave popcorn has a mean percentage of popped kernels that is higher than that of store-brand microwave popcorn:

Ha: μ1 - μ2 > 0

This hypothesis can be examined using a two-sample t-test with unequal variances. For a one-tailed test with 18 degrees of freedom and a significance threshold of 0.05, the crucial t-value is 1.734.

Based on the information provided, we can determine that the sample mean percentage of popped kernels for name-brand microwave popcorn is 90.9% with a sample standard deviation of 5.09% and the sample mean percentage of popped kernels for store-brand microwave popcorn is 85.9% with a sample standard deviation of 4.67%.

We can calculate the test statistic as follows:

t = (x1 - x2 - 0) / √(s1²/n1 + s2²/n2)

t = (90.9 - 85.9) / √((5.09²/10) + (4.67²/10))

t = 2.26

We can reject the null hypothesis and come to the conclusion that there is enough evidence to support the claim that using name-brand microwave popcorn results in a greater percentage of popped kernels than store-brand microwave popcorn at the 0.05 level of significance because the calculated t-value (2.26) is greater than the critical t-value (1.734).

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The valid conclusions about the data being surveyed is Option A: Of the students who attended the basketball game, fewer than half of them also attended the school play.

What is a survey?

Questioning a group of people in a survey is one way to collect information from them. Surveys can be carried out using a variety of methods, including paper and pencil, online forms, the telephone, or in-person interviews.

A. Of the students who attended the basketball game, fewer than half of them also attended the school play. (True)

To calculate this, we need to divide the number of students who attended both the basketball game and the school play (55) by the total number of students who attended the basketball game (118).

55/118 = 0.466 = 46.6%, which is less than half.

B. More than half of the students who were surveyed attended the school play and did not attend the basketball game. (False)

To calculate this, we need to add up the number of students who attended the school play and did not attend the basketball game (63) and divide by the total number of students surveyed (221).

63/221 = 0.285 = 28.5%, which is less than half.

C. Students who attended the school play were more likely not to attend the basketball game. (False)

To calculate this, we need to compare the number of students who attended the school play and did not attend the basketball game (63) to the number of students who did not attend the school play and did not attend the basketball game (15).

63/78 = 0.808 = 80.8% and 15/78 = 0.192 = 19.2%. Since 80.8% is greater than 19.2%, we can conclude that students who attended the school play were more likely to attend the basketball game.

Therefore, valid conclusions is A.

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a). The formula for g, which determines x's half, is g(x) = 1/2 x

b). f(x) = x + 2

c). (fog)(x) = 1/2 x + 2

d). (fog) (52) = 28

The relationship between two sets of data, known as the input and output, is described mathematically by a concept known as a function.

An operation is applied to an input value by a function, which then produces an output value that matches the input value.

a). The formula for g, which determines x's half, is g(x) = 1/2 x

b). The formula for adding 2 to x is: f(x) = x + 2

c). Plugging g(x) into f(x) yields the function (fog)(x), which is as follows:

(fog)(x) = f(g(x))

f(1/2 x) = 1/2 x + 2

d). We must evaluate (fog)(52) to obtain the sale price of a shirt with an original cost of $52 as follows:

= (fog) (52) = 1/2(52) + 2

= 26 + 2

= 28

Thus, the shirt's ultimate retail price is $28.

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The total distance covered by Jeremy is 1320 m

What is a line segment ?

A line segment in geometry is bounded by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points. A line segment has two fixed or distinct endpoints while a line has no endpoints and can stretch in both directions indefinitely.

For sapling 1 = No distance is covered.

For sapling 2, distance covered = 10 m

Return distance=10 m

For sapling 3, distance covered =20 m

Return distance=20 m and so on

Thus the distances covered for saplings can be represented as : 0,2(10), 2(20),...i.e. 0,20, 40,...

Therefore total distance covered by Jeremy for planting 12 saplings and coming back to original position = S 12

Total distance covered = 122 [2(0) + (12 − 1) 20 ]

Total distance covered = 6 (11)(20) = 1320 m

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Complete question:

There are 12 saplings to be planted in a straight line at an interval of 10 m between

two consecutive saplings. Jeremy can carry only one sapling at a time and he has to

come back to the original point to take the next sapling. He plants 12 saplings in this

manner, planting the first sapling at the original point. After planting all the saplings,

he comes back at the original point,

In the process, what is the total distance that Jeremy covers?

​

Answer: -14

Step-by-step explanation:

Break up the question.

(-11 + 3) + (-6)

   V           V

  (-9)       (-14)

-11 + 3 = -9

-9 + (-6) = -14

Answer:

The answer is -14

Step-by-step explanation:

-11+3+(-6)

= -11+3-6

= -14

Answer:

The profit equation is

Profit = Revenue - Cost

Let's assume the revenue per batch is $50,000 and the cost per batch is $35,000. Then the profit equation becomes:

Profit = ($50,000 x number of batches) - ($35,000 x number of batches)

Profit = $15,000 x number of batches

We want to find the number of batches that will give a profit of -$190,000, so we can set up the equation:

-$190,000 = $15,000 x number of batches

Solving for the number of batches, we get:

number of batches = -$190,000 / $15,000

number of batches = -12.67

This indicates that the firm would have to produce and sell around 13 batches of tyres in order to make a -$190,000 profit. However, because you can't produce and sell a fraction of a batch, the corporation would have to sell at least 14 batches to make the needed profit.

Answer: y = 2x - 2

Step-by-step explanation:

you can see two points on the graph:

(0, -2) and (3, 3)

Using these to calculate the slope gives us:

(3+2)/(3-0) = 6/3 = 2

the y intercept is -2 as we can see

so the equation in slope intercept form is:

Answer:

380.1327 square units

Step-by-step explanation:

A=pi*r^2

A=pi*121

A=380.1327

Answer:

80000

Step-by-step explanation:

4% increase of 50000 is 2000 at the end of each year

so 2000*16=32000

50000+32000=82000

nearest whole dollar is 80000

The scale factor used is Option B: One fourth.

What is scale factor?

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

To find the scale factor, we can compare any corresponding side lengths between the original triangle and the dilated triangle.

Let's choose the longest side of triangle D, which is 5.2, and compare it to the longest side of triangle D′, which is x.

We know that a dilation multiplies all corresponding side lengths by the same factor, so -

scale factor = length of corresponding side in D′ / length of corresponding side in D

scale factor = x / 5.2

We don't have enough information to find x directly, but we can use the fact that the other two corresponding side lengths are 1.2 and 1.3.

Since the side lengths of triangle D were scaled by the same factor, we can set up the following equation -

1.2 / 3.6 = 1.3 / 4.8 = x / 5.2

Simplifying the equation -

0.3333... = 0.2708... = x / 5.2

x = 5.2 × 0.2708...

x ≈ 1.41

Now we can find the scale factor -

scale factor = x / 5.2 ≈ 1.41 / 5.2 ≈ 0.271

Therefore, the scale factor used was approximately 0.271.

Answer: One fourth.

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Answer:

1/4

Step-by-step explanation:

The before that answered first was correct! I also took the quiz so you guys dont have to!

Answer:

Step-by-step explanation:

if this is decimals, I can totally do this. 10.4 x 15.7 = 163.28

look at the file attached

if one of the end points of the diameter is at the origin and the radius is 3 then the the equation of the circle in general form is:x² + y² - 3x = 0

An equation is a statement that shows the relationship between two or more variables using mathematical symbols. It expresses the equality or inequality between the values of the variables on either side of the equation.

According to the given information :

Since one of the endpoints of the diameter is at the origin, we know that the center of the circle is also at the origin. Let (x, y) be any point on the circle. Then, using the distance formula, we have:

√(x² + y²) = 3

Squaring both sides, we get:

x² + y² = 9

So, the equation of the circle in standard form is:

x² + y² - 9 = 0

Another way to write the equation of the circle is in general form, which is:

x² + y² + Dx + Ey + F = 0

where D, E, and F are constants. To find the values of D, E, and F, we substitute the coordinates of one of the points on the circle into the general form equation:

(0)² + (0)² + D(0) + E(0) + F = 0

F = 0

So, the equation of the circle in general form is:

x² + y² + Dx + Ey = 0

To find the values of D and E, we substitute the coordinates of another point on the circle into this equation. Let's use the point (3, 0) since we know it lies on the circle. Substituting these values, we get:

(3)²+ (0)² + D(3) + E(0) = 0

9 + 3D = 0

D = -3

Therefore, the equation of the circle in general form is:

x² + y² - 3x = 0

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The correct inequality that represents the graphed region in factored form is: option a.) [tex]y \leq -0.25 (x + 12)(x - 8)[/tex]

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The area of the wooden platform built by Mr. Burns for the drama club at the school is 288 square feet.

What are the dimensions of a rectangle?

A rectangle has two dimensions: a length and a width that are both perpendicular to it. An oval's or a triangle's interior likewise has two dimensions.

The area of a rectangle is determined by dividing its length by its width. Accordingly, the platform's area can be determined as follows:

Area = Length x Width

Area = 24 feet x 12 feet

Area = 288 square feet

Therefore, the area of the wooden platform built by Mr. Burns for the drama club at the school is 288 square feet.

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The trigonometric function on the graph is:

f(x)= -cos(x)

So the correct option is B.

Here we can see the graph of a trigonometric function. We can see that the x-intercept is -1.

Notice that:

sin(0)= 0

cos(0) = 1

So the function can be an inversion over the x-axis of the cosine function, we coulod write this as:

f(x) = -cos(x)

That is the graphed function.

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Answer:

it can be rewritten as a percent

Step-by-step explanation:

If a person does 1.5 hours of bicycling per day for 5 days a week, they would burn approximately 3,750 calories in a week.

A person's age, gender, height, weight, and level of activity determine the average number of calories they need to consume each day to meet their energy needs and maintain their weight.

Individual factors such as age, gender, weight, height, and level of activity influence the average calorie intake.

If an average person burns 250 calories per half-hour while bicycling, then they would burn 500 calories per hour of bicycling.

So, if a person does 1.5 hours of bicycling per day, they would burn 1.5 x 500 = 750 calories per day.

If they work out 5 days a week, then the total number of calories burn in a week would be:

750 calories/day x 5 days/week = 3,750 calories/week

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We have expressed the expression 3 sec(-x) + 2 as a single fraction (3 + 2cos(x))/cos(x).

In mathematics, an expression is a combination of symbols and/or numbers that represents a mathematical quantity or relationship. Expressions can be formed by combining variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.

To write the expression 3 sec(-x) + 2 as a single fraction, we need to use some trigonometric identities and algebraic manipulation. Here are the steps:

Step 1: Recall that secant is the reciprocal of cosine, so we can rewrite the expression as:

3 (1/cos(-x)) + 2

Step 2: Cosine is an even function, which means that cos(-x) = cos(x). Therefore, we can simplify the expression to:

3 (1/cos(x)) + 2

Step 3: Recall that multiplying by the reciprocal is the same as dividing, so we can rewrite the expression as:

3/cos(x) + 2

Step 4: To add these fractions, we need a common denominator. The denominator of the first fraction is cos(x), and the denominator of the second fraction is 1. To get a common denominator, we can multiply the second fraction by cos(x)/cos(x):

3/cos(x) + 2(cos(x)/cos(x))

Simplifying the second term:

3/cos(x) + 2cos(x)/cos(x)

Step 5: Combining the fractions, we have:

(3 + 2cos(x))/cos(x)

Therefore, we have expressed the expression 3 sec(-x) + 2 as a single fraction (3 + 2cos(x))/cos(x).

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Answer:

I do not have access to Annexure A and Annexure B, so I cannot collect the data, draw the frequency table or pie chart, or answer the last question. However, I can provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.

To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:

25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22

The sum of the values is:

25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813

Dividing by the number of values (30), we get:

Mean = 813/30 = 27.1

To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.

To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:

20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34

There are 30 values, so the median is the 15th value, which is 28.

To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:

Range = 34 - 20 = 14

To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:

20-24, 25-29, 30-34

The frequency table would look like this:

Interval | Frequency

20-24 | 4

25-29 | 18

30-34 | 8

To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:

Proportion = Frequency/Total frequency = 18/30 = 0.6

Angle = Proportion * 360° = 0.6 * 360° = 216°

We can repeat this calculation for each interval to obtain the angles for the pie chart.

In terms of the last question, it is not clear what is meant by "which data collection best describe the maximum and why?". If you could provide more context or clarification, I would be happy to try to help.

The equivalent fractions when paired up would be:

We must first simplify each fraction before categorizing them according to their simplified form in order to couple equivalent fractions. Since 2/4 and 4/8 may both be reduced to 1/2, they are equal.

The same is true of 2/3 which may be reduced to 4/6, they are both equivalent. 3/4 is the same as 6/8, they are equivalent.

Since 1/3 may be simplified to 2/6, they are equivalent.

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According to the information, the classification of the fractions would be: 3/4 = 6/8, 1/3 = 2/6, 4/6 = 2/3

To classify the fractions in the correct option box we can carry out two procedures. The first one is to simplify the fractions to identify which ones are equivalent to those in the boxes. On the other hand, we can do the divisions of the fractions and those that have the same results go in the same box. According to the above, the fractions are classified as follows:

Note: This question is incomplete. Here is the complete information:

Attached image

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Answer:

[tex]\huge\boxed{\sf 38}[/tex]

Step-by-step explanation:

= a³ + b (6 + c)

Put a = 2, b = 3 and c = 4

= (2)³ + 3 (6 + 4)

= 8 + 3(10)

= 8 + 30

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

the requied answer is 38.

according to the question the value of a=2,b=3,c=4.

here,

to find the value of   a³ + b (6 + c)we have to do it in steps:

step 1: solve the bracket (6+4) =10.

step 2:  solve the value of a³ =8.

now put these values ,

=8+3(10)

=38.

Answer:

  43.8 feet

Step-by-step explanation:

In a triangle with angle K = 110°, J = 36°, and k = 70 feet, you want the measure of side j using the law of sines.

The law of sines tells you side lengths in a triangle are proportional to the sine of the opposite angle. This means ...

  j/sin(J) = k/sin(K)

  j = k·sin(J)/sin(K) = (70 ft)·sin(36°)/sin(110°)

  j ≈ 43.8 ft

The length of side j is about 43.8 feet.

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According to the question of drop factor, the answer is 53.3ml that will be infused per hour.

Drop factor is a mathematical concept related to the concept of rate. It is a unitless coefficient used to adjust a given rate. Drop factor is commonly used to represent the rate of change in a linear equation, and can be used to calculate the rate at which a given value decreases over time. The drop factor is calculated by subtracting the previous value from the current value and dividing it by the change in time. This value can then be used to calculate the rate of change over time.

The calculation for the amount of ml that will be infused per hour is as follows:

Volume (L) x Drop Factor (gtt/ml) = Total Drops

0.8 L x 60 gtt/ml = 480 drops

Total Drops / Time (hours) = Drops/Hour

480 drops / 9 hours = 53.3 drops/hour

Since 1 drop is equal to 1 ml, this means 53.3 ml of fluid will be infused per hour.

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Answer:

The answer is 13hours

Step-by-step explanation:

360miles------>5hours

936miles------->x hours

crossmultiply

x×360=936×5

360x=4680

divide both sides by 360

360x/360=4680/360

x=13hours