The drip rate for the gravity infusion of 1000 mg of vancomycin diluted in 250 ml D5W over 2 hours with a Macro tubing of 15 gtt/ml is approximately 26 gtt/min.
What is drip rate?Drip rate, also known as infusion rate or flow rate, is the speed at which a solution is infused or delivered to a patient over a certain period of time. Drip rate is typically measured in drops per minute (gtt/min) for gravity infusions or milliliters per hour (ml/hr) for infusion pumps.
In a gravity infusion, the drip rate is calculated by dividing the volume of the solution to be infused by the time of the infusion, and then multiplying by the drop factor of the IV administration set. The resulting number is the number of drops that need to be delivered per minute to the patient.
To calculate the drip rate for a gravity infusion, we can use the formula:
Drip rate = (Volume to be infused × Drop factor) ÷ Time of infusion
where:
Volume to be infused = 250 ml (given)
Drop factor = 15 gtt/ml (given)
Time of infusion = 2 hours = 120 minutes (since the infusion is to be given over 2 hours)
To use this formula, we need to first convert the volume of vancomycin from milligrams (mg) to milliliters (ml), since the volume to be infused is given in ml. The concentration of the vancomycin solution is 1000 mg/250 ml = 4 mg/ml. Therefore, the volume of vancomycin to be infused is:
Volume of vancomycin = 1000 mg ÷ 4 mg/ml = 250 ml
Now we can replace in the values into the formula:
Drip rate = (250 ml × 15 gtt/ml) ÷ 120 minutes
Drip rate = 3125 gtt ÷ 120 minutes
Drip rate ≈ 26 gtt/min
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can someone please do this
draw the triangle and label all the things provided
show work
The length of m is 15.6 cm.
What are angles?A point where two lines meet produces an angle.
The breadth of the "opening" between these two rays is referred to as a "angle". It is depicted by the figure.
Radians, a unit of circularity or rotation, and degrees are two common units used to describe angles.
By connecting two rays at their ends, one can make an angle in geometry. The sides or limbs of the angle are what are meant by these rays.
The limbs and the vertex are the two main parts of an angle.
The common terminal of the two beams is the shared vertex.
113/7.5
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Hi i need help with this
We can conclude that the figure is a square as all 4 sides are equal with all angles being 90°.
What is a square?A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles.
It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.
A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral.
The square's angles are at a straight angle or 90 degrees. Additionally, the diagonals of the square are equal and intersect each other at 90 degrees.
Therefore, we can conclude that the figure is a square as all 4 sides are equal with all angles being 90°.
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What is the constant of this
polynomial?
2x8+ 3x6 19x3+4x-13
Answer:
-13
Step-by-step explanation:
The term in the polynomial which doesn't have any variables is called constant.
So, (-13) is the constant.
What is the equation for the table below
Answer:
i believe itś y=2x+8
i apologize if it is wrong
Given the following weekly demand figures, what is the MAD at the end of week 5?
Week / Demand / Forecast
1 / 100 / 120
2 / 120 / 130
3 / 110 / 120
4 / 130 / 125
5 / 160 / 145
A. 12.0
B. 11.8
C. 13.0
D. 10.8
The answer is A. 12.0. The mean absolute deviation MAD at the end of week 5 is 12.0, indicating that the average absolute difference between actual demand and forecast demand is 12 units.
To calculate the Mean Absolute Deviation (MAD), we need to find the absolute difference between the actual demand and forecast demand, then take the average of those differences. The formula for MAD is:
[tex]MAD = (1/n) * Σ|A - F|[/tex]
where A is the actual demand, F is the forecast demand, and n is the number of observations.
Using the provided data, we can calculate the MAD for each week:
Week 1: |100 - 120| = 20
Week 2: |120 - 130| = 10
Week 3: |110 - 120| = 10
Week 4: |130 - 125| = 5
Week 5: |160 - 145| = 15
To calculate the MAD at the end of week 5, we need to add up the absolute differences and divide by the total number of observations:
MAD = (20 + 10 + 10 + 5 + 15) / 5 = 12
Therefore, the answer is A. 12.0. The MAD at the end of week 5 is 12.0, indicating that the average absolute difference between actual demand and forecast demand is 12 units. This question is related to the topic of forecasting and measures of forecast accuracy. Specifically, it involves calculating the mean absolute deviation (MAD) as a measure of forecast error.
The MAD provides a measure of forecast accuracy and can be used to evaluate the performance of forecasting methods and to make adjustments to improve the accuracy of future forecasts.
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The line plot represents the wait time in line for a ride at a local fair.
A line plot titled Wait Time at the Fair. The horizontal line labeled Time in Minutes begins at 8, with every one unit labeled up to 20. There is one dot above 10, 11, 14, 16, and 17. There are two dots above 13. There are four dots above 12 and 15.
Which of the following best describes the shape of the data, and why?
The data is skewed and means that the wait times were less than 13 minutes for all the rides.
The data is bimodal, and it might mean that the wait times for the most popular rides were 12 and 15 minutes long.
The data is symmetric and means that the wait times were around 13 minutes for all the rides.
The data is skewed and means that the wait times were over 13 minutes for all the rides.
With wait times of 12 and 15 minutes for the most popular ride, bimodal distribution is the best way to describe the form of the data for
The line plot shows the wait time in line for a ride at a local fair, with the number of dots above each time interval representing the frequency of wait times falling in that interval.
The data is not symmetric, according to the provided line plot, which shows that there are more dots above 12 and 15 minutes than at other time intervals. This shows that the data is not normally distributed, and that the symmetric distribution assumption is consequently incorrect.
The claim that "the wait times were less than 13 minutes for all the rides" is untrue is further supported by the absence of dots over time intervals of less than 10 minutes. While there are dots above time intervals less than and equal to 13 minutes, it is equally untrue to say that "the wait times were over 13 minutes for all the rides."
Because there are two peaks in the distribution with wait times of 12 and 15 minutes for the most popular ride, bimodal distribution is the best way to describe the form of the data. This may indicate the existence of two popular rides with distinct wait times, or it may indicate that the popularity of some rides fluctuated over time, resulting in a bimodal distribution.
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Answer:it B
Step-by-step explanation:
What kinds of diseWhat is the five-number summary for {34, 47, 51, 11, 7, 9, 13, 49, 22}?ases can vaccinations prevent?
Vaccinations can prevent various infectious diseases including measles, mumps, rubella, polio, tetanus, pertussis, hepatitis A and B, varicella, HPV, and influenza.
One should consult with a healthcare professional to determine which vaccinations are recommended based on age, health status, and individual factors.
Vaccinations can prevent many infectious diseases, including:
Measles
Mumps
Rubella
Polio
Tetanus
Pertussis (whooping cough)
Hepatitis A and B
Varicella (chickenpox)
Human papillomavirus (HPV)
Influenza (flu)
Pneumococcal disease (pneumonia, meningitis, blood infections)
Rotavirus (diarrhea and vomiting)
Haemophilus influenzae type b (meningitis, pneumonia, and other infections)
Meningococcal disease (meningitis and blood infections)
Hepatitis A and B (liver infections)
and many others. It is important to consult with a healthcare professional to determine which vaccinations are recommended based on age, health status, and other individual factors
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The daily production rates for a sample of factory workers before and after a training program are shown below. Let d = After - Before
With mean=2.2, the training program was effective in increasing the production rates.
What is mean?
In mathematics, the mean represents the average value of a dataset. It is calculated by summing all the values in a dataset and dividing by the total number of values. The mean is often used as a standard measure of the central location of a dataset
Now,
The hypotheses for this problem are:
Null hypothesis (H0): The training program did not have any effect on the production rates. In other words, the mean difference in production rates (d) is equal to zero.
Alternative hypothesis (Ha): The training program was effective in increasing the production rates. In other words, the mean difference in production rates (d) is greater than zero.
To compute the test statistic, we first need to find the sample mean and standard deviation of the differences:
d = After - Before
Worker Before After d
1 6 9 3
2 10 12 2
3 9 10 1
4 8 11 3
5 7 9 2
The sample mean of the differences is:
mean(d) = (3+2+1+3+2)/5 = 2.2
The sample standard deviation of the differences is:
s = √(sum((d - mean(d))²)/(n-1)) = √((1.04)/4) = 0.57
The test statistic for testing the null hypothesis is:
t = (mean(d) - 0)/(√(n)) = (2.2 - 0)/(0.57/√(5)) = 6.07
Using a t-distribution with n-1 = 4 degrees of freedom and a significance level of 0.05, the critical value is 2.776.
Since the calculated t-value (6.07) is greater than the critical value (2.776), we reject the null hypothesis and conclude that the training program was effective in increasing the production rates.
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Correct Question:-
The daily production rates for a sample of factory workers before and after a training program are shown below. Let d = After - Before.
Worker Before After
1 6 9
2 10 12
3 9 10
4 8 11
5 7 9
We want to determine if the training program was effective.
Give the hypotheses for this problem.
Compute the test statistic.
At 95% confidence, test the hypotheses. That is, did the training program
actually increase the production rates? Please, I need the work for this problem.
Ariel has the following data:
8 18 8 v 10 8 8 18 18
If the median is 10, which number could v be?
Answer:
Any number greater than 10; 11, 12, 15, 20, 100...etc
Step-by-step explanation:
Order the data from least to greatest and strikethrough numbers on each side until you reach the middle 1 or 2 numbers. In this case there are 9 numbers, so the middle number is our median.
8, 8, 8, 8, 10, v, 18, 18, 18
the variable v can be many numbers, but in order for the median to be 10, v must be a number greater than 10. If v = 11, the median is 10. Likewise, if v = 100000, the median is still 10 because it is the middle of the set.
(100 POINTS)
The box plot displays the cost of a movie ticket in several cities.
A box plot uses a number line from 4 to 25 with tick marks every one unit. The box extends from 9 to 15 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 23. The graph is titled Movie Ticket Prices, and the line is labeled Cost Of Ticket.
Which of the following is the best measure of center for the data shown, and what is that value?
The mean is the best measure of center and equals 11.
The mean is the best measure of center and equals 11.5.
The median is the best measure of center and equals 11.
The median is the best measure of center and equals 11.5.
Answer:
The best measure of center for the data shown is the median, and its value is 11.
Step-by-step explanation:
In statistics, measures of central tendency are used to summarize a set of data and provide a single value that represents the center or typical value of the data. The three commonly used measures of central tendency are the mean, median, and mode.
The mean is calculated by adding up all the values in the data set and dividing by the total number of values. The mean is affected by outliers and can be heavily skewed by extreme values.
The median is the middle value of the data set when the values are arranged in order. It is not affected by extreme values and is a more robust measure of central tendency compared to the mean.
In the given box plot, the distribution appears relatively symmetric, with the box extending from 9 to 15 on the number line and the median line located at 11, which is the middle value of the box. Therefore, the best measure of center for the data shown is the median, and its value is 11.
The best measure of the center for the data shown is the median, and its value is 11 thus the correct option is C.
What are mean and median?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Median represents the middle value of the given data when arranged in a particular order.
In statistics, the measures of central tendency are used to summarize a set of data and provide a single value that shows the center or typical value of the data. Also, it is known that three commonly used measures of central tendency are the mean, median, and mode.
The median is not affected by extreme values and is a more robust measure of central tendency compared to the mean.
In the given box plot, we can conclude that the distribution appears relatively symmetric, with the box extending from 9 to 15 on the number line and the median line located at 11, that is the middle value of the box. the median, value is 11.
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Miguel’s coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Miguel $5.95 per pound, and Type B coffee costs $4.65 per pound. This month’s blend used three times as many pounds of Type B coffee as Type A, for a total cost of $796.00. How many pounds of Type A coffee were used?
To start, denote x as the number of lbs utilized per each coffee type (type A and type B). Further, let ax be the quantity of lbs for type A coffee and bx be the quantity of lbs for type B coffee. So, ax and bx are in units of quantity*lbs.
The cost of type A and type B coffee can be equated as follows:
Cost (A) = 5.95/lb and Cost (B) = 4.65/lb
The key information given ("This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $796.00") can be represented algebraically as follows:
Cost (Blend) = Cost(A)*ax + Cost(B)*bx = $796.00. Since the quantity of type B coffee is 3 times the quantity of type A coffee, it follows that a = 1 and b = 3.
Therefore, 5.95/lb*(x) + 4.65/lb*(3x) = 796--> 5.95/lb*(x) + 13.95/lb*(x) = 796 or (5.95+13.95)(x) = 796.
Therefore, quantity (lbs) = 796/(13.95+5.95) = 796/(19.9) = 40.
Using the previous relation, we know that 3x + x = 40 or 4x = 40. So, the number of lbs for type A coffee utilized in the blend equates to the following:
x = 10 lbs.
would someone mind helping me with this?
Answer:
$0.75 per pound
Step-by-step explanation:
On the graph, the x is the number of pounds of tomato, and the y is the price.
We see when the x is 1 pound of tomato; the y is $0.75. So the unit rate is $0.75 per pound.
4
12 + x. - 6 when x = 8
Answer:
Step-by-step explanation: 412+x-6 is also 412+8-6
If you do this by pemdas it would equal to 414
In a survey of U.S. adults with a sample size of 2055, 345 said Franklin Roosevelt was the best president since World
War II. Two U.S. adults are selected at random from this sample without replacement. Find the probability that both adults say Franklin Roosevelt was the best president since wwII
Answer:
a) 0.0281
b) 0.6924
c) 0.3081
Step-by-step explanation:
Probability that one of those sampled saying that Roosevelt was the best president since World War II = 345/2055 = 0.17
Probability that one of those sampled don't mention Roosevelt = (2055 - 345)/2055 = 1710/2055 = 0.83
a) The probability that both adults picked say Franklin Roosevelt was the best president since World War II = (345/2055) × (344/2054) = 0.0281
b) The probability that neither of the two adults say Franklin Roosevelt was the best president since World War II = (1710/2055) × (1709/2054) = 0.6924
c) The probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II = Probability that one of the two adults mention Roosevelt + Probability that the two adults mention Roosevelt
Probability that one of the adults mention Roosevelt = [(345/2055) × (1710/2054)] + [(1710/2055) × (345/2054)] = 0.280
Probability that two of the adults mention Roosevelt has been done in (a) and it is equal to 0.0281
Probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II = 0.280 + 0.0281 = 0.3081
ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST PLEASE HELP
Answer:
a. f(6)/f(5) = 60.75/81 = 3/4
b. f(n) = f(n-1) x 3/4 or f(n) = 3/4f(n-1)
Step-by-step explanation:
We have 256, 192, 144, 108, 81
common ratio r = f(n) / f(n-1) = 192/256 = 3/4
so f(n) = f(n-1) x 3/4
f(1) = 256
f(2) = 256 x 3/4 = 192
f(3) = 192 x 3/4 = 144
f(4) = 144 x 3/4 = 108
f(5) = 108 x 3/4 = 81
f(6) = 81 x 3/4 = 60.75
a. f(6)/f(5) = 60.75/81 = 3/4
b. f(n) = f(n-1) x 3/4 or f(n) = 3/4f(n-1)
La profesora Elena compró 28 lapiceros y repartió a sus estudiantes 5/7 de los lapiceros. ¿Cuántos lapiceros le quedaron a la profesora Elena?
Using the expression 2/7 × 28 it is obtained that Professor Elena has 8 pencils left after distributing 5/7 of the pencils to her students.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The total number of pencils Professor Elena bought is 28 pencils.
If Professor Elena bought 28 pencils, and she distributed 5/7 of them to her students.
The fractional expression will be -
1 - 5/7
Simplifying the expression we get -
(7 - 7) / 2
2/7
Then she kept 2/7 of the pencils for herself.
The number of pencils she has with her will be -
2/7 × 28 = 8 pencils
Therefore, Professor Elena has 8 pencils left after distributing 5/7 of the pencils to her students.
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Professor Elena bought 28 pencils and distributed 5/7 of the pencils to her students. How many pencils did teacher Elena have left?
Use the given scenario.
Keira’s coach lets each player choose a marble from a bag with 3 green, 2 blue, 5 red, and 5 yellow marbles.
If the player chooses a blue marble, they do not have to run laps at the end of practice. What is the theoretical probability a player chooses a blue marble?
15
Therefore, the potential likelihood of selecting a blue stone is roughly 0.1333 or 13.33%.
Which four kinds of chance are there?Mathematics' study of chance events is known as probability, and there are four major kinds of probability: axiomatic, classical, observational, and subjective.
To find the theoretical probability of choosing a blue marble, we need to divide the number of blue marbles by the total number of marbles in the bag.
Total number of marbles = 3 green + 2 blue + 5 red + 5 yellow = 15
Number of blue marbles = 2
Therefore, the theoretical probability of choosing a blue marble is:
P(Blue) = Number of blue marbles / Total number of marbles = 2 / 15
= 0.1333 (rounded to 4 decimal places)
So, the theoretical probability of choosing a blue marble is approximately 0.1333 or 13.33%.
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A bank account earns 1% interest each month has a balance of 1500 any interest is deposited into the account and no further deposits or withdrawals are made which expression represents the balance after two months
Therefore, the expression that represents the balance after two months is: 1500 * (1 + 0.01) * (1 + 0.01) = 1530.15.
What is percent?Percent, denoted by the symbol "%", is a way of expressing a number as a fraction of 100. For example, 50% is equivalent to the fraction 50/100, which can be simplified to 1/2. Percentages are commonly used to express ratios, proportions, or rates in various contexts such as finance, statistics, and everyday life. For instance, an interest rate of 3% means that for every $100 borrowed, the borrower will be charged $3 per year. Similarly, a score of 80% on an exam means that the student has answered 80 out of 100 questions correctly.
by the question.
To calculate the balance after two months, we first need to calculate the balance after the first month, including the interest earned:
Balance after 1 month = 1500 + (1% of 1500) = 1500 + 15 = 1515
Then, we can calculate the balance after two months, including the interest earned in the second month:
Balance after 2 months = 1515 + (1% of 1515) = 1515 + 15.15 = 1530.15
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Please help me with these question! thanks <3
The variables y and x have a proportional relationship, and y = 5 when x = 4.
What is the value of x when y = 8?
Enter your answer in the box.
X= ___
___
The variables y and x have a proportional relationship, and y = 7 when x = 2.
What is the value of y when x = 5?
Enter your answer as a decimal in the box.
y= ___
__
correct answer gets brainliest
Answer:
Enter your answer as a decimal in the b
Which sequence of transformations will produce the same results?
Answer:
A
Step-by-step explanation:
B: would lead to g being in the same spot
C: would still be missing the rotation
D:It would be the flipped version of H
Which distance is longer, 500 kilometers or 250 miles? Explain.
Answer:
1 mile = 1,609344 km
250 miles = X
X= 250 x 1,609344
X= 402,336km
So 500 km > 250 miles
Step-by-step explanation:
1 mile = 1,609344 km
250 miles = X
X= 250 x 1,609344
X= 402,336km
So 500 km > 250 miles
NO LINKS!!! URGENT HELP PLEASE!!!!!
A new airline company, The High Flyers, says that their planes can only take off at an 20° angle. The airport is considering shortening the cell tower to accommodate them. If they take off from the same spot as the other airplanes, how short must the cell tower be so that it is safe for everyone?
Answer:
shortened height = h(1 - tan(20))
Step-by-step explanation:
To solve this problem, we need to use trigonometry to find the height that the airplane reaches at a 20° angle, and then subtract this height from the height of the cell tower to determine how short it needs to be.
Let's assume that the cell tower has a height of "h", and that the airplane takes off at a 20° angle. We can use trigonometry to find the height "x" that the airplane reaches above the ground:
tan(20) = x / h
Multiplying both sides by "h", we get:
x = h * tan(20)
So the airplane reaches a height of "x" above the ground. To find how short the cell tower needs to be, we simply subtract this height from the original height of the tower "h":
shortened height = h - x
Substituting the expression we found for "x", we get:
shortened height = h - h * tan(20)
Simplifying, we get:
shortened height = h(1 - tan(20))
So, the cell tower needs to be shortened by "h(1 - tan(20))" to ensure that the airplane can take off safely at a 20° angle.
Listed below are the amounts of net worth (in millions of dollars) of the ten wealthiest celebrities in a country. Construct a 99% confidence interval. What does the result tell us about the population of all celebrities? Do the data appear to be from a normally distributed population as required?
259
196
190
166
163
162
148
148
148
143
Using the appropriate statistical relation, the confidence interval estimate for the net worth of the wealthiest celebrities is (150.35; 204.77).
Given the samples :
X = 256,196,190,166,163,162,148,148,143.
Using a calculator, we could obtain the sample mean and sample standard deviation is-
Mean, μ = [tex]\sum\frac{x}{n}[/tex] = 174.55
Standard deviation, σ = 38.8
The confidence interval can be defined thus :
Mean ± standard error
Standard Error = Tcritical × σ/√n
Tcrit ; 95% ; df = n - 1 = 9 - 1 = 8; T-critical = 2.26
Standard Error = (2.26 × 38.06/√10) = 27.20
Lower confidence boundary = 177.55 - 27.20 = 150.35
Upper confidence boundary = 177.55 + 27.20 = 204.77
Therefore, the confidence interval is (150.35; 204.77)
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2. A system of equations is shown below. Find the solution by using substitution.
7/3x-2
y=x+2
O(-1,-1)
(3,6)
O (1,2)
(2,4)
The solution to the system of equations given as y = 7/3x - 2 and y = x + 2 is (3, 5).
Calculating the solution to the system of equationsGiven that
y = 7/3x - 2
y = x + 2
To solve this system of equations using substitution, we need to isolate one of the variables in one equation and substitute the resulting expression into the other equation.
Let's start by isolating y in the second equation:
y = x + 2
Now we can use this expression for y in the first equation:
y = 7/3x - 2
We substitute x + 2 for y
x + 2 = 7/3x - 2
Next, we can solve for x by isolating it on one side of the equation:
x - 7/3x = -2 - 2
-4/3x = -4
So, we have
x = 3
Now that we have an expression for x in terms of y, we can substitute it into either of the original equations to solve for y. Let's use the second equation:
y = x + 2
Substituting
y = 3 + 2
Simplifying, we get:
y = 5
Therefore, the solution to the system of equations is (x, y) = (3, 5).
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Abigail was baking a big cake. She estimated that the height of the cake needed to be 78.25 inches. The
actual height of the cake was 75.5 inches.
What is the percent error in her calculation to the nearest tenth? Be sure to show the formula you use to
solve
Answer:
ASP please
The percent error in Abigail 's calculation for the height of the cake to the nearest tenth is 3.64 %.
Define about the percent error?When compared to the real number and expressed in percent format, percentage error seems to be the variance between the projected amount and the actual number.
By deducting the actual value from the estimated value, you may get the percentage error. Then, divide the real number's absolute value by the absolute value of the error. You will receive the error in decimal form as a result. The percentage error can then be calculated by multiplying the result by 100%.
Given data:
Required height of cake = 78.25 inches
Actual height = 75.5 inches.
Thus,
percent error = (Required height - Actual height)/actual height *100%
percent error = (78.25 - 75.5)/75.5 * 100
percent error = 3.64 %
Thus, the percent error in Abigail 's calculation for the height of the cake to the nearest tenth is 3.64 %.
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show the given equation in a graph:x-y=6
Answer:
Step-by-step explanation:
R.E.F image
f(x)=x+6
X -3 -2 -1 0 1 2
Y 3 4 5 6 7 8
Given equation is −x+y=6
That can be written as f(x)=x+6
The required graph is drawn in the figure.
solution
a tree is midway between point E and F 14 M apart a is a point on top of a tree 7m above the ground .how far is E from the bottom of the tree
The distance between E and the bottom of the tree, given the distance above the ground, is 7 m.
How to find the distance ?We are told that the tree is midway between points E and F. We are also told that points E and F are 14 meters away from each other.
The distance between E and the bottom of the tree would be half of the distance between E and point F because the tree is located midway between both points.
The distance between E and the bottom of the tree is therefore:
= 14 / 2
= 7 m
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Same set up as the problem to the left. Fill in the blanks. 39 + 25
The height of a mirror is 168.73 cm correct to 2 decimal places. a) What is the lower bound for the height of the mirror? b) What is the upper bound for the height of the mirror?
Answer:
a)168.725
b)168.735
168.725≤x<168.735
Step-by-step explanation:
a)168.73 - 0.005
168.725
b) 168.73 + 0.005
168.735
The third term and the sixth term of A geomatric sequence are 2 and 16 respectively. Find the first term and the common ratio
The first term of the geometric sequence is 1/2 and the common ratio is 2.
What is the geometric sequence?
A geometric sequence is a sequence of numbers in which each term after the first is obtained by multiplying the previous term by a fixed number called the common ratio. The general form of a geometric sequence is:
a, ar, ar², ar³, ar⁴, ...
where 'a' is the first term, 'r' is the common ratio, and the subscripts represent the position of the term in the sequence.
Let's denote the first term of the geometric sequence by "a" and the common ratio by "r".
We know that the third term of the sequence is 2, which means that:
a * r² = 2 (1)
We also know that the sixth term of the sequence is 16, which means that:
a * r⁵ = 16 (2)
Now we can solve for "a" and "r" by dividing equation (2) by equation (1):
(a * r⁵)/(a * r²) = 16/2
Simplifying, we get:
r³ = 8
Taking the cube root of both sides, we get:
r = 2
Now we can use equation (1) to solve for "a":
a * 2² = 2
Simplifying, we get:
4a = 2
a = 1/2
Therefore, the first term of the geometric sequence is 1/2 and the common ratio is 2.
To learn more about the geometric sequence visit:
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