Answers
Answer:
4
Step-by-step explanation:
To find f(-1)g(-1) which is f(-1)*g(-1), first, we must find what are values of f(-1) and g(-1) first which can be found by substituting x = -1 in both functions.
[tex]\displaystyle{f(-1)=(-1)^2+1}\\\\\displaystyle{f(-1)=1+1 = 2}[/tex]
Now we know that f(-1) is 2, next, we find g(-1).
[tex]\displaystyle{g(-1) = 3(-1)+5}\\\\\displaystyle{g(-1)=-3+5 = 2}[/tex]
Now we know that g(-1) is 2 too. Since the question wants to find f(-1)g(-1), therefore 2*2 = 4.
Hence, the answer is 4.
Answer:
D) 4
Step-by-step explanation:
Given functions:
f(x) = x² + 1
g(x) = 3x + 5
Here, we're asked to find the value of both functions when the value of x is -1. Then, we multiply the functions in order to find the value of f(-1)•g(-1).
Note: f(-1) • g(-1) is equivalent to (f • g)(-1).
Method 1: f(-1) • g(-1)
Find the value of each function when x = -1.
f(-1) = (-1)² + 1 ⇒ f(-1) = 1 + 1 ⇒ f(-1) = 2
g(-1) = 3(-1) + 5 ⇒ g(-1) = -3 + 5 ⇒ g(-1) = 2
Multiply the functions together.
f(-1) • g(-1) ⇒ 2 • 2 ⇒ 4
Method 2: (f • g)(-1)
First, multiply the functions.
⇒ (x² + 1) • (3x + 5) [ Simplify using the Distributive Property: (a + b) • (c + d) = ac + ad + bc + bd. ]
⇒ x²(3x) + x²(5) + 1(3x) + 1(5)
⇒ 3x³ + 5x² + 3x + 5
Now, substitute -1 as the value of x.
⇒ 3(-1)³ + 5(-1)² + 3(-1) + 5 [ Exponents first. }
⇒ 3(-1) + 5(1) -3 + 5 [ Multiply the numbers. ]
⇒ -3 + 5 - 3 + 5 [ Simplify. ]
⇒ 4
Therefore, the product of both functions when x = -1 is 4.
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Related Questions
PLEASE ANSWER ,in terms of the trigonometric ratios for BCD,what is the lenght of BD? insert text on the triangle in geogebrea to show the lenght of BD. take a screenshot of the triangle with the text,save it,and insert the image in the space below
Answers
By applying the law of sine, the length of side BD is equal to 9.05 cm and the image of right-angled triangle BCD is shown in the image attached below.
How to calculate the length of BD?In order to determine the length of side BD, we would apply the law of sine because both side BD and side BC represent the opposite side and hypotenuse of right-angled triangle BCD respectively.
Mathematically, the law of sine is given by this mathematical expression:
sin(θ) = Opp/Hyp
Where:
Opp is the opposite side of a right-angled triangle.Hyp is the hypotenuse of a right-angled triangle.θ is the angle.Substituting the parameters into the formula, we have;
sin(θ) = BD/BC
sin(74) = BD/9.41
Cross-multiplying, we have:
BD = 9.41 × sin(74)
BD = 9.41 × 0.9613
BD = 9.05 cm.
By applying the law of sine, the length of side BD is equal to 9.05 cm and the image of right-angled triangle BCD is shown in the image attached below.
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Helppppppp pleaseeeee
Answers
Answer:
is it asking how many times u would get then number 5 when u roll or asking how you would expect for the first 5 rolls?
DUE IN 3MINUTes
There is a strong positive linear correlation between rainfall and the number
of peaches a tree produces. Does this mean that more rainfall causes peach
trees to produce more fruit?
A. No. Any number of factors could also be affecting the number of
peaches produced.
B. No. Since rainfall and number of peaches are linearly correlated,
this means that more rainfall causes peach trees to produce less
fruit.
C. Yes. Since rainfall and number of peaches are positively
correlated, this means that more rainfall causes peach trees to
produce more fruit.
D. Yes. Since rainfall and number of peaches are linearly correlated,
this means that more rainfall causes peach trees to produce more
fruit.
Answers
Answer:
A. No.
Step-by-step explanation:
The job of science is to explain relationships in the real world. Scientists do this by making observations, forming theories regarding relationships, and conducting experiments to test those theories.
An observation of correlation may result in a theory that one of the correlated phenomena causes another. The correlation, by itself, does not demonstrate causation. Any number of other factors could be involved.
Based only on the information given in the diagram which congruence theorems or postulate could be given as reasons why LMN and OPQ
Answers
The congruence theorems or postulates could be given as reasons why LMN is congruent to OPQ are LA and AAS.
What is congruence theorems?Congruence theorems is one that explain that in a case whereby three sides of two triangles are equal to another, we can say they are congruent to each other.
From the given figure, there are two angles as well as one non-included side which is seen to be a congruent.
According to LA theorem , a triangle is congruent in a case whereby, leg as well as an acute angle of one right triangle of two right triangles are congruent to each other.
AAS theorem also explains that incase two angles and any of the side of a triangle are congruent to each other , the triangles are congruent.
Therefore, with these theorem, congruence theorems or postulates could be given as reasons why LMN is congruent to OPQ are LA and AAS.
CHECK THE FIQURE FOR THE COMNPLETE QUESTION
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Find the largest rational number r for which 5r ≤ 33.
Answers
Answer:
33/5 or 6.6
Step-by-step explanation:
Well the most 5r can be is 33, since it has the underline under it, so it's less than or equal to.
So set 5r equal to 33
5r = 33
Divide both sides by 33
r = 33/5
You can leave it in this form or convert it to a decimal which is 6.6
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathsf{5r \leq 33}[/tex]
[tex]\huge\textbf{Simplifying it:}[/tex]
[tex]\mathsf{5r \leq 33}[/tex]
[tex]\huge\textbf{Divide \boxed{5} to both sides:}[/tex]
[tex]\mathsf{\dfrac{5r}{5}\leq \dfrac{33}{5}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{r \leq \dfrac{33}{5}}[/tex]
[tex]\mathsf{r \leq 6 \dfrac{3}{5}}[/tex]
[tex]\mathsf{r \leq 6.60}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{r \leq \dfrac{33}{5}}}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
[tex]\large\textsf{The graph will be labeled down below for you :)}\downarrow[/tex]
Two student clubs were selling t-shirts and school notebooks to raise money for an upcoming school event. In the first few minutes, club A sold 3 t-shirts and 2 notebooks, and made $19. Club B sold 1 t-shirt and 1 notebook, for a total of $8. Use the given matrix equation to solve for the cost of t-shirts and notebooks that were sold. Explain the steps that you took to solve this problem.
A matrix with 2 rows and 2 columns, where row 1 is 3 and 2 and row 2 is 1 and 1, is multiplied by matrix with 2 rows and 1 column, where row 1 is x and row 2 is y, equals a matrix with 2 rows and 1 column, where row 1 is 19 and row 2 is 8.
Answers
Using a system of equations, it is found that the cost of a t-shirt is of $3 and the cost of a notebook is of $5.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables are given as follows:
Variable x: Cost of a t-shirt.Variable y: Cost of a notebook.Considering the costs of the purchases of Clubs A and B, the matrices give the equations as follows:
3x + 2y = 19.x + y = 8 -> y = (8 - x).Hence, replacing the second equation into the first:
3x + 2(8 - x) = 19
x = 3.
y = 8 - x = 8 - 3 = 5.
The cost of a t-shirt is of $3 and the cost of a notebook is of $5.
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The square shown has a perimeter of 32 units. The square is rotated about line k. what is the circumfrence of the base
Answers
The circumference equal to 25 units
What is perimeter of square?The perimeter of square is 4 times the side.
P= 4* side
The perimeter of the square,
4x = P
Now P is = 32 units then,
32 units = 4(x)
x = 8 inches
So, the diameter of the cylinder formed by the rotation of 8 inches
Now, the circumference of the base is
C = 2πr = πD
If r =8 inches
C = π(8 units) = 8π units
C = 8(3.14) = 25.12 units
Hence, the circumference equal to 25 units
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A
<
Lennox had been scheduling employees based on the assumption that the
following distribution represented when people made purchases in his store.
Time slot
Predicted
percentage
8 a.m.-12 p.m.
25%
12-4 p.m.
40%
4-8 p.m. 8-12 a.m.
25%
10%
He took a random sample of 300 purchases and recorded their time slot so he
could test whether this was an accurate distribution. Here are his results:
Time slot 8 a.m.-12 p.m. 12-4 p.m. 4-8 p.m.
Purchases
75
120
90
Choose 1 answer:
8-12 a.m.
15
He wants to use these results to carry out a x² goodness-of-fit test to determine
if the distribution of time slots of the purchases disagrees with his assumed
distribution.
What are the values of the test statistic and P-value for Lennox's test?
Answers
The test value and the p value for the probability are 10.5 and 0.0148.
How to illustrate the probability?Based on the information, the observed and expected values will be:
Observed. Expected
75. 75
100. 120
90. 75
15. 30
The p value based on the test statistic from the distribution table will be 0.0148.
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The function f(x) is graphed. It represents a translation of the square root function g(x) = .
What equation represents the graph of f(x)?
f(x) =
f(x) =
f(x) = – 1
f(x) = + 1
Answers
The equation that represents the graph of f(x) is [tex]f(x) = \sqrt {x - 1[/tex]
How to determine the equation of f(x)?The complete question is in the attached image
The parent square root function is:
[tex]g(x) = \sqrt x[/tex]
From the graph,
g(x) is shifted one unit right to get f(x)
This is represented as:
f(x) = g(x - 1)
So, we have:
[tex]f(x) = \sqrt {x - 1[/tex]
Hence, the equation that represents the graph of f(x) is [tex]f(x) = \sqrt {x - 1[/tex]
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The following graph shows a proportional relationship.
What is the constant of proportionality between y and x in the graph?
Answers
Answer:
[tex]k=2[/tex]
Step-by-step explanation:
The constant of proportionality is given as [tex]k=\frac{y}{x}[/tex] .
Notice that when [tex]x=2[/tex] it follows that [tex]y=4[/tex].
Substitute [tex]x=2[/tex] and [tex]y=4[/tex] into the formula for the constant:
[tex]k=\frac{4}{2}=2[/tex] .
Therefore, the constant is equal to 2.
What is the ratio of 12 blue marbles and 20 red marbles
Answers
Answer:
12:20
Step-by-step explanation:
i hope the answer will help you
A rectangular prism with a base that is
5 inches by 4 inches and a height of 15 inches.
Answers
The surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:
V = a × b × c unit³
The surface area of the prism = 2[(5×4)+(15×4)+(15×5)]
= 310 inches²
The volume of the prism = 5 × 4 × 15
= 300 in³
Hence, the surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.
The complete question is:
A rectangular prism with a base that is 5 inches by 4 inches and a height of 15 inches. Find the volume and the surface area of the rectangular prism?
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Solve x 6x+2=2x-1 give your answer as a fraction in its simplest form
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{6x + 2 = 2x - 1}[/tex]
[tex]\huge\textbf{SUBTRACT 2x to BOTH SIDES:}[/tex]
[tex]\mathbf{6x + 2 - 2x = 2x - 1 - 2x}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{4x + 2 = -1}[/tex]
[tex]\huge\textbf{SUBTRACT 2 to BOTH SIDES:}[/tex]
[tex]\mathbf{4x + 2 - 2 = -1 - 2}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{4x = -3}[/tex]
[tex]\huge\textbf{DIVIDE 4 to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{4x}{4} = \dfrac{-3}{4}}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{x = \dfrac{-3}{4}}[/tex]
[tex]\mathbf{x = -\dfrac{3}{4}}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -\dfrac{3}{4}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assigiment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]During the first year of life, a whale gains about 30 tons of weight what is the average weight gain per month?
Answers
Step by step
We know 30 tons gained over 12 months
(1 year)
Divide total weight by 12 months to get average weight gain per month
30/12 = 2.5 tons per month
calculate the value of the sample variance of 13,−2,−2,−2,13,13,−5
Answers
Answer:
13, -2
Step-by-step explanation:
What is the domain indicated on the graph for each
portion of the piecewise function?
-2,
2x + 1,
--—-x,
f(x)=
Domain 1st piece
Domain 2nd piece
Domain 3rd piece
Answers
Step-by-step explanation:
try this option, all the details are in the attachment.
Use
f(x) = 2x − 3
and
g(x) = 4 − x2
to evaluate the expression.
Answers
The equation based on the information given will be x⁴ + 8x² - 12.
How to compute the value?It should be noted that from the information given, the expression to compute will be:
= g - g(x)²
This will be:
= 4 - (4 - x²)²
= 4 - (4 - x)(4 - x)
= 4 - (15 - 8x² + x⁴)
= x⁴ + 8x² - 12
The complete question is:
Use f(x) = 2x − 3 and g(x) = 4 − x² to evaluate the expression g - g(x)².
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What are the medians for the height and weight distribution, respectively?
Answers
The median for height is: 167
The median for Weight is: 183
What is the Median of a Data Set?The middle value or the average of the two middle value of an ordered data set is the median of the data.
Given the following data:
Height: 178, 163, 174, 186, 154, 167, 167, 181, 159, 165, 177, 191, 158
Arranged in an ordered form, we would have:
54, 158, 159, 163, 165, 167, [167,] 174, 177, 178, 181, 186, 191
The middle value is 167. The median for height is: 167.
Weight: 157, 163, 190, 187, 183, 173, 184, 189, 193, 192, 177, 173, 168
Arranged in an ordered form, we would have:
157, 163, 168, 173, 173, 177, [183,] 184, 187, 189, 190, 192, 193
The middle value is 183. The median for weight is: 183.
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8 of 8
A vase with a circular base exerts a force of 15 N on a table with a pressure of 750 N/m2.
Find the radius of the base of the vase in cm to 2 dp.
Answers
The radius of the circular vase is 6.37 * 10^-3 m.
What is pressure?The term pressure is defined as the ratio of force to area. Hence we can write;
P = F/A
F = 15 N
P = 750 N/m2
A = F/P
A = 15 N/750 N/m2
A = 0.02 m^2
Now;
A = πr^2
r = √A/ π
r = √ 0.02/3.142
r = 6.37 * 10^-3 m
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The table below shows the number of correct answers that students gave on a recent 5-question quiz. Which of the following statements is true? Number Correct 1 2 3 4 5 3 46 9 8 Frequency
Answers
The true statement about the number of correct answers is that the: A. median = mode.
How to calculate the mean?Mathematically, the mean for the number of correct answers can be calculated by using the following formula:
Mean = [F(x)]/n
Total frequency, n = 3 + 4 + 6 + 9 + 8 = 30.
F(x) = [(1 × 3) + (2 × 4) + (3 × 6) + (4 × 9) + (5 × 8)] = 105.
Mean = 105/30
Mean = 3.5.
For the median, we have:
The median for the number of correct answers is the average of the 15th and 16th number:
Median = (4 + 4)/2
Median = 8/2
Median = 4.
For the mode, we have:
The mode for the number of correct answers is the answer with the highest frequency, which is 4 with a frequency of 9.
Therefore, the true statement about the number of correct answers is that the median is equal to mode.
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Complete Question:
The table below shows the number of correct answers that students gave on a recent -question quiz. Which of the following statements is true?
A. median = mode
B. mode > median
C. mode < mean
D. mean > median Reset Selection
Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwise indicated. ?C(lnx+y)dx−x2dy where C is the rectangle with vertices (1, 1), (3, 1), (1, 4), and (3, 4)
Answers
By Green's theorem,
[tex]\displaystyle \int_C P(x,y)\,dx + Q(x,y)\,dy = \iint_D \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \, dA[/tex]
where [tex]D[/tex] is the interior of [tex]C[/tex]. It's easy to see that
[tex]D = \left\{(x,y) ~:~ 1 \le x \le 3 \text{ and } 1 \le y \le 4\right\}[/tex]
Now,
[tex]\dfrac{\partial Q}{\partial x} = \dfrac{\partial}{\partial x}(-x^2) = -2x[/tex]
[tex]\dfrac{\partial P}{\partial y} = \dfrac{\partial}{\partial y}(\ln(x) + y) = 1[/tex]
so that the line integral reduces to
[tex]\displaystyle \int_C (\ln(x)+y)\,dx - x^2\,dy = -\int_1^3 \int_1^4 (2x+1) \, dy\,dx = \boxed{-30}[/tex]
A rectangle has length of 10 mm. • and breadth 7mm calculate its perimeter YW
Answers
Answer:
34 mm
Step-by-step explanation:
P = 2 x (L + B) for a rectangle
P = 2 x (10 + 7) = 2 x 17 = 34
2. What is the radius of a circle (rounded to the nearest tenth) that has a circumference of 87 cm?
O 10.5
27.7
13.8
5.3
Answers
3.
A = pi x r^2
48 = 3.141... x r^2
÷ by value of pi
15.278... = r^2
Square root the ans, to get r
Thus, R = 3.908..... So, radius is 3.9
2.
Circumference = pi x diameter
87. = 3.141... x d
÷ by value of pi
27.692............. = diameter
Radius is twice the diameter. So, divide diameter by 2 to find the radius.
27.692.....÷ 2 = 13.846...
Thus, radius is 13.8cm
Hope this helps!
5. The function h(t) = 1 + 4t - 1.86t? models the height of a rock thrown upward on the planet Mars, where h(t) is height in meters and t is time in seconds. Use a graph to determine:
a. the maximum height the rock reaches
b. how long the rock will be above the surface
Answers
The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
From the graph of the function h(t) = 1 + 4t - 1.86t²:
The maximum height the rock reaches 3.15 feet.
Time spent on air = 2.38 - (-0) = 2.38 seconds
The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds
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How many different strings can be made by shuffling the letters in DISCRETEMATHS?
Answers
Answer:
I found 14 but their might be more!
hope that helps! :)
Step-by-step explanation:
Use the table to work out the values of a, b,
C, and d.
X
-3
-2
-1
0
1
2
3
y = 5x
—
a
3x² + 3
- 19
-5
3
b
C
d
Answers
Insert the -3 in the x’s in the equation on the top of the table
y= 5x -3x to the second power + 3
y= 5 (-3) -3(-3) to the second power + 3
Then continue to simplify the equation
y= -15 + 9 to the second power + 3
y= -15 + 84
y = 69
Y= 69 for the chart for -3
For b, c, and d insert the number in the x values and simplify like the previous equation.
If you are confused, feel free to ask questions. I hope this is effective and helps you in your studies.
About 145 out of 500 students prefer walking instead of
riding the bus to school. About what percent of the
students prefer walking?
30%
50%
70%
145%
Answers
Answer:
30%
Step-by-step explanation:
[tex]\frac{145}{500} = 0.29[/tex] ≅ 0.30 or 30%
1. A(–6 , 2) , B(4 ,7) are endpoints of a line segment.
(2) a) Calculate the length of AB.
(2) b) Calculate the slope of AB.
(2) c) Calculate the coordinates of the midpoint of AB.
(2) 2. Determine the radius of the circle .
State the answer as an exact number, and as a decimal rounded to 1 decimal place.
(2) 3 Write the equation of a circle with centre (0, 0) that passes through the point (5, –3)
Answers
The length of the line AB as described by points A and B in the task content is; √125.
What is the length of the line?a) The length of AB as described is;
AB = √((7-2)² + (4-(-6))²)
AB = √(25 + 100) = √125.
b) The slope of AB is;
Slope, m = (7-2)/(4-(-6)) = 5/10
Slope = 1/2.
c). The coordinates of the midpoint of AB are;
x = (4+(-6))/2 = -1
y = (7+2)/2 = 4.5
The midpoint is; (-1, 4.5).
2) The radius of the circle as described with centre (0, 0) that passes through the point (5, –3) is;
Radius = √((5-0)² + (-3-0)²)
Radius = √(25+9) = √34 = 5.8
3) Hence, the equation of a circle with centre (0, 0) that passes through the point (5, –3) is;
(x-5)² + (x-3)² = 5.8².
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In AUVW, m/U = (9x - 8)°, m/V = (2x + 2)°, and m/W = (3x + 4)º.
Find m/V.
Answers
Answer:
m∠V = 28°
Step-by-step explanation:
In ΔUVW:
m∠U = (9x - 8)°m∠V = (2x + 2)°m∠W = (3x + 4)°To find the measure of angle V, first find the value of x.
Interior angles of a triangle sum to 180°.
⇒ m∠U + m∠V + m∠W = 180°
⇒ (9x - 8) + (2x + 2) + (3x + 4) = 180
⇒ 9x + 2x + 3x - 8 + 2 + 4 = 180
⇒ 14x - 2 = 180
⇒ 14x = 182
⇒ x = 13
Substitute the found value of x into the expression for angle V:
⇒ m∠V = 2(13) + 2
⇒ m∠V = 26 + 2
⇒ m∠V = 28°
Therefore, the measure of angle V is 28°.
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1000 mL of D5W is infusing at 20 gtt/min (20 macrogtt/min). Drop factor: 10 gtt/m L.
How long will it take for the IV to infuse? (Express time in hours and minutes
Answers
It would take about 8 hours 20 minutes for the 1000 mL of D5W to infuse completely.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that the drop factor is 10 gtt/mL, hence:
Infuse rate = 20 gtt/min ÷ 10 gtt/mL = 2 mL/min
Time taken = 1000 mL / 2 mL per min = 500 min = 8 hours, 20 minutes.
It would take about 8 hours 20 minutes for the 1000 mL of D5W to infuse completely.
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Answer:
Step-by-step explanation:
900mL of RL is infusing at 80 gtt/min (80 macrodrops/min). Drop factor: 15 gtt/mL