How many liters of a 25 percent saline solution must be added to 3 liters of a 10 percent saline solution to obtain a 15 percent saline solution?
Final answer:
To achieve a 15 percent saline solution by mixing a 10 percent solution with a 25 percent solution, we calculate that we need to add 1.5 liters of the 25 percent saline solution to the initial 3 liters of the 10 percent solution.
Explanation:
To solve the problem, we need to calculate how much of a 25 percent saline solution should be added to 3 liters of a 10 percent saline solution to get a 15 percent saline solution. We'll use the concept of the conservation of mass of the solute (NaCl) and set up an equation to find the required volume of the 25 percent solution.
Let V be the volume of the 25 percent solution we need to add. The amount of NaCl in the 10 percent solution is (0.10)(3 L), and the amount of NaCl in the 25 percent solution is (0.25)(V). The resulting solution has a concentration of 15 percent, so the amount of NaCl in the final solution will be (0.15)(3 L + V).
Now we set up our equation based on the mass of NaCl being equal before and after the addition of the 25 percent solution:
(0.10)(3 L) + (0.25)(V) = (0.15)(3 L + V)
Solving this equation:
0.30 + 0.25V = 0.45 + 0.15V
0.25V - 0.15V = 0.45 - 0.30
0.10V = 0.15
V = 0.15 / 0.10
V = 1.5 L
Therefore, 1.5 liters of a 25 percent saline solution must be added to the initial 3 liters of a 10 percent solution to obtain a 15 percent saline solution.
A librarian randomly selects 25 returned books one day and finds that three of them were returned late. based on this sample, how many of the 410 returned books that day are likely to be late returns?
Write the standard form of the line that has a slope of - and y-intercept of -2. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
Solve for w. 3w – 10 = -w – 8 + 3w
Carmen is going to roll an 8-sided die 200 times. She predicts that she will roll a multiple of 4 twenty-five times. Based on the theoretical probability, which best describes Carmen’s prediction?
Answer:
Carmen's prediction is low because 200 times is 50.
Step-by-step explanation:
First of all we are going to define the sample space for this exercise.
The sample space is Ω = {1,2,3,4,5,6,7,8}
Given the event A : ''Roll an 8-sided die an get a multiple of 4''
The probability for the event A is
Because they are two numbers (4 and 8) over a total of eight numbers (1,2,3,4,5,6,7,8) that are multiple of 4.
Now, given the random variable X : ''Total of numbers multiples of 4 If she rolls
an 8-sided die 200 times''
X can be modeled as a Binomial random variable.
X ~ Bi (n,p)
X ~ Bi (200,)
In which n is the total times she rolls the 8-sided die and p is the success probability. We define a success as obtain a number multiple of 4.
The mean for this variable is
We answer that Carmen's prediction is low because 200 times is 50.
If tan x° = 11 divided by r and cos x° = r divided by s, what is the value of sin x°?
Answer:
[tex]sin x = \frac{11}{s}[/tex]
Step-by-step explanation:
[tex]Tan x = \frac{11}{r}[/tex]
[tex]Cos x = \frac{r}{s}[/tex]
Property : [tex]\frac{sin \theta}{cos \theta}=Tan \theta[/tex]
So, [tex]\frac{sinx}{cosx}=Tan x[/tex]
Substitute the values
[tex]\frac{sinx}{ \frac{r}{s}}=\frac{11}{r}[/tex]
[tex]sinx =\frac{11}{r} \times \frac{r}{s}[/tex]
[tex]sinx =\frac{11}{s}[/tex]
Hence the value of sin x° is [tex]\frac{11}{s}[/tex]
What is the perimeter of a square with a side length of 5x -8 and a bottom length of 3x of a square?
The required perimeter of the square is 48 units as of the given condition.
Given that,
The perimeter of a square with a side length of 5x -8 and a bottom length of 3x of a square is to be determined.
Perimeter is the measure of the figure on its circumference.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The length of all sides of the square is always remains equal,
5x - 8 = 3x
2x = 8
x = 4
Side length,
3x = 3(4) = 12
Now,
The perimeter of the square is 4-time sides,
Perimeter = 4 (12)
Perimeter = 48 units.
Thus, the required perimeter of the square is 48 units as of the given condition.
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STVU is an isosceles trapezoid. If SV = 3x + 1 and TU = x + 21, find the value of x.
Answer:
The value of x is 10.
Step-by-step explanation:
Given information: STVU is an isosceles trapezoid, SV = 3x + 1 and TU = x + 21.
According to the properties of isosceles trapezoid, then diagonals of an isosceles trapezoid are equal.
SV and TU are diagonals of the isosceles trapezoid, so
[tex]SV=TU[/tex]
[tex]3x+1=x+21[/tex]
Separate like terms.
[tex]3x-x=21-1[/tex]
[tex]2x=20[/tex]
Divide both sides by 2.
[tex]x=10[/tex]
Therefore the value of x is 10.
Rationalize the denominator of sqrt of -49 over (7-2i)-(4+9i)
An elevator descends into a mine shaft at the rate of 6 m/min. If the descendstarts from 20 meter above the ground level, how long will it take to reach - 340m?
what is the circumference of a circle with a radius of 39
A cylinder has a radius of 1 inch and height of 1 inch.
What is the approximate volume of a cylinder?
volume = PI * radius^2* height
3.14 x 1^2 x 1
v=3.14 cubic inches
A house cost $120,000 when it was purchased. The value of the house increases by 10% each year. Find the rate of growth each month and select the correct answer below.
Does any one know how to solve this -4n^2-2n=-6-7n-5n^2
Find the GCF. 18x 3 and 30x 5
A.
6x 5
B.
90x 3
C.
6x 3
D.
90x 5
Koch's kinky curve is created by starting with a straight segment and replacing it with four segments, each 1/3 as long as the original segment. So, at the second stage the curve has three bends. At the next stage, each segments replaced by four segments, and so on. How many bends does this curve have at the third stage? The fourth stage? The nth stage?
What price do farmers get for the peach crops? in the third week of June, a random sample of 40 farming regions gave a sample mean of $6.88 per basket. assume that the standard deviation is known to be $1.92 per basket. find a 90% confidence interval for the population mean price per basket that farmers in this region get for their peach crop.
A copy center offers its customers two different pricing plans for black and white photocopies of 8.5 in. by 11 in. pages. Customers can either pay $0.08 per page or pay $7.50 for a discount card that lowers the cost to $0.05 per page. Write and solve an equation to find the number of photocopies for which the cost of each plan is the same.
A) .08c .05c - 7.50; c = 250
B) . 05c .08c + 7.50; c = 22.5
C) 7.50 = .08c + 05c; c = 58
D) .08c = .05c + 7.50; c = 250
Answer: Writting the equation and solving it, the answer is option D) .08c = .05c + 7.50; c = 250
Solution:
If the number of photocopies is c
Plan 1: Customers can pay $0.08 per page
The cost with plan 1 is: C1=0.08c
Plan 2: Customers can pay $7.50 for a discount card that lowers the cost to $0.05 per page.
The cost with plan 2 is: C2=7.50+0.05c
We want to find the number of photocopies for which the cost of each plan is the same, then we equal the cost of each plan:
C1=C2
Replacing C1 by 0.08c and C2 by 7.50+0.05c
0.08c=7.50+0.05c
Solving this equation for c: Subtracting 0.05c both sides of the equation:
0.08c-0.05c=7.50+0.05c-0.05c
Subtracting:
0.03c=7.50
Dividing both sides of the equation by 0.03
0.03c/0.03=7.50/0.03
c=250
Answer:
.08c = .05c + 7.50; c = 250
Step-by-step explanation:
i got a 100 on the test trust!
In a given quadrilateral, each side is parallel to its opposite side and the diagonals are not perpendicular. What could it be? Check all that apply.
A. Square
B. Parallelogram
C. Rhombus
D. Rectangle
The answers are D:Rectangle, and B:Parallelogram
If 1,000 students take a test that has a mean of 40 minutes, a standard deviation of 8 minutes, and is normally distributed, how many would you expect would finish in less than 40 minutes?
Answer:
500
Step-by-step explanation:
It is expected that approximately 500 students would finish the test in less than 40 minutes.
To determine the number of students who would be expected to finish the test in less than 40 minutes, we can use the concept of the standard normal distribution and the z-score.
The z-score measures the number of standard deviations an individual data point is from the mean. In this case, we want to find the proportion of students who finish the test in less than 40 minutes, which corresponds to finding the area under the curve to the left of the mean.
Using the z-score formula:
z = (x - μ) / σ
where x is the value (40 minutes), μ is the mean (40 minutes), and σ is the standard deviation (8 minutes).
Substituting the values into the formula:
z = (40 - 40) / 8
z = 0
A z-score of 0 indicates that the value is exactly at the mean.
Since we are interested in the proportion of students finishing in less than 40 minutes, we need to find the area under the curve to the left of the mean, which is represented by a z-score of 0.
By referring to a standard normal distribution table or using a statistical software, we find that the proportion of students finishing in less than 40 minutes is approximately 0.5000.
To find the expected number of students, we multiply the proportion by the total number of students:
Expected number of students = 0.5000 * 1000 = 500
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Which situation involves descriptive statistics?
A) The food cans have a mean shelf life of 14 months.
B) The study estimates that 10% of the fish died as a result of the drought.
C) According to a poll, about 12% of our customers have returned at least one item. D) The sample indicates that the mean weight of all the boxes is 3.3 kg.
Answer:
The correct answer is:
A) The food cans have a mean shelf life of 14 months.
Just took this quiz and this was the correct answer.
Step-by-step explanation:
(05.02)
Two quantities are related, as shown in the table:
x
y
2 3
4 4
6 5
8 6
Which equation best represents the relationship?
y = 1 over 2 x + 2
y = 1 over 2 x + 1
y = x + 2 y = 2x + 1
first equation y=1/2x +2
x=2 = 1/2(2) +2 =1+2 =3
x=4 = 1/2(4)+2 = 2+2 =4
first equation is the answer
Answer:
[tex]y=\dfrac{1}{2}x+2[/tex]
A is correct
Step-by-step explanation:
Given: Table of x and y
x : 2 4 6 8
y : 3 4 5 6
Using two point find the slope:
(2,3) and (4,4)
[tex]Slope=\dfrac{4-3}{4-2}[/tex]
[tex]\text{Slope }=\dfrac{1}{2}[/tex]
Now we find slope using last two point
(6,5) and (8,6)
[tex]\text{Slope }=\dfrac{6-5}{8-6}[/tex]
[tex]\text{Slope }=\dfrac{1}{2}[/tex]
Slope is equal. Thus, The given relation is linear.
[tex]y-3=\dfrac{1}{2}(x-2)[/tex]
[tex]y=\dfrac{1}{2}x+2[/tex]
Hence, The relation represents a linear equation [tex]y=\dfrac{1}{2}x+2[/tex]
Evaluate the function f(x) = 4x -1 when x= -1 ..... f(-1) =___
To evaluate the function f(x) = 4x - 1 for x=-1, you first substitute -1 into the equation, then perform multiplication before subtraction as per the order of operations resulting in f(-1) = -5.
Explanation:To evaluate the function f(x) = 4x - 1 when x is -1, we simply replace the variable x in the equation with -1. The equation becomes f(-1) = 4(-1) - 1.
Now to perform the operations indicated in the equation, we should start with multiplication before subtraction according to the order of operations.
The multiplication of 4 and -1 gives -4 so the equation becomes f(-1) = -4 - 1.
Finally subtracting 1 from -4 gives -5. Therefore, f(-1) = -5.
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Justin is a software salesman. his base salary is $1500 , and he makes an additional $40 for every copy of english is fun he sells. let p represent his total pay (in dollars), and let n represent the number of copies of english is fun he sells. write an equation relating p to n . then use this equation to find his total pay if he sells 23 copies of english is fun.
Mark owns Siberian Husky sled dogs. He knows from data collected over the years that the weight of the dogs is a normal distribution. They have a mean weight of 52.5 lbs and a standard deviation of 2.4 lbs. What percentage of his dogs would you expect to have a weight between 47.7 lbs and 54.9 lbs?
To calculate the percentage of dogs with a weight between 47.7 lbs and 54.9 lbs, we need to use the properties of the normal distribution. We can expect that around 82.7% of Mark's dogs would have a weight within this range.
Explanation:To calculate the percentage of dogs with a weight between 47.7 lbs and 54.9 lbs, we need to use the properties of the normal distribution. We know that the mean weight is 52.5 lbs and the standard deviation is 2.4 lbs.
First, we need to standardize the lower and upper bounds of the weight range using the formula: z = (x - mean) / standard deviation. For the lower bound, z = (47.7 - 52.5) / 2.4 = -1.96. For the upper bound, z = (54.9 - 52.5) / 2.4 = 1.
Next, we can use a standard normal distribution table or calculator to find the percentage of values between -1.96 and 1. The percentage is approximately 82.7%. Therefore, we can expect that around 82.7% of Mark's dogs would have a weight between 47.7 lbs and 54.9 lbs.
Using the normal distribution, calculations of z-scores, and a z-table to determine probabilities, we can expect approximately 81.85% of Mark's Siberian Husky sled dogs to weigh between 47.7 lbs and 54.9 lbs.
Explanation:To determine the percentage of Mark's Siberian Husky sled dogs that weigh between 47.7 lbs and 54.9 lbs, we need to use the properties of the normal distribution. The mean weight of the dogs is 52.5 lbs and the standard deviation is 2.4 lbs. We can calculate the z-scores for 47.7 lbs and 54.9 lbs:
Z = (X - μ) / σ
For 47.7 lbs:
Z1 = (47.7 - 52.5) / 2.4 ≈ -2.0
For 54.9 lbs:
Z2 = (54.9 - 52.5) / 2.4 ≈ 1.0
Using a z-table or a statistical software, we can find the probabilities corresponding to these z-scores. The probability between Z1 and Z2 is the area under the curve in this range.
The probabilities associated with the z-scores are approximately 2.28% for Z1 (< -2.0) and 84.13% for Z2 (< 1.0). To find the percentage between Z1 and Z2, we subtract the smaller percentage from the larger one:
Percentage between 47.7 lbs and 54.9 lbs = 84.13% - 2.28% = 81.85%
Thus, we would expect that 81.85% of Mark's dogs have a weight between 47.7 lbs and 54.9 lbs.
Iliana was part of a group that was working on changing 0.4 repeated to a fraction. Each member of the group had a different answer. Which answer is correct?
Iliana was part of a group that was working on changing 0.4 repeated to a fraction. The answer is 2.25.
How to convert percent to fraction and decimal?Percentage counts the number compared to 100.
So, if we have a%, that means for each 100, there are 'a' parts. If we divide each of them with 100, we get:
For each 1, there are a/100 parts.
Iliana was part of a group that was working on changing 0.4 repeated to a fraction.
Each member of the group had a different answer.
Let x be 0.444444[tex]\bar 4[/tex]
So,
4 / 10 = 0.4
4 / 9 = 0.4444444...
9/ 4 = 2.25
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NEED HELP PLEASE!!!!
The diameter of a hydrogen atom is about 5×10^-15 meter. Suppose 8.4×10^8 hydrogen atoms were arranged side by side in a straight line. Multiply these numbers to find the length of this line of atoms. What is the length in scientific notation?
Select one:
a. 4.2×10^−2 meter
b. 0.042 meter
c. 42×10^−3 meter
d. 4.2×10^−3meter
Answer:
I'm a few years late, lol, but um the answer is 42 x [tex]10^{-3}[/tex] meters
For all the people who still need the answer.
Step-by-step explanation:
5 x [tex]10^{-11}[/tex] and 8.4 x [tex]10^{8}[/tex]
5 x 8.4 = 42 (multiply like terms)
[tex]10^{-11}[/tex] + [tex]10^{8}[/tex] = [tex]10^{-3}[/tex] (add the exponents)
42 x [tex]10^{-3}[/tex]
The length in scientific notation is [tex]42\times10^{-7[/tex] meter.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as [tex]1.56\times10^7[/tex].
Given that, the diameter of a hydrogen atom is about [tex]5\times10^{-15}[/tex] meter. Suppose 8.4×10⁸ hydrogen atoms were arranged side by side in a straight line.
Now, multiply the numbers
[tex]5\times10^{-15}[/tex]×8.4×10⁸
= [tex]42\times10^{-7[/tex] meter
Therefore, the length in scientific notation is [tex]42\times10^{-7[/tex] meter.
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At a certain time of the day, a tree 15m tall casts a shadow of 12m, while a second tree casts a shadow of 20m. how tall is that?
Students were asked to measure a string as part of a physics experiment. The actual length of the string was 7.35 cm long. Which of the following groups of data show measurements from the most accurate group and why?
7.35 cm, 7.82 cm, 7.12 cm, because one of the measurements is closest to the actual length.
6.95 cm, 6.93 cm, 6.97 cm, because these have the most agreement between the measurements.
7.32 cm, 7.37 cm, 7.39 cm, because this group’s measurements are closest to the actual length. - My answer
7.90 cm, 7.91 cm, 7.89 cm, because these have the most agreement between the measurements.
Graph the line y = -1/4x+2.
a. Sketch the line that is perpendicular to y = -1/4x+2 that passes through the point (5,5)
b. Write the equation of the perpendicular line.
c. Where do the lines intersect?