If the number of people arriving for treatment at an emergency room is modeled by a Poisson process with a mean of 5 people per hour, we can use this information to estimate the expected number of people who will arrive during a 45-minute period.
The Poisson distribution describes the probability of a certain number of events occurring in a fixed interval of time, given the average rate at which the events occur. In this case, the Poisson distribution can be used to estimate the number of people who will arrive during a 45-minute period, given that the mean arrival rate is 5 people per hour.
To calculate the expected number of arrivals, we first need to convert the 45-minute time period into hours. There are 60 minutes in an hour, so 45 minutes is equivalent to 0.75 hours.
Next, we can use the Poisson distribution formula, which is:
P(X = k) = (e^(-λ) * λ^k) / k!
where λ is the mean arrival rate (in this case, 5 people per hour), k is the number of arrivals we are interested in, and e is Euler's number (approximately 2.71828).
Expected number of arrivals = λ * t = 5 * 0.75 = 3.75
Therefore, we can expect approximately 3.75 people to arrive for treatment during a 45-minute period, assuming that the number of arrivals follows a Poisson distribution with a mean of 5 people per hour.
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9r subtract three fifths greater than 3 and 9 tenths
the baker needs 15 gallons of milk to make 80 chocolate pies for the community festival. To translate the phrase "9r subtract three fifths greater than 3 and 9 tenths" into an expression, we first need to understand what it's asking us to do.
"Three fifths greater than 3 and 9 tenths" means we need to add 3 and 9 tenths to three fifths of 3. Three fifths of 3 is 1.8 (since 3/5 * 3 = 9/5 = 1.8), so we can write:
3 + 9/10 + 1.8
We can simplify this to a single mixed number by adding the whole numbers and the fractions separately:
3 + 1 + 8/10 + 8/5
= 4 + 1 3/5
= 5 3/5
So "three fifths greater than 3 and 9 tenths" is equal to 5 3/5.
Now we can subtract this value from 9r:
9r - 5 3/5
We can simplify this expression further by converting 5 3/5 to a fraction with a common denominator of 5:
9r - 5 3/5 = 9r - (28/5) = (45/5)r - (28/5) = (9r - 28) / 5
So the final expression is:
(9r - 28) / 5
In summary, "9r subtract three fifths greater than 3 and 9 tenths" can be translated to the expression (9r - 28) / 5. This expression represents a quantity that is 9 times "r" minus 5 3/5. We can simplify this expression further by converting the mixed number to an improper fraction and combining the terms, as shown above.
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The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 0 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 10. There are two dots above 1 and 4. There are three dots above 2 and 5. There are 4 dots above 3.
Which of the following is the best measure of center for the data, and what is its value?
The median is the best measure of center, and it equals 3.5.
The median is the best measure of center, and it equals 3.
The mean is the best measure of center, and it equals 3.
The mean is the best measure of center, and it equals 3.5.
Therefore, the best measure of center for this data is the median, and its value is 3.
What is median?The median is a measure of central tendency that represents the middle value of a set of data when it is arranged in order from lowest to highest (or highest to lowest). It is the value that divides the data set into two equal halves, with half of the values above and half below the median.
Here,
The median is the best measure of center for this data because it is skewed and not symmetrical. The value of the median can be found by ordering the data from smallest to largest: 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 10. The median is the middle value, which is 3.
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1. Which of the following describes the line of best fit for a set of data?
A. a line that goes through two representative points from the data set
B. a line that goes through every point in the data set
C. a line that fits the whole data set the best
D. a line that has half the points above it and half the points below it
2. Determine the line of best fit to predict y from x for the following data. Round to three decimal places as needed.
x 5 7 8 3 2
y 7 9 9 7 6
(1 point)
A. x=−8.722+1.806y
B. y=0.5+5.1x
C. y=5.1+0.5x
D. y=1.806−8.722x
3. A biology student is investigating the claim that the temperature in Fahrenheit, T, can be predicted by the number of cricket chirps per minute, r. She has collected the data in the table below. Find the equation for the line of best fit. Round to three decimal places as needed.
r 72 73 76 92 115 130 131 141
T 55 58 54 62 64 71 70 69
A. T=39.6+0.225r
B. T=0.225+39.6r
C. r=4.066−151.9T
D. r=−151.9+4.066T
4. Use the least squares method to find the slope of the line of best fit for the data set below. Round to three decimal places.
x −6 −4 −1 4 5
y 11 9 2 −7 -9
A. −0.531
B. 0.451
C. −1.873
D. 0.237
5. Barrett used the least squares method for the following data set and says that the slope of the line of best fit is −0.236. Wallace, without looking at Barrett's work or performing any calculations, says that Barrett's answer is wrong. How does Wallace know that Barrett is incorrect?
d 0.1 0.2 0.8 1.2 1.5 2.4 3.1 3.1
s 14 10 35 48 57 84 110 108
A. From the table, it is clear that the s-intercept would be positive. Barrett's line would have a negative intercept because the slope is negative.
B. From the table, it can be seen that there is a positive relationship, so the slope of the line of best fit must be positive.
C. The data in the table has an exponential relationship, so there would not be a line of best fit.
D. The data in the table has a quadratic relationship, so there would not be a line of best fit.
1)
A line that fits the whole data set the best.
2)
The line of best fit is y = 5.1 + 0.5x
3)
The equation of best fit is T = 39.6 + 0.225r
4)
The slope of the line of best fit is -0.531.
5)
From the table, it is clear that the s-intercept would be positive.
Barrett's line would have a negative intercept because the slope is negative.
What is line of best fit?The line of best fit is a straight line that represents the trend or pattern in a set of data. It is also known as the regression line.
This line is determined by analyzing the data and finding the line that comes closest to all of the points in the set. T
We have,
1)
The line of best fit is the line that fits the whole data set the best.
It's the line that comes closest to all of the points in the data set, and it can be used to make predictions or to describe the relationship between the two variables in the data set.
2)
To find the line of best fit, we need to calculate the slope and y-intercept of the line.
Using the least squares method, we find that the slope is 0.5 and the y-intercept is 5.1.
Therefore, the equation of the line of best fit to predict y from x is y = 5.1 + 0.5x.
3)
To find the equation of the line of best fit, we need to calculate the slope and y-intercept of the line.
Using the least squares method, we find that the slope is 0.225 and the y-intercept is 39.6.
Therefore, the equation of the line of best fit to predict T from r is T = 39.6 + 0.225r.
4)
To find the slope of the line of best fit, we need to calculate the covariance and variance of the x and y variables.
Using the least squares method, we find that the slope is -0.531.
5)
From the table, we can see that the s-intercept (the value of s when d is zero) would be positive.
Therefore, a line with a negative slope would have a negative y-intercept, which is not possible.
This means that Barrett's answer is incorrect, and the slope of the line of best fit must be positive.
Thus,
C. a line that fits the whole data set the best.
C. y = 5.1 + 0.5x
A. T = 39.6 + 0.225r
A. -0.531
A. From the table, it is clear that the s-intercept would be positive.
Barrett's line would have a negative intercept because the slope is negative.
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Which of these is a pythagorean triple?
Responses
9, 40, 41
7, 26, 89
1, 2, 3
36, 48, 62
Answer:
The first one
Step-by-step explanation:
Use the pythagoras theorem=a ^2+b^2 =c^2
Use a is 9 b is 40 because the largest value is always the hypotenuse and the hypotenuse is always c.
so you do 9 squared add 40 squared to find c squared.
Square root the answer and you get 41 so it is a pythagoras triple
how many ways are there to put beads of different colors on the vertices of a cube, if rotations of the cube (but not reflections) are considered the same?
There are 70 ways to put 8 beads of different colors on the vertices of a cube, if rotations of the cube (but not reflections) are considered the same.
Let us start by determining the number of ways to put 8 beads of different colors on the vertices of a cube without any restrictions.
We can choose the first color in 8 ways, the second color in 7 ways, the third color in 6 ways, and so on. Therefore, the total number of ways is 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320.
However, rotations of the cube (but not reflections) are considered the same. There are 24 such rotations. Specifically, there are 4 rotations that preserve the orientation of the cube (i.e., rotations by 0°, 90°, 180°, and 270° around an axis passing through the centers of opposite faces), and there are 6 pairs of rotations that exchange the two sets of 4 vertices that are symmetrically positioned with respect to the centers of opposite faces.
Each of these 24 rotations maps one arrangement of the beads to another.
Thus, we must count the number of arrangements of the beads that are mapped to each other by each rotation. If we do this for each rotation, we get a total of (40,320/24) = 1680 distinct arrangements of the beads.
If we now take any of these 1680 arrangements and apply any of the 24 rotations, we will get an arrangement that we have already counted. Therefore, there are (1680/24) = 70 arrangements of the beads that are distinct when rotations (but not reflections) are considered the same.
In other words, there are 70 ways to put 8 beads of different colors on the vertices of a cube, if reflections are not considered distinct.
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What is the value of the expression 16 + 4 − (5 x 2) + 2? (2 points) a 10 b 12 c 14 d 18
Answer: b. 12
Step-by-step explanation:
16 + 4 − (5 x 2) + 2
= 16 + 4 - 10 + 2
= 20 - 12
= 12
Answer:
Step-by-step explanation:
8
A Venn Diagram comparing swimmers and weightlifters is shown below:
An image of a Venn diagram is shown labeled swimmers and weightlifters. The label in the swimmer's portion is B. The label in the intersection of the two circles is A. The label in the weightlifter's portion is C. The label outside the circles is D.
Which area represents elements contained in open parentheses swimmers intersection weightlifters close parentheses complement?
A
D
B, C, D
A, B, C
Answer:
The area that represents elements contained in the complement of the intersection of swimmers and weightlifters is the region outside the circles labeled as D. Therefore, the answer is D.
Step-by-step explanation:
chatgpt
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the standard error tells multiple choice how often the examiner made an error. how often the experimental variable was tested. the relationship between the control and test groups. whether or not the research has been published in a scientific journal. how uncertain a particular value is.
Answer:the jimboluis
Step-by-step explanation:
that’s it
DUE TOMORROW WELL WRITTEN ANSWERS ONLY!!!!!!!!
Sketch a graph of g given by g(Θ) = sin (Θ) + 3.
Step-by-step explanation:
2 pictures are attached
sin waves are used in many medical devices like to measure heart beats
The student enrollement of a high school was 1350 in 2012 and increases 9% each year. What is the estimated enrollment in 2022
The estimated enrollment of a high school in 2022 is approximately 2775 students.
To calculate the estimated enrollment in 2022, we need to use the formula for compound interest:
A =[tex]P(1 + r)^t[/tex]
where:
A = final amount (enrollment in 2022)
P = initial amount (enrollment in 2012)
r = annual interest rate (increase rate)
t = number of years (10)
We know that P = 1350 and r = 0.09 (9%). We can plug these values into the formula:
A = [tex]1350(1 + 0.09)^{10[/tex]
A = [tex]1350(1.09)^{10[/tex]
A = 2774.92
Therefore, the estimated enrollment in 2022 is approximately 2775 students.
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the original triangle and its projection are similar. what is the missing length n on the projection?
The missing length n on the projection is y.
The original triangle and its projection are similar if the three angles are the same. In this case, the missing length n on the projection can be determined by applying the concept of similarity. First, we need to find out the ratio between the lengths of the original triangle and its projection. For example, if the length of the side of the original triangle is x, and the length of its projection is y, the ratio between them is x/y.
Then, using the similar triangles theorem, we can state that the ratio between the other lengths of the original triangle and its projection is the same. This means that if we know one of the lengths, we can calculate the other one. Therefore, if the length of the side of the original triangle is x, and the ratio is x/y, then the length of the projection must be y.
Finally, we can calculate the missing length n on the projection. We know that the length of the projection is y, and we can use the ratio x/y to calculate n. Therefore, n = x*y/x, which is equal to y.
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What are the coordinates of Point S after a dilation with the center at the origin and a scale factor of 1/2?
A (2,-1)
B (4,-2)
C (8,-4)
D (16,-8)
Therefore, the coordinates of point S after a dilation with the center at the origin and scale factor of 1/2 are (4, -2).
What is factor?In mathematics, a factor is a number or expression that divides another number or expression without leaving a remainder. For example, 2 and 3 are factors of 6 because 6 can be divided by 2 and 3 without leaving a remainder. In algebra, factors are often used to factorize an expression, which involves breaking it down into its constituent factors. This is a useful technique for simplifying algebraic expressions, solving equations, and finding common factors in polynomials. Factors are also important in number theory, where they are used to study properties of integers and prime numbers.
Given by the question.
To perform a dilation with the center at the origin and scale factor of 1/2, we need to multiply the coordinates of the point by the scale factor.
The coordinates of point S are (8, -4).
After dilation, the x-coordinate will be 1/2 of 8, and the y-coordinate will be 1/2 of -4:
x' = (1/2) * 8 = 4
y' = (1/2) * (-4) = -2
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The prism below is made of cubes which measure 1/2 of an inch on one side. What is the volume?
Answer: 24 I think if not my bad
Step-by-step explanation:
If I recall right you just have to count them
What whole number makes the equation true? x 1/2=8/2
x = 8 is the whole number that solves the equation, making it true. A whole number is a number that does not have any fractions or decimals.
It is a positive integer or zero, such as 0, 1, 2, 3, 4, 5, and so on. Whole numbers are used to count objects or things that can be represented as a whole, such as people, cars, apples, and so on.
Whole numbers are closed under addition, subtraction, and multiplication operations, which means that if you add, subtract or multiply two whole numbers, the result will always be another whole number. However, whole numbers are not closed under division operation, which means that when dividing two whole numbers, the result may not be a whole number.
To solve for x in the equation:
x 1/2=8/2
We can isolate x by multiplying both sides by the reciprocal of 1/2, which is 2/1:
x 1/2 * 2/1 = 8/2 * 2/1
Simplifying the left side, we get:
x = 16/2
x = 8
Therefore, the whole number that makes the equation true is x = 8.
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In this polygon, all angles are right angles. What is the area of this polygon? Enter your answer in the box. ___ft² 23 ft 9 ft 26 ft 13 ft
The area of this polygon is equal to 428 ft².
How to calculate the area of this polygon?In order to calculate the area of this polygon, we would have to determine the total area of the two different parts of the given composite figure.
Therefore, the total area of this polygon is the sum of the area of the each geometric figure (rectangle):
Area of rectangle A = Length × Width
Area of rectangle A = 13 × 26
Area of rectangle A = 338 ft²
Area of rectangle B = 9 × (23 - 13)
Area of rectangle B = 9 × 10
Area of rectangle B = 90 ft²
Therefore, total area is given by:
Total area = 90 + 338
Total area = 428 ft²
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A triangle has angle measures 122° and 32°. What is the measure of the third angle?
Answer:
26°
Step-by-step explanation:
We know
A triangle is 180°
A triangle has Angle measures 122° and 32°
What is the measure of the third angle?
We take
180 - (122 + 32) = 26°
So, the measure of the third angle is 26°
Diego used unit cubes to make a rectangular prism what is the volume of the prism
can we see a picture or equation
Laura has a strip of ribbon 1 m long. How many one thirds strips can be cut from it
From the given information provided, Laura can cut 3 one-thirds strips from the 1 meter long ribbon.
If Laura has a strip of ribbon 1 meter long, we need to find out how many one-thirds strips can be cut from it.
To do this, we need to divide the length of the ribbon by the length of each one-third strip:
Number of one-thirds strips = Length of ribbon / Length of one-third strip
The length of each one-third strip is 1/3 meters, since one-third of a meter is required to make each strip.
So we can substitute these values into the formula:
Number of one-thirds strips = 1 meter / (1/3 meter)
Number of one-thirds strips = 1 meter x (3/1)
Number of one-thirds strips = 3
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a square has a side length of 3 1/2 inches. the scale factor of 2/3 was used to create a new square. what is the side length of the new square
Answer:
Step-by-step explanation:
The side length of the original square is 3 1/2 inches.
To find the side length of the new square, we need to apply the scale factor of 2/3 to the original side length.
To do this, we multiply the original side length by the scale factor:
(2/3) x 3 1/2
To multiply a fraction by a whole number, we can first convert the whole number to a fraction with a denominator of 1:
(2/3) x (7/2)
To multiply two fractions, we can multiply their numerators together and their denominators together:
(2/3) x (7/2) = (2 x 7) / (3 x 2) = 14/6
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:
14/6 = (2 x 7) / (2 x 3) = 7/3
Therefore, the side length of the new square is 7/3 inches.
Question 7(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The table shows the number of goals made by two hockey players.
Player A Player B
1, 4, 5, 1, 2, 4, 5, 5, 11 1, 2, 1, 3, 2, 3, 4, 1, 8
Find the best measure of variability for the data and determine which player was more consistent.
Player A is the most consistent, with a range of 10.
Player B is the most consistent, with a range of 7.
Player A is the most consistent, with an IQR of 3.5.
Player B is the most consistent, with an IQR of 2.5.
Player B is the most consistent, with a range of 7.
The best measure of variability for this data would be the range, which is the difference between the maximum and minimum values.
For Player A: Range = 11 - 1 = 10
For Player B: Range = 8 - 1 = 7
Therefore, Player A has a higher range and thus more variability in their data. So, the correct answer is:
Player B is the most consistent, with a range of 7.
What is variability?
Variability refers to the degree of variation or diversity in a set of data or observations. It is a measure of how spread out the data points are from the central tendency, such as the mean or median.
What is range?
Range is a statistical measure that describes the difference between the maximum and minimum values in a dataset. It is calculated by subtracting the smallest value from the largest value.
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Answer:
(d) Player B is the most consistent, with an IQR of 2.5.
Step-by-step explanation:
Given these numbers of goals, you want to know which player is most consistent, and the best measure of that.
A: {1, 1, 2, 4, 4, 5, 5, 5, 11}B: {1, 1, 1, 2, 2, 3, 3, 4, 8}Variability measuresThe variability measures we're to consider here are range and IQR.
The range is the difference between the maximum and the minimum:
A: 11 -1 = 10B: 8 -1 = 7The smaller range indicates player B is more consistent.
The IQR is the difference between the upper and lower quartiles. In each of these 9-element data sets, those quartiles will be the average of elements 2 and 3, and the average of elements 7 and 8 when the data is in order.
A: ((5+5) -(1+2))/2 = 3.5B: ((3+4) -(1+1))/2 = 2.5The smaller IQR indicates player B is more consistent.
OutliersIn each case, the maximum data value is more than 1.5 times the IQR above the upper quartile value, so can be considered an outlier. The outlier has a direct effect on range, so range is not a good measure of variability.
Player B is the most consistent, with an IQR of 2.5, choice D.
__
Additional comment
If the outlier is excluded from each data set, the IQR for player A remains the same at 3.5. The IQR for player B drops to 2.0.
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Which expression is equivalent to 8x − 4x + 3?
Answer:
4x+3
Step-by-step explanation:
Answer:
A. 4x+3
Step-by-step explanation:
Combining like terms 8x and −4x
Will give you the asnwer to 4x
which will give you 4x + 3
Determine the magnitude of the force P for which the resultant of the four forces acts on the rim of the plate. Given: F= 320 N. 30° 120 N 80 N P x 250 mm F 7 The magnitude of the force P is N.
The magnitude of the force P is 464.77 N.
STEP BY STEP EXPLANATION:
Step 1: Break down each force into components.
F = 320 N at 30°
Fx = F * cos(30°) = 320 * cos(30°) = 277.13 N (horizontal)
Fy = F * sin(30°) = 320 * sin(30°) = 160 N (vertical)
120 N is in the horizontal direction (assume positive x-direction):
Fx2 = 120 N
80 N is in the vertical direction (assume positive y-direction):
Fy2 = 80 N
Step 2: Sum up the components.
Total horizontal force (Fxtotal) = Fx + Fx2
= 277.13 + 120 = 397.13 N
Total vertical force (Fytotal) = Fy + Fy2
= 160 + 80 = 240 N
Step 3: Find the magnitude of the resultant force.
Resultant force (R) = sqrt(Fxtotal^2 + Fytotal^2)
= sqrt(397.13^2 + 240^2) = 464.77 N
Step 4: Determine the magnitude of the force P.
Since the resultant of the four forces should act on the rim of the plate, it means that the force P should be equal in magnitude and opposite in direction to the resultant force R.
The magnitude of the force P is 464.77 N.
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Mai poured 2. 6 liters of water into a partially filled pitcher. The pitcher then contained 10. 4 liters. How much water did the pitcher contain before Mai added more water?
The amount of water that the pitcher contained before Mai added more water was 7.8 liters.
Let x be the amount of water the pitcher contained before Mai added more water.
When Mai poured 2.6 liters of water, the total amount of water in the pitcher became x + 2.6 liters.
According to the problem, the pitcher then contained 10.4 liters of water. Therefore, we can write:
x + 2.6 = 10.4
Subtracting 2.6 from both sides, we get:
x = 7.8
Therefore, the pitcher contained 7.8 liters of water before Mai added more water.
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What is the simplest form of 8(5k+7)−10(6k−7)
The simplest form of the given expression is -20k + 126.
To find the simplest form of the expression 8(5k+7)−10(6k−7), follow these steps:
1. Distribute the numbers outside the parentheses to the terms inside the parentheses:
8 × 5k + 8 × 7 - 10 × 6k + 10 × 7
2. Perform the multiplication:
40k + 56 - 60k + 70
3. Combine like terms (terms with the same variable and exponent):
(40k - 60k) + (56 + 70)
4. Simplify the expression by performing the subtraction and addition:
-20k + 126
The simplest form of the given expression is -20k + 126.
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suppose that you have a collection of n spins, each of which points up or down with equal probability. what is the probability that exactly n of them will point up? give both an exact expression and an approximation valid for large n. are there any additional conditions on n for your large n approximations to be valid?
The probability that exactly n of the collection of n spins will point up is given by the Binomial distribution. The Binomial distribution is a discrete probability distribution that models the number of successes (x) in a given number of trials (n) with a fixed probability of success (p) on each trial.
In this case, we have n trials, with a fixed probability of success of 0.5 (since each spin can point up or down with equal probability). The number of successes we're interested in is n. Thus, the probability of n successes is given by:P(X = n) = (nCn)(0.5)^n = 0.5^nwhere nCn is the number of ways to choose n items from n items, which is 1.Approximation for large n:When n is large, we can use the normal approximation to the Binomial distribution.
Specifically, we use the Normal distribution with mean np and variance np(1-p). In this case, p = 0.5, so the mean and variance are both (0.5)n. Therefore, the probability of n successes is approximately:P(X = n) ≈ φ(x) = (1/σ√2π)exp[-(x-μ)^2/2σ^2]where μ = np = (0.5)n and σ^2 = np(1-p) = (0.5)n(0.5) = (0.25)n.
Plugging these values in, we get:P(X = n) ≈ φ(x) = (1/σ√2π)exp[-(n/2n)^2/2(0.25)n] = (1/σ√2π)exp[-(1/8n)] = (1/√2πn)exp[-(1/8n)]Note that for the large n approximation to be valid, we require np and n(1-p) to be at least 10. In this case, np = (0.5)n and n(1-p) = (0.5)n, so this condition is satisfied for any n.
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Find the area of the shaded area of the figure.
The dimly lit area is 58 square units in size. The area of a two - dimensional figure is the area that its perimeter encloses.
Area – what is it?The area is the space occupied by any two-dimensional figure on a plane. A rectangle's area is how much space it occupies in a the double plane.
The shaded area's size will be determined using the formula
10 units multiplied by 7 units gives a total area of 70 units.
Gap size equals 2 units multiplied by 6 units, or 12 units.
The shaded figure's area is 70 units divided by 12 units, or 58 units.
As a result, 58 square units make up the area of shaded zone.
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what is the probability that the person selected will be someone whose response is never and who is a woman?
The probability that the person selected will be someone whose response is never and who is a woman is 3/7.
The probability that the person selected will be someone whose response is never and who is a woman can be found by using conditional probability.What is conditional probability?Conditional probability is the likelihood of an event occurring given that another event has already occurred. The probability of event A happening given that event B has already occurred is known as conditional probability.Mathematically, the formula for conditional probability is:P(A|B) = P(A ∩ B) / P(B)Where,P(A|B) represents the probability of event A given that event B has already occurred.P(A ∩ B) represents the probability of both A and B occurring.P(B) represents the probability of event B occurring.The given scenario states that the person selected should have two attributes: the response never and the gender woman. Let A be the event that the person selected has a response never and B be the event that the person selected is a woman. Therefore, we need to find the probability of event A given event B.P(A|B) = P(A ∩ B) / P(B)Therefore, we need to find the probability of both A and B occurring and the probability of event B occurring.P(B) = 70/120P(B) = 7/12There are 50 women in the group. The number of women who have never responded is 30. Therefore,P(A ∩ B) = 30/120P(A ∩ B) = 1/4Therefore,P(A|B) = P(A ∩ B) / P(B)P(A|B) = 1/4 / 7/12P(A|B) = 3/7The probability that the person selected will be someone whose response is never and who is a woman is 3/7.
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A pharmacist has an 18% alcohol solution and a 40% alcohol solution. How much of each should he mix together to make 10L of a 20% alcohol solution? Pls help
0.18x + 4 - 0.40x = 2
-0.22x = -2
x = 9.09
Therefore, the pharmacist should mix 9.09 liters of 18% alcohol solution and 0.91 liters of 40% alcohol solution to make 10 liters of 20% alcohol solution.
[tex]x=\textit{Liters of solution at 18\%}\\\\ ~~~~~~ 18\%~of~x\implies \cfrac{18}{100}(x)\implies 0.18 (x) \\\\\\ y=\textit{Liters of solution at 40\%}\\\\ ~~~~~~ 40\%~of~y\implies \cfrac{40}{100}(y)\implies 0.4 (y) \\\\\\ \textit{10 Liters of solution at 20\%}\\\\ ~~~~~~ 20\%~of~10\implies \cfrac{20}{100}(10)\implies 2 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{lcccl} &\stackrel{Liters}{quantity}&\stackrel{\textit{\% of Liters that is}}{\textit{alcohol only}}&\stackrel{\textit{Liters of}}{\textit{alcohol only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&x&0.18&0.18x\\ \textit{2nd Sol'n}&y&0.4&0.4y\\ \cline{2-4}&\\ mixture&10&0.2&2 \end{array}~\hfill \begin{cases} x + y = 10\\\\ 0.18x+0.4y=2 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=10\implies y=10-x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation from above}}{0.18x+0.4(10-x)=2}\implies 0.18x+4-0.40x=2 \\\\\\ -0.22x+4=2\implies -0.22x=-2\implies x=\cfrac{-2}{-0.22}\implies \boxed{x\approx 9.09} \\\\\\ \stackrel{\textit{since we know that}}{y=10-x}\implies y\approx 10-9.09\implies \boxed{y\approx 0.91}[/tex]
a rectangular container 12 cm long, 8 cm wide, and 36 cm high was one - third full. when some syrup from a bottle was poured into the container, it got half full. find the volume of the syrup poured from the bottle into the container in millimeters
when some syrup from a bottle was poured into the container, it got half full. The volume of the syrup poured from the bottle into the container in millimeters is 576,000 cubic millimeters.
Since for solving the problem we need to find the volume of the container in millimeters. We are given the length, breadth, and height which are 12 cm,8 cm, and 36 cm.Now the volume of the container is:
V = l x w x h = 12 cm x 8 cm x 36 cm = 3,456 cubic cm. Now we convert the above result into millimeters by multiplying by 1,000, so we get V= 3456 x 1000= 34560000 cubic mm
Now to find the volume of the syrup that was poured into the container, we know that the container was one-third full before the syrup was added and half full after the syrup was added.onsidering x to be the volume of the syrup poured from the bottle into a container and n to be the volume of the syrup in the container after it was added:
1/3(V) + x = 1/2(V), where v is the volume of the container in millimeters, so we substitute the calculated value of the volume we get :
=>1/3(V) + x = 1/2(V)
=>x = 1/2(V) - 1/3(V)
=> x = 1/6(V) = 1/6(3,456,000) = 576,000 cubic mm
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planets x, y and z take $360$, $450$ and $540$ days, respectively, to rotate around the same sun. if the three planets are lined up in a ray having the sun as its endpoint, what is the minimum positive number of days before they are all in the exact same locations again?
By using LCM, we find that the three planets x, y and z will be in the exact same locations again after $5400$ days.
To find the minimum positive number of days before the planets are all in the exact same locations again, we need to find the least common multiple (LCM) of the three given periods of rotation.
The prime factorization of each of the given periods of rotation is as follows
$360 =[tex]2^3 \cdot 3^2 \cdot 5$[/tex]
$450 =[tex]2 \cdot 3^2 \cdot 5^2$[/tex]
$540 =[tex]2^2 \cdot 3^3 \cdot 5$[/tex]
To find the LCM, we need to take the highest power of each prime factor that appears in any of the three factorizations. So the LCM is:
[tex]$LCM = 2^3 \cdot 3^3 \cdot 5^2 = 2^3 \cdot 27 \cdot 25 = 5400$[/tex]
Therefore, the three planets will be in the exact same locations again after $5400$ days.
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