Answer:
n > 10
Step-by-step explanation:
2n > 20
2n/2 > 20/2
n > 10
A certain small country has $10 billion in paper currency in circulation, and each day $50 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Since both old bills and new bills will come into the banks while the new currency is gradually introduced, we will need to solve a differential equation to track the amount of new currency in circulation at a given time. Let x (t) denote the amount of new currency, in billions of $, in circulation after t days. We've shown that new currency is introduced at the rate 10 - x (t) / 10 0.05, which simplifies to 0.005 (10 - x (t)). This justifies that x (t) satisfies the differential equation dx / dt = 0.005 (10 - x). (a) Solve the differential equation to find x (t). (b) At what time t will new bills make up 90% of the currency in circulation?
(a) The solution to the differential equation isx(t) = 10(1 - e^(-0.005t))
To solve the differential equation dx/dt = 0.005(10 - x), we can use separation of variables:
dx / (10 - x) = 0.005 dt
Integrating both sides:
-ln|10 - x| = 0.005t + C
where C is the constant of integration. Solving for x:
|10 - x| = e^(-0.005t - C)
Since x cannot be negative, we can drop the absolute value sign and solve for C using the initial condition that x(0) = 0:
C = -ln(10)
Therefore, the solution to the differential equation is:
x(t) = 10 - e^(-0.005t - ln(10))
Simplifying:
x(t) = 10(1 - e^(-0.005t))
(b) New bills will make up 90% of the currency in circulation after approximately 461 days.
We want to find the value of t such that x(t) = 0.9(10) = 9. Plugging this into our solution from part (a):
9 = 10(1 - e^(-0.005t))
Dividing both sides by 10 and taking the natural logarithm:
ln(0.1) = -0.005t
Solving for t:
t = 200 ln(10) = 460.51
Therefore, new bills will make up 90% of the currency in circulation after approximately 461 days.
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Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = 9x3, [1, 2] Yes, the Mean Value Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because fis not differentiable in the open interval (a, b). None of the above. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = - w f(b) – f(a) 2. (Enter your answers as a comma-separated list. If the Mean Value Theorem cannot Ent b - a be applied, enter NA.) C=
Answer: Yes, the Mean Value Theorem can be applied to f(x) = 9x^3 on the closed interval [1, 2].
To find all values of c in the open interval (1, 2) such that f'(c) = (f(b) - f(a))/(b - a), we first find the derivative of f(x):
f'(x) = 27x^2
Then, we can use the Mean Value Theorem to find a value c in the open interval (1, 2) such that:
f'(c) = (f(2) - f(1))/(2 - 1)
27c^2 = 9(2^3 - 1^3)
27c^2 = 45
c^2 = 5/3
c = +/- sqrt(5/3)
Therefore, the values of c in the open interval (1, 2) such that f'(c) = (f(b) - f(a))/(b - a) are:
c = sqrt(5/3), -sqrt(5/3)
Note that these values are not in the closed interval [1, 2], as they are not between 1 and 2, but they are in the open interval (1, 2).
Step-by-step explanation:
Help I need help with this question
Answer:
3
Step-by-step explanation:
Interval 3 ≤ x ≤ 5 means all f(x) values from x= 3 inclusive to x = 5 inclusive
At x = 3 f(x) = 2
At x = 5, f(x) = 8
Change in f(x) = Δf(x) = 8 - 2 = 6
Change in x = Δx = 5 - 3 = 2
Average rate of change
= Δf(x)/Δx
= 6/2
= 3
Find an expression that is equivalent to (a - b) ^ 3
An expression equivalent to (a - b)³ is a³ - 3a²b + 3ab² - b³.
What other expressions are the same as 2 5?The fractions 4/10, 6/15, 8/20, etc. are identical to 2/5. In the reduced form, equivalent fractions have the same value. Explanation: When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number.
One way to expand (a - b)³ is to use the binomial formula:
(a - b)³ = C(3,0) * a³ * (-b)^0 + C(3,1) * a² * (-b) + C(3,2) * a * (-b)² + C(3,3) * a * (-b)³
where C(n,k) denotes the number of ways there are to select k objects from a set of n objects, and "n choose k" is the binomial coefficient.
Simplifying the above expression, we get:
(a-b)³ = a³-3a²b+3ab²-b³.
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Which of the following examples satisfy the hypotheses of the Extreme Value Theorem on the given interval?
A. f(x)=1/x on −10≤x≤10
B. g(x)=6x^2+3 on 0≤x≤4
C. k(x)={3x^2+9 for 0≤x<2, 12x for 2≤x≤10} on 0≤x≤10
D. h(x)=(e^x)/x on 2≤x≤16
E. m(x)=6x^3+x+1 on −4
The function that satisfies the hypotheses of the Extreme Value Theorem on the given interval is given by
B. g(x)=6x^2+3 on 0≤x≤4
D. f(x) = (e^x)/x for 2 ≤ x ≤ 16.
Step 1: State the Extreme Value Theorem
The Extreme Value Theorem states that if a function is continuous on a closed interval [a,b], then the function must have a maximum and a minimum on the interval.
Step 2: Check for continuity and closed interval for each function
A. f(x) = 1/x on −10 ≤ x ≤ 10
The function f(x) = 1/x is continuous on the interval (-10, 0) and (0, 10).
However, since the interval given is [−10, 10], we see that the function is not continuous over the closed interval.
Hence the function does not satisfy the hypotheses of the Extreme Value Theorem.
B. g(x) = 6x^2+3 on 0 ≤ x ≤ 4
The function g(x) is continuous on the interval [0, 4].
Therefore, this function satisfies the hypotheses of the Extreme Value Theorem on the given interval.
C. k(x) = {3x^2+9 for 0 ≤ x < 2, 12x for 2 ≤ x ≤ 10} on 0 ≤ x ≤ 10
The function k(x) is continuous on the interval [0, 2) and (2, 10]. H
However, since the interval given is [0, 10], we see that the function is not continuous over the closed interval.
Hence the function does not satisfy the hypotheses of the Extreme Value Theorem.
D. h(x) = (e^x)/x for 2 ≤ x ≤ 16The function h(x) is continuous on the interval [2, 16].
Therefore, this function satisfies the hypotheses of the Extreme Value Theorem on the given interval.
E. m(x) = 6x^3+x+1 on −4 < x < 3
The function m(x) is continuous on the interval (-4, 3).
However, since the interval given is [-4, ∞), we see that the function is not continuous over the closed interval.
Hence the function does not satisfy the hypotheses of the Extreme Value Theorem.
Therefore, the only function that satisfies the hypotheses of the Extreme Value Theorem on the given interval is given by
B. g(x)=6x^2+3 on 0≤x≤4
D. f(x) = (e^x)/x for 2 ≤ x ≤ 16
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The bakers at healthy bakery can make 190 bagels in 10 hours. How many bagels can they make in 17 hours? What is the rate per hour?
The cookers at healthy Bakery could make 323 bagels in 17 hours, and their rate is 19 bagels according to hour.
To find out how many bagels the cookers could make in 17 hours, we will use the unitary method, which involves finding the rate at which the cookers can make bagels and additionally multiplying that price through the wide variety of hours labored.
Let the rate at which the cookers can make bagels be r bagels in line with hour. We also can set up the subsequent share
190 bagels/ 10 hours = r bagels 1 hour
Simplifying this proportion, we get
r = 190 bagels/ 10 hours
r = 19 bagels/ 1 hour
So the cookers can make 19 bagels in keeping with hour.
To find out how many bagels they could make in 17 hours, we can multiply the rate via the number of hours
19 bagels/ hour × 17 hours = 323 bagels
Therefore, the cookers at healthy Bakery could make 323 bagels in 17 hours, and their rate is 19 bagels according to hour.
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Q3 NEED HELP PLEASE HELP
Answer:
C. Rachel is saving $5 per week.
Step-by-step explanation:
The initial savings are $10, as it is the y-intercept.
And to obtain the slope we can take 2 points from the graph.
A(0,10)
B(1,15)
m=(y2-y1)/ (x2-x1)
m=(15-10)/ (1-0)
m= 5/1
m= 5 savings in dollars per (1) week
place the publication of three major books on race in chronological order, from earliest to most recent. Start by clicking the first item in the sequence or dragging it here Drag the items below into the box above in the correct order, starting with the first item in the sequence. Tomas Almaguer wrote about historical race relations in California in Racial Fault Lines Michael Omi and Howard Winant wrote about the social construction of race in Racial Formation in the United States. Ta-Nehisi Coates wrote about race and the African American experience in Between the World and Me.
The publication of three major books on race in chronological order, from earliest to most recent is:
- Micheal Omi and Howard Winant wrote about the social construction of race in Racial Formation in the United States.- Tomas Almaguer wrote about historical race relations in California in Racial Fault Lines.- Ta- Nehisi Coates wrote about race and the African American experience in Between the World and Me.Chronological order is the listing, description, or discussion of when events occurred in relation to time. Essentially, it is similar to looking at a chronology to see what happened initially and what happened after that. For example, if teachers asked their pupils to recount their first day of school, they would expect students to begin by waking up that morning and getting ready. If pupils begin from the time they enter the school, significant information is lost and the listener may become confused due to a lack of knowledge.
Helping pupils grasp what chronological order is and how to use the skill correctly can benefit students ranging from kindergarten to collegiate levels. The concept may appear simple, yet failing to master chronological sequence can cause kids to struggle academically and lack a solid educational foundation.
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Change 0.182 0.005 0.050 0.174 Table 10-3. Regression results for predicting depression at wave 2 Predictor Variable b Beta P R? Depression Score Wave 1 0.267 0.231 0.000 0.182 Sociodemographic Age -0.014 -0.024 0.538 0.187 Sex 0.165 0.034 0.370 Psychologic Health Neuroticism, wave 1 0.067 0.077 0.056 0.0237 Past history of depression 0.320 0.136 0.000 Physical Health ADL, wave 1 -0.154 0.103 0.033 0.411 ADL, Wave 2 0.275 0.283 0.012 ADL?, wave 2 -0.013 --0.150 0.076 Number of current 0.115 0.117 0.009 symptoms, wave 2 Number of medical 0.309 0.226 0.000 conditions, wave 2 BP, systolic, wave 2 -0.010 -0.092 0.010 Global health rating 0.284 0079 0.028 change Sensory impairment -0.045 -0.064 0.073 change Social support inactivity Social support-friends, -1.650 -0.095 0.015 0.442 wave 2 Social support-visits, -1.229 -0.087 0.032 wave 2 Activity level, wave 2 0.061 0.095 0.025 Services (community residents 0.207 0.135 0.001 0.438° only), wave 2 Abhreviation: BP = blood pressure 0.031 0.015€ Based on above MLRA summary Table, which of following independent variables is the strongest predictor (or factor)?
Number of medical conditions, wave 2
Number of current symptoms, wave 2
Global health rating change
Past history of depression
ADL, wave 2
The regression result of 0.320, the beta of 0.136, and the p-value of 0.000.
The strongest predictor in the MLRA summary Table is past history of depression. This is shown by the regression result of 0.320, the beta of 0.136, and the p-value of 0.000. This means that past history of depression has a strong and statistically significant influence on predicting depression at wave 2.
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mr warren the physical education teacher has 7 boxes of helmets each box has h helmets write an expression to represent the total number of helmets
Answer:
t = 7h
Step-by-step explanation:
lets have the total amount of helmets as t and helmets per box as h. Then it is t = 7h
Expand and simplify (3x - 1)(9x² + 3x + 1)
Mark the approximate location of the point determined by the given real number on the unit circle. a) 3.2 b) 9.5 c) 50 d) 263 a) Choose the unit circle with a point determined by 3.2. OA. OB. OC. 0 D. b) Choose the unit circle with a point determined by 9.5. OA. OB. OC. OD Click to select your answer. b) Choose the unit circle with a point determined by 9.5. OA. B. OC. D. Ay c) Choose the unit circle with a point determined by 50. c) Choose the unit circle with a point determined by 50. OA. OB. OC. OD. Ау AY 09 d) Choose the unit circle with a point determined by 263. OA. B. D. Ау х
The points determined by the real numbers 3.2, 9.5, 50, and 263 are all located on the unit circle at their respective distances from the origin.
The unit circle is a circle of radius 1 centered at the origin of a coordinate system, usually the Cartesian coordinate system. In this system, a point (x,y) is determined by its real number x, where x is the horizontal distance from the origin and y is the vertical distance from the origin. For example, the point determined by the real number 3.2 is located at (3.2, 0), since 3.2 is the horizontal distance from the origin. Similarly, the point determined by the real number 9.5 is located at (9.5, 0).
The point determined by the real number 50 is located at (50, 0). Finally, the point determined by the real number 263 is located at (263, 0). The unit circle is often used in trigonometry to describe the position of points on the circle with an angle in standard position (in radians). For example, if the point determined by the real number 3.2 has an angle in standard position of 3.2 radians, then the point located at (3.2, 0) on the unit circle is the same point. Similarly, if the point determined by the real number 9.5 has an angle in standard position of 9.5 radians, then the point located at (9.5, 0) on the unit circle is the same point. The same is true for the points determined by the real numbers 50 and 263, respectively.
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You are sitting in a classroom next to the wall looking at the blackboard at the front of the room. The blackboard is 12 ft
long and starts 3 ft from the wall you are sitting next to. Show that your viewing angle is
a=cot^-1 x/15 - cot^-1 x/3
if you are a ft from the front wall.
The viewing angle a of a person sitting a distance x from the front wall of a classroom with a blackboard that is 12 ft long and starts 3 ft from the wall they are sitting next to can be calculated as: a = cot-1(x/15) - cot-1(x/3)
To understand this calculation, let's consider a diagram of the classroom.
We can see from the diagram that the blackboard has length 12 ft, starting 3 ft from the wall the student is sitting next to. The student is sitting a distance x from the front wall.
The viewing angle a is the angle between the wall the student is sitting next to and the line from the student to the front wall. This angle can be calculated using the tangent of the opposite side (front wall) and adjacent side (wall the student is sitting next to).
We can therefore write: a = tan-1(12/3) - tan-1(x/3)
Simplifying this equation, we can rewrite it as: a = cot-1(x/15) - cot-1(x/3).
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Write the linear equation of a line going through (-2,7) with a y-intercept of -3.
Answer:
y = -5x - 3
Step-by-step explanation:
A linear equation is y = mx + b
m = the slope
b = y-intercept
We know
Points (-2,7) (0,-3)
Slope = rise/run or (y2 - y1) / (x2 - x1)
We see the y decrease by 10 and the x increase by 2, so the slope is
m = -10/2 = -5
Y-intercept is located at (0, -3)
So, the equation is y = -5x - 3
An urn contains eight green balls and six red balls. Four balls are randomly selected from the urn in succession, with replacement. That is, after each draw the selected ball is returned. What is the probability that all four balls drawn are red. Round your answer to three decimal places
The probability of drawing four red balls in succession, with replacement, is 0.04 or 4%.
Since we are replacing the ball after each draw, the probability of drawing a red ball remains the same for each draw. The probability of drawing a red ball on any given draw is:
P(Red) = Number of Red Balls / Total Number of Balls
P(Red) = 6 / (8 + 6)
P(Red) = 0.4286
So, the probability of drawing four red balls in a row is the product of the probability of drawing a red ball four times in a row:
P(4 Red Balls) = P(Red) * P(Red) * P(Red) * P(Red)
P(4 Red Balls) = 0.4286 * 0.4286 * 0.4286 * 0.4286
P(4 Red Balls) = 0.04 or 4%
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2x+2y= 24
x=3y
What is the value of x+y? I WILL MARK BRAINLIEST AND GIVE 20 POINTS
Answer:
x + y = 12
Step-by-step explanation:
Pre-SolvingWe are given the following system of equations:
2x + 2y =24
x = 3y
We want to find the value of x + y.
SolvingWe first need to find the values of x and y, which we will do by solving the system.
We can solve this system by substitution.
We know that x = 3y, so we can substitute 3y as x in 2x+2y=24.
This gives us:
2(3y) + 2y = 24
Multiply.
6y + 2y = 24
Add the terms together.
8y = 24
Divide both sides by 8.
y = 3
We found the y value, now let's find the value of x.
The second equation is x=3y, so if we plug the value of y in there, we can find the value of x.
Substitute 3 as y.
x = 3(3) = 9
The value of x is 9.
So, to find x+y, we substitute the values we found.
x + y = 3 + 9 = 12
use the y-and -x intercept to write the equation of the line y intercept (0,6), x intercept (-2,0)
Answer:
3x -y = -6
Step-by-step explanation:
You want the equation of the line with intercepts (0, 6) and (-2, 0).
Intercept formThe equation of the line with x-intercept 'a' and y-intercept 'b' is ...
x/a +y/b = 1
For the given intercepts, the equation is ...
x/(-2) +y/6 = 1
Standard formIn standard form, we want the leading coefficient positive and the integer coefficients mutually prime. We can get there by multiplying by -6:
3x -y = -6
__
Additional comment
You can get slope-intercept form by solving for y, or you can recognize that ...
slope = rise/run = -(y-intercept)/(x-intercept) = -6/-2 = 3
Since you already know the y-intercept, you can write the slope-intercept equation as ...
y = 3x +6
There are perhaps a dozen or more forms of the equation for a line. The "intercept form" equation is one of the more useful ones.
List all prime numbers in the 2023 February calendar
Answer:
6 29 25
Step-by-step explanation:
those are the prime numbers on the 2023 feb calendar
A line passes through the point (-4,4) and has a slope of -3
Help me help me help me help me help me
Answer: cab
Step-by-step explanation:
you start with the last point and move up
Martina made $60 for 5 hours of work. At the same rate, how many hours would she have to work to make $204 ?
Answer:
WELL 17
Step-by-step explanation:
60 DIVED BY 5 IS 12
SO 12 DIVIDED BY 204 IS 17 SOOOOOO 17 IS THE ANS
Find a vector equation and parametric equations in tfor the line through the point and parallel to the given line.(P0 corresponds to t = 0.)
P0 = (0,12, -10)
x = -4 + 2t, y = 7 - 4t, z = 5 + 8t
How do you find x,y,and z?
The vector equation and the parametric equations in t for the line through the point and parallel to the given line are:
Vector Equation= [-4 7 5] + t[2 -4 8]Parametric Equations:x= 2t - 4
y= -4t + 7
z= 8t + 5
How to find the value of x, y, and zTo find x, y, and z in the given scenario, the following steps can be followed:
1: Vector Equation of Line
To find the vector equation, use the given line and its coefficients:
x = -4 + 2t
y = 7 - 4t
z = 5 + 8t
Take the coefficients of x, y, and z, and place them in a 3 by 1 matrix:
Column Matrix= [-4 7 5]
Add the parameter t and place it in a column matrix to get the vector equation:
Vector Equation= [-4 7 5] + t[2 -4 8]
2: Parametric Equation.
To find the parametric equations, write the components of the vector equation in terms of the parameters:
x= -4 + 2t
y= 7 - 4t
z= 5 + 8t
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The Book Nook makes four times as much revenue on paperback books as on hardcover books. If last month's sales totaled $124,300, how much was sold of each type book?
The revenue from hardcover books was $24,860 and the revenue from paperback books was $99,440.
How much was sold of each type book?Let's assume the revenue from hardcover books as "x" dollars.
Then, the revenue from paperback books will be 4 times the revenue from hardcover books, i.e., 4x dollars.
The total revenue is given as $124,300, so we can set up the following equation:
x + 4x = 124300
Simplifying the above equation, we get:
5x = 124300
x = 24860
Therefore, the revenue from hardcover books was $24,860 and the revenue from paperback books was 4 times that amount, i.e., $99,440.
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a normal distribution is observed from the times to complete an obstacle course. the mean is 69 seconds and the standard deviation is 6 seconds. using the empirical rule, what is the probability that a randomly selected finishing time is greater than 87 seconds? provide the final answer as a percent rounded to two decimal places. provide your answer below: $$ %
The probability that a randomly selected finishing time is greater than 87 seconds is 14.08%. This can be calculated using the empirical rule.
The empirical rule states that for any data that is normally distributed, about 68% of the data will fall within one standard deviation of the mean (in this case, within 69 ± 6 seconds). Approximately 95% of the data will fall within two standard deviations (in this case, within 69 ± 12 seconds), and about 99.7% of the data will fall within three standard deviations (in this case, within 69 ± 18 seconds).Given the mean and standard deviation given, we can calculate the probability that a randomly selected finishing time is greater than 87 seconds.
We can do this by subtracting the area under the curve from the mean to the value we are interested in (in this case, 87 seconds). Since the total area under the curve is 1, subtracting the area from the mean to 87 seconds will give us the desired probability.To calculate the area under the curve, we need to calculate the Z-score, which is the number of standard deviations away from the mean a particular value is. In this case, the Z-score is (87 - 69) / 6, which is 2.16. Using a Z-table, the probability of a Z-score of 2.16 or higher is 0.8592. Therefore, the probability that a randomly selected finishing time is greater than 87 seconds is 1 - 0.8592, which is 0.1408. Rounding to two decimal places, this is 14.08%.
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PLEASE HELP NOW!!! What would be the experimental probability of drawing a white marble?
Ryan asks 80 people to choose a marble, note the color, and replace the marble in Brianna's bag. Of all random marble selections in this experiment, 34 red, 18 white, 9 black, and 19 green marbles are selected. How does the theoretical probability compare with the experimental probability of drawing a white marble? Lesson 9-3
Answer:
25%
Step-by-step explanation:
The experimental probability of drawing a white marble can be found by dividing the number of times a white marble was chosen by the total number of trials:
Experimental probability of drawing a white marble = number of times a white marble was chosen / total number of trials
In this case, the number of times a white marble was chosen is 18, and the total number of trials is 80, so:
Experimental probability of drawing a white marble = 18/80 = 0.225 or 22.5%
To compare the experimental probability with the theoretical probability, we need to know the total number of marbles in the bag and the number of white marbles in the bag. Let's assume that there are 4 colors of marbles in the bag (red, white, black, and green), and that each color has an equal number of marbles. This means that there are a total of 4 x 18 = 72 marbles in the bag, and 18 of them are white.
The theoretical probability of drawing a white marble can be found by dividing the number of white marbles by the total number of marbles:
Theoretical probability of drawing a white marble = number of white marbles / total number of marbles
In this case, the number of white marbles is 18, and the total number of marbles is 72, so:
Theoretical probability of drawing a white marble = 18/72 = 0.25 or 25%
Comparing the two probabilities, we can see that the experimental probability (22.5%) is slightly lower than the theoretical probability (25%). This could be due to chance or sampling error in the experiment, or it could indicate that the actual probability of drawing a white marble is slightly lower than the theoretical probability.
Benito made a wooden box to grow herbs on his patio. The box is 16 inches wide, 12 inches tall, and 28 inches long. He plans to fill the box exactly two-thirds full with potting soil. What volume of soil does Benito need? I know how to do this I just need to know if the two-thirds part is trying to throw me off
To fill the wooden box with potting soil precisely up to two-thirds of its capacity, Benito requires a volume of 3,584 cubic inches.
The volume of soil that Benito needs to fill the box two-thirds full can be calculated by finding two-thirds of the total volume of the box.
The volume of the box can be calculated by multiplying the width, height, and length:
16 inches (width) x 12 inches (height) x 28 inches (length) = 5,376 cubic inches.
Two-thirds of this volume can be found by multiplying the total volume by 2/3:
5,376 cubic inches x 2/3 = 3,584 cubic inches.
Therefore, Benito needs 3,584 cubic inches of potting soil to fill the box exactly two-thirds full.
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Stanley is making trail mix out of 10 bags of nuts and 20 bags of dried fruits. He want each new portion of trail mix to be identical, containing the same combination of dried fruits with no bags left over. What is the greatest number of portions of trail mix Stanley can make?
To solve this problem, we can use the Greatest Common Factor (GCF) of 10 and 20.
The GCF is the largest number that divides evenly into both 10 and 20. To find the GCF, we can use a factor tree.
We start with 10 and 20 as our starting numbers.
10 = 2 * 5
20 = 2 * 2 * 5
We can see that both 10 and 20 have a factor of 2 and a factor of 5. The Greatest Common Factor between 10 and 20 is 2 * 5, or 10.
Therefore, the greatest number of portions of trail mix Stanley can make is 10.
Identify and name congruent triangles
The answers are a) ASA congruence rule b) SSS congruence rule c) it is not necessary congruent.
What is Congruence ?Congruent refers to having the same height and shape. Congruent therefore involves comparing two numbers, and equivalent denotes the equality of two expressions. Therefore, to state two line segments are congruent implies that the two lines have equal measures.
According to question:a) ∠GIH is corresponding to ∠LJK
GH = KL
∠IHG = ∠KLJ
By ASA congruence rule
ΔGIH ≅ ΔJKL
b) AB = DF
AC = DE
BC = EF
By SSS congruence rule
ΔABC ≅ ΔDEF
c) Two Corresponding sides are congruent, which is not enough to make them congruent.
So, it is not necessary congruent.
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A certain population is strongly skewed to the left. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one?
I. The distribution of our sample data will be closer to normal.
II. The sampling model of the sample means will be closer to normal.
III. The variability of the sample means will be greater.
A. I and II only
B. I only
C. III only
D. II and III only
E. II only
A. I and II only true if we use a large sample rather than a small one
sampling model
Define sampling modelA sampling model is a statistical model used to describe the behavior of a sample statistic. In other words, it is a model that describes the distribution of a particular sample statistic, such as the mean or standard deviation, as it is repeatedly sampled from a population.
When a sample is drawn from a population that is strongly skewed to the left, a small sample may not accurately represent the true population mean. However, if a large sample is taken, the sample mean is more likely to be normally distributed, due to the central limit theorem. This means that both statement I and II are true.
Statement III is false because as the sample size increases, the variability of the sample means actually decreases. This is because larger samples tend to have less sampling error and are more representative of the population as a whole.
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BP = FC + VCM
The fixed costs associated with the fundraiser include: one-time charges of art ($45), screen and set-up ($60),
and advertising ($50 for a newspaper ad). In addition, the unit cost of the sweatshirt will be $16.50 per sweatshirt, with an additional charge of $.50 per shirt for shipping and individual plastic wrap. You plan to sell the sweatshirts for a retail price of $22.
A. Calculate breakeven in units.
B.calculate breakeven in dollars
1. The breakeven in units equals 31 units.
2. The dollar amount to breakeven is
What is the breakeven in units?The variable cost per unit includes the cost of the sweatshirt ($16.50) and the additional charge for shipping and plastic wrap ($0.50), so the total variable cost per unit is:
= $16.50 + $0.50
= $17.00
The contribution margin per unit is:
= 22.00 - $17.00
= $5.00
The fixed costs include the one-time charges of art ($45), screen and set-up ($60), and advertising ($50), so the total fixed costs are:
= $45 + $60 + $50
= $155
Using the breakeven formula, we can calculate the number of units required to break even:
= Fixed costs / Contribution margin per unit
= $155 / $5.00
= 31 units
What is the breakeven in dollars?To calculate the breakeven in dollars, we need to multiply the breakeven in units by the selling price per unit:
The breakeven in dollars equals to:
= Breakeven in units x Selling price per unit
= 31 x $22.00
= $682.00
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