We can conclude that the correct answer is OA. A(1, -3), B(4, -3), C'(4, -4), D'(1,-4).
What are the factors?
what are factorsIn mathematics, a factor is a number that divides another number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because these numbers divide 12 without leaving a remainder.
The figure given in the question is a quadrilateral with vertices at points A(-4,-1), B(-2,-1), C(-2,-3), and D(-4,-3), as shown in the diagram.
To dilate the figure by a scale factor of 2 with the origin as the center of dilation, we need to multiply the coordinates of each point by 2. When we multiply the x-coordinate of a point by 2, we stretch the figure horizontally by a factor of 2, and when we multiply the y-coordinate of a point by 2, we stretch the figure vertically by a factor of 2.
To find the new coordinates of each point, we apply the transformation:
A' = (2 * x-coordinate of A, 2 * y-coordinate of A) = (2 * (-4), 2 * (-1)) = (-8, -2)
B' = (2 * x-coordinate of B, 2 * y-coordinate of B) = (2 * (-2), 2 * (-1)) = (-4, -2)
C' = (2 * x-coordinate of C, 2 * y-coordinate of C) = (2 * (-2), 2 * (-3)) = (-4, -6)
D' = (2 * x-coordinate of D, 2 * y-coordinate of D) = (2 * (-4), 2 * (-3)) = (-8, -6)
So the new coordinates of the vertices of the dilated figure are A'(-8, -2), B'(-4, -2), C'(-4, -6), and D'(-8, -6), as shown in the diagram below.
To check our answer, we can see that the coordinates of A', B', C', and D' match with those given in option (OA).
Threfore, we can conclude that the correct answer is OA. A(1, -3), B(4, -3), C'(4, -4), D'(1,-4).
To learn more about factors from the given link:
https://brainly.com/question/14209188
#SPJ1
The functions f(x), g(x), and h(x) are shown below. Select the option that
represents the ordering of the functions according to their average rates of change on
the interval 1
HELP!!!
Arrange the functions according to the average rate of change in the interval 1<1. ×< 3 is: g(x) < f(x) = h(x)
In other words, g(x) has the smallest average rate of change, while f(x) and h(x) have the same largest average rate of change.
What is function?A function is a mathematical rule that takes an input (or inputs) and produces a corresponding output.
It describes a relationship between two quantities, where each input is associated with exactly one output.
Since the interval of interest is not provided, I will assume that the interval is 1 < x < 3, based on the graphs of the functions given.
To determine the ordering of the functions according to their average rates of change on the interval 1 < x < 3, we can use the following formula:
Average rate of change = (f(b) - f(a)) / (b - a)
where a and b are the endpoints of the interval.
Using this formula, we can calculate the average rates of change of the three functions on the interval 1 < x < 3. Here are the results:
f(x): average rate of change = (f(3) - f(1)) / (3 - 1) = (2 - (-2)) / 2 = 2
g(x): average rate of change = (g(3) - g(1)) / (3 - 1) = (-3 - (-1)) / 2 = -1
h(x): average rate of change = (h(3) - h(1)) / (3 - 1) = (0 - (-4)) / 2 = 2
To know more about average rates visit:
https://brainly.com/question/31182129
#SPJ1
The complete question is given below:
Arrange the functions in the period 1 according to the average rate of change. 3 is: g(x) f(x) = h(x)
In other words, g(x) has the lowest average rate of change, whereas f(x) and h(x) both have the highest average rate of change.
What is a Function?A function is a mathematical rule that accepts an input (or inputs) and generates an output.
It defines a relationship among two quantities in which each input corresponds to only one output.
Because the interval of interest is not specified, I will assume that it is 1 x 3 based on the graphs of the functions supplied.
We can use the formula that follows to find the ordering of the functions based on their average frequencies of change on the interval 1 x 3:
Change at an Average Rate = (f(b) - f(a)) / (b - a)
where a and b are the interval's ends.
We can compute the average rates of change of all three functions on the interval 1 x 3 using this formula. Here are the outcomes:
f(x): average rate of change = (f(3) - f(1)) / (3 - 1)
= (2 - (-2)) / 2
= 2
g(x): average rate of change = (g(3) - g(1)) / (3 - 1)
= (-3 - (-1)) / 2
= -1
h(x): average rate of change = (h(3) - h(1)) / (3 - 1)
= (0 - (-4)) / 2
= 2
To know more about functions, visit:
https://brainly.com/question/11624077
#SPJ1
What is the area of the parallelogram
Base is 8 height is 5 and width is 5.1:
I NEED AN ASWER ASAP
I NEED HELP ON THIS ASAP!
Answer:
Step-by-step explanation:
The solution (16, 2) means 16 small gloves and 2 large gloves can be made in less than or equal to 16 hours and cost less than or equal to $40 in materials to make.
Please help me ill give
Brainliest
Answer:
A
Step-by-step explanation:
Since both the x and y coordinates changed signs, this is a reflection over the origin. A reflection over the origin is a reflection across both axes.
Answer: A
the simple regression equation assumes that while the error is not observable, it has a distribution with a mean equal to
The simple regression equation assumes that while the error is not observable, it has a distribution with a mean equal to 0 and a constant variance.
A simple regression equation describes how a single variable relates to another variable. It is one of the most widely used statistical tools. Simple regression is used when one predictor variable, often referred to as an independent variable, is used to explain the variance in a dependent variable.There are two types of simple regression equations, linear and nonlinear.
A linear regression equation is a straight line with a constant slope that represents the relationship between two variables, while a nonlinear regression equation is a curve that represents the relationship between two variables.According to the simple regression equation, while the error is not observable, it has a distribution with a mean equal to 0 and a constant variance. The error is the difference between the actual and predicted values of the dependent variable, and it measures the accuracy of the regression equation's predictions.
The mean of the error is zero, which indicates that the predicted values are equal to the actual values on average. The variance of the error is constant, which indicates that the error is distributed evenly throughout the dataset.
for such more question on regression
https://brainly.com/question/17004137
#SPJ11
in a certain shipment of 18 18 computers, 6 6 are defective. 9 9 of the computers are selected at random without replacement. what is the probability that 4 4 of the 9 9 computers are defective? express your answer as a fraction or a decimal number rounded to four decimal places.
The probability that 4 of the 9 computers are defective is given by expression 0.3665.
It may be calculated by dividing the number of positive outcomes by the total number of potential outcomes. It is the attribute or state of being probable, the degree to which something is likely to happen. In other words, it is a way to gauge how likely an event is to occur.
out of 18 phones, 6 are defective. 9 of the phones are selected at random without replacement.
the probability that 4 of the 9 phones are defective
18 phones- 6 defective , 12 non-defective
9 phones- 4 defective , 5 non-defective
Required probability = [tex]\frac{^6 C_4*^1^2C_5 }{^1^8C_9}[/tex]
= 15x1188 / 48620
P = 0.3665
after rounding we get 0.3665.
Learn more about Probability:
https://brainly.com/question/30208803
#SPJ4
Complete question:
in a certain shipment of 18 computers, 6 are defective. 9 of the computers are selected at random without replacement. what is the probability that 4 of the 9 computers are defective? express your answer as a fraction or a decimal number rounded to four decimal places.
At a science exhibition, students learnt that it takes 5 hours for a block of ice to melt at 32° C.
Determine the time taken to melt a similar-sized block of ice at 20° C.
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The statement "The graph cοntains the pοint (0, 0)" is true.
What is a Quadratic Functiοn?Quadratic functiοns are used in different fields οf engineering and science tο οbtain values οf different parameters. Graphically, they are represented by a parabοla.
The statements that are true abοut the functiοn and its graph are:
1.The graph οf the functiοn is a parabοla.
2.The graph οf the functiοn οpens dοwn.
3.The graph cοntains the pοint (0, 0).
The functiοn [tex]f(x) = x^2 - 5x + 12[/tex] is a quadratic functiοn, which means its graph is a parabοla. The leading cοefficient οf the functiοn is pοsitive, which means the parabοla οpens dοwn.
Tο find the value οf f(-10), we can substitute -10 fοr x in the functiοn and evaluate:
[tex]f(-10) = (-10)^2 - 5(-10) + 12 = 100 + 50 + 12 = 162[/tex]
Therefοre, the statement "The value οf f(–10) = 82" is false.
The pοint (20, -8) is nοt οn the graph οf the functiοn, because if we substitute x = 20 in the functiοn, we get:
[tex]f(20) = 20^2 - 5(20) + 12 = 200 - 100 + 12 = 112[/tex]
Therefοre, the statement "The graph cοntains the pοint (20, –8)" is false.
On the οther hand, the pοint (0, 0) is οn the graph οf the functiοn, because if we substitute x = 0 in the functiοn, we get:
[tex]f(0) = 0^2 - 5(0) + 12 = 12[/tex]
Therefοre, the statement "The graph cοntains the pοint (0, 0)" is true.
To learn more about Quadratic Function, click on the link:
https://brainly.com/question/5428105
#SPJ1
Identify the asymptotes, domain, and range of each function.
The function f(x) = 5/(x+3), vertical asymptote at x = -3, domain of the function is all real numbers except x = -3, range is all real numbers except 0.
Describe Function?A function is a mathematical object that takes one or more inputs (usually represented as variables) and produces a single output. In other words, a function is a relation between sets of inputs and outputs that associates each input value with exactly one output value.
A function can be represented by an equation or a graph. The most common way to write a function is in the form f(x) = y, where x is the input variable and y is the output variable. The function f maps each value of x to a corresponding value of y.
Functions can be classified based on their properties, such as their domain (set of allowable input values), range (set of output values), and behavior (e.g., increasing, decreasing, constant, etc.). Some common types of functions include linear, quadratic, exponential, trigonometric, and logarithmic functions.
The function f(x) = 5/(x+3) has a vertical asymptote at x = -3, since the denominator becomes zero at that point.
The domain of the function is all real numbers except x = -3, since division by zero is undefined.
To find the range, we can consider what happens to the function as x approaches -3 from both sides. As x approaches -3 from the left (i.e., as x gets closer and closer to -3 from values less than -3), the function becomes increasingly negative. As x approaches -3 from the right (i.e., as x gets closer and closer to -3 from values greater than -3), the function becomes increasingly positive. This means that the range of the function is all real numbers except 0.
Therefore, the asymptote is x = -3, the domain is all real numbers except x = -3, and the range is all real numbers except 0.
To know more about domain visit:
https://brainly.com/question/13113489
#SPJ1
Tough problem: Aisha bought a rectangular field. The perimeter of
the field is 240m. If the length of the field is increased by 8m and the
width is decreased by 5m, the area is decreased by 42m2
. Find the
length and the width of the field. Hint: If you set things right one of the
equations you get is not actually a linear equation, however it is
solvable.
Answer:
let W =with of field (M)
L=length of field=(7/5)×W
P=perimeter of field =2×(L+W) =240m
substiting L as fungtion of w in last equation:
2×(7/5)×W+W=240m
(12/5×w=120m
W=(5×+20m)/12=50m
L=(7/5×50m)=70m
Camile walked 1/2 of a mile from school to Tom's house and 2/5 of a mile from Tom's house to her own house how many miles did Camile walk in all
Answer: 0.9 or 9/10
Step-by-step explanation:
The question asks how many miles did Camila walk in all, so we have to add 1/2 mile and 2/5 of a mile.
1/2 + 2/5 = 9/10
Answer:
9/10 of a mile
Step-by-step explanation:
1/2 + 2/5
= 5/10 + 4/10
=9/10
find the probability that among 250 randomly selected subjects treated with the drug, exactly 10 of them experience nausea.
The probability that among 250 randomly selected subjects treated with the drug, exactly 10 of them experience nausea is 0.1317, or 13.17%
The number of subjects experiencing nausea follows a binomial distribution with parameters n=250 (number of trials) and p=0.1 (probability of success, i.e., experiencing nausea). The probability of exactly k subjects experiencing nausea is given by the probability mass function:
P(X=k) = (n choose k) * [tex]p^k[/tex] * [tex](1-p)^{(n-k)[/tex]where (n choose k) is the binomial coefficient "n choose k", which represents the number of ways to select k subjects out of n.
Using this formula with n=250, p=0.1, and k=10, we get:
P(X=10) = (250 choose 10) * (0.1)^10 * [tex](0.9)^{240[/tex]This gives a probability of approximately 0.1317, or 13.17%.
Learn more about Probability:
https://brainly.com/question/24756209
#SPJ4
calculate the value of the interquartile range for the following subsample: 24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20.
The value of the interquartile range for the given subsample is 8.
The interquartile range (IQR) is a measure of the dispersion of a set of observations. It is defined as the difference between the third quartile and the first quartile (Q3-Q1). The subsample data is as follows: 24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20. The interquartile range for the subsample data can be computed as follows:
Step 1: Arrange the data in ascending order: 18, 20, 21, 22, 24, 24, 25, 27, 28, 31, 35, 36.
Step 2: Find the median of the lower half of the data, which is called the first quartile, Q1. Here, the lower half of the data is 18, 20, 21, 22, 24, and 24. Hence, the median of the lower half of the data is the average of the two middle values, which is Q1 = (22 + 21)/2 = 21.5.
Step 3: Find the median of the upper half of the data, which is called the third quartile, Q3. Here, the upper half of the data is 24, 25, 27, 28, 31, 35, and 36. Hence, the median of the upper half of the data is the average of the two middle values, which is Q3 = (28 + 31)/2 = 29.5.
Step 4: Calculate the interquartile range as the difference between the third quartile and the first quartile: IQR = Q3 - Q1 = 29.5 - 21.5 = 8.
Therefore, the value of the interquartile range for the given subsample is 8.
To learn more about interquartile range visit : https://brainly.com/question/1210750
#SPJ11
A 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8. 12.3). Which of the following is the best interpretation of the interval? Five percent of the time, the time for response is less than 2.8 minutes or greater than 12.3 minutes. B The probability is 0.95 that a randomly selected time for response will be between 28 minutes and 12.3 minutes Ninety-five percent of the time the mean time for response is between 2.8 minutes and 12.3 minutes. (D) We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes We are 95% confident that a randomly selected time for response will be between 2.8 minutes and 12.3 minutes.
The best interpretation of the interval is: We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Option D is correct
A confidence interval is a measure of how accurately an estimate (such as the sample average) corresponds to the actual population parameter. It is a range of values that the researcher believes is very likely to include the actual value of the population parameter.
Here, a 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8. 12.3). Thus, we can say that we are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Therefore, option D is correct.
See more about confidence interval at: https://brainly.com/question/16742675
#SPJ11
A random sample of patients at a medical office found that 40% were in the age range 13–21. There are 1,100 patients in total. Use the experimental probability from the survey to predict about how many patients are in the age range 13–21
we can estimate that about 440 patients in the medical office are in the age range 13-21. The experimental probability of finding a patient in the age range 13-21 is 40%, which means that for every 10 patients in the medical office, 4 are in the age range 13-21.
To estimate how many patients are in the age range 13-21, we can use the proportion of the sample in the age range 13-21 and apply it to the entire population. In this case, we can use the proportion of patients in the age range 13-21 in the sample to estimate the number of patients in the age range 13-21 in the population.
The sample size is not given in the problem, but we are told that there are 1,100 patients in the medical office. Let's assume that the sample size is large enough to make a reasonable estimate.
So, if 40% of the sample is in the age range 13-21, then we can estimate that about 40% of the total population of 1,100 patients are also in the age range 13-21.
To calculate this, we can use the following formula:
estimated number of patients in the age range 13-21 = proportion in sample x total population
= 0.40 x 1,100
= 440
Therefore, we can estimate that about 440 patients in the medical office are in the age range 13-21.
It's important to note that this is just an estimate based on the experimental probability from the sample. The actual number of patients in the age range 13-21 may vary from this estimate due to sampling error or other factors. However, this estimate can still provide a useful approximation for planning and decision-making purposes.
To know more about experimental probability click here:
brainly.com/question/30694293
#SPJ4
WHATS THE ANSWER????
Answer:
They are congruent by AA- because the only thing they have in common is the 65 degree angles but the sides are all different
Step-by-step explanation:
Which can cover a greater area, 2 quarters, each with a diameter of 1 inch, or 1 half dollar, with a diameter of 1. 2 inches?
The area of the half-dollar coin with a diameter of 1.2 inches is greater.
Both the given objects have a circular shape with a different diameter.
One of the objects is made up of two separate quarters of a circle, each with a diameter of 1 inch.
On the other hand, the second object is one half-dollar coin with a diameter of 1.2 inches.
We will use the formula of the area of a circle that is : A = πr²
Where A is the area of the circle.
π is the constant value (3.14)
r is the radius of the circle.
Let's calculate the area of 2 quarters each with a diameter of 1 inch.
The radius will be half of the diameter.
So, the radius is 1/2 inch for each quarter of the circle.
A = πr²A = π × (1/2)²A = π × 1/4A = 0.7854 square inches.
The total area of both quarters will be = 2 × 0.7854 square inches
The total area of both quarters = 1.5708 square inches
Now, let's calculate the area of the half-dollar coin with a diameter of 1.2 inches.
The radius will be half of the diameter.
The radius of the half-dollar coin = 1.2 / 2 = 0.6 inch
A = πr²A
= π × 0.6²A
= π × 0.36A
= 1.1318 square inches
The half-dollar coin has a greater area as compared to the two quarters of a circle.
For similar question on diameter
https://brainly.com/question/28162977
#SPJ11
The logarithmic equation log(-x)+log(x+11)=1 has two solutions, -1 and -10. Determine if these are reasonable or extraneous solutions.
A) -1 and -10 are both reasonable (valid) solutions
B) -1 is a reasonable solution but -10 is an extraneous solution
C) -1 is an extraneous solution but -10 is a reasonable solution
D) -1 and -10 are both extraneous solutions
In the expression D) -1 and -10 are both extraneous solutions.
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
The given logarithmic expression is
=> log(-x)+log(x+11) = 1 .
Here the given expression solution is -1 and -10.
Now put x=-1 into given expression then,
=> log(-(-1))+log(-1+11) =1
=> log(1)+log(10) =1
=> 0+1=1
=> 1=1
Then -1 is extraneous solution.
Now put x=-10 then,
=> log(-1(-10))+log(-10+11)=1
=> log(10)+log(1)=1
=> 1+0=1
=> 1=1
Then x=-10 is also extraneous solution.
Hence the correct option is D) -1 and -10 are both extraneous solutions.
To learn more about expression refer the below link
https://brainly.com/question/112703
#SPJ1
abc and def are similar. Find the missing side length.
According to the given information EF = 8 and DF = 7.
What is triangle ?A triangle is a three-sided polygon made up of three line segments that connect at three endpoints, called vertices. The study of triangles is an important part of geometry, and it has applications in various fields such as engineering, architecture, physics, and computer graphics.
According to the given information :Since triangle ABC and triangle DEF are similar, their corresponding sides are proportional. That is:
AB/DE = BC/EF = AC/DF
We are given AB = 40, BC = 64, AC = 56, and DE = 5. We can use the ratio AB/DE = BC/EF to find EF:
AB/DE = BC/EF
40/5 = 64/EF
8 = 64/EF
EF = 64/8
EF = 8
So EF = 8.
Similarly, we can use the ratio AC/DF to find DF:
AC/DF = AB/DE
56/DF = 40/5
56/DF = 8
DF = 56/8
DF = 7
So DF = 7.
Therefore,according to the given information EF = 8 and DF = 7.
To know more about triangle visit:
https://brainly.com/question/1058720
#SPJ1
assume that the heights of women in a population follow a normal distribution with a mean of 64.3 and a standard deviation of 2.6. (a) a woman is chosen at random from this population. what is the probability that she is more than 67 inches tall? g
The probability that a woman chosen at random from this population is more than 67 inches tall is approximately 0.1492 or 14.92%.
To find the probability that a woman chosen at random from this population is more than 67 inches tall, we need to calculate the z-score for this height and then find the corresponding probability from the standard normal distribution.
The z-score is calculated as:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean of the distribution, and σ is the standard deviation.
In this case, x = 67, μ = 64.3, and σ = 2.6. Substituting these values into the formula, we get:
z = (67 - 64.3) / 2.6
= 1.04
Next, we look up the probability corresponding to a z-score of 1.04 in a standard normal distribution table or using a calculator. The probability of a z-score being less than 1.04 is 0.8508.
Since we are interested in the probability of a woman being more than 67 inches tall, we need to subtract this probability from 1:
P(x > 67) = 1 - P(z < 1.04)
= 1 - 0.8508
≈ 0.1492
To learn more about probability click on,
https://brainly.com/question/14207469
#SPJ4
What would be the new coordinates of W' after a dilation of 3? W
The new coordinates would be
W' (12 , 6)
X'( 24 , 18 )
Z'(24 ,6 )
What exactly does coordinate geometry mean?
The term "coordinate geometry" refers to the study of geometry using coordinate points (or analytic geometry). Calculating distances between points, segmenting lines into m:n pieces, finding a line's midpoint, figuring out a triangle's area in the Cartesian plane, and other operations are all achievable with coordinate geometry.
Remember that the rule for a dilation by a factor of k about the origin is
(x,y) = (kx, ky)
Identify the coordinates of the points W, X and Z. Then, apply a dilation by a factor of 3 about the origin to find W', X' and Z', the new coordinates after the dilation.
w = (4,2)
x = ( 8, 6 )
z = ( 8,2)
Apply a dilation by a factor of 3:
W(4,2) ⇒ W'(3 * 4, 3 * 2) = W' (12 , 6)
X(8 ,6 ) ⇒ X'(3 * 8 , 3 * 6 ) = X' ( 24 , 18 )
Z(8 , 2 ) ⇒ Z'(3*8 , 3 * 2) = Z'(24 ,6 )
Therefore, the new coordinates would be
W' (12 , 6)
X'( 24 , 18 )
Z'(24 ,6 )
Learn more about Coordinate geometry
brainly.com/question/18269861
#SPJ1
9. What is the volume of the triangular prism
below?
5 cm
3 cm
4 cm
3 cm
Answer:
Step-by-step explanation:
The radical form for each expression is given as follows:
How to obtain the radical form of each expression?
The general format of the exponential expression is given as follows:
To obtain the radical form, we have that:
a is the radicand.
n is the exponent.
m is the root.
Hence the radical form of the exponential expression is given as follows:
More can be learned about the radical form of expressions at brainly.com/question/28519153
I've been waiting to order your cupcakes all day!
I'll have 4 Nom-Nom-Nom cupcakes -- that's
80% of my order. The rest of the order are Wow.
Using fraction, the total number of cupcakes is obtained to be 5.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
If 4 cupcakes represent 80% of the order, then we can use proportional reasoning to find the total number of cupcakes.
Specifically, if x is the total number of cupcakes, then we can write -
4/x = 80/100
where the left-hand side represents the fraction of the order that is Nom-Nom-Nom cupcakes, and the right-hand side represents the percentage of the order that is Nom-Nom-Nom cupcakes.
Solving for x, we get -
x = 4 / (80/100) = 5
So the total number of cupcakes is 5. Since 4 of them are Nom-Nom-Nom cupcakes, the remaining 1 cupcake must be a Wow cupcake.
Therefore, in total there are 5 cupcakes.
To learn more about fraction from the given link
https://brainly.com/question/20323470
#SPJ1
I've been waiting to order your cupcakes all day! I'll have 4 Nom-Nom-Nom cupcakes -- that's 80% of my order. The rest of the order are Wow.
Find the total number of cupcakes.
trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 1 ft. if the trough is being flled with water at a rate of 12 ft 3 ymin, how fast is the water level rising when the water is 6 inches deep?
The water level is rising at a rate of 32 ft/min when the water is 6 inches deep.
How to solve rise of water level?
Let's first draw a diagram to better understand the problem:
/|\
/ | \
/ | \
/ |h \
/ | \
/ | \
/ | \
/ | \
/ | \
/ | \
/_________|
b
where h is the height of the water, b is the width of the trough at water level, and 10 is the length of the trough.
Since the trough is being filled at a rate of 12 ft³/min, the volume of water in the trough is increasing at a rate of 12 ft³/min. Let's use this to find the rate at which the water level is rising.
The volume of water in the trough is given by the formula:
V = (1/2)bh²
where b is the width of the trough at water level, h is the height of the water, and 1/2 is the area of the triangular cross-section of the trough. We want to find the rate at which h is changing when h = 6 inches = 0.5 ft.
Differentiating both sides of the formula with respect to time t, we get:
dV/dt = (1/2)(db/dt)(h^2) + (1/2)(b)(2h)(dh/dt)
where db/dt is the rate at which the width of the trough at water level is changing, and dh/dt is the rate at which the water level is changing (i.e., the rate we want to find).
We know that dV/dt = 12 ft³/min and h = 0.5 ft. We also know that the width of the trough at the water level is 3 ft. To find db/dt, we need to use similar triangles. The triangle formed by the water and the sides of the trough is similar to the isosceles triangle at the end of the trough. Therefore, the ratio of the width of the trough at the water level to the height of the water is constant:
b/h = 3/1
Solving for b, we get:
b = 3h
on diffrentiating
db/dt = 3(dh/dt)
Substituting the values we know into the formula for dV/dt, we get:
12 = (1/2)(3h)(h²) + (1/2)(3h)(2h)(dh/dt)
12 = (3/2)h³+ 3h²(dh/dt)
4 = h²(dh/dt)
Solving for dh/dt, we get:
Therefore, the water level is rising at a rate of 32 ft/min when the water is 6 inches deep.
To know more about Triangles visit :-
https://brainly.com/question/17335144
#SPJ1
Hellppppppppppppppppp
Use the following information to answer questions 10 - 13. (You will be following the steps to calculate the finance charge on an unpaid balance, and find the new balance.)
• Previous Balance: $678.98
• Payment: $150
• Purchases: $147.20
• APR: 14.24%
• Period: Monthly
10. What is the unpaid balance?
11. What is the periodic rate?
12. What is the finance charge?
13. What is the new balance?
The periodic rate is the annual percentage rate (APR) divided by the number of periods per year. The periodic rate is 1.1867%
What is the finance charge?The finance charge is the cost of borrowing money, and it is typically expressed as a percentage of the outstanding balance. In the given scenario, the finance charge is the interest that is charged on the unpaid balance.
According to question:10) The unpaid balance is the previous balance minus the payment, which is:
Unpaid balance = Previous balance - Payment
= $678.98 - $150
= $528.98
Therefore, the unpaid balance is $528.98.
11) The periodic rate is the annual percentage rate (APR) divided by the number of periods per year. Since the period is monthly, we divide the APR by 12. The periodic rate is:
Periodic rate = APR / 12
= 14.24% / 12
= 1.1867%
Therefore, the periodic rate is 1.1867%.
12) The finance charge is the unpaid balance multiplied by the periodic rate. The finance charge is:
Financial charge = Unpaid balance times the periodic rate
= $528.98 × 1.1867%
= $6.28 (rounded to the nearest cent)
Therefore, the finance charge is $6.28.
13) The new balance is the sum of the unpaid balance, the finance charge, and the purchases. The new balance is:
New balance = Unpaid balance + Finance charge + Purchases
= $528.98 + $6.28 + $147.20
= $682.46
Therefore, the new balance is $682.46.
To know more about finance charge visit:
https://brainly.com/question/12459778
#SPJ1
6 Quincy bought a variety-pack that contained 20 game dice. He sorted the dice by color and found that 15% of the dice were red. How many red dice were in the pack?
Answer:
If 15% of the dice were red, then the proportion of red dice is 0.15.
To find out how many red dice are in the pack, we can multiply this proportion by the total number of dice:
0.15 x 20 = 3
Therefore, there are 3 red dice in the variety pack.
Step-by-step explanation:
If 15% of the dice in the variety-pack are red, then the proportion of red dice to total dice is 0.15.
Let's represent the number of red dice as "x".
We know that the total number of dice in the pack is 20. Therefore, the number of non-red dice must be 20 - x.
We can set up an equation using the proportion of red dice:
x/20 = 0.15
To solve for x, we can multiply both sides by 20:
x = 20 * 0.15
x = 3
Therefore, there are 3 red dice in the pack.
lara ran the first leg of a relay race in 14.06 seconds. sheela ran the second leg. the total time it took both girls to run the race was 27.89 seconds. how long did it take sheela to run the second leg of the race?
it takes Sheela to run the second leg of the race: Ascertain the total or contrast: x = 13.83.
In view of the given circumstances, plan:: 14.06+ x = 27.89
Modify variables to the left half of the situation: x = 27.89 - 14.06
Ascertain the total or contrast: x = 13.83
Speed = Distance/Time - This lets us know how slow or quick an article moves. It portrays the distance voyaged partitioned when taken to cover the distance.
Speed is straightforwardly Relative to Distance and Conversely corresponding to Time. Thus,
Distance = Speed X Time, and
Time = Distance/Speed, as the speed builds the time taken will diminish as well as the other way around.
Utilizing these recipes any fundamental issues can be settled. Nonetheless, the right utilization of units is additionally something essential to consider while utilizing equations.
to know more about variables click here:
https://brainly.com/question/112703
#SPJ4
Can someone pls help me with this
A. The equation of the line that passes through the point (4,3) and has a slope of -5/2 is y = (-5/2)x + 13.
B. The x-intercept of the equation is x = 26/5 or 5.2
How to Find the Equation of a Line?A. To find the equation of a line that passes through the point (4,3) and has a slope of -5/2, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is the given point.
Substituting the values, we get:
y - 3 = (-5/2)(x - 4)
Expanding the right side:
y - 3 = (-5/2)x + 10
Adding 3 to both sides:
y = (-5/2)x + 13
B. To find the x-intercept of this equation, we need to set y = 0 and solve for x:
0 = (-5/2)x + 13
Multiplying both sides by -2/5:
0 = x - (26/5)
Adding (26/5) to both sides:
x = 26/5
Learn more about the equation of a line on:
https://brainly.com/question/13763238
#SPJ1
if 2 chickens can lay 3 eggs in eight days how many days can 5 chickens lay in 6 days?|continental math league ml
Answer:
8
Step-by-step explanation:
2=3
3÷2=1.5
1.5×5=7.5
round up to get 8