In circle P, if m(QR) = 80 , and m(QRT) = 39 , m(QPR) = 39 and m(PT) = 78
Based on the information given, we know that:
- m(QR) = 80 (this is the measure of arc QR)
- m(QRT) = 39 (this is the measure of angle QRT)
To find the other measures, we can use the following formulas:
- The measure of a central angle is equal to the measure of its intercepted arc
- The measure of an inscribed angle is half the measure of its intercepted arc
Using these formulas, we can find the measure of angle QPR and the measure of arc PT as follows:
- m(QPR) = m(QRT) = 39 (since angle QRT and angle QPR intercept the same arc QR)
- m(PT) = 2 * m(QRT) = 78 (since angle QRT and angle PQT intercept the same arc PT, and the measure of an inscribed angle is half the measure of its intercepted arc)
So the final answers are:
- m(QR) = 80
- m(QRT) = 39
- m(QPR) = 39
- m(PT) = 78
To know more about angle, refer to the link below:
https://brainly.com/question/23709091#
#SPJ11
The sequence 10, 9. 5, 9. 0, 8. 5,. Has a common difference on
The sequence 200, 100, 50, 25,
has a common ratio of
The sequence 10, 9. 5, 9. 0, 8. 5,. has a common difference on -0.5
The sequence 200, 100, 50, 25, has a common ratio of 1/2
Let's start by discussing the sequence 10, 9.5, 9.0, 8.5. We can observe that each term is decreasing by 0.5. This means that the sequence has a common difference of -0.5.
In mathematical terms, the common difference is the constant value that is added or subtracted from each term in the sequence to obtain the next term. In this case, we can write the sequence as:
10, 10 - 0.5, 10 - 1.0, 10 - 1.5
where the common difference is -0.5.
Now, let's consider the sequence 200, 100, 50, 25. We can observe that each term is obtained by dividing the previous term by 2. This means that the sequence has a common ratio of 1/2.
In mathematical terms, the common ratio is the constant value that is multiplied by each term in the sequence to obtain the next term. In this case, we can write the sequence as:
200, 200/2, (200/2)/2, ((200/2)/2)/2
where the common ratio is 1/2.
To know more about sequence here
https://brainly.com/question/30262438
#SPJ4
The model q(t) = 2. 5.00E+00. 0168t predicts the world population, in billions, t years after 1955. What was the population of the world in 1955 based
on this model?
The population of the world in 1955 based on the model q(t) = 2.500[tex]e^{0.0168t}[/tex] is 2.54 billion.
The model q(t) = 2.500[tex]e^{0.0168t}[/tex] represents the world population in billions
Here, t represents the years after 1955 and e is exponential constant its value is approximately 2.718.
Here the population is growing exponentially means population is growing at faster rate.
To find the population of the world in 1955 we will take
t = 1
on putting the value of t in the given function q(t)
q(t) = 2.500e[tex]e^{0.0168(1)[/tex]
on solving the function q(t) we get
q(t) ≈ 2.54
so, the population of the world in 1955 is 2.54 billion
To know more about population click here :
https://brainly.com/question/27991860
#SPJ4
If the arch were 32 inches wide but 44 inches tall high, how could you modify your function W to model the new arch
This new function W(x) = 22 - (11/8) * (x - 16)² will model the shape of the arch with dimensions of 32 inches wide and 44 inches tall.
To modify the function W to model the new arch with dimensions of 32 inches wide and 44 inches tall, we need to adjust the formula to reflect the new proportions.
Currently, the function W is defined as:
W(x) = h/2 - h/(2a) * (x - a)²
Where h is the height of the arch and a is half of the width of the arch.
To modify the function for the new arch, we need to adjust the value of a to reflect the new width of 32 inches. Since a is half the width, we have:
a = 32/2 = 16
We also need to adjust the value of h to reflect the new height of 44 inches. Therefore, the new function for the arch would be:
W(x) = 44/2 - 44/(2*16) * (x - 16)²
Simplifying this expression, we get:
W(x) = 22 - (11/8) * (x - 16)²
This new function will model the shape of the arch with dimensions of 32 inches wide and 44 inches tall. The parabolic shape of the function will remain the same, but the specific coefficients in the function have been adjusted to reflect the new proportions of the arch.
Know more about function here:
https://brainly.com/question/12431044
#SPJ11
A random sample of 18 observations taken from a normally distributed population produced the following data:
28. 4 27. 3 25. 5 25. 5 31. 1 23. 0 26. 3 24. 6 28. 4
37. 2 23. 9 28. 7 27. 9 25. 1 27. 2 25. 3 22. 6 22. 7
What is the point estimate of μ?
Make a 99% confidence interval for μ.
What is the margin of error of estimate for μ in part b?
Point estimate of μ [tex]26.15[/tex]
99% confidence interval: [tex](24.213, 28.087)[/tex]
Margin of error:[tex]1.437[/tex]
How to estimate μ and create a 99% confidence interval ?The point estimate of (population mean) is calculated by finding the sample mean , which is the average of the given sample data. Adding up all the observations and dividing by the sample size (18), we get:
To make a 99% confidence interval for we can use the t-distribution and the sample mean. Since the sample size is 18, we have (18 - 1) = 17 degrees of freedom. Using a t-distribution table or a calculator, we find the critical value for a 99% confidence level and 17 degrees of freedom to be approximately 2.898.
Next, we calculate the standard error (SE) using the sample standard deviation (s) divided by the square root of the sample size .Assuming the population standard deviation is unknown, we estimate it using the sample standard deviation, which is approximately 3.858.
Learn more about population
brainly.com/question/15889243
#SPJ11
u = 28.8
The 99% confidence interval for μ is (27.01, 30.59).
How to solve the data28.4 + 27.3 + 25.5 + 25.5 + 31.1 + 23.0 + 26.3 + 24.6 + 28.4 + 37.2 + 23.9 + 28.7 + 27.9 + 25.1 + 27.2 + 25.3 + 22.6 + 22.7 = 518.3
The sample mean (or the point estimate of μ) is:
518.3 / 18 = 28.8
Calculate each data point's deviation from the mean, square it, and then sum up these values.
(28.4-28.8)² + (27.3-28.8)² + (25.5-28.8)² + (25.5-28.8)² + (31.1-28.8)² + (23.0-28.8)² + (26.3-28.8)² + (24.6-28.8)² + (28.4-28.8)² + (37.2-28.8)² + (23.9-28.8)² + (28.7-28.8)² + (27.9-28.8)² + (25.1-28.8)² + (27.2-28.8)² + (25.3-28.8)² + (22.6-28.8)² + (22.7-28.8)²
= 116.4
Divide by (n - 1), where n is the number of observations. In this case, n = 18, so n - 1 = 17.
So, the variance (s²) is 116.4 / 17 = 6.85 (approximately)
s = √6.85 = 2.62
CI = x ± (t * (s/√n))
CI = 28.8 ± (2.898 * (2.62/√18))
CI = 28.8 ± 1.79
So, the 99% confidence interval for μ is (27.01, 30.59).
Read more on confidence interval here https://brainly.com/question/15712887
#SPJ4
Briefly discuss the difference between indefinite integral and definite integral. Give an example to provide emphasis. *
A definite integral is defined as the signed area under a function between certain limits (bounds) of integration.
An indefinite integral represents the family of antiderivatives of a function and is also known as its general integral or antiderivative.
The difference between the integralsAn indefinite integral represents the family of antiderivatives of a function and is also known as its general integral or antiderivative. An indefinite integral does not have specific limits of integration; its result includes a constant of integration (usually denoted +C), which accounts for all possible constant shifts within its antiderivative.
A definite integral is defined as the signed area under a function between certain limits (bounds) of integration. The real number that represents its net area between it and x-axis during an interval.
Read more on indefinite integral and definite integral here:https://brainly.com/question/27419605
#SPJ4
The distance from Earth to Mercury is 9.21×10^7 kilometers. How long would it take a rocket, traveling at 3.35×10^4 kilometers per hour to travel from Earth to Mercury? Round your answer to the nearest whole number of hours.
it would take approximately 2,749 hours for a rocket traveling at 3.35×10⁴ kilometers per hour to travel from Earth to Mercury.
what is approximately ?
Approximately means "about" or "roughly". It is used to indicate that a number or value is not exact, but rather an estimate or approximation. When a value is given as approximately a certain number
In the given question,
To calculate the time it would take a rocket traveling at 3.35×10⁴ kilometers per hour to travel from Earth to Mercury, we need to divide the distance between Earth and Mercury by the speed of the rocket:
Time = Distance / Speed
Distance = 9.21×10⁷kilometers
Speed = 3.35×10⁴ kilometers per hour
Time = 9.21×10⁷ km / (3.35×10⁴ km/h)
Time = 2,748.66 hours
Rounding this value to the nearest whole number of hours gives:
Time = 2,749 hours
Therefore, it would take approximately 2,749 hours for a rocket traveling at 3.35×10⁴ kilometers per hour to travel from Earth to Mercury.
To know more about approximately , visit:
https://brainly.com/question/30945002
#SPJ1
Part A: Using computer software, a correlation coefficient of r = 0. 01 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
If the scatter plot shows no discernible relationship between the variables and the points appear randomly scattered, then the r-value of 0.01 is accurate. However, if there is a visible relationship, the value of r may need to be recalculated or checked for errors in data input or analysis.
To find whether a correlation coefficient of r = 0.01 is an accurate value for the data based on the scatter plot, it's essential to consider the following factors:
1. Visual inspection of the scatter plot: Observe the overall pattern of data points in the scatter plot. If the points seem randomly scattered with no discernible pattern, then a correlation coefficient close to 0, such as r = 0.01, would be accurate. However, if there is a clear linear or non-linear relationship between the variables, the value of r = 0.01 may not be accurate.
2. Strength of the relationship: The correlation coefficient r ranges from -1 to 1, where -1 represents a strong negative relationship, 0 represents no relationship, and 1 represents a strong positive relationship. An r-value of 0.01 indicates a very weak or no relationship between the variables. Confirm that this is consistent with the scatter plot pattern.
To determine if the r-value of 0.01 is accurate for the data, carefully examine the scatter plot and consider these factors. If the scatter plot shows no discernible relationship between the variables and the points appear randomly scattered, then the r-value of 0.01 is accurate. However, if there is a visible relationship, the value of r may need to be recalculated or checked for errors in data input or analysis.
To know more about scatter plot refer here:
https://brainly.com/question/29231735
#SPJ11
A teacher writes the following product on the board:
(372) (675) =18k7
Ana says that 3k2 is a factor of 18k7
Felipe says that 18k? is divisible by 372
Who is correct?
In the equation , Felipe is correct.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given equation is (372) (675) =18k7.
We know that the factor is a number that divides the another number and leaves no reminder .
If we divide 18k7 by 372 the we get remainder 675. So 372 is not factor of 18k7.
But 372 is divides the number 18k7.
Hence Felipe is correct.
To learn more about equation refer the below link
https://brainly.com/question/29336774
#SPJ4
For the function f(x) = 2x^4 In x, find f'(x).
To find the derivative (f'(x)) of the function f(x) = 2x^4 In x, we will need to use the product rule and the chain rule of differentiation.
Using the product rule, we have:
f'(x) = [2(In x)](4x^3) + [2x^4](1/x)
Simplifying this expression, we get:
f'(x) = 8x^3 In x + 2x^3
Therefore, the derivative of f(x) is f'(x) = 8x^3 In x + 2x^3.
Hi! To find the derivative f'(x) of the function f(x) = 2x^4 * ln(x), we'll use the product rule. The product rule states that if you have a function h(x) = u(x)v(x), then h'(x) = u'(x)v(x) + u(x)v'(x). In this case, u(x) = 2x^4 and v(x) = ln(x).
First, find the derivatives of u(x) and v(x):
u'(x) = d(2x^4)/dx = 8x^3
v'(x) = d(ln(x))/dx = 1/x
Now, apply the product rule:
f'(x) = u'(x)v(x) + u(x)v'(x)
f'(x) = (8x^3)(ln(x)) + (2x^4)(1/x)
Simplify the expression:
f'(x) = 8x^3 * ln(x) + 2x^3
This is the derivative of the given function.
Visit here to learn more about derivative : https://brainly.com/question/25324584
#SPJ11
F(x) =∣x∣ g(x)=∣x+2∣ we can think of g as a translated (shifted) version of f. complete the description of the transformation.
The transformation of f(x) to g(x) involves a horizontal shift and a reflection. The function g(x) is a transformed version of f(x) obtained by translating f(x) to the left by 2 units along the x-axis.
Specifically, to obtain g(x) from f(x), we first shift f(x) two units to the left, and then we take the absolute value of the result.
This means that the graph of g(x) will be the same as the graph of f(x) for all values of x greater than or equal to -2, but will be reflected across the y-axis for all values of x less than -2.
In other words, the transformation of f(x) to g(x) involves a horizontal shift and a reflection.
To know more about absolute value, refer here:
https://brainly.com/question/4691050#
#SPJ11
What is the process of solving this?
The solution of the trigonometric equation
cos(2x) = cos(x) + 2
is x = 180°
How to solve the trigonometric equation?Here we want to solve the equation:
cos(2x) = cos(x) + 2
First, we know that:
cos(2x) = 2cos(x)² - 1
Then we can rewrite:
2cos(x)² - 1 = cos(x) + 2
We can define:
cos(x)= y
2y² - 1 = y + 2
Then we need to solve the quadratic:
2y² - 1 - y - 2 =0
2y² - y - 3 = 0
Using the quadratic formula we will get:
[tex]y = \frac{1 \pm \sqrt{(-1)^2 - 4*2*2*-3} }{2*2} \\\\y = \frac{1 \pm 5}{4}[/tex]
so the solutions are:
y = (1 + 5)/4 = 6/4
y = (1- 5)/4 = -1
And remember that y = cos(x), then y = 6/4 can be discarded.
Then the solution comes from:
cos(x) = -1
then x = pi = 180°
Learn more about trigonometric equations at:
https://brainly.com/question/24349828
#SPJ1
A satellite orbiting Earth travels 4.95×10^7 meters for each orbit. It takes 6,600 seconds to make one orbit. What is the speed of the satellite in meters per second? Give your answer in standard form.
The value of the speed of the satellite in meters per second is,
⇒ Speed = 7.5 x 10³ m /sec
We have to given that;
A satellite orbiting Earth travels 4.95×10⁷ meters for each orbit.
And, It takes 6,600 seconds to make one orbit.
Hence, the speed of the satellite in meters per second is,
⇒ Speed = Distance / Time
⇒ Speed = 4.95×10⁷/ 6,600
⇒ Speed = 0.00075 x 10⁷
⇒ Speed = 7.5 x 10⁻⁴ x 10⁷
⇒ Speed = 7.5 x 10³ m /sec
Thus, The value of the speed of the satellite in meters per second is,
⇒ Speed = 7.5 x 10³ m /sec
Learn more about the scientific notation visit:
brainly.com/question/1767229
#SPJ1
In the figure, AABC and ADEF are similar. what’s the scale factor from AABC to ADEF?
Answer:
3
Step-by-step explanation:
We can see that in figure ABC, line segment AB is 5 ft.
We can also see that in figure DEF, line segment DE is 15 ft.
How did we get from 5 to 15?
We multiplied by 3, so the scale factor is 3.
Hope this helps! :)
Work out without a calculator.
√
45
×
√
1
20
Answer:
3
√
10
√
5
Step-by-step explanation:
write a real-world example that could be solved by useing the the inequality 4x + 8 greater than 32. Then solve the inequality.
1. 8 added to four times the product of 4 and a number is greater than 32
1. x = 6
How to determine the valueIt is important to know that inequalities are expressions showing unequal comparison between number, expressions, or variables.
From the information given, we have that;
4x + 8 greater than 32.
This is represented as;
4x + 8 > 32
collect the like terms, we get
4x > 32 - 8
subtract the values
4x> 24
Divide both sides by the coefficient of x which is 4, we have;
x > 24/4
x > 6
Learn about inequalities at: https://brainly.com/question/25275758
#SPJ1
A student usally saves $20 a month. He would like to reach a goal of saving $350 in 12 months the students writes the equation 350=12(x + 20) to represent this situation
Answer: x=55/6 or 55 over 6
Step-by-step explanation: Step 1: Distribute:
- 350= 12(x+20)
- 350= 12x + 240
Step 2: Subtract 240 from both sides:
- 350-240= 12x+240-240
Step 3: Simplify:
Subtract the numbers: 350-240= 12x+240-240= 110=12x+240-240
Subtract again: 110=12x+240-240= 110=12x
Step 4: Divide both sides by the same factor:
110=12x= 110/12= 12x/12
Step 5: Simplify:
- Divide the numbers: 110/12=12x/12= x=55/6=12x/12
- Cancel terms that are in both the numerator and denominator: 55/6=12x/12= 55/6=x
- Move the variables to the left: 55/6=x = x=55/6
Answer: x=55/6 or 55 over 6
a study of 90 randomly selected families, 40 owned at least one television. find the 95% confidence interval for the true proportion of families that own at least one television.
The 95% confidence interval for the true proportion of families that own at least one television is (0.347, 0.542).,
How do we calculate ?The formula for the confidence interval of a proportion:
CI = p ± z* (√(p*(1-p)/n))
where:
p is the sample proportion (40/90 = 0.4444)
z* is the critical value of the standard normal distribution at the 95% confidence level (1.96)
n is the sample size (90)
Substituting the values, we have
CI = 0.4444 ± 1.96 * (√(0.4444*(1-0.4444)/90))
CI = 0.4444 ± 1.96 * (√(0.00245))
CI = 0.4444 ± 1.96 * 0.0495
CI = 0.4444 ± 0.097
Hence, the 95% confidence interval for the true proportion of families that own at least one television is (0.347, 0.542) when rounded to three decimal places.
Learn more about standard normal distribution at: https://brainly.com/question/4079902\
#SPJ1
Suppose that you are gambling at a casino. Every day you play at a slot machine, and your goal is to minimize your losses. We model this as the experts problem. Every day you must take the advice of one of n experts (i. E. A slot machine). At the end of each day t, if you take advice from expert i, the advice costs you some c t i in [0, 1]. You want to minimize the regret R, defined as:
This requires an online learning algorithm that adapts to the changing costs of each expert and helps us make optimal choices
In this scenario, we can think of the slot machines as experts providing us with advice on which machine to play each day. The cost of taking advice from each expert, represented by cti, is the amount we lose by playing that particular machine.
To minimize our losses and regret, we want to choose the expert (i.e., slot machine) with the lowest cost each day. However, it's important to note that the cost of taking advice from each expert may change each day, so we need to constantly evaluate and adjust our choices.
To formalize this problem as an optimization task, we can use the concept of regret. Regret measures how much worse off we are by not knowing the best expert in advance. In other words, it's the difference between our cumulative losses if we always chose the best expert versus the losses we actually incur by following different experts each day.
To minimize our regret R, we need to choose the best expert as often as possible. One way to achieve this is by using an online learning algorithm that updates our choice based on the outcomes of each day's play. By continuously monitoring the performance of each slot machine, we can adjust our strategy and minimize our losses over time.
In summary, to minimize our losses while gambling at a casino, we need to treat each slot machine as an expert providing us with advice. We must choose the expert with the lowest cost each day and constantly update our strategy to minimize regret.
This requires an online learning algorithm that adapts to the changing costs of each expert and helps us make optimal choices.
To know more about algorithm refer here
https://brainly.com/question/31936515#
#SPJ11
Flying Home for the Holidays Does the airline you choose affect when you'll arrive at
your destination? The dataset DecemberFlights contains the difference between actual and
scheduled arrival time from 1000 randomly sampled December flights for two of the major North
American airlines, Delta Air Lines and United Air Lines. A negative difference indicates a flight
arrived early. We are interested in testing whether the average difference between actual and
scheduled arrival time is different between the two airlines.
a. Define any relevant parameter(s) and state the null and alternative hypotheses.
b. Find the sample mean of each group, and calculate the difference in sample means.
c. Use StatKey or other technology to create a randomization distribution and find the p-value.
d. At a significance level of a = 0. 01, what is the conclusion of the test? Interpret the conclusion in
context.
a
Relevant parameter is the difference between actual and scheduled arrival time. Also the difference in sample means is -1.70 minutes. We get a p-value of 0.017 and the conclusion is that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.
a. Relevant parameter: the difference between actual and scheduled arrival time.
Null hypothesis: The average difference between actual and scheduled arrival time is the same for Delta Air Lines and United Air Lines.
Alternative hypothesis: The average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.
b. Sample mean for Delta Air Lines: -2.31 minutes
Sample mean for United Air Lines: -4.01 minutes
Difference in sample means: -1.70 minutes
c. To create a randomization distribution, we can pool the data from both airlines and randomly assign them to two groups with the same sample sizes as Delta Air Lines and United Air Lines. We then calculate the difference in sample means for each random assignment. Repeating this process many times gives us a randomization distribution. Using StatKey with 10,000 iterations, we get a p-value of 0.017, which is less than 0.01.
d. At a significance level of 0.01, we reject the null hypothesis and conclude that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines. Specifically, the average difference for United Air Lines is greater than that of Delta Air Lines. This could have implications for travelers who prioritize arriving on time, as they may wish to consider
Delta over United.
To know more about Relevant parameter, visit:
https://brainly.com/question/31311746#
#SPJ11
Your brother traveled 115 miles in 2. 52 hours to come home for school break. What’s the average speed that he was traveling?
The average speed that your brother was traveling is approximately 45.63 miles per hour
The average speed is the total distance traveled divided by the total time taken. So we have:
Average speed = total distance ÷ total time
We are given the total distance as 115 miles and the total time as 2.52 hours. Therefore, the average speed is:
Average speed = 115 miles ÷ 2.52 hours
Average speed = 45.63 miles per hour
So, the average speed that your brother was traveling is approximately 45.63 miles per hour.
To learn more about average speed, click here:
https://brainly.com/question/12322912
#SPJ11
Simplify 3y(y^2-3y+2)
Answer:
3y^3-9y^2+6y
Step-by-step explanation:
= 3y^3-9y^2+6y
in the coordinate plane, point b is located at (2, -3), Point C is reflected across the y-axis. Plot and label points b and C in the coordinate plane.
Thus, we can label the points B and C' in the coordinate plane as follows
|
|
C' |
|
------B(2, -3)
|
|
|
Coordinate plane calculation.To reflect a point across the y-axis, we keep the x-coordinate the same but change the sign of the y-coordinate.
Point B is located at (2, -3), so it looks like
|
|
|
|
------B(2, -3)
|
|
|
|
To reflect point C across the y-axis, we change the sign of the y-coordinate, but keep the x-coordinate the same. If point C is located at (x, y), then its reflected image, C', would be located at (-x, y).
Since we don't have the coordinates for point C, we cannot plot it accurately. However, we know that its reflected image would be located at (-x, y), so we can label it as C' for now.
So, the reflected image of point C across the y-axis, C', would be located at (-x, y). Thus, we can label the points B and C' in the coordinate plane as follows
|
|
C' |
|
------B(2, -3)
|
|
|
Learn more about coordinate plane below.
https://brainly.com/question/27481419
#SPJ1
If AM=25CM, MC=20CM, MN=30CM, NC=35CM. What is the scale factor
The scale factor is 7/5 or 1.4.
f AM=25CM, MC=20CM, MN=30CM, NC=35CM.find scale factor
In order to determine the scale factor, we need to compare the corresponding sides of two similar figures. Let's begin by drawing a diagram to represent the given information:
M ------- N
/ \
/ \
A ---------------- C
<-----25cm----->
<-----20cm-----> <-----35cm----->
From the diagram, we see that triangle AMC is similar to triangle CNC, since they share angle C and have proportional sides:
Scale factor = corresponding side length in triangle CNC / corresponding side length in triangle AMC
We can calculate the scale factor by comparing the lengths of the corresponding sides:
Scale factor = NC / AM
Scale factor = 35 cm / 25 cm
Scale factor = 7 / 5
Learn more about scale factor
brainly.com/question/30215044
#SPJ11
if the silver sheet costs $9.75 per cm^2, the copper sheet costs $3.25 per cm^2, and the stone costs $1.75 per cm^2, what is the materials cost for the brooch
AnswerAnswer:
Step-by-step explanation:
To determine the materials cost for the brooch, we need to know the area of each material used in the brooch. Let's say that the brooch is made up of a 5 cm x 5 cm square of silver, a 2 cm x 2 cm square of copper, and a 3 cm x 1 cm rectangle of stone.
The area of the silver sheet is 5 cm x 5 cm = 25 cm^2, so the cost of the silver is 25 cm^2 x $9.75/cm^2 = $243.75.
The area of the copper sheet is 2 cm x 2 cm = 4 cm^2, so the cost of the copper is 4 cm^2 x $3.25/cm^2 = $13.
The area of the stone is 3 cm x 1 cm = 3 cm^2, so the cost of the stone is 3 cm^2 x $1.75/cm^2 = $5.25.
Therefore, the total materials cost for the brooch is $243.75 + $13 + $5.25 = $262.
A group of 150 dancers are auditioning for a dance show. 93 of the dancers trying out did not get on the show. What percentage of the dancers didn’t get in the show?
62% of the dancers did not get into the show.
To find the percentage of dancers who did not get into the show.
First, identify the total number of dancers auditioning and the number of dancers who did not get into the show.
In this case, there are 150 dancers in total, and 93 of them did not get in.
Next, divide the number of dancers who did not get into the show by the total number of dancers auditioning.
This will give us the proportion of dancers who did not get in.
Proportion = (Number of dancers who did not get in) / (Total number of dancers)
Proportion = 93 / 150
Finally, to find the percentage, multiply the proportion by 100:
Percentage = Proportion * 100
Percentage = (93 / 150) * 100.
For similar question on dancers.
https://brainly.com/question/28183590
#SPJ11
A system of equations consists of at least two equations describing a problem. True or false
True because a system of equations is a set of two or more equations that describe a particular situation or problem.
How to solve system's equations?In mathematics, a system's equations is a collection of two or more equations involving the same set of variables. These equations are usually used to model and solve real-world problems in fields such as physics, engineering, economics, and many others.
For example, consider the following system of two equations:
2x + y = 5
x - y = 3
This system of equations represents a situation where we have two unknowns, x and y, and two pieces of information that relate them. To solve the system of equations, we need to find the values of x and y that satisfy both equations simultaneously.
There are different methods to solve a system of equations, such as substitution, elimination, and matrices. The choice of method depends on the complexity of the system and personal preference. Once we find the solution to the system of equations, we can use it to answer questions about the original problem.
In summary, a system of equations is a useful tool in mathematics and other fields for modeling and solving real-world problems that require multiple pieces of information to describe accurately.
Learn more about System's equation
brainly.com/question/1161825
#SPJ11
Find the slope of the line
Answer:
m = 1/2
Step-by-step explanation:
We Know
The slope of a line is the rise/run
Pick 2 points (0,1) (2,2)
We see the y increase by 1, and the x increase by 2, so the slope of the line is
m = 1/2
Solve for f(-2).
f(x) = -3x + 3
f(-2) = [?]
Answer:
f(-2) = 9
Step-by-step explanation:
f(x) = -3x + 3 Solve for f(-2).
f(-2) = -3(-2) + 3
f(-2) = 6 + 3
f(-2) = 9
HELPPPPPPP
I have zero idea of what to do!
Answer:
72 + 7x + 24 = 180
7x + 96 = 180
7x = 84
x = 12
Let
Ф(u, v) = (3u + 9v, 9u + 9v). Use the Jacobian to determine the area of
Ф(R) for: (a)R = [0,91 × [0, 6]
(b)R = [2,20] × [1, 17]
(a)Area (Ф(R)) =
(b) Area (Ф(R)) =
a) Area (Ф(R)) = 5184 (b) Area (Ф(R)) = 25920
Let J be the Jacobian of Ф. We have J = det(DФ) = det([3 9; 9 9]) = -72.
(a) For R = [0,9] × [0,6], we have
Ф(R) = {(3u+9v,9u+9v) | 0 ≤ u ≤ 9, 0 ≤ v ≤ 6}.
The area of Ф(R) is given by the double integral over R of the Jacobian:
Area (Ф(R)) = ∬R |J| dudv
= ∫0^9 ∫0^6 72 dudv
= 5184.
Therefore, the area of Ф(R) is 5184.
(b) For R = [2,20] × [1,17], we have Ф(R) = {(3u+9v,9u+9v) | 2 ≤ u ≤ 20, 1 ≤ v ≤ 17}. The area of Ф(R) is given by the double integral over R of the Jacobian:
Area (Ф(R)) = ∬R |J| dudv = ∫2^20 ∫1^17 72 dudv = 25920.
Therefore, the area of Ф(R) is 25920.
To learn more about integral click here
brainly.com/question/18125359
#SPJ11