Answer:
1/4, 3/8, 7/12, 5/6
Step-by-step explanation:
First, change all the fractions so they have the same denominators. The least common denominator is 24. 1/4=6/24 3/8=9/24 5/6=20/24 7/12=14/24
Now, put them in order from least to greatest: 6/24, 9/24, 14/24, 20/24
Which point would be a solution to the system of linear inequalities shown below?
The coordinates in the solution to the systems of inequalities is (12, 1)
Solving the systems of inequalitiesFrom the question, we have the following parameters that can be used in our computation:
y > -4x + 6
y > 1/3x - 7
Next, we plot the graph of the system of the inequalities
See attachment for the graph
From the graph, we have solution to the system to be the shaded region
The coordinates in the solution to the systems of inequalities graphically is (12, 1)
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help asap!!!
The tables represent hat sizes measured in inches for two baseball teams.
Cougars
21.5 24.5 22
21 22 23
22.5 24 21
22 23.5 22
23.5 22 24
Panthers
22.5 20 23.5
21 24 22
20.5 21.5 23
23 22.5 21
24 22 24.5
Which team has the largest overall size hat for their players? Determine the best measure of center to compare and explain your answer.
Panthers; they have a larger median value of 22.5 inches
Cougars; they have a larger median value of 22 inches
Panthers; they have a larger mean value of about 22 inches
Cougars; they have a larger mean value of about 22.6 inches
The correct answer is, Cougars; they have a larger median value of 22 inches.
Calculating the median and mean for each data set, we get:
Cougars:
Median = 22 inches
Mean = 22.3 inches
Panthers:
Median = 22.5 inches
Mean = 22.2 inches
Since the median of the Cougars data set is larger than the median of the Panthers data set, we can conclude that the Cougars have the largest overall size hat for their players.
Therefore, the correct answer is, Cougars; they have a larger median value of 22 inches.
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A survey of 81 randomly selected homeowners finds that they spend a mean of $73 per month on home maintenance. Construct a 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners. Assume that the population standard deviation is $10 per month. Round to the nearest cent.
We are 98% confident that the true mean amount of money spent per month on home maintenance by all homeowners is between $70.19 and $75.81.
A confidence interval is a range of values that is likely to contain the true value of the population parameter with a given level of confidence. A confidence interval for the population mean μ can be constructed as follows:
μ = sample mean ± margin of error where the margin of error is given by:margin of error = (critical value) x (standard error)
Here, we want to construct a 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners. We are given that a survey of 81 randomly selected homeowners finds that they spend a mean of $73 per month on home maintenance.
The population standard deviation is assumed to be $10 per month.
Therefore, the standard error of the mean is given by:standard error = σ / sqrt(n) = 10 / sqrt(81) = 10 / 9 = 1.11
where σ is the population standard deviation and n is the sample size.To find the critical value, we need to look up the t-distribution table with 80 degrees of freedom and a significance level of 0.01 (since we want a 98% confidence interval).
The corresponding value is 2.527.
Therefore, the margin of error is:margin of error = (critical value) x (standard error) = 2.527 x 1.11 = 2.81
Finally, we can construct the confidence interval as follows:73 ± 2.81 = (70.19, 75.81)The confidence interval is rounded to the nearest cent.
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On a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 40. Find the z-score of a person who scored 300 on the exam.
A z-score of 0 indicates that the person's score is equal to the mean, so they are right at the Average Performance level.the z-score of a person who scored 300 on the exam is 0.
The z-score of a person who scored 300 on the exam, we can use the formula:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
In this case, the person scored 300 on the exam, which is equal to the mean (μ). Therefore, we can substitute these values into the formula:
z = (300 - 300) / 40
Simplifying the equation, we have:
z = 0 / 40
Since any number divided by zero is undefined, we can conclude that the z-score of a person who scored 300 on the exam is 0.
The z-score measures the number of standard deviations a data point is away from the mean. In this case, a z-score of 0 indicates that the person's score is equal to the mean, so they are right at the average performance level.
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Jordan is putting new tile on the bathroom floor. The width of the floor is 4 2/4 feet and the length
is 6 3/4 feet.
Part A:
What is the area of the bathroom floor?
Part B:Each box of tiles has enough tiles to cover 5 ft.² how many boxes of tiles will Jordan need?
a) The area of the rectangular shaped bathroom floor is A = 30.375 feet²
b) The number of boxes of tiles = 25 boxes
Given data ,
Jordan is putting new tile on the bathroom floor. The width of the floor is 4 2/4 feet and the length is 6 3/4 feet
Now , Area of Rectangle = Length x Width
On simplifying , we get
Width = 4 2/4 feet = (4 x 4 + 2)/4 = 18/4 feet
Length = 6 3/4 feet = (6 x 4 + 3)/4 = 27/4 feet
Area = (18/4) x (27/4) = (18 x 27)/(4 x 4) = 30.375 feet²
Therefore , the area of bathroom floor is A = 30.375 feet²
Now , the number of boxes is given by
Number of boxes of tiles = Total area of bathroom floor / Area covered by each box of tiles
B = 30.375 / 5
B = 6.075
B = 6 tiles
Hence , the area of bathroom floor is A = 30.375 feet²
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I NEED HELP WITH STATISTICS
The claims are this year some of their clients will have a starting salary of at least $38,500 and last year at least one of their clients had a starting salary of exactly $38,500. Correct options are A and B.
Based on the given information, option A can be true. This is because the average starting salary of the job placement agency's clients was $38,500 last year, which means some clients had a starting salary equal to or greater than that amount.
Option B is also true because the mean includes all values, including the value of $38,500, so it is likely that at least one client had that starting salary.
Option C cannot be determined from the given information as it is unclear what percentage of clients had a starting salary above $38,500. Option D is not necessarily true as there is no information on the starting salary of any client exceeding $42,000.
Option E is also not true as the average salary of $38,500 does not guarantee that all clients had that same starting salary. Therefore, the correct answer is A and B, and the rest cannot be determined from the given information.
Correct options are A and B.
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NO LINKS!! URGENT PLEASE!!!
1. Vanessa invested $2500 into an account that will increase in value by 3.5% each year. Write an exponential function to model this situation, then find when the account will have $5000?
2. The average price of a movie ticket in 1990 was $4.22. Since then, the price has increased by approximately 3.1% each year. Write an exponential function to model this situation, then find how many years until tickets cost $9.33.
The exponential function that model this situation is [tex]A(t) = 2500(1 + 0.035)^t.[/tex]
The account will have $5000 in 20 years.
What is the exponential function for Vanessa's investment growth?Let A be the amount in the account after t years.
Then, we can model this situation with the function A(t) = 2500(1 + 0.035)^t with the use of compound intererst formula which is [tex]P = A*(1+r)^t[/tex]
To find when the account will have $5000, we can set A(t) = 5000 and solve:
5000 = 2500(1 + 0.035)^t
2 = (1.035)^t
Taking the natural logarithm:
ln(2) = t ln(1.035)
t = ln(2)/ln(1.035)
t = 20.148791684
t = 20 years.
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Answer:
1) 21 years
2) 26 years
Step-by-step explanation:
Question 1To model the account balance of Vanessa's account at t years, we can use an exponential function in the form:
[tex]\large\boxed{A(t) = A_0(1 + r)^t}[/tex]
where:
A(t) is the value of the investment after t years.A₀ is the initial amount of the investment.r is the annual interest rate (as a decimal).t is the time elapsed (in years).Given Vanessa invested $2500 into the account and it will increase in value by 3.5% each year:
A₀ = $2500r = 3.5% = 0.035Substitute these values into the formula to create an equation for A in terms of t:
[tex]A(t) = 2500(1 + 0.035)^t[/tex]
[tex]A(t) = 2500(1.035)^t[/tex]
To find when the account balance will be $5000, set A(t) equal to $5000 and solve for t:
[tex]A(t)=5000[/tex]
[tex]2500(1.035)^t=5000[/tex]
[tex](1.035)^t=\dfrac{5000}{2500}[/tex]
[tex](1.035)^t=2[/tex]
[tex]\ln (1.035)^t=\ln 2[/tex]
[tex]t \ln 1.035=\ln 2[/tex]
[tex]t=\dfrac{\ln 2}{ \ln 1.035}[/tex]
[tex]t=20.1487916...[/tex]
[tex]t=20.15\; \sf years\;(2\;d.p.)[/tex]
Therefore, it will take approximately 20.15 years for Vanessa's account to reach a value of $5000.
Since the interest rate is an annual rate of 3.5%, it means that the interest is applied once per year, at the end of the year. Therefore, we need to round up the number of years to the next whole number.
So Vanessa's account will have $5,000 after 21 years.
Note: After 20 years, the account balance will be $4,974.47. After 21 years, the account balance will be $5,148.58.
[tex]\hrulefill[/tex]
Question 2To model the increase in movie ticket prices over time, we can use an exponential function in the form:
[tex]\large\boxed{P(t) = P_0(1 + r)^t}[/tex]
where:
P(t) is the price of the ticket (in dollars) after t years.P₀ is the initial price of the ticket (in dollars).r is the annual growth rate (as a decimal).t is the time elapsed (in years).Given the initial price of the ticket was $4.22 and the price has increased by 3.1% each year:
P₀ = $4.22r = 3.1% = 0.031Substitute these values into the formula to create an equation for P in terms of t:
[tex]P(t) = 4.22(1 + 0.031)^t[/tex]
[tex]P(t) = 4.22(1.031)^t[/tex]
To find how many years until tickets cost $9.33, we can set P(t) equal to $9.33 and solve for t:
[tex]P(t)=9.33[/tex]
[tex]4.22(1.031)^t=9.33[/tex]
[tex](1.031)^t=\dfrac{9.33}{4.22}[/tex]
[tex]\ln (1.031)^t=\ln \left(\dfrac{9.33}{4.22}\right)[/tex]
[tex]t \ln (1.031)=\ln \left(\dfrac{9.33}{4.22}\right)[/tex]
[tex]t =\dfrac{\ln \left(\dfrac{9.33}{4.22}\right)}{\ln (1.031)}[/tex]
[tex]t=25.9882262...[/tex]
Therefore, it will take approximately 26 years for movie ticket prices to reach $9.33, assuming the annual growth rate remains constant at 3.1%.
Sean A = < - 7, 5 ] U [10, 18 >, B = [ - 2, 8 > U < 13, 23 ]
C = < 1, 15>.
Hallar: (A ∩ B ) - C
The result of the expression (A ∩ B) - C is [-2, 5] U [13, 18] is [-2,5,13,18].
To find the result of the expression (A ∩ B) - C, where A, B, and C are sets, we need to perform the following steps:
Find the intersection of sets A and B, denoted as (A ∩ B).Subtract set C from the intersection (A ∩ B).Given the sets:
A = < - 7, 5 ] U [10, 18 >
B = [ - 2, 8 > U < 13, 23 >
C = < 1, 15 >
1.Find the intersection of sets A and B (A ∩ B):
To find the intersection, we need to find the overlapping region between the intervals.The intersection of the intervals [-7, 5] and [-2, 8] is [max(-7, -2), min(5, 8)] = [-2, 5].The intersection of the intervals [10, 18] and [13, 23] is [max(10, 13), min(18, 23)] = [13, 18].Therefore, the intersection of sets A and B is [-2, 5] U [13,18].2. Subtract set C from the intersection (A ∩ B):
Subtracting set C = <1, 15> from the intersection [-2, 5] U [13, 18] means removing any elements that are present in set C from the intersection.
Since set C = <1, 15> does not overlap with either [-2, 5] or [13, 18], the subtraction (A ∩ B) - C results in the same set as the intersection:
(A ∩ B) - C = [-2, 5] U [13, 18].
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7 x 7 87 x 9 999 x 866 what is my out come
Answer:
47703169206
Step-by-step explanation:
7 x 787 x 9999 x 866 = 47703169206 via the process of multiplication
Answer:
8,9740 that is your answer and then I hope you have a good day and hope this helps
The other day, I was taking care of two girls whose parents are mathematicians. The
girls are both whizzes at math. When I asked their ages, one girl replied,
our ages is 18.= The other stated, The difference of our ages is 4.= What is the
product of the girls’ ages?
Answer:
hey it is
Step-by-step explanation:
22 × 18 or 12 into 18
The following are the populations for the top twelve largest cities in the U. S. New York City, NY: 8,336,817 Los angeles CA: 979.576 Chicago, il:2,693,976 Houston, TX: 2,320,268 Phoenix AZ: 1,680,992 Philadelphia PA: 1,584,064 San Antonio TX: 1, 547,253 San Diego CA: 1,423,851 Dallas TX: 1,343,573 San Jose CA: 1,021,795 Austin TX:978,908 Jacksonville FL: 911,507. What is the mean population?, what is the median population?, what is the mode?, what is range?, what is the standard Deviation?
Mean: Mean = (8,336,817 + 979,576 + 2,693,976 + 2,320,268 + 1,680,992 + 1,584,064 + 1,547,253 + 1,423,851 + 1,343,573 + 1,021,795 + 978,908 + 911,507) / 12=2688602
Median = 1,643,032
Mode: Determine the value(s) that appear most frequently in the population list. In this case, there is no mode as none of the population values repeat.
Range = 8,336,817 - 911,507 = 7,425,310.
Standard Deviation = √( Σ ( xi - μ )² / N )
To find the mean, median, mode, range, and standard deviation of the given population data for the top twelve largest cities in the U.S., we can perform the following calculations:
Performing these calculations will yield the mean population, median population, mode (if any), range, and standard deviation of the given population data for the top twelve largest cities in U.S .
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100 Points! Geometry question. Photo attached. Determine if the quadrilateral is a parallelogram. Please show as much work as possible. Thank you!
The quadrilateral given on the image can be said to be a parallelogram because the diagonals bisect each other.
How to determine a parallelogram ?An effective way to check if a four-sided figure is a parallelogram is through the diagonal test, which involves inspecting its diagonals. According to the examination, if the two diagonals of a four-sided shape intersect at their midpoint, the shape is classified as a parallelogram.
The two diagonals in a parallelogram intersect at their midpoint, although they may not have the same length. This implies that the intersection point of every diagonal bisects the diagonal into two identical parts. Despite the unequal length of its diagonals, the parallelogram is still considered as such due to the bisecting property.
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Which graph shows the solution to the inequality?
The solutions of the given inequality is: x ≥ -1 or x ≤ -5, the correct number line is 2nd.
To solve the inequality |x + 3| ≥ 2, we need to consider two cases:
Case 1: (x + 3) ≥ 2
If x + 3 is greater than or equal to 2, then the absolute value of (x + 3) will also be greater than or equal to 2. Solving this case:
x + 3 ≥ 2
x ≥ 2 - 3
x ≥ -1
So, for this case, the solution is x ≥ -1.
Case 2: -(x + 3) ≥ 2
If -(x + 3) is greater than or equal to 2, then the opposite of (x + 3) will also be greater than or equal to 2. Solving this case:
-(x + 3) ≥ 2
x + 3 ≤ -2
x ≤ -2 - 3
x ≤ -5
So, for this case, the solution is x ≤ -5.
Combining the solutions from both cases, we have the final solution:
x ≥ -1 or x ≤ -5
Hence the number line showing the given inequality is 2nd.
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The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a normal distribution with mean 115 and standard deviation σ=25
. You suspect that incoming freshman have a mean μ
which is different from 115 because they are often excited yet anxious about entering college. To test your suspicion, you test the hypotheses H0:μ=115
, Ha:μ≠115
. You give the SSHA to 25 students who are incoming freshman and find their mean score. Based on this, you reject H0
at significance level α=0.01
. Which of the following would be most helpful in assessing the practical significance of your results?
A. Take another sample and retest just to make sure the results are not due to chance.
B. Report the P-value of your test.
C. Construct a 99% confidence interval for μ
in order to see the magnitude of the difference between 115 and your sample results.
D. Test the hypotheses again, this time using significance level α=0.001
.
(b) In testing hypotheses, if the consequences of rejecting the null hypothesis are very serious, we should
A. insist that the level of significance be smaller than the P-value.
B. use a very small level of significance.
C. insist that the P-value be smaller than the level of significance.
D. use a very large level of significance.
(c) A medical researcher is working on a new treatment for a certain type of cancer. The average survival time after diagnosis on the standard treatment is two years. In an early trial, she tries the new treatment on three subjects who have an average survival time after diagnosis of four years. Although the survival time has doubled, the results are not statistically significant even at the 0.10 significance level. The explanation is
A. the calculation was in error. The researchers forgot to include the sample size.
B. the sample size is small.
C. the placebo effect is present, which limits statistical significance.
D. that although the survival time has doubled, in reality the actual increase is really two years.
a) The correct option is C. Construct a 99% confidence interval for μ in order to see the magnitude of the difference between 115 and your sample results.
b) The correct option is B. Use a very small level of significance.
c) The correct option is B. The sample size is small.
d) The lack of statistical significance at the 0.10 significance level suggests that the observed doubling of survival time may not be practically significant as the actual increase is only two years.
(a) To assess the practical significance of the results, the most helpful approach would be to construct a 99% confidence interval for the population mean, μ. This would provide a range of values within which the true population mean is likely to fall. By comparing this interval to the hypothesized value of 115, you can evaluate the magnitude of the difference and determine if it is practically significant.
Therefore, the correct option is C. Construct a 99% confidence interval for μ in order to see the magnitude of the difference between 115 and your sample results.
(b) When the consequences of rejecting the null hypothesis are very serious, it is important to be cautious and use a very small level of significance. The level of significance determines the threshold for rejecting the null hypothesis. By using a very small level of significance, you are setting a higher standard for rejecting the null hypothesis, reducing the likelihood of making a Type I error (false positive). This ensures that strong evidence is required to support rejecting the null hypothesis when the consequences are significant.
Therefore, the correct option is B. Use a very small level of significance.
(c) In this scenario, the explanation for the lack of statistical significance at the 0.10 significance level, despite the survival time doubling, is likely due to the small sample size. With only three subjects, the sample may not provide enough statistical power to detect a significant difference. The variability in survival times within the sample might also influence the lack of significance. A larger sample size would provide more reliable and statistically significant results.
Therefore, the correct option is B. The sample size is small.
d) The explanation for the lack of statistical significance in this scenario is that although the survival time has doubled from two years to four years, the actual increase is still only two years. This means that the difference between the standard treatment and the new treatment is not as substantial as it may initially seem.
When conducting statistical tests, it is important to consider both statistical significance and practical significance. While the survival time doubling may be a positive outcome, if the actual increase is only two years, it may not be considered practically significant in the context of cancer treatment.
Statistical significance is determined by conducting hypothesis tests and examining the p-value. In this case, even at the 0.10 significance level, the results are not statistically significant, indicating that the observed difference in survival times could likely be due to chance.
It is important to interpret the results in the context of the specific situation and consider factors such as sample size, variability, and clinical significance. In this case, the small sample size of three subjects may limit the statistical power to detect a significant difference. Additionally, the placebo effect or other factors may also play a role in limiting the statistical significance of the results.
In summary, the lack of statistical significance at the 0.10 significance level suggests that the observed doubling of survival time may not be practically significant as the actual increase is only two years.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
1. The proportion is; x/4 = 12/18
2. The height of the mailbox is 2.7 feet
What is proportion?In mathematics, a proportion is an equation that states that two ratios are equal. It expresses the relationship between the quantities in terms of their relative sizes or magnitudes. Proportions are used in various areas of mathematics and real-life applications, such as ratios
We have;
Length of the mail box shadow = 4 feet
Length of the tree shadow = 18 feet
Height of the mail box = x
Height of the tree = 12 feet
Thus;
x/4 = 12/18
x = 4 * 12/18
x = 2.7 feet
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Answer this question please
The correct option is D, the parent quadratic function is:
f(x) = x²
Which one is the parent quadratic function?First, we define the parent functions as the simplest function for each type.
For example, the parent linear function is.
y = x
The parent square root function is:
y = √x
The parent absolute value function is:
y = |x|
And so on.
So the parent quadratic function is a polynomial of degree 2 where we only have the quadratic term (and no coefficient).
Thus, the correct option is D; f(x) = x²
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Over the past few years Donald made 4 trips to the amusement park he drove 399KM in all the distance traveled by him on each trip to the park is
Donald traveled approximately 100 kilometers on each of his trips to the amusement park.
Now, the distance Donald traveled on each of his trips to the amusement park.
If he drove a total of 399 kilometers over the course of four trips, we can find the average distance he traveled per trip by dividing the total distance by the number of trips.
So, We get;
= 399 divided by 4
= 399 / 4
= 99.75 kilometers per trip
≈ 100 kilometers per trip.
Therefore, Donald traveled approximately 100 kilometers on each of his trips to the amusement park.
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estimate the original volume of the pyramid in fig 15.28 given that it's frustum has a 4 m by 4 m squared top which is 12 m vertically above the square base which is 20 m by 20 m (assume that the original problem was raised to a point . Neglect the volume of the entrance of the right of the photograph)
Answer:
Step-by-step explanation:
To estimate the original volume of the pyramid in Figure 15.28, we can use the formula for the volume of a frustum of a pyramid. The frustum is the portion of the pyramid between the top and bottom, created by removing the top section.
The formula for the volume of a frustum of a pyramid is:
V = (1/3) * h * (A + sqrt(A * B) + B)
Where:
V = Volume of the frustum
h = Height of the frustum (vertical distance between the top and bottom)
A = Area of the top base
B = Area of the bottom base
Given the dimensions provided, we can calculate the areas of the bases:
Area of the top base (A) = 4 m * 4 m = 16 m²
Area of the bottom base (B) = 20 m * 20 m = 400 m²
The height of the frustum (h) is given as 12 m.
Now we can plug these values into the formula:
V = (1/3) * 12 m * (16 m² + sqrt(16 m² * 400 m²) + 400 m²)
Calculating the square root and simplifying:
V = (1/3) * 12 m * (16 m² + 20 m² + 400 m²)
V = (1/3) * 12 m * (436 m²)
V = 1744 m³
Therefore, the estimated original volume of the pyramid in Figure 15.28 is approximately 1744 cubic meters.
The Martinez family has a large lot. They have decided to create a square garden in
one corner of the lot. They want to put a walkway around the garden. The walkway
will be 5 feet wide on one side of the square and 8 feet wide on the other side. The
total area of the garden and the walkway must be 700 square feet.p
The length of a side of the square garden is 5.75 feet.
How to calculate the length(x+10)(x+5) - x² + (x+13)(x+8) - x² = 700
Simplifying and solving for x, we get:
2x^2 + 46x - 177 = 0
Using the quadratic formula, we can solve for x:
x = (-46 ± ✓46² - 4(2)(-177))) / (2(2))
x = (-46 ± 26) / 4
x = 5.75
The length of a side of the square garden is 5.75 feet.
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Create an example that will show and explain the difference between
- band b-1
Band B-1 is a band of the electromagnetic spectrum that is used for cellular communications. It is located in the 2100 MHz frequency range.
How to explain the informationBand B-2 is also a band of the electromagnetic spectrum that is used for cellular communications. It is located in the 1900 MHz frequency range.
The main difference between band B-1 and band B-2 is their range. Band B-1 has a longer range than band B-2. This is because it is located in a higher frequency range. Higher frequency ranges have shorter wavelengths, which means that they can travel through objects more easily. This makes them better for use in areas where there are a lot of obstacles, such as buildings and trees.
Band B-2 has a shorter range than band B-1, but it is better for use in areas where there are a lot of people. This is because it is located in a lower frequency range
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please help me solve
Answer:
130 degrees
Step-by-step explanation:
DE+DA=130
x-y=-1
x=-9
solution problem i am having trouble trying to solve or figure out
The solution to the System of equations is x = -9 and y = 8
We have the equation x - y = -1 and the equation x = -9. We can use the second equation to substitute the value of x in the first equation and solve for y.
Given x = -9, we substitute this value into the first equation:
(-9) - y = -1
Simplifying, we have:
-9 + y = -1
To isolate y, we can add 9 to both sides of the equation:
-9 + 9 + y = -1 + 9
This gives us:
y = 8
Therefore, the solution to the system of equations is x = -9 and y = 8.
We can check this solution by substituting the values of x and y back into the original equations:
Equation 1: x - y = -1
Substituting x = -9 and y = 8:
-9 - 8 = -1
Simplifying, we have:
-17 = -1
The equation is true, so our solution is valid.It is important to note that the solution provided is derived from the given equations and standard algebraic methods.
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160 students went on a field trip. Five buses were filled and 15 students traveled in cars. How many students were in each bus?
Each bus had ____ students.
Use the Law of Cosines to solve the problem. You must solve for BC first. Solve this problem in order.
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it turn when it changed direction? Show your work.
In a case whereby A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position the degrees north of west it turned is 72°
How can the degree be calculated?From trigonometry, the law of cosines states the side c of a triangle can be found as
c² = a² + b² - 2abcos(C)
where
C = angle opposite to side c.
a and = lengths of the other sides.
a = 94, b = 119, c = 173.
c² = a² + b² - 2abcos(C)
173² = 94² + 119² - 2 x 94 x 119cos(C)
22327cos(C) = -6932
cos(C) = -6932/22327
C = arccos(-6932/22327)
C = 108º.
Then,
T = 180 - C
= 180 - 108 = 72º.
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Mrs Sinha bought one-third metre of pink material and five-sixths metre of purple material. How much material did she buy in total?
Answer:
1 1/6 metre
Step-by-step explanation:
1/3 pink + 5/6 purple
To add, we need to get a common denominator
1/3 *2/2 = 2/6
2/6 + 5/6
7/6
Change from an improper fraction to a mixed number
1 1/6 metre
1
The dimensions of a cube and a rectangular prism are shown below.
Cube
B
2x
3x
Rectangular Prism
4x
Which statement is true?
A The surface area of the rectangular prism is 24 times larger than the surface area of
the cube.
26
The surface area of the rectangular prism is times larger than the surface area of
the cube.
C The volume of the rectangular prism is 48 times larger than the volume of the cube.
D
8
The volume of the rectangular prism is 3 times larger than the volume of the cube.
The surface area of the rectangular prism is (26/3) times larger than the surface area of the cube.
Given data ,
Let the surface area of the cube be S₁
Let the surface area of the rectangular prism be S₂
Let the volume of the cube be V₁
Let the volume of the prism be V₂
On simplifying , we get
The side length of cube = x
So , surface area of cube = 6x²
The volume of cube = x³
And , the surface area of prism = 2 ( 12x² + 8x² + 6x² )
S₂ = 52x²
And , volume of prism = l x w x h
V₂ = ( 2x ) ( 3x ) ( 4x ) = 24x²
So , S₂ = ( 26/3 ) S₁
52x² = ( 26/3 ) ( 6x² )
52x² = 52x²
Hence , The rectangular prism's surface area is (26/3) times greater than the cube's surface area.
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The complete question is attached below :
The dimensions of a cube and a rectangular prism are shown below.
Which statement is true?
A The surface area of the rectangular prism is 24 times larger than the surface area of the cube.
The surface area of the rectangular prism is times larger than the surface area of the cube.
C The volume of the rectangular prism is 48 times larger than the volume of the cube.
D The volume of the rectangular prism is 3 times larger than the volume of the cube.
You walk along the outside of a park starting at point P to point Q. You then take a shortcut back to point P, represented by PQ on the graph.
The length of the shortcut is 1 mile
The total length of your walk in the park is 1.4 miles
Given that you walk along the outside of a park starting at point P to point Q
The point P is at (0, 0)
The point Q is located at (0.6, 0.8)
We have to find the length of the shortcut
Distance=√(x₂-x₁)²+(y₂-y₁)²
PQ=√(0.6-0)²+(0.8)²
=√0.36+0.64
=√1 units
=1 mile
The total length of the park is PR+RQ
PR=√(0.6-0)²
=0.6
RQ==√(0.8-0)²
=0.8
The total length is 0.6+0.8
Which is 1.4 miles
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here is my ? hrlp mr please
Based on the information, we can infer that the correct answer is 90° clockwise (option A).
How to identify the correct rotation?To identify the correct rotation of this figure we must perform the following procedure:
1. We must identify the reference figure.
2. We must identify the figure that expresses the rotation.
3. We must identify the angle of rotation of the figure.
4. Select the option that correctly expresses the sense of rotation.
Based on the above, we can infer that the correct answer is A. 90° Clockwise because the rotation is to the right.
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a) Write the value of sin 0 for the right-angled triangle below as a fraction. b) Using your answer to part a), work out the size of angle 0, Give your answer in degrees to 1 d.p. 18 cm 13 cm 0
a. The value of sin θ = 13/18
b. The size of sin θ is 46.2 degrees
How to determine the valueFirst, we need to know the different trigonometric identities.
These trigonometric identities are listed thus;
sinecosinetangentcotangentsecantcosecantFrom trigonometric relations, we have that the ratio for sine identity is represented as;
sin θ = opposite/hypotenuse
Then, we have from the information given that;
Hypotenuse side = 18cm
Opposite side = 13cm
Substitute the values, we have;
sin θ = 13/18
Divide the values
sin θ = 0. 7222
Find the sine inverse value, we have;
so, θ = sin⁻¹(13/18) = 46. 2 degrees
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How do I divide this somebody please help
Answer:
3
Step-by-step explanation:
factorize whats common in the question
division turns to multiplication by Inverwing the fraction
at the end of the day you will be left with 3
I hope you understand