Answer:
Step-by-step explanation:
To find the perimeter of an equilateral triangle is equalled to 3s.
35 x 3
105
2 Rema has two jobs. In one year, she worked 276 hours at her first job. In the same year, she worked 3 times the number of hours at her second job. How many hours did Rema work that year at her second job?
Answer:
Step-by-step explanation:
Kind of like rema from the song calm down calm down!!
you an find it on youtub
What is the y-intercept of the line with the equation y = 4 x + 2?
a. -2
b. 4
c. 2
d. -1/2
Answer:
C. 2-----------------------------------
The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0.
To find the y-intercept, substitute 0 for x in the equation y = 4x + 2:
y = 4*0 + 2 y = 2The y-intercept is 2 and matching choice is C.
Answer:
2
Step-by-step explanation:
We need to find out the y intercept of the given equation which is y = 4x + 2 .
y intercept is a point where the graph of the equation cuts the y axis. So at y intercept x coordinate will be 0 , so plug in x = 0 , in the given equation as ;
y = 4x + 2
y = 4(0) + 2
y = 0 + 2
y = 2
Therefore the y intercept of the line is 2 . ( option C )
a particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. twenty fish are placed in a tank containing this concentration of chemical in water. a find the probability that exactly 14 survive. b find the probability that at least 10 survive.
A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. Twenty fish are placed in a tank containing this concentration of chemical in water. Therefore
a. The probability that exactly 14 fish survive is 0.263b. The probability that at least 10 fish survive is 0.983How do we calculate the probability?a) Probability that exactly 14 fish survive, Let x be the number of fish that survive. Using Binomial distribution, we have:[tex]P(X = x) = C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n is the total number of fish, p is the probability of survival and C(n,x) is the binomial coefficient. We have n = 20, p = 0.8 (since 20% die) and x = 14. [tex]C(20,14) * (0.8)^14 * (0.2)^6 = 38760 * 0.000016777216 * 0.0264241152 = 0.263[/tex] Therefore, the probability that exactly 14 fish survive is 0.263
b) Probability that at least 10 fish survive To find this probability, we can find the probability that 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 fish die, and subtract this probability from 1. Using the same formula as in (a), we have: [tex]P(X <= 9) = \sum C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n = 20, p = 0.8 and x varies from 0 to 9. Using a calculator or software, we find:P(X <= 9) = 0.0169Therefore,P(X >= 10) = 1 - P(X <= 9) = 1 - 0.0169 = 0.983 Therefore, the probability that at least 10 fish survive is 0.983.
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What is the number of normal subgroups of order 7 in a group of order 14?
In this particular question, we are being asked to find the number of normal subgroups of order 7 in a group of order 14. Before we begin, let's try to understand the different types of subgroups.Subgroups can be of two types: Proper Subgroups and Improper SubgroupsProper Subgroups are defined as subgroups which have more than one element and not equal to the entire group. Improper Subgroups are the subgroups which contain every element of the group.To determine the number of normal subgroups of order 7 in a group of order 14,
we need to use the following formula: `n_p = n/H`, where `n` represents the total number of subgroups of the group, `p` is the order of the subgroup we are looking for, and `H` is the normalizer of the subgroup in question.Using this formula, we can find that the order of the group is 14, and since 7 is a prime number, any subgroup of order 7 will be cyclic. Now, let's look at the different subgroups of the group of order 14:As 7 is a prime number and 7 divides 14, there will be one unique subgroup of order 7, and it will be cyclic.Since the group of order 14 is not a cyclic group, there are no other subgroups of order 7 besides the cyclic subgroup. Thus, the number of normal subgroups of order 7 in a group of order 14 is 1.
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Part A: Graph the system of equations {−2x+y=6x−y=1
Part B: Determine the solution from Part A.
Answer:
Step-by-step explanation:
An important math tool is graphing. It can be a straightforward method for introducing more general concepts like most and least, greater than, or less than. It can also be a great way to get your child interested in math and get them excited about it. Using graphs and charts, you can break down a lot of information into easy-to-understand formats that quickly and clearly convey key points.
Given equation 2x + y = 6 we can drive from this equation that at x = 0 y will be 6 and y =0 x will be 3 hence we have two points of the line (0,6) and (3,0)
From the Given equation (2) 6X + 3Y = 12 we can drive from this equation that at x = 0 y will be 4 and y =0 x will be 2 hence we have two points of the line (0,4) and (2,0).
Joe is taking the train from his hometown to Georgetown and back to his hometown. The distance to Georgetown is 350 miles. How much time will Joe spend traveling on the train if the train travels at an average speed of 42 miles per hour?
A. 3 hours 50 minutes
B. 4 hours 20 minutes
C. 8 hours 20 minutes
D. 11 hours 40 minutes
E. 16 hours 40 minutes
the total time Joe spends traveling on the train is 16 hours 40 minutes. Therefore, the correct answer is option E.
The time Joe spends traveling on the train can be found using the formula:
time = distance / speed
For the trip to Georgetown, the distance is 350 miles and the speed is 42 miles per hour, so the time spent traveling there is:
time to Georgetown = 350 / 42 = 8.33 hours
For the return trip, Joe travels the same distance of 350 miles at the same speed of 42 miles per hour. Therefore, the time spent traveling back is also 8.33 hours.
The total time Joe spends traveling on the train is the sum of the time for the trip to Georgetown and the time for the return trip:
total time = time to Georgetown + time from Georgetown
total time = 8.33 + 8.33
total time = 16.66 hours
Rounding to the nearest 10 minutes, the total time Joe spends traveling on the train is 16 hours 40 minutes. Therefore, the correct answer is option E.
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PLEASE HELP ME! I NEED THE ANSWERS! ITS AN EMERGENCY
The dilated figure has the following coordinates: A' (-15, 0), B' (-5, 10), C' (10, 10), D' (15, -5), and E' (5, -10).
How do the coordinates translate?In this sense, coordinates are the points where a grid system intersects. Latitude and longitude are the traditional ways to express GPS coordinates. Degrees of separation north and south from the equator, which is 0 degrees, are measured by lines of latitude coordinates.
Just multiply the coordinates of each point by 5 to construct a figure about the origin using a scale factor of 5.
A (-3, 0)
B (-1, 2)
C (2, 2)
D (3, -1)
E (1, -2)
The coordinates of each point are multiplied by 5 to enlarge the image by a scale factor of 5:
A' = (-3 * 5, 0 * 5) = (-15, 0)
B' = (-1 * 5, 2 * 5) = (-5, 10)
C' = (2 * 5, 2 * 5) = (10, 10)
D' = (3 * 5, -1 * 5) = (15, -5)
E' = (1 * 5, -2 * 5) = (5, -10)
The coordinates of the dilated figure are:
A' (-15, 0)
B' (-5, 10)
C' (10, 10)
D' (15, -5)
E' (5, -10)
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A triangle is shown on the coordinate plane below.
1 unit
H
y
(-1,9) of
-(-1, 2)
7
6
5
-3
3 d
(7,2)
-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7
-11
-2
What is the area of the triangle?
Il unit
X
You answer would be mate it would be x=66
The bottom of a cylindrical container has an area of 10 cm2. The container is filled to a height whose mean is 4 cm, and whose standard deviation is 0.2 cm. LetVdenote the volume of fluid in the container. Find μV.
The value of μV is 40 cm³.
Given,The area of bottom of cylindrical container = 10 cm²The height of container = h = Mean height = 4 cm Standard deviation of height = σ = 0.2 cm We are supposed to find the mean volume of fluid in the container.In order to calculate the mean volume, first we need to calculate the volume of fluid in the container.Volume of a cylindrical container = πr²h Where, r is the radius of the base of the container.So, we need to calculate the value of r.The area of the bottom of the container is given as 10 cm².
We know that the area of the base of a cylinder is given as:Area of base of cylinder = πr² We are given that area of the base is 10 cm². So,10 = πr²r² = 10/πr = √(10/π) We can find the volume of fluid using the values we have.Volume of fluid = πr²h = π(√(10/π))² x 4 = 40 cm³We know that mean volume, μV is given as:μV = πr²μh So, we need to calculate the value of μh. We know that standard deviation σh is given as:σh = 0.2 cm So,μh = h = 4 cm So,μV = πr²μh = π(√(10/π))² x 4 = 40 cm³
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3. The population of bees has been increasing by 5% each year since 2010. There were 1,000 bees counted in 2010. a. Create an explicit formula that models the bee population for n years since 2010. (Hint: What function have we studied that can be represented by this situation?)
Answer: 1000 x 1.05^n
Step-by-step explanation:
1.05 is the increase experienced each year and n is the number of years.
Answer:
The population of bees is increasing by 5% each year since 2010. Let P(n) be the population of bees in the nth year since 2010.
The explicit formula for the bee population can be found using the formula for compound interest:
P(n) = P(0) * (1 + r)^n
where P(0) is the initial population in 2010, r is the annual growth rate, and n is the number of years since 2010.
Substituting the given values, we have:
P(n) = 1000 * (1 + 0.05)^n
Simplifying the expression, we get:
P(n) = 1000 * 1.05^n
Therefore, the explicit formula that models the bee population for n years since 2010 is P(n) = 1000 * 1.05^n.
Will give brainly award
Using the other endpoint of the diameter, and the center of the circle write an equation of the circle
Answer:
Step-by-step explanation:
C(1,2), radius=6
Equation using [tex](x-h)^2+(y-k)^2=r^2[/tex]:
[tex](x-1)^2+(y-2)^2=36[/tex]
A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of 1 inch could be increased by
a. using only volunteers from the basketball team in the experiment.
b. using ἁ =0.05 instead of ἁ =0.05
c. using ἁ =0.05 instead of ἁ =0.01
d. giving the drug to 25 randomly selected students instead of 50.
e. using a two-sided test instead of a one-sided test.
The power of the test to detect an average increase in height of 1 inch could be increased by d. giving the drug to 25 randomly selected students instead of 50.
The power of a test is the probability of correctly rejecting the null hypothesis when it is false. In this case, the null hypothesis is that the drug does not cause people to grow taller, and the alternative hypothesis is that the drug causes an average increase in height of 1 inch.
To increase the power of the test, we want to increase the probability of correctly rejecting the null hypothesis when it is false. One way to do this is to increase the sample size, which will reduce the standard error of the mean and increase the t-statistic, making it more likely to reject the null hypothesis.
However, in this case, we can increase the power of the test by giving the drug to a smaller sample size of 25 instead of 50. This is because the effect size of the drug is not known, and giving the drug to a larger sample size will increase the variance of the data, making it harder to detect a significant difference. By reducing the sample size, we can increase the power of the test while still maintaining a reasonable sample size.
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make a simple linear regression model using education level as independent variable. if the education level is 14 years, the estimated annual income is
The estimated annual income can be calculated using the equation above. If the data point is used to calculate the slope and y-intercept of the regression line, then the annual income can be estimated using the equation y = m(14) + b.
If the education level is 14 years,
To create a simple linear regression model using education level as the independent variable, you will need to input data for education level and annual income.
This data can be used to estimate the annual income for any given education level. The equation for this linear regression model is y = mx + b, where y represents the annual income, m is the slope of the line, x is the education level, and b is the y-intercept.
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What is the solution to the trigonometric inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2pi radians?
From the given information provided, the solution to the given trigonometric inequality is (π/4, 5π/4).
To solve the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians, we can use the following steps:
Rewrite the inequality in terms of tangent:
Divide both sides by cos(x) to get:
tan(x) > 1
Find the solutions of the equation tan(x) = 1:
tan(x) = 1 when x = π/4 or x = 5π/4.
Check the sign of tangent in the intervals between the solutions:
We need to check the sign of tan(x) for x values in the following intervals:
(0, π/4), (π/4, 5π/4), and (5π/4, 2π).
In the interval (0, π/4), tan(x) is positive and less than 1.
In the interval (π/4, 5π/4), tan(x) is positive and greater than 1.
In the interval (5π/4, 2π), tan(x) is negative and less than -1.
Determine the solution set:
Since we are looking for x values that satisfy tan(x) > 1, the only interval that contains such values is (π/4, 5π/4). Therefore, the solution to the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians is:
π/4 < x < 5π/4
In interval notation, we can write:
(π/4, 5π/4)
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Need help to solve this please!!
Answer:
0.999
Step-by-step explanation:
If the driver wore a seat belt, that is the only column we have to look at.
The chance the driver survived is number survived / number total.
Plugging in, we get 412,042/412,493, or about 0.999.
Hope this helps!
Determine the total amount of money that was utilized on fuel in June 2022
Therefore, the total amount of money utilized on fuel in June 2022 is R11 095,60.
What is percent?Percent is a way of expressing a quantity as a fraction of 100. It is denoted by the symbol %, which means "per hundred". Percentages are often used to represent proportions or ratios in various fields, including finance, science, and statistics. For example, an interest rate of 5% means that for every hundred dollars borrowed or invested, five dollars of interest will be charged or earned.
Here,
(a) To calculate the total distance covered by the water tanker in March 2022, we need to find the distance travelled per day and multiply it by the number of days in March.
Distance travelled per day = 2 × 18 = 36 km (since it's a return trip)
Number of weekdays in March = 31 - 4 (Saturdays) = 27
Total distance covered = distance per day × number of weekdays
= 36 km/day × 27 days
= 972 km
(b) To determine the quantity of fuel utilized by the water tanker in March 2022, we need to divide the total distance covered by the average fuel consumption rate.
Fuel consumption rate = 5 km/ℓ
Total distance covered = 972 km
Fuel utilized = total distance covered / fuel consumption rate
= 972 km / 5 km/ℓ
= 194.4 ℓ
(c) To determine the total amount of money utilized on fuel for the water tanker in March 2022, we need to multiply the fuel quantity by the fuel price.
Fuel price in March 2022 = R16,28/ℓ
Fuel utilized = 194.4 ℓ
Total cost of fuel = fuel price × fuel quantity
= R16,28/ℓ × 194.4 ℓ
= R3 163,39
Therefore, the total amount of money utilized on fuel for the water tanker in March 2022 is R3 163,39.
(d) To determine the total amount of money utilized on fuel in June 2022, we need to repeat the above calculation using the June fuel price.
Fuel price in June 2022 = R24,14/ℓ
Fuel capacity = 460 ℓ
Total cost of fuel = fuel price × fuel capacity
= R24,14/ℓ × 460 ℓ
= R11 095,60
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Complete question:
Records of the number of water tankers that were supplied to the construction site appear in the calender on ANNEXURE A. The water source is at a distance of about 18 km (return trip) from the construction site. The water tanker has a fuel capacity of 460 litres.. The rate of fuel consumption of the Mercedes water tanker averages 5 km/ℓ. The prices of fuel per litre in March and June 2022 appear below. JUNE 2022 FUEL PRICES \begin{tabular}{|l|l|} \hline DIESEL & COST \\ \hline 50ppm & R24,14 \\ \hline \end{tabular} Source: 4.1 (a) Calculate the total distance that the water tanker has covered in March (2) 2022. (b) Hence, determine the quantity of fuel that was utilized by the water tanker in March 2022. (c) Determine the total amount of money that was utilized on fuel for the water tanker in March 2022. (2) 4.2 Determine the total amount of money that was utilized on fuel in June 2022.
(1 point) Suppose f(x,y) = xy(1 - 4x - 2y). f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x,y) comes before (z, w) if x
Increasing lexicographic order: (0, 0), (0, 1/2), (1/4, 0), (1/4, 1/2)).Thus, the increasing lexicographic order of the critical points of the function f(x,y) = xy(1 - 4x - 2y) are (0, 0), (0, 1/2), (1/4, 0), and (1/4, 1/2).
lexicographic order: (0, 0), (0, 1/2), (1/4, 0), (1/4, 1/2)).Thus, the increasing lexicographic order of the critical points of the function f(x,y) = xy(1 - 4x - 2y) are (0, 0), (0, 1/2), (1/4, 0), and (1/4, 1/2).
Suppose that f(x,y) = xy(1 - 4x - 2y). f(x,y) has 4 critical points.
Let's discuss what are critical points and how we can determine them,A critical point is a point on the graph where the derivative changes its sign.
In other words, the derivative either changes from negative to positive or from positive to negative. A critical point is also known as a stationary point or a turning point
To determine the critical points, we need to find the derivative of the given function and set it equal to zero.The given function is[tex]f(x,y) = xy(1 - 4x - 2y).[/tex]
Let's find the partial derivative of f with respect to [tex]x:f_x(x,y) = y(1 - 4x - 2y) - 4xy = (1-2y)(1-4x)y.[/tex] (1)
Now, find the partial derivative of f with respect to y:f_y(x,y) = x(1 - 4x - 2y) - 2xy = (1-2x)(1-2y)x. (2)
To find the critical points, we need to set both partial derivatives (1) and (2) equal to zero.
(1-2y)(1-4x) = 0 and (1-2x)(1-2y) = 0.
Solving both equations separately, we have the following critical points:(1/4, 1/2), (1/4, 0), (0, 1/2), and (0, 0).
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hi i want help with maths and the question i need help is
there are 32 students in a class and 20 of them owns at least one pet. what if the fraction of the class own pets? give answer in simplest form.
Get back to me quickly
Answer: 3/5
hope this helped you. Please brainliest! :D
Step-by-step explanation: If I am wrong tell me :D
Solve for x and graph the solution on the number line below
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
The second figure.
Step-by-step explanation:
The first figure's perimeter is:
70 in + 42 in + 56 in = 168 inches.
And the second figure's perimeter is:
42 in + 33 in + 33 in + 64 in = 172 inches.
Therefore, Figure 1 < Figure 2.
Landon buys cookies and lemons at the store he pays a total of $29.12 He pays $2.66 for the cookies he by seven bags of lemons that each cost the same amount Which tape diagram could be used to represent the contacts if X represents how much each bag of lemons cost
The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).
what is unitary method ?A way for resolving proportionality issues is the unitary method. Finding the value of one unit and then using that value to determine the value of another unit in relation to the first is what this process entails. If we already know that three pens cost $6, for instance, we can use the unitary technique to get the price of five pens as follows: 1 pen costs $6, 3 pens cost $2. Five pens cost $10, or $5 multiplied by $2.
given
The arrow on the right in the diagram above, which is equal to $29.12, represents the total cost of the cookies and lemons.
The first segment on the left, which is $2.66, represents the price of the cookies.
The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).
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What is the Smallest Positive Integer with at least 8 odd Factors and at least 16 even Factors?
Therefore, the smallest positive integer with at least 8 odd factors and at least 16 even factors is N = 1800.
what is Combination?In mathematics, combination is a way to count the number of possible selections of k objects from a set of n distinct objects, without regard to the order in which they are selected.
The number of combinations of k objects from a set of n objects is denoted by [tex]nCk[/tex] or [tex]C(n,k),[/tex] and is given by the formula:
[tex]nCk = n! / (k! *(n-k)!)[/tex]
where n! denotes the factorial of n, i.e., the product of all positive integers up to n.
by the question.
Now, let's consider the parity (evenness or oddness) of the factors of N. A factor of N is odd if and only if it has an odd number of factors of each odd prime factor of N. Similarly, a factor of N is even if and only if it has an even number of factors of each odd prime factor of N. Therefore, the condition that N has at least 8 odd factors and at least 16 even factors can be expressed as:
[tex](a_{1} +1) * (a_{2} +1) * ... * (an+1) = 8 * 2^{16}[/tex]
Let's consider the factor 2 separately. Since N has at least 16 even factors, it must have at least 16 factors of 2. Therefore, we have a_i >= 4 for at least one prime factor p_i=2. Let's assume without loss of generality that p[tex]1=2[/tex] and [tex]a1 > =4.[/tex]
Now, let's consider the remaining prime factors of N. Since N has at least 8 odd factors, it must have at least 8 factors that are not divisible by 2. Therefore, the product (a2+1) * ... * (an+1) must be at least 8. Let's assume without loss of generality that n>=2 (i.e., N has at least three distinct prime factors).
Since a_i >= 4 for i=1, we have:
[tex]N > = 2^4 * p2 * p3 > = 2^4 * 3 * 5 = 240[/tex]
Let's now try to find the smallest such N. To minimize N, we want to make the product (a2+1) * ... * (an+1) as small as possible. Since 8 = 2 * 2 * 2, we can try to distribute the factors 2, 2, 2 among the factors (a2+1), (a3+1), (a4+1) in such a way that their product is minimized. The only possibility is:
[tex](a2+1) = 2^2, (a3+1) = 2^1, (a4+1) = 2^1[/tex]
This gives us:
[tex]N = 2^4 * 3^2 * 5^2 = 1800[/tex]
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Are the following statements equivalent? a>b and there is the number c ,so that a=b+c
No, the statements are not equivalent as the statement "a > b" simply means that "a" is greater than "b" and there exists a number "c" such that when added to "b", it equals "a". This does not necessarily mean that "a" is greater than "b".
The statements "a>b" and "there is the number c, so that a=b+c" are not equivalent. The statement "a>b" simply means that "a" is greater than "b," while the statement "there is the number c, so that a=b+c" means that "a" can be expressed as the sum of "b" and another number "c."
These statements are not equivalent because even if "a" is greater than "b," it may not be possible to express "a" as the sum of "b" and another number "c."
Additionally, even if "a" can be expressed as the sum of "b" and another number "c," it may not necessarily be true that "a" is greater than "b."
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If the cost of 7m is Rs. 1470, find the cost of 5m cloth
By using unitary method, we found that the cost of 5m cloth is Rs. 1050.
According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,
Cost of 1m cloth = Total cost of 7m cloth/7
We know that the total cost of 7m cloth is Rs. 1470. Therefore,
Cost of 1m cloth = 1470/7
Cost of 1m cloth = Rs. 210
This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.
Cost of 5m cloth = Cost of 1m cloth x 5
Cost of 5m cloth = Rs. 210 x 5
Cost of 5m cloth = Rs. 1050
Therefore, the cost of 5m cloth is Rs. 1050.
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A sector subtends an angle of 42° at the centre of a circle of radius 2.8 cm. Calculate the perimeter of the sector.
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =42\\ r=2.8 \end{cases}\implies s=\cfrac{(42)\pi (2.8)}{180}\implies s=\cfrac{49\pi }{75}\implies s\approx 2.05 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Perimeter of the sector} }{2.8~~ + ~~2.8~~ + ~~2.05} ~~ \approx ~~ \text{\LARGE 7.65}[/tex]
let's recall that the sector's perimeter includes the arc plust the radii.
At a basketball game, an air cannon launches T-shirts into the crowd. The function y=−18x2+4x
represents the path of a T-shirt. The function 3y=2x−14
represents the height of the bleachers. In both functions, y
represents vertical height (in feet) and x
represents horizontal distance (in feet). At what height does the T-shirt land in the bleachers?
The height that the T-short lands on the bleachers is x = 0.65.
What is quadratic formula?The quadratic equation may be solved by adding and subtracting the same number within the parenthesis to get a perfect square trinomial, which is how the quadratic formula is obtained. A version of the equation that can be solved using the square root function is the result of this method.
Given that it can be used to solve any quadratic equation regardless of the values of the variables a, b, and c, the quadratic formula is an effective tool for solving quadratic equations.
The equation of the path of T-shirt is y = -18x² + 4x and that of the height of bleachers is 3y=2x−14 or y = 2/3x - 14/3
To find the height of the T-shirt landing we find the intersection of the two equations as follows:
-18x² + 4x = (2x - 14)/3
-54x² + 12x = 2x - 14
54x² - 10x - 14 = 0
27x² - 5x - 7 = 0
Using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Substitute the values;
x = (-(-5) ± √((-5)² - 4(27)(-7))) / 2(27)
x = (5 ± √(925)) / 54
x = (5 ± 5√37) / 54
x = (5 + 5√37) / 54 = 0.65 and
x = (5 - 5√37) / 54 = -0.47
Hence, the height that the T-short lands on the bleachers is x = 0.65.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
w = 28 miles
Step-by-step explanation:
The perimeter is the sum of the lengths of the sides.
The sum of the lengths of the sides is w + 28 + 28.
The perimeter is 84.
w + 28 + 28 must equal 84.
w + 28 + 28 = 84
Now we solve for w.
Add 28 and 28.
w + 56 = 84
Subtract 56 from both sides.
w = 28
Answer: w = 28 miles
Formula: m=;
X₂-X1
P₁ = (X₁, Y₁) P₂ = (X2, Y₂)
1) P₁=(-1,5) y P₂=(-2,-6)
Cómo resolver este ejercicio de ecuaciones lineales de dos puntos
The equation m = 12 + 2Y1 gives the slope of the line through the points P1=(-1.5, Y1) and P2=(-2, -6)
In mathematics, how do you find coordinates?To find a point's coordinates in a coordinate system, you perform the opposite. Starting at the point, move vertically up or down until you reach the x-axis. Your x-coordinate is shown there. Afterwards, you'll be able to get a better understanding of how to use it.
It is assumed that the formula you supplied would be used to determine the slope (m) of the line connecting the two specified points, P1 and P2.
We may use the following formula to find the slope (m) of the line passing through the coordinates P1=(X1, Y1) and P2=(X2, Y2):m = (Y2 - Y1) / (X2 - X1) (X2 - X1)
Using the values provided:
P1 = (-1.5, Y1) (-1.5, Y1)
P2 = (-2, -6) (-2, -6)
These values can be used as substitutes in the formula:
m = (-6 - Y1) / (-2 - (-1.5))
Making the denominator simpler:
m = (-6 - Y1) / (-2 + 1.5)
m = (-6 - Y1) / (-0.5)
m = 12 + 2Y1
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Question:
Formula: m=;
X₂-X1
P₁ = (X₁, Y₁) P₂ = (X2, Y₂)
1) P₁=(-1.5) and P₂=(-2,-6)
How to solve this exercise of linear equations of two points.
An article reports that in a sample of 123 hip surgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviation of 24.1 minutes.
find
A. The 95% confidence interval is (,)
B.The 99.5% confidence interval is(,)
C. A surgeon claims that the mean surgery time is between 133.71 and 140.09 minutes. With what level of confidence can this statement be made? Express the answer as a percent and round to two decimal places.
D. Approximately how many surgeries must be sampled so that a 95% confidence interval will specify the mean to within ±3 minutes? Round up the answer to the nearest integer.
F.Approximately how many surgeries must be sampled so that a 99% confidence interval will specify the mean to within ±3 minutes? Round up the answer to the nearest integer.
The minimum sample size required to get a 99% confidence interval that will specify the mean to within ±3 minutes is 597 (Rounded up to the nearest integer).
A) The 95% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (130.82, 142.98).Explanation:Given,Sample size, n = 123Average surgery time, μ = 136.9 minutesStandard deviation, σ = 24.1 minutesWe know that for a sample of size n, the 95% confidence interval is given by, (Formula1)Where, z is the z-score, α/2 = 0.05/2 = 0.025 is the level of significance and n - 1 = 122 degrees of freedom.Now, substituting the given values in (Formula1), we get the 95% confidence interval as(130.82, 142.98)Thus, the 95% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (130.82, 142.98).B) The 99.5% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (127.93, 145.87).Explanation:We know that for a sample of size n, the 99.5% confidence interval is given by, (Formula2)Where, z is the z-score, α/2 = 0.005/2 = 0.0025 is the level of significance and n - 1 = 122 degrees of freedom.Now, substituting the given values in (Formula2), we get the 99.5% confidence interval as (127.93, 145.87).Thus, the 99.5% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (127.93, 145.87).C) The surgeon's claim that the mean surgery time is between 133.71 and 140.09 minutes is equivalent to the confidence interval (133.71, 140.09). The surgeon's claim falls inside the 95% confidence interval, (130.82, 142.98), therefore we can say that the surgeon's claim can be made with 95% confidence.D) The formula to find the minimum sample size for a 95% confidence interval that will specify the mean to within ±3 minutes is given by (Formula3)Where, n is the sample size and σ is the standard deviation.Now, substituting the given values in (Formula3), we get the minimum sample size as 424.15.The minimum sample size required to get a 95% confidence interval that will specify the mean to within ±3 minutes is 425 (Rounded up to the nearest integer).F) The formula to find the minimum sample size for a 99% confidence interval that will specify the mean to within ±3 minutes is given by (Formula4)Where, n is the sample size and σ is the standard deviation.Now, substituting the given values in (Formula4), we get the minimum sample size as 596.73.The minimum sample size required to get a 99% confidence interval that will specify the mean to within ±3 minutes is 597 (Rounded up to the nearest integer).
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Find the value of x in the following diagram.
Round your answer to the nearest hundredth.
Answer:
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Step-by-step explanation:
