Answers
\(\text{Here,}\\\\\text{Opposite side,}~ O = 2\\\\\text{Hypotenuse,}~ H = \sqrt 5 \\\\\text{Adjacent side,}~ A = \sqrt{5-4} = \sqrt 1 =1 ~~ ;[\text{By using Pythagorean theorem}]\\\\\\\sin \theta = \dfrac{O}H = \dfrac 2{\sqrt 5}\\\\\\\cos \theta = \dfrac{A}{H} = \dfrac{1}{\sqrt 5} \\ \\\\ \tan \theta = \dfrac{O}{A} = \dfrac 21 = 2\)
\(csc \theta = \dfrac{1}{\sin \theta} = \dfrac{\sqrt 5}2\\\\\\\sec \theta = \dfrac{1}{\cos \theta} = \sqrt 5 \\\\\\\cot \theta = \dfrac 1{\tan \theta} = \dfrac 12\)
Related Questions
ou need to rent a truck for one day to move to a new house. uhaul charges $50 a day plus $0.99 per mile. to rent the same size truck from penske will cost $350 a day with no mileage charge. at how many miles will both companies have the same total cost? round your answer to the nearest whole number if needed.
Answers
The miles will be around 303 miles, both Uhaul and Penske will have the same total cost.
To determine at what point both companies have the same total cost, we need to set up an equation.
Let x be the number of miles driven.
For Uhaul, the cost will be $50 + $0.99x.
For Penske, the cost will be $350.
Setting these two expressions equal to each other, we get:
$50 + $0.99x = $350
Simplifying this equation, we get:
$0.99x = $300
U-Haul: Cost_UH = 50 + 0.99 * miles
Penske: Cost_P = 350
Set the equations equal to each other to find the number of miles where the costs are equal.
50 + 0.99 * miles = 350
Solve for the number of miles.
0.99 * miles = 350 - 50 0.99 * miles = 300 miles = 300 / 0.99
Calculate the number of miles and round to the nearest whole number if needed.
miles ≈ 303
So,
At approximately 303 miles, both companies will have the same total cost for renting a truck for one day.
Dividing both sides by $0.99, we get:
x ≈ 303.03
It is important to note that this calculation assumes that the only cost for Uhaul is the rental fee and mileage charge, and does not include any additional fees or charges that may be incurred during the rental period.
It is also important to consider other factors such as the availability of trucks, customer service, and any additional services offered by the rental companies before making a final decision.
For more questions related to total cost:
https://brainly.com/question/30355738
#SPJ11
For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
8
14
X
Answers
So, we have:
8^2 + 14^2 = x^2
Simplifying:
64 + 196 = x^2
260 = x^2
Taking the square root of both sides:
x = 16.12
So, the length of the hypotenuse is approximately 16.12.
Write an equation in slope-intercept form that describes that data in the table
Answers
From the data points given the linear equation in slope-intercept form is y = -1/2x + 4.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The first two data points are - (-3,5.5) and (-1,4.5)
The slope-intercept form of the equation is -
y = mx + b
m represents the slope of the linear equation.
To find the value of m use the formula -
(y2 - y1)/(x2 - x1)
Substitute the values into the equation -
(4.5 - 5.5)/[(-1) - (-3)]
Use the arithmetic operation of subtraction -
(-1)/(-1 + 3)
-1 / 2
So, the slope m is m = -1/2
Now, the equation becomes y = -1/2x + b
To find the value of b substitute the values of x and y in the equation -
5.5 = -1/2(-3) + b
5.5 = 3/2 + b
5.5 = 1.5 + b
b = 5.5 - 1.5
b = 4
So, now the equation becomes - y = -1/2x + 4
The graph for the equation is plotted.
Therefore, the equation is y = -1/2x + 4.
To learn more about equation from the given link
https://brainly.com/question/28871326
#SPJ1
In 2014, a survey stated that 51% of 650 randomly sampled North Carolina residents planned to set off fireworks on July 4th. a) Determine the margin of error for the 95% confidence interval for the proportion of North Carolina residents that plan to set off fireworks. Give your answer to three decimal places. Margin of Error = _____% b) How many randomly sampled residents do we need to survey if we want the 95% margin of error to be less than 3%? Sample size > _____ People
Answers
To find the required sample size for a margin of error less than 3%, we can rearrange the formula for the margin of error:
\(n = (Z^2 * p * (1 - p)) / (E^2)\)
Here, Z represents the critical value, p is the estimated proportion (0.51), and E is the desired margin of error (0.03)
To determine the margin of error for the 95% confidence interval, we need to use the formula:
Margin of Error = Critical value * Standard error
The critical value for a 95% confidence level can be obtained from the standard normal distribution table, which corresponds to 1.96. The standard error can be calculated using the following formula:
Standard error = \(\sqrt{(p * (1 - p) / n)}\)
Given that the proportion of North Carolina residents planning to set off fireworks is estimated to be 51% (0.51) based on the survey, we can substitute the values into the formula. However, the sample size (n) is not provided in the question, so we need to determine it in the next part.
To find the required sample size for a margin of error less than 3%, we can rearrange the formula for the margin of error:
\(n = (Z^2 * p * (1 - p)) / (E^2)\)
Here, Z represents the critical value, p is the estimated proportion (0.51), and E is the desired margin of error (0.03). Substituting these values into the formula, we can solve for the required sample size.
Learn more about standard normal distribution here:https://brainly.com/question/15103234
#SPJ11
Graph linear equations
Answers
Answer:
(3,-6)(1,-4)=9
Step-by-step explanation:
8) (3,-6) (1,-4)
so (3,-6)(1,-4) = 9
hope this is correct! :)
when light strikes the surface of a medium such as water or glass, its intensity decreases with depth. the beer-lambert-bouguer law states that the percentage of decrease is the same for each additional unit of depth. in a certain lake, intensity decreases about 85% for each additional meter of depth. (a) explain why intensity i is an exponential function of depth d in meters. intensity i is an exponential function of depth since i increases by a decreasing percentage as a function of depth. intensity i is an exponential function of depth since i decreases by an increasing percentage as a function of depth. intensity i is an exponential function of depth since i decreases by a decreasing percentage as a function of depth. intensity i is an exponential function of depth since i decreases by a constant percentage as a function of depth. intensity i is an exponential function of depth since i increases by an increasing percentage as a function of depth. (b) use a formula to express intensity i as an exponential function of d. (use i0 to denote the initial intensity.) i(d)
Answers
what is the answer for 2(5/3+3/4)-4/3s
Answers
10/3 + 3/4 - 4/3s
Change the denominator of 10/3 and 3/4 so they are equal. Multiply 10/3 by 4, 3/4 by 3, and 4/3 by 4 to get:
40/12 + 9/12 - 16/12s
49/12 - 16/12s
if a process is best situated close to the information corner of the om triangle, then this must mean:
Answers
Capacity is very expensive, so it is run at high utilization. There is a lot of variability in arrivals and processing times. Waiting or throughput times are long for this process.
Gaining understanding of the trade-offs operations managers must make is a major contribution of OR/MS models. One such trade-off concerns capacity, inventory, and variability: while the firm would want to function at 100% capacity utilization with very no inventory and tolerate high levels of unpredictability, this is not realistic.
The trade-off between these three competing goals is demonstrated and clarified using the conventional G/G/1 queueing paradigm. This insight can be described as a relationship between capacity, inventory, and the third parameter of information in situations where greater information can be used to lessen the variability in services or in arrivals (rather than variability).
Adopting the terminology of Lovejoy (1998), this inter- relationship is referred to as the OM triangle. Finding her company's ideal location in relation to the OM triangle is the manager's responsibility, as was mentioned in this article.
With variable arrival and processing times, there is a long wait period. It should have high utilization because of expensive capacity.
Therefore, the correct option is All the other answers are correct (A).
For more such questions on om triangle:
https://brainly.com/question/12982210
#SPJ4
complete question: If a process is best situated close to the inventory corner of the OM triangle, then this must mean:
a. All the other answers are correct.
b. Capacity is very expensive, so it is run at high utilization.
c. There is a lot of variability in arrivals and processing times.
d. Waiting or throughput times are long for this process.
What is the least common multiple of 7, 3, and 4?
Answers
Dakota and Cody sold a total of 16 items during their winter fundraising event. Cody sold four more than twice the number of items Dakota sold.
Formulate a system of equations that can be used to determine number of items Dakota sold, x, and Cody sold, y, then solve the system using substitution. Check your work by graphing.
Answers
The system of linear equation is x + y = 16 and y = 2x + 4. Dakota sold 4 items and Cody sold 12 items
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Let x represent the number of items Dakota sold and y represent the number of items Cody sold.
Dakota and Cody sold a total of 16 items, hence:
x + y = 16
y = 16 - x (1)
Also, Cody sold four more than twice the number of items Dakota sold, hence:
y = 2x + 4 (2)
substituting y = 16 - x:
16 - x = 2x + 4
3x = 12
x = 4
y = 16 - x = 16 - 4 = 12
Dakota sold 4 items and Cody sold 12 items
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
can someone help me
Simplify: (3 + 4i) (7 + 8i)
Answers
Answer:
-11
Explanation:
Answer:
-11 + 52i
Step-by-step explanation:
The border of a susan b. Anthony dollar is in the shape of a regular polygon. How many sides does the polygon have what is the measure of each angle of the border round your answer to the nearest degree
Answers
The polygon has 12 sides and each angle has a measure of 30°.
The border of a Susan B. Anthony dollar is in the shape of a regular polygon. A regular polygon is a polygon with equal sides and equal angles. To calculate the number of sides and measure of the angles, the formula for finding the measure of the interior angles of a regular polygon is used. The formula is (n-2)180/n where n is the number of sides. For the Susan B. Anthony dollar, the number of sides is 12, so the measure of the interior angles is (12-2)180/12 = 30°. Therefore, the polygon has 12 sides and each angle has a measure of 30°, rounded to the nearest degree.
Learn more about angle here
https://brainly.com/question/28451077
#SPJ4
i need help with this, graphing
Answers
Answer:
30 baloons per hourStep-by-step explanation:
Use some points on the graph:
(0, 0), (2, 60), (4, 120), (8, 240)The graph is a line passing through the origin, so this is a proportional relationship.
Standard form of such relationship is
y = kx, where k- coefficient of proportionalityUsing one of the coordinate pairs find the value of k
60 = 2kk = 60/2k = 30This is indicating the number of baloons filled per hour is 30.
Lori wants to deposit $2,500 in a simple interest account. It has a 4% annual interest rate. How long will it take for Lori to earn $200 in interest?.
Answers
Answer:
2 years
Step-by-step explanation:
First, we'll work out what the annual interest is.
\(2500*0.04=100\) (USD).
So it will take \((200\div100)=2\) years for Lori to earn $200 in interest.
Answer:
2 years
Step-by-step explanation:
TTM </3
pls answer this asap
Answers
Answer:
its c or d
Step-by-step explanation:
wait i love food sooooooooooooooooooooo much
Answers
Answer:
Me toooooooooo..!!!!!!!
Anyone know the answer?!
Answers
Answer:
Slop intercept form hopefully this helps
Is (1, 2) a solution to the equation y = 5x − 9?
Answers
Answer:
No
Step-by-step explanation:
Looking at the graph below, the dot (1,2) does not cross through the line and as a result it is not one of the points on the line.
Answer: no
Step-by-step explanation:
WILL MARK SOMEONE BRAINLIEST!!!! The chart below shows the age of the volunteers for the local pet hospital. When combined which two age groups would be greater than the 27-39 age group?
A. 0-13 and 14-26
B. 0-13 and 53-65
C. 40-52 and 14-26
D. 53-65 and 14-26
Answers
Answer:
C
Step-by-step explanation:
60+80=140 which is definitely higher than 100-120
Answer:
C. 40-52 and 14-26
Step-by-step explanation:
The age groups that can be more than 120 in number as the 27-39 age group can only be 2 groups.
The 40-52 is an age group which has 80 in number and below it the 14-28 age group has 60 in age group.
60+80 is more than the 27-39 ager group by 20 in number. Therefore, the C. 40-52 and 14-26 age groups are the 2 groups that have more than the 27-39 age group.
after subtraacting 3x^2 +4x -5 from 7x^2 +x +9 results in a polynomial. After subtracting 4x^2 - 3x from this polynomial, the difference is?
Answers
Answer:
14
Step-by-step explanation:
7x^2 + x + 9 - ( 3x^2+4x-5) - ( 4x^2-3x) =
(7x^2 -3x^2 -4x^2) + (x-4x+3x) + (9+5) = 14
U7L2 Cool Down
The measure of the arc from B to A not passing through C is 26 degrees.
1. What is the measure of angle BOA ?
2. What is the measure of angle BDA?
3. What is the measure of angle BCA ?
degrees
degrees
degrees
Answers
Using the inscribed angle theorems, the measure of the indicated angles are:
1. m∠BOA = 26°
2. m∠BDA = 13°
3. m∠BCA = 13°
What is the Inscribed Angle Theorems?Based on the inscribed angle theorem, the following relationships are established:
Inscribed angle = 2(measure of intersected arc)Central angle = measure of intersected arcGiven:
Intercepted arc BA = 26°
1. ∠BOA is central angle
Thus:
m∠BOA = 26° (inscribed angle theorems)
2. ∠BDA is inscribed angle.
m∠BDA = 1/2(30) = 13° (inscribed angle theorems)
3. m∠BCA = m∠BDA = 13° (inscribed angle theorems)
Learn more about inscribed angle theorems on:
https://brainly.com/question/30494878
How many ways can a football team of 6 players be selected from
a group of 12 boys?
Answers
there are 924 ways to select a football team of 6 players from a group of 12 boys.
To calculate the number of ways a football team of 6 players can be selected from a group of 12 boys, we can use the concept of combinations.
The number of ways to select a team of 6 players from a group of 12 is denoted by C(12, 6) or "12 choose 6". It can be calculated using the formula:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of items (boys in this case) and r is the number of items to be selected (players in the team).
Using this formula, we can calculate:
C(12, 6) = 12! / (6! * (12 - 6)!)
= (12 * 11 * 10 * 9 * 8 * 7) / (6 * 5 * 4 * 3 * 2 * 1)
= 924
To know more about number visit:
brainly.com/question/3589540
#SPJ11
the height of basketball players is considered a continuous variable. group of answer choices true false
Answers
TRUE: Basketball players' height is seen as a continuous variable.
Explain the term Continuous Random Variable?For any statistical researcher, the precise estimation of random variables including their classification are crucial.For instance, the type of distribution we can employ with a random variable depends on the nature of a random variable.Yes, as lengths are continuous variables, the random variable does indeed refer to length.
It should be noted that a length value may include as many decimal places is necessary without producing an error. A basketball player, for instance, can be 180 cm, 180.9 cm, or 188.99 cm tall.Thus, Basketball players' height is seen as a continuous variable
To know more about the Continuous Random Variable, here
https://brainly.com/question/17217746
#SPJ4
A package of floor tiles contains 26 one-foot-square tiles. find how many packages should be bought to cover a
square ballroom floor whose side measures 66 feet. note: partial packages cannot be bought.
___ packages should be bought to cover the floor
Answers
We need to buy 4,357 packages of floor tiles to cover the square ballroom floor. However, we cannot buy partial packages, so we need to round up to the nearest whole number
To cover a square ballroom floor with a side length of 66 feet, we need to calculate the total number of one-foot-square tiles required.
Since each package contains 26 tiles, we can divide the total area of the floor (66 feet * 66 feet) by the area of each tile (1 foot * 1 foot). This gives us 4,356 tiles needed to cover the entire floor.
However, we cannot buy partial packages, so we need to round up to the nearest whole number. Therefore, we need to buy 4,357 packages of floor tiles to cover the square ballroom floor.
To know more about square ballroom visit:-
https://brainly.com/question/29170070
#SPJ11
A ballet school wants to buy new slippers for students in a class. They collected the sizes and displayed them in a line plot.
A horizontal number line starting at 3.5 with tick marks every 0.5 units up to 8. The following values are labeled: the value of 4 has one dot, the value of 4.5 has two dots, the value of 5 has two dots, the value of 6 has one dot, the value of 6.5 has two dots, the value of 7 has one dot, and the value of 8 has one dot. The image is titled Ballet Shoe Sizes.
What is the range, and what does it mean in terms of this data set?
The range is 4.5, and it means that the data varies by a value of 4.5.
The range is 3.5, and it means that it is the value that occurs the most.
The range is 4.0, and it means that the data varies by a value of 4.0.
The range is 4.0, and it means that it is the value that is the smallest.
Answers
As a result, the answer to the following question, This implies that the ballet shoe range in the class vary significantly, with some students having significantly bigger or smaller feet than others.
What is range?The variable's range is calculated by taking its greatest observed value and subtracting its minimum observed value (minimum). Possible range or variational bounds: a variety of steel costs; a variety of styles; The scope or size of a method or action: perception. The maximum or anticipated range of a weapon's projectile. A list or set's range is the number between the lowest and maximum. Align all of the numbers before determining the region. Next, subtract (reduce) the lowest number from the greatest number. The solution includes the range of the list. The solution specifies the range of the list.
The range is 4.5, which implies that the difference between the data set's biggest and lowest values is 4.5. The range is 8 - 3.5 = 4.5 since the biggest number is 8 and the smallest value is 3.5. This implies that the ballet shoe sizes in the class vary significantly, with some students having significantly bigger or smaller feet than others.
To know more about range visit:
https://brainly.com/question/28135761
#SPJ1
Your first job as a new engineer is to estimate the cost of a new 3000−ft
2
heat exchange system for a plant retrofit. Your company paid $75,000 for a 1200- ft
2
heat exchanger 7 years ago. After a quick check in the literature, you determine the price index 7 years ago was 1360 and is 1478 today. If the power-sizing exponent is 0.55, determine a rough estimate for the cost of the new heat exchanger system.
Answers
To estimate the cost of a new 3000-ft² heat exchange system for a plant retrofit, we can use the price index and the information about the cost of a previous heat exchanger. Given that the price index 7 years ago was 1360 and is now 1478, and assuming a power-sizing exponent of 0.55, rough estimate for the cost of the new heat exchanger system is $77,700.
To estimate the cost, we need to account for the change in the price index over the years. The price index ratio is calculated as (new price index)/(old price index), which in this case is 1478/1360 = 1.085. Since the power-sizing exponent is 0.55, we raise the price index ratio to the power of 0.55, resulting in \(1.085^{0.55 {\)≈ 1.036.
Next, we multiply the cost of the previous heat exchanger by this factor to estimate the cost of the new system. The cost of the previous heat exchanger was $75,000, so the rough estimate for the cost of the new heat exchanger system is approximately $75,000 × 1.036 ≈ $77,700.
It's important to note that this estimate is a rough approximation and does not account for other factors such as inflation or changes in technology. It serves as a starting point for estimating the cost of the new heat exchanger system based on the given information and assumptions.
Learn more about estimate here:
https://brainly.com/question/30876115
#SPJ11
A. Graph A
B. Graph B
C. Graph
D. Graph D
Answers
Answer:
Graph C
Step-by-step explanation:
in fall 2020, the department has a cohort of 100 mds juniors. students in the class are enrolled in various classes including stor 435 (undergraduate probability), math 547 (linear algebra for applications) and comp 401 (foundations of programming). to simplify notation below i will denote these as prob., la and comp. assume the classes are not taught at the same time so there can be students who are taking all 3 courses. further there can also be students who are taking none of these 3 courses. 65 of these students are in prob, 45 in la and 40 in comp. there are 25 students that are in both prob. and comp, 20 that are in both la and comp, and 30 that are in both prob. and la. in addition, there are 10 students taking all 3 classes. how many students are taking none of the classes? (you can use venn diagrams for this problem.)
Answers
30 students are taking none of the classes.
We can use the Principle of Inclusion-Exclusion (PIE) to determine the number of students taking none of the classes. The PIE states that the total number of elements in the union of several sets is equal to the sum of elements in each set, minus the sum of elements in the pairwise intersections, plus the sum of elements in the three-way intersections, and so on.
In this case, we want to find the number of students taking none of the classes, which is equal to the total number of students (100) minus the number of students taking at least one class.
So, we can apply PIE as follows:
students taking none of the classes = 100 - (students in prob. + students in la + students in comp - students in prob. & comp - students in la & comp - students in prob. & la + students in prob., comp & la)
Using the given information, we have:
students taking none of the classes = 100 - (65 + 45 + 40 - 25 - 20 - 30 + 10)
students taking none of the classes = 100 - (95 - 25)
students taking none of the classes = 100 - 70
students taking none of the classes = 30
Hence, 30 students are taking none of the classes.
To learn more about intersection visit: brainly.com/question/28337869
#SPJ4
30 students are taking none of the classes.
We can use the Principle of Inclusion-Exclusion (PIE) to determine the number of students taking none of the classes. The PIE states that the total number of elements in the union of several sets is equal to the sum of elements in each set, minus the sum of elements in the pairwise intersections, plus the sum of elements in the three-way intersections, and so on.
In this case, we want to find the number of students taking none of the classes, which is equal to the total number of students (100) minus the number of students taking at least one class.
So, we can apply PIE as follows:
students taking none of the classes = 100 - (students in prob. + students in la + students in comp - students in prob. & comp - students in la & comp - students in prob. & la + students in prob., comp & la)
Using the given information, we have:
students taking none of the classes = 100 - (65 + 45 + 40 - 25 - 20 - 30 + 10)
students taking none of the classes = 100 - (95 - 25)
students taking none of the classes = 100 - 70
students taking none of the classes = 30
Hence, 30 students are taking none of the classes.
To learn more about Intersection
brainly.com/question/28337869
#SPJ4
Evaluate the expression 2(8 − 4)2 − 10 ÷ 2
Answers
Step-by-step explanation:
\(2(8 - 4)2 - 10 \div 2\)
Follow PEMDAS
\(2 \times (2 \times 8 - 2 \times 4) - 10 \div 2 \\ 2(16 - 8) - 10 \div 2 \\ 2(8) - 10 \div 2 \\ 16 - 10 \div 2 \\ 16- 5 \\ =11\)
Answer:i think the answer is 27
Step-by-step explanation:
solve for n.
-3n + 2 = 23
Answers
Answer:
Step-by-step explanation:
-3n + 2 = 23
Bringing like terms on one side
-3n = 23 - 2
-3n = 21
n = 21/ - 3
n = - 7
Answer:
Step-by-step explanation:
-3n + 2 = 23
Bringing like terms on one side
-3n = 23 - 2
-3n = 21
n = 21/ - 3
n = - 7