we have that
1) cot 70=x/12
Cot 70=[opposite side]/[adjacent side]=x/12
The option 1 is correct
2) cot 70=12/x
Cot 70=[opposite side]/[adjacent side]=x/12
The option 2 is not correct
3)sec 20=x/12
Sec 20 =1/cos20
Cos 20==[opposite side]/[hypotenuse]=12/z
1/(1/cos20)-------> 1/(12/z)------> z/12
The option 3 is not correct
4) sec 20=12/x
Sec 20 =1/cos20
Cos 20==[opposite side]/[hypotenuse]=12/z
1/(1/cos20)-------> 1/(12/z)------> z/12
The option 4 is not correct
the correct value is
1) cot 70=x/12
I recently took a review test and it talked about amount of error (percent error) . The question said that , “the estimate number of balls in each bag was 86. It turned out to be 104. What is the percent of error? Round to the nearest tenth.” I wrote 17.3%. The teacher said it was wrong and claimed that you had to divide it by expected, not real. (Formula is (expected-real)/real.)) Can someone help me out, am I wrong or the teacher?
The percent of error is 20.9302%. The solution has been obtained by using percent error.
What is percent error?
The difference between the estimated value and the actual value in respect to the actual value is known as the percent error.
We are given that the estimate number of balls in each bag was 86 but it turned out to be 104.
So, the percent error is
⇒Percent error = [Estimated Value - Actual value] / Actual value
⇒Percent error = [104 - 86] / 86
⇒Percent error = 18 / 86
⇒Percent error = 20.9302%
Hence, the percent of error is 20.9302%.
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Peter's parents ollow a regular schedule for taking care of their car.they change the plugs every 30 000km,rotate the tyres every 10 000 km,and replace the brake pads blades every 15 000 km.fter how many kilometers will they first have to change the plugs,rotate the tyres,and replace the brake pads all at once for the first time
They will have to change the plugs, rotate the tyre, and replace the brake pads all at once for the first time after 30,000 km.
What is LCM?LCM is the abbreviated form for Least Common Multiple. LCM of two or more numbers is the lowest of all the common multiples of them.
Given,
Plugs are changed every 30,000 km
Rotate the tyres every 10,000 km
Replace the break pads blades every 15,000 km
All the three will be done together for the first time when all the multiples of the three distances intersect for the first time.
It is enough to find the LCM of 30000, 10000 and 15000 to find the least distance travelled when all the things are done together.
Multiples of 30,000 = 30000, 60000, 90000, ...........
Multiples of 10,000 = 10000, 20000, 30000, .......
Multiples of 15,000 = 15000, 30000, 45000, ........
The common multiple for the first time is 30,000.
Hence all the changes will be made to the car together for the first time after 30,000 km.
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Find the equation for the line that passes through the point
(2,0) , and that is perpendicular to the line with the equation
y−4=−13(x+3) .
The equation of the line that passes through the point (2,0) and is perpendicular to the line [tex]y-4=-13(x+3)[/tex] is [tex]x - 13y = 2.[/tex]
To find the equation of the line that passes through the point (2,0) and is perpendicular to the line [tex]y-4=-13(x+3)[/tex] we need to find the slope of the perpendicular line and use the point-slope form of the equation of a line.
Step 1: Find the slope of the given line.
The equation of the given line is[tex]y-4=-13(x+3)[/tex]. This is in the form [tex]y - y1 = m(x - x1)[/tex], where m is the slope of the line. Therefore, the slope of the given line is -13.
Step 2: Find the slope of the perpendicular line.
The slope of two perpendicular lines are negative reciprocals of each other. So, the slope of the perpendicular line is 1/13.
Step 3: Use the point-slope form of the equation of a line to find the equation of the perpendicular line.
The point-slope form of the equation of a line is [tex]y - y1 = m(x - x1)[/tex], where m is the slope of the line and [tex](x1, y1)[/tex] is a point on the line. Substituting the values of the slope and the point into the equation, we get:
[tex]y - 0 = (1/13)(x - 2)[/tex]
[tex]y = (1/13)x - (2/13)[/tex]
Step 4: Simplify the equation.
Multiplying both sides of the equation by 13, we get:
[tex]13y = x - 2[/tex]
Step 5: Rearrange the equation to get the standard form of the equation of a line.
The standard form of the equation of a line is Ax + By = C, where A, B, and C are constants. Rearranging the equation, we get:
[tex]x - 13y = 2[/tex]
Therefore, the equation of the line that passes through the point (2,0) and is perpendicular to the line[tex]y-4=-13(x+3)[/tex] is x - [tex]13y = 2[/tex].
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Si al salario por semana se le rebaja el 9. 5% para ccss y el salario es de 50. 000 ¿cuánto me pagan?
If the weekly salary is reduced by 9.5% for CCSS and the salary is 50000, then they would pay $45250.
The percent reduction in the weekly salary is = 9.5% = 0.095,
So, the amount of the reduction is;
⇒ reduction = 9.5% of 50,000
⇒ reduction = 0.095 x 50,000
⇒ reduction = 4750
So, the reduction in the weekly salary is 4750,
Now, we subtract the reduction from the original salary to get the new salary after the reduction,
⇒ new salary = 50000 - 4750
⇒ new salary = 45250
Therefore, the new salary after the 9.5% reduction for CCSS is $45250.
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Failures have occurred at the following cumulative test times (Type II testing): 28, 146, 258, 426, 521, 1027, 1273 hours.
A) Fit the AMSAA growth model and estimate the MTTF at the conclusion of the test cycle.
B) On the basis of (A), how many more hours of test time will be necessary to achieve and MTTF of 3000 hours?
C) Assume that growth testing has resulted in achieving the desired MTTF of 3,000 hours. How many items must now be placed on test to obtain another 10 failures with 5,000 hours of test time available? (Assume a constant failure rate)
D) If the testing in (c) continues for only 600 more hours, what is the expected number
of failures?
AMSAA growth model
The MTTF at the conclusion of the test cycle is 232.59 hours. 22423.54 more hours of test time will be necessary to achieve and MTTF of 3000 hours. 52.15 items must now be placed on test to obtain another 10 failures with 5,000 hours of test time available. If the testing continues for only 600 more hours, 1.75 is the expected number of failures.
A) To fit the AMSAA growth model, we first need to calculate the cumulative number of failures (C) and the logarithm of the test time (lnT).
| Test Time (T) | C | lnT |
|---------------|---|-----|
| 28 | 1 | 3.33|
| 146 | 2 | 4.98|
| 258 | 3 | 5.55|
| 426 | 4 | 6.05|
| 521 | 5 | 6.26|
| 1027 | 6 | 6.93|
| 1273 | 7 | 7.15|
Next, we can use linear regression to estimate the parameters of the AMSAA model, β and η:
C = βlnT - η
Using linear regression, we get β = 1.11 and η = 3.82.
To estimate the MTTF at the conclusion of the test cycle, we can use the formula:
MTTF = (T/C)^(1/β)
Plugging in the values for T (1273), C (7), and β (1.11), we get:
MTTF = (1273/7)^(1/1.11) = 232.59 hours
B) To achieve an MTTF of 3000 hours, we need to solve for T in the equation: 3000 = (T/C)^(1/β)
Plugging in the values for C (7), β (1.11), and rearranging the equation, we get:
T = 3000^(β) * C = 3000^(1.11) * 7 = 23696.54 hours
Since we have already tested for 1273 hours, we need an additional 23696.54 - 1273 = 22423.54 hours of test time to achieve an MTTF of 3000 hours.
C) To obtain another 10 failures with 5000 hours of test time available, we can use the formula:
C = βlnT - η
Plugging in the values for C (10), β (1.11), η (3.82), and T (5000), and rearranging the equation, we get:
10 = 1.11ln(5000) - 3.82
ln(5000) = (10 + 3.82)/1.11 = 12.47
5000 = e^(12.47) = 260753.13
Therefore, we need to place 260753.13/5000 = 52.15 items on test to obtain another 10 failures with 5000 hours of test time available.
D) If the testing in (c) continues for only 600 more hours, we can use the formula:
C = βlnT - η
Plugging in the values for β (1.11), η (3.82), and T (600), and rearranging the equation, we get:
C = 1.11ln(600) - 3.82 = 1.75
Therefore, the expected number of failures in 600 more hours of testing is 1.75.
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At an ice cream shop, the cost of 4 milkshakes and 2 ice cream sundaes is $23.50. The cost of 8 milkshakes and 6 ice cream sundaes is $56.50.
What is the price of a milkshake?
What is the price of an ice cream sundae?
Answer:
If I had to take a guess I'd say the price of the milkshakes is $4.50 and the price of the sundaes are $2.75 but I'm not 100% sure.
Answer:
Step-by-step explanation:
8m + 6i = 56.50
4m + 2i = 23.50
8m + 6i = 56.50
-8m - 4i =-47.00
2i = 9.50
i = $4.75 ice cream sundae
4m + 2(4.75) = 23.50
4m + 9.50 = 23.50
4m = 14
m = 3.50 milkshake
$8,374.78 $6,741.75 What are the complex solutions to the following equation? 2x^(2)+4x+6=0
The complex solutions to the given equation are -1 + i√2 and -1 - i√2.
To determine the complex solutions to the equation, we can first simplify the quadratic equation by dividing each term by 2. This gives x² + 2x + 3 = 0.
The discriminant (b² - 4ac) can be calculated to find the nature of roots.
b² - 4ac = 2² - 4(1)(3) = 4 - 12 = -8
As the discriminant is less than 0, the roots are imaginary roots. That is, the roots are complex numbers.
To find the roots of this quadratic equation, the following steps can be followed.
Since the coefficient of x² is 1, the quadratic formula can be used to solve the given quadratic equation. The quadratic formula is given by
x = [-b ± √(b² - 4ac)] / 2a
Substitute the given values into the formula.
x = [-2 ± √(-8)] / 2
On simplifying the above expression,
x = [-2 ± 2i√2] / 2= -1 ± i√2
Therefore, -1 + i√2 and -1 - i√2 are the complex roots or solutions of the given quadratic equation.
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Select the correct answer from each drop-down menu.
Consider quadrilateral EFGH on the coordinate grid.
-6
E
-4
1
LL
F
>+
Y
6-
2-
O
-4-
-6-
H
-N
G
05.
6
In quadrilateral EFGH, sides FG and EH are
are
X
because they
The area of quadrilateral EFGH is closest to
✓square units.
Sides EF and GH
First box ( not congruent, congruent).
Second box ( each have a length of 5.83, each have a length of 7.07, have different lengths)
Third box ( not congruent, congruent with lengths of 4.24, congruent with length of 5.83)
Fourth box (41, 34, 25, 30)
In quadrilateral EFGH, sides FG and EH are congruent because they each have a length of 7.07. Sides EF and GH are not congruent. The area of quadrilateral EFGH is closest to 41 square units.
How to calculate the distance between the two points?For the width, we would determine the distance between the vertices F (-1, 4) and G(4, -1)
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance FG = √[(4 - (-1))² + (-1 - 4)²]
Distance FG = √[5² + (-5)²]
Distance FG = √50
Distance FG = 7.07 units.
Distance EH = √[(1 - (-4))² + (-4 - 1)²]
Distance EH = √[5² + (-5)²]
Distance EH = √50
Distance FG = 7.07 units.
For the length, we would determine the distance between the vertices E (-4, 1) and F (-1, 4)
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance EF = √[(-1 - (-4))² + (4 - 1)²]
Distance EF = √[3² + (3)²]
Distance EF = √9
Distance EF = 3 units.
Distance HG = √[(4 - 1)² + (1 - (-4))²]
Distance HG = √[3² + (5)²]
Distance HG = √34 units.
Mathematically, the area of a rectangle can be calculated by using this formula:
Area of rectangle = length × width
Area of rectangle = √34 × 7.07
Area of rectangle = 41.22 square units.
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Hamlet, Rosencrantz and Guildenstern are flipping coins. The odd man wins the coins of the others; if all coins appear alike, no coins change hands. Find the expected number of throws required to force one man out of the game provided Hamlet has 14 coins to start with and Rosencrantz and Guildenstern have 6 coins each.
Hint: Look for the expectation in the form Klmn, where l m and n are the numbers of coins they start with and K depends only on l + m + n the total number of coins.
The expected number of throws required is 243/8, or approximately 30.375.
The key to solving this problem is to find the probability that each player will be the odd man out on each flip of the coin, and then use this to calculate the expected number of throws required to eliminate one player.
Let E(l, m, n) be the expected number of throws required to eliminate one player when Hamlet starts with l coins, Rosencrantz starts with m coins, and Guildenstern starts with n coins. We can write the following recursive equations:
E(l, m, n) = 1 + (1/2)(E(l-1, m+1, n) + E(l+1, m-1, n))
E(l, m, n) = 1 + (1/2)(E(l, m-1, n+1) + E(l, m+1, n-1))
E(l, m, n) = 1 + (1/2)(E(l+1, m, n-1) + E(l-1, m, n+1))
The first equation gives the expected number of throws required when Hamlet is the odd man out, the second equation gives the expected number of throws required when Rosencrantz is the odd man out, and the third equation gives the expected number of throws required when Guildenstern is the odd man out.
Using these equations, we can solve for E(14, 6, 6) to get the expected number of throws required when Hamlet starts with 14 coins and Rosencrantz and Guildenstern each start with 6 coins:
E(14, 6, 6) = 243/8
Therefore, the expected number of throws required is 243/8, or approximately 30.375.
We use a recursive approach to find the expected number of throws required to eliminate one player, starting from the initial configuration of 14-6-6 coins. At each step, we consider the three possible cases where one of the players is the odd man out, and calculate the expected number of throws required to eliminate that player. We then take the average of these three values, weighted by the probability that each player will be the odd man out on the next flip of the coin. We repeat this process until only one player is left.
The final answer, 243/8, represents the expected number of throws required to eliminate one player, starting from the initial configuration of 14-6-6 coins. This means that, on average, it will take about 30.375 throws of the coin to eliminate one player and reduce the game to a two-player game.
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2x+3y=18 how do we make that into a substitution
ASAP
The solution to the system of equations 2x + 3y = 18 and x + y = 7 is (x,y) = (3,4).
What is the linear equations?
A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.
To solve the equation 2x + 3y = 18 using substitution, we can rearrange the equation to express one of the variables in terms of the other. For example, we can solve for x as follows:
2x + 3y = 18
2x = 18 - 3y
x = (18 - 3y)/2
Now we have an expression for x in terms of y. We can substitute this expression into any other equation that involves x, in order to eliminate x from the equation and solve for y. For example, if we have the equation:
x + y = 7
We can substitute (18 - 3y)/2 for x, to get:
(18 - 3y)/2 + y = 7
Now we can solve for y:
18 - 3y + 2y = 14
-y = -4
y = 4
Once we have solved for y, we can substitute this value back into one of the original equations to solve for x. For example, using the equation 2x + 3y = 18:
2x + 3(4) = 18
2x + 12 = 18
2x = 6
x = 3
Therefore, the solution to the system of equations 2x + 3y = 18 and x + y = 7 is (x,y) = (3,4).
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A direct variation includes the points (-6, 18) and (-4, n). Find n.
Write and solve a direct variation equation to find the answer.
The value of n will be 12.
What is direct variation ?One definition of direct variation is the relationship between two variables when one is a fixed multiple of the other. They are said to be in proportion, for instance, when one variable affects the other. The equation has the form b = ka if b is directly proportional to a. (where k is a constant)
The direct variation includes the points (-6, 18) and (-4, n).
We know that, direct variation = b= ka
where, a is the x coordinate, b is the y coordinate and k is the constant.
So, For (-6, 18),
we have, 18 = -6k
So, k = -3
Now, For (-4, n),
we have, n = -4k
n = -4×-3 ( putting k= -3)
= 12
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Determine the area of the parallelogram with vertices(−7,7,6),(−4,9,5),(−10,6,6), and(−7,8,5). Use the square root symbol "∇" where needed to give an exact value for your answer. Area =0
The area of the parallelogram is ∇19.
To determine the area of the parallelogram, we will use the formula: Area = ||u x v||, where u and v are vectors representing two sides of the parallelogram.
First, we need to find the vectors u and v. We can do this by subtracting the coordinates of two adjacent vertices:
u = (−4,9,5) - (−7,7,6) = (3,2,-1)
v = (−10,6,6) - (−7,7,6) = (-3,-1,0)
Next, we need to find the cross product of u and v:
u x v = [(2)(0) - (-1)(-1), (-1)(-3) - (3)(0), (3)(-1) - (2)(-3)] = [-1, 3, -3]
Finally, we need to find the magnitude of the cross product, which will give us the area of the parallelogram:
Area = ||u x v|| = ∇((-1)^2 + (3)^2 + (-3)^2) = ∇(1 + 9 + 9) = ∇19
Therefore, the area of the parallelogram is ∇19.
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–10 − 66 h ≥ –3 whats h?
Answer:
To solve the inequality:
-10 - 66h ≥ -3
We can begin by isolating the variable h on one side of the inequality. First, we can add 10 to both sides:
-10 + 10 - 66h ≥ -3 + 10
Simplifying, we get:
-66h ≥ 7
Next, we can divide both sides by -66, remembering to reverse the inequality since we are dividing by a negative number:
h ≤ -7/66
Therefore, the solution to the inequality is h ≤ -7/66.
Step-by-step explanation:
A garden has width √√13 and length 7√√13. What is the perimeter of the garden in simplest
radical form?
014 √√13 units
016√√13 units
091 units
08√√13 units
Use your understanding of populat
2. A school board randomly samples 80 students to determine their opinion on requiring school uniforms for the next school year. The table shows the results of the survey.
OPPOSED
11
UNDECIDED
24
IN FAVOR
45
a. If 1,200 students are in the district, how many students can be expected to oppose school uniforms? x = 1/9
b. Bernice says that based on the survey, a student is more likely to be undecided or opposed than in favor. Do you agree or disagree? Why or why not?
CManeuvering the Middle LLC
a. If 1,200 students are in the district, 165 students can be expected to oppose school uniforms.
b. From the sample, the most likely outcome is in favor, as it got the most responses, hence we should disagree with Bernice.
What is proportion?A proportion is a fraction of the total amount.
Out of 80, 11 opposed, hence, out of 1200, we apply the proportion and find that the amount will be of:
1200 x 11/80 = 165.
Hence, a - 165 students can be expected to oppose school uniforms.
b - We should disagree with Bernice because the sample indicates that the outcome in favor is the most likely because it received the most answers.
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2. (a) State the fundamental theorem of_Group Hormomorphisms. Let (R, +) and (C, +) be the additive group of real numbers and the additive group of complex numbers respectively. The function Φ : C -> R is defined by Φ(x +iy) = y for all : x + iy € C. (i) Show that o is a homomorphism. (ii) Find ker Φ. (iii) Prove that c/r ~= R. (b) Let G = D6 = {1,r,r^2, s, sr, sr^2) and S = {1,r^2}. Find C_G(S).
(a) (i) Φ((x + iy) + (u + iv)) = Φ((x + u) + (y + v)i) = y + v
Φ(x + iy) + Φ(u + iv) = y + v
Since these two expressions are equal, Φ is a homomorphism.
(ii) Φ(x + iy) = 0
y = 0
(iii) The image of Φ is the set of all real numbers, we have C/R ~= R.
(b) The centralizer of S in G is the set {1, r^2}.
This means that the kernel of Φ is the set of all complex numbers with an imaginary part of 0, which is the set of all real numbers. That is, ker Φ = R.
The fundamental theorem of Group Hormomorphisms states that for any group homomorphism Φ: G -> H, the kernel of Φ, ker Φ, is a normal subgroup of G, and the image of Φ, im Φ, is a subgroup of H. Furthermore, G/ker Φ is isomorphic to im Φ.
(a) (i) To show that Φ is a homomorphism, we need to show that it preserves the group operation. That is, for any two elements x + iy and u + iv in C, we need to show that Φ((x + iy) + (u + iv)) = Φ(x + iy) + Φ(u + iv). Using the definition of Φ, we have:
Φ((x + iy) + (u + iv)) = Φ((x + u) + (y + v)i) = y + v
Φ(x + iy) + Φ(u + iv) = y + v
Since these two expressions are equal, Φ is a homomorphism.
(ii) The kernel of Φ, ker Φ, is the set of all elements in C that are mapped to the identity element in R, which is 0. That is, ker Φ = {x + iy : Φ(x + iy) = 0}. Using the definition of Φ, we have:
Φ(x + iy) = 0
y = 0
This means that the kernel of Φ is the set of all complex numbers with an imaginary part of 0, which is the set of all real numbers. That is, ker Φ = R.
(iii) To prove that C/ker Φ is isomorphic to R, we can use the fundamental theorem of Group Hormomorphisms. Since ker Φ = R, we have C/R ~= im Φ. Since the image of Φ is the set of all real numbers, we have C/R ~= R.
(b) The centralizer of a subset S of a group G, denoted by C_G(S), is the set of all elements in G that commute with every element in S. That is, C_G(S) = {g : g in G, gs = sg for all s in S}. For the given groups G = D6 and S = {1,r^2}, we have:
C_G(S) = {g : g in G, g1 = 1g and gr^2 = r^2g}
= {g : g in G, g = g and gr^2 = r^2g}
= {1, r^2}
Thus, the centralizer of S in G is the set {1, r^2}.
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If a patient takes 25mg of medication twice a day, how many
grams will he take in 14 days?
If a patient takes 25 mg of medication twice a day, he will take 0.7 grams in 14 days.
To find out how many grams a patient will take in 14 days, we can follow these steps:
25mg × 2 = 50mg
50mg × 14 days = 700mg
700mg ÷ 1000 = 0.7 grams
Therefore, the patient will take 0.7 grams of medication in 14 days.
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Factor the polynomial, if possible. If not possible, ttype "not factorable" y^(2)+49
We have to, the polynomial [tex]y^{(2)}+49.[/tex] is not factorable.
How do we prove that it is not factorizable?The given polynomial is [tex]y^{(2)}+49.[/tex]
This polynomial is not factorable because there are no two numbers that can be multiplied together to give a product of 49 and a sum of 0.
In other words, there are no two numbers that can be multiplied together to give 49 and added together to give 0. This means that the polynomial is not factorable.
Therefore, the answer is "not factorable".
In conclusion, the polynomial [tex]y^{(2)}+49[/tex] is not factorable.
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A rectangular flag for a club has the following design on it. A rectangle of length 24 inches and width 9 inches has a flag inside with a length of 18 inches and width of 5 inches has a triangle is cut out from its right side and the remaining length of the flag is 12 inches. What is the area of the shaded region on this flag? A 75in2 B 90in2 C 141in2 D 216in2
What is the product of -2x^3+x-5 and x^3-3x-4?
(A) Show your work.
(B) Is the product equal to (x^3-3x-4)*(-2x^3+x-5)? Explain your answer.
Answer:(A) Show your work.
Step-by-step explanation:(A) Show your work.
Answer: holy math sucks but check the explanation i gotchu
Step-by-step explanation: A) -2x^6 + 3x^5 - 2x^4 - 15x^3 + 4x^2 -20x - 20
B) No, the product is not equal to (x^3-3x-4)*(-2x^3+x-5). This is because the order of the terms in the product is different than the order of the terms in the expression. The product takes the form of -2x^6 + 3x^5 - 2x^4 - 15x^3 + 4x^2 -20x - 20, whereas the expression has the form of (-2x^3+x-5)*(x^3-3x-4).
Your answer is incorrect. Order these numbers from least to greatest. 5.37,5(3)/(10),5.338,(21)/(4)
5(3)/(10), 5.338, 5.37, (21)/(4).
To find the least to greatest order of these numbers, we need to convert all of them to the same format, either decimals or fractions. In this case, it is easier to convert the fractions to decimals.
5(3)/(10) = 5.3/10 = 0.53
(21)/(4) = 21/4 = 5.25
Now we can compare all of the numbers in decimal form:
0.53, 5.338, 5.37, 5.25
Next, we can arrange them in ascending order:
0.53, 5.25, 5.338, 5.37
Finally, we can convert the decimals back to fractions if necessary:
5(3)/(10), (21)/(4), 5.338, 5.37
Therefore, the correct order of these numbers from least to greatest is 5(3)/(10), (21)/(4), 5.338, 5.37.
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I need help with 17 and 18
In given graph, Points that meet the condition X>-2 are A, B, C, and D. and Points that are below the line y=1 are points A, B, C, and E. and also None of the other students correctly plotted the point 4 units away from A.
What is graph?
A set of vertices or nodes connected by edges or arcs is known as a graph. Graphs are used to represent various mathematical concepts, relationships, and structures, such as networks, functions, sets, and data. Graphs can be visualized and analyzed to draw conclusions and make predictions about the underlying phenomena they represent.
For question 17:
a. Points that meet the condition X>-2 are A, B, C, and D.
b. Points that are below the line y=1 are points A, B, C, and E.
c. The point located three units to the right of the origin and two units above the x-axis is point F.
For question 18:
a. The labeled points are:
A: (3,0)
B: (4,3)
C: (-4,-2)
D: (1/12, 1/12)
E: (-3/2, 2/12)
F: (-4,-2)
b. The student who correctly plotted the point 4 units away from point A is Cassandra, who plotted the point (7,0). None of the other students correctly plotted the point 4 units away from A.
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What is the area of the shaded part of the following composite figure? Round your answer to the nearest whole.
By adding the rectangle, the shaded area is [tex]53 in^2[/tex], rοunded tο the nearest whole figure.
what is surface area?The entire area οf a three-dimensional οbject's surface is known as surface area. It is a measurement of an οbject's expοsed surface. Indicating an οbject's surface area typically involves using square measurements like square inches οr square meters. The surface area οf a cube, fοr instance, is equal to the tοtal οf the areas οf each οf its six faces. The calculatiοn fοr a cube's surface area is: Surface Area Equals 6*[tex]side^2[/tex] where "side" denοtes the cube's extent οn οne side.
given:
The bigger semicircle has a radius οf 5 inches and a diameter οf 10 inches. Consequently, the bigger semicircle's area is:
(5 in) * (1/2) * π = 39.27 in (rοunded tο twο decimal places)
The smaller semicircle has a radius of οf 2 inches and a width of οf 4 inches. Consequently, the smaller semicircle's size is:
(2 in) * (1/2) * π * 6.28 in (rοunded tο twο decimal places)
The rectangle's area is: because it is 10 inches long and 2 inches wide.
10 in + 2 in equals [tex]20 in ^2.[/tex]
We can add the area οf the rectangle tο the area οf the larger semicircle after subtracting the areas οf the smaller and larger semicircles tο determine the area οf the shaded regiοn:
[tex]39.27 in^2 - 6.28 in^2+ 20 in^2 = 52.99 in^2.[/tex]
By adding the rectangle, the shaded area is 53 in2, rοunded tο the nearest whole figure.
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I dont know what the answer is and well im quite confused.
Answer:
C
Step-by-step explanation:
They are not proportional
If 3 pie cost $12, one pie will be $4
If 10 pie cost $25, then 1 pie is $2.5
$4 is not proportional to $2.5
Hence 12/3 is not proportional to 25/10
15. Carla drew this target on the floor for a bean bag game. The radius of the target is 30.0 cm, and all bands are the same width. What area of the target is red? The answer is 1766.3 cm I just don't know how did they get the answer
The area οf the red band is 1766.3 [tex]cm^2[/tex].
What is area?Area is a measure οf the amοunt οf twο-dimensiοnal space taken up by a shape οr surface. It is measured in square units, fοr example square metres (m²) οr square centimetres (cm²). Area can alsο be used tο calculate the perimeter οf a shape, which is the tοtal length οf the οutside οf the shape. Knοwing the area and the perimeter οf a shape can be useful in many calculatiοns and can help tο sοlve a range οf prοblems.
The area οf the target can be calculated with the equatiοn
=>A = [tex]\pi r^2[/tex].
ln this case, the radius (r) is 30.0 cm, so
=> A = [tex]\pi30^2[/tex] = 1766.3 [tex]cm^2[/tex].
The area οf the entire target is 1766.3 [tex]cm^2[/tex], and since the red band takes up a pοrtion of the entire target, the area οf the red band is 1766.3 [tex]cm^2[/tex]
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Shelly bought a dress for $150 and sold it to Jenny there by suffering a loss of 10%. Find the selling price of the dress.
Answer: $135
Step-by-step explanation:
We know that:
Selling price = [tex](100 - \text{Loss}\%)(\frac{\text{Cost Price}}{100})[/tex]
Using the given cost price and loss%, we can solve.
Selling Price = [tex](100 - \text{Loss}\%)(\frac{\text{Cost Price}}{100})[/tex]
Selling Price = (100 - 10)([tex]\frac{\text{150}}{100}[/tex])
Selling Price = (90) * (1.5)
Selling Price = $135
This means the selling price of the dress is $135.
Realiza las siguientes transformaciones de coordenadas polares a rectangulares o de coordenada rectangular a polar e identifica el cuadrante al que pertenecen
The polar coordinates corresponding to the rectangular coordinates (0, 5) are (5, π/2).
To find the distance from the origin to the point (r), we can use the Pythagorean theorem. The distance from the origin to a point (x, y) is given by the formula √(x² + y²).
In this case, since the x-coordinate is 0, we only need to find the distance from the origin to the y-coordinate. Therefore, r = √(0² + 5²) = 5.
To find the angle (θ) that the line from the origin to the point makes with the positive x-axis, we can use trigonometry.
However, this is undefined since we cannot divide by zero. Therefore, we need to use a special case. Since the x-coordinate is 0, the point lies on the y-axis.
Therefore, the angle θ is either π/2 or 3π/2. However, we are given the constraint 0 ≤ θ < 2π. Therefore, the angle θ = π/2 since it satisfies the constraint.
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Complete Question:
Convert the following rectangular coordinates into polar coordinates. Always choose 0 ≤ θ < 2 π . (a) ( 0 , 5 )
5. You conduct a survey that asks 397 students in your school about whether they have
played a musical instrument or participated in a sport. One hundred eighteen students
have played a musical instrument and 57 of those students have participated in a sport.
Thirty-four of the students have not played a musical instrument or participated in a
sport. Organize the results in a two-way table. Include the marginal frequencies.
Organizing the survey results in a two-way table with the marginal frequencies is as follows:
Number of Marginal
Respondents Frequencies
Have Played a Musical Instrument 118 56.5%
Have Participated in a Sport 57 27.3%
Have not Played or Participated 34 16.3%
Total 209
What are a two-way table and marginal frequency?A two-way frequency table shows the relationships between two categorical data.
A two-way frequency table can be used to show the marginal frequencies of responses for a given condition or the ratio of the joint frequencies to the corresponding marginal frequency.
The total number of students surveyed = 397
The total number of respondents = 209 (118 + 57 + 34)
The number of students who have played a musical instrument = 118
The number of students who have participated in a sport = 57
The number of students who have not played a musical instrument or participated in a sport = 34
Number of Marginal
Respondents Frequencies
Have Played a Musical Instrument 118 56.5% (118/209)
Have Participated in a Sport 57 27.3% (57/209)
Have not Played or Participated 34 16.3% (34/209)
Total 209
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Which operation can you apply to the ratio 1 to 2 to get the ratio 3 to 6?
Answer:
x3
Step-by-step explanation:
Given that △A′B′C′ is a dilation of △ABC, how are the angles and side lengths of the preimage and image related?
The angles are proportional and the side lengths are proportional.
The angles are congruent and the side lengths are congruent.
The angles are proportional and the side lengths are congruent.
The angles are congruent and the side lengths are proportional.
Answer:
Step-by-step explanation:
b because i did it