In what quadrant does the terminal side of its positive reference angle lie?

Answer:

The LCM of 18, and 32 is

Answer: The LCM is 288.

Step-by-step explanation:

To find the least common multiple of 18 and 32, you will find the multiples of 18 and 32 and look for least multiple number that matches 18 and 32.

Multiples of 18 are:    18,36,54,72,90,108,126,144,162,180,198,216,234,252,270,288

Multiples of 32 are:  32, 64,96,128, 160,192,224, 256, 288

The last digit 288 is the least multiple number that appears in both multiples for the two numbers.

Answer:

18.25

Step-by-step explanation:

Add 5.50 and 12.75

5.50 + 12.75 = 18.25

Answer: 18.25

Step-by-step explanation:

The magnitude of the average velocity vector is approximately 3.651 m/s.

To find the magnitude of the average velocity vector, we need to calculate the displacement and divide it by the time taken.

Representation:

Initial position: D1 = (50 m North, 10 m East)

Final position: D2 = (5 m North, 35 m East)

Time taken: t = 15 seconds

Equations:

Displacement vector (ΔD) = D2 - D1

Average velocity vector (\(V_{avg}\)) = ΔD / t

Algebra work:

ΔD = D2 - D1

   = (5 m North, 35 m East) - (50 m North, 10 m East)

   = (-45 m North, 25 m East)

|ΔD| = √((-45)^2 + 25^2)  [Magnitude of the displacement vector]

\(V_{avg}\) = ΔD / t

       = (-45 m North, 25 m East) / 15 s

       = (-3 m/s North, 5/3 m/s East)

|\(V_{avg}\)| = √((-3)^2 + (5/3)^2)  [Magnitude of the average velocity vector]

Symbolic answer:

The magnitude of the average velocity vector is approximately 3.651 m/s.

Units check:

The units for displacement are in meters (m) and time in seconds (s). The average velocity is therefore in meters per second (m/s), which confirms the units are consistent with the calculation.

Therefore, the magnitude of the average velocity vector is approximately 3.651 m/s.

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Answer:

Step-by-step explanation:

Answer:

1,2, and 4 are the correct answers

Step-by-step explanation:

Answer:

1. The sides that were parallel in the pre-image are parallel in the image.

2. The angle measures of ABCD are equal to the corresponding angle measures of A’B’C’D’.

4. The segments connecting the center of rotation to the corresponding vertices create a 270° angle.

Step-by-step explanation:

Edge 2021

The Process Capability Index (Cpk) is 0.24

The process capability index (Cpk) for the organic yogurt processing plant can be calculated as follows:

Cpk = min[(USL - μ) / (3σ), (μ - LSL) / (3σ)]

Where:

- USL is the upper specification limit (16.9 ounces)

- LSL is the lower specification limit (15.1 ounces)

- μ is the process mean (16.0 ounces)

- σ is the process standard deviation (1.25 ounces)

To calculate Cpk, we need to consider the specifications and the process performance. The formula compares the process variation to the specification limits. The numerator represents the distance between the process mean and the nearest specification limit, while the denominator represents three times the process standard deviation.

In this case, the process mean (μ) is 16.0 ounces, the upper specification limit (USL) is 16.9 ounces, and the lower specification limit (LSL) is 15.1 ounces. The process standard deviation (σ) is 1.25 ounces.

By plugging these values into the Cpk formula, we can determine the smaller value between the two ratios, representing the capability of the process to meet the specifications. This Cpk value indicates how well the process fits within the specification limits, with higher values indicating better capability.

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Answer:

\(1(16 {n}^{2} - 1)\)

hope its helpful ❤❤❤

THANK YOU.

Answer:   \(2^x + 4\)

==================================================

Explanation:

We simply add the expressions we are given, though we cannot combine the terms (as they aren't like terms). There's not much to show in terms of steps, though I guess you could have the following:

\(h(x) = f(x)+g(x)\\\\h(x) = 2^x+4\\\\\)

Adding 4 onto 2^x means we shift the 2^x curve up four units.

To evaluate a function with a specific value in the domain you susbtitute in the equation of the function the independient variable (x) for the value in domain.

For x = -1 (a number n powered to a negative number (m) n^-m is equal to 1/n^m

For x=0 (any number powered to 0 is equal to 1)

For x = 1

For x = 2

For each quadratic equation, the value of a, b and c are mentioned below. Also maximum or minimum points are mentioned here.

A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.

Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.

The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.

a. y = 3x²-3x + 5, comparing this with general quadratic equation ax² + bx + c and get a = 3 and b = -3 and c = 5

thus x = - (b/2a)

x = - (-3/6)

x = -1/2

as a > 0 thus the equation has the minimum value and that is:

y = 3(-1/2)² -3(-1/2) + 5

y = 3/4 + 3/2 + 5

y = 13/2

b. y = -2x² + x  comparing this with general quadratic equation ax² + bx + c and get a = -2 and b = 1 and c = 0

thus x = - (b/2a)

x = - (1/-4)

x = 1/4

as a < 0 thus the equation has the maximum value and that is:

y = -2(1/4)² + (1/2)

y = -1/8 + 1/2

y = 3/8

c. y = 1/2x² + 6 comparing this with general quadratic equation ax² + bx + c and get a = 1/2, b = 0 and c = 6

thus x = - (b/2a)

x = - (1/2×0)

x = 0

as a > 0 thus the equation has the minimum value and that is:

y = 1/2(0)² + 6

y = 6

d. y=-3x² + 1/2x - 2 comparing this with general quadratic equation ax² + bx + c and get a = -3, b = 1/2 and c = -2

thus x = - (b/2a)

x = - [(1/2)/-6]

x = 1/12

as a < 0 thus the equation has the maximum value and that is:

y=-3(1/12)² + 1/2 (1/12) - 2

y = - 1/48 + 1/24 - 2

y = -45/48

e. y=x²-2x+6 comparing this with general quadratic equation ax² + bx + c and get a = 1, b = -2 and c = 6

thus x = - (b/2a)

x = - (-2/2)

x = 1

as a > 0 thus the equation has the minimum value and that is:

y=(1)²-2(1)+6

y = 5

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Answer:

\(6/17\)

Step-by-step explanation:

I assume you want the question in the picture solved as your written question is different but appears to be copied and pasted from the text.

1. When adding fractions the denominator (number on the bottom) must be the same between the two fractions, i.e. having a common denominator. In this case they are already the same, that is, 17 and 17. Just add the top numbers (numerators) together, and leave the denominator the same. So,

\(\frac{3}{17} +\frac{3}{17} =\frac{6}{17}\)

There are total of 152 students in 5th grade, then the number of pencils altogether will be equal to 2,736 pencils.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Total number of students in 5th grade = 152

Amount of pencil each student have = 18

Then, the total number of pencils altogether,

= 152 × 18

= 2,736 pencils.

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10 procent

Step-by-step explanation:

150 / 150 = 10

Answer:10%

Step-by-step explanation:

The SAS Similarity Theorem asserts that two triangles are similar if two sides in one triangle are proportionate to two sides in another triangle and the included angle in both is congruent.

what is side-angle-side similarity theorem?

The side-angle-side (SAS) theorem is one such example. Triangles are congruent if their two sides and included angles are equivalent to those of another triangle's two sides and included angle. SAS similarity analysis: When the ratio of two sides' lengths in one triangle equals the ratio of sides' lengths in another triangle, and the included angles are also equal, the two triangles are said to be comparable.

and also by heron's formula

here s = half the perimeter,

a+b+c /2

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Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

Answer:180

Step-by-step explanation:

hope this helps

Answer:

0.8 mm

Step-by-step explanation:

Given that you require the actual size.

The ant has been magnified by 15 X

To find the actual size divide magnified size by 15

actual size = 12 mm ÷ 15 = 0.8 mm

The definitional formula is easy to use when the mean is a whole number, the range of scores is small, and there are either relatively few scores or many of them are zero.

The definitional formula is an equation used to calculate the mean of a set of scores. It is easy to use when the mean of the scores is a whole number, meaning there is no need to round. Additionally, if the range of scores is small, it is easier to find the mean, as there is less data to consider. Furthermore, the formula is easier to use when there are either relatively few scores or many of them are zero. This is because there is less data to consider, meaning the mean can be found more quickly. When there are many scores, and the range is large, it can be difficult to calculate the mean using the definitional formula. In this case, it is often more efficient to use an alternate method such as the arithmetic mean.

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The complete question is

Under what circumstances is the definitional formula easy to use

-When the mean is a whole number and there are relatively few scores

-When the mean is a whole number and the range is small

-When the mean is a whole number and there are many scores

-When there are relatively few scores and many of them are zero

The required probability of the coin landing tails up at least two times is 15/16.

Given that,
A fair coin is flipped seven times. what is the probability of the coin landing tails up at least two times is to be determined.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
In the given question,
let's approach inverse operation,
The probability of all tails  = 1 / 2^7 because there is only one way to flip these coins and get no heads.
The probability of getting 1 head = 7 /2^7
Adding both the probability = 8 / 2^7
Probability of the coin landing tails up at least two times = 1 - 8/2^7
                                                                                     = 1 - 8 / 128
                                                                                     = 120 / 128
                                                                                     = 15 / 16

Thus, the required probability of the coin landing tails up at least two times is 15/16.

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Answer:

When you are adding a negative number to a positive number you are effectively subtracting the second number from the first. ... And then you add the negative number, which means you are moving to the left – in the negative direction. Basically you are subtracting the 2. The answer is 2.

Step-by-step explanation:

Answer:

half a metre

Step-by-step explanation:

The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.

The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:

(a) Local non-satiation:

This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.

(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:

MU1 = α * xi^(α−1) * x2^(β)

The marginal utility of x2 can be obtained as:

MU2 = β * xi^(α) * x2^(β−1)

Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.

(c) Quasi-concavity:

The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.

(d) Homotheticity:

The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.

In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.

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Answer:

b = 30

Step-by-step explanation:

The sum of the 2 angles above the line will equal the angle below the line

3b + b - 15 = 2b + 45

4b - 15 = 2b + 45 ( subtract 2b from both sides )

2b - 15 = 45 ( add 15 to both sides )

2b = 60 ( divide both sides by 2 )

b = 30

The value of v in the given inequality 9v - 8 ≥ 8v + 2 is v≥10.

The given inequality is 9v - 8 ≥ 8v + 2

Now, we have to solve the value for v in the above inequality.

9v - 8 ≥ 8v + 2

Now, we subtract 8v on both sides.

9v - 8 - 8v ≥ 8v + 2 - 8v.

v - 8 ≥ 2.

Now, we add 8 on both sides

v - 8 + 8 ≥ 2 + 8

v ≥ 10.

Therefore, the value for v is v ≥ 10, which means all the values greater than 10 satisfy the given inequality.

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Step-by-step explanation:

☄ \( \underline {\underline{ \text{Given}}} : \)

☄ \( \underline{ \underline{ \text{To \: find}}}: \)

☄ \( \underline{ \underline{ \text{Solution}}} : \)

Part 1 : \( \boxed{\text{Area \:of \:a \:path \: running \:outside = 2d(l + b + 2d)}}\)

plug the known values and simplify :

⟹ \( \sf{2 \times 2.5(55 + 35 + 2 \times 2.5)}\)

⟹ \( \sf{5 \times 95}\)

⟹ \( \sf{475 \: {m}^{2} }\)

Part 2 : \( \boxed{ \sf{Total \: cost = Area \: of \: paths \: \times Rate}}\)

⟹ \( \sf{475 \times 120}\)

⟹\( \sf{Rs \: 57000}\)

\( \purple{ \boxed{ \boxed{ \sf{ \tt{⟿ \: Our \: final \: answer : (i) = 475 \: {m}^{2} \: and \: (ii ) = Rs \: 57000}}}}}\)

Hope I helped ! ♡

Have a wonderful day /night ツ

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer and Step-by-step explanation:

How to know if the side lengths can form a triangle:

Add together two of the lowest numbers. If it is greater than the largest number, it can form a triangle.

13. Yes, these side lengths can form a triangle.

-- 4 + 5 = 9.

-- 9 is greater than 7, the largest length.

14. No, these side lengths can't form a triangle.

-- 2 + 3 = 6

-- 6 is equal to 6, not greater than.

15. Yes, these side lengths can form a triangle.

-- 2 + 4 = 6

-- 6 is greater than 5, the largest number.

16. Yes, these side lengths can form a triangle.

-- Don't get confused when you see that there are two side lengths that are the same (it means that this is an isosceles triangle); the rules still apply.

-- 2 + 8 = 10

-- 10 is greater than 8, the largest number.

17. Yes, these side lengths can form a triangle.

-- 5 + 6 = 11

-- 11 is greater than 9, the largest number.

18. Yes, these side lengths can form a triangle.

-- 4 + 5 = 9

-- 9 is greater than 8, the largest number.

I hope this helps!!

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Answer:

2x+5=15

Step-by-step explanation:

If u need one I'll be happy to explain

Answer:

C. 9

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Number of students need to be sampled = 610

A study to determine the true average number of alcoholic drinks consumed by Greek students is conducted.

Standard Deviation, σ = 6.3

Margin Error of population mean, E = 0.5

Probability = 95% = 0.95

The p-value corresponding to 0.95 probability = (1+0.95)/2 = 0.975

The z-score corresponding to this p-value = 1.96 [from the z-tables]

Now, The margin error, E = zσ/√n, where n is the sample size

⇒ n = (zσ/E)²

⇒ n = (1.96 x 6.3/0.5)²

⇒ n ≈ 610

Hence 610 students need to be sampled.

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