56x^2y as a prime factorization
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The exterior angle of each polygon and the adjacent interior angle are

supplementary.

(a) 72°    (b) \(\displaystyle 51 \frac{3}{7} ^{\circ}\)    (c) 36°    (d) 20°    (e) 18°

Reasons:

The formula for the exterior angle of a regular polygon is, \(\displaystyle \theta = \mathbf{ \frac{360 ^{\circ}}{n}}\)

Where;

θ = The exterior angle of the polygon

n = The number of sides of the regular polygon

(a) The number of sides in a pentagon, n = 5 sides

Therefore, for a regular pentagon, we have;

\(Exterior \ angle , \displaystyle \theta = \frac{360 ^{\circ}}{5} = \mathbf{{72^{\circ}}}\)

The measure of the exterior angle of a pentagon, is 72°

(b) An heptagon has n = 7 sides

The measure of the exterior angle, θ, of a regular heptagon is therefore;

\(Exterior \ angle \ of \ a \ heptagon , \,\displaystyle \theta = \frac{360 ^{\circ}}{7} = \underline{51 \frac{3}{7} ^{\circ}}\)

(c) A decagon has n = 10 sides, which gives;

\(The \ exterior \ angle \ of \ a \regular \ decagon, \,\displaystyle \theta = \frac{360 ^{\circ}}{10} = \underline{36^{\circ}}\)

(d) The exterior angle of an 18-gon with n = 18 sides is given as follows;

\(The \ exterior \ angle \ of \ a \ regular \ 18-gon, \,\displaystyle \theta = \frac{360 ^{\circ}}{18} = \underline{20^{\circ}}\)

(e) A regular 20-gon has n = 20 sides

The exterior angle of a regular 20-gon is \(\displaystyle \frac{360 ^{\circ}}{20} = \underline{ 18^{\circ}}\)

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The expression that is equivalent to \(\sqrt{x^{2}+81 } =x+10\) is \(x^{2} +81 = x^{2} +20x+100\).

Given equation is:

\(\sqrt{x^{2}+81 } =x+10\)

Squaring both sides:

\(x^{2} +81 = (x+10)^2\)

The formula for (a+b)² is a²+2ab+b²

So, the above equation can be expressed as,

\(x^{2} +81 = x^{2} +20x+100\)

Therefore, The expression that is equivalent to \(\sqrt{x^{2}+81 } =x+10\) is \(x^{2} +81 = x^{2} +20x+100\).

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Answer:

b

Step-by-step explanation:

Answer: 450 Minutes

Step-by step explanation:

135-x)/5 = hours connie runs

x/7 = hours Bonnie runs

(135-x)/5 + x/7 = 24

135-x + 5x/7 = 120

945-7x+5x = 840

-2x = -105

x = 52.5 miles = distance of Bonnie

52.5 miles / 7 m/hr = 7.5 hours = 450 minutes

Answer:

2% of 1kg

Step-by-step explanation:

20g/1kg x 100

= 20g/1000g x 100

1/50 x 100

=2

Therefore, 20g is 2% of 1kg

Hope it helps you

Answer:

2%

Step-by-step explanation:

1kg=1000g

=20/1000×100%

=2%

Answer:

see below

Step-by-step explanation:

There are 52 cards in the deck

4 kings

P(king) = king/total = 4/52 = 1/13

replacement

52 cards , 4 queens

P(queen) = queen/total = 4/52 = 1/13

P(king, replacement, queen) = 1/13 * 1/13 =1/169

There are 52 cards in the deck

4 kings

P(king) = king/total = 4/52 = 1/13

no replacement

51 cards , 4 queens

P(queen) = queen/total = 4/51 =4/51

P(king,  no replacement, queen) = 1/13 * 4/51 =4/663

The area burned as a function of time is (4t² + 4t + 1)π.

There is a forest fire. The forest fire leaves behind an area of grass burned in an expanding circular pattern.

The radius of the circle of burning grass is increasing with time according to the formula r(t) given below :

r(t) = 2t + 1

We need to find the area burned as a function of time.

The equation for the area of the circle is given below :

The area of the circle is πr².

We need to replace the value of radius "r" in the equation with the function given above in terms of time.

A = πr²

A = π(2t + 1)²

A = π(4t² + 1 + 4t)

The area burned as a function of time is (4t² + 4t + 1)π.

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Answer:

$3228

Step-by-step explanation:

39236 - 500 = 38736

38736 / 12 = 3228

4. f(x,y) is homogeneous of degree 2.

5. a) f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1

4. Show that f(x,y)=\(x^2\)y is homogeneous, and find its degree of homogeneity:

A function is said to be homogeneous of degree k, if it satisfies the condition:

f(tx,ty) = \(t^k\)f(x,y)

We have f(x,y) = \(x^2\)y. Let’s check if it satisfies the above condition:

f(tx,ty) = \((tx)^2(ty) = t^3x^2y = t^2(x^2y\)) = \(t^2\)f(x,y)

Hence f(x,y) is homogeneous of degree 2.

5. Which of the following functions f(x,y) are homothetic? Explain.

(a) f(x,y)=\((xy)^2\)+1

(b) f(x,y)=\(x^2+y^3\)

Let us first understand the meaning of homothetic transformation.

A homothetic transformation is a non-rigid transformation of the Euclidean plane that preserves the direction of the straight lines but not their length. It stretches or shrinks the plane by a constant factor called the dilation.

Let’s now find out whether the given functions are homothetic or not.

(a) f(x,y)=\((xy)^2\)+1

In order to check if f(x,y) is homothetic or not, we need to check if the function satisfies the following condition:

f(x,y) = g(h(x,y))

where g is a strictly monotonic function and h is a homogeneous function with degree 1

We have

f(x,y) = \((xy)^2\)+1

Let’s assume g(x) = x - 1, then g(x+1) = x

Similarly, let’s assume h(x,y) = (xy), then h(tx,ty) = \(t^2\)h(x,y)

Now, we have

g(h(x,y)) = h(x,y) - 1 = (xy) - 1

Thus f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1

(b) f(x,y)=\(x^2+y^3\)

We can’t write this function in the form f(x,y) = g(h(x,y)) where h(x,y) is a homogeneous function with degree 1. Hence this function is not homothetic.

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Using the P-value method of testing hypotheses with a significance level of 0.05, the sample provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

To test the claim that the mean score of job applicants from the university is greater than 160, we will perform a one-sample t-test using the P-value method. The null hypothesis (H0) assumes that the mean score is equal to 160, while the alternative hypothesis (Ha) assumes that the mean score is greater than 160.

First, we calculate the test statistic, which is the t-value. The formula for the t-value is:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values, we have:

t = (183 - 160) / (12 /   √(25))

  = 23 / (12 / 5)

  = 23 * (5 / 12)

  ≈ 9.58

Next, we find the P-value associated with the test statistic. The P-value represents the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. Since the alternative hypothesis is one-sided (greater than 160), we calculate the P-value by finding the probability of the t-distribution with 24 degrees of freedom being greater than the calculated t-value.

Consulting statistical tables or using software, we find that the P-value is very small (less than 0.0001).

Since the P-value (less than 0.0001) is less than the significance level (0.05), we reject the null hypothesis. This provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

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Answer:

5

Step-by-step explanation:

\( {100}^{ \frac{1}{2} } - {125}^{ \frac{1}{3} } \\ \\ = ( {10}^{2} ) ^{ \frac{1}{2} } - ( {5}^{3} )^{ \frac{1}{3} } \\ \\ = {10}^{2 \times \frac{1}{2} } - {5}^{3 \times \frac{1}{3} } \\ \\ = 10 - 5 \\ \\ = 5\)

Answer:

7. m=3 b=-4

Equation y=3x-4

8. m=-6/4 b=7

Equation y=-6/4x+7

Step-by-step explanation:

Answer:

7. m=3 b= -4 , Equation y=3x-4

8. m= -6/4 b=7 , Equation y=-6/4x+7

Step-by-step explanation:

look in the chart

The equation for this relationship is \(3a+2c=23\)

Given,

Tickets to a zoo cost $12 for each adult and $8 for each child. A family has $72 for the zoo trip

\(=12a + 8c=72\\=4(3a+2c)=72\\=3a+2c=\frac{72}{4} \\=3a+2c=23\)

Therefore, the equation for this relationship is \(3a+2c=23\)

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Answer:

156

Step-by-step explanation:

1) The formula for finding the sum of interior angles of an n-gon is 180(n-2)

2) Plug in 15 for n

180(15-2)

3) Solve

180(15-2)

180(13)

2340

4) There are 15 angles in a 15-gon

5) Divide sum of interior angles by number of interior angles

2340/15 = 156

6) So, the answer is 156 degrees

3(-5)+4(6)<=10

(3*-5)+(4*6)<=10

(15)+(24)<=10

39<=10 N

3(2)+4(-1)<=10

(6)+(-4)<=10

2<=10 Y

3(-1)+4(4)<=10

-3+16<=10

13<=10 N

3(4)+4(0)<=10

12+0<=10 N

3(-3)+4(4)<=10

-9+16<=10

7<=10 Y

here ya go bud, im doing the same thing lol

The ordered pairs make the open sentence true values are  (2, -1), (-3, 4), and (-5, 6).

To determine which ordered pairs make the open sentence 3x + 4y ≤ 10 true, to substitute the values of x and y from each ordered pair into the inequality and check if the inequality holds.

Let's go through each ordered pair:

(4, 0):

3(4) + 4(0) = 12 + 0 = 12

12 ≤ 10 (False)

(2, -1):

3(2) + 4(-1) = 6 - 4 = 2

2 ≤ 10 (True)

(-1, 4):

3(-1) + 4(4) = -3 + 16 = 13

13 ≤ 10 (False)

(-3, 4):

3(-3) + 4(4) = -9 + 16 = 7

7 ≤ 10 (True)

(-5, 6):

3(-5) + 4(6) = -15 + 24 = 9

9 ≤ 10 (True)

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The value of the line integral \( \int_{C} (2x - 3y) \, ds \) along the curve \( C \) is \( -15 \).

To find the value of the line integral \( \int_{C} (2x - 3y) \, ds \), we need to evaluate the integral along the curve \( C \), which is parameterized by \( r(t) = \langle 3t, 4t \rangle \), where \( 0 \leq t \leq 1 \).

First, let's calculate the derivative of the parameterization:

\( r'(t) = \langle 3, 4 \rangle \)

Next, we need to find the magnitude of \( r'(t) \) to obtain the differential element \( ds \):

\( \lVert r'(t) \rVert = \sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \)

Now we can rewrite the line integral in terms of the parameterization:

\(\( \int_{C} (2x - 3y) \, ds = \int_{0}^{1} (2(3t) - 3(4t)) \cdot 5 \, dt \)Simplifying:\( \int_{0}^{1} (6t - 12t) \cdot 5 \, dt = \int_{0}^{1} (-6t) \cdot 5 \, dt \)\( = -30 \int_{0}^{1} t \, dt \)Now we can evaluate the integral:\( = -30 \left[ \frac{t^2}{2} \right]_{0}^{1} \)\( = -30 \left( \frac{1^2}{2} - \frac{0^2}{2} \right) \)\( = -30 \left( \frac{1}{2} - 0 \right) \)\( = -30 \cdot \frac{1}{2} \)\( = -15 \)\\\)
Therefore, the value of the line integral \( \int_{C} (2x - 3y) \, ds \) along the curve \( C \) is \( -15 \).

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Answer:

1.5+1.5= 3 hours

Step-by-step explanation:

if you take 1.5 hours two times it will get you 3 hours. so it will be 3 hours in the water if the boat goes 24 miles. hope this helps.

The answer of the given question based on finding the m∠LKM from the given circle the answer is the measure of ∠LKM is 140° degrees.

In geometry,  diameter of circle is  line segment that passes through  center of  circle and has both endpoints on circle. The diameter is the longest chord (line segment connecting two points on  circumference) of  circle. The length of  diameter is twice the length of radius, which is distance from the center of  circle to any point on  circumference.

The diameter i important property of a circle and is used to calculate other properties, like the circumference and area of the circle

Since MK is a diameter of the circle, it passes through the center of the circle, which we can label as point O. Therefore, ∠LKM is an inscribed angle that intercepts arc LM.

By the Inscribed Angle Theorem, we know that the measure of an inscribed angle is equal to half the measure of the arc that it intercepts. Therefore, to find the measure of ∠LKM, we need to find the measure of arc LM.

We are given that the measure of arc LK is 100° degrees. Since arc LM is the sum of arcs LK and KM, and MK is a diameter (so arc KM is also a semicircle with a measure of 180 degrees), we can write:

m(arc LM) = m(arc LK) + m(arc KM) = 100 + 180 = 280° degrees

Therefore, the measure of ∠LKM is:

m∠LKM = 1/2 * m(arc LM) = 1/2 * 280 = 140° degrees

So the measure of ∠LKM is 140° degrees.

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Having an unbiased sample means that the sample is selected in a way that accurately represents the larger population without favoring any specific characteristics or groups. It ensures that every member of the population has an equal chance of being included in the sample.

An unbiased sample is important because it allows researchers to make valid inferences and generalizations about the entire population based on the characteristics of the sample. If the sample is biased, the results may not accurately reflect the population, leading to skewed conclusions and potentially incorrect decisions or actions.

Bias can arise from various factors such as non-random sampling methods, voluntary participation, or self-selection. To minimize bias, researchers use random sampling techniques and try to obtain a representative sample that reflects the diversity of the population. By doing so, they can increase the external validity of their findings and improve the reliability and credibility of their research. An unbiased sample is crucial in various fields, including market research, social sciences, and public health, to ensure accurate results and inform evidence-based decision-making.

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Answer:

y = - x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 4 ) and (x₂, y₂ ) = (2, 0 )

m = \(\frac{0-4}{2-(-2)}\) = \(\frac{-4}{2+2}\) = \(\frac{-4}{4}\) = - 1 , then

y = - x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 0 )

0 = - 2 + c ⇒ c = 0 + 2 = 2

y = - x + 2 ← equation of line

Answer:

4.5

Step-by-step explanation:

60/20=3

3*1.5=4.5

The flexible air-filled container has volume of -33 liter (A) at 20 meter in sea water.

At the surface, the pressure is 1 atm (atmosphere). As we go deeper into the sea, the pressure increases by 1 atm for every 10 meters. Therefore, at 20 meters, the pressure is 3 atm (1 atm at the surface + 2 atm for the 20 meters).

The relationship between pressure and volume is described by Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at a constant temperature. This means that as the pressure increases, the volume decreases, and vice versa.

Using Boyle's Law, we can calculate the volume at 20 meters:

P1V1 = P2V2

Where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.

Plugging in the values:

(1 atm)(100 liter) = (3 atm)(V2)

Solving for V2:

V2 = (1 atm)(100 liter) / (3 atm)

V2 = 33.33 liter

Rounding off to the nearest whole number, the volume at 20 meters is 33 liter.

Therefore, the correct answer is A - 33 liter.

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Answer:

c = 196

Step-by-step explanation:

To obtain a perfect square trinomial

Add ( half the coefficient of the x- term )² to x² + 28x

x² + 2(14)x + (14)², that is

x² + 28x + 196

= (x + 14)² ← a perfect square

Answer:

c = 196

Step-by-step explanation:

28 /2 = 14

14 x 14 = 196

formula =( b/2) x 2

Answer:

x=9

Step-by-step explanation:

plug in the number 9

-2(9)= -18

-18+3= -15

The relationship between the cups of juice sold and time is y = 25x

A variation is a relation between a set of values of one variable and a set of values of other variables.

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other.

Direct variation means increase in a quantity will be increase in the other quantity and vice versa.

Direct variation is expressed in the form;

y = Kx

let x be the number of hours and y be the number of juice sold.

When 25 cups is sold for 1 hr

25 = k 1

k = 25

Therefore the relationship can be written as;

y = 25x

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The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.

In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.

In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.

n = 18 (number of trials)

π = 0.60 (probability of success for each trial)

To find the expected value:

E(X) = np

Substitute the given values:

E(X) = 18 * 0.60

Calculate the expected value:

E(X) = 10.8

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What is diameter:

in geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere.

What is radius:

In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the Latin radius, meaning ray but also the spoke of a chariot wheel.

Explanation:

The diameter is the line that goes across the center of the circle and double the radius which is half, therefore KR is the correct answer.

Answer:

KR, D, or the last option.

Statement answer:

Segment KR is the Diameter of Q.

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We're asked to develop a polynomial

Integer coefficient that has zero at 3 is (x-3)

Multiplicity of 2 gives (x - 3) (x - 3)

And a zero at -5/4 gives (x + 5/4)

Put together, we have: (x - 3) (x - 3)(x + 5/4) = (x - 3)^2 (x + 5/4) = 0