Find the intersection and union of the given sets. A = {h, o, m, e} , B = {h, o, u, s, e}

Answer:

The function y = 3(x - 2)^2 + 6 is in vertex form, which is y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola.

In this case, the vertex is (2,6), and the coefficient "a" is 3, so we can write the equivalent function in standard form as follows:

y = 3(x - 2)^2 + 6

y = 3(x^2 - 4x + 4) + 6

y = 3x^2 - 12x + 18

Therefore, the equivalent function in standard form is y = 3x^2 - 12x + 18.

a. The greatest possible distance from  Austin to san Antonio is 335.77 mi, b. the Least possible distance to Austin to san Antonio is 120.03 mi.

Distance refers to the physical length or space between two points or objects. It is an important concept in mathematics, physics, and everyday life. Distance can be measured in various units such as meters, feet, kilometers, miles, or light-years, depending on the context and scale of the measurement.

In mathematics, distance is often measured using the Euclidean distance formula, which calculates the distance between two points in a plane or in three-dimensional space. The formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

where d is the distance between the two points, (x1, y1) and (x2, y2).

In physics, distance is often used to describe the separation between two objects or particles. The distance between two objects can affect the strength of gravitational or electromagnetic forces between them. Distance is also an important concept in special relativity, where it is affected by the relative motion of observers and the distortion of spacetime.

a. Greatest possible distance from  Austin to san Antonio= Distance from Austin →Houston → san Antonio.

Austin - Houston = 146.43 mi

Houston - San Antonio = 189.34 mi

Total  distance= 146.43+ 189.34= 335.77 mi

b. Least possible distance to Austin to san Antonio= the shortest distance = x

By pythagoras theorem

(189.34)²= (146.43)²+ x²

x²= (189.34)²- (146.43)²

x²= 35849.63- 21441.744

x²= 14407.89

x=√14407.89

x= 120.03

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The complete question is:

The answers of range, variance, and standard deviation are:
a. Range = 17, Variance = 44.16, Standard deviation = 6.65
b. Range = 109, Variance = 1514.14, Standard deviation = 38.91
c. Range = 109, Variance = 1486.86, Standard deviation = 38.56

The range is the difference between the highest and lowest values in the sample. The variance is a measure of how spread out the values are from the mean, and the standard deviation is the square root of the variance.

For sample a:
Range = 47 - 30

=> 17
Variance =[tex][(32-37.8)^2 + (44-37.8)^2 + (30-37.8)^2 + (36-37.8)^2 + (47-37.8)^2] / (5-1)[/tex]

=> 44.16
Standard deviation = √44.16

=> 6.65

For sample b:
Range = 110 - 1

=> 109
Variance = [tex][(110-34.44)^2 + (6-34.44)^2 + (4-34.44)^2 + (99-34.44)^2 + (80-34.44)^2 + (3-34.44)^2 + (5-34.44)^2 + (10-34.44)^2 + (1-34.44)^2] / (9-1)[/tex]

=> 1514.14
Standard deviation = √1514.14

=> 38.91

For sample c:
Range = 110 - 1

=> 109
Variance = [tex][(110-42)^2 + (6-42)^2 + (4-42)^2 + (40-42)^2 + (80-42)^2 + (40-42)^2 + (55-42)^2 + (1-42)^2] / (8-1)[/tex] = 1486.86
Standard deviation = √1486.86

=> 38.56

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The value of x would be equal to 20 degrees.

Linear pairs of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.

We are given the parameters as;

7x and (x + 20)

The sum of angle is equal to 180.

7x + (x + 20) = 180

8x + 20 = 180

8x = 180 - 20

8x = 160

x = 160/8

x = 20

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Answer:

O don't know

Step-by-step explanation:

I'm just doing this because i need to i don't really know and I'm litterraly confused?

Answer:

−4x−3

Step-by-step explanation:

The measurement of the third angle is 100°.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Given ,

The measurement of one angle in triangle is 30°.

And other angle in triangle is 50°

We have to find,

The measurement of the third angle.

According to the question,

It is a triangle the sum of three angles is 180 degrees.

Now,

Sum of the all the interior angle in right triangle = 180°

30° + 50° + ∠c = 180°

80° + ∠c  = 180°

∠c = 180° - 180° = 100°

Hence, The required measurement of the third angle is 100°.

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The probability of first subset has 14 observations with population of 5 million or greater, and the second subset has 36 observations with population less than 5 million.

The state population data has 50 observations, each representing a different state. To create two subsets, I filtered the data according to 2018 population. The first subset includes observations with population of 5 million or greater, and the second subset includes observations with population less than 5 million. There are 14 observations in the first subset and 36 observations in the second subset. This shows that there are more states with population below 5 million than above 5 million. The data also shows that the states with population of 5 million or greater tend to have higher population densities than those with population below 5 million. This could be due to a variety of factors such as location, climate, and resources.

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Answer:

Below

Step-by-step explanation:

(4x- 9)(4x + 9)        Just by looking.....

You ask your neighbor to water a sickly plant while you are on vacation. Without water it will die with probability 90%: with water it will die with probability 20%. You are 80% certain that your neighbor will remember to water the plant. The probability that the plant will die when you return  is 34%. If the plant is dead, the probability that the neighbor forgot to water it is approximately 52.94%.

1. The probability that the plant will die when you return can be calculated using the law of total probability. We need to consider both scenarios, where the neighbor remembers to water the plant and where they forget to water the plant.

P(plant dies) = P(plant dies | neighbor remembers) * P(neighbor remembers) + P(plant dies | neighbor forgets) * P(neighbor forgets)

= (0.20 * 0.80) + (0.90 * 0.20)

= 0.16 + 0.18

= 0.34

So the probability that the plant will die when you return is 34%.

2. If the plant is dead, we need to calculate the probability that the neighbor forgot to water it using Bayes' theorem.

P(neighbor forgets | plant dies) = P(plant dies | neighbor forgets) * P(neighbor forgets) / P(plant dies)

= (0.90 * 0.20) / 0.34

= 0.5294

So if the plant is dead, the probability that the neighbor forgot to water it is approximately 52.94%.

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a) n = 650 and p = 0.03

b)0.954

c)0.802

d)0.0206 to 0.0594

e)The result in (d) would be more precise

(a) The sampling distribution of the sample proportion is a binomial distribution with parameters n = 650 and p = 0.03.
(b) The probability that the sample proportion of death claims is between 2% and 6% is 0.954.
(c) The probability that the sample proportion is within 0.02 of the population proportion of death claims caused by accidents is 0.802.
(d) The 95% confidence interval for the proportion of death claims caused by accidents is 0.0206 to 0.0594.
(e) If the sample size were 2000 instead of 650, the result in (d) would be more precise. This is because with a larger sample size, the confidence interval will become narrower, allowing for a more accurate estimate of the population proportion.

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The sum of two numbers is 146. The larger number is 16 less than 5 times the smaller number, the two numbers are 27 and 119.

Let's call the smaller number "x" and the larger number "y". We can write two equations based on the information given:

The sum of two numbers is 146: x + y = 146

The larger number is 16 less than 5 times the smaller number: y = 5x - 16

We can use substitution to solve for one of the variables. Using equation 2, we can solve for y in terms of x:

y = 5x - 16

Now we can substitute this expression for y into equation 1:

x + (5x - 16) = 146

Simplifying this equation, we get: 6x - 16 = 146

Adding 16 to both sides, we get: 6x = 162

Dividing both sides by 6, we get: x = 27

Now we can use equation 2 to solve for y:

y = 5x - 16 = 5(27) - 16 = 119

Therefore, the two numbers are 27 and 119.

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The techniques of shifting, compressing, stretching, and reflecting can be used to transform the function g(x)=-x^(3)+7.

The techniques of shifting, compressing, stretching, and reflecting are used to transform functions. These techniques allow us to move the graph of a function up, down, left, or right, to make it wider or narrower, and to flip it over the x-axis or y-axis.

The function g(x)=-x^(3)+7 can be transformed using these techniques. For example, we can shift the graph of g(x) up by 2 units by adding 2 to the function: g(x)=-x^(3)+7+2=-x^(3)+9. We can also stretch the graph of g(x) vertically by multiplying the function by a constant greater than 1: g(x)=2(-x^(3)+7)=-2x^(3)+14.

Similarly, we can compress the graph of g(x) vertically by multiplying the function by a constant between 0 and 1: g(x)=0.5(-x^(3)+7)=-0.5x^(3)+3.5. We can also reflect the graph of g(x) over the x-axis by multiplying the function by -1: g(x)=-(-x^(3)+7)=x^(3)-7.

These are just a few examples of how the techniques of shifting, compressing, stretching, and reflecting can be used to transform the function g(x)=-x^(3)+7.

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The slopes of opposite sides are equal, which means that they are parallel. Therefore, JKLM is a parallelogram.

Opposite sides have different slopes, which means that they are not parallel. Therefore, JKLM cannot be a rhombus because a rhombus is a special case of a parallelogram where all four sides are congruent and opposite sides are parallel.

A parallelogram is a quadrilateral (a four-sided polygon) in which opposite sides are parallel.

A rhombus is a special type of parallelogram in which all four sides are congruent.

To prove that quadrilateral JKLM is a parallelogram, we need to show that opposite sides are parallel.

We can find the slope of each side by using the formula:

[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

The slope of JK:

(-5 - 1) / (1 - (-3)) = -6/4 = -3/2

The slope of LM:

(4 - (-2)) / (3 - 7) = 6/-4 = -3/2

The slope of KL:

(-2 - (-5)) / (7 - 1) = 3/6 = 1/2

The slope of MJ:

(1 - (-5)) / (-3 - 1) = 6/-4 = -3/2

We can see that the slopes of opposite sides are equal, which means that they are parallel. Therefore, JKLM is a parallelogram.

To prove that JKLM is not a rhombus, we need to show that at least one pair of opposite sides are not congruent.

We can find the length of each side using the distance formula:

Length of JK:

√[(1 - (-5))² + (1 - (-3))²] = √[36 + 16] = √[52]

Length of KL:

√[(-2 - (-5))² + (7 - 1)²] = √[9 + 36] = √[45]

Length of LM:

√[(4 - (-2))² + (3 - 7)²] = √[36 + 16] = √[52]

Length of MJ:

√[(-5 - 1)² + (-3 - 1)²] = √[36 + 16] = √[52]

We can see that all four sides have the same length, which means that they are congruent. Therefore, JKLM is a rhombus.

However, we can also see that opposite sides have different slopes, which means that they are not parallel. Therefore, JKLM cannot be a rhombus because a rhombus is a special case of a parallelogram where all four sides are congruent and opposite sides are parallel.

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The unknown side 'x' is found using pythagorean theorem as: x = 12.69.

The Pythagorean Theorem has a name for Pythagoras of Samos, a religious figure and mathematician who held the view that everything in the cosmos is made up of numbers.

Pythagorean Theorem is also known as:

a²+ b² = c²

Given sides are:

13, 3 and x.

Then,

3²+ x² = 13²

x² = 13² - 3²

x² = 169 - 9

x² = 160

x = √160

x = 12.69

Thus, the unknown side 'x' is found using pythagorean theorem as: x = 12.69.

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Answer:

7 and 4

Step-by-step explanation:

take away 3 each time so

10-3=7

7-3=4

The time interval for which the patient will receive pain relief is [1.3, 8.3] hours.

To determine this, we can use the equation C(t) = 60t + 12t + 6, where t is the number of hours after the surgery. Setting C(t) = 1010 and solving for t, we get t = 13.3, so the patient will receive pain relief for t > 13.3 hours, or [1.3, 8.3] hours.

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The correct match of the accounting terms such as assets, debits, and credit, would be:

This is a matching exercise that matches various accounting terms with their definitions. Here are the meanings of the terms:

These are some terms in accounting which are used to ensure that proper records are taken.

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This function rule represents the original function f(x) = √x, shifted up 5 units, vertically stretched by a factor of 2, and shifted to the right 3 units.

The function rule for g(x) from f(x) = √x can be found by applying the given transformations to f(x). First, we shift up 5 units by adding 5 to the function. Then, we apply a vertical stretch by a factor of 2 by multiplying the function by 2. Finally, we shift to the right 3 units by replacing x with (x - 3) in the function. The resulting function rule for g(x) is:

g(x) = 2√(x - 3) + 5

This function rule represents the original function f(x) = √x, shifted up 5 units, vertically stretched by a factor of 2, and shifted to the right 3 units.

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Answer: if under 15 miles, then use Red cab company. if over 15 miles, then use Yellow cab company

Step-by-step explanation:

first, need to identify equations for the each cab company.

let X be the mile driven and Y be the fare cost

red cab cost:   Y= 1.25X + 3.50

yellow cab cost:   Y = 1.15X + 5

I like to use the combination method to eliminate one variable

multiply -1 to one of the equation so -1[  Y= 1.25X + 3.50 ] = -Y = -1.25X -3.50

combine (add) them and eliminate the Y value

-Y = -1.25X - 3.50

Y =   1.15X + 5

-------------------------

0 = -0.1X  + 1.5

0.1X  = 1.5

X = 1.5/0.1 = 15

input X = 15 to the original equation(s) to find Y

Y = 1.15(15) + 5 = 17.25 +5 = 22.25

Y= 1.25(15) + 3.50 = 18.75 + 3.5 = 22.25

X = 15 miles and Y = $ 22.25

these values represents the red and yellow cab companies will charge the same amount when going exact 15 miles.

What if X is under or over 15 miles?

if X = 10 (under 15 miles)

red cab cost:   Y= 1.2(10) + 3.50 = 12 + 3.50 = 15.50 (cheaper)

yellow cab cost:   Y = 1.15(10) + 5 = 11.50 + 5 = 16.50

You can test out the X when greater than 15 miles

Conclusion.

if under 15 miles, then use Red cab company. if over 15 miles, then use Yellow cab company

Answer: $4.28 per quart

Step-by-step explanation:

So there is 4 quarts in one gallon. Since there is 2 gallons that means there is 8 quarts total. now you want to take $34.24 and divide it by 8 and you will get $4.28

Answer:4/3

Step-by-step explanation:

If each hamburger she makes has a mass of about 0. 125 kg she can make a maximum of 16 hamburgers with the amount of ground beef she has.

To determine how many hamburgers Kendra can make, we need to divide the total mass of ground beef by the mass of each hamburger:

Total mass of ground beef = 0.652 kg + 0.545 kg + 0.824 kg = 2.021 kg

Number of hamburgers = Total mass of ground beef / Mass of each hamburger

Number of hamburgers = 2.021 kg / 0.125 kg = 16.168

Since Kendra can only make whole hamburgers, she can make a maximum of 16 hamburgers with the amount of ground beef she has.

Calculation of how many items can be made with a given amount of material, based on the mass of each item and the total mass of the material available.

In the context of the question, Kendra has three packages of ground beef with different masses and wants to make hamburgers, each with a specific mass. To determine how many hamburgers she can make, we need to calculate the total mass of ground beef available and then divide it by the mass of each hamburger.

This concept can be applied in many different situations, such as determining how many cookies can be made with a given amount of dough or how many pieces of clothing can be made with a certain amount of fabric. It is a useful skill in cooking, baking, and manufacturing, as it helps to ensure that resources are used efficiently and waste is minimized.

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Answer:

3, 18 , 24

Step-by-step explanation:

f(- 2) with x = - 2 < 0 , then f(x) = 3x + 9 , that is

f(- 2) = 3(- 2) + 9 = - 6 + 9 = 3

f(0) with x = 0 then f(x) = 3x + 18 , that is

f(0) = 3(0) + 18 = 0 + 18 = 18

f(2) with x = 2 ≥ 0 , then f(x) = 3x + 18, that is

f(2) = 3(2) + 18 = 6 + 18 = 24

Given the function f(x) = {3x + 9 if x < 0; 3x + 18 if x ≥ 0}, the following values  as follows:

f(-2) = 3

f(0) =  18

f(2) = 24

The function f(x) is a piecewise function, meaning it has different rules for different values of x. We need to use the appropriate rule for each value of x we are given.

For f(-2), we use the rule 3x+9 because x<0. Plugging in -2 for x, we get:

f(-2) = 3(-2) + 9
f(-2) = -6 + 9
f(-2) = 3

For f(0), we use the rule 3x+18 because x≥0. Plugging in 0 for x, we get:

f(0) = 3(0) + 18
f(0) = 0 + 18
f(0) = 18

For f(2), we use the same rule as f(0) because x≥0. Plugging in 2 for x, we get:

f(2) = 3(2) + 18
f(2) = 6 + 18
f(2) = 24

So the final answers are f(-2) = 3, f(0) = 18, and f(2) = 24.

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Therefore, the height (in feet) of the lighthouse is 88 feet.

A person's or something's height can be described as their vertical position or their vertical extension (how "tall" they are) (how "high" a point is). For example, "The height of the structure is 50 m" or "The height of an airplane in-flight is roughly 10,000 m".

Let's use proportions to solve the problem. We can set up a ratio of the height of the lighthouse to the length of its shadow, and another ratio of the height of the lamppost to the length of its shadow, and then equate the two ratios:

height of lighthouse / length of shadow of lighthouse = height of lamppost / length of shadow of lamppost

Let's plug in the given values:

h / 144 = 5.5 / 9

To solve for the height of the lighthouse, we can cross-multiply and simplify:

9h = 144 × 5.5

9h = 792

h = 88

Therefore, the height of the lighthouse is 88 feet.

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The triplets 20, 48, 52 is a Pythagorean triplet.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

We know, Any three numbers to be a Pythagorean triplet,

The sum of the squares of any smaller side must be equal to the square of the third side.

Now, 20² + 48² = 52².

400 + 2304 = 2704

2704 = 2704.

So, The first option 20, 48, 52 it self is a Pythagorean triplet and we don't need to check further options.

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maxima_value = sp.sin(maxima)
minima_value = sp.sin(minima)

For part (a), to find the minima and maxima of the function y=sin(x) in the interval [2π, 4π], you can use the SymPy solves

et() function, which takes an equation, a variable and an interval (numn1​, num2​) as inputs. To do this, you can use the following code:

minima, maxima = sp.solveset(sp.Eq(sp.sin(x), 0), x, (sp.pi*2, sp.pi*4))

For part (b), to determine the x-values at which the maxima and minima occurs, you can use the minima and maxima values from the previous solveset() function and evaluate the sin(x) at those points. For example:

maxima_value = sp.sin(maxima)
minima_value = sp.sin(minima)

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Answer:

Step-by-step explanation: