Find a set of smallest possible size that has both {1,3,5,6,8} and {2,6,7,10} as subsets.

Answer:

312,000,000

Step-by-step explanation:

Standard notation is when you move the decimal however many times the 10 is being squared by. In this case, it is 8.

Since the 8 is not negative, we move it 8 times to the right.

Since there are only 2 digits, we add 6 more zeros because 2+6=8

that is how you get 312,000,000

To calculate the concentrations of all species present in a 0.72 M NH3 solution (Kb=1.8×10−5), we can use the principles of the equilibrium expression for the dissociation of NH3 in water.

NH3 (ammonia) is a weak base that reacts with water to form NH4+ (ammonium) and OH- (hydroxide) ions. The equilibrium expression for this reaction can be written as:

NH3 + H2O ⇌ NH4+ + OH-

Since the initial concentration of NH3 is 0.72 M, we can assume that x mol/L of NH3 will dissociate to form x mol/L of NH4+ and OH-. Therefore, the concentrations of NH4+ and OH- will also be x mol/L.

To calculate the value of x, we can use the Kb expression, which relates the equilibrium constant to the concentrations of the species. In this case, Kb = [NH4+][OH-]/[NH3]. Substituting the known values, we have:

1.8×10−5 = x * x / (0.72 - x)

Solving this equation will give us the value of x, which represents the concentration of NH4+ and OH-. Finally, we can express the concentrations of NH3, NH4+, and OH- using two significant figures, separated by commas, based on the calculated value of x.

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Answer:

#7 m∠4 = 30°  

#8. m∠5 = 150

#22. A'(-6, -3), B'(-3, 4), C'(3, 5)
*** You may just want to put the coordinate points: (-6, -3), (-3, 4), (3, 5) without the A', B', C'. ***

#23. A'(6, -3), B'(3, 4), C'(-3, 5)

Step-by-step explanation:

#7 Angles 30° and ∠4 are corresponding angles and hence equal

#8 ∠4 and ∠5 are supplementary linear angles and add up to 180° So m∠5 = 180 - m∠4 = 180 - 30 = 150°

#22 Reflection about the x-axis means the x-coordinates do not change but the new y-coordinate is the negative of the original y coordinate

In other words, a point(x, y) in the pre-image becomes (x, -y) in the image

#23 With a 180° rotation both x and y axes change signs. (x, y) becomes (-x, -y)

Answer:

Step-by-step explanation:

The inverse of the function is f-1(x) = (x - 5)³ - 2

From the question, we have the following parameters that can be used in our computation:

f(x)= ^3√x+2 -5

Express properly

So, we have the following representation

f(x)= ∛(x + 2) -5

Rewrite as

y = ∛(x + 2) -5

Swap x and y

x = ∛(y + 2) -5

This gives

y + 2 = (x - 5)³

Make y the subject of fomula

y = (x - 5)³ - 2

Express as inverse function

f-1(x) = = (x - 5)³ - 2

Hence, the inverse is f-1(x) = (x - 5)³ - 2

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Answer:

4

Step-by-step explanation:

an=-4+3(n-1)=-4+3n-3=3n-7

a1=3×1-7=3-7=-4

a5=3×5-7=15-7=8

a1+a5=-4+8=4

The perpendicular distance from the point (-1, 4) to the line joining A(4, 1) and B(8, 3) is (11sqrt(5) / 5) units.

To calculate the perpendicular distance from a point to a line, we can use the formula:

d = |(Ax - Bx)(By - Py) - (Ay - By)(Bx - Px)| / sqrt((Ax - Bx)^2 + (Ay - By)^2)

Given:

A(4, 1)

B(8, 3)

P(-1, 4)

Substituting the values into the formula:

d = |(4 - 8)(3 - 4) - (1 - 3)(8 - (-1))| / sqrt((4 - 8)^2 + (1 - 3)^2)

Simplifying:

d = |(-4)(-1) - (-2)(9)| / sqrt((-4)^2 + (-2)^2)

= |4 + 18| / sqrt(16 + 4)

= 22 / sqrt(20)

= 22 / 2sqrt(5)

= 11 / sqrt(5)

To rationalize the denominator, we multiply both the numerator and denominator by sqrt(5):

d = (11 / sqrt(5)) * (sqrt(5) / sqrt(5))

= 11sqrt(5) / 5

Therefore, the perpendicular distance from the point (-1, 4) to the line joining A(4, 1) and B(8, 3) is (11sqrt(5) / 5) units.

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The fraction of total hemispherical emissive power leaving a diffuse surface in the directions π/4 < θ ≤ π/2 and 0 < φ ≤ π is 1/8.

To determine this, recall that diffuse surfaces emit energy equally in all directions. The solid angle for a hemisphere is given by Ω = 2π, and the range for θ is π/4 to π/2, making the difference Δθ = π/4.

The range for φ is from 0 to π, so Δφ = π. The fraction of the total hemispherical emissive power is calculated by the ratio of the solid angle in the specified range to the total solid angle for a hemisphere:

Fraction = (Δθ * Δφ) / Ω = (π/4 * π) / 2π = π²/8π = 1/8

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Step 1:

Write the graph of the parent function y = f(x)

Step 2

Given the graph of y=f(x)as shown, sketch y = f(-x).

Step 3

The function y = f(x) will reflect about the y-axis to form the function y = f(-x).

Final answer

y-axis

Answer:

I beleive the answer is 9

(sorry if its wrong)

Answer:

27 i think

Step-by-step explanation:

a. 36, 000 stadia = 5,664 km. b. 129 yojanas = 1,987 km. Stadia was an ancient unit of length, equal to about 185 meters. It was used in Greece, Rome, and other parts of the Mediterranean world.

Yojana was an ancient unit of length, equal to about 13 kilometers. It was used in India and other parts of Asia.

a. 36, 000 stadia = 5,664 km

1 stadia = 0.1575 km

36,000 stadia x 0.1575 km/stadia = 5,664 km

b. 129 yojanas = 1,987 km

1 yojana = 13.2 km

129 yojanas x 13.2 km/yojana = 1,987 km

To convert from stadia to kilometers, we can use the following conversion factor:

1 stadia = 0.1575 km

To convert from yojanas to kilometers, we can use the following conversion factor:

1 yojana = 13.2 km

In addition to the above, here are some additional information about stadia and yojanas:

Both stadia and yojanas are no longer in use as official units of measurement, but they are still sometimes used in historical and archaeological contexts.

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The minimum possible order of the group is the least common multiple (LCM) of the orders of its elements, which is LCM(1, 2, 3, 4, 5, 6, 7, 8, 9, 10) = 2520.

To see why, consider that the order of an element in a group is the smallest positive integer n such that the element raised to the nth power is equal to the identity element. If we have elements of orders 1 through 10 in a group, then the LCM of these orders represents the smallest number of times we need to repeat any of these elements to get the identity element.

Therefore, the order of the group must be at least the LCM of these orders, since we need enough elements and combinations of elements to generate the identity element. It's possible that the group could have a higher order, depending on the specific elements and how they interact with each other, but the LCM gives us a lower bound on the group's order.

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The sampling distribution of the sample mean will always have the same Mean as the original distribution.

Sampling distribution:

Sampling distribution means a probability distribution of a statistic that is obtained through repeated sampling of a specific population.

Given,

Here we have the statement "The sampling distribution of the sample mean will always have the same _________ as the original distribution."

Now, we have to find the missing word in the statement.

We know that, the mean of the sampling distribution of the sample mean will always be the same as the mean of the original non-normal distribution. Simply said that the sample mean is equal to the population mean.

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Answer:

2x-3x- x=-12

-2x= -12

x=6

The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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Answer:

C. 78 cm

Step-by-step explanation:

The mean of any given data set is calculated as sum of all data set divided by the number of data set given.

The data set for the height of Bella's corn given, is 81, 88, 69, 65, 87

Mean height of Bella's corn = \( \frac{81 + 88 + 69 + 65 + 87}{5} \)

\( mean = \frac{390}{5} \)

\( mean = 78 cm \)

You are required to calculate the mean of the height, in other words, the average of the height

The mean of the height is 78

Given height

81, 88, 69, 65, 87

Mean = Total height / number of height

= (81 + 88 + 69 + 65 + 87) / 5

= 390 / 5

= 78

Mean of the height = 78

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The data-set in this problem is given by the stem-and-leaf plot, which shows each observation in the problem.

Hence each observation is given as follows:

32, 34, 40, 43, 44, 47,48, 49, 49, 49, 50, 51, 51, 52, 53, 54, 55, 70, 71, 92

The data-set has 20 elements, which is an even cardinality, hence the median is the mean of the two middle elements, the 10th and the 11th, as follows:

Median = (50 + 51)/2 = 50.5.

The mean of the data-set is given by the sum of all observations divided by the number of observations, hence:

Mean = (32 + 34 + 40 + 43 + 44 + 47 + 48 + 3 x 49 + 50 + 2 x 51 + 52 + 53 + 54 + 55 + 70 + 71 + 92)/20

Mean = 51.7.

The problem is given by the image presented at the end of the answer.

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Answer: A)  \(x < -4 \ \text{ or } \ x \ge 3\)

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

Explanation:

The left portion of the graph is \(x < -4\) to indicate values smaller than -4. We exclude the endpoint -4 due to the open hole. So we don't have "or equal to" as part of the inequality sign.

In contrast, we do include the endpoint 3 since there's a filled in endpoint here. The right side of the shaded graph shows values that are 3 or larger. So that's why we have \(x \ge 3\) which says "x is greater than or equal to 3".

Put those two pieces together and we end up with \(x < -4 \ \text{ or } \ x \ge 3\)

You must use "or" instead of "and" because they mean different things. Saying \(x < -4 \ \text{ and } \ x \ge 3\) is not correct because there are no numbers that are both less than -4 and greater than or equal to 3 at the same time. Visually there are no numbers that are to the left of -3 and also to the right of 3 at the same time.

a) The volume of the box (in cubic inches) when the cutout length is 0.8 inches can be represented using function notation as f(0.8).

b) The volume of the box (in cubic inches) when the cutout length is 1.2 inches can be represented using function notation as f(1.2).

c) The change in volume of the box (in cubic inches) when the cutout length increases from 0.8 inches to 1.2 inches can be represented using function notation as f(1.2) - f(0.8).

d) The change in volume of the box (in cubic inches) when the cutout length increases from 5.6 inches to 5.7 inches can be represented using function notation as f(5.7) - f(5.6).

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The function f(x) = 2x + 1, where f is defined from the positive integers (Z+) to the real numbers (R), is a one-to-one function, but not a bijection or onto function.

A one-to-one function, also known as an injective function, is a function in which each input value (x) maps to a unique output value (f(x)). In the given expression, f(x) = 2x + 1, every positive integer will have a unique real number output since the coefficient of x is 2, ensuring distinct outputs for distinct inputs. Hence, f is a one-to-one function.

However, a bijection requires that a function be both one-to-one and onto. An onto function, also known as a surjective function, means that every element in the codomain (R) has a corresponding element in the domain (Z+) such that f(x) maps to that element. In this case, the function f(x) = 2x + 1 is not onto because there are real numbers that do not have corresponding positive integers. For example, there is no positive integer x that can satisfy f(x) = 2x + 1 = 0.

In conclusion, the function f(x) = 2x + 1 is a one-to-one function, but it is not a bijection or an onto function.

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the answer

155

324

5/9 (87/3(1/12)= 155/324

Answer:

angle SXV

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

If she has 3 chews and 2 mints left, the probability that she picks a mint is 2/5 as they are only 2 mints and 3 chews and 2+3 = 5. So the awnser is 2/5.

The acceleration of the object moving at a constant speed in a circular path of radius r at a rate of 1 revolution per second is given by option C, 2π^2r^2.

The object experiences centripetal acceleration towards the center of the circle. Although its speed remains constant, the direction of its velocity continuously changes, resulting in acceleration. The magnitude of centripetal acceleration can be calculated using the formula a = (v^2) / r, where v is the linear velocity and r is the radius of the circular path. In this case, the linear velocity is the circumference of the circle (2πr) divided by the time (1 second), squared, and divided by the radius (r), resulting in 2π^2r^2.

The acceleration of an object moving in a circular path is directed toward the center of the circle and is known as centripetal acceleration. In this scenario, the object moves at a constant speed of 1 revolution per second, which means it completes a full circular path in 1 second. The linear velocity can be calculated by dividing the circumference of the circle (2πr) by the time taken to complete one revolution (1 second). Since the speed is constant, there is no tangential acceleration. However, the object experiences centripetal acceleration due to the continuously changing direction of its velocity. The magnitude of the centripetal acceleration is given by the formula a = (v^2) / r, where v is the linear velocity and r is the radius. Plugging in the values, we get a = ((2πr) / 1)^2 / r = 4π^2r^2 / r = 4π^2r, which corresponds to option D, 4π^2r.

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Answer:

The answer is below

Step-by-step explanation:

Tony is opening a pizza restaurant and needs to determine the amounts of ingredients he will use in his pizzas. He wants the amount of dough for a medium pizza to be 3/2 times the amount of dough for a small pizza. And, he wants the amount of dough for a large pizza to be 5/2 times the amount of dough for a small pizza. Also, the amount of dough used for one large pizza should to be equal to the amount of dough used for one medium and one small pizza. So, he needs to determine how much dough to use for a small pizza. Use this information to complete the following tasks.

Answer:

Let the amount of dough needed for a small pizza be S, the amount of dough needed for a medium pizza be M and the dough needed for a large pizza be L.

The amount of dough for a medium pizza to be 3/2 times the amount of dough for a small pizza, therefore:

M = (3/2)S

The amount of dough for a large pizza to be 5/2 times the amount of dough for a small pizza. Therefore

L = (5/2)S

the amount of dough used for one large pizza should to be equal to the amount of dough used for one medium and one small pizza. That is:

L = M + S

(5/2)S = (3/2)S + S

5S = 5S

The equation cannot be solved.

But if he wants the amount of dough for a large pizza to be 5/2 kg.

L = M + S

(5/2) = (3/2)S + S

S = 1 kg

Answer:

Point form:

(11/7, -5/7)

Equation form:

x = 11/7, y = -5/7

Answer: There are 16 quarters and 10 dimes.

Step-by-step explanation:

Let x = Number of quarters

y= Number of dimes.

As per given,

x+y = 26  (i)

x= y+6  (ii), substitute this in (i), we get

y+6+y= 26

⇒2y+6=26

⇒ 2y = 26-6=20

⇒ 2y =20

⇒ y =10   [Divide both sides by 2]

Put this in (ii),  x= 10+6 =16

So there are 16 quarters and 10 dimes such that 16 (0.25)+10(0.10)= $5 .

Answer: 0.95k + 3.15

Step-by-step explanation:

0.95k is because each of k kilometers costs $0.95.  + 3.15 is because it costs 3.15 as a flat rate regardless of distance

Hope it helps <3

Answer:

.95k+3.15

Step-by-step explanation:

To write an expression you need a variable (k). I look at the directions and I see that the length of the trip is 'k' kilometers. So I pay the flat fee of 3.15 ONE TIME. Then I pay $0.95 for every kilometer I go, so the expression is

->   .95k+3.15