Let us define L = {x | x is a member of {a,b}* and the number of
a's in x is even and the number of b's in x is odd}.
Which of the following sets are subsets of L?
A) {aa}*{b}{bb}*
B) {baa}*{bb}*
C) {

Answer:

It's fine. It is a function. The language can be very convoluted. Put simply a domain value cannot have 2 different range values.

Step-by-step explanation:

The confusing part I think, is probably the fact that -1 and 1 both have an answer of 5.

That's fine. Parabolas do that and they are functions. Two different xs can have the same value. The thing that eliminates functions is when the x value (the domain) has two different y values (the range values). Then you don't have a function.

To try and make it clearer if 1 pointed at both 3 and 5 you would not have a function.

Answer:

The null hypothesis describes the population parameters represented by the sample data if the predicted relationship does not exist.

Step-by-step explanation:

The average rate of change between day 12 and day 15 is given as follows:

B. -5/3.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.

The volumes on day 12 and day 15 are given as follows:

The change in the output is given as follows:

10 - 15 = -5 inches.

The change in the input is given as follows:

15 - 12 = 3.

Hence the average rate of change is given as follows:

B. -5/3.

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Answer:

14x+8

Step-by-step explanation:

Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

The given information is as follows:A random sample of 150 teachers in an​ inner-city school district found that​ 72% of them had volunteered time to a local charitable cause within the past 12 months.

The formula for calculating the standard error of sample proportion is given as:$$Standard\(\ error=\frac{\sqrt{pq}}{n}$$\)where:p = proportion of success in the sampleq = proportion of failure in the samplen = sample sizeGiven:Sample proportion, p = 72% or 0.72Sample size, n = 150

The proportion of failure in the sample can be calculated as:q = 1 - p= 1 - 0.72= 0.28Substituting the known values in the above formula, we get:\($$Standard \ error=\frac{\sqrt{pq}}{n}$$$$=\frac{\sqrt{0.72(0.28)}}{150}$$$$=0.0372$$\)Rounding off to the nearest thousandth, we get the standard error of sample proportion as 0.037

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The option "1,000 kg" is the best choice to satisfy the request for an order of magnitude estimate of the mass of a normal American passenger car.

The estimated mass of a normal American passenger car to the order of magnitude is around 1,000 kilograms, which best satisfies the request.

Among the given options, 1,000 kg is the most reasonable estimate for the mass of a normal American passenger car. Cars typically range in mass from around 1,000 kg to 2,000 kg, depending on their size, model, and other factors. While it is possible for some cars to be lighter or heavier, 1,000 kg provides a good order of magnitude estimate that aligns with the average mass of passenger cars. Therefore, the option "1,000 kg" is the best choice to satisfy the request for an order of magnitude estimate of the mass of a normal American passenger car.

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Answer:

2280

Step-by-step explanation:

Answer:

-27

Step-by-step explanation:

-5-9=-14

-14-13=-27

Answer:

2/5

Step-by-step explanation:

We can find the slope by using the slope formula

m = ( y2-y1)/(x2-x1)

   = ( 7 -5)/(9 - 4)

   = 2/5

Answer:

Step-by-step explanation:

If the polynomial function has rational coefficients, then the missing root must be conjugate with 3 + √11, which is achieved by reversing the sign of root:

\( \LARGE{ \underline{\underline{ \purple{ \bf{Required \: answer:}}}}}\)

Since 3 roots are rational but one of the four is irrational. Then, there must be a conjugate pair for that which we can do by reversing the sign between the rational and the non-rational part.

Hence, Another root of the polynomial function f(x) will be ofcourse the conjugate pair of 3 + √11 i.e. 3 - √11 (Ans)

Answer:

12

Step-by-step explanation:

The Roman Numerals can be confusing, but XII is equal to 12.

All correct proportions include the following:

A. \(\frac{AC}{CE} =\frac{BD}{DF}\)

D. \(\frac{CE}{DF} =\frac{AE}{BF}\)

In Mathematics and Geometry, two geometric figures are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Hence, the lengths of the pairs of corresponding sides or corresponding side lengths are proportional to one another when two (2) geometric figures are similar.

Since line segment AB is parallel to line segment CD and parallel to line segment EF, we can logically deduce that they are congruent because they can undergo rigid motions. Therefore, we have the following proportional side lengths;

\(\frac{AC}{CE} =\frac{BD}{DF}\)

\(\frac{CE}{DF} =\frac{AE}{BF}\)

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To prove that every linear map on a subspace of V can be extended to a linear map on V. We have to show that there exists a linear map T from V to W that extends S and satisfies Tu = Su for all u in U.

Let U be a subspace of a finite-dimensional vector space V, and let S be a linear map from U to another vector space W. du in U.

Since V is finite-dimensional, ready to select a premise {u1, u2, ..., um} of U and expand it to the premise {u1, u2, ..., um, v1, v2, ... increment. Let {w1, w2, ..., wk} be the premise of W.

 You can define T using the base elements of V as follows:

T(uj) = S(uj) for j = 1, 2, ..., m (since uj is in U and S is a linear map from U to W)

T(vi) = 0 for i = 1, 2, ..., n (to ensure that T is a linear map)

We can extend T linearly to all of V by defining T as

For any vector v in V, we can write v as a linear combination of basis elements.

v = a1u1 + a2u2 + ... + amount + b1v1 + b2v2 + ... + bnvn

Then we can define T(v) as

T(v) = a1T(u1) + a2T(u2) + ... + amT(um) + b1T(v1) + b2T(v2) + ... + bnT(vn)

Structurally, this definition of T agrees with the definition of S on the subspace U, since T(uj) = S(uj) for j = 1, 2, ..., m. Since T is a linear map on V, it is also well-defined and satisfies the linear property.

T(cv + w) = cT(v) + T(w)

For every vector v, w in V, and every scalar c. Thus, we showed that there exists a linear map T from V to W that extends S and satisfies Tu = Su for all u in U.

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There are 180 degrees of longitude, which is divided into 360 lines of longitude (meridians).

Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is measured in degrees, with a full circle consisting of 360 degrees. The Prime Meridian is located at 0 degrees longitude, and each degree is further divided into 60 minutes and each minute is divided into 60 seconds. Therefore, there are 180 degrees of longitude east of the Prime Meridian and 180 degrees of longitude west of the Prime Meridian.

There are 180 degrees of longitude, which is divided into 360 lines of longitude (meridians).

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Answer:

The interest on the savings account is $46.47

Step-by-step explanation:

Here, we want to know the interest earned on the savings account.

The difference between the new and previous balance will be; 12,098.12 - 9,053.20 = $3,044.92

The difference between amount deposited and amount withdrawn is 3,298.45 - 300 = 2,998.45

This is the amount that is supposed to be on the account without interest

So the interest earned would be; 3044.92 - 2,998.45 = $46.47

Step-by-step explanation:

70+1

Steps:

write tens and then ones

Answer:

21 miles per gallon.

420÷20

Step-by-step explanation:

A cheerful teen willing to help,

who listens to ,"Fight Song,"

stay salty,

stay positive...

Answer:

It is (D)

\(f(x) = \frac{ - 1}{2} x + 6\)

Step-by-step explanation:

I hope that is useful for you

The horizontal velocity with which the ball should be imparted to land on the rooftop of the second building is approximately 4.42 meters/second.

To find the horizontal velocity with which the ball should be imparted to land on the rooftop of the second building, we can use the fact that the horizontal distance travelled is 20 meters.

We know that horizontal distance (x) equals horizontal velocity (\(v_x\)) multiplied by time (t).

Since the horizontal distance is 20 meters, we have:

\(20 = v_x * t\)

We need to find the value of \(v_x\).

We also know that the time it takes for the ball to reach the rooftop of the second tower is t, which we calculated earlier as approximately 4.52 seconds.

We can plug in this value of t into the equation to find \(v_x\):

\(20 = v_x * 4.52\\v_x = 20 / 4.52\\v_x \approx4.42 meters/second\)

Therefore, the correct answer is : 4.42 meters/second.

The horizontal velocity with which the ball should be imparted to land on the rooftop of the second building is approximately 4.42 meters/second.

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Answer:

Option (D)

Step-by-step explanation:

Polygon Q(16, 4), R(8, 16), S(4, 4) mapped to polygon T(-2, 5), U(-4, 8), V(-5, 5).

Polygon QRS was dilated initially by using the rule,

(x, y) → (0.25x, 0.25y)

Therefore, coordinates of QRS will be,

Q(16, 4) → Q'(4, 1)

R(8, 16) → R'(2, 4)

S(4, 4) → S'(1, 1)

Followed up by the translation,

(x, y) → (x + a, y + b)

By applying this rule,

Q'(4, 1) → T(-2, 5)

Q'(4, 1) → T(4 - 6, 1 + 4)

Rule applied in the translation of this point is,

Q'(x, y) → T[(x-6), (y+4)]

Therefore, Option (D) will be the answer.

Answer:

-1.517

Need to know:

Integral constant rule: ∫ (ax)dx = a ∫ (x)dx

Integral power rule: ∫ xⁿ = xⁿ⁺¹/(n + 1)

\(\int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)

Quadratic formula: \(\frac{-b +-\sqrt{b^{2} -4ac} }{2a}\)

Step-by-step explanation:

First, we have to find the average value of f over the interval [-2, 2]

To find that, calculate the integral of 3x(x - 2)

∫ 3x(x - 2)dx = 3 ∫ x(x - 2)dx = 3 ∫ x² - 2xdx (pulled out the 3 because of the constant rule)

Use the power rule to solve the integral

3 [x²⁺¹/(2 + 1) - 2x¹⁺¹/(1 + 1)] = 3[x³/3 - 2x²/2]

Distribute the 3

3[x³/3 - 2x²/2] = x³ - 3x² = F(x)

We plug in 2 in place of x

F(2) = 2³ - 3(2)² = -4

Do the same with -2

F(-2) = (-2)³ - 3(-2)² = -20

We have to remember that  \(\int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)

let a = -2    b = 2

F(2) - F(-2) = -4 - (-20) = -4 + 20 = 16

The average value of f over the given interval is 16.

Now we make it to where f(x) = 16 to find c

3x(x - 2) = 16

3x² - 6x = 16

Subtract 16 from both sides to make it equal to zero

3x² - 6x = 16

       - 16    - 16

3x² - 6x - 16 = 0

a = 3 b = -6 c = 16

Plug these numbers into the quadratic formula

\(\frac{-(-6) +-\sqrt{(-6)^{2} -4(3)(-16)} }{2(3)}\)

\(\frac{6 +-\sqrt{36 + 192} }{6}\)

\(\frac{6 +\sqrt{228} }{6}\) = -1.51661

\(\frac{6 -\sqrt{228} }{6}\) = 3.51661

-1.51661 is the only number out of the two that fits in the given interval [-2,2], so c would have to be -1.517 in order for f(c) to equal the average value of f over the given interval.

Answer:

36 square units

Step-by-step explanation:

The figure is made up of a rectangle above with length 6 and width 4.

The bottom part is a triangle with a base of 6 and a height of 4.

total area = area of rectangle + area of triangle

total area = LW + bh/2

total area = 6 × 4 + 6 × 4/2

total area = 24 + 12

total area = 36

Answer:

36 square units

Step-by-step explanation:

We can split the given figure into two familiar figure by drawing a line segment as shown in the attached figure

This splits the composite figure into a rectangle at the top and an inverted triangle at the bottom

The rectangle has a length(horizontal portion) of 6 units and a width(vertical portion) of 4 units

Area of rectangle = length x width = 6 x 4 = 24 square units

The triangle has a base of 6 units and a height of 4 units

Area of rectangle = 1/2 x base x height = 1/2 x 6 x 4 = 1/2 x 24 = 12 square units

Area of figure = 24 + 12 = 36 square units

The answers to each part is -

Given is to find -

We can write the expression as -

{x} = \(5\frac{1}{3} - 3\frac{2}{3}\)

{x} = 16/3 - 11/3

{x} = 5/3

We can write the expression as -

{x} = \(8\frac{4}{7} - 7\frac{5}{7}\)

{x} = 60/7 - 54/7

{x} = 6/7

Therefore, the answers to each part is -

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Yes, the connection between the semimajor axis and an orbit's period varies as the eccentricity of the orbit changes.

In geometry, the eccentric definition is the distance from any point on a conic section to the focus divided by the perpendicular distance from that point to the nearest directrix. In general, eccentricity aids in determining the curvature of a form. The eccentricity grows as the curvature lowers.

Here,

In general, an orbit's period is proportional to the square root of the semimajor axis multiplied by three. This connection, however, is only valid for circular orbits with zero eccentricity. When the eccentricity is larger than zero, the period of the orbit is still determined by the magnitude of the semimajor axis, but it is also determined by the form of the orbit as given by the eccentricity. The relationship between the semimajor axis and the period in this situation is not as straightforward as a proportionate relationship.

As a result, modifying an orbit's eccentricity modifies the connection between the semimajor axis and the period.

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Answer:

£15.48

Step-by-step explanation:

just divide 92.88 by 6 to find how much they should each pay

92.88÷6= 15.48

hope this helps chu <3

Answer = 15.48

Step-by-step explanation:

92.88:6 = 15,48

To prove it 15,48×6 = 92,88

Answer:B

Step-by-step explanation:the line touches the graph on the y axis at 3 so the y intercept has to be a positive 3. Then it goes up 1 over 3 each time. Meaning it’s Y=1/3X+3

Radians are a unit of measurement for angles used in mathematics and physics. They are defined as the ratio between the length of an arc of a circle and the radius of that circle.

One of the most important benefits of using radians to measure angles is that they simplify calculations involving angles, making them easier to work with.

Additionally, they allow for a more elegant and unified approach to mathematical and physical problems involving angles. So, in short, the word "radian" might be associated with concepts such as circles, arcs, and the measurement of angles in mathematics and physics.

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