Divide. Express your answer in simplest form.

8 ÷ 2 4/9

Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

The probability that a randomly selected student studies Hindi or Maths is 0.60 or 60%.

We can use the formula P(A or B) = P(A) + P(B) - P(A and B) to find the probability that a randomly selected student studies Hindi or Maths is calculated by adding the probabilities of studying Hindi and Maths and subtracting the probability of studying both Hindi and Maths.

P(Hindi or Maths) = P(Hindi) + P(Maths) - P(Hindi and Maths)

P(Hindi or Maths) = 0.30 + 0.45 - 0.15

P(Hindi or Maths) = 0.60

Therefore, if a student is selected randomly, then the probability that he/she studies Maths or Hindi is 0.60 or 60%.

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a) If one block represents 2 feet, the number of blocks of the model is 725.

b) If one block represents 5 feet, the number of blocks of the model is 290.

c) Based on the scale factors from Parts a and b above, they represent a reduction of the Empire State Building.

A scale factor shows the ratio of the enlargement or reduction of an object in the model.

An enlarged scale factor increases the size from the actual size of the object.

On the other hand, a reduced scale factor decreases the size of the model based on the actual size.

The estimated height of the Empire State Building = 1,450 feet

a) If one block represents 2 feet, the number of blocks of the model = 725 (1,450/2)

b) If one block represents 5 feet, the number of blocks of the model = 290 (1,450/5)

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Work Shown:

-1 < x+3 < 5

-1-3 < x+3-3 < 5-3 ... subtract 3 from all sides

-4 < x < 2

Let X be the number of fixed points of a random permutation of n elements. A fixed point is an element that remains in the same position after the permutation. Thus, the probability that an element is fixed is 1/n, and the probability that it is not fixed is (n-1)/n.

Using the linearity of the expected value, we can calculate the expected value of X as:

E(X) = E(X1 + X2 + ... + Xn) = E(X1) + E(X2) + ... + E(Xn)

where Xi is the indicator random variable that is equal to 1 if the i-th element is fixed and 0 otherwise. Since the probability of an element being fixed is 1/n, we have E(Xi) = 1/n. Therefore,

E(X) = n * (1/n) = 1

To find the variance of X, we need to compute E(X^2) - E(X)^2. We can use the fact that X^2 = X1 + X2 + ... + Xn, where Xi is the indicator random variable that is equal to 1 if the i-th and j-th elements are both fixed and 0 otherwise. Then,

E(X^2) = E(X1 + X2 + ... + Xn)^2 = E(X1^2 + X2^2 + ... + Xn^2) + 2 E(X1X2 + X1X3 + ... + X(n-1)n)

Since there is only one way to fix two elements out of n, we have E(XiXj) = 1/(n(n-1)). Therefore,

E(X^2) = n * (1/n) + n(n-1) * (1/(n(n-1))) = 1 + 1/n

Finally, the variance of X is

Var(X) = E(X^2) - E(X)^2 = 1 + 1/n - 1^2 = 1/n

Therefore, the variance of the number of fixed elements of a randomly selected permutation of n elements is 1/n.

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Given:

\(\Delta ABE\cong \Delta MNP\)

To find:

The congruent angles and sides, then find the another valid congruency statement.

Solution:

We have,

\(\Delta ABE\cong \Delta MNP\)

We know that, corresponding parts of congruent triangles are congruent (CPCTC).

Using CPCTC, we get

Angles:

\(\angle A\cong \angle M\)

\(\angle B\cong \angle N\)

\(\angle E\cong \angle P\)

Sides:

\(AB\cong MN\)

\(BE\cong NP\)

\(AE\cong MP\)

The another congruent statement is \(\Delta BEA\cong \Delta NPM\).

Therefore, the required table is

Angles                                              Sides

\(\angle A\cong \angle M\)                                        \(AB\cong MN\)

\(\angle B\cong \angle N\)                                        \(BE\cong NP\)

\(\angle E\cong \angle P\)                                        \(AE\cong MP\)

The another congruent statement is \(\Delta BEA\cong \Delta NPM\).

Answer:

Is located in quadrant III

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

The following are the variables that could be of interest to generate environmental data: Pollution levels: Pollution levels are a measure of the degree to which the air is contaminated.

Contaminants in the air, such as particulate matter and toxic gases, can be hazardous to human health and the environment, and monitoring them can provide valuable data on air quality.Air quality: Air quality refers to the level of pollution in the air. This could include measurements of various pollutants, such as nitrogen dioxide, sulfur dioxide, and particulate matter. This data can be gathered by a variety of sensors, including gas analyzers, particle counters, and spectrometers.Ozone concentration: Ozone concentration refers to the amount of ozone in the air. Ozone is a powerful oxidant that can have both beneficial and harmful effects on human health and the environment. Storm intensity: Storm intensity refers to the severity of a storm.

This could include measurements of wind speed, rainfall, and lightning activity. Data on storm intensity can be gathered using weather stations, Doppler radar, and lightning detection systems.Vegetation density: Vegetation density is a measure of how much plant life is present in a given area. This data can be used to monitor changes in ecosystems over time and to assess the impact of human activities on the environment. Vegetation density can be measured using satellite imagery, ground-based surveys, and remote sensing technologies.Earthquake intensity: Earthquake intensity refers to the strength of an earthquake. This could include measurements of ground motion, ground acceleration, and ground displacement. Data on earthquake intensity can be gathered using seismometers and other ground-based sensors. Wildlife diversity can be measured using a variety of techniques, including surveys, camera traps, and acoustic monitoring.

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Answer:

1/14

Step-by-step explanation:

Answer: 4 1/8

Step-by-step explanation:

1 6/8 + 2 3/8 = 33/8 = 4 1/8

Answer:

4 1/8

Step-by-step explanation:

first turn the fractions into improper fractions...

so 1 6/8 = 14/8

and 2 3/8 = 19/8

then add together.. 14/8+19/8=33/8

change into a mixed number = 4 1/8

or

do 1+2=3

and 6/8+3/8=9/8=1 1/8

and add the two values together... 3+ 1 1/8 = 4 1/8

Answer:

<BAD = 60 , <ACB = 30, <ABC = 90

Step-by-step explanation:

if AD // BC then the diagonal must have the same angle, which <DAC = <ACB = 30

<ABC seems has 90 degree. the total of triangle's angle is 180. so <BAD is 60

To find the extraneous solutions of an equation, you need to solve a related equation that is obtained by reversing the operation that was applied to the original equation.

An equation is a statement that asserts the equality of two expressions. In an equation, the expressions on both sides of the equals sign (=) represent the same value, so they must be equivalent.

Extraneous solutions are solutions of an equation that are obtained when a mathematical operation (such as taking the square root or the logarithm) is applied to both sides of the equation and then the equation is solved for the variable, but the operation introduces new solutions that are not actually solutions of the original equation.

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The value of c is 1/2. The function E(X) is 2 - e^(-1), and V(X) is 1 - e^(-1). The moment generating function is, 1/(2(1-t)²). The moment generating function of U is 1/(2(1+(t/2))²).

To find the value of c, we need to integrate the function over its domain and set it equal to 1 (since f(x) is a probability density function).

\(\int_0^1 cxe^{-x} dx\) = 1

Solving this integral gives:

c = \(\dfrac{1}{\int_0^1 xe^{-x} dx}\)  = 1/2

Therefore, c = 1/2.

To find E(X), we use the formula:

E(X) = \(\int_0^1 xf(x) dx\)

Substituting in the value of f(x) from above:

E(X) = \(\int_0^1 x \dfrac{1}{2}x e^{-x} dx\)

This can be simplified to:

E(X) = \(\dfrac{1}{2} \int_0^1 x^2 e^{-x}dx\)

Using integration by parts:

E(X) = 1/2 [x² (-e^(-x)) - \(\int -e^{-x} 2x dx\)] from 0 to 10

E(X) = 1/2 [(0 - 0) - (-2 + 4e^(-1))]

E(X) = 2 - e^(-1)

To find V(X), we use the formula:

V(X) = E(X²) - [E(X)]²

Using the same approach as above, we find:

E(X²) = \(\dfrac{1}{2} \int_0^1 x^3 e^{-x} dx\) = 6 - 6e^(-1)

Therefore,

V(X) = (6 - 6e^(-1)) - (2 - e^(-1))²

V(X) = 1 - e^(-1)

The moment generating function of X is given by:

M(t) = E(e^(tX))

= \(\int_0^1 e^{tx} \dfrac{1}{2} x e^{-x} dx\)

= \(\dfrac{1}{2} \int_0^1 e^{(-1-t)tx} x dx\)

= (1/2) [x(-1/(1-t)) e^(-(1-t)x) - \(\int \dfrac{-1}{(1-t)} e^{-(1-t)x} dx\)]

= (1/2) [(0 - 0) - (-1/(1-t))²] = 1/(2(1-t)²)

If U = -X/2, then the moment generating function of U is given by:

M_U(t) = E(e^(tU)) = E(e^(-tX/2))

= \(\int_0^1 e^{-tx/2} \dfrac{1}{2} x e^{-x} dx\)

= \(\dfrac{1}{2} \int_0^1 x e^{-(2+t)x/2} dx\)

= (1/2) [x(-2/(2+t)) e^(-(2+t)x/2) - \(\int \dfrac{-2}{(2+t)} e^{-(2+t)x/2} dx\)]

= (1/2) [(0 - 0) - (-2/(2+t))²] = 1/(2(1+(t/2))²)

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In a normal distribution, approximately 89% of the observations are expected to be contained within 1.25 standard deviations of the mean.

This can be determined using the empirical rule, also known as the 68-95-99.7 rule, which states that:

- Approximately 68% of the observations fall within 1 standard deviation of the mean.

- Approximately 95% of the observations fall within 2 standard deviations of the mean.

- Approximately 99.7% of the observations fall within 3 standard deviations of the mean.

Since 1.25 standard deviations is between 1 and 2 standard deviations, we can estimate that about 89% of the observations will fall within this range.

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Put all the point and equation on graph we get parabola.

What is a parabola in simple terms?

according to question we follow the steps and get parabola.

f(x) = x² - 5x + 6

eq   x= 1

B = ( 2.5 , - 2.5)

A = (1 ,2 )

C = ( 2,0)

D = ( 3,0)

E = ( 0,6)

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The skip interval should be 40 if the sampling frame has 2000 names and the desired sample size is 50.

Systematic sampling is a type of sampling which uses the probability method where researchers select members of the group or population at a regular interval.

To determine the skip interval, it is necessary to first determine the sample size. Then the skip interval can be determined by dividing the total population by the target/desired sample size. Therefore;

skip interval = population / target sample size

Substituting the given values;

skip interval = 2000 / 50

skip interval = 40

Hence, the skip interval is calculated to be 40 if the frame has 2000 names and the desired sample size is 50.

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The value of the integral is 2pi.

To interpret the given integral in terms of areas, we need to recognize that the integrand, \(\sqrt(4-x^2),\) represents the upper half of a circle with radius 2 centered at the origin.

First, we can sketch the graph of\(y = \sqrt(4-x^2)\)over the interval [-2, 2]:

      |         /\            |

   2 |       /    \          |

      |      /        \       |

     |     /            \     |

     |_/_____  __\_|

         -2         2

The integral can be evaluated as follows:

\(int_(-2)^2 \sqrt(4-x^2) dx\) = area of upper half of circle with radius 2 and center at (0, 0)

                         = (1/2) * pi *\(r^2\), where r = 2

                         = (1/2) * pi * 4

                         = 2pi

Therefore, the value of the integral is 2pi.

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Answer:

A lower price and quantity would result.

Answer:

let me see hold up

Step-by-step explanation:

The company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.

What is meant by days?

Days refer to the 24-hour period of time that is based on the rotation of the Earth on its axis. It is a unit of time commonly used in calendars, schedules, and daily life.

Explain whole numbers

Whole numbers are positive integers including zero. They are used to count and represent quantities of discrete objects or entities in mathematics.

According to the given information

The sum of the first n terms of a geometric sequence with first term a and common ratio r is given by the formula S_n = a(1 - rⁿ)/(1 - r).

In this case, we want to find the sum of the first 18 terms of the sequence, so n = 18. Substituting the values for a, r, and n into the formula for S_n, we get:

S_18 = 120(1 - 0.9¹⁸)/(1 - 0.9)

    ≈ 1200

So the company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.

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Answer:

A reflection across line y = 4

Step-by-step explanation:

If you can imagine folding the figure using the red or green line, it will not fold over to the opposite corner.  Draw a rectangle and fold it diagonally and you will see that it will not work.  If you rotate 90 degrees at (4,4) it will make the short sides horizontal and the long sides vertical.

If you reflect it over the line y= 4. Points A and C will switch places and Point B and D will switch places, but the image (new shape) will be identical to the original shape.

Answer:

C = 7p

Step-by-step explanation:

Each pound costs 7 dollars, and he buys P, an unknown amount. This equals C.

Answer:

2

Step-by-step explanation:

Simplify the following:

(1 + 1/9)/(5/9)

Multiply the numerator of (1 + 1/9)/(5/9) by the reciprocal of the denominator. (1 + 1/9)/(5/9) = ((1 + 1/9)×9)/5:

((1 + 1/9)×9)/5

Put 1 + 1/9 over the common denominator 9. 1 + 1/9 = 9/9 + 1/9:

(9/9 + 1/9 9)/5

9/9 + 1/9 = (9 + 1)/9:

((9 + 1)/9×9)/5

9 + 1 = 10:

(10/9×9)/5

10/9×9 = (10×9)/9:

((10×9)/9)/5

((10×9)/9)/5 = (10×9)/(9×5):

(10×9)/(9×5)

(10×9)/(9×5) = 9/9×10/5 = 10/5:

10/5

The gcd of 10 and 5 is 5, so 10/5 = (5×2)/(5×1) = 5/5×2 = 2:

Answer:  2

Given the rate of change, the differential equation is dy/dx = k × y²

The given statement is "The rate of change of y with respect to x is proportional to y²".

To write a differential equation for the given statement, we use the formula,

"rate of change = constant of proportionality × y²".

The differential equation is: dy/dx = k × y²

where k is the constant of proportionality.

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Answer:

O.4x 0.25

Step-by-step explanation:

It just is as a decimal

The choice function c satisfies finite nonemptiness and choice coherence, but there does not exist a utility function U , which does not contradict the Fundamental Theorem of Mindless Economics.

A. To show that the choice function c satisfies finite nonemptiness, we need to demonstrate that for each choice set Bn, c(Bn) is non-empty.

To show that the choice function c satisfies choice coherence, we need to demonstrate that for any two choice sets Bn and Bm, if Bn ⊆ Bm, then c(Bn) ⊆ c(Bm).

From the given information, we have B1 = {x, y}, B2 = {y, z}, and B3 = {x, z}. Let's consider the possible pairs of choice sets:

B1 and B2: B1 ⊆ B2 since {x, y} is a subset of {y, z}. In this case, c(B1) = {x} and c(B2) = {y}. We can observe that {x} ⊆ {y}, which satisfies the condition of choice coherence.

B1 and B3: B1 ⊆ B3 since {x, y} is a subset of {x, z}. In this case, c(B1) = {x} and c(B3) = {z}. We can observe that {x} ⊆ {z}, which satisfies the condition of choice coherence.

B2 and B3: B2 ⊈ B3 since {y, z} is not a subset of {x, z}. Therefore, the condition of choice coherence does not apply in this case.

Overall, the choice function c satisfies finite nonemptiness and choice coherence, except for the pair of choice sets B2 and B3.

B. To show that there does not exist a utility function U: {x, y, z} → R that can produce these choices via the usual formula c(Bn) = {x ∈ Bn : U(x) ≥ U(y) for all y ∈ Bn}, we need to demonstrate that such a utility function does not exist.

Let's consider the pairs of choice sets B1 and B2:

For B1 = {x, y}, we have c(B1) = {x}. To satisfy the usual formula, we would need a utility function U(x) ≥ U(y). However, since there is no order or preference provided for x, y, and z, we cannot assign numerical values to them in a way that U(x) ≥ U(y) holds.

Similarly, for B2 = {y, z}, we have c(B2) = {y}. Again, we cannot assign numerical values to y and z that satisfy U(y) ≥ U(z) since there is no preference or order specified.

Therefore, there does not exist a utility function U: {x, y, z} → R that can produce these choices via the usual formula.

C. The answers to parts (a) and (b) do not contradict the Fundamental Theorem of Mindless Economics because the choices made by the individual in this scenario do not adhere to the assumptions of utility maximization based on preferences.

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The complete question is:

Suppose X = {X, Y, Z}, And B = {B1 , B2 , B3} Where B1 = {X, Y}, B2 = {Y, Z} And B3 = {X, Z}. We Have The Following Information About An Individual’s Choice Function: C (B1) = {X}, C (B2) = {Y}, And C (B3) = {Z}, A. Show That C Satisfies Finite Nonemptiness And Choice Coherence. B. Show That There Does Not Exist A Utility Function U : {X, Y, Z} → R, That Can.

Suppose X = {x, y, z}, and B = {B1 , B2 , B3} where B1 = {x, y}, B2 = {y, z} and B3 = {x, z}. We have the following information about an individual’s choice function:c (B1) = {x}, c (B2) = {y}, and c (B3) = {z},A. Show that c satisfies finite nonemptiness and choice coherence.

B. Show that there does not exist a utility function U : {x, y, z} → R, that can produce these choices via the usual formula (discussed in class): c (Bn) = {x ∈ Bn : U (x) ≥ U (y) for all y ∈ Bn} , for n = 1, 2, 3.

C.Explain why your answers to parts (a) and (b) do not contradict the Fundamental Theorem of Mindless Economics.