Triangle ABC is taken to triangle A' B'C' by a dilation. Which of these scale factors for the
dilation would result in an image that was larger than the original figure?

(a) Compute E[X] and E[X|Y].

To compute E[X], we need to find the expected value of X. Since X follows a uniform distribution on (0, y) given Y = y, we can use the formula for the expected value of a continuous random variable:

E[X] = ∫[0,1] x * fX(x) dx

Since X follows a uniform distribution on (0, y), its probability density function (pdf) is fX(x) = 1/y for 0 < x < y, and 0 otherwise. Substituting this into the formula, we have:

E[X] = ∫[0,1] x * (1/y) dx

To integrate this, we need to determine the limits of integration based on the range of values for x. Since X is defined as (0, y), the limits become 0 and y:

E[X] = ∫[0,y] x * (1/y) dx

= (1/y) * ∫[0,y] x dx

= (1/y) * [x^2/2] evaluated from 0 to y

= (1/y) * (y^2/2 - 0^2/2)

= (1/y) * (y^2/2)

= y/2

Therefore, E[X] = y/2.

To compute E[X|Y], we need to find the conditional expected value of X given Y = y. Since X follows a uniform distribution on (0, y) given Y = y, the conditional expected value of X is equal to the midpoint of the interval (0, y), which is y/2.

Therefore, E[X|Y] = y/2.

(b) Compute the mgf Mx(t) of X.

The moment-generating function (mgf) of a random variable X is defined as Mx(t) = E[e^(tX)].

Since X follows a uniform distribution on (0, y), its mgf can be computed as:

Mx(t) = E[e^(tX)] = ∫[0,y] e^(tx) * (1/y) dx

To integrate this, we need to determine the limits of integration based on the range of values for x. Since X is defined as (0, y), the limits become 0 and y:

Mx(t) = (1/y) * ∫[0,y] e^(tx) dx

= (1/y) * [e^(tx)/t] evaluated from 0 to y

= (1/y) * [(e^(ty)/t) - (e^(t0)/t)]

= (1/y) * [(e^(ty)/t) - (1/t)]

= (1/y) * [(e^(ty) - 1)/t]

Therefore, the mgf Mx(t) of X is (1/y) * [(e^(ty) - 1)/t].

(c) Using differentiation, obtain the expectation of X from the mgf computed above.

To obtain the expectation of X from the mgf, we differentiate the mgf with respect to t and evaluate it at t = 0.

Differentiating the mgf Mx(t) = (1/y) * [(e^(ty) - 1)/t] with respect to t:

Mx'(t) = (1/y) * [(y * e^(ty) * t - e^(ty)) / t^2]

= (1/y) * [(y * e^(ty) * t - e^(ty)) / t^2]

To evaluate this at t = 0, we can use l'Hôpital's rule, which states that if we have an indeterminate form of the type 0/0, we can take the derivative of the numerator and denominator and then evaluate the limit.

Taking the derivative of the numerator and denominator:

Mx'(t) = (1/y) * [(y^2 * e^(ty) * t^2 - 2y * e^(ty) * t + e^(ty)) / 2t]

= (1/y) * [(y^2 * e^(ty) * t - 2y * e^(ty) + e^(ty)) / 2t]

Evaluating the limit as t approaches 0:

Mx'(0) = (1/y) * [(y^2 * e^(0) * 0 - 2y * e^(0) + e^(0)) / 2(0)]

= (1/y) * [(-2y + 1) / 0]

= undefined

The derivative of the mgf at t = 0 is undefined, which means the expectation of X cannot be obtained directly from the mgf using differentiation.

The expectation of X is E[X] = y/2, and the mgf of X is Mx(t) = (1/y) * [(e^(ty) - 1)/t]. However, differentiation of the mgf does not yield the expectation of X in this case, and an alternative method should be used to obtain the expectation.

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Answer:

108$.

Step-by-step explanation:

Answer:

lol is this a test? are u cheating!!!!???

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Your are right i think?

Answer:

472.76

Step-by-step explanation:

6:29

Multiplying decimals: place value (video)

Khan Academy · Khan Academy

Mar 23, 2021

Answer:

y = 3/2x - 3

Step-by-step explanation:

y = 3/2x + b

3 = 3/2 (4) + b

3 = 6 + b

-3 = b

y = 3/2x - 3

<3

Answer:

(a)Grade =7.5% (No warning sign is needed)

(b)Rise =90 feet

Step-by-step explanation:

\(\text{Slope = }\dfrac{Rise}{Run}\)

(a)

Rise = 63 feet

Run (Horizontal distance) = 840 feet.

\(\text{Slope = }\dfrac{63}{840}=0.075\\\\$Grade=Slope \times 100 = 0.075 \times 100 = 7.5\%\)

A warning sign should not be posted since its grade is less than 8%.

(b)

Grade = 9%

Run (Horizontal distance) = 1000 feet.

Recall that:

Grade = Slope X 100

\(9 =\dfrac{Rise}{1000} \times 100\\\\9 =\dfrac{Rise}{10}\\\\$Rise = 9 \times 10 \\$Rise=90 feet\)

The road rises 90 feet over a distance of 1000 feet.

Answer:405

Step-by-step explanation:

750/50=15

15*27=405

Amount of pretzel each person receives is 17/16 lb.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Total weight of the bag of pretzels = 34 ounce

Elisa shares this among her two sisters equally.

Share of pretzels each sister gets = 34 / 2 = 17 ounces

We need this amount in pounds.

We know that,

16 ounce = 1 lb.

17 ounces = 17/16 lb.

Hence the amount of pretzels each get is  17/16 lb.

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Answer:

x = 3, y = 30.4

Step-by-step explanation:

From the given diagram;

8x - 3 = 6x+3 (alternate exterior angle are equal)

Collect like terms

8x - 6x = 3 + 3

2x = 6

x = 6/2

x = 3

Also;

8x - 31 + 5y + 35 = 180 (sum of angle on a straight line is 180)

8(3) - 31 + 5y + 35 = 180

5y + 24 - 31 + 35  = 180

5y + 28 = 180

5Y = 180 - 28

5Y = 152

y = 152/5

y = 30.4

Hence x = 3, y = 30.4

The given piecewise function f(x) is evaluated at the specified value x ≤ -3.

To evaluate the piecewise function f(x) at x ≤ -3, we need to consider the given conditions.

If x ≤ -3, then we substitute this value into the corresponding expression of the function, which is 2x - 5 - x^2 - 2x - 14.

Simplifying the expression, we have -x^2 - 2x - 19.

Therefore, when x ≤ -3, the value of f(x) is -x^2 - 2x - 19.

It's important to note that the function f(x) is defined differently for different intervals or conditions. In this case, when x is less than or equal to -3, the function takes the form of -x^2 - 2x - 19. For other values of x, a different expression or condition would be used to evaluate f(x).

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The contact force acting on the 0.28 kg block from the 0.62 kg block is 2.37 N.What is contact force?Contact force is the force exerted when two or more objects are in contact with each other.

Given,Masses of the boxes are m1=3.61 kg, m2=0.62 kg and m3=0.28 kg. A push force of F=8.46 N is applied on m1.Therefore, force acting on m1 is F= 8.46 N.To find the contact force acting on the 0.28 kg block from the 0.62 kg block,First, we need to calculate the net force acting on the 0.62 kg block. This is given by: F1 + F2 = m2a Where,F1 is the force acting on the block due to m1,F2 is the force acting on the block due to m3a is the acceleration of the blocks Let the force acting on the 0.62 kg block due to m3 be F23.

Hence,F1 = F23

a = acceleration of the blocks = 8.46/ (m1 + m2 + m3)

= 8.46/ (3.61 + 0.62 + 0.28)

= 1.98 m/s²

Now, we can use the equation F1 + F2 = m2a to solve for F2.

F2 = m2a - F1F2

= 0.62 x 1.98 - F23F2

= 1.2276 - F23

Now, for the 0.28 kg block, the net force acting on it is given by: F3 + F23 = m3a Where,F3 is the force acting on the block due to m1F23 is the force acting on the block due to m2a is the acceleration of the blocks We know that,F1 = F23 Hence, the net force equation can be written as: F3 + F1 = m3aF3 + F23

= 0.28 x 1.98F3 + F23 = 0.5544

Now, substituting F23 = F1 = 8.46 N,

we get: F3 + 8.46 = 0.5544

F3 = -8.46 + 0.5544 = -7.9056 N

We get a negative force here because the force is acting in the opposite direction to the applied force. Therefore, the contact force acting on the 0.28 kg block from the 0.62 kg block is:|F23| = |F1| = 8.46 N|F3| = 7.9056 NNet force = F3 + F23 = 8.46 - 7.9056 = 0.5544 N The magnitude of the contact force is:|F3| = 2.37 N (approx)Therefore, the contact force acting on the 0.28 kg block from the 0.62 kg block is 2.37 N.

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Integers between, but not including, 20 and 30 have a prime factorization with exactly 3 factors is 0 integers.

To find the integers between 20 and 30 with a prime factorization with exactly 3 factors that are not 1, we can start by listing out all the prime numbers up to 30.

The prime numbers up to 30 are 2, 3, 5, 7, 11, 13, 17, 19, and 23.

Next, we can list out all the integers that have exactly 3 factors in their prime factorization that are not 1. This can be done by finding all the products of exactly 3 primes. For example, the product of

2 * 3 * 5 = 30 has 3 prime factors.

However, 30 is not between 20 and 30, so we need to find another example.

The product of 2 * 3 * 7 = 42 is not between 20 and 30 either, so we need to keep finding examples until we find one that falls between 20 and 30.

The product of 2 * 5 * 7 = 70 is too large, but the product of 2 * 3 * 5 = 30 is between 20 and 30, so we have found one example.

We can continue this process to find all the examples and count how many there are. In this case, there is only 1 example, so the answer is 1.

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Answer:

Devon's sister is NOT correct

Units price=0.50

Step-by-step explanation:

Based on the information given Devon's sister is NOT correct

For Devon's sister to find the correct price what she has to do is to find the unit price by dividing the total cost of the amount of $2.99 by the number of items which is 6.

Using this formula

Units price=Total cost/ Numbers of items

Where,

Total cost=$2.99

Numbers of items=6

Let plug in the formula

Units price=$2.99/6

Units price=0.498*100

Units price=49.8

Units price=0.50 Approximately

Therefore Devon's sister is NOT correct and the correct price is 0.50

On solving the provided question, we can say that the equation is  x = t - yz => y = t-x / z

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation is

x = t - yz

x = Amount down

y = Money each month

z = Number of months

t = Total price

x-t = yz

y = t-x / z

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The correct question is -

Jeremy wants to buy a new computer. The saleswoman says that he can make a down payment and then pay for the computer in installments.

Here's a formula that describes this scenario:

x=t-yz

x = Amount down

y = Money each month

z = Number of months

t = Total price

Rewrite the formula to solve for the amount of money Jeremy must pay each month.

Using Distributive Property, the product of 6x13 is 78.

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

The steps of distributive property are -

                                                 6 × 13

                                              6 × (10 + 3)

                                          (6 × 10) + (6 × 3)

                                  ((3 + 3) × (5 +5)) + ((3 + 3) × 3)

                 (3 × 5 + 3 × 5 + 3 × 5 + 3 × 5 ) + ((3 × 3) + (3 × 3))

                                     (15 + 15 +15 + 15 ) + (9 + 9)

                                                  60 + 18

                                                    = 78

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Answer:

\(\angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

Step-by-step explanation:

\(\frac{\sin(\angle BAC)}{13}=\frac{\sin 23^{\circ}}{6} \\ \\ \sin \angle BAC=\frac{13\sin 23^{\circ}}{6} \\ \\ \angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

The Nyquist sampling rate for the signal m(t) = 3 cos(500πt) + 4 sin(1000πt) is 2000π.

To determine the Nyquist sampling rate for the signal m(t) = 3 cos(500πt) + 4 sin(1000πt), we need to find the highest frequency component in the signal.

The Nyquist sampling rate states that in order to accurately represent a signal, the sampling rate must be at least twice the highest frequency present in the signal.

In the given signal, we have two frequency components: 500π and 1000π. The highest frequency component is 1000π.

Therefore, the Nyquist sampling rate for this signal would be at least twice the value of 1000π. Let's calculate it:

Nyquist sampling rate = 2 * 1000π

Nyquist sampling rate = 2000π

So, the Nyquist sampling rate for the given signal is 2000π.

In conclusion, the Nyquist sampling rate for the signal m(t) = 3 cos(500πt) + 4 sin(1000πt) is 2000π.

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Answer:

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

The angle formed by a tangent and secant is half the difference of the intercepted arcs:

Find the measure of ∠MLJ by substituting 4 for x in the angle measure:

Answer:

300 seconds

Step-by-step explanation:

The first dog run at v₁ = 15 m/sec     the second one run at  v₂ = 12 m/sec

we know that  d = v*t  then  t  =  d/v

Then the first dog will take  300/ 12  =  25 seconds to make a turn

The second will take   300 / 15   =   20 seconds to make a turn

Then the first dog in 12 turns 12*25 will be at the start point, and so will the second one at the turn 15.

To check  first dog    12 *  25 = 300

And the second dog 15 * 20 = 300

That means that time required for the two dogs to be at the start point together is

300 seconds, in that time the first dog finished the 12 turns, and the second had ended the 15.

Another procedure to solve this problem is as follows:

between  12  m/sec and  15 m/sec   the minimum common multiple  is 300 ( 300 is the smaller number that accept 12 and 15 as factors         12*15 = 300) Then when time arrives at 300 seconds the two dogs will be again in the starting point

Answer:

The graph of the data presented is shown in the attached image to this solution.

It shows that the relationship between distance travelled in miles and the time take in hours is D = 55t

Step-by-step explanation:

The distance travelled with the corresponding time taken are presented in the table

Note: D - Distance travelled (miles)

t - Time (hours)

D | t

55 | 1

110 | 2

165 | 3

220 | 4

275 | 5

330 | 6

We are then told to plot these distance travelled on a graph with the time taken.

The distance travelled is plotted on the y-axis and the time in hours is plotted on the x-axis.

The image of the graph of this function will be attached to this answer

It is evident that the graph shows the relationship between the distance travelled and time taken to be D = 55t

Hope this Helps!!!

Graph of relationship \(D=55t\) on coordinate plane attached below.

Since, the table below shows the distance traveled as a function of time.

Time(t)                                           Distance (D)

1                                                       55

2                                                      110

3                                                      165

4                                                      220

5                                                      275

6                                                      330

In the graph, X - axis represent timer in hours and Y - axis represent that distance travelled in miles.

Slope = \(\frac{y}{x} =\frac{55}{1}=\frac{110}{2}=\frac{165}{3} =55\)

It is observed that, in each relationship slope is same .Therefore, relationship is a line passing through the origin.

Relationship is,      \(D=55t\)

Graph is attached below,

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The probability of selecting 2 red marbles and 1 blue marble is equal to the probability of selecting 1 red marble from Jar A and the other two blue marbles from Jar B and Jar C. Simplifying the expression gives the numerator and denominator of the probability, which is the quotient of the numerator and denominator of the simplified expression.

The probability of selecting 2 red marbles and 1 blue marble is equivalent to the probability of selecting 1 red marble from Jar A and the other two blue marbles from Jar B and Jar C. To simplify the expression, the numerator and denominator of the simplified expression are (r(a-r)st + abct - r(a-r)b(t+s) - a(t+s)st)/(a(b+c-t-s)). The probability for selecting exactly 2 red marbles is the quotient of the numerator and denominator of the simplified expression. The above solution explains how to determine the probability that exactly 2 of the 3 marbles you select are red.

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well, let's take a look at the tickmarks on the triangle, the tickmarks mean that AC = CB, both AC and CB stemming out of vertex C, and both twin sides will make twin angles at the "base" or namely ∡A = ∡B, that means that 34 = x - 5, let's also recall that the sum of all interior angles in a triangle is 180°, so

\(34=x-5\implies \boxed{39=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle A}{34}~~ + ~~\stackrel{\measuredangle B}{34}~~ + ~~\stackrel{\measuredangle C}{4y}~~ = ~~180\implies 68+4y=180 \\\\\\ 4y=112\implies y=\cfrac{112}{4}\implies \boxed{y=28}\)

Answer:

y = 28

Step-by-step explanation:

The dashes on line segments AC and BC indicate that the line segments are equal in length.

Therefore, as the triangle has two sides of equal length, it is an isosceles triangle.

The base angles of an isosceles triangle are equal, therefore ∠A = ∠B.

Interior angles of a triangle sum to 180°.  

Therefore:

⇒ ∠A + ∠B + ∠C = 180°

⇒ 34° + 34° + 4y° = 180°

⇒ 68° + 4y° = 180°

⇒ 4y° = 112°

⇒ y = 112° ÷ 4°

⇒ y = 28

Answer:

p/2-6

Step-by-step explanation:

Answer:

First one, true

Second one, 23/45

Third one, 11/29

Step-by-step explanation:

There's thy answer for thy self t-t

Answer:

1.)true

2.) 23/45

3.)11/29

Step-by-step explanation:

In conclusion, the function f(x) = x^(1/lnx) is always positive and approaches 0 as x approaches 0+ and approaches 1 as x approaches ∞. The equation x^(1/lnx) = 2 has no solution.

To show that the equation x^(1/lnx) = 2 has no solution, we can analyze the properties of the function f(x) = x^(1/lnx) and examine its behavior.

Let's consider the domain of the function f(x). Since we have a logarithm in the denominator, we need to ensure that x is positive and not equal to 1, so x > 0 and x ≠ 1.

Now, let's investigate the behavior of f(x) as x approaches 0 from the positive side (x → 0+). In this case, ln(x) approaches negative infinity, and the exponent 1/ln(x) approaches 0. Therefore, f(x) approaches 0 as x approaches 0+.

Next, let's examine the behavior of f(x) as x approaches positive infinity (x → ∞). In this case, ln(x) approaches infinity, and the exponent 1/ln(x) approaches 0. Therefore, f(x) approaches 1 as x approaches ∞.

Considering the behavior of the function, we see that it is always positive (since x^(1/lnx) is positive for positive x) and approaches 0 as x approaches 0+ and approaches 1 as x approaches ∞.

Now, let's consider the equation x^(1/lnx) = 2. If such an x exists as a solution, it would mean that there is a point where the function f(x) equals 2. However, based on the behavior of the function described above, we can see that f(x) can never equal 2. Therefore, the equation x^(1/lnx) = 2 has no solution.

In conclusion, the function f(x) = x^(1/lnx) is always positive and approaches 0 as x approaches 0+ and approaches 1 as x approaches ∞. The equation x^(1/lnx) = 2 has no solution.

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Answer:

\(\huge\boxed{\sf -\frac{2}{9} }\)

Step-by-step explanation:

\(\sf \frac{\frac{2}{3}-\frac{5}{6} }{\frac{3}{4} } \\\\= \frac{\frac{2(2)-5}{6} }{\frac{3}{4} } \\\\= \frac{\frac{4-5}{6} }{\frac{3}{4} } \\\\= \frac{-1}{6} / \frac{3}{4} \\\\= \frac{-1}{6} * \frac{4}{3} \\\\= -\frac{1*4}{6*3} \\\\= -\frac{1*2}{3*3} \\\\= -\frac{2}{9} \\\\\rule[225]{225}{2}\)

Hope this helped!

~AH1807

Answer:

The cost of slices of pizza = x = $2.82

The cost of garlic knots = y = $0.55

Step-by-step explanation:

David and joe went to the pizzeria.

Let

The cost of slices of pizza = x

The cost of garlic knots = y

David ordered 3 slices of pizza and 4 garlic knots and paid 10.65.

3x + 4y = 10.65....Equation 1

Joe ordered 2 slices of pizza nd 10 garlic knots and paid 9.30.

2x + 10y = 9.30.... Equation 2

Hence:

3x + 4y = 10.65....Equation 1

2x + 10y = 9.30.... Equation 2

We solve using Elimination method:

Multiply Equation 1 by 2 and Equation 2 by 3 to eliminate x

3x + 4y = 10.65....Equation 1 × 2

2x + 10y = 9.30.... Equation 2 × 3

6x + 8y = 21.30.....Equation 3

6x + 20y = 27.9...Equation 4

Subtract Equation 4 from 3

12y = 6.6

y = $0.55

We solve for x using Equation 1

3x + 4y = 10.65....Equation 1

3x + 4($0.55) = $10.65

How much is the cost of each item

3x + $2.2 = $10.65

3x = $10.65 - $2.2

3x = $8.45

x = $8.45/3

x = $2.8166666667

x = $2.82

The cost of each items

The cost of slices of pizza = x = $2.82

The cost of garlic knots = y = $0.55

Answer:

the answer would be y^6/x^2

Step-by-step explanation:

so (Y) to the sixth power over (X) to the second power