Let X be a RV (note that we don’t assume anything about what type of a RV it is) and let H(x) = P(X < x). Rigorously discuss the continuity properties of H: is it continuous / left-continuous / right-continuous / not guaranteed to be any of those?

Answers:

Level 1 Q:

[tex]5x+4x=90\\9x=90\\x=10[/tex]

Level 2 Q:

[tex]48+2x=90\\2x=42\\x=21[/tex]

Level 3 Q:

[tex]25+(x-18)=90\\x=83[/tex]

The least nonnegative residue of 64!/52! modulo 13 is 4.

Wilson's theorem states that for any prime number 'p', the factorial of (p-1) is congruent to -1 modulo p. This can be written as (p-1)! ≡ -1 (mod p).

Using Wilson's theorem, we can find the least nonnegative residue modulo 89 for the integer 861.

For n = 861 and m = 89, we need to calculate (n mod m) as follows:

861 mod 89 = 861 - (89 * (861 // 89))

= 861 - (89 * 9)

= 861 - 801

= 60

Therefore, the least nonnegative residue of 861 modulo 89 is 60.

Now let's move on to the second part.

For n = 64!/52! and m = 13, we can simplify the expression using cancelation:

64!/52! = (64 * 63 * 62 * ... * 53 * 52!)/52!

Most of the terms in the numerator and denominator cancel out, leaving:

64 * 63 * 62 * ... * 53

To find the least nonnegative residue modulo 13, we can calculate the product of the remaining terms and take the result modulo 13.

(64 * 63 * 62 * ... * 53) mod 13 ≡ (11 * 12 * 1 * 2 * ... * 3) mod 13

≡ (11 * (-1) * 1 * 2 * ... * 3) mod 13

≡ (-11 * 1 * 2 * ... * 3) mod 13

Since (-11) ≡ 2 (mod 13), we have:

(-11 * 1 * 2 * ... * 3) mod 13 ≡ (2 * 1 * 2 * ... * 3) mod 13

Calculating the product, we find:

(2 * 1 * 2 * ... * 3) mod 13 ≡ 4 (mod 13)

Therefore, the least nonnegative residue of 64!/52! modulo 13 is 4.

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Answer:

2

Step-by-step explanation:

because if 10 is the whole line of the base at the bottom of the trapezoid

and 8 is the whole top 10-8=2

Answer:

a) x-intercepts at -6 and 2

b) y-intercept at -12

c) minimum at (-2, -16)

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

We can do this problem by doing the absolute value of the difference between 2 and -2.

2-(-2)=4. Absolute value of 4 is 4.

Hope this helped.

~cloud

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are 12 marbles in total with three of them being striped. The chance of pulling out a striped marble is 3/12 which can be reduced to 1/4. And 1/4 of 600 is 150.

Answer:

The answer would have to be shown in your working out, so look down below for an explanation.

Step-by-step explanation:

You would make each equation with the same letter equal to each other

5x- 10= 7x-20

3y= 5y-16

Then you would solve the equations

5x-10 = 7x-20

+20        +20

5x +10= 7x

-5x        -5x

10= 2x

x= 5

-

3y = 5y-16

+16      +16

3y+16=5y

-3y       -3y

16 = 2y

y = 8

And there's  how you would prove that x=5 and y=8

The calculated probability will indicate the likelihood of a break-in given that the alarm has gone off. If the probability is high, it suggests a higher chance of an actual break-in. If the probability is low, it indicates that the alarm might have been triggered by some other reason.

To calculate the probability that someone is breaking into your neighbour's house if the alarm goes off tomorrow night, we can use Bayes' Theorem. Let's denote the events as follows:

A: Someone is breaking into the house

B: The alarm goes off

We need to get P(A|B), the probability of A and B.

Using Bayes' Theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

P(B|A) = 0.98 (the likelihood of the alarm sounding if someone breaks in)

P(A) = 3/10,000 (the chances of being broken into in your neighbourhood)

P(B) = ?

To obtain P(B), we can use the law of total probability:

P(B) = P(B|A) * P(A) + P(B|A') * P(A')

Since the alarm has gone off on 8 different nights for no apparent reason, we can assume P(B|A') is high, let's say 0.99.

P(A') = 1 - P(A) = 1 - 3/10,000 = 9,997/10,000

Now we can calculate P(B):

P(B) = (0.98 * 3/10,000) + (0.99 * 9,997/10,000)

Finally, we can calculate P(A|B) using Bayes' Theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

After calculating the values, we can obtain the probability that someone is breaking into your neighbor's house if the alarm goes off tomorrow night.

ii) The calculated probability will indicate the likelihood of a break-in the alarm has gone off. If the probability is high, it suggests a higher chance of an actual break-in. If the probability is low, it indicates that the alarm might have been triggered by some other reason.

To improve the situation, the manufacturer would need to reduce the false alarm rate, as the alarm going off for no apparent reason undermines its effectiveness. This can be achieved by enhancing the alarm system's technology or implementing stricter criteria for triggering the alarm. By minimising false alarms, the manufacturer can increase the reliability and credibility of the alarm system, ensuring that it only alerts for genuine break-ins.

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To find the reflection of point P = (2, 6) across the y-axis, we need to change the sign of the x-coordinate while keeping the y-coordinate the same.

When reflecting a point across the y-axis, the x-coordinate becomes its opposite. Therefore, the reflected point R_y-axis (P) will have the coordinates (-2, 6).

So, R_y-axis (P) = (-2, 6).

Answer:

82 ☺️

Step-by-step explanation:

Answer:

Easy,

1) To find the area you need to multiply. Therefore 10 x 4 = 40 square centimeters.

2) 20, why? A calculator online for area of a triangle, it really helps! :) just look up triangle area in the future.

Step-by-step explanation:

Answer:

184 in²

Step-by-step explanation:

Given :

Width, w = 6 inches

Length, l = 10 inches

Height, h = 2 inches

To obtain how much wrapping paper is needed ; we take the surface area of the box

Surface area = 2(lw + lh + wh)

Surface area = 2((6*10) + (6*2) + (10*2))

Surface area = 2(60 + 12 + 20)

Surface area = 2(92)

Surface area = 184 in²

The amount of wrapping paper needed = 184 in²

Answer:

y=9

x= -2, 4

Step-by-step explanation:

Answer:

The arc length is about 12.57.

Step-by-step explanation:

Formula for arc length: 2πr( degrees/360)

For ours lets do 2π8(90/360)

Simplify the 90 and 360: 16π(1/4)

This gives you: 16π/4

Divide by 4

You get: 4π

4π ≅ 12.57

Answer:

4/5 to 80%

7/20 to 35%

9/4 to 225%

25/1000 to 2.5%

Step-by-step explanation:

Answer:

2. n(2n+5)=26.

Step-by-step explanation:

If Sam has n stamps, and Nate has 5 more than twice that amount, the equation would be: 2. n(2n+5)=26.

Answer: Decrease it’s a negative

Step-by-step explanation:

Answer:

I couldn't see the picture it is black

Step-by-step explanation:

the formula for the area of a trapezoid is:

[tex]\frac{b1+b2}{2} h[/tex]

insert 7 for b1, 13 for b2, and 10 for h

[tex]\frac{7+13}{2} 10[/tex]

100

Hope that helps

The solution is, the area of the trapezoid is: 100cm^2.

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

given that,

A trapezoid has a height of 10 centimeters. One parallel base has a length of 7 centimeters, and the other parallel base has a length of 13 centimeters.

now, we know that,

the area of the trapezoid = 1/2 ( a+b)*h

so, substituting the values, we get,

the area of the trapezoid is:

= 1/2 (7+ 13) * 10

=10 * 10

=100

Hence, The solution is, the area of the trapezoid is: 100cm^2.

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To represent this situation, we can use the following equation:x = the number of packs of stickers Isabella bought x packs of stickers, and each pack costs $3.

So the total cost of the stickers is given by the following equation:3x = total cost of stickers Since she spent a total of $18 on stickers, we can set the equation equal to 18 to get:3x = 183x/3 = 18/3x = 6Therefore, Isabella bought 6 packs of stickers to give to her friends.

To solve this problem, let's assume that Isabella bought "x" packs of stickers.

According to the given information, each pack costs $3. So, the total amount Isabella spent on stickers is $18.

We can represent this situation with the following equation:

3x = 18

Here, "3x" represents the cost of "x" packs of stickers, and it is equal to $18.

To find the number of packs Isabella bought, we can solve the equation for "x".

Dividing both sides of the equation by 3, we get:

x = 18 / 3

x = 6

Therefore, Isabella bought 6 packs of stickers.

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The given information is that Isabella bought packs of stickers, each pack costs $3. She spent a total of $18 on stickers. It is asked to find number of packs did she buy.

Therefore, the answer for this question is that Isabella bought 6 packs of stickers.

Let the number of packs that Isabella bought be p. Each pack costs $3, so she spent a total of $18 on stickers. Using these terms, we can set up the equation:3p = 18To solve for p, we divide both sides of the equation by 3:p = 6. Therefore, the answer for this question is that Isabella bought 6 packs of stickers.

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The degree of precision of a quadrature formula whose error term is h4/120 f(5)) is 4. Option a is the correct answer.

The degree of precision of a quadrature formula measures how many terms of the Taylor series can be reproduced by the formula. It is also known as the order of the formula or the number of nodes used in the quadrature.

The degree of precision of a quadrature formula that produces a zero error on all polynomials of degree less than or equal to n is n.

Therefore, the degree of precision for this quadrature formula is 4, indicating its accuracy in approximating integrals involving functions up to the fourth degree. The correct option is a.

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Complete question

The degree of precision of a quadrature formula whose error term is h4 120 f(5)) is:

Option a - 4

Option b - 2

Option c-  3

Option d- 5

The perimeter of the wood deck can be expressed, based on the length and width of the swimming pool to be 80 + 8c + 8w feet.

The perimeter of a rectangle is given by the formula 2x ( length + width ). With the walkway installed, the length becomes (28 + 2c) feet and the width becomes ( 12 + 2c ) feet.

Therefore, the length with the wood deck is ( 28 + 2c + 2w ) feet and the width with the deck is ( 12 + 2c + 2w ) feet.

The perimeter would therefore be:

P = 2 x [ ( 28 + 2c + 2w ) + (12 + 2c + 2w )]

P = 2 x [ 40 + 2c + 2w + 2c + 2w ]

P = 80c + 8 c + 8 w

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Answer:

15.98cm

Step-by-step explanation:

Given data

Volume= 602.88cm^3

Radius= 6cm

The formula for the volume of a cone is

V= 1/3 πr^2h

substitute

602.88= 1/3*3.142*6^2*h

602.88=1/3*3.142*36*h

602.88=37.704*h

h= 602.88/37.704

h= 15.98cm

Hence the height is 15.98cm

The general solution to the given system of differential equations is:

x(t) = c1 + c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)

y(t) = c1 + c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)

where c1, c2, and c3 are constants determined by initial conditions or specific constraints.

To solve the system using the elimination method, we need to eliminate one variable at a time. Let's start by eliminating x.

x' = x - y ...........(1)

y'' = -2x' + e^t ...........(2)

First, differentiate equation (1) with respect to t to get:

x'' = x' - y' ...........(3)

Now substitute the value of x' from equation (3) into equation (2):

y'' = -2(x' - y) + e^t

y'' = -2x' + 2y + e^t ...........(4)

To eliminate x', we subtract equation (4) from equation (2):

y'' - y' = e^t ...........(5)

Next, differentiate equation (5) with respect to t:

y''' - y'' = e^t ...........(6)

Now we have two equations:

y'' - y' = e^t ...........(5)

y''' - y'' = e^t ...........(6)

To solve these equations, we can solve equation (6) for y'' and substitute it into equation (5):

(y''' - e^t) - (y'' - y') = e^t

y''' - y'' + y' - e^t = e^t

y''' - y'' + y' = 2e^t ...........(7)

Equation (7) is a third-order linear homogeneous differential equation for y.

To find the general solution to equation (7), we solve its characteristic equation:

r^3 - r^2 + r = 0

Factoring out an r, we get:

r(r^2 - r + 1) = 0

This equation has one real root r = 0 and two complex roots r = (1 ± √3i)/2.

Therefore, the general solution for y is:

y(t) = c1 + c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)

Now, we can substitute the general solution for y into equation (5) to solve for x:

y'' - y' = e^t

(c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2))' - (c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)) = e^t

Differentiating and simplifying, we get:

(-c2e^t(√3/2)sin((√3t)/2) + c3e^t(√3/2)cos((√3t)/2)) - (c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)) = e^t

Simplifying further, we get:

(-c2e^t(√3/2)sin((√3t)/2) + c3e^t(√3/2)cos((√3t)/2)) - c2e^tcos((√3t)/2) - c3e^tsin((√3t)/2) = e^t

Now, equating the coefficients of e^t and the trigonometric terms, we can solve for c1, c2, and c3.

This completes the solution process using the elimination method for the given system of differential equations.

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Answer:

B

Step-by-step explanation:

Just put B

The test statistic for this problem is given as follows:

t = -0.7.

We have the standard deviation for the sample, hence the t-distribution is used to calculate the test statistic.

The equation for the test statistic is given as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 68.4, \mu = 69, s = 10.5, n = 152[/tex]

Hence the test statistic is given as follows:

[tex]t = \frac{68.4 - 69}{\frac{10.5}{\sqrt{152}}}[/tex]

t = -0.7.

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The approximately 59.90 percent of the observations differ from the mean by less than 0.56o.

The standard deviation is a measure of the amount of variation or dispersion in a set of observations.

For a normal distribution, it is straightforward to determine the proportion of values that are more than a certain number of standard deviations above or below the mean.

Here's how to determine the percentage of observations that differ from the mean by more than 2.50 or less than 0.56o in a normally distributed set of observations.

Solution:

(a)  The percentage of observations that differ from the mean by more than 2.50 is given by the formula below:P(Z > 2.50) + P(Z < -2.50) = 0.00621 + 0.00621 = 0.0124

To obtain the proportion in percentage, multiply by 100: 0.0124 * 100 = 1.24%.

Therefore, about 1.24 percent of the observations differ from the mean by more than 2.50.

(b) The proportion of observations that differ from the mean by less than 0.56o is given by:

P(-0.56/σ < Z < 0.56/σ) = P(Z < 0.84) − P(Z < -0.84) = 0.7995 - 0.2005 = 0.5990

To obtain the proportion in percentage, multiply by 100: 0.5990 * 100 = 59.90%.

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If a set of observations is normally distributed.

Therefore, about 0.62% of the observations differ from the mean by more than 2.50.

About 29.24% of the observations differ from the mean by less than 0.56.

Solution: (a) If a set of observations is normally distributed, then the percentage of observations that differ from the mean by more than 2.50 is given by:

This is calculated using the z-score formula: where x is the observation value, μ is the mean of the distribution, and σ is the standard deviation of the distribution. When we substitute the values of the given parameters, we get: Therefore, about 0.62% of the observations differ from the mean by more than 2.50.

(b) Similarly, the percentage of observations that differ from the mean by less than 0.56 is given by: This is calculated using the z-score formula: When we substitute the values of the given parameters, we get: Therefore, about 29.24% of the observations differ from the mean by less than 0.56.

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Answer:

x = 12

Step-by-step explanation:

3х+7 = 5x-17

-2x = -24

Answer:

d. 9

Step-by-step explanation:

i friken used all my attempts guessing on this and got it wrong all times so 9 is the last answer