Please write out the steps in explanation on how to solve these

1836-1347 and 4865-3956

Answer:

Follows are the solution to this question:

Step-by-step explanation:

In point a:

Although both variables are non - stationary, for both the respective pmf, multiply all pmf principles. For example:

\(\to P(x=0,y=0)=P(x=0)\times P(y=0)\)

                                     \(X\)                                                    

                   \(0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ pmf Y\)

\(0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.01 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.02 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.03\ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.02\ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.02\ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1\)

\(Y \ \ \ \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ \ \ 0.03 \ \ \ \ \ \ \ \ \ \ \ 0.06 \ \ \ \ \ \ \ \ \ \ \ 0.09 \ \ \ \ \ \ \ \ \ \ \ 0.06 \ \ \ \ \ \ \ \ \ \ \ 0.06 \ \ \ \ \ \ \ \ \ \ \ 0.3\)

              \(2 \ \ \ \ \ \ \ \ \ 0.04\ \ \ \ \ \ \ \ \ 0.08\ \ \ \ \ \ \ \ \ 0.12 0.08\ \ \ \ \ \ \ \ \ 0.08\ \ \ \ \ \ \ \ \ 0.4\\\\ 3\ \ \ \ \ \ \ \ \ 0.02\ \ \ \ \ \ \ \ \ 0.04\ \ \ \ \ \ \ \ \ 0.06\ \ \ \ \ \ \ \ \ 0.04\ \ \ \ \ \ \ \ \ 0.04\ \ \ \ \ \ \ \ \ 0.2\\\\pmf X \ \ \ \ \ \ \ \ \ 0.1\ \ \ \ \ \ \ \ \ 0.2\ \ \ \ \ \ \ \ \ 0.3\ \ \ \ \ \ \ \ \ 0.2\ \ \ \ \ \ \ \ \ 0.2\)`

In point b:

\(\to P(x<=1,y<=1)=0.01+0.02+0.03+0.06=0.12\\\\\to P(x<=1)=0.1+0.2=0.3 \\\\\to P(y<=1)=0.1+0.3=0.4\\\\\to P(x<=1 \ and\ y<=1)=P(x<=1) \times P(y<=1)=0.3 \times 0.4=0.12 \\\\\)

In point c:\(\to P(X+Y<=1)=P(X=0,Y=1)+(X=1,Y=0)+P(X=0,Y=0)=0.02+0.03+0.01=0.06\)

In point d:

\(\to P(X=0,Y=1)+P(X=0,Y=2)+P(X=0,Y=3)+P(X=0,Y=0)+P(X=1,Y=0)+P(X=2,Y=0)+P(X=3,Y=0)+P(X=4,Y=0) \\\\ \to 0.03+0.04+0.02+0.01+0.02+0.03+0.02+0.02=0.19\)

Answer:

-5/3

Step-by-step explanation:

trust me bro

Answer:

Use desmos

Step-by-step explanation:

Basically it is a graphing calculator put your points

Answer:

see below

Step-by-step explanation:

L = 2W-6

given: (L+3)*(W+3) = 270

so (2W-6+6)*(W+6) = 270

so 2W*(W+6) = 270

open up the brackets

2w²+12W = 270

so solve quadratic equations of 2w²+12W - 270 =0

w = 9 or -15

so dimensions of the unframed photograph = width 9, length 12

Kevin's kick can be considered the best among the four.

To determine the most impressive kick, we can compare the distances and heights achieved by each player.

Andre's kick reached a maximum height of 17 yards and landed 48 yards away from the goal.

Juana's kick followed the path y = -x + 14 - 24, where y represents the height of the ball in yards and x represents the horizontal distance from the goal line. From the graph, we can estimate that her kick landed about 38 yards from the goal and reached a maximum height of 14 yards.

Kevin's kick is shown in the graph, indicating that it landed approximately 19 yards from the goal and had a peak height of 20 yards.

Emiko's kick reached a maximum height of 18 yards and landed approximately 20 yards from the goal.

Considering these measurements, Kevin's kick stands out. It traveled the farthest, landing closest to the goal line, and it achieved the highest height, reaching 20 yards. Consequently, Kevin's kick can be considered the best among the four.

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Answer:

2·2·2·2 = 16

Step-by-step explanation:

everytime a number is raised by another, that means you are going to multiply the base number  times itself as many times as the exponents tells you. this is a little but tricky to explain, so let me give you some examples:

2² → in this case the base number is 2 and the exponent is 2 as well, so you will multiply 2 times itself, 2 times:

2² = 2 · 2 = 4

2³ → in this case the base number is 2 and the exponent is 3, so you will multiply 2 times itself, 3 times:

2³ = 2 · 2 · 2 = 8

In the question asked, 2 is being raised by 4, so you will multiply 2 times itself, 4 times:

2^4 = 2·2·2·2 = 16

the same format will be used regardless of the base number and the exponent

i hope this helps! :)

1/4π radians is approximately equal to 45 degrees.

To convert a value from radians to degrees, multiply the value by 180/π. For example, to convert π/4 radians to degrees, multiply π/4 by 180/π to get 45 degrees. This conversion is useful for converting angles between the two units of measurement.

Degrees = Radians × 180/π.

Therefore, to convert 1/4π radians to degrees, we have:

Degrees = (1/4π) × (180/π) ≈ 45°

Hence, 1/4π radians is approximately equal to 45 degrees.

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Step-by-step explanation:

2(3(7)-1)

= 2(21-1)

=2(20)

=40

The logarithmic function graph takes the shape of a graph with an

argument of x - 3.

The key features of the logarithmic function are;

The characteristic features of the graph are the features that represents

the graph and includes the definition of the domain and/or range of the

graph.

Key features includes;

The x-intercept

The x-intercept, is the location the graph crosses the x-axis, and where, the y = 0

Vertical asymptote;

The vertical asymptote is a vertical line to which the graph approaches

but does not reach as the y-value increases (or decreases) to ∞ (or -∞)

Therefore, the correct option is;

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The value of y is am-z/7

The expression is given as follows

3y +z= am-4y

The first step is to collect the like terms in both sides, this way the numbers that both have y as their coefficient will be on the same side

3y + 4y= am-z

y(3+4)= am -z

7y= am-z

Divide both sides by the coefficient of y which is 7

7y/7= am-z/7

y= am-z/7

Hence the value of y in the expression is am-z/7

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Answer:

in 20 miles she would have taken her 100 minutes (or 1 hour and 40 mins)

Step-by-step explanation:

Divide 10 by 2 to see how many mins its takes to travel 1 mile which is 5 mins, then multiply 20 by 5 to get 100 minutes

2:10

1:5

2.5/1

your welcome

Answer:

4.5

Step-by-step explanation:

4 * 1.5 = 6

3* 1.5 = 4.5

The total number of pages Leah filled in her journal is 15 pages.

Number of pages filled today = 3

Total pages filled = 5 × as many pages filled today

Total pages filled = 5 × 3

= 15 pages

Therefore, the total number of pages Leah filled in her journal is 15 pages

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Answer:

-7/5

Step-by-step explanation:

Candles(c) cost = $0.75 sold = $1.75

Soap(s) cost = $1.25 soap = $3.25

Total money = 200

Done

\( \huge {\star }\: Answer\)

The above equation is applicable for each and every value of a,

So, Correct option is A. True

_____________________________

\(\mathrm{ \#TeeNForeveR}\)

To factor the expression 4x^2 - 25, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, we have 4x^2 - 25, which can be written as (2x)^2 - 5^2. Comparing it with the difference of squares formula, we can identify that a = 2x and b = 5. Therefore, the correct option is:

b. (2x)^2 - (5)^2

Using the difference of squares formula, we can factor it as follows:

(2x + 5)(2x - 5)

Hence, the correct factorization of 4x^2 - 25 is (2x + 5)(2x - 5), which is equivalent to option b.

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Answer:

Step-by-step explanation:

Finding the median is finding the number that is in the middle.

Finding the range is looking for the highest and lowest number, then

subtracting both of them to get your answer.

Hope this helps! <3

Answer:

The answers are:

13-D

14-A

Step-by-step explanation:

Median is the number that is in the middle of the set when going from smallest to largest

Range=top number minus bottom number.

2300-1000= 1300(A)

Brainliest?

Answer:

Step-by-step explanation:

p = 8

q = 9

r = 26

Answer:

∠DBC = 155°

Step-by-step explanation:

Assuming that ABC is a straight line.

Angles on a straight line sum to 180°.

⇒ (2x² + 3x - 2) + ∠DBC = 180°

⇒ ∠DBC = 180° - (2x² + 3x - 2)

The sum of the interior angles of a triangle is 180°:

⇒ (x² + 1) + (4x + 3) + ∠DBC = 180°

⇒ ∠DBC = 180° - (x² + 1) - (4x + 3)

Therefore, we can equate the equations and solve for x:

⇒ ∠DBC = ∠DBC

⇒ 180 - (2x² + 3x - 2) = 180 - (x² + 1) - (4x + 3)

⇒ 180 - 180 = (2x² + 3x - 2) - (x² + 1) - (4x + 3)

⇒ (2x² + 3x - 2) - (x² + 1) - (4x + 3) = 0

⇒ 2x² + 3x - 2 - x² - 1 - 4x - 3 = 0

⇒ x² - x - 6 = 0

⇒ x² + 2x - 3x - 6 = 0

⇒ x(x + 2) - 3(x + 2) = 0

⇒ (x + 2)(x - 3) = 0

Therefore,  x = -2, x = 3

As angles are positive, x = 3 only

Substituting found value of x into the angle expressions:

⇒ ∠BDC = x² + 1 = (3)² + 1 = 10°

⇒ ∠DCB = 4x + 3 = 4(3) + 3 = 15°

The sum of the interior angles of a triangle is 180°:

⇒ ∠DBC  + ∠BDC + ∠DCB = 180°

⇒ ∠DBC = 180° - ∠BDC - ∠DCB

⇒ ∠DBC = 180° - 10° - 15°

⇒ ∠DBC = 155°

Sum of two interiors=exterior

Take it positive

Now

Now

<DBC=180-25=155°

The length of BD is 18.5 units.

In the given right triangle ABC, with altitude BD drawn to hypotenuse AC, we are given the lengths AD = 22 and DC = 15. We need to find the length of BD.

Let's consider triangle ABD. Since BD is the altitude, it divides the right triangle ABC into two smaller right triangles: ABD and CBD.

In triangle ABD, we have the following sides:

AB = AD = 22 (given)

BD = ?

Now, let's consider triangle CBD. In this triangle, we have the following sides:

BC = DC = 15 (given)

BD = ?

Since triangles ABD and CBD share the same base BD, and their heights are the same (BD), we can say that the areas of these triangles are equal.

The area of triangle ABD can be calculated as:

Area(ABD) = (1/2) * AB * BD

Similarly, the area of triangle CBD can be calculated as:

Area(CBD) = (1/2) * BC * BD

Since the areas of ABD and CBD are equal, we can equate their expressions:

(1/2) * AB * BD = (1/2) * BC * BD

We can cancel out the common factor (1/2) and solve for BD:

AB * BD = BC * BD

Dividing both sides of the equation by BD (assuming BD ≠ 0), we get:

AB = BC

In triangle ABC, the lengths AB and BC are equal, which implies that triangle ABC is an isosceles right triangle. In an isosceles right triangle, the leg's length are congruent, so AB = BC = AD = DC.

BD is equal to half of the hypotenuse AC:

BD = (1/2) * AC

Substituting the given values, we have:

BD = (1/2) * (AD + DC) = (1/2) * (22 + 15) = (1/2) * 37 = 18.5

Therefore, the length of BD is 18.5 units.

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Answer:

see below

Step-by-step explanation:

519 sold

studnets = x

non students = y

so x+y =519, so x = 519-y

3x+5y =1909

so 3(519-y) +5y = 1557 +2y =1909

2y = 352

y=176 non students

x = 519-176 = 343 students

Answer:

10

Step-by-step explanation:

Change the fraction to a decimal:

2 1/2 = 2 + 1/2 = 2 + 0.5 = 2.5

Multiply:

4 x 2.5 = 10

10 is your answer.

~

Answer:

10 percent

Step-by-step explanation:

- Before 1997, people with a minimum FBGL of 140mg/dl were diagnosed as diabetic

- After 1997, people with a minimum FBGL of 126mg/dl were diagnosed as diabetic

- What is the proportion of people who were not considered diabetic before 1997 but are now considered diabetic (after 1997)?

140 - 126 = 14

In percentage, this proportion is = 14/140 × 100

= 10%

Hence, 10% of the people who were not considered diabetic before 1997 are now or will now be considered diabetic.

x = 6

Step-by-step explanation:

\(\sf3(x - 2) = 12 \\ \sf3x - 6 = 12 \\\sf3x = 12 + 6 \\ \sf3x = 18 \\ \sf \: x = \frac{18}{3} \\ \sf \: x = 6\)

Answer: (negative solution): x=-2, (positive solution): x=6

In order to calculate the expected value of x, we can divide the total number of billboards by the total number of cities:

So the expected value of x is 93.15.

Answer:

The area is changing at 15.75 square feet per second.

Step-by-step explanation:

The triangle between the wall, the ground, and the ladder has the following dimensions:

H: is the length of the ladder (hypotenuse) = 10 ft

B: is the distance between the wall and the ladder (base) = 6 ft

L: the length of the wall (height of the triangle) =?

dB/dt = is the variation of the base of the triangle = 9 ft/s        

First, we need to find the other side of the triangle:  

\(H^{2} = B^{2} + L^{2}\)

\( L = \sqrt{H^{2} - B^{2}} = \sqrt{(10)^{2} - B^{2}} = \sqrt{100 - B^{2}} \)

Now, the area (A) of the triangle is:            

\( A = \frac{BL}{2} \)  

Hence, the rate of change of the area is given by:

\( \frac{dA}{dt} = \frac{1}{2}[L*\frac{dB}{dt} + B\frac{dL}{dt}] \)      

\( \frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - B^{2}}*\frac{dB}{dt} + B\frac{d(\sqrt{100 - B^{2}})}{dt}] \)        

\(\frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - B^{2}}*\frac{dB}{dt} - \frac{B^{2}}{(\sqrt{100 - B^{2}})}*\frac{dB}{dt}]\)  

\(\frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - 6^{2}}*9 - \frac{6^{2}}{\sqrt{100 - 6^{2}}}*9]\)      

\(\frac{dA}{dt} = 15.75 ft^{2}/s\)  

Therefore, the area is changing at 15.75 square feet per second.

I hope it helps you!                                    

The rate of change (ROC) of the area with respect to (w.r.t.) time can be

found from the ROC of the area w.r.t. x and the ROC of x w.r.t. time.

Reasons:

The length pf the ladder = 10 feet

Rate at which the ladder is pulled from the wall, \(\displaystyle \frac{dx}{dt}\) = 9 feet per second

Required:

The rate at which the area of the triangle formed by the ladder, the wall

and the ground, is changing at the instant the ladder is 6 feet from the wall.

Solution:

The area the triangle, A = 0.5·x·y

Where;

x = The distance of the ladder from the wall

y = The height of the ladder on the wall

By Pythagoras's theorem, we have;

10² = x² + y²

Which gives;

y = √(10² - x²)

Therefore;

The area the triangle, A = 0.5 × x × √(10² - x²)

By chain rule, we have;

\(\displaystyle \frac{dA}{dt} = \mathbf{\frac{dA}{dx} \times \frac{dx}{dt}}\)

\(\displaystyle \frac{dA}{dx} = \frac{d\left(0.5 \cdot x \cdot \sqrt{10^2 - x^2} }{dx} = \mathbf{\frac{\left(x^2 - 50\right) \cdot \sqrt{100-x^2} }{x^2-100}}\)

\(\displaystyle \frac{dA}{dx} = \frac{\left(x^2 - 50\right) \cdot \sqrt{100-x^2} }{x^2-100}\)

Therefore;

\(\displaystyle \frac{dA}{dt} = \mathbf{\frac{\left(x^2 - 50\right) \cdot \sqrt{100-x^2} }{x^2-100} \times 9}\)

When the ladder is 6 feet from the wall, we have;

x = 6

\(\displaystyle \frac{dA}{dt} = \frac{\left(6^2 - 50\right) \cdot \sqrt{100-6^2} }{6^2-100} \times 9 = \mathbf{15.75}\)

At the time the ladder is 6 feet from the wall, the area is increasing at 15.75 ft.²/sec.

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Without additional information about the model house, it is impossible to accurately describe the surface that Molly does not need to paint. It could be any surface that will not be visible when the model house is displayed, such as the underside of a roof, the back of a wall, or the bottom of a floor.

Answer:

\(\theta=79.7^{\circ}\)

Step-by-step explanation:

Given that,

v = 2i - j and w = 3i + 4j

We need to find the angle between v and w.

Magnitude of |v|, \(|v|=\sqrt{2^2+(-1)^2} =\sqrt5\)

Magnitude of |w|, \(|w|=\sqrt{3^2+4^2} =5\)

The dot product of v and w,

\(u{\cdot}w=2(3)+(-1)4\\\\=2\)

The formula for the dot product is given by :

\(u{\cdot}w=|u||w|\cos\theta\\\\\cos\theta=\dfrac{u{\cdot}w}{|u||w|}\\\\=\dfrac{2}{\sqrt5\times 5}\\\\\theta=\cos^{-1}(\dfrac{2}{\sqrt5\times 5})\\\\\theta=79.69^{\circ}\\\\=79.7^{\circ}\)

So, the angle between u and v is \(79.7^{\circ}\).

Answer:

The angle between two vectors

 \(\alpha = cos^{-1} (\frac{2}{5\sqrt{5} } )\)

  ∝ = 79.700°

Step-by-step explanation:

Explanation

Given V =  2i - j and w = 3 i + 4 j

Let '∝' be the angle between the two vectors

           \(cos \alpha = \frac{v^{-} .w^{-} }{|v||w|}\)

         \(cos \alpha = \frac{(2i-j).(3i+4j) }{\sqrt{2^{2}+1^{2} )\sqrt{3^{2} +4^{2} } } }\)

        \(cos \alpha = \frac{(2(3)-4(1) }{\sqrt{5 )\sqrt{25 } } } = \frac{2}{\sqrt{5})5 } = \frac{2}{5\sqrt{5} }\)

          \(cos\alpha = \frac{2}{5\sqrt{5} } \\\alpha = cos^{-1} (\frac{2}{5\sqrt{5} } )\)

 The angle between two vectors

        ∝ = 79.77°

The required reverse Euclidean algorithm is the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

Given that (5*x) mod 91 =32.

To solve the modular equation (5*x) mod 91 =32 using reverse Euclidean algorithm is to find the modular inverse of 5 modulo 91.

Consider  (5*x) mod 91 =32.

5x = 32(mod 91)

Apply the Euclidean algorithm to find GCD of 5 and 91 is

91 = 18 * 5 + 1.

Rewrite it in congruence form,

1 = 91 - 18 *5

On simplifying the equation,

1 = 91 (mod 5)

The modular inverse of 5 modulo 91 is 18.

Multiply equation by 18 on both sides,

90x = 576 (mod91)

To obtain the smallest positive  solution,

91:576 = 6 (mod 91)

Divide both sides by the coefficient of x:

x = 6 * 90^(-1).

Apply the Euclidean algorithm,

91 = 1*90 + 1.

Simplify the equation,

1 + 1 mod (90)

The modular inverse of 90 modulo 91 is 1.

Substitute the modular inverse in the given question gives,

x = 6*1(mod 91)

x= 6 (mod91)

Therefore, the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

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