What is the probability of spinning a 1 or 2? Write your answer as a fraction AND decimal

Answer:

(x-5)(x-2)

Step-by-step explanation:

x^2-7x-10

= x^2-2x-5x+10

= x(x-2)-5(x-2)

= (x-5)(x-2)

Answer:

are they seperate equations?

Step-by-step explanation:

Step-by-step explanation:

x²+3x-10 =

(x+5)(x-2)

______

d) Tthe probability that there is a moving object given that both sensors detect motion is approximately 0.98.

(a) To find the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

A = Movement outside

B = Sensor V does not detect motion

C = Sensor L detects motion

We are given:

P(A) = 0.7 (probability of movement outside)

P(B|A) = 0.05 (probability of sensor V not detecting motion given movement outside)

P(C|A) = 0.8 (probability of sensor L detecting motion given movement outside)

We want to find P(C|A', B), where A' denotes the complement of event A.

Using Bayes' theorem:

P(C|A', B) = [P(A' | C, B) * P(C | B)] / P(A' | B)

We can calculate the values required:

P(A' | C, B) = 1 - P(A | C, B) = 1 - P(A ∩ C | B) / P(C | B) = 1 - [P(A ∩ C ∩ B) / P(C | B)]

             = 1 - [P(B | A ∩ C) * P(A ∩ C) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / [P(B | C) * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A')]]

P(B | C) = 0 (since sensor V does not detect motion when there is motion outside)

P(C | A') = 0 (since sensor L does not detect motion when there is no motion outside)

Substituting these values:

P(C | A', B) = 1 - [0 * P(A) * P(C | A) / (0 * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A'))]

             = 1 - [0 / (0 + P(B | C') * P(A') * P(C | A'))]

             = 1 - 0

             = 1

Therefore, the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion is 1.

(b) To find the probability that the home security system alerts the police given that there is a moving object, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

M = There is a moving object

We need to calculate P(D | M). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | M) = P(D, V detects motion, L detects motion | M) + P(D, V does not detect motion, L detects motion | M)

We know:

P(D, V detects motion, L detects motion | M) = P(V detects motion | M) * P(L detects motion | M) = 0.95 * 0.8 = 0.76

P(D, V does not detect motion, L detects motion | M) = P(V does not detect motion | M) * P(L detects motion | M) = (1 - 0.95) * 0.8 = 0.04

Substituting

these values:

P(D | M) = 0.76 + 0.04

        = 0.8

Therefore, the probability that the home security system alerts the police given that there is a moving object is 0.8.

(c) To find the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

NM = There is no movement

We need to calculate P(D | NM). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | NM) = P(D, V detects motion, L detects motion | NM) + P(D, V does not detect motion, L detects motion | NM)

We know:

P(D, V detects motion, L detects motion | NM) = P(V detects motion | NM) * P(L detects motion | NM) = 0.1 * 0.05 = 0.005

P(D, V does not detect motion, L detects motion | NM) = P(V does not detect motion | NM) * P(L detects motion | NM) = (1 - 0.1) * 0.05 = 0.045

Substituting these values:

P(D | NM) = 0.005 + 0.045

         = 0.05

Therefore, the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, is 0.05.

(d) To find the probability that there is a moving object given that both sensors detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

M = There is a moving object

V = Sensor V detects motion

L = Sensor L detects motion

We want to find P(M | V, L).

Using Bayes' theorem:

P(M | V, L) = [P(V, L | M) * P(M)] / [P(V, L)]

We can calculate the values required:

P(V, L | M) = P(V | M) * P(L | M) = 0.95 * 0.8 = 0.76

P(M) = 0.7 (given probability of movement)

P(V, L) = P(V, L | M) * P(M) + P(V, L | M') * P(M')

        = 0.76 * 0.7 + 0.04 * 0.3

        = 0.532 + 0.012

        = 0.544

Substituting these values:

P(M | V, L) = (0.76 * 0.7) / 0.544

           ≈ 0.98

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Answer:

32 gallons

Step-by-step explanation:

A standard showerhead in Marty's house dispenses 7 gallons of water per minute. If he showers for 8 minutes, he uses:

1 minute = 7 gallons

8 minutes = x

x = 7 × 8 minutes = 56 gallons of water

We are told that:

Marty changed this showerhead to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new showerhead. y = 3x

The equation for the energy saving shower:

y = 3x

Where x is the number of minutes spent in the shower

For 8 minutes

y = 3 × 8

y = 24 gallons

The gallons of water Marty saved each day with the change in showerheads if he uses the shower for 8 minutes each day is calculated as:

56 gallons - 24 gallons

= 32 gallons

Answer:

3/8 = 9/24 ; 1/3 = 8/24 ; 3/8 > 1/3

Step-by-step explanation:

You have to multiply 8 and 3 to obtein the same number as denominatoe (24).

Once you have the same number you can use < = >

Answer:

Step-by-step explanation:

Use the distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\) For us that will look like this:

\(d=\sqrt{(6-(-3))^2+(-2-4)^2}\) which simplifies to

\(d=\sqrt{(9)^2+(-6)^2}\) and a bit more to

\(d=\sqrt{81+36}\) so

\(d=\sqrt{117}\)

Answer:

(axh)/2 30

Step-by-step explanation:

Answer:

6 Apples

Step-by-step explanation:

There would be six apples and 2 oranges left over.

Hope this Helps!

:D

Answer:

I was kind of confused on this one but is it 15 apples?

Step-by-step explanation:

3, 6, 9, 12, 15

4, 8, 12, 16, 20

I think the answer is 15 apples.

Answer:

some advantages is that you can not pay all at once some disadvantage is that you can feel like you can. do that always then you can get late fees that can cost more the the product it self

Step-by-step explanation:

QR = ST

⅔x = 0.4

times 3

2x = 1.2

x = 1.2 /2

x = 0.6

0.6

QR = ST

⅔x = 0,4 × 3

2x = 1.2

x = 1.2 ÷ 2

x = 0.6

(i) If f is an even function, then f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx.

(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.

The Fourier transform pair for a function f(x) is defined as follows:

F(k) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx

f(x) = (1/2π) ∫[-∞,∞] F(k) \(e^{2\pi iyx}\) dk

Now let's prove the given properties:

(i) If f is an even function, then f(y) = 2∫[0,∞] f(x) cos(2πxy) dx.

To prove this, we start with the Fourier transform pair and substitute y for k in the Fourier transform of f(x):

F(y) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx

Since f(x) is even, we can rewrite the integral as follows:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx + ∫[-∞,0] f(x) \(e^{2\pi iyx}\) dx

Since f(x) is even, f(x) = f(-x), and by substituting -x for x in the second integral, we get:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx + ∫[0,∞] f(-x) \(e^{2\pi iyx}\)dx

Using the property that cos(x) = (\(e^{ ix}\) + \(e^{- ix}\))/2, we can rewrite the above expression as:

F(y) = ∫[0,∞] f(x) (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dx

Now, using the definition of the inverse Fourier transform, we can write f(y) as follows:

f(y) = (1/2π) ∫[-∞,∞] F(y) \(e^{2\pi iyx}\) dy

Substituting F(y) with the expression derived above:

f(y) = (1/2π) ∫[-∞,∞] ∫[0,∞] f(x) \(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\)/2 dx dy

Interchanging the order of integration and evaluating the integral with respect to y, we get:

f(y) = (1/2π) ∫[0,∞] f(x) ∫[-∞,∞] (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dy dx

Since ∫[-∞,∞] (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dy = 2πδ(x), where δ(x) is the Dirac delta function, we have:

f(y) = (1/2) ∫[0,∞] f(x) 2πδ(x) dx

f(y) = 2 ∫[0,∞] f(x) δ(x) dx

f(y) = 2f(0) (since the Dirac delta function evaluates to 1 at x=0)

Therefore, f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx, which proves property (i).

(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.

The proof for this property follows a similar approach as the one for even functions.

Starting with the Fourier transform pair and substituting y for k in the Fourier transform of f(x):

F(y) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx

Since f(x) is odd, we can rewrite the integral as follows:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx - ∫[-∞,0] f(x) \(e^{-2\pi iyx}\) dx

Using the property that sin(x) = (\(e^{ ix}\) - \(e^{-ix}\))/2i, we can rewrite the above expression as:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) - \(e^{2\pi iyx}\)/2i dx

Now, following the same steps as in the proof for even functions, we can show that

f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx

This completes the proof of property (ii).

In summary:

(i) If f is an even function, then f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx.

(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.

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Answer:

\(0 = -8t + 96\\\\\Rightarrow\ 8t=96\\\\\Rightarrow\ t=\dfrac{96}{8}\\\\=12\)

Step-by-step explanation:

Given :

Tanya is printing a report.

There are 96 sheets of paper in the printer, and the number of sheets of paper p left after t minutes of printing is given by the function

\(p(t) = -96 - 8t\)

When all the 96 sheets printed , then the number of sheets will left to print =0

Substitute p(t)=0 in the given function, to find the value of t, we get

\(0 = -8t + 96\\\\\Rightarrow\ 8t=96\\\\\Rightarrow\ t=\dfrac{96}{8}\\\\=12\)

Answer:

Set your calculator to degree mode.

\( \tan(39) = \frac{12}{x} \)

\(x \tan(39) = 12\)

\(x = \frac{12}{ \tan(39) } = 14.818766\)

So the area of this triangle is

(1/2)(14.818766)(12) = 88.91 (B)

Answer:

11) -104÷8=x

-13=x

x=-13

12) b=-56÷14

b=-4

13) -6×18=b

b=-108

14) n=40÷10

n=4

Answer:

40 Batches

Step-by-step explanation:

16 ounces in a pound

16*30=480

There are 480 ounces of flour

480/12=40

It is the 3rd one from the top

Answer:

I believe the answer would be C.

Step-by-step explanation:

First of all, the solution to the answer really is 1/20. If you figure out the decimal form of 4/5, it is 0.80, which is closer to 1 than to 1/2 and 0. The decimal form of 3/4 is 0.75, which is equally close to 1 and 1/2, being 0.25 from both. But it is closer to 1 than 0. I hope I’m right, and I hope this helps. :)

The correct option is (d). The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the y axis

The difference between the areas beneath the two curves that form a boundary is the area between the curves. You will then have the area between the two curves, or the difference, between them.

The washer method enables us to use cylindrical discs with holes to compute the volume of solids in a rotation.

\($$\begin{aligned}& V=\int_a^b \pi\left(x_1^2-x_2^2\right) d y \\& =\int_0^1 \pi\left(y^2-\left(y^2\right)^2\right) d y \\& =\int_0^1 \pi\left(y^2-y^4\right) d y\end{aligned}$$\)

Therefore, the solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y² around the y axis.

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Answer:

Answer is given in the attachment

hope it's helpful!!

Answer:

$1080 or 13

Step-by-step explanation:

If you are finding the percentage : 90% ÷ 1200 = 1080

If you wanna know how much for each: 13

The yield to maturity for the given loan is 73.1%.

The yield to maturity (YTM) is the discount rate that renders the bond's present value equal to its price. It is the total return that an investor receives if they own a bond until maturity. When an investor buys a bond at face value and holds it until maturity, they will earn a yield equivalent to the coupon rate. In general, yield to maturity refers to the yield an investor earns over the life of a bond if they hold it until maturity.

Let's calculate the yield to maturity if you take a simple loan of $1000 and you have to return $1322.5 in two years.Given,Face Value = $1000Amount to be paid at maturity = $1322.5Time to maturity = 2 yearsWe can use the following formula to calculate the yield to maturity:PV = PMT/(1+r)¹ + PMT/(1+r)² + ...+ PMT/(1+r)ⁿ + FV/(1+r)ⁿWhere, PV = Present ValuePMT = Annual Paymentr = Yield to maturityFV = Face Valuen = Number of yearsIn this problem, PMT is the same for both years since it's a simple loan and the amount to be paid will be the principal plus interest. PMT = $1322.5/2 = $661.25Now, substitute all the values in the above formula:$1000 = $661.25/(1+r)¹ + $661.25/(1+r)² + $1322.5/(1+r)² .

Applying the formula, we get the quadratic equation:r² + r - 1.5145 = 0Using the quadratic formula, we get:r = (-b ± √(b² - 4ac))/2aPutting the values in the formula, we get:r = (-1 ± √(1 + 6.058))/2r = (-1 ± 2.462)/2Since the interest rate cannot be negative, the correct solution is:r = (-1 + 2.462)/2r = 0.731So, the yield to maturity for the given loan is 73.1%.Answer:Yield to maturity for the given loan is 73.1%.

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Answer:

The first answer is incorrect

Step-by-step explanation:

45 divided by 9 is 5 not 40

The equation that represents the statement is j / 9 = 5.

An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.

The statement j divided by 9 is 5 can be written in equation form as follows:

j / 9 = 5

j = 45

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Answer:

13.3

Step-by-step explanation:

By using sinus rule

Therefore, the global maximum value of the function on the region B is 12, and the global minimum value is 4.

To find the global maximum and minimum values of the function f(x, y) = x² + y² + x²y + 4y² + x²y + 4 on the region B = {(x, y) ∈ R² | −1 ≤ x ≤ 1, -1 ≤ y ≤ 1}, we need to evaluate the function at its critical points within the given region and compare the function values.

1. Critical Points:

To find the critical points, we need to find the points where the gradient of the function is zero or undefined.

The gradient of f(x, y) is given by:

∇f(x, y) = (df/dx, df/dy) = (2x + 2xy + 2x, 2y + x² + 8y + x²).

Setting the partial derivatives equal to zero, we get:

2x + 2xy + 2x = 0          (Equation 1)

2y + x² + 8y + x² = 0      (Equation 2)

Simplifying Equation 1, we have:

2x(1 + y + 1) = 0

x(1 + y + 1) = 0

x(2 + y) = 0

So, either x = 0 or y = -2.

If x = 0, substituting this into Equation 2, we get:

2y + 0 + 8y + 0 = 0

10y = 0

y = 0

Thus, we have one critical point: (0, 0).

2. Evaluate Function at Critical Points and Boundary:

Next, we evaluate the function f(x, y) at the critical point and the boundary points of the region B.

(i) Critical point:

f(0, 0) = (0)² + (0)² + (0)²(0) + 4(0)² + (0)²(0) + 4

       = 0 + 0 + 0 + 0 + 0 + 4

       = 4

(ii) Boundary points:

- At (1, 1):

f(1, 1) = (1)² + (1)² + (1)²(1) + 4(1)² + (1)²(1) + 4

       = 1 + 1 + 1 + 4 + 1 + 4

       = 12

- At (1, -1):

f(1, -1) = (1)² + (-1)² + (1)²(-1) + 4(-1)² + (1)²(-1) + 4

         = 1 + 1 - 1 + 4 + (-1) + 4

         = 8

- At (-1, 1):

f(-1, 1) = (-1)² + (1)² + (-1)²(1) + 4(1)² + (-1)²(1) + 4

         = 1 + 1 - 1 + 4 + (-1) + 4

         = 8

- At (-1, -1):

f(-1, -1) = (-1)² + (-1)² + (-1)²(-1) + 4(-1)² + (-1)²(-1) + 4

          = 1 + 1 + 1 + 4 + 1 + 4

          = 12

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Answer:

23 gallons per hour

Step-by-step explanation:

5 3/4 * 4 = 23

times the amount drank in 1/4 hours by 4 to get the amount drank in 1 hour

(1/4 * 4 = 1 hour (example))

Answer:

20 + 6L ≤ 60 :)

Answer:

2+2=4

Step-by-step explanation:

v(t)=vt p=¥€

Answer:

the answer is

Step-by-step explanation:

5%
A

Answer: I HOPE IT HELPS OR WATCH  VIDOES  ABOUT IT

Step-by-step explanation:

Two unique points define a line.  Other geometric figures also may pass through those two points (you will learn those later).

There are several forms of the equation of a line:

     Standard form                           Ax + By = C

     Slope-intercept form                  y = mx + b

     Point-slope form                        y – y1 = m(x – x1)

     Two-point form              y – y1 = [ (y2 – y1)/(x2 – x1) ](x – x1)

O.K., you picked the two-point form, right?    

               The points are  P1:  (5,5) and P2: (7,-4)

    y - 5 = [ ((-4) - 5)/(7 - 5) ] (x - 5)          (put in x and y values of points)

    y - 5 = [  -9 / 2 ](x - 5)                         (simplify)

    y - 5  =  -9/2x  + 45/2                           (distribute -9/2)

     y =  f(x) = -9/2x + 55/2                   (add 5 to both sided)

Check (very important):

  Is (5,5) on the line?      5 = (-9/2)(5) +  55/2  ?

                                         5 =  -45/2   +  55/2  ?

                                          5 =  10/2         yes.

  Is (7,-4) on the line?     -4 = (-9/2)(7) + 55/2       ?

                                          -4  =  -63/2   + 55/2   ?

                                          -4  =   -8/2   ?       yes.

Therefore , the solution of the given problem of triangle comes out to be goalpost is 9.25 metres high.

Given that they consist of four sides or more, triangles are categorized as polygons. It has a straightforward geometric shape. The letters of the ABC form a triangle with a right angle when put together. Euclidean geometry generates a single rectangle or squares when the borders must not match. Due to their three sides and three corners, triangles are polygons. A triangle's corners are formed by the point where its three sides meet. A triangle has angles that total 180 degrees.

Here,

According to the physics principle of reflection,

Angle of reflection equals angle of incident

Both angles (), as seen in the attached image, are equal.

m∠ACB = m∠ECD = 90° - θ

m∠ABC = m∠ADC = 90°

As a result, the triangles ABC and EDC will be comparable.

They will also have proportionate comparable sides because related triangles have that feature.

=>1.75 / ED = 2.6 /13.75

=> ED = 1.75 * 13.75 / 2.6

=> ED = 9.25 m

ED = 9.25 m

The goalpost is 9.25 metres high.

Therefore , the solution of the given problem of triangle comes out to be goalpost is 9.25 metres high.

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