a system is tested for faults once per hour. if there is no fault, none will be detected. if there is a fault, the probability is 0.78 that it will be detected. the tests are independent of one another. given that a fault has gone undetected for 2 hours, what is the probability that it will be detected in the next hour? round the answer to two decimal places. numeric response

We will use the  distributive property to take a common factor in the next step:

(1/5)*x - (1/10)*x = (1/5 - 1/10)*x

Using that we will see that the solution is x = 10.

The distributive property can be written as:

A*(B + C) = A*B + A*C

Now we have the equation:

(1/5)*x + 8 = (1/10)*x + 9

If we group like terms we get:

(1/5)*x - (1/10)*x = 9 - 8

Here we apply the property, we can rewrite the left side as:

(1/5)*x - (1/10)*x = (1/5 - 1/10)*x

Then we can write:

(1/5)*x - (1/10)*x = 9 - 8

(1/5 - 1/10)*x = 1

(1/10)*x = 1

x = 10*1

x = 10

And that is the solution.

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The coordinates of the vertices of triangle ΔABC, A(0, -1), B(6, 5), and C(-4, 3), indicates that the triangle ΔABCD is a right triangle with all sides of different length.

A right triangle is a triangle that has an interior angle of 90°, and therefore, it has two sides known as the legs that are perpendicular.

The lengths of the sides of the triangle ΔABC can be found using the Pythagorean formula for finding the distance, d, between two points, (x₁, y₁) and (x₂, y₂) on the coordinate plane as follows;

d² = (x₂ - x₁)² + (y₂ - y₁)²

The vertices of the triangle ΔABC are; A(0, -1), B(6, 5), and C(-4, 3), which gives;

[tex]\overline{AB}^2[/tex] = (6 - 0)²+ (5 - (-1))² = 72, AB = 6·√2

[tex]\overline{AC}^2[/tex] = (-4 - 0)² + (3 - (-1))² = 32, AC = 4·√2

[tex]\overline{BC}^2[/tex] = (-4 - 6)² + (3 - 5)² = 104, BC = 2·√(26)

72 + 32 = 104

Therefore; [tex]\overline{AB}^2[/tex] + [tex]\overline{AC}^2[/tex] = [tex]\overline{BC}^2[/tex]

ΔABC is a right triangle

The slopes of the equation of the lines of the sides of the triangle are;

Slope of side AB = (5 - (-1))/(6 - 0) = 1

Slope of side BC = (3 - 5)/(-4 - 6) = 0.2

Slope of side AC = (3 - (-1))/(-4 - 0) = -1

Therefore;

[tex]\overline{AB}[/tex] ⊥ [tex]\overline{AC}[/tex]

Which gives;

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The pit [2, 2]'s prior probability tends to be 0 and its posterior probability tends to be 1.

Compute the probabilities of Pits Each square in the Wumpus world do consist of a pit with the probability of 0.01 and consist of independent contents of the squares.

As suppose there are total of N/2 pits that are scattered randomly among the total of N squares. To compute the probabilities of the pits in [1, 3] and [2,2], consider that the probabilities of the assignments to complete where the other assignments doesn't gets off.

Thus, the total number of the 3-pit assignment rather remains consistent with the three assigned partial assignments here P 1,3 =true.Thus, in 21 assignment completes when the P 1,3 =true. Next the 55 assignment completes when the

P 1,3, = false.

Thus, it gives P(P 1.3 ) = a' (0.01(0.0001+0.0099+0.0099), 0.99(0.0001+ 0.0099)) = (0.1674, 0.8326)

While when the value of Pay = true, then there are basically four assignments that are partialenough with the total value of 0.0001, 0.0099, 0.0099, 0.9801, through the assignment gets completed.

Next when the value of Pa, = false, then there is only a single assignment that is partial with the value of 0.0001 that completes the assignments. Thus, then the final value of P (P2.2 ) is given asP(P2.2) = a' (0.01(0.0001+ 0.0099+0.0099+0.9801), 0.99x 0.0001) = (0.9902, 0.0098

Thus, the prior probability of the pit [2, 2] tends to be 0 and the posterior probability tends to be one (1).

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Answer:

400 minutes

Step-by-step explanation:

25 % *4 =100 %

100*4=400 minutes

Answer:

Completely satisfied with their car:  60.00%

Step-by-step explanation:

I'll assume that "180 percent of people not satisfied . ." is meant to read "180 people not satisfied . . ."

Add the people in the groups to find a total.  Then divide the numeber of people in each group by the total.  This will provide a decimal number which can be multiplies by 100% to give the breakdown requested.

   Group              Count   Percent(%)

Not S.                      180        7.20

Somewhat S.          820      32.80

Completely S.       1500       60.00

Total People:       2500      100.00%

Answer:

sum= 1080

Step-by-step explanation:

Answer:

The sum of an octagon is always 1080 degrees. The interior angles are usually all equal to 135 degrees, but this is an irregular octagon, making that not the case. Because the angles are not all equal, that does not mean that the octagon's sum is any different. Thus, the sum of the interior angles is 1080 degrees.

Hope this helps!

Answer:45

Step-by-step explanation:

75*3/5

Answer: 27

Step-by-step explanation:

Well we already know that n is 12 and d is 15

So based on what I see we do n + d which would equal 27.

Answer: -5,5 = B

Step-by-step explanation:

Answer: the i8 49

Step-by-step explanation:98493

Answer:

Can't be solved

Step-by-step explanation:

Using Pythagoras theorem,

H2= O2 + A2 (where, H= Hypotenuse,O=Opposite,A=Adjacent)

The hypotenuse,H=7feet long

If the opposite side of the triangle is 4 feet longer than the adjacent side, then;

O=A+4

while, A=A

,then using H^2= O^2 + A^2(The 2 are power,that is square)

7^2 = (A+4)^2 + A^2

49= (A+4)(A+4) + A^2

49=A^2 +4A+4A+16 + A^2

49=A^2+8A+16+A^2

(collect like terms)

49-16=A^2+A^2+8A

33=2A^2+8A

Then a quadratic equation,

2A^2+8A=33

2A^2+8A-33=0,

using (-b+/-√4ac) /2a

where b=8, a=2, c=-33

[-8 +/-√4*2*(-33) ]/2(2)

-8 +/-

The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

The equation of the parabola

f(x) = [tex]7x^2[/tex]

The standard vertex form of a parabola is

y = [tex]a(x-h)^2[/tex] + k

The coordinates of the vertex of a parabola = (3, 5)

Where (h, k)  is the coordinates

From the given function of the parabola f(x) =  [tex]7x^2[/tex]

The value of a = 7

Substitute the values in the vertex form of a parabola

y = [tex]7(x-3)^2[/tex] + 5

Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

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Answer:

f(f(x)) = [tex]x^{4}[/tex] + 2x² + 2

Step-by-step explanation:

to evaluate f(f(x)), substitute x = f(x) into f(x)

f(f(x))

= f(x² + 1)

= (x² + 1)² + 1 ← expand factor using FOIL

= [tex]x^{4}[/tex] + 2x² + 1 + 1

= [tex]x^{4}[/tex] + 2x² + 2

Answer:

[tex]f[f(x)]=x^4+2x^2+2[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=x^2+1[/tex]

To find the composite function f[f(x)], substitute the function f(x) in place of the x in function f(x):

[tex]\begin{aligned}\implies f[f(x)]&=f(x^2+1)\\&=(x^2+1)^2+1\\&=(x^2+1)(x^2+1)+1\\&=x^4+x^2+x^2+1+1\\&=x^4+2x^2+2\end{aligned}[/tex]

Answer:

3

Step-by-step explanation:

Answer:

Step-by-step explanation:

5/6 is closest to 1 and 2/5 is closest to 1/2 so the difference is closest to 1/2.

The algebra properties associated to each case are listed below:

Case 1: Distributive property

Case 3: Associative property (multiplication)

Case 5: Existence of inverse (addition)

In this question we find three algebraic expressions, in which we need to determine what algebra property is used. The most important properties in real algebra are listed below:

Now we proceed to determine the property associated to corresponding operation:

Case 1

9 · (x + y) = 9 · x + 9 · y → Distributive property

Case 3

[8 · (3 / 2)] · 15 = 8 · [(3 / 2) · 15] → Associative property (multiplication)

Case 5

(6 · x + 1) + (- 6 · x + 1) = 0 → Existence of inverse (addition)

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The test statistic's p-value is -2.785.

According to A publisher, 45% of its readers own a particular make of car.

Claim: An executive in marketing would like to test the claim that the percentage is different from what is reported.

[tex]H_{o}[/tex]: p = 0.45

[tex]H_{a}[/tex]: p ≠ 0.45

a random sample of 300 found that 37% of the readers owned a particular make of car.

= 37% × 300

= (37 ÷ 100) × 300

X = 111

n= 300

One sample proportion test should be used.

p-vector = x ÷ n,

p-vector = 111 ÷ 300

p-vector = 0.37

The test statistic's formula,

= [tex]\frac{p-q}{\sqrt{\frac{pq}{n} } }[/tex]

test statistic = [tex]\frac{0.37- 0.45}{\sqrt{\frac{0.45(1-0.45)}{300} } }[/tex]

≈ -2.7851

thus, the p-value of the test statistic is -2.7851.

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Answer:

your answer is 16

Step-by-step explanation:

So, to solve (1 + 3)²

first add 1 and 3

then you will get 4

and your equation would be (4)²

then you just square 4.

(4)² > 4x4 = 16

hope this helps (can you mark as brainiest pls)

Answer:

expanded: x^2+8x+15

Step-by-step explanation:

(x+3)(x+5)

x^2+5x+3x+15

The complete two-column proof that shows that ΔAKZ ≅ ΔAKC by AAS is explained below.

The AAS congruence theorem states that if two angles and one non-included side in one triangle have measures that are equal to the two corresponding angles and a corresponding side of another triangle, the two triangles are therefore congruent to each other.

In the image above, we are given two triangles that share a common side, AK. We are informed that line AK bisects an angle, ZKC, and also angles Z and C are congruent.

Therefore, using the information we are given, the two-column proof that can be written to show that the triangles are congruent by the AAS is explained below.

Statements                             Reasons                                      

1. ∠Z ≅ ∠C                              1. Given

AK bisects ∠ZKC

2. ∠ZKA ≅ ∠CKA                   2. Definition of bisection

3. AK ≅ AK                             3. Reflexive property

4. ΔAKZ ≅ ΔAKC                   4. AAS

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The value of y when x = 17 is 66.5

From the question, we understand that:

The variation is a direct variation

The equation of a direct proportion can be represented as

y = kx

Where:

From the question, we have

When x = 11, we have = 43

So, we have

11k = 43

Make k the subject

k = 43/11

Substitute k = 43/11 in y = kx

y = 43/11x

When x = 17, we have

y = 43/11 x 17

This gives

y = 66.5

Hence, the value of y is 66.5

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The equivalent ratios of the given quantity of silver parts of paint to green which is 3:4 are: 6:8 and 9:12.

Equivalent ratios can be described as ratios that have the same values when compared to each other. For example, 8/16, 4/8 and 1/2 re equivalent ratios because:

8/16 = 1/2

4/8 = 1/2

Therefore, 8:16 = 4:8 = 1:2.

Given the table that shows the ratio of the number of parts silver to number of parts green as 3 parts silver to 4 parts green, the ratio is: 3:4.

This means that for 3 parts of silver paint, we would require 4 parts of green paint to give the shade of paint that is needed.

Therefore:

6/8 = 3/4

9/12 = 3/4

6/8 = 9/12 = 3/4

This implies that 6:8, 9:12 and 3:4 are all equivalent ratios.

Therefore, the ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.

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Answer:

A and C

Step-by-step explanation:

For every x value, there should be at most 1 y value.

B and D violate that constraint.

Veremos que originalmente tenias $300, y el valor de la compra fue de $90

Definamos X como la cantidad original de dinero. Ahora trabajaremos con porcentajes.

Sabemos que tu gastaste 30% de esto, entonces lo que te sobra es:

0.7*X

Sabemso qe si hubieras gastado el 40% (en este caso te sobra 0.6*X), te sobrarian 30 dolares menos, entonces podemos escribir:

0.7*X = 0.6*X + $30

Resolviendo para X

0.7*X - 0.6*X = $30

0.1*X = $30

X = $30/0.1 = $300

Originalmente tenias $300 dolares, y gastaste:

$300*0.3 = $90

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the figure for m3 in the above question is 50

Answer:

The quote seems to have a little to much shooting. Don’t you think?

Step-by-step explanation:

Answer:

lair lair

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Total money = €150

1 pair of sunglasses = €70

3 pairs of shorts = €15 × 3 = €45

then, Total = €70 + €45 + x

€150 = €115 + x

x = €150 - €115

x = €35

Which means Eddie got only €35 left on him which is not enough for him to buy the trainers

Answer:

The second answer:

5cubrt10 + 4cubrt10

Step-by-step explanation:

In order to get a cubrt10 answer you have to add cubrt10's.

The first answer has squareroots, so that's a no.

The last two have cubrt + sqrt, which cannot be simplified.

5cubrt10 + 4cubrt10 = 9cubrt10

The value of y when x = -2, 0,2 is 1/49, 7, 49.

Simplification is an algebraic expression is when we utilize a range of approaches to make algebraic expressions more efficient and compact - in their simplest form - without changing the value of the original expression.

Given function y =[tex]7^{x}[/tex]

We have to determine the y values when x = -2, 0, 2

Now substitute the x values in the given function

If x = -2 then

Y = 7(-2)

Y = 1/49

If x = 0 then

Y = 7(0)

Y = 1

If x = 2 then

Y = 7(2)

Y = 49

Therefore the value of y when x = -2, 0 ,2 is 1/49, 7 , 49

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