If a system reliability of 0. 998 is required, what reliability of two components in series is required?

Answer: 18

Step-by-step explanation: 18=1+8=9

its complicated but when you check something like

23= 2+3 =5

 10 = 1+0=1

the individual digits of 18 are 1 and 8

Sum = 1+8=9

multiply 9 by 2 we get 18

18 is also a multiple of 9.

I hope this helps

Answer:

range is 10

Step-by-step explanation:

highest number is 49

loweest number is 39

49 - 39 = 10

Answer:

10

Step-by-step explanation:

The range is found by taking the largest number and subtracting the smallest number

The largest number is 49

The smallest number is 39

The range is 49-39 = 10

Answer:

-4t-11

Step-by-step explanation:

rearrange the numbers

2t-6t-9+2

Add negative 2

2t-6t-11

2-6

-4t-11

Answer:

Step-by-step explanation:

Answer: 16.8°C

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {z}^{2} - 14z + 48 }{ {z}^{2} + 6x - 27} ÷ \cfrac{z -8}{z-3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {z}^{2} - 8z - 6z+ 48 }{ {z}^{2} + 9z- 3z- 27} ÷ \cfrac{z -8}{z-3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {z(}^{} z- 8) - 6(z - 8) }{ {z}^{} (z+ 9)- 3(z + 9)} ÷ \cfrac{z -8}{z-3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {(}^{} z- 8) (z - 6) }{ {}^{} (z+ 9)(z - 3)} ÷ \cfrac{z -8}{z-3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ (z - 6) }{ {}^{} (z+ 9)}[/tex]

Break into two parts and simplify

[tex]\\ \rm\dashrightarrow \dfrac{z^2-14z+48}{z^2+6z-27}[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{z^2-8z-6z+48}{z^2+9z-3z-27}[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{(z-8)(z-6)}{(z+9)(z-3)}[/tex]

Now divide by the denominator

[tex]\\ \rm\dashrightarrow \dfrac{(z-8)(z-6)(z-3)}{(z+9)(z-3)(z-8)}[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{z-6}{z+9}[/tex]

The p-value that would be given as the evidence would be given as p-value = 0.00002 and also P value = 0.00003

The sample size of the first sample = 100

x1 = success 0f 86%

We have to find the proportion of this = 0.86

The sample size of the second sample n2 = 100

x12 = success 0f 60%

We have to find the proportion of this = 60/100

= 0.6

The difference = 0.86-0.6= 0.26

Next we have to find the pooled proportion. This is taken given as p = (x1+x2)/(n1+n2) this gives us 0.73

Next we have to find the standard error

= √(p*(1-p)*(1/n1+ 1/n2)= 0.06279

Z stat = (0.26-0)/0.0628= 4.1411

From here the p value would have to be

p-value = 0.00002 and also

P value = 0.00003

Read more on p value here:

https://brainly.com/question/4621112

Answer:

1  i(sqrt5)

2  7i

3  -9i

4  -64i

5  -5i(sqrt2)

6  -4i(sqrt3)

7  10i(sqrt3)

8  2i(sqrt2)

9  3i(sqrt7)

10  -30i(sqrt2)

Step-by-step explanation:

i is the square root of (-1). We can simplify each one as such.

I'll focus on part (b) only.

======================================================

Explanation:

Replace the variable b with the commonly used variable x and c with some other constant, let's say the letter m. These replacements will become apparent when we use the quadratic formula shortly later on.

After the replacements are made, we have -3c²-4cb+4b²​ turn into -3m²-4mx+4x²​

This is the same as 4x²​-4mx-3m²

Compare this to the format of ax²​+bx+c

We can see that

Once again, m is constant.

Let's compute the discriminant.

[tex]d = b^2 - 4ac\\\\d = (-4m)^2-4(4)(-3m^2)\\\\d = 16m^2+48m^2\\\\d = 64m^2\\\\[/tex]

This discriminant is under the square root as part of the quadratic formula.

So 4x²​-4mx-3m² would have roots of...

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-b\pm\sqrt{d}}{2a}\\\\x = \frac{-(-4m)\pm\sqrt{64m^2}}{2(4)}\\\\x = \frac{4m\pm\sqrt{(8m)^2}}{8}\\\\x = \frac{4m\pm 8m}{8}\\\\x = \frac{4(m\pm 2m)}{4*2}\\\\x = \frac{m\pm 2m}{2}\\\\x = \frac{m+ 2m}{2} \ \text{ or } \ x = \frac{m-2m}{2}\\\\x = \frac{3m}{2} \ \text{ or } \ x = \frac{-m}{2}\\\\[/tex]

The whole time, the term "m" is treated as a constant. It is fixed to some unchanging number.

So why did we go through all that trouble to use the quadratic formula in the first place? It turns out that this formula is helpful to factoring quadratics. Recall that the roots of a polynomial tie very closely to its factorization.

For example, x²-4 factors to (x-2)(x+2) to have roots of x = 2 or x = -2. You could use the quadratic formula to solve x²-4 = 0 or x²+0x-4 = 0 and you should get x = 2 or x = -2 as the two solutions.

Anyways, back to the problem at hand.

Let's use the first root we found to form one of the factors needed.

The idea is to do a bit of algebra to get everything to one side. If fractions are present, then multiply both sides by the LCD to clear them out. We need to have 0 isolated on its own side.

[tex]x = \frac{3m}{2} \\\\ 2x = 3m\\\\ 2x-3m = 0[/tex]

So (2x-3m) is one factor

Through similar steps, you would find that the root [tex]x = \frac{-m}{2}[/tex] yields the factor of (2x+m)

Therefore, the factors are (2x-3m) and (2x+m)

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

In summary so far, 4x²​-4mx-3m² factors to (2x-3m)(2x+m)

From here we replace x with b and replace m with c, so that we return back to the original variables used.

(2x-3m)(2x+m) becomes (2b-3c)(2b+c)

This can be confirmed using WolframAlpha. You could use the FOIL rule to expand out (2b-3c)(2b+c) and you should get 4b²​-4bc-3c²​ aka -3c²-4cb+4b²​

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

Those previous sections talked about part (i)

Part (ii) is where we plug in b = 4 and c = 3. In other words, we replace every copy of b with 4, and every copy of c with 3.

If you use the original expression, then,

-3c²-4cb+4b²​ = -3(3)²-4(3)(4)+4(4)²​ = -3(9)-4(12)+4(16) = -11

Or you could use the factored expression.

(2b-3c)(2b+c) = (2*4-3*3)(2*4+3) = (8-9)(8+3) = (-1)*(11) = -11

This very partially confirms that -3c²-4cb+4b² = (2b-3c)(2b+c) is indeed the case. Unfortunately you'd have to use infinitely many numeric examples to confirm the answer to part (i); however, something like the FOIL rule is far more efficient.

D box plot correctly represents the data

A box plot or boxplot is a technique for illustratively displaying the localization, dispersion, and skewness groups of numerical data through their quartiles.

Using a five-number summary (the minimum, first quartile (Q1), median, third quartile (Q3), and "maximum"), a boxplot is a common method of visualizing data distribution.

The median value for the provided data will be the sixth data point's value, or 3.

The median of the data's lower half is now the first quartile. The third data point's value of 1 will therefore be in the lower quartile.

The median of the data's upper half is now referred to as the upper or third quartile. This means that the value of the ninth data point, which is 6, will represent the upper quartile.

Thus, box-plot D effectively displays the data from above.

To know more about Box plot visit:

https://brainly.com/question/16134337

#SPJ4

Answer:

The answer is D.

Edg 2023.

The hypotenuse is [tex]c = a\sqrt{2}[/tex]  times the length of each leg 'a'. Triangle XYZ is a isosceles right triangle, therefore the Pythagoras theorem becomes  and this can be evaluated by using properties of isosceles triangle.

According to the statement

we have given that a theorem and we have to prove it.

So, For this purpose,

The given information is :

Isosceles triangle XYZ where [tex]Angle X = 45^{0}[/tex] [tex]Angle Y = 45^{0}[/tex] [tex]Angle Z = 90^{0}[/tex]

Let the sides of triangle XYZ be a, b, and c. Then side XY = c, YZ = b and ZX = a.

Now, it is given that triangle XYZ is isosceles triangle therefore, the shorter sides must be equal that is, a = b.

Now use Pythagoras theorem

[tex]a^{2} + b^{2} = c^{2}[/tex]

But here a= b then the equation become

[tex]a^{2} + a^{2} = c^{2}[/tex]

Then after solving it become

[tex]2a^{2} = c^{2}[/tex]

And here we have to find the value of the hypotenuse,

so we solve it for c.

Then

[tex]c = a\sqrt{2}[/tex]

From this it is clear that the

it can be concluded that the hypotenuse is  times the length of each leg 'a'.

Learn more about Pythagoras theorem here

https://brainly.com/question/343682

#SPJ1

Answer:

First number = 33, Second number = -19

Step-by-step explanation:

We can use F to represent the first number and S to represent the second number.

Our two equations then are F + S = 14 and 2F + 3S = 9

We can use substitution:

[tex]F+S = 14\\2F+3S=9\\F=14-S\\2(14-S)+3S=9\\28-2S+3S=9\\28+S=9\\S=-19\\\\F-19=14\\F=33[/tex]

The percentage of respondents who play only hockey is 27.24%.

According to the given question.

Total number of respondents = 2302

And, the number of reposdents who play only hockey = 627

Therefore,

The percentage of respondents said that they play only hockey

= (number of respondents who play only hockey/ total number of respondents)  × 100

[tex]= \frac{627}{2302} \times 100[/tex]

= 27.237 %

≈ 27.24%

Hence, the percentage of respondents who play only hockey is 27.24%.

Find out more information about percentage here:

https://brainly.com/question/8191920

#SPJ4

The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

To find the probability that at least 1 ball was​ red, given that the first ball was replaced before the second draw. Not replaced before the second draw:

Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

Know more about probability here:

https://brainly.com/question/251701

#SPJ4

The complete question is given below:

Two balls are drawn in succession out of a box containing 2 red and 5 white balls. Find the probability that at least 1 ball was​ red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw.

Answer:

y = 3x + 4

Step-by-step explanation:

Substituting into point-slope form and converting to slope-intercept form,

[tex]y+5=3(x+3) \\ \\ y+5=3x+9 \\ \\ \boxed{y=3x+4}[/tex]

Answer:

f(x)=(x-1)^2+3

Step-by-step explanation:

Both equations vertexes equal (1, 3) while the rest do not match.

f(x) = (x - 1)² + 3 function in vertex form is equivalent to f(x) = 4 + x² - 2x.

We can use the technique of completing the square to rewrite the given function f(x) in vertex form.

f(x) = 4 + x² - 2x

f(x) = (x² - 2x) + 4

Adding and subtracting (1) inside the parentheses

f(x) = (x² - 2x + 1) + 4 - 1

f(x) = (x - 1)² + 3

So, the equivalent function in vertex form is f(x) = (x - 1)² + 3.

Therefore, the correct option is f(x) = (x - 1)² + 3.

To learn more on Functions click:

https://brainly.com/question/30721594

#SPJ5

Answer:

(4x - 1)^2.

Step-by-step explanation:

16x^2 - 8x + 1

Multiplying the first and last coefficients:

16 * 1 = 16

We need 2 numbers whose product is 16 and whose sum is -8.

These are - 4 and -4.

So we now write:

16x^2 - 4x - 4x + 1

Now factor by grouping :

= 4x(4x - 1) - 1(4x - 1)

= (4x - 1)(4x - 1)

= (4x - 1)^2

This method of factoring quadratics is called the 'ac' method - you split the middle term ( in this case the -8x) into 2 parts.

Answer:

[tex](4x-1)^2[/tex]

Step-by-step explanation:

Given quadratic expression:

[tex]16x^2-8x+1[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b:

Therefore, two numbers are: -4 and -4

Rewrite the middle term as the sum of these two numbers:

[tex]\implies 16x^2-4x-4x+1[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 4x(4x-1)-1(4x-1)[/tex]

Factor out the common term (4x - 1):

[tex]\implies (4x-1)(4x-1)[/tex]

Apply the exponent rule:  aa = a²

[tex]\implies (4x-1)^2[/tex]

Learn more about factoring quadratics here:

https://brainly.com/question/27956741

https://brainly.com/question/27947331

Answer: True

Step-by-step explanation:

The base is less than 1.

f(x) = 2 * (1/2)^x

f(3) = 2 * (1/2)^3

f(3) = 2 * (1/2 * 1/2 * 1/2)

f(3) = 2 * 1/8

f(3) = 2/8

f(3) = 1/4

Hope this helps!

Answer:

[tex]f(x) = 2 \times ( { \frac{1}{2} })^{x} \\ \\ f(3) = 2 \times ({ \frac{1}{2}})^{3} \\ \\ = 2 \times \frac{1}{8} \\ \\ f(3) = \frac{1}{4} = 0.25[/tex]

Carries two brothers each ate 4 pieces, the rest of carries family ate 14 pieces and there were 14 pieces remaining given that Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces. This can be obtained by multiplying the fractions given with the total number.

From the question it is given that,

Carries family broke a package of graham crackers into 32 pieces.

Therefore total number of pieces will be 32 pieces.

carries two brothers each ate 1/8 of the pieces

This means that out of 32, 1/8 of the pieces were ate by the two brothers.

1/8 of 32 = 1/8 × 32 = 4 pieces

⇒ Carries two brothers each ate 4 pieces

the rest of the family ate 7/16 of the pieces

This means that out of 32, 7/16 of the pieces were ate by the rest of the family

7/16 of 32 = 7/16 × 32 = 14 pieces

⇒ the rest of carries family ate 14 pieces

remaining pieces = 32 - (4 + 14) = 32 - 18 = 14 pieces

⇒ there were 14 pieces remaining

Hence Carries two brothers each ate 4 pieces, the rest of carries family ate 14 pieces and there were 14 pieces remaining given that Carries family broke a package of graham crackers into 32 pieces.

Learn more about fraction here:

brainly.com/question/10354322

#SPJ1

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces.

carries two brothers each ate ____ pieces

the rest of carries family ate ____ pieces

there were ____ pieces remaining

Answer:

y = 5x - 6

Step-by-step explanation:

We are given a line, which is parallel to the line y=5x+3.

We also know that this line passes through the point (3,9).

We want to find the equation of this line.
Parallel lines have the same slopes, yet different y intercepts.
So, let's find the slope of the line y=5x+3.

The line is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.

As 5 is in the place of where the slope (m) is, 5 is the slope of the line.

It is also the slope of the line parallel to it (which is the line we are trying to find).

We can write the equation of this new line in slope-intercept form as well, which is also the format your system wants.

Before we write the equation of the line in slope-intercept form, we can write it in point-slope form, then convert it into slope-intercept form.

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.

As we have already found the slope (5), we can immediately plug it into the formula.

[tex]y-y_1=5(x-x_1)[/tex]

Now, remember that we were also given a point, that passes through the line. This point is (3,9).

We can use its values in the formula.

Substitute 3 as [tex]x_1[/tex] and 9 as [tex]y_1[/tex].

y - 9 = 5(x-3)

Now, we have written the line in point-slope form.

However, we're not done yet; remember that we want it in slope-intercept form.

We can solve the equation for y to get slope-intercept form.

So, on the right, open up the parentheses and distribute 5 to both x and -3.

y - 9 = 5x - 15

Now add 9 to both sides.

y = 5x - 6

Considering the given graph, we have that:

The slope of a function, given two points, is given by the change in y divided by change in x.

When x = -3, y = -3, and while x = -2, y = -2, hence when x changes by 1, y also changes, hence the slope of the graph of the function is equal to 1 for x between x = -3 and x = -2.

When x = 3, y = 4, and when x = 4, y = 4, hence the slope of the graph is equal to 0 for x between x = 3 and x = 4.

Looking at the vertical axis:

More can be learned about the graph of a function at https://brainly.com/question/19376563

#SPJ1

The windmill's blade measures 7 feet in length.

To find the measure of the windmill's blade:

Therefore, the windmill's blade measures 7 feet in length.

Know more about equations here:

https://brainly.com/question/2972832

#SPJ4

The correct question is given below:

The equation h=7sin(pi/21t)+28 can be used to model the height, h, in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, t, in seconds. How long is the blade? Assume that the blade is pointing to the right, parallel to the ground, at t = 0, and that the windmill turns counterclockwise at a constant rate. 7 feet 14 feet 21 feet 28 feet

The series is a convergent p-series with p = 3

We would know that a series is a convergent p series when we have ∑ 1 np. Then you have to be able to tell if the series is a divergent p series or it is a convergent p series.

The way that you are able to tell this is if the terms of the series do not approach towards 0. Now when the value of p is greater than 1 then you would be able to tell that the series is a convergent series.

The value of [tex]\sqrt{9}= 3[/tex]

The formular for this is

∑[tex]\frac{1}{n^p} \\[/tex]

where n = 1

we know it is convergent because p is greater than 1. 3>1

Read more on convergent series here:

https://brainly.com/question/337693

#SPJ1

(a) The radius of the small sphere is 2 centimeters.

(b) The measure of the angle XAB is approximately 36.870°.

(c) The area of the shaded region is approximately 3.107 square centimeters.

Herein we have a geometric system formed by three big semicircles and a small circle, whose geometric diagram is attached below. (a) The relationship between the semicircles and the circle is represented by two formulae:

8² + h² = (8 + r)²     (1)

h + r = 8                  (2)

Where r is the radius of the small circle.

Then, we solve the system:

8² + (8 - r)² = (8 + r)²

64 + 64 - 16 · r + r² = 64 + 16 · r + r²

32 · r = 64

r = 2

The radius of the small sphere is 2 centimeters.

(b) The measure of the angle XAB is found by trigonometric relations:

cos m ∠ XAB = OA / AX

cos m ∠ XAB = 8 / 10

m ∠ XAB ≈ 36.870°

The measure of the angle XAB is approximately 36.870°.

(c) The area of the shaded region is the area of the triangle minus the area of the three circular sections:

A = 0.5 · (16 cm) · (10 cm) · sin 36.870° - (36.870° /180) · π · (8 cm)² - 0.5 · (106.260° / 180) · π · (2 cm)²

A ≈ 3.107 cm²

The area of the shaded region is approximately 3.107 square centimeters.

To learn more on triangles: https://brainly.com/question/2773823

#SPJ1

Answer:

10,000

Step-by-step explanation:

Tbh this was pretty simple. If he makes twice the money as you, he pays twice as much too. Meaning he makes 40k a year and pays 10k for taxes

The direction of the parabola is determined by the leading coefficient of the polynomial (a > 0 - Upwards, a < 0 - Downwards). The y-intercept of the polynomial is c and the two zeros of the polynomial are x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c).

Herein we have a quadratic equation of the form f(x) = a · x² + b · x + c. To determine the direction of the parabola, we must transform this expression into its vertex form and looking for the sign of the vertex constant:

f(x) = a · x² + b · x + c

f(x) = a · [x² + (b / a) · x + (c / a)]

f(x) + b² / (4 · a) - c = a · [x² + (b / a) · x + b² / (4 · a²)]

f(x) + b² / (4 · a) - c = a · [x + b / (2 · a)]²

If a > 0, then the direction of the parabola is upwards, but if a < 0, then the direction of the parabola is downwards.

The y-intercept is found by evaluating the quadratic equation at x = 0:

f(0) = a · 0² + b · 0 + c

f(0) = c

And the zeros are determined by the quadratic formula:

x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c)

The direction of the parabola is determined by the leading coefficient of the polynomial (a > 0 - Upwards, a < 0 - Downwards). The y-intercept of the polynomial is c and the two zeros of the polynomial are x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c).

To learn more on parabolas: https://brainly.com/question/4074088

#SPJ1

Answer:

797

Step-by-step explanation:

First, we need to find the number of pizzas sold last week by finding the sum of the pizzas sold:

307 + 224 + 161 + 191 = 883

Next, we need to find the proportion of stuffed crust and pan style pizzas sold last week by adding the number of both sold and dividing by the total number of pizzas sold:

(191+161) / 883 = 352 / 883

Now we need to multiply this proportion by 2000 to find the expected number of stuffed crust or pan style pizzas:

(352 / 883) * 2000 = 797.28 = 797

Answer:

140 in^2

Step-by-step explanation:

Take the outside dimensions of the LARGE rectangle

11 x 17 = 187 in^2

 subtract the two corner cutout rectangles

    187 - 8x4   -  3 x 5   = 140 in^2

Diagram