A person trying to gain access to a bank vault must pass through a series of three security doors. If an attempt to pass through a door is a failure, then the person will not make any further attempts. Let P denote a successful pass and F denote a failed pass. What is the sample space for this random experiment

Answer:

471 square feet

Step-by-step explanation:

150

x3.14

471

Answer:

#8. 2

#9. 7

#10. 2

#11. 2

#12. 0

#13. -4

#14. 17

#15. 1

Answer:#8=2

#9=-11

#10=8

#11=2

#12=0

#14=17

#15=1

Step-by-step explanation: #8-13 (Subtract the numbers using a number line, than add the numbers using a integer chips, after that calculate the sum of the differences) #14-15( normal solving stepping for integers(recommend using a T1-84 Calculator)

Answer:

x <= 10

<= means less or equal to

Step-by-step explanation:

At least means less or equal to

Answer:

c

Step-by-step explanation:

3X-x+2=14

3*6-6+2=14

14=14

plz make me brainliest

Answer:

the square root is 2.2

Answer:

2.2

Step-by-step explanation:

make me brainestly

the guy who did the second answer wants beef

Answer: D. 15 square root with 3 inside

Step-by-step explanation:

Just try it

Answer:

c

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

cause i said so

Answer:

2,3

Step-by-step explanation:

2 and 3 are consecutive numbers, and when you multiply them, you get 6.

Hope this helps.

Have a nice day.

Answer:

Step-by-step explanation:

You'll be given an equation that contains an x and a y.

You'll also be given an ordered pair. Plug the ordered pair into the equation and see if the equation is true.

For example:

Is (0,4) a solution to the equation 2x+3y = 15 ?

Plug the coordinates of (0,4) into the equation:

2·0 + 3·4 = 15

This simplifies to 12 = 15, which is obviously false, so (0,4) is not a solution to the equation.

Answer: 14/16

Step-by-step explanation:

Answer:

14/8 BUT Simplified even further = 7/8

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

are given:

\displaystyle \frac{\sin^2(x)-\sin(x)-2}{\sin(x)-2}

sin(x)−2

sin

2

(x)−sin(x)−2

To make it simpler and more clear, we can let u = sin(x). So:

\displaystyle \frac{u^2-u-2}{u-2}

u−2

u

2

−u−2

Now, it becomes obvious that we can factor, which produces:

\displaystyle =\frac{(u-2)(u+1)}{u-2}=

u−2

(u−2)(u+1)

Cancel:

=u+1=u+1

And substituting back:

=\sin(x)+1=sin(x)+1

Hence, our answer is A.

Answer:

a.2^(a+b+c)

b.2^(a+b+a-b)=2^(2a)or 4^a

c.2^(a+b+c)/2^(a+b)=2^(a+b+c-a-b)=2^c

Answer:

y = 37/5x + 9

Step-by-step explanation:

The points are not plotted on a single straight line, so I will find the general slope using the first and last point on the graph.

(5, 46) & (10, 83)

slope-intercept form: (y₂ - y₁) / (x₂ - x₁)

(83 - 46) / (10 - 5)

Simplify.

(37)/(5)

Your slope is 37/5.

y = 37/5x + b

To find b, plug in a point to x and y.

46 = 37/5(5) + b

46 = 37 + b

b = 9

Your equation is: y = 37/5x + 9

Check by plugging in the other point.

83 = 37/5(10) + 9

83 = 74 + 9

83 = 83

Your equation is correct.

Hope this helps!

Answer:

The area would reduce to 1/4 the original area

Step-by-step explanation:

The area of a triangle = (1/2)(base)(height) or bh/2

If the triangle base and height were to reduce by one-half, the formula would change to:

Area = (1/2)(1/2 base)(1/2 height) or bh/8. Which is a reduction by 1/4

Answer:

-15

Step-by-step explanation:

-2 to the power 0 = -1

-2 to the power 1 = -2

-2² = -4

-2³ = -8

-1 + -2 + -4 + -8 = -15

s(3)=4(3)-7+(3+1)^2

s(3)=12-7+16

s(3)=21

Answer:

21

Step-by-step explanation:

We find that  s(x) = 4x - 7 + (x + 1)^2. Expanding, we get s(x) = x^2 + 6x - 6. Plugging in x = 3, we have s(3) = 3^2 + 6 x 3 - 6 = 21.

Alternatively, we can compute that f(3) = 5 and g(3) = 16, so  s(3) = f(3) + g(3) = 21.

Problem 15

Answers:

Each interval is interval notation.

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

Explanation:

To get the graph, you can plug in various x values to find their paired y values, then draw a curve through those points. You can only plug in x values that are 3 or larger, as I'll mention later in the next paragraph. A quicker way to get the graph is to use technology. I used GeoGebra to generate the graphs below.

To get the domain, we need to ensure that the stuff under the square root is never negative. So we need to make the x-3 to be 0 or larger. Solving [tex]x-3 \ge 0[/tex] leads to [tex]x \ge 3[/tex] showing that 3 is the smallest value we can plug in. The domain is the interval from 3 to positive infinity. We can write that as [tex]3 \le x < \infty[/tex] which condenses to the interval notation [3, infinity). Note how the square bracket is used to include the endpoint.

The range can be determined from the graph. The lowest point is when y = 2, so the range consists of y outputs that are 2 or larger. We write the interval notation [2, infinity) to mean [tex]2 \le y < \infty[/tex]

The graph also helps us see where the curve is increasing or decreasing. In this case, the curve goes uphill as we move from left to right. Therefore, the graph is increasing over its entire domain. We write the domain as the answer here. Because the function increases over the entire domain, there's no room for the function to decrease.

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

Problem 16

Answers:

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

Explanation:

We follow the same idea as the previous problem.

This time we want the x+1 under the square root to be 0 or larger, so [tex]x+1 \ge 0[/tex] solves to [tex]x \ge -1[/tex] telling us the smallest input allowed. The value of x can be this or larger.

Since this is an increasing function throughout the domain (similar to the previous problem), this means that the smallest domain value corresponds exactly to the smallest range value. Plugging in x = -1 leads to y = -3 which is the smallest possible output. As x gets bigger, so does y. The graph shows that the lowest point occurs when y = -3 to visually confirm this.

The increasing interval is over the entire domain, so we just write the domain again for the increasing interval. This means we write "none" for the decreasing interval.

Side note: The graphs are shown together on the same xy coordinate axis, but for your hw problem, you'll have the graphs on their own separate grid.

Answer:

Since [tex]q(\frac{3}{4}) \neq 0[/tex], 3/4 cannot be a root of q(x).

Step-by-step explanation:

Root of a function:

If [tex]x^{\ast}[/tex] is a root of a function f(x), we have that [tex]f(x^{\ast}) = 0[/tex].

In this question.

We have to find [tex]q(\frac{3}{4})[/tex]. So

[tex]q(\frac{3}{4}) = 6(\frac{3}{4})^3 + 19(\frac{3}{4})^2 - 15(\frac{3}{4}) - 28[/tex]

[tex]q(\frac{3}{4}) = \frac{162}{64} + \frac{171}{16} - \frac{45}{4} - 28[/tex]

[tex]q(\frac{3}{4}) = \frac{162}{64} + \frac{684}{64} - \frac{720}{64} - \frac{1792}{64}[/tex]

[tex]q(\frac{3}{4}) \neq 0[/tex]

Since [tex]q(\frac{3}{4}) \neq 0[/tex], 3/4 cannot be a root of q(x).

Answer:

we have

m<2=m<7

4x+2=5(x-2)

4x+2=5x-10

10+2=5x-4x

x=12

Answer:

x=54 degrees

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

In this case, angle 126 and angle x are supplementary.

126+x=180

x=54 degrees.

Let me know if this helps!

Answer:

n = 14

Step-by-step explanation:

let 'n' = the number

3n - 5 = 2n + 9

n - 5 = 9

n = 14

Answer:

14

Step-by-step explanation:

We have to replace the unknown quantity with "x" and work with it.

The result of multiplying a number by 3 and substracting 5

3x - 5

Is the same as

3x-5= (__)

Doubling the number and adding 9

3x- 5= 2x+9

Then we solve it like any equation

3x - 5 = 2x + 9

3x - 2x = 9 + 5

x = 14

Hope it was helpful ;)

Answer:

7.5%

Step-by-step explanation:

280 - 259 = 21

21 / 280 = 0.075 = 7.5%

Answer:

[tex]F_x=43.30\ N[/tex]

Step-by-step explanation:

Given that,

Force, F = 50 pounds

It is directed at 30° from the horizontal.

The force will be given by :

[tex]F_x=F\cos\theta\\\\=50\times \cos(30)\\\\=43.30\ N[/tex]

So, the required force is 43.30 N.

9514 1404 393

Answer:

  61°

Step-by-step explanation:

An angle and its complement total 90°. Your angle of interest is ...

  90° -29° = 61° . . . complementary angle to 29°

Answer:

20

11

Step-by-step explanation:

10^1+10 steps:

10^1+10

Calculate 10 to the power of 1 and get 10.

10+10

Add 10 and 10 to get 20.

20

10^0+10 steps:

10^0 +10

Calculate 10 to the power of 0 and get 1.

1+10

Add 1 and 10 to get 11.

11

Answer:

0.028 ; 0.649 ; 4

Step-by-step explanation:

P(correctly activation), p = 0.7

Number of sprinklers, n = 10

q = 1 - p = 1 - 0.7 = 0.3

Using the binomial probability relation :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

Probability that all sprinklers activate correctly;

P(x = 10) = 10C10 * 0.7^10 * 0.3^0

P(x = 10) = 1 * 0.0282475249 * 1

P(x = 10) = 0.028

Probability that atleast 7 will operate correctly :

P(x ≥ 7) = p(x = 7) + p(x = 8) + p(x = 9) + p(x = 10)

P(x ≥ 7) = 0.267 + 0.233 + 0.121 + 0.028

P(x ≥ 7) = 0.649

3.)

Probability of atleast 1 operates :

P(x ≥ 1) = 0.98

1 - probability of 0 operates

1 - p(x =0)

P(x = 0) = nC0 * 0.7^0 * 0.3^n = 0.02

Recall :

nC0 = 1 ;

1 - p(x = 0)

P(x = 0) = 1 * 1 * 0.3^n = 0.02

0.3^n = 0.02 - - - (1)

0.3^3.24 = 0.02 - - - (2)

Comparing (1) and (2)

n = 3.24

Since, n cannot be a fraction ;

Then n is rounded to the next whole number = 4

Answer:

Probability = 2/2