The times of first sprinkler activation for a series of tests with fire prevention sprinkler systems using an aqueous film-forming foam were (in sec)
27 41 22 27 23 35 30 33 24 27 28 22 24
(see "Use of AFFF in Sprinkler Systems," Fire Technology, 1976: 5). The system has been designed so that true average activation time is at most 25 sec under such conditions. Does the data strongly contradict the validity of this design specification? Test the relevant hypotheses at significance level .05 using the P-value approach.

Answer:

x=-1

Step-by-step explanation:

the middlepoint is where its symetrical, and so you take the x part of the point. the point is (-1,4), and all we need is x, so you have x=-1

Answer: 180 degrees rotation, center (1.5, -0.5)

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Explanation:

Notice how point (1,-1) on triangle A moves to (-2,0) and then that rotates to (2,0)

Form a line segment from (1,-1) to (2,0) to show the beginning and end states. The equation of the line through these two points is y = x-2

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Similarly, the point (1,-4) moves to (-2,-3) after applying the translation vector, then it rotates to (2,3). Draw a line through (1,-4) and (2,3). The equation of this line is y = 7x-11

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We have this system of equations

[tex]\begin{cases}y = x-2\\y = 7x-11\\\end{cases}[/tex]

Equate the right hand sides and solve for x

7x-11 = x-2

7x-x = -2+11

6x = 9

x = 9/6

x = 3/2

x = 1.5

which leads to

y = x-2 = 1.5-2 = -0.5

or

y = 7x-11 = 7(1.5)-11 = 10.5-11 = -0.5

Either way, x = 1.5 leads to y = -0.5

We get the ordered pair (x,y) = (1.5, -0.5)

This is the center of rotation when rotating figure A to have it match up with triangle C (the triangle in the upper right quadrant)

Notice in the diagram below point D is that center of rotation. Also, notice that if we use the distance formula, you should find that

AD = A''D

BD = B''D

CD = C''D

Step-by-step explanation:

5(x + 7) = 15

x+7=3

x=-4!!!!!!

Answer:

x = -4

Step-by-step explanation:

Solve for x

Divide each side by 5

subtract 7 from both side

the answer for this question is A

Answer:

The slope is 7/4 and the y intercept is -10

Step-by-step explanation:

y=7/4x-10

This equation is written is slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 7/4 and the y intercept is -10

Answer:

2025 is not a perfect cube

Solution :

Assuming [tex]$\sigma_1^2=\sigma_2^2$[/tex]

We have to test

[tex]$H_0:\mu_1=\mu_2$[/tex]

Against [tex]H_a: \mu_1 \neq \mu_2[/tex]

Level of significance, [tex]$\alpha = 0.05$[/tex]

[tex]$s_p=\sqrt{\frac{(n_1-1)s_1^2+ (n_2-1)s_2^2}{n_1+n_2-2}}$[/tex]

[tex]$s_p=\sqrt{\frac{(25-1)(425)^2+ (20-1)(415)^2}{25+20-2}}$[/tex]

   = 420.6107

Under [tex]H_0[/tex], the t-statistics is as follows:

[tex]$t=\frac{(\overline{x_1} - \overline{x_2})}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} \sim $[/tex]             [tex]$\text{t with }(n_1+n_2-2) \ DF$[/tex]

[tex]$t=\frac{(7200-7087)}{(420.6107)\sqrt{\frac{1}{25}+\frac{1}{20}}}$[/tex]

 = 0.90

DF = (25 + 20 - 2)

    = 43

P-value of the test = 0.375

Since the p value is more than 0.05, we fail to reject our null hypothesis.

There is no difference between then mean tensile strength of the ropes that is produced in the Bozeman and Challis.

Answer:

(a) Tree (see diagram)

(b)   (i) 9/64   (ii) 3/8

Step-by-step explanation:

3 black, 5 white, picks two at random with replacement.

SEE DIAGRAM FOR EXPLANATIONS

(a) Tree (see diagram)

(b)

(i) 9/64

(ii) 3/8

In the given problem we have 3 black ball and 5 white ball, the probability tree be constructed as per ball picks from bag.

(a) Refer the attached figure for the probability tree.

(b)

(i) The probability that Paul picks two black balls is [tex]\dfrac{9}{64}[/tex].

(ii) The probability that Paul picks a black ball in his second draw is [tex]\dfrac{3}{8}[/tex].

Given:

The bag contain 3 black and 5 white balls.

(a)

Refer the attached figure for the construction of probability tree.

(b)

(i)

Since the getting two black ball are independent event so multiply the branch B ( refer attached figure)

[tex]P(\rm two\: black)=\dfrac{3}{8}\times\dfrac {3}{8}\\P(\rm two\: black)=\dfrac{9}{24}[/tex]

Thus, the probability that Paul picks two black balls is [tex]\dfrac{9}{64}[/tex].

(ii)

There should be two outcomes either (B,B) or (W, B).

From the attached figure,

[tex]P(\rm B,B)=\dfrac{9}{64}[/tex]

[tex]P(\rm W, B)=\dfrac{15}{64}[/tex]

Calculate the probability of second ball black.

[tex]P(\rm second\: ball\: black)=P(B, B) + P(W, B)\\P(\rm second\: ball\: black)=\dfrac{9}{64}+\dfrac{15}{64}\\P(\rm second\: ball\: black)=\dfrac{3}{8}[/tex]

Thus, the probability that Paul picks a black ball in his second draw is [tex]\dfrac{3}{8}[/tex].

Learn more about probability here:

https://brainly.com/question/11234923

Answer:

x = 1/2

hope it helps

have a nice day

Answer:

maybe  x=3.5

Step-by-step explanation:

6x= 1/2 (2x+5)

we take the 1/2 and distribute it into (2x+5) so we end up with

6x= 1x (or just x) + 2.5

We subtract 2.5 from both sides of the equation and we end up with

3.5x= 1x

we then need to isolate the x, so we divide both sides of the equation by x

and then we end up with

3.5= x/x, which ends up just being

3.5=x

Answer:

3/4 ft / second

Step-by-step explanation:

15 ft / 20 seconds

Divide the top and bottom by 5

3/4 ft / second

Answer:

[tex] \frac{3}{4} [/tex]ft/sec

Step-by-step explanation:

[tex] \frac{feet}{sec} = \frac{15}{20} [/tex]

[tex] \frac{15}{20} \frac{ \div 5}{ \div 5} = \frac{3}{4} [/tex]

Answer:

64km/h

Step-by-step explanation:

Average speed= 48km÷45 minutes

= 48km÷0.75h

= 64km/h

Answer:

[tex]1. \: \: \: 2x = 5 \\ x = \frac{5}{2} \\ 2. \: \: \: \: \: \: y + 1.8 = 14.7 \\ y = 14.7 - 1.8 \\ y = 12.9 \\ 3. \: \: \: \: \: 6 = \frac{1}{2} z \\ z = 6 \times 2 \\ z = 12 \\ 4. \: \: \: \: \: 3\frac{1}{4} = \frac{1}{2} + w \\ w = \frac{1}{2} - 3 \frac{1}{4} \\ w = \frac{12 + 2}{4} \\ w = \frac{14}{4} = \frac{7}{2} \\ please \: mark \: brainliest[/tex]

Answer:

1/24

Step-by-step explanation:

13/6x = 52

1/6x = 52/13

1/6x = 4

1 = 4(6x)

1 = 24x

24x = 1

x = 1/24

Answer:

because one pair of congruent corresponding angles is sufficient to determine similar triangles.

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

domain is x component so

domain = {-3 , -2 , -1 , 0 , 1 , 2 , 3 }

range is y component so

range = { -22 , -8 , 2 , 8 , 10 , 2 }

note : repeated element can be written only one time. For eg here in range 8 is 2 times but we can write only one time because it is the rule for lisying range and domain.

Answer:

1.84metres

Step-by-step explanation:

convert 76cm to metres

76/100=0.76m

convert 8cm to metres

8/100=0.08m

therefore we have,

1+0.76+0.08=1.84metres

Answer:

option B

Step-by-step explanation:

Given :

 [tex]y = 7x^2 - 10[/tex]

Replace x and y :

  [tex]x = 7y^2 - 10 \\[/tex]

Now solve for y :

[tex]x = 7y^2 - 10 \\\\x + 10 = 7y^2 - 1 0+ 10[/tex]                               [tex][ \ adding \ 10 \ on \ both \ sides \ ][/tex]

[tex]x + 10 = 7y^2\\\\\frac{x + 10 }{7 } = \frac{7y^2}{7}[/tex]                                              [tex][ \ dividing\ by \ 7 \ on \ both \ sides \ ][/tex]

[tex]\frac{x+ 10}{7} = y^2\\\\\pm \ \sqrt{\frac{x+ 10}{7}} = y[/tex]

I think the choose (2)

[tex]y = - + \sqrt{ \frac{x + 10}{7} } [/tex]

Answer:

The current value of the stamp collection is of $2,191.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

A stamp collection is purchased for $1,000.

This means that [tex]P = 1000[/tex]

The rate of return on the stamp collection is 4% per year

This means that [tex]n = 1, r = 0.04[/tex]

So

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(t) = 1000(1 + 0.04)^{t}[/tex]

[tex]A(t) = 1000(1.04)^{t}[/tex]

What is the current value of the stamp collection?

This is A(20). So

[tex]A(20) = 1000(1.04)^{20} = 2191[/tex]

The current value of the stamp collection is of $2,191.

Answer:

Step-by-step explanation:

y = 1000(1+0.04)^20

y = 1000(1.04)^20

Rounded to the nearest hundredth

y = 1000(2.19)

y = $2190

Answer:

10. Where was the medical mission held? A. At Barangay Tatalon Marikina B. At Barangay Almanza Las Piñas City C. At Barangay Pamplona Las Piñas City D. At Barangay CAA BF INT'L Las Piñas City

Answer:

y = 6/5x -7

Step-by-step explanation:

Answer:

7 hours

Step-by-step explanation:

9 : 30 to 17:00 = 7 hours 30 minutes

Minus 30 minutes = 7 hours

Answer:

(last part)

25%

27.8%

290%

300%

67%

Step-by-step explanation:

Given:

The two sets are:

[tex]A=\{1,4\}[/tex]

[tex]B=\{2,3,5\}[/tex]

To find:

The [tex]A\times B[/tex] and the number of relations from A to B.

Solution:

If A and B are two sets, then

[tex]A\times B=\{(x,y)|x\in A, y\in B\}[/tex]

We have,

[tex]A=\{1,4\}[/tex]

[tex]B=\{2,3,5\}[/tex]

Then,

[tex]A\times B=\{(1,2),(1,3),(1,5),(4,2),(4,3),(4,5)\}[/tex]

If number of elements in set A is m and the number of element in set B is n, then the number of relations from A to B is [tex]2^{m\times n}[/tex].

From the given sets, it is clear that,

The number of elements in set A = 2

The number of elements in set B = 3

Now, the number of relations from A to B is:

[tex]2^{m\times n}=2^{2\times 3}[/tex]

[tex]2^{m\times n}=2^{6}[/tex]

[tex]2^{m\times n}=64[/tex]

Therefore, the required relation is [tex]A\times B=\{(1,2),(1,3),(1,5),(4,2),(4,3),(4,5)\}[/tex] and the number of relations from A to B is 64.

Answer:

B) $85,167

Step-by-step explanation:

u got discount 45% so u just have to pay 55% of it

cost = 55% x $154,85 = $85,1675

49 dollars

Step-by-step explanation:

14 times 3 is 42 and 3.50 times 2 is 7, so 42 plus 7 is 49.

Total cost with 2 snacks = $35

Total cost with x  snacks = 28+3.50x

Given :

Carson is going to see a movie and is taking his 2 kids. Movie ticket costs $14 and snacks cost $3.50.

Explanation :

Carson buys 2 snacks . we need to find the total cost that Carson have to pay where he buy 2 snacks.

Total cost = cost of ticket (2 kids) + cost of 2 snacks

[tex]Total \; cost = 14(2) + 2(3.50)=35[/tex]

Total cost with 2 snacks = $35

Total cost with x snacks = cost of ticket (2 kids) + cost of x snacks

[tex]Total \; cost = 14(2) + 3.50(x)\\Total \; cost = 28+3.50x[/tex]

Total cost with x  snacks = 28+3.50x

Learn more :  brainly.com/question/17565961

Answer:

54

Step-by-step explanation:

Angle 2 and Angle 3 are vertical angles

Vertical angles are congruent ( equal to each other )

So if angle 2 = 54 then angle 3 also equals 54

Answer:

∠3 = 54°

Step-by-step explanation:

54° and ∠3 are vertical angles, which means they are equal .

54° = ∠3

Answer:

9-4+(5x3)

Step-by-step explanation:

9-4+15

24-4

20

Answer:

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