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solong [7]
3 years ago
10

Find the values of a and b such that

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
3 0

Answer:

a = 1.5

b = 1.75

Step-by-step explanation:

First, we need to solve (x+a)^2 and replace the result in the initial equation as:

x^2+3x+4=(x+a)^2+b\\x^2+3x+4=x^2+2ax+a^2+b

Then, this equality apply only if the coefficient of x is equal in both sides and the constant is equal in both sides.

It means that we have two equations:

3x=2ax\\4=a^2+b

So, using the first equation and solving for a, we get:

3x=2ax\\3=2a\\a=\frac{3}{2}=1.5

Finally, replacing the value of a in the second equation and solving for b, we get:

4=a^2+b\\4=1.5^2+b\\b=4-1.5^2\\b=4-2.25\\b=1.75

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A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed
AURORKA [14]

Answer:

A 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].

Step-by-step explanation:

We are given that Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured.

For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 and For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09.

Firstly, the pivotal quantity for finding the confidence interval for the difference in population mean is given by;

                     P.Q.  =  \frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }  ~  t__n_1_+_n_2_-_2

where, \bar X_1 = sample mean speed for the 25-mil film = 1.15

\bar X_1 = sample mean speed for the 20-mil film = 1.06

s_1 = sample standard deviation for the 25-mil film = 0.11

s_2 = sample standard deviation for the 20-mil film = 0.09

n_1 = sample of 25-mil film = 8

n_2 = sample of 20-mil film = 8

\mu_1 = population mean speed for the 25-mil film

\mu_2 = population mean speed for the 20-mil film

Also,  s_p =\sqrt{\frac{(n_1-1)s_1^{2}+ (n_2-1)s_2^{2}}{n_1+n_2-2} } = \sqrt{\frac{(8-1)\times 0.11^{2}+ (8-1)\times 0.09^{2}}{8+8-2} } = 0.1005

<em>Here for constructing a 98% confidence interval we have used a Two-sample t-test statistics because we don't know about population standard deviations.</em>

<u>So, 98% confidence interval for the difference in population means, (</u>\mu_1-\mu_2<u>) is;</u>

P(-2.624 < t_1_4 < 2.624) = 0.98  {As the critical value of t at 14 degrees of

                                             freedom are -2.624 & 2.624 with P = 1%}  

P(-2.624 < \frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } } < 2.624) = 0.98

P( -2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } } < 2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } } <  ) = 0.98

P( (\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } } < (\mu_1-\mu_2) < (\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } } ) = 0.98

<u>98% confidence interval for</u> (\mu_1-\mu_2) = [ (\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } } , (\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } } ]

= [ (1.15-1.06)-2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } } , (1.15-1.06)+2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } } ]

 = [-0.042, 0.222]

Therefore, a 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].

Since the above interval contains 0; this means that decreasing the thickness of the film doesn't increase the speed of the film.

7 0
2 years ago
Need Answer Fast Please to solve the Linear Expression: 5(5n+2)+(3-2n)
tatyana61 [14]

Answer:

23n +13

Step-by-step explanation:

5(5n+2)+(3-2n)

Distribute

25n + 10 +3 -2n

Combine like terms

25n -2n  + 10+3

23n +13

3 0
3 years ago
Read 2 more answers
382 3/10 - 191 87/100= math difficulties please answer this question
prohojiy [21]
3/10 = .3 and 87/100 = .87
382.3 - 191.87= 190.43
so the answer is 190.43

Hope this helped!! :))
7 0
3 years ago
What does c equal in this equation 6c + 11 = 2c + 59
irinina [24]
Combine like terms you would get 4c=48 then divide it by 4 you'll get c=12
8 0
3 years ago
Order these ratios from least to greatest- 7:2, 12 to 4, 20/6, 21:14, 10:5<br> pls :,)
Brrunno [24]

Answer:

21:14, 10:5, 12 to 4, 20/6, and 7:2

Step-by-step explanation:

first simplify all the ratios.

the first one is already simplified

12 to 4 = 3 to 1

20/6 = 10/3

21:14 = 3:2

10:5 = 2:1

Next find the least common factor the the three digits, 1, 2, and 3 and which is 6.

Multiply the simplified factors into the least common factor. So 7:2 will be multiplied by 6 so it will be 21:6

Do it with the rest of the factors and get

21:6, 18 to 6, 20/6, 9:6, and 12:6

Finally order them from least to greatest,

9:6, 12:6, 18 to 6, 20/6, and 21:6

or

21:14, 10:5, 12 to 4, 20/6, and 7:2

4 0
3 years ago
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