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4 years ago

Find the sum of the first 25 terms of the arithmetic sequence.

Mathematics

1 answer:

Marta_Voda [28]4 years ago

3 0

Answer:

Step-by-step explanation:

$\frac{n}{2}*(a+l)=\frac{25}{2}*(100+220)\\\\=\frac{25}{2}*320=\frac{25*320}{2}\\\\=25*160=4000$

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Paired t-test Application (Part 1)An environmental engineer is tasked with determining whether a power plant cooling system is h

qaws [65]

Complete Question

The complete question is shown on the first and second uploaded image

Answer:

Part 1

The correct option is B

Part 11

The correct option is H

Step-by-step explanation:

From the question we are told that

The sample size is n = 15

Generally the sample mean for the input temperature is mathematically represented as

$\= x _1 = \frac{\sum x_i}{n}$

$\= x _1 = \frac{57.6 + 68.9 \cdots +60.4 }{15}$

$\= x _1 = 62.57$

Generally the sample mean for the output temperature is mathematically represented as

$\= x _2 = \frac{\sum x_i}{n}$

$\= x _2 = \frac{65.1 + 74.4 \cdots +67.3 }{15}$

$\= x _2 = 55.97$

Generally the difference between the mean of the input temperature and that of the output temperature is

$d = \= x_1 - \= x_2$

=> $d = 62.57 - 55.97$

=> $d = 6.6$

Generally the standard deviation of the difference between the input temperature and the output temperature is mathematically represented as

$s_d = \sqrt {\frac{1}{n-1 } \sum [d_i - d]^2}$

=> $s_d = \sqrt{\frac{[(57.6 - 65.1) - 6.6]^2+[(68.9 - 74.4) - 6.6]^2+ \cdots +[(68.1 - 74.7) - 6.6]^2 }{15-1} }$

=> $s_d = 1.732$

The null hypothesis is $H_o : \mu_1 -\mu_2 = 6$

The alternative hypothesis is $H_a : \mu _1 - \mu_2\ne 6$

Generally the test statistics is mathematically represented as

$t = \frac{d - 6}{ \frac{s_d}{ \sqrt{n} } }$

$t = \frac{6.6- 6}{ \frac{1.732}{ \sqrt{15} } }$

$t = 1.342$

Generally the p-value is mathematically represented as

$p-value = 2 * P(t > 1.342)$

From the student t distribution table( reference - danielsoper(dot)com(slash)statcalc(slash)calculator) at a degree of freedom of df = n-1 = 15-1 = 14

$P(t > 1.342) = t_{1.342 , 14} = 0.100478$

$p-value = 2 * 0.100478)$

$p-value = 0.201$

From the values obtained we see that the $p-value > \alpha$ hence the decision rule is fail to reject the null hypothesis

The conclusion is

The cooling system changes the temperature of the water by 6 degrees.

5 0

4 years ago

Define and compare radian measure to degree measure

Lelechka [254]

Radian: is the standard unit of angular measure, used in many areas of mathmatics.
degree: is a measuement of plane angle, defined by representing a full rotation as 360 degrees.

Both are two units for measuring angles. There are at least four such units, but degrees and radians are most likely to encounter high school and college.

7 0

3 years ago

What is the value of X?

Leviafan [203]

Answer:

x=20

Step-by-step explanation:

First, find LJ

Angle L = 60 (180 - 30 - 90)

The cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.

cos(L)=adj/hyp

cos(60)=LJ/40√2

LJ = cos(60)*40√2

LJ = 20√2

Now you can use LJ to find x. You also know the value of each angle, 45

x=20√2⋅cos(45)

x=20

4 0

3 years ago

Angelina factored (x - 4)8 and wrote that it was equal to (x2 - 42)2(x2 + 42). Use complete sentences to explain how you could c

lapo4ka [179]

There are several ways to confirm that the two expressions are equal. One method is to simply factor the first expression and see it you get a result equal to the second expression. An easier method is to set a value for x and substitute it to the two expressions. If the resulting value is that same, this means that the two expressions are equal.

3 0

3 years ago

Which of the following is an example of empirical probability?A. Darren threw a football to Ted 15 times, and Ted caught it 13 t

MrMuchimi

Empirical probability is the ratio of the number of outcomes with the actual number of trials. This means that it relies on experimental data and not on the theoretical probability.

The only options that makes use of actual data or the trials done is
A. Darren threw a football to Ted 15 times, and Ted caught it 13 times. The probability Ted will catch a throw is .

7 0

3 years ago