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Reil [10]
2 years ago
8

Alison used a coordinate grid to show where the trees are in her backyard. She wants to put a birdbath exactly halfway between t

he two oak trees. What are the coordinates of this location? If each grid represents 1 foot, how far apart are the two oak trees? What is the perimeter of the triangle determined by the three trees? (Round your answer to the nearest foot)

Mathematics
1 answer:
Degger [83]2 years ago
3 0

Answer:(5,4)

Step-by-step explanation:

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Two machines are used for filling glass bottles with a soft-drink beverage. The filling process have known standard deviations s
stellarik [79]

Answer:

a. We reject the null hypothesis at the significance level of 0.05

b. The p-value is zero for practical applications

c. (-0.0225, -0.0375)

Step-by-step explanation:

Let the bottles from machine 1 be the first population and the bottles from machine 2 be the second population.  

Then we have n_{1} = 25, \bar{x}_{1} = 2.04, \sigma_{1} = 0.010 and n_{2} = 20, \bar{x}_{2} = 2.07, \sigma_{2} = 0.015. The pooled estimate is given by  

\sigma_{p}^{2} = \frac{(n_{1}-1)\sigma_{1}^{2}+(n_{2}-1)\sigma_{2}^{2}}{n_{1}+n_{2}-2} = \frac{(25-1)(0.010)^{2}+(20-1)(0.015)^{2}}{25+20-2} = 0.0001552

a. We want to test H_{0}: \mu_{1}-\mu_{2} = 0 vs H_{1}: \mu_{1}-\mu_{2} \neq 0 (two-tailed alternative).  

The test statistic is T = \frac{\bar{x}_{1} - \bar{x}_{2}-0}{S_{p}\sqrt{1/n_{1}+1/n_{2}}} and the observed value is t_{0} = \frac{2.04 - 2.07}{(0.01246)(0.3)} = -8.0257. T has a Student's t distribution with 20 + 25 - 2 = 43 df.

The rejection region is given by RR = {t | t < -2.0167 or t > 2.0167} where -2.0167 and 2.0167 are the 2.5th and 97.5th quantiles of the Student's t distribution with 43 df respectively. Because the observed value t_{0} falls inside RR, we reject the null hypothesis at the significance level of 0.05

b. The p-value for this test is given by 2P(T0 (4.359564e-10) because we have a two-tailed alternative. Here T has a t distribution with 43 df.

c. The 95% confidence interval for the true mean difference is given by (if the samples are independent)

(\bar{x}_{1}-\bar{x}_{2})\pm t_{0.05/2}s_{p}\sqrt{\frac{1}{25}+\frac{1}{20}}, i.e.,

-0.03\pm t_{0.025}0.012459\sqrt{\frac{1}{25}+\frac{1}{20}}

where t_{0.025} is the 2.5th quantile of the t distribution with (25+20-2) = 43 degrees of freedom. So

-0.03\pm(2.0167)(0.012459)(0.3), i.e.,

(-0.0225, -0.0375)

8 0
2 years ago
Triangular numbers can be represented with equilateral triangles formed by dots. The first five triangular numbers are 1, 3, 6,
Novosadov [1.4K]
Position in the sequence    triangular number    relation

1                                          1                              1 = 1*(1+1)/2

2                                          3                              3 = 2(2+1)/2

3                                          6                              6 = 3(3+1)/2

4                                         10                            10 = 4(4+1)/2

5                                         15                              15= 5(5+1)/2

Call n the position in the sequence, then the triangular number is: n(n+1)/2
 



7 0
2 years ago
Read 3 more answers
Trey went to the batting cages to practice hitting. he rented a helmet for $4 and paid $0.75 for each group of 20 pitches. if he
matrenka [14]
My man paid for 4 groups of 20.
7 0
2 years ago
If x and y satisfy both 9x+2y=8 and 7x+2y=4, then y=?
Alex

Answer:

The value of y is -5

Step-by-step explanation:

we have

9x+2y=8 ------> equation A

7x+2y=4 ------> equation B

we know that

If x and y satisfy both equations, then (x,y) is the solution of the system of equations

Using a graphing tool

Remember that

The solution of the systems of equations is the intersection point both graphs

The intersection point is (2,-5)

therefore

The solution of the system of equations is the point (2,-5)

The value of y is -5

7 0
2 years ago
Which represents the compound inequality x &lt; -2 or x ≥ 3 using interval notation?
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We are given the inequality x < -2 or x ≥ 3 in which the problem asks to determine the domain of the inequality. In this case, this means numbers less than -2 or numbers equal to 3 and greater than three. The relation that illustrates the previous statement is B. x e(-∞,-2) n[3,∞) 
5 0
2 years ago
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