Answer:
(- 1, 8 ) and (5, 2 )
Step-by-step explanation:
Given the 2 equations
y = - x + 7 → (1)
y = 0.5(x - 3)² → (2)
Substitute y = 0.5(x - 3)² into (1)
0.5(x - 3 )² = - x + 7 ← expand and simplify left side
0.5(x² - 6x + 9) = - x + 7 ( multiply both sides by 2 )
x² - 6x + 9 = - 2x + 14 ( subtract - 2x + 14 from both sides )
x² - 4x - 5 = 0 ← in standard form
(x - 5)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 1 = 0 ⇒ x = - 1
Substitute these values into (1) for corresponding values of y
x = 5 : y = - 5 + 7 = 2 ⇒ (5, 2 )
x = - 1 : y = 1 + 7 = 8 ⇒ (- 1, 8 )
Frequency=(speed of sound)/(wavelength)
that means
wavelength =(speed of sound )/(frequency)
speed of sound=344 m/s
4.
frequency=587. 33 Hz
thus
wavelength=344/587.33
=0.586 m
5.
frequency=493.88 nHz
thus
wavelength=344/493.88
=0.69653 m
6. Frequency= 698.46 Hz
wavelength= 344/698.46
wavelength=0.4925 m
9. Frequency =783.99 Hz
wavelength=344/783.99
wavelength=0.439 m
Answer:
Null hypothesis: 
Alternative hypothesis: 
Step-by-step explanation:
For this question we need to take in count that the the claim that they want to test is "if the proportion is greater than 0.3". Our parameter of interest for this case is
and the estimator for this parameter is given by this statistic
obtained from the info of sa sample obtained.
The sample proportion would be given by:

Where X represent the success and n the sample size selected
The alternative hypothesis on this case would be specified by the claim and the complement would be the null hypothesis. Based on this the system of hypothesis for this case are:
Null hypothesis: 
Alternative hypothesis: 
And in order to check the hypothesis we can use the one sample z test for a proportion with the following statistic:

Answer:
Mean: 45.1
Median: 44
Mode: 41
Step-by-step explanation:
To find the mean, add up all the values, and then divide the sum by the number of values:
46 + 41 + 44 + 39 + 50 + 43 + 41 + 49 + 53 = 406
406 ÷ 9 ≈ 45.1
The mean is 45.1
To find the median, list all the values in numerical order, and find the value in the middle:
39, 41, 41, 43, 44, 46, 59, 50, 53
The median is 44
To find the mode, find the number of time each value appears. The value the appears the most times is the mode:
41 appears twice, and every other number appears once.
The mode is 41