sub y = x - 1 into equation 1
2x + x - 1 = 5
3x = 6
x = 2
sub x = 2 into equation 2
y = 2 - 1
y = 1
Noise levels at 5 airports were measured in decibels yielding the following data:
117,118,140,116,119
1. Construct the 90% confidence interval for the mean noise level at such locations. Assume the population is approximately normal.
2. Calculate the sample mean for the given sample data.
3. Find the critical value that should be used in constructing the confidence interval.
Answer:
1. 112.364<μ,131.636
2. mean = 122
3. critical value = +-2.1318
Step-by-step explanation:
117+118+140+116+119/5
= 610/5
= 122
the sample mean = 122
the sample standard deviation
s² = (117-122)²+(118-122)²+(140-122)²+(116-122²)+(119-122)²/5-1
= 25+16+324+36+9/4
= 410/4
= 102.5
s² = 102.5
s = √102.5
s= 10.12
SE = s/√n
= 10.12/√5
= 4.52
degree of freedom = 5-1 = 4
critical value of t = +-2.1318 using soft ware
confidence interval =
mean +- t(SE)
122-(2.1318)(4.52), 122+(2.1318)(4.52)
= [112.364, 131.636]
112.364<μ,131.636
therefore these are the answers in the ordre it was given in the question
1. 112.364<μ,131.636
2. mean = 122
3. critical value = +-2.1318
Two small space probes have been slowed to 10 m/s as they approach the Moon from the same direction. Probe 1 has a mass of 86 kg, and probe 2 has a mass of 100 kg. What is their total momentum? A. 8600 kg O B. 1000 kg-m/s O C. 860 kg-m/s O D. 1860 kg-m/s SUBMIT
The total momentum of the two probes with given mass and velocity is equal to option D. 1860 kg m/s.
velocity of probe = 10m/s
mass of probe 1 = 86kg
mass of probe 2 = 100kg
The momentum of an object is given by the product of its mass and velocity.
So, to calculate the total momentum of the two probes,
Find the momentum of each probe, and then add them together.
The momentum of probe 1 is equal to,
p₁ = m₁ × v
Substitute the value we have,
⇒ p₁ = 86 kg × 10 m/s
⇒ p₁ = 860 kg m/s
The momentum of probe 2 is equal to,
p₂ = m₂ × v
⇒ p₂ = 100 kg × 10 m/s
⇒ p₂ = 1000 kg m/s
The total momentum of the two probes is the sum of their individual momenta is equal to
p = p₁ + p₂
⇒ p = 860 kg m/s + 1000 kg m/s
⇒ p = 1860 kg m/s
Therefore, the total momentum of the two probes is option D.1860 kg m/s.
Learn more about momentum here
brainly.com/question/13473688
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33√8
9√20
444÷333
5552×333
3÷99
44√5
6622÷33
Step-by-step explanation:
93.340.21.318488163398.3200.6if u want it by step by step thn tell me i will do that..
HELP PLS MIGHT GIVE BRAINLIST BUT ONLY IF 2 PEOPLE ANSWER!
Answer:
two hundred and forty inches
Answer:40
Step-by-step explanation:Parallelogram
Solve for area
A=40
Solution
A=bh=8·5=40
formula A=base*height
need help with this ‼️
It is desired to compare the hourly rate of an entry-level job in two fast-food chains. Eight locations for each chain are randomly selected throughout the country, the selections for each chain being independent. The following hourly rates are recorded:
Chain A 4.25 4.75 3.80 4.50 3.90 5.00 4.00 3.80
Chain B 4.60 4.65 3.85 4.00 4.80 4.00 4.50 3.65
Under the assumption of normality and equal variances, can it be concluded at the 5% significance level that chain A pays more than chain B for the job under consideration?
Answer:
It can be concluded that at 5% significance level that there is no difference in the amount paid by chain A and chain B for the job under consideration
Step by Step Solution:
The given data are;
Chain A 4.25, 4.75, 3.80, 4.50, 3.90, 5.00, 4.00, 3.80
Chain B 4.60, 4.65, 3.85, 4.00, 4.80, 4.00, 4.50, 3.65
Using the functions of Microsoft Excel, we get;
The mean hourly rate for fast-food Chain A, [tex]\overline x_1[/tex] = 4.25
The standard deviation hourly rate for fast-food Chain A, s₁ = 0.457478
The mean hourly rate for fast-food Chain B, [tex]\overline x_2[/tex] = 4.25625
The standard deviation hourly rate for fast-food Chain B, s₂ = 0.429649
The significance level, α = 5%
The null hypothesis, H₀: [tex]\overline x_1[/tex] = [tex]\overline x_2[/tex]
The alternative hypothesis, Hₐ: [tex]\overline x_1[/tex] ≠ [tex]\overline x_2[/tex]
The pooled variance, [tex]S_p^2[/tex], is given as follows;
[tex]S_p^2 = \dfrac{s_1^2 \cdot (n_1 - 1) + s_2^2\cdot (n_2-1)}{(n_1 - 1)+ (n_2 -1)}[/tex]
Therefore, we have;
[tex]S_p^2 = \dfrac{0.457478^2 \cdot (8 - 1) + 0.429649^2\cdot (8-1)}{(8 - 1)+ (8 -1)} \approx 0.19682[/tex]
The test statistic is given as follows;
[tex]t=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{S_{p}^{2} \cdot \left(\dfrac{1 }{n_{1}}+\dfrac{1}{n_{2}}\right)}}[/tex]
Therefore, we have;
[tex]t=\dfrac{(4.25-4.25625)}{\sqrt{0.19682 \times \left(\dfrac{1 }{8}+\dfrac{1}{8}\right)}} \approx -0.028176[/tex]
The degrees of freedom, df = n₁ + n₂ - 2 = 8 + 8 - 2 = 14
At 5% significance level, the critical t = 2.145
Therefore, given that the absolute value of the test statistic is less than the critical 't', we fail to reject the null hypothesis and it can be concluded that at 5% significance level that chain A pays the same as chain B for the job under consideration
find the area of the right triangle.
Answer:
16 units²
Step-by-step explanation:
1/2x4x8=16
A bus left Lagos on Monday at 6.30a.m. and arrived Kaduna on Tuesday at 3.00p.m. How long did the journey take?
Answer:
8 hours and 30 minutes
Step-by-step explanation:
well 6:30am monday to 6:30am tuesday would be 24 hours
plus 9 hours until 3:30pm
then subtract 30 minutes to have 3:00
so 8 1/2 hours
PLEASE HELP!!!!! WILL GIVE BRAINLIEST
WILL GIVE BRAINLIEST
Answer:
B. 12
Step-by-step explanation:
First, we need the degrees for A. So, cosx = 5/13 = 67.4
Now it will be easy to solve a. tan67.4° = a/5 = 12.011728511....
we round it to the nearest tenth and we get 12.
Step-by-step explanation:
By pythagoras theoram
[tex]c = \sqrt{a2 + b2} [/tex]
13=a²+5²a²=13²--5²a²=169--25a²=144I think this is a helpful for youIt costs $6 per hour for a park to water the grass. How much will it cost to water the grass for
7/3
hours?
Answer:
I think the answer is $14 hope this helps!
Step-by-step explanation:
answer the questions, please I will give you 10 points
WILL MARK BRAINLIST
Which set of side lengths below will NOT form a right triangle?
A. 3 ft, 4 ft, 5 ft
B. 8 m, 15 m, 17 m
C. 1 in, 2 in, 3 in
D. All sets of side lengths above will form a right triangle.
Answer:
C. 1 in, 2 in, 3 in
if you think about it- the 3inch side will be as long as the other 2 sides put together. it wouldn't form a triangle at all- just one line on top of the other 2.
The coordinate plane shows a line traveling through two points.
The coordinates that represent another point on the line are
a (3,5)
b (3,2)
c (5,3)
d (6,7)
10. A vehicle averages 68 km/h. How many kilometres can the car travel in 3 hours?
Answer:
15 I believe. ...
Step-by-step explanation:
uhhhhhh
WILL GIVE BRAINLIEST
Answer:
C
Step-by-step explanation:
It's not A and B because an exponent to the negative number leads to the fraction.
e.g. 10^-a = 1/(10^a)
It's not D because 5,030,000 rounds to 5,000,000 and not 6,000,000.
hellllllllllllllllllllllp
Answer:
1200
Step-by-step explanation:
Solve the equation for y. 6x+y=12
List two solutions for the equation: y = 4.5x + 9
Answer:
say 5 and 6
Step-by-step explanation
you just multiply it
Help me help me help me pls pls pls
Answer:
x = 121
Step-by-step explanation:
all angles sum = 540
87 + 92 + 105 + 135 = 419
540 - 419 = 121
I’m stuck on this one. Can any one help me?
3, and apparently its "too short of an answer on this website"
Find the indicated limit, if it exists.
Answer:
2
Step-by-step explanation:
[tex]Lim_{x\to 8} f(x), \: f(x) \begin{cases} x + 10 \: \: \: \: x < 8 \\ \\ 10 - x \: \: \: \: x \geqslant 8\end{cases}[/tex]
[tex] Lim_{x\to 8} f(x) = Lim_{x\to 8} 10 - x \\ \\ = 10 - 8 \\ \\ = 2[/tex]
What is the volume of of a rectangular prism with the following measurements:
Length: 3 yd
Width: 1/2 yd
Length: 1/2 yd
A 3/4 yd cubed
B 2/3 yd. cubed
C 6/2 yd. cubed
D 6/8 yd. cubed
I will give brainleast
Answer:
b
Step-by-step explanation:
What is the solution to the following system? Type answer in (x,y) format, do not use spaces,
(Graphing)
(Worth 10 points)
Answer:
The solution is: (4,-7)
Step-by-step explanation:
Given
The attached graph
Required
Determine the solution
The solution is the point where both lines meet.
From the attached graph, the two lines meet at:
[tex]x =4\\y = -7[/tex]
Hence, the solution is: [tex](4,-7)[/tex]
Calculate the volume of the given pyramid to the nearest tenth
Answer:(A.)
Step-by-step explanation:The reason why its a its because that 13x8=104x17=1,768/3=589.3. Therefore 589.3 can not be round to the nearest tenth.
An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $30,000. If the economy grows at a moderate pace, the investment will result in a profit of $10,000. However, if the economy goes into recession, the investment will result in a loss of $30,000. You contact an economist who believes there is a 20% probability the economy will remain strong, a 60% probability the economy will grow at a moderate pace, and a 20% probability the economy will slip into recession. What is the expected profit from this investment?
factor g(x) =6x^3 +13x^2 -2x -1 if (2x + 3) is a factor.
HELP I WILL GIVE BRAINLEIST OR WHATEVER 50 POINTS
answer:
a. scarf costs today = $6
b. scarf costs 3 days from now = $3
step-by-step explanation:
1/2 off means you would multiply the amount by 1/2 then subtracta. original price of scarf: $12
12 X 1/2 = 6
12 - 6 = 6
— scarf costs today = $6
do the same thing but this time it is a different numberb. 12 X 3/4 = 9
12 - 9 = 3
— scarf costs 3 days from now = $3
FREE BRAINLIST NEED HELP ASAP
Answer:
A)4.6 yard
Step-by-step explanation:
[tex]x^{2} +10^{2} =11^{2} \\x^{2} =21\\x=\sqrt[2]{21} \\[/tex]
x≅4.6
Hoped I helped, have a nice day!
Find the area of the polygon 2cm 2cm 3cm in square centimeters
Answer:
12sq cm
Step-by-step explanation:
For Area, we do lenth x width x height. Here, the lenth and the width is 2, so we do 2x2 which is 4. Next the height is 3 so we do 4x3 which is 12. There is your answer. Hope it helps!