Answer:
We conclude that the true average lifetime is smaller than what is advertised.
Step-by-step explanation:
The complete question is: Light bulbs of a certain type are advertised as having an average lifetime of 800 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 21 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using SPSS, resulting in the accompanying output.
Sample Mean Sample Standard Deviation
Lifetime 738.44 38.30
Test the appropriate hypothesis for this study (i.e., state the hypotheses, compute the test statistics, compute the p-value, and make a conclusion). What conclusion would be appropriate for a significance level of 0.05?
We are given that Light bulbs of a certain type are advertised as having an average lifetime of 800 hours.
A potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised.
Let [tex]\mu[/tex] = true average lifetime of the light bulbs.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 800 hours {means that the true average lifetime is greater than or equal to what is advertised}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 800 hours {means that the true average lifetime is smaller than what is advertised}
The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean lifetime = 738.44 hours
s = sample standard deviation = 38.30 hours
n = sample of bulbs = 21
So, the test statistics = [tex]\frac{738.44-800}{\frac{38.30}{\sqrt{21} } }[/tex] ~ [tex]t_2_0[/tex]
= -7.36
The value of t-test statistics is -7.36.
Also, the P-value of test-statistics is given by;
P-value = P([tex]t_2_0[/tex] < -7.36) = Less than 0.05% {from t-table}
Since the P-value of our test statistics is less than the level of significance of 0.05, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the true average lifetime is smaller than what is advertised.
In the figure points A B C D and E are collinear. If AE = 38 and BD = 15
Answer:
D. 30.5
Step-by-step explanation:
Given that A, B, C, D, and E are collinear,
AE = 38,
BD = 15, since segment BC = CD = DE, therefore
BD = ⅔ of BE
15 = ⅔*BE (substitution)
Solve for BE
Multiply each side by 3
15*3 = ⅔*BE*3
45 = 2*BE
Divide both sides by 2
45/2 = BE
22.5 = BE
BE = 22.5
Find AB:
AB + BE = AE (segment addition postulate)
AB + 22.5 = 38 (Substitution)
AB = 38 - 22.5 (Subtracting 22.5 from each side)
AB = 15.5
Find length of segment AD:
AB + BD = AD (segment addition postulate)
15.5 + 15 = AD (Substitution)
30.5 = AD
AD = 30.5
I need help! Please. Justify answer using Intermediate value theorem (IVT)
Step-by-step explanation:
N(t) is continuous at t = 6, so f(6) = 25(6) + 150 = 300.
f(0) = 80.
f(t) is continuous, so by Intermediate Value Theorem, f(t) must equal 250 at some point between t=0 and t=6.
A machine was able to make 32 bags of Hot Cheetos in 8 seconds. What is
the rate made per second? *
Answer: 32÷8=4
Please brainliest
Solve for x
X + 2w = m
Answer:
X = m - 2w
Step-by-step explanation:
just isolate the variable.
Answer:
x=m-2w
Step-by-step explanation:
Just take the +2w to the other side where it becomes negative.
On a road map, the locations A, B and C are collinear. Location C divides the road from location A to B, such that AC:CB = 1:2. If location A is at (5,16) and location C is at (3,10). Find the coordinates of location B. A. (1,4) B. (4,13) C. (-1,-2)
Answer:
C. (-1,-2)
Step-by-step explanation:
Since C internally divides AB in the ratio AC/CB = 1/2 = m/n where m = 1 and n = 2, we use the formula for internal division.
Let A = (x₁, y₁) = (5, 16), B = (x₂, y₂) and C = (x, y) = (3, 10)
So x = (mx₂ + nx₁)/(m + n)
y = (my₂ + ny₁)/(m + n)
Substituting the values of the coordinates, we have
x = (mx₂ + nx₁)/(m + n)
3 = (1 × x₂ + 2 × 5)/(2 + 1)
3 = (x₂ + 10)/3
multiplying through by 3, we have
9 = x₂ + 10
x₂ = 9 - 10
x₂ = -1
y = (my₂ + ny₁)/(m + n)
10 = (1 × y₂ + 2 × 16)/(2 + 1)
10 = (x₂ + 32)/3
multiplying through by 3, we have
30 = y₂ + 32
y₂ = 30 - 32
y₂ = -2
So, the coordinates of B are (-1, -2)
What is the solution to the equation 1 + 3x = -13 + 5x? Convert your answer to a decimal, if necessary.
Answer:
x=7
Step-by-step explanation:
[tex]1 + 3x = - 13 + 5x[/tex]
Collect like terms and simplify
[tex]3x - 5x = - 13 - 1 \\ - 2x = - 14[/tex]
Divide both sides of the equation by -2
[tex] \frac{ - 2x}{ - 2} = \frac{ - 14}{ - 2} [/tex]
Simplify
[tex]x = 7[/tex]
Answer:
Step-by-step explanation:
1 + 3x = 5x - 13
-2x + 1 = -13
-2x = -14
x = 7
is 5(a + b) and (a + b)5 equal?
Answer:
yes totally
Step-by-step explanation:
5a+5b=5a+5b
McCoy Brothers manufactures and sells two products, A and Z in the ratio of 5:2. Product A sells for $86; Z sells for $124. Variable costs for product A are $45; for Z $49. Fixed costs are $429,500. Compute the contribution margin per composite unit.
Answer:
the contribution margin per composite unit is $365
Step-by-step explanation:
The computation of the contribution margin per composite unit is shown below:
= Contribution margin per unit for product A × ratio of A + Contribution margin per unit for product B × ratio of B
= ($86 - $45) × 5 + ($124 - $49) × 2
= $205 + $160
= $365
Hence the contribution margin per composite unit is $365
simplify
4( 2u - 2) - 3(u + 5)
Answer:
5u - 23
Step-by-step explanation:
Answer:
4( 2u - 2) - 3(u + 5)
(4*2u + 4*-2)-(3*u + 3*5)
8u-8-3u+15
8u-3u-8+15
5u+7
Step-by-step explanation:
I hope this helped you.
Please mark Brainliest.
Have a great day!!!!!!!!!
2. Kevin drives to the pizza place for lunch.
He walks 5 km east, then 5 km south, then 5
km east again.
Distance:
Displacement:
Answer: Distance = 15km ; Displacement ≅ 11'2km
Step-by-step explanation:
In Physics when we speak of distance we refer to the space traveled that is always measured on the trajectory, while displacement refers to the space from an initial position to a final position regardless of the path. When the path is a straight line, the space traveled is equal to the module of the displacement.
Distance: 5km + 5km + 5km = 15km (Red lines)
Displacement² : (10km)² + (5km)² = 100km² + 25km² = 125km²
Displacement : √125km² ≅ 11'2km (Blue line)
(See attached image)SpymoreP(t) = 520/1+5e^-0.2t
Find the initial population size
An artist makes a scale drawing of a parallelogram-shaped sculpture. The scale is 10 cm on the drawing for every 8 meters on the sculpture. What is the area of the scale drawing? Show your work.
Answer:
Area of drawing= 0.315 m²
Step-by-step explanation:
Base = 6m
Height = 4.2 m
Area = height* base
Area= 4.2*6
Area= 25.2 m²
The scale is 10 cm on the drawing for every 8 meters on the sculpture.
Which is 10 cm to 800 cm
Or
0.1m to 8m
Arra of sculpture= 25.2 m²
area of drawing= (25.2*0.1)/8
Area of drawing= 0.315 m²
A product costs $70 today, how much will the product cost in t days if the price is reduced by $5 a day
Answer:
P ($)=70-5(t)
Where p = price at t days
t = number of days
Step-by-step explanation:
The product price initially = $70
Now, every day , it reduces $5
The rate=$5 per day reduction
The price in the days will be determined by the formula below
P ($)=70-5(t)
Where p = price at t days
t = number of days
So let's assume it's on the second day
The price after the second day
P($) = 70-5(2)
P($) = 70-10
P($)= $60
The price after two days will be reduced to $60
Rachael gets 94 marks in her exams.these are 47% of the total marks.find the maximum number of mark
Answer:
200 is the maximum amount
Step-by-step explanation:
94x100=9400
9400/47=200
can i have brainliest?
bfnskalalalallsmsmsm help
Answer:
x>18
Step-by-step explanation:
Simplify 200xyz3 .
Simplify the Integer part of the SQRT
Step-by-step explanation:
Factor 200 into its prime factors
200 = 23 • 52
Question
of 27
Which of the following shows an element of the sample space for first
tossing a coin and then rolling a number cube?
Α.Τ, Η
B. T, 2
C. 6,1
D. 4, H
The sample space for first tossing a coin and then rolling a number cube is (T, 2).
What are Outcomes of Probability?An outcome is a possible result of an experiment or trial in probability theory. Each experiment's possible outcomes are distinct, and alternative outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment).
As, the outcomes for tossing a coin is Head (H) and Tail (T).
and, the outcome for rolling a die
{1, 2, 3, 4, 5, 6}.
So, the sample space for first tossing a coin and then rolling a number cube
= ( T, 2)
Learn more about Outcome of Probability here:
https://brainly.com/question/30661698
#SPJ5
What is the value of 30-2(7+2)-1?
O 11
0 14
017
019
PLS HELP! 10 POINTD ILL MARK BRAINLIEST
l=3w
3w(4)=48
12w=48
w=4
l=12
hope it helps
comment if u have any questions
Answer:
Length is 18; width is 6.
Step-by-step explanation:
The formula for the perimeter of a rectangle is:
[tex]P=2l+2w[/tex]
We are given that the perimeter is 48 feet. We are also told that the length is 3 times the width. In other words:
[tex]l=3w[/tex]
So, substitute this for l and 48 for P. Thus:
[tex]48=2(3w)+2w[/tex]
Distribute:
[tex]48=6w+2w[/tex]
Combine like terms:
[tex]48=8w[/tex]
Divide both sides by 8:
[tex]w=6[/tex]
So, the width is 6.
The length as we know is 3 times the width, so the length is 3(6) is 18.
And we are done!
this is easy but im hella lazy and dont feel like doing this pls help me, i mark brainliest! ty ❤️
Answer:
D. It is a decimal that terminates after 3 decimal places
I hope this helps!
Select the correct answer.
Angela uses 3 cup of strawberries to make 6 of a liter of smoothie. What is the unit rate in cups of strawberries per liter of smoothie?
OA. cups per liter
B. cups per liter
OC. cups per liter
OD. cups per liter
If there are 3 cups of strawberries per 6 liters of smoothie, that means that there is [tex]\frac{1}{2}[/tex] cups of strawberries per liter of smoothie.
[tex]\frac{3}{6}=\frac{1}{2}[/tex]
Hope this helps.
頑張って!
What is the common ratio of the Fibonacci sequence called
Answer:
1.618
The Fibonacci sequence is significant because of the so-called golden ratio of 1.618, or its inverse 0.618. In the Fibonacci sequence, any given number is approximately 1.618 times the preceding number, ignoring the first few numbers.
Step-by-step explanation:
Plz Mark me as brainliest
[tex]\Large \boxed{\sf golden \ ratio}[/tex]
A series of integers known as the Fibonacci sequence begins with a zero, is followed by a one, another one, and then a series of increasing numbers. Each number in the series equals the sum of the two numbers before it. Every succeeding pair of Fibonacci numbers has a quotient resembling the golden ratio.
I need help with this please
Answer:
C
Step-by-step explanation:
Help I am stuck on this.
Answer:
i think is the second one
Step-by-step explanation:
solve the equation
[tex] 5 = \frac{z}{4} - 3[/tex]
Answer:
z=32Step-by-step explanation:
[tex]5=\frac{z}{4}-3[/tex]
[tex]\frac{z}{4}-3=5[/tex]
[tex]\frac{z}{4}=5+3[/tex]
[tex]\frac{z}{4}=8[/tex]
[tex]z=8\cdot \:4[/tex]
[tex]z=32[/tex]
what is the slope and the g intercept ? ( i added the picture )
Step-by-step explanation:
A straight line graph is of the form:
y = mx+b
So we get our equation in this form:
9=2x+3y
or, 9-2x=3y
or, -2x+9 = 3y
or, y= (-2x+9)/3
or, y = -2/3x + 3
So,
Slope(m)=−2/3
y-intercept (b) = 3
Therefore, slope(m) is -2/3x and y-intercept(b) is 3.
*
True or False? Natural Numbers are closed under division.
Answer: False
Natural numbers are not closed under division
Some natural numbers divide to get another natural number. For example, divide 10 over 2 to get 10/2 = 5.
However, there are infinitely many natural numbers that divide to get something that isn't a natural number. Example: 10/7 = 1.43 approximately. All we need is one counterexample to contradict the original statement.
A set is considered closed under division if dividing any two values in that set leads to another value in the set. More formally, if a & b are in some set then a/b must also be in the same set for that set to be closed under division.
If we changed "natural numbers" to "rational numbers", then that set is closed under division. If p, q are rational numbers then p/q is also rational. Basically, dividing any two fraction leads to some other fraction. The value of q cannot be zero.
41 2/3 divined by 4 1/4
Answer:
Exact form: [tex]9 \frac{41}{51}[/tex]
Decimal form: [tex]9.80392156[/tex]
Step-by-step explanation:
[tex]41\frac{2}{3}[/tex] ÷ [tex]4\frac{1}{4}[/tex]
Let's put everything into a fraction.
[tex]\frac{41\frac{2}{3} }{4\frac{1}{4} }[/tex]
Now we have an answer.
Exact form: [tex]9\frac{41}{51}[/tex]
Decimal form: [tex]9.80392156[/tex]
Hope this helps!
E Solve for x 6(x - 1) = 9(x + 2) x = -8 x= 3 x = 8
Answer:
x = -8
Step-by-step explanation:
[tex]6(x - 1) = 9(x + 2)[/tex]
Expand :
[tex]6(x - 1) = 6x - 6 \\ 9(x + 2) = 9x + 18[/tex]
[tex]6x - 6 = 9x + 18[/tex]
Collect like terms and simplify
[tex]6x - 9x = 18 + 6 \\ - 3x = 24[/tex]
Divide both sides of the equation by -3
[tex] \frac{ - 3x}{ - 3} = \frac{24}{ - 3} \\ x = - 8[/tex]
Answer:
Step-by-step explanation:
6x - 6 = 9x + 18
-3x - 6 = 18
-3x = 24
x = -8 is the solution
Dimensional analysis. How many seconds are in a year?
Answer:
31536000
Step-by-step explanation:
365 days x 24 hours x 60 minutes x 60 seconds = 31536000