Sunspots have been observed for many centuries. Records of sunspots from ancient Persian and Chinese astronomers go back thousands of years. Some archaeologists think sunspot activity may somehow be related to prolonged periods of drought in the southwestern United States. Let x be a random variable representing the average number of sunspots observed in a 4-week period. In a random sample of 40 such periods from Spanish colonial times, the sample mean is x¯ = 47.0. Previous studies of sunspot activity during this period indicate that σ = 35. It is thought that for thousands of years, the mean number of sunspots per 4-week period was about µ = 41. Sunspot activity above this level may (or may not) be linked to gradual climate change. Do the data indicate that the mean sunspot activity during the Spanish colonial period was higher than 41? Use α = 0.05. (a) State the appropriate null and alternate hypothesis. (b) Compute the value of test statistic. (c) Using P-value method, state a conclusion.
Answers
Answer:
(a) Null Hypothesis, \(H_0\) : \(\mu\) \(\leq\) 41
Alternate Hypothesis, \(H_A\) : \(\mu\) > 41
(b) The value of z test statistics is 1.08.
(c) We conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.
Step-by-step explanation:
We are given that in a random sample of 40 such periods from Spanish colonial times, the sample mean is x¯ = 47.0. Previous studies of sunspot activity during this period indicate that σ = 35.
It is thought that for thousands of years, the mean number of sunspots per 4-week period was about µ = 41.
Let \(\mu\) = mean sunspot activity during the Spanish colonial period.
(a) Null Hypothesis, \(H_0\) : \(\mu\) \(\leq\) 41 {means that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41}
Alternate Hypothesis, \(H_A\) : \(\mu\) > 41 {means that the mean sunspot activity during the Spanish colonial period was higher than 41}
The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;
T.S. = \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\) ~ N(0,1)
where, \(\bar X\) = sample mean = 47
σ = population standard deviation = 35
n = sample of periods from Spanish colonial times = 40
So, the test statistics = \(\frac{47-41}{\frac{35}{\sqrt{40} } }\)
= 1.08
(b) The value of z test statistics is 1.08.
(c) Now, the P-value of the test statistics is given by;
P-value = P(Z > 1.08) = 1 - P(Z < 1.08)
= 1 - 0.8599 = 0.1401
Since, the P-value of the test statistics is higher than the level of significance as 0.1401 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.
Related Questions
A function and its inverse are shown on the same graph. A function and its inverse are shown on the same graph.
Which statement describes the relationship between the function and its inverse?
The slope of f–1(x) is the same as the slope of f(x).
The slope of f–1(x) is the opposite as the slope of f(x).
The x-intercept of f–1(x) is the same as the y-intercept of f(x).
The x-intercept of f–1(x) is the opposite as the y-intercept of f(x).
Answers
Then the x-intercept of the inverse is the same as the y-intercept of f(x), this means that the correct statement is the third option.
Which statement is the correct one?
On the image, we can see two linear equations, such that the orange one is f(x) and the blue one is the inverse.
If you follow the orange line, you can see that the y-intercept of f(x) is y = 1.If you follow the blue line, you can see that the x-intercept of the inverse is x =1.Then the x-intercept of the inverse is the same as the y-intercept of f(x), this means that the correct statement is the third option.
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A painting attributed to Vermeer (1632-1675), which should contain no more than 96.2% of its original carbon-14, contains 99.3% instead. Using the fact that Carbon-14 has half-life of 5730 years, determine the age of the forgery._____ years old.
Answers
The forgery is approximately 23,878 years old when A painting attributed to Vermeer (1632-1675), which should contain no more than 96.2% of its original carbon-14, contains 99.3% instead.
The half-life of a substance is the time it takes for half of the initial amount of the substance to decay or disintegrate.
The fact that the painting contains 99.3% of its original carbon-14 means that only 0.7% of the original carbon-14 has decayed. We can use the half-life formula to find how long it would take for 0.7% of the carbon-14 to decay:
\(0.007 = (1/2)^{(t/5730)\)
where t is the time in years. Solving for t, we get:
\(t = 5730 * ln(0.007) / ln(0.5) \approx 23877.56\)
Therefore, the forgery is approximately 23,878 years old.
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Erica finds a block of cheese in her
fridge. Originally, the block weighed
126 g, but there is only 60% of it left.
How many 10-g wedges can she cut
from the cheese that is left?
Answers
Answer:
7 wedges
Step-by-step explanation:
=60% of 126g
=60 ÷ 100 × 126g
=75.6g
=75.6 g ÷ 10g
=7.56 = 7 wedges
for each of the number lines, write an absolute value equation in the form |x-c|=d, where c and d are some numbers, to satisfy the given solution set.
Answers
An absolute value is the numerical value of a number without consideration of its sign. It can be represented graphically by a straight line known as a number line. Absolute value equations are equations that include absolute values of variables or unknown quantities. The following are examples of how to write an absolute value equation in the form |x-c|=d to fit the provided solution sets:
Example 1:
Solution set: {x|x≤-3 or x≥1}
Absolute value equation: |x-(-1)|=4
Explanation: -1 is the midpoint of the two ranges (-3 and 1) in the solution set. |x-(-1)|=|x+1| is the absolute value expression for the midpoint -1. The distance d from -1 to the solutions' furthest endpoints, 1 and -3, is four, hence the value of d in the absolute value equation is 4.
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Aryana's hair grows 0.5 cm per month. How long will her hair grow in 5 months? Show using a model and/or box method.
Answers
Answer:
o.5*5=2.5
Step-by-step explanation:
2,5
Answer:
2.5cm
Step-by-step explanation:
0.5 x 5 = 2.5
What's the area of this figure?
Answers
Answer:
58.5
Step-by-step explanation:
the area for a square is l x l so 9
the area for a rectangle is l x w so 33
the area for a rectangle is l x w /2 so 33 /2 = 16,5
so after adding them all up you get 58.5
Jan had 30 dollars saved for a new bike. This was one third of needed to save. how much does the bicycle cost?
Answers
Answer:
90 dollars
Step-by-step explanation:
I did maths hghbhhbghfggghggfgy
Erika's toy is valued at €450. Its value increased by 10% then decreases by 10% the year after. What is the value of Erika's toy after these two changes?
Answers
Answer:
€445.50-------------------------
Initial value of the toy is €450.
After 10% increase the value is:
€450 + 10% = €450*1.1 = €495After further 10% decrease the value becomes:
€495 - 10% = €495*0.9 = €445.50The final value of the toy is €445.50.
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 20 feet. Container B has a diameter of 16 feet and a height of 12 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
Answers
Answer:
After the pumping, Container B is 11.8\%11.8% empty.
Step-by-step explanation:
The volume of water inside Container B equals the entire volume of Container A. The empty portion of Container B is equal to the entire volume of Container B minus the volume of water inside Container B. So the volume of empty space inside Container B is equal to 1570.7963-1385.44241570.7963−1385.4424 which equals 185.3539. The percent of Container B that is empty can be found by setting up a proportion with the entire volume of Container B: 11.8 %
What is the scale factor of Figure B to Figure A?
Answers
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of 2916 with a mean life of 518 minutes.
If the claim is true, in a sample of 81 batteries, what is the probability that the mean battery life would be less than 526.4 minutes? Round your answer to four decimal places.
Answers
The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.
What is probability?The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.
Given:
The variance = 2916,
The mean life of a battery, m = 518 min,
The total number of samples, n = 81
Calculate the probability of a mean battery life of lower than 526.4 minutes by the following formula,
z = x - m / (σ / √ n)
Here, x is the expected value, σ is the deviation, and z is the probability.
Substitute the values,
z = 526.4 - 518 / (54 / √81) [σ = √ variance = √2916 = 54]
z = 1.4
Consult the cumulative standard normal table
P (z < 526.4) = 0.9192,
But we know that
P (z > 526.4) = 1 - P (z < 526.4)
P (z > 526.4) = 1 - 0.9192 = 0.0808
Therefore, The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.
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What is the answer to 11 = x/-5 + 8
Answer Formula: x = ?
Answers
Answer: x=-15
Step-by-step explanation:
11=x/-5+8
minus 8 on both sides
3=x/-5
multiply by -5 on both sides
x=-15
Answer:
x = -15
Step-by-step explanation:
Given: 11 = x/-5 + 8
We need to get x by itself to make a formula or get an answer
Step 1: Subtract 8 on both sides
We need to subtract 8 on both sides in order to cancel out the 8 on the right and bring it to the left
so, 11 -8 = x/-5 +8 -8 = 3 = x/-5
Step 2: Multiply by -5
We need to multiply by -5 in order to cancel our the -5 on the right and bring it to the left
so, 3*-5=x/-5*5 = -15 = x
Therefore, x = -15.
Write your answer anywhere in the open area of each question
1)
The tape diagram models the lengths of two snowboarding trails. The beginner trail is
200 meters long. How long is the expert trail?
Beginner Trail
Expert Trail
The expert trail is
meters long
2)
Answers
The length of the expert trail is 800 meters. We can find our answer by using given tape diagram and simple mathematical calculations.
What is tape diagram?
A tape diagram is a visual model resembling a piece of tape, that is used to assist with the calculations of ratios and addition, subtraction and commonly multiplication.
Here,
Length of the Beginner trail is 200 meters
And also expert trail is 4 times to Beginner trail.
So, Expert trail = 4 * Length of beginner trail.
Expert trail = 4* 200
= 800 meters.
Hence, we get the answer.
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1) Find all the critical numbers of the given function
f(x) = X 1 - 4
-
3
Answers
Answer:
(0,-4)
Step-by-step explanation:
Given
\(f(x) = x^\frac{1}{3} - 4\)
Required
Determine the critical numbers
\(f(x) = x^\frac{1}{3} - 4\)
Differentiate:
\(f'(x) = \frac{1}{3}x^{\frac{1}{3} - 1}\)
\(f'(x) = \frac{1}{3}x^{-\frac{2}{3}}\)
Equate to 0
\(f'(x) = \frac{1}{3}x^{-\frac{2}{3}} = 0\)
\(\frac{1}{3}x^{-\frac{2}{3}} = 0\)
Multiply through by 3
\(3 * \frac{1}{3}x^{-\frac{2}{3}} = 0*3\)
\(x^{-\frac{2}{3}} = 0\)
\(x = 0\)
Substitute 0 for x in \(f(x) = x^\frac{1}{3} - 4\)
\(f(0) = 0^\frac{1}{3} - 4\)
\(f(0) = 0- 4\)
\(f(0) = - 4\)
Hence, the critical point is: (0,-4)
Need the correct answers for this. Can you help me?
Answers
The length of PQ is 3√5 and its slope is -2
The length of SR is 3√5 and its slope is -2
The length of SP is 5√2 and its slope is -7
The length of RQ is 5√2 and its slope is -1
So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.
Understanding QuadrilateralTo find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:
D = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)
and the slope formula:
m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)
1. Length PQ:
Using the distance formula, the length PQ can be calculated as follows:
PQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)
= √((3 - 0)² + (-4 - 2)²)
= √(3² + (-6)²)
= √(9 + 36)
= √45
= 3√5
2. Length SR:
Using the distance formula, the length SR can be calculated as follows:
SR = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)
= √((1 - (-2))² + (-5 - 1)²)
= √((1 + 2)² + (-6)²)
= √(3² + 36)
= √(9 + 36)
= √45
= 3√5
3. Length SP:
Using the distance formula, the length SP can be calculated as follows:
SP = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)
= √((1 - 0)² + (-5 - 2)²)
= √(1² + (-7)²)
= √(1 + 49)
= √50
= 5√2
4. Length RQ:
Using the distance formula, the length RQ can be calculated as follows:
RQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)
= √((-2 - 3)² + (1 - (-4))²)
= √((-2 - 3)² + (1 + 4)²)
= √((-5)² + 5²)
= √(25 + 25)
= √50
= 5√2
Now, let's calculate the slopes of the sides:
1. Slope PQ:
The slope of PQ can be calculated using the slope formula:
m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)
= (-4 - 2) / (3 - 0)
= -6 / 3
= -2
2. Slope SR:
The slope of SR can be calculated using the slope formula:
m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)
= (-5 - 1) / (1 - (-2))
= -6 / 3
= -2
3. Slope SP:
The slope of SP can be calculated using the slope formula:
m =\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)
= (-5 - 2) / (1 - 0)
= -7 / 1
= -7
4. Slope RQ:
The slope of RQ can be calculated using the slope formula:
m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)
= (1 - (-4)) / (-2 - 3)
= 5 / (-5)
= -1
Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:
Length PQ: 3√5
Length SR: 3√5
Length SP: 5√2
Length RQ: 5√2
Slope PQ: -2
Slope SR: -2
Slope SP: -7
Slope RQ: -1
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Sort the angles as acute, right, obtuse, or straight.
Answers
The top angle is right (90 degrees, kinda looks like a bent elbow).
The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).
The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).
4th is acute.
5th is straight because it's a straight line.
6th is also obtuse.
Have a good day :)
1. Find the 8th term of the following linear sequences.
i) 2,4,6,8,...
ii) -7,-4,-1.2- iii)0,-1/2,-1,-1 1/2
iv) 12,5,-2. v) 8,14, 20,...
vi) 63,58, 53, ...
Answers
We know the formula,
t =n =ar
n−1
Here n=8
Common ratio =−2 and first term =a=−6
t =8
=(−6)×(−2)
8−1
t =8
Use this formula
=(−6)×(−2)
7 t= 8
=768
Makesha lost 58.5 pounds in 18 weeks. Find her rate of loss in pounds per week.
Answers
what is 21 5/8% as a decimal
Answers
Answer: 21.625
Step-by-step explanation:
The percentage of 21 (5/8)% in decimal form is 173/800.
We have,
The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying by 100.
The given percentage expression.
21(5/8) %
Divide by 100 to remove the %.
This can be written as,
21(5/8) / 100
Now,
21(5/8)
= (21 x 8 + 5) / 8
Simply the fraction.
= 173/8
Now,
173/8 / 100
Simplify the fraction.
= 173/800
Thus,
The percentage of 21 (5/8)% in decimal form is 173/800.
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A construction uses a protactor and a ruler true or false
Answers
Answer:
True
Step-by-step explanation:
I just did a whole essay about thin in Geometry and I got an A.
Hope this helps! （づ￣3￣）づ╭❤～
Help me please. I don't know what to do or where to start.
Answers
The number of cars in the parking lot at 5 pm is 106.1.
The formula for the number of cars in the parking lot n hours after 3 pm is:
\(A_{n} = 92(1.09)^n\)
where:
\(A_{n}\) is the number of cars in the parking lot n hours after 3 pm
92 is the initial number of cars in the parking lot
1.09 is the growth rate of the number of cars in the parking lot
n is the number of hours after 3 pm
For example, if it is 5 pm, then n = 2. Plugging this value into the formula, we get:
\(A_{5} = 92(1.09)^2\)
\(A_{5} = 106.1\)
Therefore, the number of cars in the parking lot at 5 pm is 106.1.
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The probability that a high school senior wins a prestigious scholarship is 0.13. The probability that a high school senior plays a varsity sport is 0.22 . If the probability that someone plays a varsity sport given that they won the scholarship is 0.55 , then what's the probability that someone wins the scholarship given that they play a varsity sport?
Answers
Answer:
0.325
Step-by-step explanation:
Let A represent the event: winning a prestigious scholarship
Let B represent the event: plays a varsity sport
Given
P(A) = 0.13P(B) = 0.22P(plays a varsity sport given that they won the scholarship)= P(B|A) = 0.55We are asked to find P(wins the scholarship given play a varsity sport) = P(A|B)The formula for conditional probability is
\(P(A|B) = \dfrac{P(A \cap B)}{P(B)}\\\\\\P(B|A) = \dfrac{P(A \cap B)}{P(A)}\)where P(A ∩ B) is the probability of both A and B occurring togetherRewriting the above two equations we get
\(P(A \cap B) = P(A|B)P(B) = P(B|A)P(A)\)
→ \(P(A|B)P(B) = P(B|A)P(A)\)
Plugging in known probabilities,
\(P(A|B) (0.22) = P(0.55)(0.13)\)
\(\begin{aligned}P(A|B) & = \dfrac{0.55 \times 0.13}{ 0.22 }\\& = 0.325\end{aligned}\)
Therefore the probability that someone wins the scholarship given that they play a varsity sport is 0.325
How do we write an equation for the line graphed below?
Answers
The equation for the line graphed is y = 2x + 4
Determine the domain of which the following function is increasing
Answers
Answer:
domain : - ∞ < x < 1
Step-by-step explanation:
the function is increasing on the upward part of the curve. that is
from negative infinity to the vertex at (1, 3 )
domain : - ∞ < x < 1
Estimate the sum -14 1/9 x -2 9/10
Answers
Answer:
ज्ध्ध्द्न्द्
Step-by-step explanation:
क्क्न्क्
A rowing team rowed 60 miles while going with the current in the same amount of time as it took to row 10 miles going against the current. The rate of the
current was 5 miles per hour.
Answers
The rate of the rowing team in still water is: 8.4 mph
How to solve Algebra Word Problems?Algebraic word problems are defined as problems that require converting a sentence into an equation and solving that equation. The equations that need to be written contain only basic arithmetic. and a single variable. Usually in real-life scenarios variables represent unknown quantities.
Let us denote the following:
Rowing boat speed = x mph with no current
Current speed = 6 mph
Speed against current = x - 6 mph
Speed with current = x + 6 mph
Distance against current = 10 miles
Distance with current = 60 miles
Time is:
t = d/r
10 /(x- 6 ) = 60 /(x+ 6 )
10 *(x+ 6 )= 60 *(x- 6 )
10 x + 60 = 60 x -360
10 x -60 x = -360 + -60
-50 x = -420
-420/ -50
x = 8.4 mph
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Complete question is:
A rowing team rowed 60 miles while going with current in the same amount of time as it took to row 10 miles going against the current. The rate of the current was 5 miles per hour. Find the rate of the rowing team in still water.
What’s the answer to If =3+23
, what is
when =1
and =2
?
Answers
The value of y when a = 1 and b = 2 is 22.
How to solve an equation?The equation of can be solved as follows: We will substitute the value of a and b in the equation to find the value of y.
Therefore,
y = 3ab + 2b³
Let's find y when a = 1 and b = 2
Hence,
y = 3(1)(2) + 2(2)³
y = 6 + 2(8)
y = 22
Therefore,
y = 22
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Find the distance between point P and line L
Answers
The distance between point P and line L is 16/9√(13).
To find the distance between point P and line L, we can use the formula for the distance between a point and a line in two-dimensional space. The formula is as follows:
Let P = (x1, y1) be the point and L be the line ax + by + c = 0. Then the distance between P and L is:
|ax1 + by1 + c|/√(a² + b²)
To find a, b, and c for the given line, we need to put it in slope-intercept form y = mx + b by solving for y.
2x - 3y = 12=> 2x - 12 = 3y=> (2/3)x - 4 = y
The slope of the line, m, is the coefficient of x, which is 2/3. Therefore, the line is:
y = (2/3)x - 4The values of a, b, and c are: a = 2/3b = -1c = -4
Now we can substitute the coordinates of P and the values of a, b, and c into the formula for the distance between a point and a line.
Let P = (3, 5).|a(3) + b(5) + c|/√(a² + b²)= |(2/3)(3) - 1(5) - 4|/√[(2/3)² + (-1)²]= |-4/3 - 4|/√(4/9 + 1)= 16/9√(13).
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Help and i will give brainliest no links 5/9−(−3 1/3) (the pics just for fun)
Answers
Answer:
3.88888888889
Step-by-step explanation:
Conversion a mixed number -3 1/3
to a improper fraction: -3 1/3 = -3 1/3= -3 · 3 + (-1)/3= -9 + (-1)/3 = -10/3
To find a new numerator:
a) Multiply the whole number -3 by the denominator 3. Whole number -3 equally -3 * 3/3 = -9/3
b) Add the answer from previous step -9 to the numerator 1. New numerator is -9 + 1 = -8
c) Write a previous answer (new numerator -8) over the denominator 3.
Minus three and one third is minus eight thirds
Subtract: 5/9- (-10/3) = 5/9- (-10) · 3/
3 · 3 = 5/9 - (-30/9) = 5 - (-30)/9 = 35/9
The perimeter of the triangle below is 54 units. Find the value of y.
Answers
Answer:
y = 7
Step-by-step explanation:
3y + (y+1) + (4y-3) = 54
3y + y + 4y + 1 - 3 = 54
8y - 2 = 54
8y = 54 + 2
8y = 56
y = 56/8
y = 7
Check:
3*7 + (7+1) + ((4*7)-3) = 54
21 + 8 + 28-3 = 54
29 + 25 = 54