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.
Answer:
(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 41
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 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 [tex]\mu[/tex] = mean sunspot activity during the Spanish colonial period.
(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 41 {means that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 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. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean = 47
σ = population standard deviation = 35
n = sample of periods from Spanish colonial times = 40
So, the test statistics = [tex]\frac{47-41}{\frac{35}{\sqrt{40} } }[/tex]
= 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.
20 points
April’s garden has 42 plants in each row. She has 2 rows of yellow corn and 20 rows of white corn.
SHOW how much yellow corn and white corn has been planted in the garden.
Please answer using complete sentences. Use of diagrams, tables, or charts will increase grade. Be sure to show your expressions and or equations in your explanation.
Answer:
Yellow corns = 84
White corns = 840
Step-by-step explanation:
We are given the following details:
Number of plants in each row = 42
Number of rows of yellow corn = 2
Number of rows of white corn = 20
To count the number of yellow corns planted, we can add the number 42, 2 number of times i.e.
42 + 42 = 84 .
OR
We can multiply 42 by 2 i.e. 42[tex]\times[/tex] 2 = 84
To count the number of white corns planted, we can add the number 42, 20 number of times i.e.
42 + 42+ 42+ 42+ 42 ..... + 42 (20 times ) .
OR
We can multiply 42 by 20 i.e. 42[tex]\times[/tex] 20 = 84
In other words, the formula can be seen as:
Number of corns of one type = Number of plants in a row [tex]\times[/tex] Number of rows of one type
So, number of white corns = 42 [tex]\times[/tex] 20 = 840
Hence, the answer is:
Yellow corns = 84
White corns = 840
What’s the correct answer for this?
The square root of 10 is a number with the following property: when you square it, you get 10.
So, if we have [tex]a<\sqrt{10}<b[/tex], where [tex]a[/tex] and [tex]b[/tex] are positive integers, if we square the whole inequality we have
[tex]a^2<10<b^2[/tex]
Let's analyse option A for example. Given everything we said so far, we would have
[tex]1<\sqrt{10}<2 \iff 1^2<10<2^2 \iff 1<10<4[/tex]
which is false.
Option B is again false, because we would have
[tex]2<\sqrt{10}<3 \iff 2^2<10<3^2 \iff 4<10<9[/tex]
which is again false. Keep trying with options C and D following those same steps, and see which one is correct
Answer:
C
Step-by-step explanation:
√10=3.16
3.16 is between 3 and 4 hence C is the answer
PLZZ HELP
Graph the function f(x)=x^2-4x-12 on the coordinate plane.
A)What are the x-intercepts
B)What is the y-intercept?
C)What is the vertex?
Answer:
A) (-2,0) and (6,0)
B) (0,-12)
C) (2,-16)
Step-by-step explanation:
In the graph you see below, you can tell that the two x intercepts are at (-2,0) and (6,0), while the y intercept is at (0,-12). You can also see that the vertex is at (2,-16). Hope this helps!
The x intercept will be ( -2,0 ) and ( 6,0 ) , y intercept will be ( 0, -12 ) and vertex will be at ( 2 , -16 ).
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
Given the function,
f(x)=x²-4x-12
A) x-intercept;
For the x-intercept, the value of y or f(x) will be 0 so.
0 = x² -4x -12 ⇒ x = -2 , 6
So
x-intercept will be ( -2,0 ) and ( 6,0 ).
B) y-intercept
At the y-intercept the value of x will be 0 so
f(x) = -12
So
The y-intercept will be ( 0, -12 ).
C) Vertex
For vertex the slope will be 0 so
f'(x) = 0 ⇒ 2x - 4 = 0 ⇒ x = 2
The value of y at x = 2 will be
f(2) = -16
so
vertex will be at ( 2, -16 ).
For more about the function
brainly.com/question/23712366
#SPJ2
What is the next step after using the distributive
property?
Answer:
If it's a simple equation such as 2 (x + y), the next step after applying the distributive property is to do the multiplication and simplify the terms.
But in solving an equation such as
2(x + 3) = 3(x + 1)
After applying the distributive property, the next step is to separate the variables to one side, like collecting like terms and then solving the now simplified equation.
Step-by-step explanation:
For a normal equation, the distributive property, also called the distributive law of division and multiplication helps to use the variable outside the bracket to multiply the sum of terms in the bracket. For example.
2 (x + y)
The distributive property enables us to say
2×x + 2×y = 2x + 2y
So, the next step after applying the distributive property is to simplify the equation.
But in solving an equation such as
2(x + 3) = 3(x + 1)
Applying the distributive property
2x + 6 = 3x + 3
We then operate variables, collect like terms on one side
6 - 3 = 3x - 2x
3 = x
x = 3
Hope this Helps!!!
Answer:
-102 + (-25.5)
Step-by-step explanation:
Express this number in stand
5.401 x 10-1 = ?
Answer:
0.5401
Step-by-step explanation:
In Standard form
due to the negativity of the power, you move the decimal point to the left...and u move it once
Given the function f(x)= x^2-7 and g(x) = 2x-x^3 what is the value of f(g(2))
Answer:
9
Step-by-step explanation:
First lets find g(2) because thats inside the f equation.
g(x) = 2x-x^3
g(2) = 2(2) - (2)^3
g(2) = 4 - 8
g(2) = - 4
So now we are finding
f(g(2)) => f(-4)
f(x) = x^2 - 7
f(-4) = (-4)^2 - 7
Remember, because the square is outside the parentheses due to us plugging in a value, it becomes positive
f(-4) = 16 - 7
f(-4) = 9
What’s the correct answer for this?
Answer:
A = 13.0
Step-by-step explanation:
In the attached file
PLZ SOMEONE ANSWER QUICK, A packing company is in the planning stages of creating a rectangular prism box that includes a three-dimensional diagonal support inside the box. The box has a width of 5 feet, a length of 6 feet, and a height of 8 feet. To the nearest tenth, how long is the diagonal support?
Answer:
I think it’s 240
Step-by-step explanation:
Hope this helps
Answer:
approx. 11.18 ft.
Step-by-step explanation:
formula: d=√L²+W²+H²
d=√5²+6²+8²
5²+6²+8²=125
√125 ≈ 11.18 ft
d(diagonal)= 11.18ft
Graph the line with slope 1/2 passing through the poin
Answer:
See explanation below.
Step-by-step explanation:
To make use of the tools they give you, start at the point (-5, -2) which you know is a point the line goes through, then draw a line that goes towards the right following the rule given by the slope "1/2" (rise/run) which means that every 2 units to the right, you go one unit up. so from the point -5 in x, you go to the point -3 in x, and from -2 in y you move up one unit to -1
Therefore the line joins (-5, -2) to the point (-3, -1)
6. At Shimla, temperature was -1 degree Centigrade on Saturday and rose 2 po
by 3 degree Centigrade on Sunday. What was the temperature on Sunday?
O a) 2 degree centigrade
b) -2 degree centigrade
Oc) 3 degree centigrade
O d) -4 degree centigrade
Answer:
Step-by-step explanation:
Make sure that all words are spelled correctly.
Try different keywords.
Try more general keywords.
Try fewer keywords.
Please Help Marshmello.
Answer:
its A bc 9 x 2 = 18 -2 =16
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
there are two identical fridges for desserts. one of the fridge has 5/8 of its room left and the other fridge is only 1/8 full. how much room is left?
Answer:
1.5
Step-by-step explanation:
5/8 + 7/8= 1.5 or 1 1/2
Answer:
Read below.
Step-by-step explanation:
First fridge: [tex]\frac{8}{8} -\frac{5}{8} =\frac{3}{8}[/tex]
Second fridge: [tex]\frac{8}{8} -\frac{1}{8} =\frac{7}{8}[/tex]
[tex]\frac{7}{8} +\frac{3}{8} = \frac{10}{8} = 1 \frac{2}{8}=1\frac{1}{4}[/tex]
Combined [tex]1 \frac{1}{4}[/tex] fridge space is left.
What does the term human capital refer to?
Answer:
its a captial of humans
Step-by-step explanation:
Answer: knowledge
Step-by-step explanation:
Human capital is a loose term that refers to knowledge, experience and skills of an employee. ... It states that companies have an incentive to seek productive human capital and to add to the human capital of their existing employees.
The circle shown below has a diameter of 18 centimeters. What is the
approximate area of the shaded sector?
A. 763 cm2
B. 509 cm2
C. 212 cm2
D. 191 cm2
Answer:
191cm^2
Step-by-step explanation:
What does Markup meaning
Answer:
the amount added to the cost price of goods to cover overhead and profit.
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
Meaning in my own words: The amount applied to the depreciation and production factor price of the product.
Example: Sells for $126 costs $100. Price is increase.
Synonyms for markup: increase, Profit
Hope this helps.
pls check the attachment thank you
What is the slope of the line shown below?
Answer:
6/5
Step-by-step explanation:
slope: (y1-y2)/(x1-x2)
(11-(-1))/(5-(-5))= 12/10 = 6/5
Ariana wants to buy sunglasses
that cost $20 the regular sales tax is 5% how much money in dollars is the sales
To find the total multiply the sale price by 1 + tax rate.
Total = 20 x 1.05
Total = $21.00
given that sin theta= 1/4, 0 is less than theta but less than pi/2, what is the exact value of cos theta
Answer:
[tex]\cos{\theta} = \frac{\sqrt{15}}{4}[/tex]
Step-by-step explanation:
For any angle [tex]\theta[/tex], we have that:
[tex](\sin{\theta})^{2} + (\cos{\theta})^{2} = 1[/tex]
Quadrant:
[tex]0 \leq \theta \leq \frac{\pi}{2}[/tex] means that [tex]\theta[/tex] is in the first quadrant. This means that both the sine and the cosine have positive values.
Find the cosine:
[tex](\sin{\theta})^{2} + (\cos{\theta})^{2} = 1[/tex]
[tex](\frac{1}{4})^{2} + (\cos{\theta})^{2} = 1[/tex]
[tex]\frac{1}{16} + (\cos{\theta})^{2} = 1[/tex]
[tex](\cos{\theta})^{2} = 1 - \frac{1}{16}[/tex]
[tex](\cos{\theta})^{2} = \frac{16-1}{16}[/tex]
[tex](\cos{\theta})^{2} = \frac{15}{16}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{15}{16}}[/tex]
Since the angle is in the first quadrant, the cosine is positive.
[tex]\cos{\theta} = \frac{\sqrt{15}}{4}[/tex]
Answer:
b.[tex]\frac{\sqrt{15} }{4}[/tex]
Step-by-step explanation:
Kensie has started a part-time job in order to save money for college. She plans to earn $800 per
month. Kensie and her mom decide to create a budget, as shown below. Which of the statements
does not represent the budget?
CATEGORY
AMOUNT
College Savings
Cell Phone Bill
Entertainment
$600
$80
$120
Kensie will save 75% of her income towards college each month
Kensie will use 10% of her income towards her cell phone bill each month.
Exactly 85% of her income will go towards college savings and entertainment
Exactly 15% of her income will go towards entertainment
Answer:
Exactly 85% of her income will go towards college savings and entertainment
Step-by-step explanation:
Kensie's college savings are 600/800×100% = 75% of her budget.
Kensie's cell phone bill is 80/800×100% = 10% of her budget.
Kensie's entertainment is 120/800×100% = 15% of her budget.
Her total of savings and entertainment is 75% +15% = 90% of her budget. Savings and entertainment do not total 85% of Kensie's budget.
please help with this
Answer:
x^2 +8x+12
Step-by-step explanation:
The area of the blue is
x*x = x^2
The area of the pink is
x*6 = 6x
The area of the green is
x*2 = 2x
The area of the orange is 2*6 =12
Add them together
x^2 + 6x+2x +12
Combine like terms
x^2 +8x+12
P-20 =30 as a additon equation
Answer:
50
Step-by-step explanation:
[tex]p - 20 = 30 \\ adding \: 20 \: both \: sides \\ p - 20 + 20 = 30 + 20 \\ p = 50[/tex]
Answer:
50
Step-by-step explanation:
50-20=30
What is a scale factor
Answer:
To find the scale factor, locate two corresponding sides, one on each figure. Write the ratio of one length to the other to find the scale factor from one figure to the other.
Step-by-step explanation:
XYUV=123=4
The scale Factor is 4!
Now this is Part B. The second part of the equation. If you answer this right you will win Brainliest. Don’t tell me what you think the answer is and if you can’t see zoom in, don’t answer the question saying you can’t seem.
Answer:
We can replace the 'm' with the value of 'm' on the table to get the value of 't'.
Using the equation [tex]t=0.5m+15[/tex] from the first part of the question to complete the table:
When 'm' equals 5:[tex]t=0.5(5)+15\\\rightarrow 0.5*5 = 2.5\\t=2.5 + 15\\t=17.5[/tex]
When 'm' is 10:[tex]t=0.5(10)+15\\\rightarrow 10 * 0.5 =5\\t = 5+15\\t=20[/tex]When 'm' is 15:[tex]t=0.5(15)+15\\\rightarrow 0.5 * 15 = 7.5\\t=7.5+15\\t=22.5[/tex]
When 'm' is 20:[tex]t=0.5(20)+15\\\rightarrow 0.5*20=10\\t=10+15\\t=25[/tex]Hope this helps.
ashley drove to her father's house, which was 164 miles away. It took her 2 hours to get there. After seeing her father for 2 hours, she went to her cousin's house to stay overnight, which was 125 miles from her father's house. How many minutes does it take Ashley to get to her cousin's if she drives the same speed as when she went to her father's? Do not include units in your answer and round to the nearest hundredth. Example, if answer is 19.546 minutes, put 19.55.
Answer:
Time Spent = 91.46 minutes
Step-by-step explanation:
Given
To Her Father's house
Distance = 164 miles
Time Taken = 2 hours
To Her Cousin's house
Distance = 125 miles
Required
Time Taken to get to her cousins house.
First, her average speed to her father's house needs to be calculated.
Speed is calculated as thus;
[tex]Speed = \frac{Distance}{Time}[/tex]
In this case, Distance = 164 miles and Time = 2 hours
Substitute these values;
[tex]Speed = \frac{164 miles}{2 hours}[/tex]
[tex]Speed = 82miles/hour[/tex]
It's stated in the question that; she maintains the same speed when going to her cousin's residence to spend the night;
Using the same formula for speed;
[tex]Speed = \frac{Distance}{Time}[/tex]
But in this case, Speed = 82 miles/hour and Distance = 125 miles
Substitute these values
[tex]82 = \frac{125}{Time}[/tex]
Multiply both sides by Time
[tex]82 * Time = \frac{125}{Time} * Time[/tex]
[tex]82 * Time = 125[/tex]
Divide both sides by 82
[tex]\frac{82 * Time}{82} = \frac{125}{82}[/tex]
[tex]Time = \frac{125}{82} hours[/tex]
To convert this time to minutes
If 1 hour = 60 minutes
Then,
[tex]\frac{125}{82} hours[/tex] is equivalent to [tex]\frac{125}{82} * 60 minutes[/tex]
Hence,
[tex]Time = \frac{125}{82} * 60 minutes[/tex]
[tex]Time = 91.463415 minutes[/tex]
[tex]Time = 91.46 minutes[/tex] (Approximated)
Hence, she spends 91.46 minutes to get to her cousin's place from her father's house
7 less then four times M expression
Answer:
If you were to write that in an expression it would be 4m-7
Step-by-step explanation:
I think this is what you're looking for...hope it helps :)
What is the constant proportionality y/x
Answer:
The constant of proportionality is k
Step-by-step explanation:
The sum of the first 12 terms of a geometric sequence with 10 as the first term and a common ratio of 0.3 is __________.
Answer: 14.2638366937
Step-by-step explanation:
A geometric sequence is a sequence in which each term is multiplied by a number, called the common ratio, to get the next term.
So, if the first term of the geometric sequence is 10 and the common ratio is 0.3, the sequence would be 10, 0.3(10), 0.3 x 0.3 x 10... and so forth. This becomes:
10, 3, 0.9, 0.27, 0.081, 0.00243, 0.00729, 0.002187, 0.0006561, 0.00019683, 0.000059049, 0.0000177147...
You add these first 12 terms to get 14.2638366937.
Maricopa's Success scholarship fund receives a gift of $ 150000. The money is invested in stocks, bonds, and CDs. CDs pay 6 % interest, bonds pay 2.2 % interest, and stocks pay 11.7 % interest. Maricopa Success invests $ 15000 more in bonds than in CDs. If the annual income from the investments is $ 10805 , how much was invested in each account?
Maricopa Success invested _____ in stocks.
Maricopa Success invested _____ in bonds.
Maricopa Success invested _____ in CDs.
Answer:
$65,000 , $50,000 and $35,000
Step-by-step explanation:
Lets us assume the CDs be C, stocks be S and Bonds be B
Given that
Total scholarship fund received = $150,000
i.e
C + S + B = $150,000 ......................... (1)
Now the each items invested percentage is given
And, the annual income from investment is $10,805
So, the next equation is
0.06C + 0.022B + 0.117S = $10,805 ....................... (2)
And, it is mentioned that
The $15,000 more in bonds than in CDs
B = C + $15,000 ........................ (3)
Now put the equation 3 in equation C is
2C + S = $135,000 ........................... (4)
0.082C + 0.117S = $10,475 ........................... (5)
Now multiply the 0.117S in equation 4
So
0.234C + 0.117S = $15,795
0.082C + 0.117S = $10,475
After solving this
0.152C = $5,320
C = CDS = $35,000
So
B = $35,000 + $15,000
B= Bonds = $50,000
And S = Stock = $65,000
Answer:
CDs = 35000, Bonds = 50000, Stock = 65000
Step-by-step explanation:
Let amount invested in : CDs be 'C' , stock be 'S' , bonds be 'B'
As per total funds : C + B + S = 150000 [E1]
As per interest rates : 0.06C + 0.022B + 0.117S = 10805 [E2]
Given (15000 more invested in bonds than CDs : B = C + 15000 [E3]
Putting equations : [E3] in [E2] & [E1]
C + (C+15000) + S = 150000 → 2C + 15000 + S = 150000
2C + S = 135000 [E4]0.06C+0.022(C+15000)+0.117S = 10805 → 0.06C+0.022C+330+0.117S = 10805
0.082C + 0.117S + 330 = 10805 → 0.082C + 0.117S = 10475 [E5]By putting value of S from [E4] in [E5] :
0.082C + 0.117 (135000 - 2C) = 10475 → 0.082C + 15795 - 0.234C = 10475
5320 = 0.152C → C = 5320 / 0.152 = 35000 [CDs]
B = C + 15000 = 35000 + 15000 = 50000 [Bonds]
By [E1]: 35000+50000+S = 150000 → S = 150000 - 85000 = 65000 [Stocks]