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.
Una pregunta porque ella no me ama ? :,v
Answer: Porque no te merecen
Step-by-step explanation:
Which is the simplified form of -7+5-12?
Answer:
[tex] - 14[/tex]
Step-by-step explanation:
[tex] - 7 + 5 - 12 \\ ( - 7 + 5) - 12 \\ - 2 - 12 \\ = - 14[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
So the right answer is -14.
Look at the attached picture
Hope it will help you
Good luck on your assignment
two solutions of salt water contain 0.1% and 0.22% salt respectively. A lab technician wants to make 1 liter of solution which contains 0.19% salt. How much of each solution should she use?
Answer:
0.25 L at 0.1% and 0.75 L at 0.22%
Step-by-step explanation:
We have to:
percent quantity
Salt solution # 1 0.1 x L
Salt solution # 2 0.22 (1 - x) L
Mixture 0.19% 1
We are left with the following equation:
0.1 * x + 0.22 * (1-x) = 0.19 * 1
solving:
0.1 * x + 0.22-0.22 * x = 0.19
0.1 * x- 0.22 * x = 0.19 - 0.22
-0.12 * x = -0.03
x = -0.03 / -0.12
x = 0.25
Which means
Salt solution # 1 0.1% 0.25 L should be used and for salt solution # 2 0.22% 0-75 (1 - 0.25) L
Answer this one please
Answer:
volume is 6.72
width is 1.6
Step-by-step explanation:
Why can't you use the product of powers rule to simplify
this expression? Explain.
3^4 * 2^8
Answer:
Both expressions have different base.
Step-by-step explanation:
Product rule can only be use for the similar bases. For example 2² × 2⁴ have the same base.
For this question, 3⁴ × 2⁸ have different bases which is 3 and 2.
The graphed line shown below is y=-3x+6
-2 -1
Which equation, when graphed with the given equation, will form a system that has no solution?
Step-by-step explanation:
right option
...............
x^2- 20x + y^2 - 10y+25=0
Identify the value of the radius and center is the circle
Answer:
Center = (10, 5)
Radius = 10
Step-by-step explanation:
Look at the picture
Which of the following is equal to sin(0)?
Answer:
i think C
Step-by-step explanation:
NOT SURE THO :)
A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation of 14 pounds.
Answer:
There is not enough evidence to support the claim that the liquid diet yields a higher mean weight loss than the powder diet (P-value = 0.15).
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that the liquid diet yields a higher mean weight loss than the powder diet.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2< 0[/tex]
The significance level is 0.05.
The sample 1 (powder diet group), of size n1=49 has a mean of 42 and a standard deviation of 12.
The sample 2 (liquid diet group), of size n2=36 has a mean of 45 and a standard deviation of 14.
The difference between sample means is Md=-3.
[tex]M_d=M_1-M_2=42-45=-3[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{12^2}{49}+\dfrac{14^2}{36}}\\\\\\s_{M_d}=\sqrt{2.939+5.444}=\sqrt{8.383}=2.895[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-3-0}{2.895}=\dfrac{-3}{2.895}=-1.04[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-1=49+36-2=83[/tex]
This test is a left-tailed test, with 83 degrees of freedom and t=-1.04, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.04)=0.15[/tex]
As the P-value (0.15) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the liquid diet yields a higher mean weight loss than the powder diet.
In the past month, Rafael rented 4 video games and 1 DVD. The rental price for each video game was $2.30. The rental price for the DVD was $3.30 . What is the total amount that Rafael spent on video game and DVD rentals in the past month?
Answer:
$12.50
Step-by-step explanation:
(2,30*4)+3.30
9.20+3.30=12.50
a rental car cost $20 per day, and a room cost $50 per day, for how many days can a room and car be rented, so that the total cost does not exceed $350
Answer:
5
Step-by-step explanation:
The total cost per day is $20 +50 = $70. Then the number of days that expenditure can be made on a budget of $350 is ...
$350/($70/day) = 5 days
Answer:
Step-by-step explanation:
let number of days =x
(20+50)x≤350
70 x≤350
x≤350/70
or x≤5
He can rent both at the most 5 days.
NEED YOUR HELP ASAP!!!!
Answer:
One blue square equals 4.2 grams
Step-by-step explanation:
If the triangle is equal to three of the blue squares then you would have to divide the triangles value by three to get the squares value.
12.6/3 = 4.2
Answer:
dont braly me do it for him
Step-by-step explanation:
A general rule-of-thumb for used car dealers is that the trade-in value of a car decreases by 30%
each year. How much will a $25,000 car be worth in 6 years?
Answer:
-$20,000
Step-by-step explanation:
30% of $25,000 is $7,500 Therefore..
$7,500 x 6 = $45,000 ( 6 being the years )
$45,000 - $25,000 = $20,000
Hope this helps.
-Conrad
The intercept of line 3x-5y-15=0 is
Answer:
The y-intercept should be 3
Find the area of ABC if area of Triangle formed by joining midpoint of the sides
is 25 sq units
Answer: Wait so the sides are both 25 squares?
Step-by-step explanation:
In the diagram below, RSTU is a rectangle, and the two shaded regions are squares.
If the length of SR is 4 m and the length of ST is 8 m, what is the length of PQ in meters?
Answer:
length PQ = 8.9 m
Step-by-step explanation:
The picture below completes the question you asked. From the picture above RSTU is a rectangle . The two shaded square has a length of sides 8 m and 4 m respectively. The legs of the triangle is the sides of the 2 squares. Therefore, the triangle is a right angle triangle. The adjacent side is 4 m while the opposite side is 8 m.
Using Pythagoras theorem the hypotenuse of the triangle can be calculated below.
Pythagoras theorem
c² = a² + b² Therefore,
c² = 4² + 8²
c² = 16 + 64
c² = 80
square root both sides
c = √80
c = 8.94427191
c ≈ 8.9 m
length PQ = 8.9 m
Sqrt(1-costheta)(1+costheta)
Answer:
sinθ
Step-by-step explanation:
[tex]\sqrt{1-cos^{2}x }[/tex]
[tex]\sqrt{sin^{2}x }[/tex]
sinx
(replace x with theta)
Ruth has 12 feet of ribbon.
She uses 7 feet of it for a craft project and gives 28 inches of it to her sister.
How many inches of ribbon does she have left?
Enter your answer in the box.
Answer:
See I don't know the answer but I did another one like this if it doesn't help you can report it no problem
Step-by-step explanation:
There are 2 different ways you can solve this problem and you'll get the same answer.
To help you visualize what you have to do, it might be easiest to translate your problem to a unit that easier to use.
Since you only have a ribbon 5 feet long, but you must cut it into 6 pieces, you know it won't even be 1 foot long.
One way to solve the problem would be to translate your 5-foot ribbon into a ribbon divided into inches.
1 foot = 12 inches
To find out how many inches long your ribbon is, you'll need to multiply the number of feet by 12.
Once you know that, then you can more easily divide it by 6. This will tell you how many inches each ribbon is.
Careful! the answer is to be put into feet so once you know how many inches long the ribbon is, you must then divide by 12 to get the correct answer in feet. Don't forget to round to the nearest tenth.
Another way to solve the problem is to simply divide the 5 feet by the number 6 and then round your number to the nearest tenth. It may be harder to visualize the answer this way, but you will get the same answer as if you translated your ribbon into inches and then divided by 12.
Good luck! I hope this helps!
What is the value of x in the equation 2(x-3)+9=3(x+1)+x?
O x= -3
O x= -1
O x = 0
O x= 3
Answer:
x = 0
Step-by-step explanation:
2(x-3)+9=3(x+1)+x . . . . given equation
2x -6 +9 = 3x +3 +x . . . . eliminate parentheses
2x +3 = 4x +3 . . . . . . . . collect terms
0 = 2x . . . . . . . . . . . . . . subtract (2x +3)
x = 0 . . . . . . . . . . . . divide by 2
Answer:
[tex]x = 0[/tex]
Third answer is correct.
Step-by-step explanation:
[tex]2(x - 3) + 9 = 3(x + 1) + x \\ 2x - 6 + 9 = 3x + 3 + x \\ 2x - 3x - x = 6 - 9 + 3 \\ - 2x = 0 \\ \frac{ - 2x}{2} = \frac{0}{2} \\ x = 0[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
An urban planner is researching commute times in the San Francisco Bay Area to find out if commute times have increased. In which of the following situations could the urban planner use a hypothesis test for a population mean? Check all that apply. Group of answer choices The urban planner asks a simple random sample of 110 commuters in the San Francisco Bay Area if they believe their commute time has increased in the past year. The urban planner will compute the proportion of commuters who believe their commute time has increased in the past year. The urban planner collects travel times from a random sample of 125 commuters in the San Francisco Bay Area. A traffic study from last year claimed that the average commute time in the San Francisco Bay Area is 45 minutes. The urban planner will see if there is evidence the average commute time is greater than 45 minutes. The urban planner asks a random sample of 100 commuters in the San Francisco Bay Area to record travel times on a Tuesday morning. One year later, the urban planner asks the same 100 commuters to record travel times on a Tuesday morning. The urban planner will see if the difference in commute times shows an increase.
Answer:
Step-by-step explanation:
The urban planner collects travel times from a random sample of 125 commuters in the San Francisco Bay Area. A traffic Study from last year claimed that the average commute time in the San Francisco Bay Area is 45 min. The urban planner will see if there is evidence the average commute time is greater than 45 minutes
( Here in this case, Null hypothesis will be Η :μ = 45
And the Alternate Hypoyhesis will be H, :μ> 45 )
C. The urban planner asks a random Sample of 100 commuters in the San Francisco Bay Area to record travel times on a Tuesday morning. One year later, the urban planner asks the same 100 commuters to record travel times on a tuesday morning . The urban planner will see the difference in commute time shows an increase.
Here in this case the null hypothesis will be, H₀ : [tex]\mu _d[/tex] = 0
And the Alternate Hypothesis will be H, : [tex]\mu _d[/tex] <0 The commute time after 1 year is more
Answer:
Step-by-step explanation:
The required hypothesis test is that for a single population mean. It wouldn't involve population proportion or difference between two population means. The correct answer choice would be
A traffic study from last year claimed that the average commute time in the San Francisco Bay Area is 45 minutes. The urban planner will see if there is evidence the average commute time is greater than 45 minutes.
Which line segment is not a diagonal through the interior of the cube shown? Side B E Side C H Side C E Side D G
Answer
Your answer is C.
C. side CE
Answer:
C
Step-by-step explanation:
help please!!! screenshot
You have $4000 to invest. If you'd like to earn exactly $638
in interest each year, how much should you invest in each of
two accounts, one that earns 8% per year and one that
earns 21% per year. (Round your answer to the nearest
dollar)
8%: $
21%: $
Answer:
8%: $1554
21%: $2446
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex].
In this question:
Two earnings, that i am going to call A(8% per year) and B(21% per year).
Two principals, for A i am going to call P and for B it is the rest, so 4000 - P.
A:
One year, so [tex]t = 1[/tex]
8% interest, so [tex]r = 0.08[/tex]
Earnings A.
[tex]A = P*I*t[/tex]
[tex]A = 0.08P[/tex]
B:
21% interest, so [tex]r = 0.21[/tex]
Principal (4000 - P).
[tex]B = P*I*t[/tex]
[tex]B = 0.21*(4000 - P)[/tex]
You'd like to earn exactly $638 in interest each year.
This means that [tex]A + B = 638[/tex]
Then
[tex]B = 638 - A[/tex]
Now we have to solve the following system:
[tex]A = 0.08P[/tex]
[tex]638 - A = 0.21*(4000 - P)[/tex]
So, on the second equation:
[tex]A = 638 - 0.21*(4000 - P)[/tex]
Replacing on the first:
[tex]A = 0.08P[/tex]
[tex]638 - 0.21*(4000 - P) = 0.08P[/tex]
[tex]638 - 840 + 0.21P = 0.08P[/tex]
[tex]0.21P - 0.08P = 840 - 638[/tex]
[tex]0.13P = 202[/tex]
[tex]P = \frac{202}{0.13}[/tex]
[tex]P = 1553.8[/tex]
Rounding up to the nearest integer
P = 1554.
So on A, the 8% interest, you invest $1554.
On B, the 21% interest, you invest 4000 - 1554 = $2446.
Which expression represents the length of the hypotenuse, c, of the triangle below?
C
b
a? - 62
va2 +62
a? + b2
a2
62
Answer:
Length of hypotenuse = √( a² + b²)
Step-by-step explanation:
The question is incomplete and unclear. From the question, it is clear we are to determine the hypotenuse of the triangle. Hence the triangle is a right angled triangle.
Find attached the diagram used in solving the question.
From the diagram,
a = opposite
b = adjacent
c = hypotenuse
To find the hypotenuse of a right angled triangle, we apply Pythagoras theorem.
Using Pythagoras theorem
Hypotenuse² = opposite ² + adjacent²
Insert the values of each, we have:
c² = a² + b²
Then we find the Square root both sides
c = √( a² + b²)
So we can insert the values of a and b if we are given.
For instance, if b = 6
c = √( a² + 6²)
Using the diagram,
Hypotenuse: c = √( a² + b²)
Answer:
Step-by-step explanation:
The probabilty of being born a male is 0.466. The probabilty of being born in north america is 0.153846. The probabilty of being born in an urban location is 0.3571428. Find the exact probabilty that a baby will be born a male, in North America, in an urban location
Answer:0.0256
Step-by-step explanation:
Given
Probability of being a male is [tex]P_1=0.466[/tex]
Probability of being born in america is [tex]P_2=0.153846[/tex]
Probabilty of being born in an urban location is [tex]P_3=0.3571428[/tex]
So probabilty of that a baby will be born a male,in North america, in an urban area=P
Since, [tex]P_1, P_2, P_3[/tex] are independent of each other therefore
[tex]P=P_1\times P_2\times P_3[/tex]
[tex]P=(0.466)\times (0.153846)\times (0.3571428)[/tex]
[tex]P=0.02560[/tex]
Which point represents the unit rate?
On a coordinate plane, point A is (0, 1), point B is (1, 0), point C is (1, 0.5), and point D is (2, 1).
Answer:
Hey it’s C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
in triangleABC the side lengths are b=13, ac=21 and bc=x. write a compound inequality the represents the range of possible values for x
Answer:
8 < x < 34
Step-by-step explanation:
ab = 13, ac = 21, bc = x
The longest side of a triangle must be less than the sum of the other two sides.
If 21 is the longest side:
21 < 13 + x
8 < x
If x is the longest side:
x < 13 + 21
x < 34
Therefore, 8 < x < 34.
PLEASE ANSWER WILL GIVE BRAINLIEST!!
Rewrite the expression in the form 5^n
(5^3)^2 =
Answer: 5^6
Step-by-step explanation:
Since the expression has parenthesis, it means to multiply. When you multiply the powers, you get it in the form 5^n.
The first line in the system of equations is graphed on the coordinate plane. Graph the second line to find the solution to the system.
2 x minus 3 y = negative 6. y = negative one-third x minus 4
Enjoli’s Graph
Answer:
(A) (-6,-2)
Step-by-step explanation:
Answer:
(-6, -2)
Step-by-step explanation:
I WILL MARK AS BRANLIEST
65 POINTS!
Solve the system of equations using subtraction.
{y=x+4
{y=2x+4
Answer:
x=0, y=4
(0,4)
Step-by-step explanation:
y=x+4
y=2x+4
The directions say substitution not subtraction
Set the two equations equal to each other
x+4 = 2x+4
Subtract x from each side
x+4-x = 2x+4-x
4 = x+4
Subtract 4 from each side
4-4 =x+4-4
0 =x
Now find y
y = x+4
y = 0+4
y = 4
Answer:
(0, 4)
Step-by-step explanation:
Our two equations are:
y = x + 4
y = 2x + 4
We need to use substitution, so let's substitute x + 4 in for y in the second equation:
y = 2x + 4
x + 4 = 2x + 4
x = 0
Plug this value back into one of the equations to solve for y:
y = x + 4
y = 0 + 4 = 4
Thus, the answer is (0, 4).