Answer:
(a) H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test.
Step-by-step explanation:
We formulate the
H0: μ1=μ2; null hypothesis that the two means are equal and alternate hypothesis that the two mean are not equal.
Ha:μ1≠μ2 Two tailed test
Test statistic used is
t= x1`-x2` / s√n as the variances are equal and sample size is same
T value for 9 degrees of freedom for two tailed test at α = 0.05 is 2.26
P- value for t test for 9 degrees of freedom is 0.125 from the table.
Hence only a is correct .
Which statement is true about figures ABC D & ABCD
Answer:
it's option b that is the right answer
A sample of radioactive material disintegrates from 6 to 4 grams in 100 days. After how many days will just 3 grams remain?
Answer:
150 days
Step-by-step explanation:
6-4=2
100/2=50
50*3=150
The number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
The rate of disintegration varies directly proportional to the quantity of the material.
As such, we can say:
[tex]\mathbf{=\dfrac{dN}{dt}\ \alpha \ N}[/tex]
[tex]\mathbf{\implies \dfrac{dN}{N}\ = k dt}[/tex]
Taking the integral form;
[tex]\mathbf{\implies \int \dfrac{dN}{N}\ =\int k dt}[/tex]
[tex]\mathbf{\implies In N =kt+ C---- (1)}[/tex]
When t = 0, N = 6 grams
In(6) = C
∴
When t = 100, N = 4 grams
In (4) = 100k + In6
100 k = 1n (4) - In(6)
[tex]\mathbf{100 k = In (\dfrac{4}{6})}[/tex]
[tex]\mathbf{k = \dfrac{1}{100} In(\dfrac{4}{6})}[/tex]
∴
From equation (1):
[tex]\mathbf{In N = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
when,
n = 3 grams; we have:[tex]\mathbf{In (3) = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
[tex]\mathbf{\implies \dfrac{t}{100} In(\dfrac{4}{6}) = In \dfrac{ 3}{ 6}}[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{In (\dfrac{ 3}{ 6})}{ In(\dfrac{4}{6}) }\Big) }[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{0.69314}{ 0.40048}\Big) }[/tex]
t = 173.077 days
Therefore, the number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
Learn more about radioactive materials here:
https://brainly.com/question/24339152?referrer=searchResults
Bryan invests $500 in an account earning 3.5% interest that compounds annually. If he makes no additional deposits or withdraws, how much will be in the account:
After 10 years?
After 15 years?
After 20 years?
Answer:
$705.30, $837.67, $994.89 Respectively
Step-by-step explanation:
Given
P= $500
r= 3.5%= 3.5/100= 0.035
Applying the compound interest formula we have
[tex]A= P(1+r)^t[/tex]
where
A = final amount
P = initial principal balance
r = interest rate
t = number of time periods elapsed
1. for t= 10 years[tex]A= 500(1+0.035)^1^0\\\ A= 500(1.035)^1^0\\\\ A= 500*1.410598\\\ A=705.299[/tex]
A= $705.30
2. for t= 15 years[tex]A= 500(1+0.035)^1^5\\\ A= 500(1.035)^15\\\\ A= 500*1.67534\\\ A=837.67[/tex]
A= $837.67
3. for t= 20 years[tex]A= 500(1+0.035)^2^0\\\ A= 500(1.035)^2^0\\\\ A= 500*1.98978\\\ A=994.89[/tex]A= $994.89
Can you help me with this.
Answer:
You would basically expand all the equations!
1. 7(4z+8b) is equal to 28z+56b.
2. 8(2x+3^2) is equal to 16x+72
3. 4(r+r+r+r) is equal to 4r+4r+4r+4r
4. 9(3+8x) is equal to 27+72x
5. 4^2(3+6f) is equal to 48+96t
6. (t+t+t)/4 is equal to t/4+t/4+t/4
7. 2(4s^3+2) is equal to 8s^3+4
8. 30(3x+4) is equal to 90x+120
9. 6(5a+9b) is equal to 30a+54b
10. 9(3x+5^4) is equal to 27x+5625
11. 7(c+c+c) is equal to 7c+7c+7c
12. 9(2+7f) is equal to 18+63f
13. 7^5(4g-8d) is equal to 67228g-134456d
Step-by-step explanation:
Line d is parallel to line c in the figure below. Parallel lines d and c are intersected by lines q and p to form 2 triangles. At lines d and p, the angle is 2, at d and q, the angle is 1, and at q and p the angle is 3. At lines c and q, the angle is 4, at p and c, the angle is 5, and the third angle is 6. Which statements about the figure are true? Select three options. Vertical angles prove that Angle 2 is congruent to angle 5. In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles. Vertical angles prove that Angle 3 is congruent to angle 6. The triangles are similar because alternate interior angles are congruent. In the two similar triangles, Angle 2 and Angle 4 are corresponding angles. The triangles are similar because corresponding sides are congruent.
Answer:
A B C
Step-by-step explanation:
Answer:
abc or 123
Step-by-step explanation:
Find the volume of the solid shown or described. If necessary, round to the nearest tenth.
Answer:
37.7
Step-by-step explanation:
Well use the formula for the volume of a cylinder which is,
,[tex]\pi r^2 h[/tex]
So the radius is 2 and the height is 3, so we plug those numbers into the formula,
(pi)(2)^2(3)
2^2 is 4 4*3 is 12
12*pi is about 37.7 rounded to the nearest tenth.
If you would like to check look at the image below.
Select the correct text in the table. Use the fundamental theorem of algebra to determine whether each statement is sometimes true, always true, or never true.
1. A quadratic function has 2 distinct roots. always sometimes never
2. A cubic function has at least 1 real root. always sometimes never
3. A function with a degree of 5 has 5 roots. always sometimes never
4. A quadratic function can have only 1 complex solution. always sometimes never
Answer:
1. Sometimes
2. Sometimes
3. Always
4. Sometimes
Step-by-step explanation:
1. Quadratic function : in which maximum power of [tex]x[/tex] is two.
The roots of quadratic function can be either equal or different.
For example:
[tex]x^{2} -2x+1[/tex] will have two equal roots i.e. 1 and 1.[tex]x^{2} -3x+2[/tex] will have two different roots i.e. 1 and 2.So, sometimes is the correct answer.
2. Cubic function has atleast 1 real root.
Cubic function has maximum power of [tex]x[/tex] as 3.
If the coefficients are real numbers then atleast 1 real root.
If the coefficients are imaginary in nature, then this is not true.
For example:
Cubic equation [tex]x^3 +i = 0[/tex] does not have any real root.
Cubic equation [tex]x^3 +1 = 0[/tex] has a real root x = -1.
So, it is sometimes true.
3. A function with degree 5 i.e. maximum power of [tex]x[/tex] as 5 will have 5 roots.
It is always true that a function will have number of roots equal to its degree.
4. Quadratic function can have only 1 complex solution.
Two complex solutions are also possible for a quadratic function.
For example:
[tex]x^{2} +1=0[/tex] will have two imaginary roots: [tex]x=i, -i[/tex]
It is also possible to have 1 complex solution,
For example:
[tex](x-1)(x-i) = 0[/tex] will have one complex root and one real root.
So, the statement is sometimes true.
Answer:
MY ANSWER IS CORRECT IN PLATO!!!
1. Sometimes
2. Always
3. Always
4. Never
Step-by-step explanation:
1. A quadratic function has 2 distinct roots SOMETIMES
2. A cubic Function has at least 1 root ALWAYS
3. A function with a degree of 5 has 5 roots ALWAYS
4. A quadratic function can have only 1 complex solution NEVER
I JUST GOT 100% on the quiz in PLATO
Find the value of x.
Answer:
[tex]\huge\boxed{y=\sqrt{55}}[/tex]
Step-by-step explanation:
ΔADC and ΔDBC are similar (AAA)
Therefore the cooresponging sides are in proportion:
[tex]\dfrac{AC}{CD}=\dfrac{CD}{BC}[/tex]
Substitute:
[tex]AC=6+5=11\\BC=5\\CD=y[/tex]
[tex]\dfrac{11}{y}=\dfrac{y}{5}[/tex] cross multiply
[tex](11)(5)=(y)(y)\\\\55=y^2\to y=\sqrt{55}[/tex]
A retailer charges a flat handling fee of $5.00, plus $0.75 per quarter pound, to ship an item. Bailey pays $9.50 to have an item shipped from the retailer. What is the weight of the item? A- 1.50 pounds B- 1.75 pounds C- 3.75 pounds D- 6.00 pounds
Answer:
D. 6 pounds
Step-by-step explanation:
$9.50-$5.00=$4.50; $4.50/$0.75= 6 pounds
Answer:
A - 1.50 pounds
Step-by-step explanation:
The original price of a 2018 Honda Shadow to the dealer is $17,715, but the dealer will pay only $16,985 after rebate. If the dealer pays Honda within 15 days, there is a 2% cash discount.
Answer:
The final price to be paid after the 2% discount has been made will be $ 16,645.30.
Step-by-step explanation:
Since there is a 2% discount on the price of the Honda Shadow in the event that the dealer pays Honda within 15 days, and that after a rebate the price of the vehicle is $ 16,985, to obtain the value of the discount and the final amount to be paid must be calculated as follows:
16,985 x 2/100 = X
33,970 / 100 = X
339.70 = X
Thus, the discount to be made will be $ 339.70, with which the final price to be paid after the 2% discount has been made will be $ 16,645.30.
PLEASE HELP ?
A: 111.6 square centimeters
B: 323 square centimeters
C: 7.75 square centimeters
Answer:
B. 323 square centimeters
Step-by-step explanation:
multiply the inches by the conversion number
50 x 6.45 = 322.5
Answer:
[tex]\boxed{Option \ B}[/tex]
Step-by-step explanation:
[tex]1 \ inch^2 = 6.45 \ cm^2[/tex]
Multiplying both sides by 50
[tex]1 * 50 \ inch^2 = 6.45 * 50 \ cm^2\\[/tex]
[tex]50 \ inch^2 = 323 \ cm^2[/tex]
Write Given f(x)=2−4x−−−−−√ and g(x)=−3x, find the following: a. (g∘f)(x) the domain and range of the function using interval notation.
Answer:
If we have two functions g(x) and f(x)
I suppose that the functions here are:
f(x) = 2 - √(4*x)
g(x) = -3*x
First, let's analyze the functions:
g(x) as not any problem for any value of x, so the domain is the set of all the real numbers.
f(x) has a square root on it, and we know that the square root of a negative number is equal to a complex number, so here we can not have negative values of x.
The domain of f is D = x ∈ {0, ∞}
Then (gof)(x) = g(f(x)) = -3*(2 - √(4*x)) = -6 + 3*√(4*x)
We can see that g(x) does not have any problem, and the problems with f(x) remain there, so the domain of the composition is equal to the domain of f(x):
D = x ∈ {0, ∞}
In graphing a trigonometric function, how does one establish which are the EXTREMUM coordinates and which are the MIDLINE INTERCEPTION coordinates. I can find the x values and the y values but do not know which X goes with which Y and the graphs end up incorrect! It is EXTREMELY frustrating. How do I discern which is which!!!!! Thank You.
Answer:
If I getting the question correctly, your doubt is the order of the values you get after doing the math. I mean, you can do the calculations, but in the end, you don't form the coordinate pairs correctly, that's why I understand from your question. So, here is what you need to do.
One way to graph is by using the definitions of those kinds of functions. For example, let's say we want to find the points to draw the function: [tex]y=sin(x)[/tex]
Remember that trigonometric functions have a specific period, that means, their drawing repeats over and over again after a certain number. That period is [tex]2 \pi[/tex], that means this number represents a cycle.
So, the main thing you need to do is to pick a starting point to then, draw the curve according to the [tex]2 \pi[/tex] period.
Now, we know that sine functions intercept the origin of the coordinate system, as you can observe in the image attached, there you can see that from the origin you draw those waves making sure you intercept the x-axis at every [tex]\pi[/tex] number. In the end, you will have a sine function.
On the other hand, if you want to have a chart with all x-values and y-values. First, you need to set x-values: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. Then, you need to find each y-values for each of them.
Now, you have to draw a chart value, to keep in other the coordinate pairs, that way, you'll have the correct pairs at the end.
For example, for [tex]x=-5[/tex], we get [tex]y=-0.09[/tex], that means in the chart value, you are gonna form the pair [tex](-5, -0.09)[/tex], and now you have your first point of the drawing. Then, you keep repeating the process until you complete all the chart values.
As you can imagine, you're going to get really small decimal numbers, that's why I explained to you the first method, it's faster and easier.
Which system type is a linear system with infinitely many solutions?
Answer:
down b3low
Step-by-step explanation:
The point where the two lines intersect is the only solution. An inconsistent system has no solution. Notice that the two lines are parallel and will never intersect. A dependent system has infinitely many solutions.
Simplify the rate:
46 cans of Soda / 8 people
Only enter the numeric amount:
Answer: 23 cans of soda/4 people.
or (23/4) cans of soda per person.
Step-by-step explanation:
So we have the rate:
46 cans of soda/ 8 people
First, 46 and 8 are multiples of 2, so we can divide both numerator and denominator by 2:
46/2 = 23
8/2 = 4
Then the rate can be:
23 cans of soda/4 people.
Now 23 is a prime number, so we can not simplify it furthermore
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an = (n − 2)! n!
Answer: Diverging
Step-by-step explanation:
Find explanations in the attached file
You are looking to invest in several different real estate deals. You have received ceconomic reports that explain the probability of good economic conditions will be .6 and .4 for bad economic conditions. Below is the Payoff Table, and after calculating the expected value for each decision, you determine the best "payoff deal is:
Good Economic Bad Economic
Conditions Condition (.60) Conditions (.40)
Apartment Building 50,000 30,000
Office Building $100,000 $-40,000
Warehouse 30,000 $10,000
A. Apartment Building
B. Office Building
C. Warehouse
D. None of the above.
Answer:
Real Estate Deals
The best "payoff deal:"
B. Office Building
Step-by-step explanation:
A) Payoff Table
Good Economic Bad Economic
Conditions Conditions
Probability (.60) (.40)
Apartment Building $50,000 $30,000
Office Building $100,000 $-40,000
Warehouse $30,000 $10,000
B) Calculation of Expected Values:
Good Economic Bad Economic Expected Values
Conditions Conditions
Probability (.60) (.40)
Apartment Building $30,000 $12,000 $42,000
Office Building $60,000 $-16,000 $44,000
Warehouse $18,000 $4,000 $22,000
b) The expected value for these real estate deals can be derived as the sum of the payoffs under the two economic conditions after they have been weighed with their odds of occurrence. The office building, in this example, showed the best payoff deal as the expected payoff from it results to a payoff of $44,000, which is higher than the expected payoff from the Apartment and Warehouse. However, it is also the riskiest, especially when bad economic conditions occur. This also accords with the general economic risk-return pattern that higher risky investments attract higher returns.
The school district uses the Hamilton method to apportion its 22 board members to the 4 towns. How many board members are assigned to each town, using this method? 2. The following year, 900 people move out of Town D. Two hundred of these people move Town C, and 700 of them move to Town B. Now, how many board members does each town have? (Be careful. Make sure you assign a total of 22 board members). 3. Compare the results from the 2 years. Do you think they make sense? How do you think each town would react? Are they fair? Why or Why not?
Answer:
(A, B, C, D) = (2, 2, 6, 12)(A, B, C, D) = (2, 2, 6, 12)identical results; yes, they make senseyes they are fairStep-by-step explanation:
1. The Hamilton method has you compute the number represented by each board member (total population/# members). Using this factor, the number of board members for each district are computed. This raw value is rounded down.
Because this total does not allocate all board members, the remaining members of the board are allocated to the districts based on the size of the fraction that was truncated when rounding down. Allocations start with the largest fraction and work down until all board members have been allocated.
The attached spreadsheet implements this algorithm using a "threshold" that is adjusted to a value between 0 and 1, signifying the cutoff point between a fraction value that gets an additional member and one that doesn't. (Often, that threshold can be set at 0.5, equivalent to rounding the raw board member value to the nearest integer.)
The resulting allocations are ...
Town A: 2
Town B: 2
Town C: 6
Town D: 12
__
2. The second attachment shows the result after the population move. The allocations of board members are identical.
__
3. The "factor" (persons per board member) is about 4500, so we don't expect a move of 900 people to make any difference in the allocation. These results make complete sense.
__
4. Of course each town will consider its own interest at the expense of everyone else, so they may or may not consider the results fair. The towns have population ratio of about 9 : 9 : 25 : 56, so the ratios 2 : 2 : 6 : 12 are quite in line. Even in the second year, when the ratios are closer to 9 : 10 : 26 : 56, the changes are small enough that the allocation of board members still makes sense. The results are fair.
_____
Comment on "fair"
The reason there are different methods of allocation is that each seeks to rectify some perceived flaw in one or more of the others. The reason there is not a general agreement on the method to be used is that some benefit more from one method than from another. "Fair" is in the eye of the beholder. I believe in this case it would be very difficult to justify any other allocations than the ones computed here.
What is the measure of ∠BCD?
Answer: 77 degrees
Step-by-step explanation:
interior angles on the same side of transversal are supplementary. Thus,
103+x=180
x = 77
Hope it helps <3
Answer:
Hey there!
This is a parallelogram, and we have the angles next to each other add to 180 degrees. Angle ABC+Angle BCD=180
103+x=180
x=77
BCD=77 degrees.
Let me know if this helps :)
Solve the equation.
y + 3 = -y + 9
y= 1
y=3
y = 6
y = 9
Answer: y=3
Step-by-step explanation:
To solve the equation, we want to get the same terms onto the same side and solve.
y+3=-y+9 [add y on both sides]
2y+3=9 [subtract 3 on both sides]
2y=6 [divide 2 on both sides]
y=3
Answer:
y=3
Step-by-step explanation:
15x - 30 x 0 + 40 = 89
Answer:
x = 49/15
Step-by-step explanation:
15x - 30 x 0 + 40 = 89 PEMDAS
15x + 40 = 89 Isolate the variable
15x = 49
x = 49/15
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 49/15 or 3 4/15 or 3.26
▹ Step-by-Step Explanation
15x - 30 * 0 + 40 = 89
15x - 0 + 40 = 89
15x + 40 = 89
15x = 89 - 40
15x = 49
x = 49/15 or 3 4/15 or 3.26
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
all summer olympics championship distamces in the triple jump from 1896 through 2012 avereged 16.38 meters, with standard deviation of 1.34 meters. what is the probability that a randomly selected distance from the distribution would fall into each of the following intervals 16.8 meters and 17.9 meters?
Answer: 0.2487
Step-by-step explanation:
Given: Mean: [tex]\mu=16.38[/tex] meters
Standard deviation: [tex]\sigma= 1.34[/tex] meters
Let X denote the distance in the triple jump.
The probability that a randomly selected distance from the distribution would fall into interval 16.8 meters and 17.9 meters = [tex]P(16.8<X<17.9)=P(\dfrac{16.8-16.38}{1.34}<\dfrac{X-\mu}{\sigma}<\dfrac{17.9-16.38}{1.34})[/tex]
[tex]=P(0.3134<Z<1.1343)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=P(Z<1.1343)-P(Z<0.3134)\\\\=0.8717- 0.6230\ [\text{By z-table}]\\\\=0.2487[/tex]
Hence, the probability that a randomly selected distance from the distribution would fall into interval 16.8 meters and 17.9 meters= 0.2487
jogged the track 5/9 miles long and jogged around it 4 times
Answer:
The answer is 2 1/5 miles.
Step-by-step explanation:
You have to multiply 5/9 with 4 since you are going around 4 times. You could also use addition which is 5/9 + 5/9 + 5/9 + 5/9.
Answer:
Hey there!
The person jogged a total of 20/9 miles.
Hope this helps :)
What is 7/8×3/9 reduced to lowest terms
Answer:
7/24
Step-by-step explanation:
7/8×3/8= 21/72
divide using 3
= 7/24
Rewrite2(4)(6) in a different way, using the Commutative Law of Multiplication.
Answer:
2(6)(4)
Step-by-step explanation:
The commutative law of multiplication states that the order of the numbers does not affect the answer. To rewrite 2(4)(6) using the commutative law of multiplication, rearrange the order of the numbers.
Assume the weight of Valencia oranges is normally distributed with a mean 9 oz and standard deviation 2 oz. What is the probability that a sample of 100 units show a mean weight of less than 9.5 oz?
Answer:
0.99379
Step-by-step explanation:
The first thing to do here is to calculate the z-score
mathematically;
z-score = x-mean/SD/√(n)
From the question x = 9.5 ,
mean = 9, SD = 2 and n = 100
Plugging the values we have;
z-score = (9.5-9)/2/√(100) = 0.5/2/10 = 0.5/0.2 = 2.5
So the probability we want to calculate is;
P(z<2.5)
We use the standard table for this
and that equals 0.99379
A group of 10 students participate in chess club, karate club, or neither.
Answer:
P(A︱B) =0.50
Step-by-step explanation:
That's the answer
assume that the salaries of elementary school teachers in the united states are normally distributed with a mean of
Please show step by step of working out the value of r for which is A minimum and calculate the minimum surface area of the container.
The total surface area, Acm^2, of each container is modelled by function A= πr^2+100/r.
(remember to use the derivative to show you have found the minimum)
Answer:
A = 59.63cm^2
Step-by-step explanation:
You have the following function for the surface area of the container:
[tex]A=\pi r^2+\frac{100}{r}[/tex] (1)
where r is the radius of the cross sectional area of the container.
In order to find the minimum surface are you first calculate the derivative of A respect to r, to find the value of r that makes the surface area a minimum.
[tex]\frac{dA}{dr}=\frac{d}{dr}[\pi r^2+\frac{100}{r}]\\\\\frac{dA}{dr}=2\pi r-\frac{100}{r^2}[/tex] (2)
Next, you equal the expression (2) to zero and solve for r:
[tex]2\pi r-\frac{100}{r^2}=0\\\\2\pi r=\frac{100}{r^2}\\\\r^3=\frac{50}{\pi}\\\\r=(\frac{50}{\pi})^{1/3}[/tex]
Finally, you replace the previous result in the equation (1):
[tex]A=\pi (\frac{50}{\pi})^{2/3}+\frac{100}{(\frac{50}{\pi})^{1/3}}}[/tex]
[tex]A=59.63[/tex]
The minimum total surface area is 59.63cm^2
please help me, i will give you brainliest
Answer:
Refeect circle A over the the y line = x
Step-by-step explanation: