Answer:
It take 12 hours for 2 lawnmowers to cut 6 acres of grass
Step-by-step explanation:
We are given that It takes 4 lawnmowers to cut 2 acres of grass in 2 hours.
Let [tex]T_1 , M_1 and W_1[/tex] denotes the time taken , No. of land mowers and Amount of grass respectively in case 1 .
[tex]T_1=2 \\W_1=2\\M_1=4[/tex]
Now The amount of time varies directly with the amount of grass and inversely with the number of lawnmowers
Let [tex]T_2 , M_2 and W_2[/tex] denotes the time taken , No. of land mowers and Amount of grass respectively i case 2
[tex]T_1=? \\W_1=6\\M_1=2[/tex]
So, [tex]\frac{M_1 \times T_1}{W_1}=\frac{M_2 \times T_2}{W_2}[/tex]
Substitute the values
[tex]\frac{4 \times 2}{2}=\frac{2 \times ?}{6}[/tex]
[tex]\frac{4 \times 2 \times 6}{2 \times 2}=?[/tex]
[tex]12=?[/tex]
Hence it take 12 hours for 2 lawnmowers to cut 6 acres of grass
Answer:
D. 12
Step-by-step explanation:
hope this helps :)
Which composition of transformations will create a pair of similar
Answer:
A rotation, then a dilation
Step-by-step explanation:
When two triangles are congruent, the three sides and angles will be the same.
A dilation is a type of transformation that works with scale factors and enlarges or reduces a figure, to create a new figure.
Now, the composition of transformations that will create a pair of similar but not congruent triangles are - a rotation, then a dilation.
A composition of a rotation followed by a dilation will create a pair of similar, but not congruent, triangles, option D.
The question asks which composition of transformations will create a pair of similar, but not congruent, triangles. In the realm of Euclidean geometry, certain transformations maintain the shape and size of geometric figures, while others maintain only the shape but not the size.
Among the choices given, a rotation followed by a reflection, a translation followed by a rotation, and a reflection followed by a translation will all produce congruent triangles, as they are types of isometries which preserve shape and size.
However, a rotation followed by a dilation is the correct composition that will result in triangles that are similar but not congruent. This is because rotation preserves the shape and size, but when followed by dilation, the size is changed while the shape remains the same, satisfying the condition of the question. Option D is correct.
A certain country's postal service currently uses 55-digit zip codes in most areas. How many zip codes are possible if there are no restrictions on the digits used? How many would be possible if the first number could not be 33?
Answer:
a) 100000
b) 90000
Step-by-step explanation:
We have the possibility of 10 digits
(0,1,2,3,4,5,6,7,8,9)
If there are no restrictions on the digit, there are 10 possibilities for each of the five digits
We then have;
10*10*10*10*10
= 10^5
= 100000
This means 100000 zip codes are possible if there are no restrictions.
b) If the first digit cannot be 3, there are 9 possibilities. This is because the possibility of the first digit being 3 is 1 out of 10. Therefore the possibility of not being 3 is 9 out of 10
The other four digits have 10 possibilities each.
So we have
9*10*10*10*10
= 90000
This means there are 90000 zip codes if the first digit does not start with 3
Han spent 75 minutes practicing the piano over the weekend. Priya practiced the violin for 152% as much as Han practiced the piano. How long did she practice
Priya practiced the violin for 114 minutes
Solution:Given that
Han spent 75 minutes practicing the piano over the weekend
Priya practiced the violin for 152% as much as Han practiced the piano
Need to determine how long did priya practice
Duration of Han practicing the piano over weekend = 75 minutes
As given that Priya practiced the violin for 152% as much as Han practiced the piano
=> Duration of Priya practicing the piano = 152% of Han practicing the piano
=> Duration of Priya practicing the piano = 152% of 75 minutes
We know that a % of b is written in fraction as [tex]\frac{a}{100} \times b[/tex]
[tex]\Rightarrow \text { Duration of Priya practicing the piano }=\frac{152}{100} \times 75=114 \text { minutes }[/tex]
Hence Priya practiced the violin for 114 minutes
Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. [5,0] sin(x^2) dx, n = 5 M5 =
PLZZZZZZ HELP ME ASAP
deltax = (56-0)/4 = 14
number of intervals 4
The intervals are:
(0,14),(14,28),(28,42),(42,56)
The Midpoint Rule =
f(7)+f(21)+f(35)+f(49)
[0.47577]+[-0.99159]+[-0.35892]+[0.65699]
deltax =14
sum = -0.21774
Multiplying by deltax = -3.0484
To approximate the integral of sin(x^2) dx from 0 to 5 using the Midpoint Rule with n=5, first calculate Δx = 1. Next, perform calculations with x values 0.5, 1.5, 2.5, 3.5, and 4.5. Finally, use the Midpoint Rule formula to calculate the approximated integral.
Explanation:To solve this problem, you'll need to use the Midpoint Rule, which is a numerical method used to approximate definite integrals. In this case, we want to approximate ∫ from 0 to 5 of sin(x^2) dx with an n value of 5.
The Midpoint Rule can be represented as: Mn = Δx[f(x1) + f(x2) + ... + f(xn)], where Δx = (b-a)/n and each xi = a + (Δx/2) + (i-1)Δx.
Here, we'll first find our Δx = (5-0)/5 = 1, then calculate each xi and plug those into our function. Our xi values will be 0.5, 1.5, 2.5, 3.5, and 4.5. Finally, we plug into our formula and solve to find our approximated integral value.
A detailed and step-by-step solution would involve calculating each f(xi) with the xi values given above, and then adding these up
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By driving 8 mph faster than Bob, John can make a 230 mile trip in one half hour less. How fast does Bob drive on the trip? Round your answer to the nearest mile per hour. Enter only the numerical value in the answer box
Answer: The speed of Bob is 56.8 km/hr.
Step-by-step explanation:
Let the speed of Bob be 'x'.
Let the speed of John be 'x-8'.
Distance covered = 230 miles
time = [tex]1\dfrac{1}{2}=\dfrac{3}{2}\ hr[/tex]
According to question, we get that
[tex]\dfrac{230}{x}-\dfrac{230}{x+8}=\dfrac{3}{2}\\\\230\dfrac{x+8-x}{x(x+8)}=\dfrac{3}{2}\\\\\dfrac{230\times 8}{x^2+8x}=\dfrac{3}{2}\\\\\dfrac{1840}{x^2+8x}=\dfrac{3}{2}\\\\1840\times 2=3x^2+24x\\\\3680=3x^2+24x\\\\3x^2+24x-3680=0\\\\x\approx 56.8\ km/hr[/tex]
Hence, the speed of Bob is 56.8 km/hr.
HELP NEEDED, GIVING BRAINLIEST!!
Identify the statement as true or false and justify your answer.
Plane M is perpendicular to line s through point Q. Therefore it is the only plane perpendicular to s through point Q.
A. False; If a line is perpendicular to a plane, any line perpendicular to that line at the point of intersection of the line and the plane is contained by the plane.
B. True; If a line is perpendicular to a plane, any line perpendicular to that line at the point of intersection of the line and the plane is contained by the plane.
C. True; Given a point on a line, there is one and only one plane perpendicular to the line through that point.
D. False; Given a point on a line, there is one and only one plane perpendicular to the line through that point.
The statement is false. Multiple planes can be perpendicular to the same line through a given point.
Explanation:The statement is False. If a line is perpendicular to a plane, it does not mean that it is the only plane perpendicular to the line.
There can be multiple planes perpendicular to the same line through a given point. For example, consider a line s passing through point Q and a plane M perpendicular to s at point Q. Now, we can also have another plane N perpendicular to line s at point Q, which is different from plane M. Therefore, the statement is false.
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. (5 points)
f(x) = x2 - 3 and g(x) = square root of quantity three plus x
Answer:
f(g(x)) = g(f(x)) = x and f and g are the inverses of each other.
Step-by-step explanation:
Here, the given functions are:
[tex]f(x) = x^2 - 3, g(x) = \sqrt{({3+x)} }[/tex]
To Show: f (g(x)) = g (f (x))
(1) f (g(x))
Here, by the composite function:
[tex]f (g(x)) = f (\sqrt{3+x} ) = \sqrt{(3+x)} ^2 - 3 = (3 + x) - 3 = x[/tex]
⇒ f (g(x)) = x
(2) g (f(x))
Here, by the composite function:
[tex]g(f(x)) = g(x^2 -3) = \sqrt{3 +(x^2 -3) } = \sqrt{x^2} = x[/tex]
⇒ g (f(x)) = x
Hence, f(g(x)) = g(f(x)) = x
⇒ f and g are the inverses of each other.
If you doubled the surface area of a sphere how would the surface area change
A boat's crew rowed 7.5 miles downstream, with the current, in 1.5 hours. The return trip upstream, against the current, covered the same distance, but took 2.5 hours. Find the crew's average rowing velocity in still water and the average velocity of the current.
Answer:
Average rowing velocity of boat in still water is 4 miles per hour and average velocity of the current is 1 mile per hour.
Step-by-step explanation:
We are given the following in the question:
Let x be the average rowing velocity of boat in still water and y be the the average velocity of the current.
[tex]\text{Speed} = \displaystyle\frac{\text{Distance}}{\texr{Time}}[/tex]
The boat rowed 7.5 miles downstream, with the current, in 1.5 hours.
Velocity with the current =
[tex]=\text{average rowing velocity of boat in still water} + \text{ average velocity of the current} = x + y[/tex]
Thus, we can write the equation:
[tex]7.5 = (x+y)1.5\\x+y = 5[/tex]
The return trip upstream, against the current, covered the same distance, but took 2.5 hours.
Velocity against the current =
[tex]=\text{average rowing velocity of boat in still water} - \text{ average velocity of the current} = x - y[/tex]
Thus, we can write the equation:
[tex]7.5 = (x-y)2.5\\x-y = 3[/tex]
Solving, the two equations:
[tex]2x = 8\\x = 4, y = 1[/tex]
Thus, average rowing velocity of boat in still water is 4 miles per hour and average velocity of the current is 1 mile per hour.
A student randomly draws a card from a standard deck and checks to see if it is his favorite suit. He then returns the card to the deck, shuffles, and repeats the experiment. He performs the experiments 30 times. Can the probability of drawing his favorite suit be found by using the binomial probability formula? Why or why not?
Yes. The events are dependent; however, the 5% guideline can be applied to this situation.
No. The trials are fixed, but the probability of success changes for every trial.
No. The probability of success remains the same for every trial, but the trials are not fixed.
Yes. The outcomes can be classified into two categories, the trials are fixed, and the events are independent.
Answer:
Yes. The outcomes can be classified into two categories, the trials are fixed, and the events are independent.
Step-by-step explanation:
Hope this helps!!
A construction crew has just built a new road. It took them 8 weeks to build 20.48 kilometers of road. At what rate did they build the road?
Answer:The rate per week =
20.48/8 = 2.56 kilometers per week
Step-by-step explanation:
A construction crew has just built a new road. It took them 8 weeks to build 20.48 kilometers of road. To determine the rate at which the road was built, we would divide the total length of road that was built by the construction company by the number of weeks or days or even hours used in the construction.
The rate per week =
20.48/8 = 2.56 kilometers per week
If we want to find the rate per day,
1 week = 7 days
8 weeks will be 8×7 = 56 days
So the rate per day =
20.48/56 = 0.366 kilometers per day.
Which function is graphed on the right?
y = 2x+3 – 2
y = 2x–3 + 2
y = 2x–2 + 3
y = 2x–2 – 3
Answer:
y = 2^(x–2) + 3
Step-by-step explanation:
The equation above is the one that is graphed. You can pick it from the offered choices by recognizing that the horizontal asymptote on the graph is y=3. That is 3 units above the horizontal asymptote of the parent exponential function. Hence, you must have ...
y = (some exponential) +3
_____
Please note that the exponent indicator (^) and the grouping parentheses on the exponent are essential. Without those, the equation is that of the line y=2x+1, which is not what is graphed.
Machine A working alone can complete a job in 3 1/2 hours. Machine B working alone can do the same job in 4 2/3 hours. How long will it take both machines working together at their respective constant rates to complete the job?A. 1 hr 10 minB. 2hrC. 4hr 5 minD. 7hrE. 8 hr 10 min
Answer:
B) 2 hours
Step-by-step explanation:
If machine A complete a job in 3 1/2 hours or 7/2 of an hour
means that in one hour finished 1÷ 7/2 or 2/7
If machine B complete a job in 4 2/3 hours or 14/3 of an hour
means that in one hour finished 1÷ 14/3 or 3/14 of an hour
Then the two machines working together in one hour will make
2/7 + 3/14 = (4 + 3)/ 14
or 7/14 = 1/2
half of the job. Therefore these two machines working together will take two hours
The 8 leaders of the G8 nations convene in Rome and stand in a row as they get ready to have some pictures of them taken by the press. What is the probability that the picture that the New York Times' editors will randomly select for publishing the next day is one in which Berlusconi is not standing next to Obama? (assuming that there are pictures of all possible standing arrangements).
Answer:
The required probability is [tex]\frac{3}{4}[/tex].
Step-by-step explanation:
Consider the provided information.
There are 8 leaders.
Thus, the total number of ways to arrange 8 leaders are 8!.
Assume that Obama and Berlusconi is one person.
Therefore the total number of leaders are 7 (As Obama and Berlusconi is one person).
The number of ways in which 7 leader can be arranged: 7!
Although Obama and Berlusconi is one unit but they can interchange their place in 2 ways. Like Obama and Berlusconi or Berlusconi and Obama
That means the total number of ways : 7!×2
The number of ways in which they are not next to each other = Total number of ways - The number of ways in which they are next to each other
Number of ways they are not next to each other = 8!-7!×2
The probability that they are not next to each other = [tex]\frac{8!-7!\times2}{8!}=\frac{3}{4}[/tex]
Hence, the required probability is [tex]\frac{3}{4}[/tex].
A study of a company's practice regarding the payment of invoices revealed that an invoice was paid an average of 20 days after it was received. The standard deviation equaled five days. Assuming that the distribution is normal, what percent of the invoices were paid within 15 days of receipt?
Answer:
15.87% of the invoices were paid within 15 days of receipt
Step-by-step explanation:
An invoice was paid an average of 20 days after it was received.
Mean = [tex]\mu = 20[/tex]
Standard deviation = [tex]\sigma = 5[/tex]
Now we are supposed to find what percent of the invoices were paid within 15 days of receipt i.e.P(x<15)
Formula : [tex]Z=\frac{x-\mu}{\sigma}[/tex]
At x = 15
Substitute the values
[tex]Z=\frac{15-20}{5}[/tex]
[tex]Z=-1[/tex]
Refer the z table for p value
So, p value = 0.1587
So, 15.87% of the invoices were paid within 15 days of receipt
Simplify the following polynomial expression??
Answer:
B
Step-by-step explanation:
just multiply and add
Use the Pythagorean Theorem to find the length of the missing side of the right triangle. Then find the value of each of the six trigonometric functions of ∅
The length of the missing side of the right triangle is __(?)
Answer:
Step-by-step explanation:
Pythagorean theorem is given as
a² +b² = c²
a² = c² - b²
a² = 252 – 202
a² = 625 – 400
a² = 225
a = √225
a = 15
Length of the missing side is 15
To find the value of the six trigonometric function
1) sin x = a/c
= 15/25
sin x = 0.6, x = sin⁻¹ 0.6 = 36.86
2) cos x = b/c
= 20/25
cos x = 0.8, x = cos⁻¹ 0.8 = 36.86
3) tan x = a/b
= 15/20
tan x = 0.75, x = tan⁻¹ 0.75 = 36.86
∴ Θ = 36.86°
4) csc x = c/a
= 25/15
csc x = 1.67 x = csc⁻¹ 1.67
5) sec x = c/b
= 25/20
sec x = 1.25 x = sec⁻¹ 1.25
6) cot x = b/a
= 20/15
cot x = 1.33 x = cot⁻¹ 1.33
a. Find PR in the diagram
b. Find the perimeter of quadrilateral PQRS
Answer:
Step-by-step explanation:
The quadrilateral has 4 sides and only two of them are equal.
A) to find PR, we will consider the triangle, PRQ.
Using cosine rule
a^2 = b^2 + c^2 - 2abcos A
We are looking for PR
PR^2 = 8^2 + 7^2 - 2 ×8 × 7Cos70
PR^2 = 64 + 49 - 112 × 0.3420
PR^2 = 113 - 38.304 = 74.696
PR = √74.696 = 8.64
B) to find the perimeter of PQRS, we will consider the triangle, RSP. It is an isosceles triangle. Therefore, two sides and two base angles are equal. To determine the length of SP,
We will use the sine rule because only one side,PR is known
For sine rule,
a/sinA = b/sinB
SP/ sin 35 = 8.64/sin110
Cross multiplying
SPsin110 = 8.64sin35
SP = 8.64sin35/sin110
SP = (8.64 × 0.5736)/0.9397
SP = 5.27
SR = SP = 5.27
The perimeter of the quadrilateral PQRS is the sum of the sides. The perimeter = 8 + 7 + 5.27 + 5.27 = 25.54 cm
A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X-bar = $50.50 and s2 = 400. Construct a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain's new store in the mall.
Answer: (39.424, 61.576)
Step-by-step explanation:
When population standard deviation([tex]\sigma[/tex]) unknown ,The confidence interval for population mean is given by :-
[tex]\overline{x}\pm t^*\dfrac{s}{\sqrt{n}}[/tex]
, where n= Sample size
[tex]\overline{x}[/tex] = sample mean.
s= sample standard deviation
[tex]t^*[/tex] = Critical t-value (two-tailed)
Given : n= 15
Degree of freedom= 14 [df=n-1]
[tex]\overline{x}=\ $50.50[/tex]
[tex]s^2=400\\\\\Rightarrow\ s=\sqrt{400}=20[/tex]
Significance level = [tex]\alpha=1-0.95=0.05[/tex]
For [tex]\alpha=0.05[/tex] and df = 14, the critical t-values : [tex]t^*=\pm2.1448[/tex]
Then the 95% confidence interval for population mean will be :
[tex]50.50\pm (2.1448)\dfrac{20}{\sqrt{15}}\\\\=50.50\pm(2.1448)(5.1640)\\\\\approx50.50\pm11.076\\\\=(50.50-11.076,\ 50.50+11.076)\\\\=(39.424,\ 61.576)[/tex]
Hence, a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain's new store in the mall. : (39.424, 61.576)
The 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain's new store in the mall is calculated using the sample mean ($50.50), sample size (15), sample standard deviation (20), and Z-value for a 95% confidence interval (1.96). The calculated interval is (-$1.11, $102.11).
Explanation:To construct a 95% confidence interval for the average amount that the department store's credit card customers spent on their first visit to their new store, we would use the formula for a confidence interval:
CI = X-bar ± (Z-value * (s/√n)),
where X-bar is the sample mean = $50.50, n is the sample size = 15, s is the sample standard deviation = √400 = 20, and Z-value is the critical value from the Z-table which, for a 95% confidence interval, equals 1.96.
Plug these values into the formula,
CI = 50.5 ± (1.96 * (20/√15))
Using a calculator, the confidence interval comes out to (-$1.11, $102.11).
So, we are 95% confident that the average amount its credit card customers spent on their first visit to the chain's new store in the mall lies between $-1.11 and $102.11.
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How many bit strings of length 10 have________.a) exactly three 0s?b) more 0s than 1s?c) at least seven 1s?d) at least three 1s slader
Answer: a. 120, b. 386, c. 176, d. 968.
Step-by-step explanation:
For a combination of any number, is given as
C n,r = n!/r!(n-r)!
Please note that "n,r" is a subscript, and the exclamation mark "!" is called factorial.
From the question, n = 10
EXACTLY 3 0s
10 combination 3
r is exactly 3, that is equal 3.
C 10,3= 10!/3!(10-3)! = 10!/3!7!= 120.
For clarification,
10!/3!7!=10×9×8/3×2×1 = 120.
You can also use a calculator to compute the factorials.
MORE 0s than 1s
There will be more 0s than 1s when < 5bits are 0s.
We have r<5
Therefore for r=4
C 10,4 = 10!/4!(10-4)!=10!/4!6!=210
r=3
C 10,3= 10!/3!(10-3)!=10!/3!7!=120
r=2
C 10,2=10!/2!(10-2)!=10!/2!8!=45
r=1
C 10,1=10!/1!(10-1)!=10!/1!9!=10
r=0
C 10,0=10!/0!(10-0)!=10!/0!10!=1
Summing the answers gives us our final answer
210+120+45+10+1= 386.
AT LEAST 7 1s
To get this combination, the value of r will be greater than or equal to 7
r>=7
We have,
r=7
C 10,7=10!/7!(10-7)!=10!/7!3!=120
r=8
C 10,8=10!/8!(10-8)!=10!/8!2!=45
r=9
C 10,9=10!/9!(10-9)!=10!/9!1!=10
r=10
C 10,10=10!/10(10-10)!=10!/10!0!=1
120+45+10+1= 176
AT LEAST 3 1s
the value for r will be greater than or equal to 3:
We can the values of r from 3 to 10.
r=3
C 10,3=10!/3!(10-3)!=120
r=4
C 10,4=10!/4!(10-4)!=10!/4!6!=210
r=5
C 10,5=10!/5!(10-5)!=10!/5!5!=252
r=6
C 10,6=10!/6!(10-6)!=10!/6!4!=210
r=7
C 10,7=10!/7!(10-7)!=10!/7!3!=120
r=8
C 10,8=10!/8!(10-8)!=10!/8!2!=45
r=9
C 10,9=10!/9!(10-9)!=10!/9!1!=10
r=10
C 10,10=10!/10!(10-10)!=10!/10!0!=1
Adding our answers gives 968.
The bits can be either 1 or 0. The total number of bit string for each specified case is:
Exactly three 0s : 120 stringsMore 0s than 1s: 386 stringsAt least seven 1s: 176 stringsAt least three 1s: 968 stringsHow to choose r items out of n indistinguishable items?Since the items are indistinguishable, their arrangements doesn't matter.
They can be chosen in [tex]^nC_r = \dfrac{n.(n-1).(n-2)...(n-(r+2)).(n-(r+1))}{r.(r-1).(r-2)...3.2.1} \: \rm (r \leq n)[/tex]
The bit string is of length 10.
Each bit can be in one of the two states, viz 0 or 1.
Evaluating the count of bit strings for given cases:
Case 1: Exactly three 0sThink of it as if there are 10 seats and 3 people to sit on. They're going to be 0s. 3 seats can be chosen from 10 seats in [tex]^{10}C_3 = \dfrac{10\times 9\times 8}{3 \times 2\times 1} = 120[/tex] ways.
The three 0s are identical, so no intra-arrangement between them matters.
Thus, total 120 such strings exist.
Case 2: More 0s than 1s:It means, 0s can be 6,7,8,9, or 10 places.
Just similar to above case, 0s on x places out of 10 places can be in [tex]^{10}C_x[/tex] ways.
Thus, total such strings of 0s being more than 1s and being 10 bit strings are:
[tex]^{10}C_6 + ^{10}C_7 + ^{10}C_8 + ^{10}C_9 + ^{10}C_{10} =210+120+45+10+1=386[/tex]
Case 3: At least seven 1s:At least seven 1s means either 7, 8, 9, or 10 ones.
Total count of such strings are:
[tex]^{10}C_7 + ^{10}C_8 + ^{10}C_9 + ^{10}C_{10} =120+45+10+1=176[/tex]
Case 4: At least three 1s:They are three or more ones. Total count of such strings is:
[tex]^{10}C_3 + ^{10}C_4 + ^{10}C_5+^{10}C_6 + ^{10}C_7 + ^{10}C_8 + ^{10}C_9 + ^{10}C_{10} =120 + 210 + 252 + 210+120+45+10+1=386+582=968[/tex]
Thus, the total number of bit string for each specified case is:
Exactly three 0s : 120 stringsMore 0s than 1s: 386 stringsAt least seven 1s: 176 stringsAt least three 1s: 968 stringsLearn more about combinations here:
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4x+9+3x=30
solve for x
Answer:
the answer is 3
7x + 9= 30
7x = 21
x = 3
Answer:
x = 3
Step-by-step explanation:
Collect like terms;
7x + 9 = 30
Subtract 9 from both sides;
7x = 21
Divide both sides by 7;
x = 3
Which of the following is NOT required to determine minimum sample size to estimate a population mean? Choose the correct answer below.
A. The desired confidence level
B. The desired margin of error
C. The size of the population, N
D. The value of the population standard deviation, sigma
Answer: c
Step-by-step explanation:
The minimum sample size does not depend on the size of the population
The size of the population, N, is NOT required to determine the minimum sample size for estimating a population mean, contrasting with the required elements like the desired confidence level, margin of error, and population standard deviation.
The question asks which factor is NOT required to determine the minimum sample size needed to estimate a population mean. The options are:
The desired confidence levelThe desired margin of errorThe size of the population, NThe value of the population standard deviation, sigmaThe correct answer is C. The size of the population, N. When estimating a population mean, the key factors required include the desired confidence level, the desired margin of error, and the value of the population standard deviation (sigma), but not necessarily the size of the population. This is especially true in cases where the population is very large or infinite, and the sample size needed for a specific confidence level and margin of error can be calculated without this information.
write the slope-intercept form of an equation that passes through (4,4) and is perpendicular to y=2x-4
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = y intercept
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. The equation of the given line is
y=2x-4
Slope = 2
Therefore, the slope of the perpendicular line is -1/2
It passes through point (4,4)
We would determine the intercept, by substituting m = -1/2 , y = 4 and x = 4 into the slope intercept equation
y = mx + c
4 = -1/2 ×4 + c
4 = -2 + c
c = 4 + 2 = 6
The equation becomes
y = -x/2 + 6
A fish tank contains tetras,guppies,and minnows. The ratio of tetras of guppies.Is 4:2.The ratio is minnows of guppies is 1:3. There are 60 fish on the fish tank. How many more tetras are there then minnows .
To find the difference between the number of tetras and minnows, set up a system of equations using the given ratios. Solve the system to find the number of tetras, guppies, and minnows. Finally, subtract the number of minnows from the number of tetras to find the difference.
Explanation:To determine the difference between the number of tetras and minnows in the fish tank, we need to first find the number of each type of fish. We can do this by setting up a system of equations using the given ratios. Let T represent the number of tetras, G represent the number of guppies, and M represent the number of minnows.
From the first ratio, we have T/G = 4/2. Simplifying this equation, we get T = 2G.
From the second ratio, we have M/G = 1/3. Simplifying this equation, we get M = (1/3)G.
Since we know there are a total of 60 fish in the tank, we can create the equation T + G + M = 60. Substituting the previous equations into this equation, we get 2G + G + (1/3)G = 60. Solving for G, we find G = 9. Plugging this value into the equations for T and M, we get T = 2(9) = 18 and M = (1/3)(9) = 3.
Therefore, there are 18 tetras and 3 minnows in the fish tank. The difference between the number of tetras and minnows is 18 - 3 = 15.
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Write a possible polynomial function in factored form with roots 0, -5, and 9.
Answer:
p(x) = x(x +5)(x -9)
Step-by-step explanation:
If r is a root, then (x -r) is a factor of the polynomial. For the given roots, the factorization is ...
p(x) = (x -0)(x -(-5))(x -9)
p(x) = x(x +5)(x -9)
A number that is multiplied by one or more numbers to get a product
Answer:
A factor
Step-by-step explanation:
Take the equation 2 x 4 = 8 as an example.
2 and 4 are multiplied together to get 8.
2 and 4 are factors, and 8 is the product.
In a study of 30 customers' utility bills in which the monthly bill was the dependent variable and the number of square feet in the house is the independent variable, the resulting regression model is = 23.40 + 0.4x. Based on this model, the expected utility bill for a customer with a home with 2,300 square feet is approximately $92.00.True / False.
Answer:
False
Step-by-step explanation:
If we take this equation at face value, the expected utility bill is ...
23.40 +0.4×2300
= 23.40 +920
= 943.40 ≠ 92.00
The equation does NOT predict a bill of $92.00.
The statement is false. Using the provided regression model (23.40 + 0.4x), the expected utility bill for a house of 2,300 square feet is $923.40, not $92.00.
Explanation:The subject of this question lies within the field of Mathematics, specifically within statistics and regression analysis. In the given example, we have a study of 30 customers focusing on their utility bills. The regression model for this study is 23.40 + 0.4x, where 'x' denotes the number of square feet in a house. This model shows the relationship between the size of the house (in square feet) and the monthly utility bill.
To address the student's question, we use this model to calculate the expected utility bill for a customer who has a 2,300 square feet house by substituting 'x' with 2300. The calculation becomes: 23.40 + 0.4*2300 = 923.40, not $92.00. Therefore, the expected utility bill is approximately $923.40, not $92.00. So, the statement in the question is False.
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You have been saving money in a piggy bank. Your piggy bank contains 75 coins that are all nickels and dimes. You take the money out of the bank to count, and find out that you have $5.95 saved up. How many dimes and how many nickels do you have?
You have 31 nickels and 44 dimes.
Step-by-step explanation:
Total coins = 75
Worth of coins = $5.95 = 5.95*100 = 595 cents
1 nickel = 5 cents
1 dime = 10 cents
Let,
Number of nickels = x
Number of dimes = y
According to given statement;
x+y=75 Eqn 1
5x+10y=595 Eqn 2
Multiplying Eqn 1 by 5
[tex]5(x+y=75)\\5x+5y=375\ \ \ Eqn\ 3\\[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](5x+10y)-(5x+5y)=595-375\\5x+10y-5x-5y=220\\5y=220[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{220}{5}\\y=44[/tex]
Putting y=44 in Eqn 1
[tex]x+44=75\\x=75-44\\x=31[/tex]
You have 31 nickels and 44 dimes.
Keywords: linear equations, subtraction
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Simplify the rational expressions. state any excluded values.
1. 2x-8/x-4
2. 4x-8/4x+20
3. x+7/x^2+4x-21
4. x^2-3x-10/x+2
5. x^2-4/2-x
I need help pleeeese
See the answers in explanation
Explanation:Let's solve this problem as follows:
First.[tex]\bullet \ \frac{2x-8}{x-4} \\ \\ Common \ factor \ 2 \ from \ the \ numerator: \\ \\ \frac{2x-8}{x-4}=\frac{2(x-4)}{x-4} =2[/tex]
Second.[tex]\bullet \ \frac{4x-8}{4x+20} \\ \\ Common \ factor \ 4 \ from \ the \ numerator \ and \ denominator: \\ \\ \frac{4x-8}{4x+20}=\frac{4(x-2)}{4(x+5)}=\frac{(x-2)}{(x+5)}[/tex]
Third[tex]\bullet \ \frac{x+7}{x^2+4x-21} \\ \\ Rearranging \ denominator: \\ \\ \frac{x+7}{x^2-3x+7x-21}=\frac{x+7}{x(x-3)+7(x-3)}=\frac{x+7}{x(x-3)+7(x-3)} \\ \\ Common \ factor \ x-3 \ from \ denominator: \\ \\ \frac{x+7}{(x-3)(x+7)}=\frac{1}{x-3}[/tex]
Fourth.[tex]\bullet \ \frac{x^2-3x-10}{x+2} \\ \\ Rearranging \ numerator: \\ \\ \frac{x^2-3x-10}{x+2}=\frac{x^2-5x+2-10}{x+2}=\frac{x(x-5)+2(x-5)}{x+2} \\ \\ Common \ factor \ x-5 \\ \\ \frac{(x-5)(x+2)}{x+2}=x-5[/tex]
Fifth.[tex]\bullet \ \frac{x^2-4}{2-x} \\ \\ Difference \ of \ squares \ from \ numerator: \\ \\ \frac{(x-2)(x+2)}{2-x} \\ \\ Common \ factor \ -1 \ from \ denominator: \\ \\ \frac{(x-2)(x+2)}{-(x-2)}=-(x+2)[/tex]
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The moving averages method refers to a forecasting method that
a. relates a time series to other variables that are believed to explain or cause its behavior.
b. uses regression relationship based on past time series values to predict the future time series values.
c. uses the average of the most recent data values in the time series as the forecast for the next period.
d. is used when considerable trend, cyclical, or seasonal effects are present
Answer:
c. uses the average of the most recent data values in the time series as the forecast for the next period.
Step-by-step explanation:
We assume you want to complete the description of moving averages method.
The moving in moving averages refers to the fact that the data points used to compute the average are some number of most recent data points. As data is accumulated, the data used to compute the average "moves" to include the newest data and exclude the oldest data.