Answer:
The correct option is false
Step-by-step explanation:
Generally the Central Limit Theorem tells us that the sample means will be normally distributed with sufficiently large sample size( i.e [tex]n \ge 30[/tex] ) regardless of the shape of the population distribution.
But the question states that the mean is normally distributed if the sample size is 5 or more which is false hence the statement is false
Evaluate: [(- 16) + 4] ÷ [(-2) + 5]
Answer:
We need to evaluate this: [(-16)+4] / [(-2)+5]
First, we do the brackets:
[(-16)+4][(-2)+5][(-16)+4] = -16 + 4 = -12
[(-2) + 5] = -2 + 5 = 3
Now, we only need to divide, as we have calculated both brackets:
-12/3 = -4
(Remember that when dividing a negative number by a positive one, we always obtain a negative)
So the result is -4
Let un be the nth Fibonacci number. Prove that the Euclidean algorithm takes precisely n steps to prove that gcd(un+1, un) = 1.
Hello, Please consider the following.
Fibonacci numbers are defined as
[tex]u_0=1\\\\u_1=1\\\\u_{n+2}=u_{n+1}+u_{n} \ for \ n\geq 0[/tex]
Step 1 - The proposition is true for n = 1
[tex]GCD(u_2,u_1) ?\\[/tex]
Let's apply Euclidean algorithm
[tex]u_1=1, u_2=2\\\\u_2=2\times u_1+0 = 2 \times 1 +0[/tex]
This is exactly 1 step and [tex]GCD(u_2,u_1) =1[/tex]
Step 2 - We assume that this is true for k, meaning that the Euclidean algorithm takes precisely k steps to prove that [tex]GCD(u_{k+1},u_{k})=1[/tex]
[tex]u_{k+2}=u_{k+1}+u_k \ and \ 0 < u_k < u_{k+1}[/tex]
So, the first step of the algorithm is
[tex]u_{k+2}=u_{k+1}\times 1 +u_{k}[/tex]
And from now, we need to find [tex]GCD(u_{k+1},u_k)[/tex] which is 1 and takes k steps, by induction Hypothesis. Therefore, it takes k + 1 steps to find [tex]GCD(u_{k+2},u_{k+1})=1[/tex]
Step 3 - Conclusion
We have just proved that the Euclidean algorithm takes precisely n steps to prove that [tex]GCD(u_{n+1},u_{n})=1[/tex]
Thanks
1. Write 206 in base 7 2. The number 3, 956, 427, 8ab is divisible by 72. Calculate a and b.
Answer:
k
Step-by-step explanation:
Annie is running a trail that is 4 1/2 miles long. She ran the first 2/3 of the distance. Then the trail became very steep, so she slowed down to a walk. Annie walked for 1/2 of the remaining distance and then ran again for the rest of the way. How far did Annie walk? Write the answer as a simplified fraction.
Answer:
Annie walked 1 11/12 miles
Step-by-step explanation:
Trail= 4 1/2 miles
Annie ran the first 2/3 miles
Remaining miles= Total miles - Miles covered first
= 4 1/2 - 2/3
= 9/2 - 2/3
= 27-4 / 6
= 23/6 miles
Remaining miles = 23/6 miles
Annie walked for 1/2 of the remaining distance
1/2 of the remaining miles= 1/2 × 23/6
=23 / 12
= 1 11/12
Annie walked 1 11/12 miles
Which of the following is an example of earning income from capital gains?
a hourly employee earning $17 per hour
b. salaried employee earning $56,000 per year
c. selling a car and making a profit of $3,000
d. selling stocks for a total of $5,000
Answer:
C. selling a car and making a profit of $3,000
Step-by-step explanation:
An example of earning income from capital gains is selling a car and making a profit of $3,000 which the correct answer would be an option (C).
What is capital gross?Gross capital formation for a unit or sector is calculated using the total value of gross fixed capital growth, changes in inventories, and asset acquisitions with fewer asset disposals.
As we know, from the meaning of capital gain:
When a capital asset is sold, the rise in value is known as a capital gain.
Selling a car and getting $3,000 in profit is one example of making money through capital gains.
An example of earning income from capital gains is selling a car and making a profit of $3,000
Hence, the answer would be option (C).
Learn more about the capital gross here:
https://brainly.com/question/2948028
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explain please!!
12. A shipment of TV sets, some weighing 30 kg each and the other weighing 50 kg each, has a total weight of 220 kg. If there
are 20 TV sets all together, how many weigh 50 kg and how many weigh 30 kg?
A. 6 weigh 50 kg and 14 weigh 30
B. 15 weigh 50 kg and 5 weigh 30.
C. 2 weigh 50 kg and 18 weigh 30
D. 14 weigh 50 kg and 6 weigh 30
E. 4 weigh 50 kg and 16 weigh 30
F. 11 weigh 50 kg and 9 weigh 30
Answer:
D
Step-by-step explanation:
Let a be the number of TV sets that weight 30 kg and let b be the number of TV sets that weigh 50 kg.
So, all together, they have a total weight of 880. In other words:
[tex]30a+50b=880[/tex]
And, there are 20 TV sets all together. Thus:
[tex]a+b=20[/tex]
This is a system of equations. Solve by substitution. Subtract b from both sides in the second equation:
[tex]a+b=20\\a=20-b[/tex]
Substitute this into the first:
[tex]30a+50b=880\\30(20-b)+50b=880[/tex]
Distribute:
[tex]600-30b+50b=880[/tex]
Subtract 600 from both sides:
[tex]-30b+50b=280[/tex]
Combine like terms:
[tex]20b=280[/tex]
Divide both sides by 20:
[tex]b=14[/tex]
So, there are 14 TV sets that weight 50 kg.
Plug this in for the second equation to solve for a:
[tex]a+b=20[/tex]
Plug in 14 for b:
[tex]a+14=20[/tex]
Subtract 14 from both sides:
[tex]a=6[/tex]
Therefore, there are 6 TV sets that weigh 30 kg and 14 TV sets that weigh 50 kg.
Our answer is D :)
Step-by-step explanation:
Total number of T..V sets we have 20
Let x be the number of T.V sets that weigh 30 kg and y be the no. of sets that weigh 50 kg
When we add all we get a total of 880
[tex]\blue\star[/tex] 30a + 50b = 880
It is given to us that
[tex]\blue\star[/tex]a + b = 20. eq 1
[tex]\blue\star[/tex]a = 20-b
Put the value of a in ist equation we get,
[tex]\blue\star[/tex]30(20-b) + 50b =880
[tex]\blue\star[/tex]600 - 30b+50b = 880
[tex]\blue\star[/tex]600 + 20b = 880
[tex]\blue\star[/tex]20b = 280
[tex]\blue\star[/tex] b = 14
so there are 14 T.V sets that weigh 50 kg
put it in eq 1 we get
[tex]\blue\star[/tex] a + b =20
[tex]\blue\star[/tex]a + 14 = 20
[tex]\blue\star[/tex]a = 6
Hope it helps.
n ΔABC, AB = 10 and BC = 5. Which expression is always true? A. 5 < AC < 10 B. AC = 5 C. 5 < AC < 15 D. AC = 10
Answer:
A. 5 < AC < 10
Step-by-step explanation:
We are given the ∆ABC
To solve for the sides of ∆ABC , we make use of Pythagoras Theorem
Pythagoras Theorem states that:
AB² = AC² + BC²
Where AB = Longest side, hence its length is always more that AC and BC.
In the above Question, we are given the values of AB and BC
AB = 10
BC = 5
Inputting these values into the Pythagoras Theorem,
10² = AC² + 5²
100 = AC² + 25
AC² = 100 - 25
AC² = 75
AC = √75
AC = 8.6602540378
According to the above calculation, we can see that the expression that is always true = Option A "5 < AC < 10"
Factor the trinomial completely.
4u^4 + 4u^3 - 6u^2
Answer:
See below.
Step-by-step explanation:
So we have the expression:
[tex]4u^4+4u^3-6u^2[/tex]
First, factor out the GCF.
The GCF is 2u². Thus:
[tex]=2u^2(2u^2+2u-3)[/tex]
And this is the simplest it can get.
So we are done :)
Payton leaves to go on an 85 minute bike ride at 3:27 p.m.Payton's family eats dinner at 5:45 p.m How much time will Payton have between finishing her bike ride and eating dinner?
He starts to ride at 3:27 p.m.
85 minutes -> hours = 1 h 25 minutes (85/60 = 1 with 25 of rest)
3:27 + 1 h 25 min = h. 4:52
between 4:52 and 5:45 =>
5 hours 45 min - 4 hours 52 minutes =
4h 105 min ( 1h = 60min ) - 4h 52 min =
0h 53min
Payton has 53 minutes
Answer:
53 minutes
Step-by-step explanation:
Payton leaves at 3:27 p.m. and rides for 85 minutes. When she has finished, the time will be 3:27 + 0:85, or
3:27 + 1:25, since 1 hr = 60 min
4:52 p.m.
Dinner will be at 5:45 p.m. That means Payton will have (5:45 - 4:52) hours until dinner: Borrowing 60 minutes from 5:45, we get
4:105 - 4:52 = 0:53. That's 53 minutes to while away before dinner.
What is 9+(5x10)+1-(15x2)
Step-by-step explanation:
Answer:30. hope this helps
Answer:
30
Step-by-step explanation:
9+(5x10)+1-(15x2)
Multiply the numbers
9+(50)+1-(30)
9+50+1-30
30
how do you determine when a counting problem involves a permutation or a combination?
Find two consecutive whole numbers that \sqrt(48)
lies between.
Answer:
6 and 7
Step-by-step explanation:
Step 1: Find 2 perfect square roots
√36 = 6
√49 = 7
√36 < √48 < √49
6 < √48 < 7
So, between 6 and 7
Janine completed 36 math problems. Craig completed 9 math problems. The number of problems that Janine completed is how many times the number of problems that Craig completed?
Divide the number Janine did by the number Craig did:
36/9 = 4
Janine did 4 times as many as Craig
Answer:
4 times
Step-by-step explanation:
Because 36 divided by 9 = 4
So your answer is 4 times the number of problems.
3/4 times 7 i need help plz
Answer:
5.25 or 21/4 or 5 1/4
Step-by-step explanation:
hope this helps
Mark borrowed $5,500 at 11.5 percent for five years. What is the amount of Mark's total payment? $8,520 $8,160 $7,410 $7,257
Answer:
7,257
Step-by-step explanation:
use the formula of: M = amount/discount factor
State the domain and range for the following relation. Then determine whether the relation represents a function
Choose the correct answer below.
A.) Domain : {Red, Yellow
Range - Color
B.) Domain : {XS, Red, Yellow, 45, A}
Range = {Size, Color, Number, Letter)
C.) Domain : {Size, Color, Number, Letter}
Range : XS, Red, Yellow. 45. A}
D.) Domain : {Size Number, Letter)
Range : XS, 45, A
can someone please help me figure this out i think its B but im not sure
Answer:
Domain: {XS, Red, Yellow, 45, A}
Range: {Size, Color, Number, Letter}
Step-by-step explanation:
The domain of the function shown in the mapping above are all variables that fall under "A word", while the range consists of all variables under "category".
The mapping shows that the relation represents a function, because each domain variable has exactly one range variable. No single domain variable is mapped to two different range variable.
The correct answer is:
Domain: {XS, Red, Yellow, 45, A}
Range: {Size, Color, Number, Letter}
A truck rental serivce charges a $20 insurance fee and $30 an hour to rent a trick. Write an equation that can be used to find c,the cost for rent a truck for n hours.
Answer:
c=30n+20 represents the cost to rent a truck for n hours.
Step-by-step explanation:
$30 dollars an hour multiplied by n.
30n
+20 for the insurance for the truck.
Jessica takes 4 business trips a month for x months in a row. Write an expression to show how many business trips Jessica has taken.
Answer:
[tex] t = 4x [/tex]
Step-by-step explanation:
We are given that in 1 month, Jessica takes 4 business trips. Take 4 as our coefficient or constant.
Let t be the total number of business trips Jessica has taken.
For 1 month, 4 trips are taken.
For x months, total business trips taken will be expressed as,
[tex] t = 4x [/tex]
Let's say for example, we have 5 months in a row, i.e. x = 5. Total business trips taken by Jessica can be gotten by simply plugging in the value of x.
[tex] t = 4(5) = 20 trips [/tex]
In 5 months in a row, Jessica takes 20 business trips.
Which product will be negative?
7 x (-9)
-3x(-5)
-2x (-1)
6x6
Answer:
7*(-9)
Step-by-step explanation:
A negative multiplied by a negative causes them to cancel out and become positive and two positives being multiplied are always positive
HOPE THIS HELPS!!!!! :)
<3333333333
Answer:
7 x (-9)
Step-by-step explanation:
7 x (-9) = -63
-3 x (-5) = 15
-2 x (-1) = 2
6 x 6 = 36
Can you multiply it all out? Yes. Did you need to? No. That was just to prove that the first choice is correct.
All you have to know to answer this is that:
positive * positive = positive; + * + = +
negative * negative = negative; - * - = +
positive * negative (or negative * positive; remember that the order of the numbers you're multiplying does not matter) = negative; + * - = - or - * + = -
Or if you learn better in words:
If two factors have the same sign, the answer is positive.
If two factors have different signs, like if one is positive and the other is negative, then the answer is negative.
Please mark as Brainliest! :)
Solve the system of equations using Gaussian elimination.
[tex]4x+y-3z &= 11 \\2x-3y+2z &= 9 \\x+y+z &= -3[/tex]
The solution (with steps) and answer are included in the images below.
Best of Luck!
Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 + 1/32 squareroot + 1/243 squareroot 3 + 1/1024 squareroot 4 + 1/3125 squareroot 5 + p = ______
converges
diverges
Answer:
Diverges
Step-by-step explanation:
since the value of P = 5/6 < 1 the p-series diverges
summation of 1/n^5/6 at n = 1 and infinity
attached below is the detailed solution using Theorem 9.11 to determine the convergence or divergence of the p-series
The value of the p in the p-series is less than one. Then the p-series is a divergence.
What is p-series?It is an infinite type of series.
The p-series is given below.
[tex]1 + \dfrac{1}{\sqrt[6]{32} } +\dfrac{1}{\sqrt[6]{243} }+\dfrac{1}{\sqrt[6]{1024} }+\dfrac{1}{\sqrt[6]{3125} }[/tex]
The series can be written as
[tex]\dfrac{1}{1^{5/6}}+\dfrac{1}{2^{5/6}}+\dfrac{1}{3^{5/6}}+\dfrac{1}{4^{5/6}}+\dfrac{1}{5^{5/6}}[/tex]
Then the sum will be
[tex]\rm \Rightarrow \Sigma _{n=0} ^{\infty} \dfrac{1}{n^{5/6}} \\\\\\\Rightarrow P = \dfrac{5}{6} < 1[/tex]
Since the value of the p is <1. Then the series is divergence.
More about the p-series link is given below.
https://brainly.com/question/24249275
Solve the linear equation for y in terms of x. -8x-y=12
Answer:
1.5
Step-by-step explanation:
Answer: y=-8x -12
Step-by-step explanation:
-8x - y =12 to solve for y add -8x to both sides
+8x +8x
-y = 12 +8x Now divide each side by -1
y = -8x -12
A rectangular field is nine times as long as it is wide. If the perimeter of the field is 1200 feet, what are the dimensions of the field?
A) Write an equation you can use to answer the given question. Let
w be the width of the field. Do not solve the equation yet.
What is the equation?
(Make sure you use the correct variable.)
B) Use your equation to find the dimensions of the field.
The width of the field is how many feet?
The length of the field is how many feet?
Answer:
width=60 length=540
Step-by-step explanation:
(w+9w)*2=1200
what is -0.4 as a fraction or mixed number?
Answer:
-0.4 = −2/5
Step-by-step explanation:
Rewrite the decimal number as a fraction.
-0.4/1
Multiply to remove 1 decimal places.
-0.4/1 x 10/10 =4/10
Find the GCF.
4 ÷ 2/10 ÷ 2 = 2/5
x = 2/5
-2/5
Twice the difference of x and 7, is -23
Answer:no its 24
Step-by-step explanation:
bc x is like 15
Find the equation of a line through B(5,2) which is perpendicular to the line 3x+5=0. Hence find the coordinate of the foot of the perpendicular from B to the line.
Answer:
y=2, the equation of a line which is perpendicular to the line 3x+5=0
A(-5/3,2) the foot of the perpendicular from B to the line
Step-by-step explanation:
d1 : 3x+5=0, so 3x=-5, x=-5/3
y=2, the equation of a line which is perpendicular to the line 3x+5=0
A(-5/3,2) the foot of the perpendicular from B to the line
The phrase "linear regression" pertains to regression models with normal equations that can be expressed in matrix form using linear algebra to determine coefficient estimates.
A. True
B. False
Answer:
TRUE ( A )
Step-by-step explanation:
linear regression represents/ models the linear relationship between a dependent/scalar variable and an independent variable or one or more independent variables
Linear regression pertains to regression models with normal equations because Linear regressions can be calculated using a linear equation/algebra
example : Y= a + bX
the side lenghts of a square measures 10x+5. the side lenghts of a triangle are 30x,3x and 6x+30. the square and triangle have the same perimeter. find the perimeter
PLEASEEEEE HELPP<333
Answer:
58
Step-by-step explanation:
We can use the Pythagorean theorem to find the area of the square for the third side.
The equation for the Pythagorean theorem is
a^2 + b^2 = c^2
where a and b are the lengths of the two legs of the triangle, and c is the length of the hypotenuse.
a^2 + b^2 = c^2
3^2+7^2=x^2
9+49=x^2
58=x^2
The area of the square for the third side of the triangle is 58 units^2 squared.
Create an example of a situation where there is a negative cash flow.
Answer:
when say your expenses are $400 a month but your income is only $350 a month that is -$50 every month so in that case you aren't getting a positive cash flow (which would be making more money than your expenses) So you must be getting a negative cash flow in which you are losing money and going into debt.
Hope this Helps :)
PLSSS HELP WITH THIS ONE !!! MARKING AGAIN THE BRAINLIST ANSWER!!!
Answer:
Step-by-step explanation:
He earned $15.20. Just multiply the 2.00x4 and the 2.40x3