Answer:
Greatest number = 9867
Smallest number = 1027
Step-by-step explanation:
Greatest number:
- - - 7
In order to form the greatest number, we should simply put the greatest available digit at the thousands place, the second greatest at the hundreds place and the third greatest at the tens place (which would be 9, 8, and 6 respectively).
9867
Smallest number:
- - - 7
In order to form the greatest number, we should simply put the lowest available digit at the thousands place (excluding zero since a number can't start with a zero), put zero at the hundreds place and the third lowest at the tens place (which would be 1, 0, and 2 respectively).
1027
26.355 rounded to the nearest hundredth tell anser
Answer:
26.36
Step-by-step explanation:
Hundredths are the second decimal place from the decimal. You would round up to 26.36 because the number before that is up to 5. If it was below 5 you would round down to 26.35.
Please help me I will mark BRAINLIEST THANK YOUUUUU
Answer:
33%
Step-by-step explanation:
The multiples of 3 are 3,6,9,12
Sum is 6+14+12+1 = 33
The total is 3+6+8+11+14+16+15+12+9+5+1=100
The experimental probability is number of multiples of 3 over the total
33/100 = 33%
John is going for a walk. He walks for 6.4 miles at a speed of 2 miles per hour. For how many hours does he walk?
Answer:
t = d/s
t = 6.4 / 2 miles
t = 3.2 miles
Step-by-step explanation:
follow me plzzz
2. Ricardo descended to a depth of 24 feet
below sea level. His friend Martin
descended 3 times as far. Write the
depth of Martin's descent as an integer.
Answer:
-72
Step-by-step explanation:
3*24=72
So he is 72 foot below see level or -72
Martin descended to a depth of 72 feet below sea level.
How to calculate the integerRicardo descended to a depth of 24 feet below sea level. His friend Martin descended 3 times as far.
If Ricardo descended to a depth of 24 feet below sea level, and Martin descended three times as far, we can calculate Martin's descent by multiplying Ricardo's depth by 3.
Martin's depth = Ricardo's depth * 3
Martin's depth = 24 feet * 3
Martin's depth = 72 feet
Therefore, Martin descended to a depth of 72 feet below sea level.
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Help pls any kind soul pls help
Answer:
3x
Step-by-step explanation:
If Dan is x years old and Olly is 3 times as old, that means that Olly's age is 3 * x or 3x for short.
Answer:
3x
Step-by-step explanation:
If Dan is x years old and Olly is 3 times old as Dan, then the expression is 3x.
The Greatest Common Factor (GCF) of 4x3 - 2x2 + 8x is:
A. 2x
B. 2.
C. X
D.None of these choices are correct.
Answer:
A. 2x
Step-by-step explanation:
Step 1: Factor out a 2
2(2x³ - x² + 4x)
Step 2: Factor out an x
2x(2x² - x + 4)
So our answer is B.
Select the correct answer for the blank: If everything else stays the same, the required sample size ____ as the confidence level decreases to reach the same margin of error. Answer:
Answer:
The required sample size increases.
Step-by-step explanation:
The margin of error of a confidence interval is given by:
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which z is related to the confidence level(the higher the confidence level the higher z), [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this question:
The confidence level decreases, so z decreases.
For the margin of error to stay the same, the sample size also has to decrease.
The required sample size increases.
69/8 as a mixed number
Answer:
Hey!
69/8 as a mixed number is...
8 5/8!
To get this answer, simply divide 69 by 8, then subtract the WHOLE NUMBER from 69 and then the left over number is the numerator over 8
Hope this helps!
Answer:
8 5/8
Step-by-step explanation:
Divide and answer in simplest form: 1/5 ÷ 7
Answer: 1/35
Step-by-step explanation:
1/5 = 0.2
0.2/7= 1/35
Answer:
[tex] \frac{1}{35} [/tex]Step by step explanation
[tex] \frac{1}{5} \div 7[/tex]
Dividing is equivalent to multiplying with the reciprocal:
[tex] \frac{1}{5} \times \frac{1}{7} [/tex]
Multiply the fraction
[tex] \frac{1 \times 1}{5 \times 7} [/tex]
[tex] = \frac{1}{35} [/tex]
Hope this helps...
Good luck on your assignment.
David and Tina share their profit in a ratio of 5:7. Tina gets £70 more than David. How much money did David receive?
Answer:
Amount of money David received = £ 175
Step-by-step explanation:
Both of them share their profit in a ratio of 5:7 . Tina got £70 more than David. Let
the amount David received = a
amount Tina received = 70 + a
the total profit = 70 + 2a
Amount David received = 5/12 × 70 + 2a = a
Therefore,
5/12 × 70 + 2a = a
350 + 10a/12 = a
cross multiply
350 + 10a = 12a
collect like terms
350 = 12a - 10a
350 = 2a
divide both sides by 2
a = 350/2
a = 175
Amount of money David received = £ 175
Which expression is not requivalent to
3x - 2?
Answer:
anything that is not -2+3x or x=2/3 is wrong
Step-by-step explanation:
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The calculated value for the test statistic equals a. 20. b. 4. c. 2. d. -2.
Answer:
[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The expected values for all the categories is :
[tex] E_i =\frac{150}{3}=50[/tex]
And then the statistic would be given by:
[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]
And the best option would be:
b. 4
Step-by-step explanation:
For this problem we have the following observed values:
Yes 40 No 60 No Opinion 50
And we want to test the following hypothesis:
Null hypothesis: All the opinions are uniformly distributed
Alternative hypothesis: Not All the opinions are uniformly distributed
And for this case the statistic would be given by:
[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The expected values for all the categories is :
[tex] E_i =\frac{150}{3}=50[/tex]
And then the statistic would be given by:
[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]
And the best option would be:
b. 4
Any help would be greatly appreciated
Answer: (-3, -2)
Step-by-step explanation:
Plug in -2 for y to find x
x - 5(-2) = 7
Multiply -5 and -2
x + 10 = 7
Subtract 10 from both sides
x = -3
The first ordered pair is (-3, -2)
Basic kinematics. Please help! Will give brainliest! Show all work!
Answer: 3.5 m/s
Step-by-step explanation:
[tex]v=\frac{vf+vi}{2}[/tex]
[tex]v=\frac{5+2}{2}[/tex]
5+2=7
7/2= 3.5
Find two paths of approach from which one can conclude that the function has no limit as (x, y) approaches (0, 0).
Answer:
for us to be able to ascertain whether a function has no limit we approach from two points which are from zero and infinity.
Step-by-step explanation:
the two best path to approach a function is to approach from zero and approach from infinity, literary what we are trying to do is approach from the smallest to the greatest and it each point we can conclude with certainty whether the function has a limit or not.
The larger of two numbers is 33 more than the smaller. When added together, the sum of the larger number and five times the smaller number is 129. What are the two numbers? larger number = ___ smaller number = ____ Please Help!
Step-by-step explanation:
let the larger number be x and smaller number be y
according to this question
x=y+33----------(1)
y+33+5y=129----------(2)
6y+33=129
y=16
x=16+33(takimg equation (1)
x=49
Answer:
Larger number: 49.
Smaller number: 16.
Step-by-step explanation:
Let's say that the larger number is represented by y, and the smaller is represented by x.
y = 33 + x
y + 5 * x = 129
(33 + x) + 5x = 129
6x + 33 = 129
6x = 96
x = 16
y = 33 + 16
y = 49
Check our work...
49 + 5 * 16 = 49 + 80 = 129
49 = 33 + 16 = 49
Since it all works out, the larger number is 49 and the smaller number is 16.
Hope this helps!
Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D is the triangular region with vertices (0, 0), (2, 1), (0, 3); rho(x, y) = 2(x + y)
The mass of the lamina is 6 units.
The center of mass of the lamina is (X,Y) = (-3/2, 9/2).
Here,
To find the mass and center of mass of the lamina, we need to integrate the density function ρ(x, y) over the triangular region D.
The mass (M) of the lamina is given by the double integral of the density function over the region D:
M = ∬_D ρ(x, y) dA
where dA represents the differential area element.
The center of mass (X,Y) of the lamina can be calculated using the following formulas:
X = (1/M) ∬_D xρ(x, y) dA
Y = (1/M) ∬_D yρ(x, y) dA
Now, let's proceed with the calculations:
The triangular region D has vertices (0, 0), (2, 1), and (0, 3). We can define the limits of integration for x and y as follows:
0 ≤ x ≤ 2
0 ≤ y ≤ 3 - (3/2)x
Now, let's calculate the mass (M):
M = ∬_D ρ(x, y) dA
M = ∬_D 2(x + y) dA
We need to set up the double integral over the region D:
M = ∫[0 to 2] ∫[0 to 3 - (3/2)x] 2(x + y) dy dx
Now, integrate with respect to y first:
M = ∫[0 to 2] [x(y²/2 + y)] | [0 to 3 - (3/2)x] dx
M = ∫[0 to 2] [x((3 - (3/2)x)²/2 + (3 - (3/2)x))] dx
M = ∫[0 to 2] [(3x - (3/2)x²)²/2 + (3x - (3/2)x²)] dx
Now, integrate with respect to x:
[tex]M = [(x^3 - (1/2)x^4)^2/6 + (3/2)x^2 - (1/4)x^3)] | [0 to 2]\\M = [(2^3 - (1/2)(2^4))^2/6 + (3/2)(2^2) - (1/4)(2^3)] - [(0^3 - (1/2)(0^4))^2/6 + (3/2)(0^2) - (1/4)(0^3)]\\M = [(8 - 8)^2/6 + 6 - 0] - [0]\\M = 6[/tex]
So, the mass of the lamina is 6 units.
Next, let's calculate the center of mass (X,Y):
X = (1/M) ∬_D xρ(x, y) dA
X = (1/6) ∬_D x * 2(x + y) dA
We need to set up the double integral over the region D:
X = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] x * 2(x + y) dy dx
Now, integrate with respect to y first:
X = (1/6) ∫[0 to 2] [x(y² + 2xy)] | [0 to 3 - (3/2)x] dx
X = (1/6) ∫[0 to 2] [x((3 - (3/2)x)² + 2x(3 - (3/2)x))] dx
X = (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x² + 6x - (3/2)x²)] dx
X = (1/6) ∫[0 to 2] [(9/4)x³ - (3/2)x⁴ + 15x - (3/2)x³] dx
Now, integrate with respect to x:
[tex]X = [(9/16)x^4 - (3/8)x^5 + (15/2)x^2 - (3/8)x^4] | [0 to 2]\\X = [(9/16)(2)^4 - (3/8)(2)^5 + (15/2)(2)^2 - (3/8)(2)^4] - [(9/16)(0)^4 - (3/8)(0)^5 + (15/2)(0)^2 - (3/8)(0)^4]\\X = [9/2 - 12 + 15 - 0] - [0]\\X = 15/2 - 12\\X = -3/2[/tex]
Next, let's calculate Y:
Y = (1/M) ∬_D yρ(x, y) dA
Y = (1/6) ∬_D y * 2(x + y) dA
We need to set up the double integral over the region D:
Y = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] y * 2(x + y) dy dx
Now, integrate with respect to y first:
Y = (1/6) ∫[0 to 2] [(xy² + 2y²)] | [0 to 3 - (3/2)x] dx
Y = (1/6) ∫[0 to 2] [x((3 - (3/2)x)²) + 2((3 - (3/2)x)²)] dx
Y= (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x²) + 2(9 - 9x + (9/4)x²)] dx
Y = (1/6) ∫[0 to 2] [(9x - 9x² + (9/4)x³) + (18 - 18x + (9/2)x²)] dx
Now, integrate with respect to x:
[tex]Y= [(9/2)x^2 - 3x^3 + (9/16)x^4) + (18x - 9x^2 + (9/6)x^3)] | [0 to 2]\\Y = [(9/2)(2)^2 - 3(2)^3 + (9/16)(2)^4) + (18(2) - 9(2)^2 + (9/6)(2)^3)] - [(9/2)(0)^2 - 3(0)^3 + (9/16)(0)^4) + (18(0) - 9(0)^2 + (9/6)(0)^3)]\\Y = [18 - 24 + 9/2 + 36 - 36 + 12] - [0]\\Y= 9/2[/tex]
So, the center of mass of the lamina is (X,Y) = (-3/2, 9/2).
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An electrician earns $50 per hour, and expects to earn $5 additional per hour as each year passes. Find the electrician’s hourly wage after 8 years have elapsed.
Consider the two savings plans below. Compare the balances in each plan after 14 years. Which person deposited more money in the plan? Which of the two investment strategies is better? Yolanda deposits $100 per month in an account with an APR of 5%, while Zach deposits $1200 at the end of each year in an account with an APR of 5%.
Step-by-step explanation:
It is not specified the compounding period, which in general is a month these days. So we will assume money is compounded each month, otherwise there is no point depositing monthly.
1. Yolanda:
APR=5% is equivalent to
Monthly interest = 5%/12 = 5/12% = 5/1200 = 1/240 = i
Monthly deposit = 100 = A
Future value after 14 years = 14*12 months = 168 months = n
FV1 = A((1+i)^n-1)/i
=100*((1+1/240)^168-1)/(1/240)
= $24259.83
2. Zach
He deposits 1200 at the end of the year. The last payment does not benefit from interest.
Since it is a yearly payment, each amount earns interest over a year, giving an annual interest of
(1+i)^12 -1 = 1.051161897881733 -1 =0.051161897881733 = j
Thus for 13 annual payments with annual interest j gives a compounded amount after 14 years, plus the last payment which does not earn interest
FV2 = A((1+j)^n-1)/j
= 1200((1.051161897881733)^13-1)/(0.051161897881733)+1200
= 22613.34
Summary
Total investments:
Yolanda = 12*100*14 = 16800
Zach = 1200 * 14 = 16800
So both investors have invested $16800 over the 14 year period.
Since Yolanda achieves a higher future value after 14 years ($24259.83) over that of Zach ($22613.34), financially Yolanda has a better strategy.
Note:
If zach had invested annually at the beginning of the year, he would have obtained:
A((1+j)^n-1)/j
= 1200((1.051161897881733)^14-1)/(0.051161897881733)
= 24908.88
which is superior over Yolanda's return.
Please answer this correctly
Answer:
12.5%
Step-by-step explanation:
There is only 1 seven card from the 8 total cards.
1 out of 8.
1/8 = 0.125
P(7) = 12.5%
Answer:
12.5%
Step-by-step explanation:
Total Cards = 8
Number 7 = 1
P(7) = 1/8
In %age:
=> 12.5%
Convert 58% to a decimal
Answer: 0.58
Step-by-step explanation: To write a percent as a decimal, first remember that a percent is a ratio that compares a number to 100.
So we can think of 58% as the ratio 58 to 100 or 58/100.
Dividing by 100 moves the decimal point 2 places to the left so 58/100 would move the decimal point 2 places to the left which would give us .58 or 0.58. So 58% can be written as the decimal 0.58.
Simplify the square root of 2 times the cube root of 2.
two to the one sixth power
two to the two thirds power
two to the five sixths power
two to the seven sixths power
Answer:
2 to the 1/6 th power
Step-by-step explanation:
square root = 1/2
Cube root = 1/3
so 1/3 x 1/2= 1/6
can i please have brainlest
Answer:
2 to the 1/6 th power
Step-by-step explanation:
square root = 1/2
Cube root = 1/3
so 1/3 x 1/2= 1/6
can i please have brainlest
Two bond funds pay interest at rates that differ by 4%. Money invested for one year in the first fund earns $550 interest. The same amount invested in the other fund earns $770. Find the lower rate of interest. _________ %
Answer:
10% interest.
Step-by-step explanation:
Interest I = PRT/100
If the rate R = x% we have
550 = P*x *1 / 100
and
770 = P*(x + 4) * 1 / 100
so From first equation
Px = 55000 and from the second
Px + 4P = 77000
So Px = 77000 - 4P
Therefore 77000 - 4P = 55000
4P = 22000
P = 5,500
So x = 55000/5500 = 10%.
And the rate for the other fund is 10 + 4 = 14%.
Triangle L M N is shown. Angle L M N is a right angle. Angles N L M and L M N are 45 degrees. The length of L N is x. Which statements are true regarding triangle LMN? Check all that apply. NM = x NM = LM = x StartRoot 2 EndRoot tan(45°) = StartFraction StartRoot 2 EndRoot Over 2 EndFraction tan(45°) = 1
Answer:
A.) NM= x
C.) LM = x√2
E.) tan (45°) = 1
Step-by-step explanation:
If the legs are both x, then the hypotenuse is equal to [tex]x\sqrt{2[/tex]
Therefore, LM= [tex]x\sqrt{2[/tex] is correct and MN= x
Disclaimer: The sum is done according to the picture attached as the question given is wrong.
The true statements regarding the given isosceles right triangle ΔLMN are:
NM = xLM = x√2tan 45° = 1.What are isosceles right triangles?An isosceles triangle is a triangle where two sides and their corresponding angles are equal.
A right triangle is a triangle with one angle = 90°.
An isosceles right triangle is a right-angled triangle with two legs including the right angle are equal. Their corresponding angles are equal and each of them = 45°. So, the three angles of an isosceles right triangle are 45°, 45°, and 90°, always.
How do we solve the given question?In the figure, we can see that we have a ΔLMN, with ∠L = 45°, ∠M = 45°, and ∠N = 90°. Also, we can see that LN = x.
The given angles of ΔLMN determine that it is an isosceles right triangle with a right angle at N.
Since, the two legs involving the right angle, that is N, are equal, we can say that, NM = LN = x.
The hypotenuse of the ΔLMN, that is the side opposite to ∠N, that is LM, can be found using the Pythagoras theorem, by which in a right-angled triangle,
Hypotenuse² = Base² + Perpendicular².
∴ LM² = LN² + NM² = x² + x² = 2x².
or, LM = √(2x²) = x√2.
The tangent of an angle ∅, that is, tan ∅ is computed using the formula,
tan ∅ = Perpendicular/Base.
To calculate tan 45°, that is, tangent to ∠L, we take Perpendicular = NM and Base = LN.
∴ tan 45° = NM/LN = x/x = 1.
Now, we check all the given options:
NM = x. TRUE (computed)NM = x√2. FALSE (∵ NM = x)LM = x√2. TRUE (computed)tan 45° = √2/2. FALSE (∵ tan 45° = 1)tan 45° = 1. TRUE (computed)∴ The true statements regarding the given isosceles right triangle ΔLMN are:
NM = xLM = x√2tan 45° = 1.Learn more about isosceles right triangle at
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Find the value of X.
Answer:
x = 4√5
Step-by-step explanation:
The triangles are all similar, so corresponding lengths are proportional.
hypotenuse/short side = x/5 = (11+5)/x
x^2 = 80 . . . . cross multiply
x = 4√5 ≈ 8.94427
PLEASE HELP ME!!!!!!!!!! What polygon is tesellated to form this image?
Answer:
Pentagon
Step-by-step explanation:
the head is the closest I see
mohsin is writing a 2400 words essay for his school project he writes 1/5 of the essay on the first day 2/3 of the remainder on the second day 220 words on third day now he has to write the conclusion how long was his conclusion
Answer: 420 words
Step-by-step explanation:
First find how much he did the first day by doing 1/5*2400=480.
Then find out how much he did the second day by doing 2400-480=1920, then doing 1920*(2/3)=1280.
Then, because he did 220 words the third day, simply do 2400-480-1280-220=420.
Hope it helps <3
Ans420 words per min
Step-by-step explanation:
What is the difference?
StartFraction x Over x squared + 3 x + 2 EndFraction minus StartFraction 1 Over (x + 2) (x + 1) EndFraction
StartFraction x minus 1 Over 6 x + 4 EndFraction
StartFraction negative 1 Over 4 x + 2 EndFraction
StartFraction 1 Over x + 2 EndFraction
StartFraction x minus 1 Over x squared + 3 x + 2 EndFraction
Answer:
The answer is option D.Step-by-step explanation:
First we must first find the LCM
The LCM of x² + 3x + 2 and (x + 2)(x + 1 ) is
x² + 3x + 2
So we have
[tex] \frac{x}{ {x}^{2} + 3x + 2 } - \frac{1}{(x + 2)(x + 1)} \\ \\ = \frac{x - 1}{ {x}^{2} + 3x + 2 } [/tex]
Hope this helps you
Answer:
The answer is OPTION D!
Step-by-step explanation:
HoPe ThIs HeLpS!
When plotting points on the coordinate plane below, which point would lie on the y-axis? A coordinate plane. (0, 1) (7, 0) (6, 8) (8, 2)
Answer:
Numbers 1,0,8,2 would lie on y-axis.
Step-by-step explanation:
This is because for example, (0,1)
we must prefer 0 as x-axis and 1 as y-axis. That's means left number or side will always be x-axis and right side will always be y-axis.
Answer: (0, 1)
Step-by-step explanation:
When the x is 0 is lies on the y axis.
I NEED HELP PLEASE, THANKS! :) Write the augmented matrix for the system of linear equations. –9w + x + 8y + 2z = –6 –5x + 9y – 7z = 6 –3w – 6x + 4y + 9z = 4 –3w – 8x + y = –2
Answer:
3rd Matrix
Step-by-step explanation:
When you start putting the coefficients in as the matrix, you see that -9 has to be the 1st number, so that eliminates choice B and choice D as answers. You are left with choices A and C. C is the correct choice because when you plug in the second equation, your coefficient is -5, not 0.
Answer:
First Matrix
Step-by-step explanation:
Looking at the first equation, we see that the leading coefficient is -9. This gets rid of choice B and D because the first number in these matrices are not -9. You are left with choices A and C. Looking at the second equation, we see that there is no "w" variable, so we need to add one. The coefficient of this "w" is going to be 0. This means that A is the correct choice. Just to be sure though, evaluate all other coefficients to see if they line up with the matrix. Hope this helps.