Answer:
The square root of 2, or the (1/2)th power of 2, written in mathematics as √2 or 21⁄2, is the positive algebraic number that, when multiplied by itself, equals the number 2. Technically, it is called the principal square root of 2, to distinguish it from the negative number with the same property
Step-by-step explanation:
In a naval engagement, one-third of the fleet was captured, one-sixth was sunk, and two ships were destroyed by fire. One-seventh of the surviving ships were lost in a storm after the battle. Finally, the twenty-four remaining ships sailed home. How many ships were in the fleet before the engagement?
Answer:
60 ships.
Step-by-step explanation:
Let the total number of ships in the naval fleet be represented by x
One-third of the fleet was captured = 1/3x
One-sixth was sunk = 1/6x
Two ships were destroyed by fire = 2
Let surviving ships be represented by y
One-seventh of the surviving ships were lost in a storm after the battle = 1/7y
Finally, the twenty-four remaining ships sailed home
The 24 remaining ships that sailed home =
y - 1/7y = 6/7y of the surviving fleet sailed home.
Hence
24 = 6/7y
24 = 6y/7
24 × 7/ 6
y = 168/6
y = 28
Therefore, total number of ships that survived is 28.
Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4
Total number of ships in the fleet(x) =
x = 1/3x + 1/6x + 2 + 28
Collect like terms
x - (1/3x + 1/6x) = 30
x - (1/2x) = 30
1/2x = 30
x = 30 ÷ 1/2
x = 30 × 2
x = 60
Therefore, ships that were in the fleet before the engagement were 60 ships.
The pH of 0.0001 M solution of Ca(OH)2 is
Step-by-step explanation:
Since Ca(OH)2 is Basic, we need to find pOH:
pOH = - log [OH-]
pOH = - log(0.0001)
pOH = - ( - 4)
pOH = 4
Since, pH + pOH = 14
Therefore,
pH of 0.0001M sol. of Ca(OH)2 = 10
What is the value of w? inscribed angles (Image down below)
Answer:
w = 100°
Step-by-step explanation:
Opposite angles in an inscribed quadrilateral in a circle are supplementary.
Therefore, [tex] w + 80 = 180 [/tex]
Subtract 80 from both sides
[tex] w + 80 - 80 = 180 - 80 [/tex]
[tex] w = 100 [/tex]
The value of w = 100°
please help!!!!!!!!!!!!! Select ALL the correct answers. Choose the statements that are true about a cube with side length 1 unit.
Answer:
i think it is 2
Step-by-step explanation:
Find the constant of proportionality (r) in the equation y = r x
Answer:
r = 11Step-by-step explanation:
y = r x
r is the constant of proportionality
To find r pick any values of x and y provided and substitute it into the above formula and solve for r.
That's
using
x = 2
y = 22
We have
22 = 2r
Divide both sides by 2
r = 11Therefore the constant of proportionality is 11
Hope this helps you
Let f (x) = |2). Write a function g whose graph is a vertical shrink by a factor of
followed by a translation 2 units up of the graph of f.
Answer:
This is poorly written, so i will answer it as it was:
"Let f (x) = |2). Write a function g(x) whose graph is a vertical shrink by a factor of A, followed by a translation 2 units up of the graph of f."
I don't really know what you do mean by I2), so i will answer it in a general way.
First, we do a vertical shrink of factor A.
A must be a number smaller than one and larger than zero., then if g(x) is a vertical shrink of factor A of the graph of f(x), we have that:
g(x) = A*f(x)
As 0 < A < 1
We will have that the graph of g(x) is a vertical compression of the graph of f(x)
Now we do a vertical shift of 2 units up.
A general vertical shift of N units up is written as:
g(x) = f(x) + N
Where N is a positive number.
So in our case, we have:
g(x) = A*f(x) + 2.
Where you will need to replace the values of A and f(x) depending on what the actual question says,
Dr. Potter provides vaccinations against polio and measles. Each polio vaccination consists of 6 doses, and each measles vaccination consists of 3 doses. Last year, Dr. Potter gave a total of 60 vaccinations that consisted of a total of 225 doses. How many more measles vaccines did Mr. Potter give than polio? Show All Work !!
Answer:
The number of measles vaccines that Dr. Potter give than polio vaccines is 30
Step-by-step explanation:
The parameters given are;
The number of doses given in a polio vaccine = 6 doses
The number of doses given in a measles vaccine = 3 doses
The number of vaccinations given by Dr. Potter last year = 60 vaccinations
The number of doses given in the 60 vaccinations = 225 doses
Let the number of polio vaccine given last year by Dr. Potter = x
Let the number of measles vaccine given last year by Dr. Potter = y
Therefore, we have;
6 × x + 3 × y = 225.......................(1)
x + y = 60.......................................(2)
From equation (2), we have;
x = 60 - y
Substituting the derived value for x in equation (1), we get;
6 × x + 3 × y = 225
6 × (60 - y) + 3 × y = 225
360 - 6·y + 3·y = 225
360 - 225 = 6·y - 3·y
135 = 3·y
y = 45
x = 60 - y = 60 - 45 = 15
Therefore;
The number of polio vaccine given last year by Dr. Potter = 15
The number of measles vaccine given last year by Dr. Potter = 45
The number of measles vaccines that Dr. Potter give than polio vaccines = 45 - 15 = 30 vaccines.
The number of measles vaccines that Dr. Potter give than polio vaccines = 30 vaccines.
PLEASE help me solve this question! No nonsense answers please!
Answer:
[tex]\boxed{\sf Option \ 1}[/tex]
Step-by-step explanation:
The profit is revenue (R ) - costs (C ).
Subtract the expression of costs (C ) from revenue (R ).
[tex]10x-0.01x^2-(2x+100)[/tex]
Distribute negative sign.
[tex]10x-0.01x^2-2x-100[/tex]
Combine like terms.
[tex]8x-0.01x^2-100[/tex]
The first option has a positive 100, which is wrong.
The rest options are right, when we expand brackets the result is same.
Sophie is making a copy of an angle. The original angle will be labeled G and the new angle will be labeled B. She has just finished using a compass, with the point on G, to draw an arc that intersects both rays of angle G. Which of the following should she do next
Answer:
The next step is;
Label the two intersection points
Step-by-step explanation:
To make a copy of an angle, the steps are;
1) Draw the rays of the original angle passing through the point B
2) Open the compass slightly and place the compass point on the vertices G where the two rays meet to draw an arc that intersect both rays
3) Label the point of intersection of both rays points C and D
4) With the compass still opened to the same width, move the compass to the point B on the line the angle is to be copied and draw a similar arc intersecting the ray at J
5) Open the compass to the width of C and D on the original angle and place the compass at point J to mark the arc on the copied angle location at M
6) Draw a line from B passing through M to complete the second ay of the copied angle.
Micha is playing a game with five cards numbered 1 through 5. He will place the cards in a bag and draw one card at random three times, replacing the card each time. To win a prize, he must draw the number 5 all three times. What is the probability he will draw the number 5 all three times?
Answer: 0.008
Step-by-step explanation:
We have 3 experiments.
Each experiment is exactly the same: "Drawing the card with the number 5, out of a bag with five cards".
in a random selection all the cards have exactly the same probability of being drawn, so the probability of drawing the 5, is equal to the quotient between the number of cards with the 5 (only one) and the total number of cards in the bag (5) then the probability is:
p = 1/5.
And we want this event to happen 3 consecutive times, then the total probability is equal to the product of the probabilities for each event:
P = (1/5)*(1/5)*(1/5) = 1/125 = 0.008
The quotient of x^2+x-6/x^2-6x+5*x^2+2x-3/x^2-7x+10 has ___ in the numerator and ______ in the denominator.
Answer:
So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.
Step-by-step explanation:
[tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex]
Factorizing the expressions we have
[tex]\frac{x^{2} + 3x -2x - 6}{x^{2} -x - 5x + 5} X \frac{x^{2} + 3x - x - 3}{x^{2} -2x -5x + 10}[/tex]
[tex]\frac{x(x + 3)- 2(x + 3)}{x(x -1) - 5(x - 1)} X \frac{x(x + 3) - 1(x + 3)}{x(x - 2) - 5(x - 2)}[/tex]
[tex]\frac{(x + 3)(x - 2)}{(x - 5)(x - 1)}X\frac{(x + 3)(x - 1)}{(x - 2)(x - 5)}[/tex]
Cancelling out the like factors, (x -1) and (x - 2), we have
[tex]\frac{(x + 3)(x + 3)}{(x - 5)(x - 5)}[/tex]
= [tex]\frac{(x + 3)^{2} }{(x + 5)^{2} }[/tex]
So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.
If BH = 66, find DE. Round your answer to two decimal places if necessary.
Answer:
BH= 66
DE= ...?
We know that
BH is 1 to 6 = 66
DE is only take one space of that--> 3 to 4
so 66/6 = 11
1 space = 11 = DE
Hope it helps ^_^
suppose we want to choose 6 letters without replacement from 13 distinct letters. A) how many ways can this be done if order does not matter? B) how many ways can this be done if order of choices matters
Answer: A) 1716 B) 1235520
Step-by-step explanation:
If order doesn't matter , then we use combinations, where the number of combinations of selecting r things from n is given by :-[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
If order matters , then we use permutations, where the number of permutations of selecting r things from n is given by :-[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Given, Total distinct letters = 13
To choose = 6 letters
A) Number of ways to choose (if order does not matter)=[tex]^{13}C_6[/tex]
[tex]=\dfrac{13!}{6!7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!}{(720)\times 7!}\\\\= $$1716[/tex]
B) Number of ways to choose (if order matters)=[tex]^{13}P_6[/tex]
[tex]=\dfrac{13!}{7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!} 7!}\\\\= $$1235520[/tex]
Hence, A) 1716 B) 1235520
With which set of information can you construct a unique triangle?
OA the measurements of all the angles
ОВ.
the lengths of two sides
OC. the measurements of two angles
OD. the lengths of all the sides
OE the measurement of one angle
Answer:
D
Step-by-step explanation:
This would be using the SSS.
Which means knowing three sides.
The other options do not relate to any of the SSS, SAS, ASA, RHS
Hope that helped!!! k
Which of the following best represents the average rate at which the human hair grows (1 point)
a
0.25 inches per second
b
0.25 meters per hour
с
0.25 meter per month
d
0.25 inches per month
Answer:
D.0.25 inches per months
Step-by-step explanation:
The average rate or speed of human hair growth is about 0.25inches per month.
Write the equation of a circle with a center at (12, 6) and a radius of 6.
Answer:
(x-12)² + (y-6)² = 36 (Option C)
Step-by-step explanation:
use circle formula
(x-h)² + (y-k)²= r²
h= 12 and k= 6 and r= 6
(x-12)² + (y-6)² = 6²
6 squared = 36 (6·6)
(x-12)² + (y-6)² = 36
Helppppp!!!! Thank you
Greetings from Brasil...
In a triangle the sum of the internal angles is 180 °.... Thus,
Ô = 180 - 30
Ô = 60
The desired area is the area of the rectangle triangle, minus the area of the circular sector whose angle 60
A1 = area of the rectangle triangle
TG B = OA/AB
AB = OA / TG B
AB = 6 / TG 30
AB = 6√3
A1 = (AB . OA)/2
A1 = (6√3 . 6)/2
A1 = 18√3A2 = area of the circular sector
(rule of 3)
º area
360 ------------ πR²
60 ------------ X
X = 60πR²/360
X = 6π
So,
A2 = 6πThen the area shaded is:
A = A1 - A2
A = 18√3 - 6πWhat is the divisor of 5.2 and 0.052
Answer:
5.2/0.052 is 100, and 100 is 10^2, so the missing divisor is 10^2
Answer:
100
Step-by-step explanation:
5.2/x = 0.052
Since the decimal place moves 2 places to the left from 5.2 to 0.052, the divisor is 100.
5.2/100 = 0.052
How many triangles exist with the given side lengths? 2mm,6mm,10mm
Answer:
Zero
Step-by-step explanation:
2+6=8 which means it can't be. It has to be a length higher than 10
The projected worth (in millions of dollars) of a large company is modeled by the equation w = 206(1.1) t. The variable t represents the number of years since 2000. What is the projected annual percent of growth, and what should the company be worth in 2011? A. 10%; $534.31 million B. 11%; $646.52 million C. 10%; $587.74 million D. 11%; $226.60 million
Answer:
Hey There!! The Correct answer is: The equation is w = 241(1.06)t
And here variable t represents the number of years since 2000.
In 2001 means t=2001 -2000 = 1
So we plug 1 for t in the given expression , that is w = 241(1.06)1 = 241 * 1.06 = 255.46
Therefore in 2001, it should be worth to 255.46.
And in the given expression 1.06=1 +0.06, where 0.06 is the annual percent of growth that is 6 % .
Hope It Helped!~ ♡
ItsNobody~ ☆
The projected annual percent of growth is 10% and the company worth in 2011 will be $587.74 millions. Then the correct option is C.
What is an exponent?Consider the function:
y = a (1 ± r) ˣ
Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is a plus sign, then there is exponential growth happening by r fraction or 100r %.
If there is a minus sign, then there is exponential decay happening by r fraction or 100r %.
The projected worth (in millions of dollars) of a large company is modeled by the equation is given as,
[tex]\rm w = 206\times (1.10)^t\\\\w = 206\times (1+0.10)^t[/tex]
Then the projected annual percent of growth is 10%.
The variable t represents the number of years since 2000.
Then the company worth in 2011 will be
w = 206 × 1.1¹¹
w = $587.74 millions
The projected annual percent of growth is 10% and the company worth in 2011 will be $587.74 millions.
Then the correct option is C.
More about the exponent link is given below.
https://brainly.com/question/5497425
#SPJ2
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
Answer: 280 tons
Step-by-step explanation: divide all at tons/pound which accumulated to 280 tons
Answer: 10 ships
Step-by-step explanation:
Simplify (5x3y) (2xy4)
Answer: 10x^4y^5
Step-by-step explanation:
5x^3y^1•2x^1y^4
5•2=10
x^3•x^1=x^4
y^1•y^4=y^5
10x^4y^5
What is the main difference between simplifying and solving? Which one gives you a value for a variable? How do you know the difference?
Answer:
when you simplify you continue until you get to the simplest form but when you solve you continue until you get an answer. Solving gives you a value for a variable. You mean simplify and get 2x - 10 but when you solve you continue until you get x as 5
Step-by-step explanation:
Answer: ok, so simplifying is when you make something less complex or complicated. Solving means an expression can be used for representating the solutions. for Example, say if you have the equation x+y=2x-1 is solved for the unknown x by the expression x=y+1. solving gives you the value for the variable. you know the difference by when you are simplifying you are trying to make the problem less complicated or less complex. and when you are solving you are trying to find the answer to the problem..
Step-by-step explanation:
what is mean absolute deviation (MAD) and how do I find it?
Steps to find MAD:
Step 1. Calculate mean([tex]\overline{x}[/tex]) of the data using formula: [tex]\overline{x}=\dfrac{\sum x}{n}[/tex] , where x denotes data points and n is the number of data points.
Step 2. Calculate distance of each data point from mean :
Distance = [tex]|x-\overline{x}|[/tex]
Step 3. Divide distance of each data point from mean by n:
MAD = [tex]\dfrac{\sum |x-\overline{x}|}{n}[/tex] , which is the final computation to find MAD.
An empty row in a frequency table is a mistake True or false
Answer:
False I think
Step-by-step explanation:
use the formula S = 40,000 (1.06)t to calculate your salary after 4 years. Round your answer to the nearest dollar.
a. $42,400
b. $44,944
c. $47,641
d. $50,499
Answer:
d. $50,499
Step-by-step explanation:
Given:
S = 40,000 (1.06)^t
Where,
t=4 years
S=40,000(1.06)^4
=40,000(1.26247696)
=50,499.0784
To the nearest dollar
S=$50,499
The answer is d. $50,499
Hint: is the picture
Alonso estimated the distance across
a river as 1232 meters. What is the
approximate distance across the river to
the nearest thousandth of a meter?
Answer:
1232.000
Step-by-step explanation:
Estimated distance across the river=1,232 meters
Find the approximate distance across the river to
the nearest thousandth of a meter
Note: Thousandth is having 3 values after the decimal point
This means we will round 1,232 meters to the nearest thousandth
1,232 is an whole number and decimal point can only be added at the end like this 1,232.
So we need 3 values after the decimal point.
We must add only values that wouldn't change the original 1,232 meters.
Therefore, zero (0) will be added
1232.000
Is to the nearest thousandth
PLEASE help me with this question!!! REALLY URGENT!
Answer:
The third table is the correct answer
Step-by-step explanation:
Here in this question, we are concerned with determine which of the tables correctly represents what an exponential function is.
An exponential function is a function of the form;
y = x^n
where the independent variable x in this case is raised to a certain exponent so as to give the results on the dependent variable axis (y-axis)
In the table, we can see that we have 2 segments, one that contains digits 1,2 and so on while the other contains purely the powers of 10.
Now, let’s set up an exponential outlook;
y = 10^x
So we have;
1 = 10^0
10 = 10^1
1/10 = 10^-1
1000 = 10^3
1/100 = 10^-2
We can clearly see here that we have an increase in the value of y, depending on the value of the exponent.
However it is only this table that responds to this successive correctness as the other tables in the answer do have a point where they fail.
For example;
10^-2 is not 10 which makes the fourth table wrong
10^4 is not 100 which makes the first table wrong
we have same error on second table too
10) Find the least number that must be subtracted from the following numbers to make them perfect squares. a) 1098 b) 4498
Answer:
a. 9
b. 9.
Step-by-step explanation:
a) √1098 = 33.136
33^3 = 1089
So the answer is 1098 - 1089
= 9.
b) √4498 = 67.067
67^2 = 4489
Answer = 9.
Answer:
a). 9
b). 9
Step-by-step explanation:
a) If you try to subtract 1 to 8 from 1098, it won't make a perfect square. But if you subtract 9 from 1098 (that will make it 1089), it will make a perfect square.
√1089 = 33
33² = 33 × 33 = 1089
So the answer is 9.
b). If you try to subtract 1 to 8 from 4498, it won't make a perfect square. But if you subtract 9 from 4498 (that will make it 4489), it will make a perfect square.
√4489 = 67
67² = 67 × 67 = 4489
So the answer is 9.
Hope you understand ◉‿◉ (◠‿◕)
A rectangle with sides 13 cm and 7 cm has the same diagonal as a square. What is the length of the side of the square. Give your answer as a surd.
Answer:
Step-by-step explanation:
The diagonal ^2= 13^2+7^2
=169+49=218
diagonal = V218
the lengh of the square=l
l^2+l^2= 218
2l^2=218
l^2= 218/2= 109
l= ✓109
