The conversion of 1.256 grams is as follows: 1,256,000 micrograms, 1256 milligrams, and 0.001256 kilograms.
Explanation:To convert 1.256 grams (g) to different units of mass, you use the following conversion factors:
Micrograms (μg): 1 g = 1 × 10⁶ μg. So, 1.256 g = 1.256 × 10⁶ μg = 1,256,000 μg. Milligrams (mg): 1 g = 1000 mg. Thus, 1.256 g = 1.256 × 10³ mg = 1256 mg. Kilograms (kg): 1 g = 1 × 10⁻³ kg. Hence, 1.256 g = 1.256 × 10⁻³ kg = 0.001256 kg. Learn more about Mass Conversion here:
https://brainly.com/question/16756626
1.256 grams is equal to 1,256,000 micrograms, 1,256 milligrams, and 0.001256 kilograms. These conversions use basic multiplication and division of the metric system.
To convert 1.256 grams to different units, you should be familiar with the respective conversion factors:
1 gram (g) = 1,000 milligrams (mg)1 gram (g) = 1,000,000 micrograms (µg)1 gram (g) = 0.001 kilograms (kg)Steps to Convert:
Micrograms: Multiply the number of grams by 1,000,000:Therefore, the conversions are:
1.256 grams = 1,256,000 micrograms1.256 grams = 1,256 milligrams1.256 grams = 0.001256 kilogramsProblem 2.191 A researcher receives 93 containers of oxygen. Of those containers, 20 have oxygen that is not ionized and the rest are ionized. Two samples are randomly selected, without replacement, from the lot. Round your answers to three decimal places (e.g. 98.765). (a) What is the probability that the first one selected is not ionized? (b) What is the probability that the second one selected is not ionized given that the first one was ionized? (c) How does the answer in part (b) change if samples selected were replaced prior to the next selection? Find the probability. (d) What is the probability that both are ionized?
Answer:
Step-by-step explanation:
Given that there are 20 non ionized containers and 73 ionized containers
Two samples are drawn without replacement
a) the probability that the first one selected is not ionized=[tex]\frac{20}{93} =0.215[/tex]
b) the probability that the second one selected is not ionized given that the first one was ionized
= When first one was ionized we got left over as 20 and 72
Hence = [tex]\frac{20}{92} =0.217[/tex]
c) If with replacement left over 20 and 73 and hence prob = 0.215 as in part a
d) the probability that both are ionized=[tex]\frac{73C2}{93C2} =0.614[/tex]
If we assume the population of Grand Rapids is growing at a rate of approximately 4% per decade, we can model the population function with the formula
P( t ) = 181843 ( 1.04 )^(t / 10).
Use this formula to compute the average rate of change of the population on the intervals [ 5 , 10 ] , [ 5 , 9 ] , [ 5 , 8 ] , [ 5 , 7 ] , and [ 5 , 6 ] .
Answer:
The average rate of change of the population on the intervals [ 5 , 10 ] , [ 5 , 9 ] , [ 5 , 8 ] , [ 5 , 7 ] , and [ 5 , 6 ] are 734.504, 733.06, 731.62, 730.185 and 728.75 respectively.
Step-by-step explanation:
The given function is
[tex]P(t)=181843(1.04)^{(\frac{t}{10})}[/tex]
where, P(t) is population after t years.
At t=5,
[tex]P(5)=181843(1.04)^{(\frac{5}{10})}=185444.20[/tex]
At t=6,
[tex]P(6)=181843(1.04)^{(\frac{6}{10})}=186172.95[/tex]
At t=7,
[tex]P(7)=181843(1.04)^{(\frac{7}{10})}=186904.57[/tex]
At t=8,
[tex]P(8)=181843(1.04)^{(\frac{8}{10})}=187639.06[/tex]
At t=9,
[tex]P(9)=181843(1.04)^{(\frac{9}{10})}=188376.44[/tex]
At t=10,
[tex]P(10)=181843(1.04)^{(\frac{10}{10})}=189116.72[/tex]
The rate of change of P(t) on the interval [tex][x_1,x_2][/tex] is
[tex]m=\frac{P(x_2)-P(x_1)}{x_2-x_1}[/tex]
Using the above formula, the average rate of change of the population on the intervals [ 5 , 10 ] is
[tex]m=\frac{P(10)-P(5)}{10-5}=\frac{189116.72-185444.20}{5}=734.504[/tex]
The average rate of change of the population on the intervals [ 5 , 9 ] is
[tex]m=\frac{P(9)-P(5)}{9-5}=\frac{188376.44-185444.20}{4}=733.06[/tex]
The average rate of change of the population on the intervals [ 5 , 8 ] is
[tex]m=\frac{P(8)-P(5)}{8-5}=\frac{187639.06-185444.20}{3}=731.62[/tex]
The average rate of change of the population on the intervals [ 5 , 7 ] is
[tex]m=\frac{P(7)-P(5)}{7-5}=\frac{186904.57-185444.20}{2}=730.185[/tex]
The average rate of change of the population on the intervals [ 5 , 6 ] is
[tex]m=\frac{P(6)-P(5)}{6-5}=\frac{186172.95-185444.20}{1}=728.75[/tex]
Therefore the average rate of change of the population on the intervals [ 5 , 10 ] , [ 5 , 9 ] , [ 5 , 8 ] , [ 5 , 7 ] , and [ 5 , 6 ] are 734.504, 733.06, 731.62, 730.185 and 728.75 respectively.
Ms. Jones deposited $100 at the end of each month for 10 years into a savings account earning 6% interest compounded monthly. However, she deposited an additional $1000 at the end of the first year. How much money was in the account at the end of the tenth year?
Answer:
$1895.64
Step-by-step explanation:
Given:
Principle for the first year = $100
rate of interest = 6% compounded monthly
thus,
rate per month, r = \frac{\etxtup{6}}{\textup{12}}= 0.5% = 0.005
Total time = 10 year\
Now,
for the first year
number of months, n = 12
Amount at the end of first year = Principle × ( 1 + r )ⁿ
on substituting the values, we get
Amount at the end of first year = 100 × ( 1 + 0.005 )¹²
or
Amount at the end of first year = $106.17
Therefore,
The principle amount for the consecutive years will be
= $1000 + Amount at the end of first year
= $1000 + $106.17 = $1106.17
Thus, for the rest 9 years
n = 9 × 12 = 108
Principle = $1106.17
Final amount after the end of 10th year = Principle × ( 1 + r )ⁿ
or
Final amount after the end of 10th year = $1106.17 × ( 1 + 0.005 )¹⁰⁸
or
Final amount after the end of 10th year = $1895.64
An IV fluid contains 75 mg of Drug B in 500 ml of the IV fluid. If the patient needs 300 mg of this medication, how much of this IV fluid should be infused
Answer:
2000ml = 2L of this IV fluid should be infused.
Step-by-step explanation:
This problem can be solved by a simple rule of three, in which the relationship between the measures is direct, which means that there is a cross multiplication.
The problem states that each 75 mg of the medication contains 500 ml of IV fluid. How many ml of IV fluid are there in 300 mg of the medication?
So
75mg - 500ml
300 mg - x ml
[tex]75x = 300*500[/tex]
[tex]x = \frac{300*500}{75}[/tex]
[tex]x = 4*500[/tex]
[tex]x = 2000[/tex]ml
2000ml = 2L of this IV fluid should be infused.
To administer 300 mg of Drug B, given that 75 mg is in 500 ml of IV fluid, you need infuse 2000 ml of the IV fluid. This was calculated using proportional relationships based on the concentration of the drug in the fluid.
To determine how much IV fluid should be infused to provide the patient with 300 mg of Drug B, we can use a simple proportion based on the concentration of the drug in the IV fluid.
We know that 75 mg of Drug B is contained in 500 ml of the IV fluid.This corresponds to a concentration of 75 mg/500 ml or 0.15 mg/ml.To find out how many milliliters (ml) are needed for 300 mg, we set up the following proportion:0.15 mg/ml = 300 mg / X ml
Solving for X, we get:
X = 300 mg / 0.15 mg/ml
X = 2000 ml
Thus, 2000 ml of the IV fluid should be infused to provide the patient with 300 mg of Drug B.
Given the proposition,
P(n): 1 + 2 + 2^2 + 2^3 + . . . + 2n = 2n+1 - 1, n = 0, 1, 2, . . .
Find the values of:
P(0)
P(1)
P(2)
P(n+1)
Answer and Explanation:
Given : [tex]P(n): 1 + 2 + 2^2 + 2^3 + . . . + 2^n = 2^{n+1} - 1[/tex], n=0,1,2,..
To find : The values of following expression ?
Solution :
The function is [tex]P(n)=2^{n+1} - 1[/tex]
1) Value of P(0),
[tex]P(0)=2^{0+1} - 1[/tex]
[tex]P(0)=2^{1} - 1[/tex]
[tex]P(0)=2 - 1[/tex]
[tex]P(0)=1[/tex]
2) Value of P(1),
[tex]P(1)=2^{1+1} - 1[/tex]
[tex]P(1)=2^{2} - 1[/tex]
[tex]P(1)=4- 1[/tex]
[tex]P(1)=3[/tex]
3) Value of P(2),
[tex]P(2)=2^{2+1} - 1[/tex]
[tex]P(2)=2^{3} - 1[/tex]
[tex]P(2)=8- 1[/tex]
[tex]P(2)=7[/tex]
4) Value of P(n+1),
[tex]P(n+1)=2^{n+1+1} - 1[/tex]
[tex]P(n+1)=2^{n+2} - 1[/tex]
use matrices and elementary row to solve the following system:
5x - 3x + 2x =13
2x - y - 3z =1
4x - 2y + 4z =12
I assume the first equation is supposed to be
[tex]5x-3y+2z=13[/tex]
and not
[tex]5x-3x+2x=4x=13[/tex]
As an augmented matrix, this system is given by
[tex]\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\4&-2&4&12\end{array}\right][/tex]
Multiply through row 3 by 1/2:
[tex]\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\2&-1&2&6\end{array}\right][/tex]
Add -1(row 2) to row 3:
[tex]\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\0&0&5&5\end{array}\right][/tex]
Multiply through row 3 by 1/5:
[tex]\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\0&0&1&1\end{array}\right][/tex]
Add -2(row 3) to row 1, and add 3(row 3) to row 2:
[tex]\left[\begin{array}{ccc|c}5&-3&0&11\\2&-1&0&4\\0&0&1&1\end{array}\right][/tex]
Add -3(row 2) to row 1:
[tex]\left[\begin{array}{ccc|c}-1&0&0&-1\\2&-1&0&4\\0&0&1&1\end{array}\right][/tex]
Multiply through row 1 by -1:
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\2&-1&0&4\\0&0&1&1\end{array}\right][/tex]
Add -2(row 1) to row 2:
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&-1&0&2\\0&0&1&1\end{array}\right][/tex]
Multipy through row 2 by -1:
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&0&-2\\0&0&1&1\end{array}\right][/tex]
The solution to the system is then
[tex]\boxed{x=1,y=-2,z=1}[/tex]
A company asks an investor for an investment of $950,000 in exchange for 25% equity in the business. What is the implied valuation of the business?
Answer:
$2,850,000
Step-by-step explanation:
Data provided in the question:
Investment amount asked for by the company = $950,000
Exchange of equity = 25%
Now,
Equity exchanged = [tex]\frac{\textup{Amount invested}}{\textup{Post money evaluation}}\times100[/tex]
or
Post money evaluation = [tex]\frac{\textup{950,000}}{\textup{25}}\times100[/tex]
or
Post money evaluation = $3,800,000
Therefore,
Implied valuation = Post money evaluation - Amount invested
or
Implied valuation = $3,800,000 - $950,000 = $2,850,000
7:( 4 11 m)=56:3.2
I'm too lazy to do this....Please can someone do this for meh.
Who ever does it with steps gets a virtual hug. -w-
Answer:
0.000973236=m
Step-by-step explanation:
Given the question as;
7:(411m) = 56 : 3.2
7/411m =56/3.2
7×3.2=56×411m
(7×32)/(560×411)=m
224/230160=m
0.000973236=m
checking the answer
7: (411 *0.000973236) = 56: 3.2
7: (0.4)= 56 : 3.2
7/0.4 =56/3.2
70/4=560/32
17.5 =17.5
Show that the area of a right triangle of sides 5, 12 and 13 cannot be a square
Answer and Explanation:
Given : Sides of right triangle 5,12 and 13.
To find : Show that the area of a right triangle of sides 5, 12 and 13 cannot be a square ?
Solution :
If 5,12 and 13 are sides of a right angle triangle then
13 is the hypotenuse as it is largest side.
then we take perpendicular as 12 and base as 5.
The area of the right angle triangle is
[tex]A=\frac{1}{2}\times b\times h[/tex]
Here, h=12 and b=5
[tex]A=\frac{1}{2}\times 5\times 12[/tex]
[tex]A=5\times 6[/tex]
[tex]A=30[/tex]
The area of the right angle triangle is 30 units.
30 is not a perfect square as [tex]30=2\times 3\times 5[/tex]
There is no square pair formed.
An airplane over the Pacific sights an atoll at 20 degree angle of depression. If the plane is 425 m above water, how many kilometers is it from a point 425 m above the center of the atoll?
Answer:
[tex]1.167 km[/tex]
Step-by-step explanation:
We are given with-
Height of airplane from water [tex]a[/tex] = [tex]425 m[/tex]
Angle of depression (∅)= 20°
Now,
[tex]tan(20) = \frac{b}{a}[/tex]
[tex]a = \frac{b}{tan(20)} \\a = \frac{425}{tan(20} \\a = 1167.677 m[/tex]
[tex]a = 1.167 km[/tex]
If we have a 90% confidence interval for a population parameter, then A. 10% of the time, the population parameter will lie outside of the interval. B. 10% of the time, the population parameter will be lower than the LCL. C. 10% of the time, the population parameter will be higher than the UCL. D. All of the above will hold.
Answer: A. 10% of the time, the population parameter will lie outside of the interval.
Step-by-step explanation:
If we have [tex]b\%[/tex] confidence interval is that we are [tex]b\%[/tex] certain that it contains the true population parameter in it.
Similarly , if we have a 90% confidence interval for a population parameter, then we are 90% certain that it contains the true population parameter in it.
i.e. 10% not certain that it contains the true population parameter in it.
i.e. 10% of the time, the population parameter will lie outside of the interval.
An experimenter is studying the effects of temperture, pressure, and type of catalyst on yield from a certain chemical reaction. Three different temperatures, four different pressures, and five different catalysts are under consideration.
(a) If any particular experiental run involves the use of single temperature, pressure, and catalyst, how many experimental runs are possible?
(b) How many experimental runs are there that involve use of the lowest temperature and two lowest pressure?
Answer:
Step-by-step explanation:
Given that an experimenter is studying the effects of temperture, pressure, and type of catalyst on yield from a certain chemical reaction. Three different temperatures, four different pressures, and five different catalysts are under consideration.
a) Experimental runs possible if use of single temperature, pressure and catalyst is there = no of temperatures x no of pressures x no of catalysts
= [tex]3*4*5 = 60[/tex]
b) Here pressure and temperature have no choice as lowest is selected.
no of methods = no of catalysts x 1 x1
= 5
Your third-grade classroom has 32 boys and girls. Two-thirds of the boys and three-fourths of the girls are going on a field trip. There are 9 children left. What is the ratio of boys to girls in your class?
Draw diagrams to support your answer.
Answer: The ratio of boys to girls would be 3 : 5 .
Step-by-step explanation:
Since we have given that
Number of boys and girls = 32
Fraction of boys are going on a field trip = [tex]\dfrac{2}{3}[/tex]
Fraction of girls are going on a field trip = [tex]\dfrac{3}{4}[/tex]
Number of children left = 9
Let the number of boys be 'b'.
Let the number of girls be 'g'.
According to question, it becomes ,
[tex]b+g=32------------(1)\\\\32-9=\dfrac{2}{3}b+\dfrac{3}{4}g\\\\23=\dfrac{2b}{3}+\dfrac{3g}{4}-------------(2)[/tex]
From eq(1), we get that g = 32-b
So, it becomes,
[tex]\dfrac{2}{3}b+\dfrac{3}{4}(32-b)=23\\\\\dfrac{2}{3}b+24-\dfrac{3}{4}b=23\\\\\dfrac{2}{3}b-\dfrac{3}{4}b=23-24=-1\\\\\dfrac{8b-9b}{12}=-1\\\\\dfrac{-b}{12}=-1\\\\b=-1\times -12\\\\b=12[/tex]
so, number of girls would be 32 - b = 32 - 12 = 20
So, Ratio of boys to girls in class would be 12 : 20 = 3 : 5.
Therefore, the ratio of boys to girls would be 3 : 5 .
Consider a nuclear power plant that produces 1200 MW of power and has a conversion efficiency of 34 percent (that is, for each unit of fuel energy used, the plant produces 0.34 units of electrical energy. Assuming continuous operation, determine the amount of nuclear fuel consumed by the plant per year.
Answer:
The amount of nuclear fuel required is 1.24 kg.
Step-by-step explanation:
From the principle of mass energy equivalence we know that energy generated by mass 'm' in an nuclear plant is
[tex]E=m\cdot c^2[/tex]
where
'c' is the speed of light in free space
Since the power plant operates at 1200 MW thus the total energy produced in 1 year equals
[tex]E=1200\times 10^6\times 3600\times 24\times 365=3.8\times 10^{16}Joules[/tex]
Thus using the energy produced in the energy equivalence we get
[tex]3.8\times 10^{16}=mass\times (3\times 10^{8})^2\\\\\therefore mass=\frac{3.8\times 10^{16}}{9\times 10^{16}}=0.422kg[/tex]
Now since the efficiency of conversion is 34% thus the fuel required equals
[tex]mass_{required}=\frac{0.422}{0.34}=1.24kg[/tex]
2m + 7 = 9
Answer when solved??
translate phrases into algebraic expressions, the difference between the cube of a number and the square of the number
Answer:
[tex]x^3-x^2.[/tex]
Step-by-step explanation:
The word "difference" represents a subtraction. Then the algebraic expression will be of the form a-b.
Now, the difference is between the cube of a number and the square of the number, then let's call the number x. The square of the number is raise to two. Then the square of the number is [tex]x^2[/tex].
The cube of the number is raise to three. Then the cube of the number is [tex]x^3[/tex].
So, the difference between the cube of a number and the square of the number (we are talking about the same number in the square and the cube) is [tex]x^3-x^2[/tex].
If $5000 is deposited into an account which pays 6% compounded
monthly, approximately how much money will be in the account at the
end of 8 years?
Answer:
The amount in the account at the end of 8 years is about $8070.71.
Step-by-step explanation:
Given information:
Principal = $5000
Interest rate = 6% = 0.06 compounded monthly
Time = 8 years
The formula for amount after compound interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where,
P is principal.
r is rate of interest.
n is number of times interest compounded in a year.
t is time in years.
Substitute P=5000, r=0.06, n=12 and t=8 in the above formula.
[tex]A=5000(1+\frac{0.06}{12})^{(12)(8)}[/tex]
[tex]A=5000(1.005)^{96}[/tex]
[tex]A=5000(1.61414270846)[/tex]
[tex]A=8070.7135423[/tex]
[tex]A\approx 8070.71[/tex]
Therefore the amount in the account at the end of 8 years is about $8070.71.
eight increased by the product of a number and 4 is at most 20
Answer:
I am not entirely sure what you are asking, but I believe the answer is 4*2=8
Step-by-step explanation:
This is because:
8 increased by the product of a number and 4 is at most 20.
8 + p + 4 = 20
We are trying to find p.
8 +4= 12
20 - 12= 8
So I believe the answer is 8.
(If the answer is wrong, plz tell me in the comments)
Answer:
3
Step-by-step explanation:
eight increased by the product of a number and 4 is at most 20
these implies
8 + a x4 = 20
a is the number whose product with 4 is increased by eight to give at most 20
8 + a x4 = 20
8 + 4a = 20
subtract 8 from both sides
4a = 20 -8
4a= 12
divide both sides by 4
a = 12/4 = 3
the number is 3
You are the owner of a small bakery. This week the bakery has orders for 48 birthday cakes. Each cake sells for $52. Suppose you spend 1/4
of each cake's selling price for ingredients. How much will the ingredients cost for all of the birthday cake orders?
Answer:$624
Total sales: $52 x 48 = $2,496
Cost of ingredients:
$2,496
4
= $624
Step-by-step explanation:
$624
Total sales: $52 x 48 = $2,496
Cost of ingredients:
$2,496
4
= $624
Answer:
The ingredients will cost $624 for all of the birthday cakes.
Step-by-step explanation:
This week the bakery has orders for 48 birthday cakes. Each cake sells for $52.
1/4 of each cake's selling price is spent on ingredients.
This becomes [tex]\frac{1}{4}\times52= 13[/tex] dollars
Hence, the total cost of ingredients for 48 cakes will be "
[tex]13\times48=624[/tex] dollars
Therefore, the ingredients will cost $624 for all of the birthday cakes.
translate into algebraic expression 10 more than a number
Answer:
x+10
Step-by-step explanation:
An algebraic expression is an expression which consist of variables(whose values are not fixed like in the form of x,y,a,...), the constants and operators (like +,×,±,-,≤,≥,=,...).
Now for this question we have to give a an algebraic expression for 10 more than a number.
Let the number be x.
We have to show a relation of 10 more than the number. Thus are algebraic expression is of the form x+10.
Algebraic expression: x+10
where x is our variable
+ is our operator and
10 is a constant.
Find an equation of the line L that passes through the point (-8, 4) and satisfies the given condition. The x-intercept of L is -10.
Final answer:
To find the equation of a line that passes through a given point and has a given x-intercept, we can use the point-slope form of a line.
Explanation:
To find the equation of a line that passes through the point (-8, 4) and has an x-intercept of -10, we can use the slope-intercept form of a line, which is y = mx + b.
First, let's find the slope of the line using the given information. The x-intercept represents the point where the line crosses the x-axis, so if the x-intercept is -10, we know that the point (-10, 0) is on the line.
Using the formula for slope, which is m = (y2 - y1) / (x2 - x1), we can calculate the slope of the line as (0 - 4) / (-10 - (-8)) = -4 / -2 = 2.
Now, we can use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line.
Substituting the values (-8, 4) and m = 2 into the equation, we have y - 4 = 2(x - (-8)).
Simplifying the equation, we get y - 4 = 2x + 16.
Finally, isolating y, we arrive at the equation of the line: y = 2x + 20.
3p - 5 = 19
Answer when solved??
Answer: P=8
Step-by-step explanation:
3p-5=19
U turn -5 to +5
Then u add 5 to both sides, -5 and 19
3p-5=19
+5=+5
-5 and +5 cancel each other out so know it’s
3p=24
Because 19 plus 5 is 24
Now u have to get the variable by itself by dividing 3 on both sides of the equal sign 3p and 24
3 and 3 cancel each other out so now you only have p=24 but then 24 divided 3 is 8
dy/dx = (sin x)/y , y(0) = 2
Answer:
The solution for this differential equation is [tex]y=\sqrt{-2cos(x)+6}[/tex]
Step-by-step explanation:
This differential equation [tex]\frac{dy}{dx}=\frac{sin(x)}{y}[/tex] is a separable First-Order ordinary differential equation.
We know this because a first-order differential equation is separable if and only if it can be written as
[tex]\frac{dy}{dx}=f(x)g(y)[/tex] where f and g are known functions.
And we have
[tex]\frac{dy}{dx}=\frac{sin(x)}{y}\\ \frac{dy}{dx}=sin(x)\frac{1}{y}[/tex]
To solve this differential equation we need to integrate both sides
[tex]y\cdot dy=sin(x)\cdot dx\\ \int\limits {y\cdot dy}= \int\limits {sin(x)\cdot dx}[/tex]
[tex]\int\limits {y\cdot dy}=\frac{y^{2} }{2} + C[/tex]
[tex]\int\limits {sin(x) \cdot dx}=-cos(x) + C[/tex]
[tex]\frac{y^{2} }{2} + C=-cos(x) + C[/tex]
We can make a new constant of integration [tex]C_{1}[/tex]
[tex]\frac{y^{2} }{2}=-cos(x) + C_{1}[/tex]
We need to isolate y
[tex]\frac{y^{2} }{2}=-cos(x) + C_{1}\\y^2=-2cos(x)+2*C_{1}\\\mathrm{For\:}y^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}y=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\y=\sqrt{-2cos(x)+c_{1} } \\y=-\sqrt{-2cos(x)+c_{1} }[/tex]
We have the initial conditions y(0)=2 so we can find the value of the constant of integration for [tex]y=\sqrt{-2cos(x)+c_{1} } [/tex]
[tex]2=\sqrt{-2\cos \left(0\right)+c_1}\\2= \sqrt{-2+c_1} \\c_1=6[/tex]
For [tex]y=-\sqrt{-2cos(x)+c_{1} } [/tex] there is not solution for [tex]c_{1}[/tex] in the domain of real numbers.
The solution for this differential equation is [tex]y=\sqrt{-2cos(x)+6}[/tex]
Given f(x)=2x-1
find the domain value if the range value is 4.
Answer:
5/2
Step-by-step explanation:
You want to find x when f(x) = 4
4 = 2x -1
5 = 2x . . . . . add 1
5/2 = x . . . . . divide by 2
The input corresponding to an output of 4 is 5/2.
A boat is heading due east at 22 km/hr (relative to the water). The current is moving toward the southwest at 10 km/hr.(a) Give the vector representing the actual movement of the boat. (Round each component to two decimal places.)
The actual movement of the boat is calculated by adding the vectors representing the velocity of the boat and the water current. The net vector shows both the speed and direction of the actual movement.
Explanation:The actual movement of the boat is determined by adding vectorially, the velocity of the boat and the velocity of the current. This is because we need to consider both the speed and direction of the boat (traveling due east) and the current (flowing southwest).
Let's assume East as +i direction, and North as +j direction. So, the velocity of the boat is 22i km/hr and the velocity of the current is -10i/√2 -10j/√2 km/hr (as it is moving southwest).
To find the net velocity or actual movement, we add these two vectors.
Resultant velocity = 22i -10i/√2 -10j/√2 // Adding the i-components and the j-components
= (22 -10/√2)i -10/√2 j km/hr
Therefore, the actual movement of the boat is (22 -10/√2)i -10/√2 j km/hr.
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1.How much will $5,000 accumulate in 5 years if it earns 6% per annum for the first 3 years and then 8% per annum for the next 2 years?
Answer: Amount after 5 years become $5937.60.
Step-by-step explanation:
Since we have given that
Principal amount = $5000
Time period = 5 years
Rate of interest for 3 years = 6%
Rate of interest for 2 years = 8%
so, Amount becomes
[tex]Amount=5000(1+\dfrac{6}{1000})^3(1+\dfrac{8}{100})^2\\\\Amount=5000(1+0.006)^3(1+0.08)^2\\\\Amount=5000(1.006)^3(1.08)^2\\\\Amount=\$5937.60[/tex]
Hence, Amount after 5 years become $5937.60.
If f(x) = c is constant for all x in R, why lim x-> infinite (gap P) no equal to 0
Answer:
[tex]\lim_{x\rightarrow \infty}C=C[/tex]
Step-by-step explanation:
We are given that f(x)=c=Constant for all x in R
We have to find that why f(x) not equal to zero when x approaches to zero.
[tex]\lim_{x\rightarrow \infty}f(x)[/tex]
[tex]\lim_{x\rightarrow \infty}C=C[/tex] not equal to zero
We are given that function which is constant for all x in R.
When x approaches then the value of function does not change. it remain same for all x in R because function is constant.
Hence, when x tends to infinity then f(x) is not equal to zero.
Determine whether the description below corresponds to an observational study or an experiment.
In a study sponsored by a company, 12,543 people were asked what contributes most to their happiness commahappiness, and 87% of the respondents said that it was their job.
is the study described above an observational study or an experiment?
(A) The study is an observational study because the responses of the survey subjects were observerd.
(B) The study is an observational study because the survey subjects were not given any treatment
(C) The study is an experiment because it was done with statistical methods.
(D) The study is an experiment because the survey subjects were given a treatment.
Answer:
The correct option is B) The study is an observational study because the survey subjects were not given any treatment.
Step-by-step explanation:
Consider the provided information.
In a study sponsored by a company, 12,543 people were asked what contributes most to their happiness, and 87% of the respondents said that it was their job.
Observational study is the study in which observer only observe the subjects, and measure variables of interest without allocating treatments to subjects.
Experiment study is the study in which the researchers are applying treatments to experimental units in the research, then the effect of the treatments on the experimental units is observed.
Now consider the provided statement.
The research is based on information that nobody manipulates any experimental variables.
Hence, the study is an observational study where no treatment is given.
Thus, the correct option is B) The study is an observational study because the survey subjects were not given any treatment.
Prove that the each element of a group G has a unique inverse. That is, if a, b, W E G satisfy then b
Step-by-step explanation:
Say [tex]a[/tex] is an element of [tex]G[/tex] which might have more than 1 inverse. Let's call them [tex]b[/tex], and [tex]c[/tex]. So that [tex]a[/tex] has apparently two inverses, [tex]b[/tex] and [tex]c[/tex].
This means that [tex]a*b = e[/tex] and that [tex]a*c=e[/tex](where [tex]e[/tex] is the identity element of the group, and * is the operation of the group)
But so we could merge those two equations into a single one, getting
[tex]a*b=a*c[/tex]
And operating both sides by b by the left, we'd get:
[tex]b*(a*b)=b*(a*c)[/tex]
Now, remember the operation on any group is associative, meaning we can rearrange the parenthesis to our liking, gettting then:
[tex](b*a)*b=(b*a)*c[/tex]
And since b is the inverse of a, [tex]b*a=e[/tex], and so:
[tex](e)*b=(e)*c[/tex]
[tex]b=c[/tex] (since e is the identity of the group)
So turns out that b and c, which we thought might be two different inverses of a, HAVE to be the same element. Therefore every element of a group has a unique inverse.
how many numbers are there that have distinct digits and are greater than 4500? how many 5 digit odd numbers are there that have distinct digits?how many 5 digit even number are there that have distinct digits?
Answer:
4-digit numbers with distinct digits and greater than 4500: 2800 numbers
5-digit numbers with distinct digits: 27216 numbers.
Step-by-step explanation:
If we represent a 4 number digit by ABCD, we have 9 posibilities for A (1,2,3,4,5,6,7,8 and 9, all but 0).
If every digit has to be different, we have 9 posibilities for B: ten digits (0,1,2,3,4,5,6,7,8 and 9 minus the one already used in A).
Int he same way, we have 8 posibilities for C and 7 for D.
Considering all 4-digits numbers, we have 9*9*8*7 = 4536 numers with distinct digits.
To know how many of these numbers are greater than 4500, we can substracte first the numbers that are smaller than 4000: A can take 3 digits (1,2 and 3) and B, C and D the same as before.
3*9*8*7 = 1512 numbers smaller than 4000
Then we can substrat the ones that are between 4000 and 4500
1*4*8*7 = 224 numbers between 4000 and 4500
So, if we substract from the total the numbers that are smaller than 4500 we have the results:
4-digit numbers with distinct digits greater than 4500 = 4536-(1512+224) = 2800
For 5-digit numbers, we can call the number ABCDE.
For A we have 9 digits possible (all but 0).
For B, we also have 9 posibilities (all digits but the one used in A).
For C, we have 8 digits (all 10 but the ones used in A and B).
For D, we have 7 digits.
For E, we have 6 digits.
Multiplying the possible combinations, we have:
9*9*8*7*6 = 27,216 5-digit numbers with distinct digits.
Two thousand five hundred twenty numbers have distinct digits and are more significant than 4500. There are 15120 5-digit odd numbers and 15120 5-digit even numbers with different numerals.
Explanation:In Mathematics, to calculate how many numbers have distinct digits and are more significant than 4500, consider that any number greater than 4500 and less than 10000 is a 4-digit number. The thousands place can be filled by any number from 5 to 9, giving five options. Any ten digits can fill the hundreds place minus the one used in the thousands, giving nine options. The tens place, similarly, has eight votes. Similarly, the one's site has seven options, as the digit in that place cannot duplicate any of the prior digits. So, the answer is 5*9*8*7 = 2520 distinct numbers.
For the second part of your query, the 5-digit odd numbers with non-repeating digits, the tens place must be filled by five possible odd digits (1, 3, 5, 7, 9), and the first place can be filled by any number from 1 to 9, giving nine options. The other three areas have 8, 7, and 6 votes, respectively, leading to 9*8*7*6*5 = 15120 distinct numbers.
As for the 5-digit even numbers with non-repeating digits, the tens place can be filled by five possible even digits (0, 2, 4, 6, 8), and the first place can be filled by any number from 1 to 9, giving nine options. The other three areas have 8, 7, and 6 votes, respectively. So there are 9*8*7*6*5 = 15120 five-digit, distinct digit, even numbers.
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