Answer:
The system is inconsistent.
Step-by-step explanation:
Consider the provided information.
The augmented matrix for a given system has a pivot in every column.
Let us understand this fact with the help of an example.
Suppose an 8 × 6 augmented matrix has a pivot in every column.
The above matrix is augmented and has a pivot in every column, that means the rightmost column in the above matrix must be a pivot column.
The rightmost column of the above matrix will be something like this:
0 0 0 0 0 | b
Where b≠0 because if b is 0 then it can't be a pivot position.
But from the above 0 = b, which is false.
This means that the system is not consistent,
Hence, the system is inconsistent.
There are 100 centimeters in a meter, 2.54 centimeters in an inch, 12 inches in a foot, 3 feet in a yard, and 1760 yards in a mile 1) A race is 6.2 miles long. Use conversion factors and dimensional analysis to determine the length of the race measured in: a) yards. b) meters.
Answer:
a) 10912 Yards
b) 9977.93 meters
Step-by-step explanation:
We are given the following information in the question.
1 Meter = 100 Centimeter
1 Inch = 2.54 Centimeter
1 Foot = 12 Inch
1 Yard = 3 Foot
1 Mile = 1760 Yards
The length of race is 6.2 miles.
a) We have to find length of race in yards.
Since we know 1 Mile = 1760 Yards
Thus, 6.2 Miles = 6.2 × 1760 Yards = 10912 Yards
Thus , the race is 10912 yards in length.
b) We have to calculate the length of the race in meters.
Since we know 1 Mile = 1760 Yards
Thus. 6.2 miles = [tex]\frac{(6.2)(1760)(3)(12)(2.54)}{100}[/tex] = 9977.93 meters
The Social Security Administration increased the taxable wage base from $106,800 to $110,100. The 6.2% tax rate is unchanged. Joe Burns earned over $120,000 each of the past two years.
a.
What is the percent increase in the base?(Round your answer to the nearest hundredth percent.)
Percent increase
%
b.
What is Joe’s increase in Social Security tax for the new year?(Round your answerto the nearest cent.)
Increase in social security tax
$
Answer:
The Social Security Administration increased the taxable wage base from $106,800 to $110,100.
A:
The percent increase in the base =
[tex]\frac{110100-106800}{106800}\times100=3.09[/tex]%
B:
Previous year tax = [tex]0.062\times106800=6621.60[/tex] dollars
This year tax = [tex]0.062\times110100=6826.20[/tex] dollars
Increase in tax = [tex]6826.20-6621.60=204.60[/tex] dollars
Hence, Joe’s increase in Social Security tax for the new year is $204.60.
The taxable wage base increased by 3.09%. The additional amount that Joe will pay in Social Security tax due to this increase is $204.60.
Explanation:The percent increase in the base can be found by subtracting the old base from the new base, dividing the difference by the old base, and finally multiplying by 100 to convert to a percentage. So, the percent increase is: ((110,100 - 106,800) / 106,800 ) * 100 = 3.09%.
To calculate Joe's increase in Social Security tax, you need to determine the taxable increase, which is the difference between the new and old taxable wage bases, and then multiply this amount by the tax rate. For Joe, the taxable increase is $3,300 (110,100 - 106,800). Therefore, Joe's increase in Social Security tax is: 3,300 * 6.2% = $204.60.
Learn more about Percent and Tax Calculations here:https://brainly.com/question/31171066
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Is .13 less than .32
Yes, .13 is less than .32
Describe the variable Yr_Built. Choose the correct answer below. A. The variable Yr_Built is quantitative, with units years. B. The variable Yr_Built is an identifier variable. C. The variable Yr_Built is categorical and ordinal. D. The variable Yr_Built is categorical and nominal.
Answer:
A. The variable Yr_Built is quantitative, with units years.
Step-by-step explanation:
Since, Yr_Built means the year built, Also year has a numerical value like 2008, 2000, 1865, etc.
So, it is quantitative.
Further, Data is said to be quantitative if it has a numerical value.
Categorical data is that data which has categories. For example, Gender: It has two categories Female and Male.
The data which as ordering is called ordinal data. Example, Bad, Average, Good.
Identifier Variable is the variable that is used for identity. Example, Employee No., etc.
For what side length(s) is the area of an equilateral triangle equal to 30 cm?? Only enter the number, in centimeters, rounded to two decimal places. A cm ►
Answer: The sides length are 8.32 cm
Step-by-step explanation:
An equilateral triangle has all his sides of the same lenght, so we assume that the triangle has an L lenght in his sides.
The area of a triangle is [tex]Area = \frac{base * height}{2}[/tex] where the base is L, the Area is 30 and an unknown height.
To determine the height, we cut the triangle in half and take one side. By simetry, one side has a base of [tex]\frac{L}{2}[/tex], a hypotenuse of L and a the unknown height.
Then we apply the Pythagoras theorem, this states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, or, [tex]hypotenuse = \sqrt{c^{2} + c^{2} }[/tex] Where one c is [tex]\frac{L}{2}[/tex] and the other is the height.
Then we find one of the c of the equation wich will be the height.
[tex]height = \sqrt{hypotenuse^{2}-base^{2} }[/tex]
[tex]height = \sqrt{ L^{2} -\frac{L}{4} ^{2}}\\height = \sqrt{\frac{ 3L^{2}}{4} } \\\\height = \frac{\sqrt{3}L }{2}[/tex]
Finally, we use the triangle area mentioned before an find the value of L.
[tex]30 = \frac{L*\frac{\sqrt{3}L }{2} }{2} \\\\L = \sqrt{\frac{120}{\sqrt{3} } } \\\\L = 8.32 cm[/tex]
what geometric postulates justifies the statement below
If AB is congruent to CD and CD is congruent to EF, then AB
iscongruent to EF.
Answer: Transitive property of congruence.
Step-by-step explanation:
Transitive property of congruence is similar to transitive property of equality , it says that if a is congruent to b and b is congruent to c , then a is congruent to c.
Given statement : If AB is congruent to CD and CD is congruent to EF, then AB is congruent to EF.
Here a= AB , b= CD and c= EF
Therefore, the geometric postulates justifies given the statement must be Transitive property of congruence.
Everyone in a group is being assigned a secret code of 3 characters. The first character must be a letter and the second and third are numbers which can not be the same. How many possible codes can be made? O A. 46 O B. 126 C. 2340 O D. 2600
Answer: C. 2340
Step-by-step explanation:
Hi!
The first character is a letter. There are 26 letters in the alphabet. For each letter you choose a two digit number, but you cannot repeat the digits. There are 100 (0 to 99) two digit numbers, and you have to discard 00, 11, 22, 33, 44, 55, 66, 77, 88, 99. Those are the 10 numbers with repeated digits.
So, for each letter, you have any of 90 possible numbers. The answer is then 26*90 = 2340
According to Newton’s law of cooling, the temperature u(t) of an object satisfies the differential equationdu/dt= −k(u−T)where T is the constant ambient temperature and k is a positive constant. Suppose that the initial temperature of the object is u(0)= u0.(a) Find the temperature of the object at any time. (I know how to resolve this)
Answer:
[tex]u(t)=T+(u_{0}-T})e^{-kt}[/tex]
Step-by-step explanation:
We know:
[tex]\frac{du}{dt} = -k(u-T)[/tex]
We integrate in order to find u(t):
[tex]\int\limits^u_{u_{0}} {\frac{1}{-k(u-T)} \, du } = \int\limits^t_0 \, dt[/tex]
[tex]ln(\frac{u-T}{u_{0}-T} )=-kt\\[/tex]
[tex]u(t)=T+(u_{0}-T})e^{-kt}[/tex]
kindly solve using the second shifting theorem. thanks. please include explanation that I can understand. many thanks. L[t^2 u(t – 3)] -3)]
Answer:
[tex]\dfrac{2}{s^3}e^{-3s}\ +\ \dfrac{6}{s^2}e^{-3s}\ +\ \dfrac{9}{s}e^{-3s}\ -\ \dfrac{3}{s}[/tex]
Step-by-step explanation:
Given polynomial,
[tex]f(t)\ =\ t^2.u(t-3)\ -\ 3[/tex]
we can write above polynomial as
[tex]f(t)\ =\ (t-3+3)^2.u(t-3)\ -\ 3[/tex]
[tex]=\ ((t-3)^2\ +\ 2\times 3\times (t-3)\ +\ 3^2).u(t-3)-3[/tex]
[tex]=\ (t-3)^2.u(t-3)\ +\ 6(t-3).u(t-3)\ +\ 9.u(t-3)\ -\ 3[/tex]
Now, we have to calculate the Laplace of above polynomial
according to shifting property of Laplace transform, we can write
[tex]f(t-t_0)\ =\ F(s).e^{-st_0}[/tex]
So, we can write the Laplace transform of above polynomial as
[tex]L[f(t)]\ =\ L[(t-3)^2.u(t-3)\ +\ 6(t-3).u(t-3)\ +\ 9.u(t-3)\ -\ 3][/tex]
[tex]=\ \dfrac{2}{s^3}e^{-3s}\ +\ \dfrac{6}{s^2}e^{-3s}\ +\ \dfrac{9}{s}e^{-3s}\ -\ \dfrac{3}{s}[/tex]
So, the Laplace transform of the given polynomial will be[tex]\ \dfrac{2}{s^3}e^{-3s}\ +\ \dfrac{6}{s^2}e^{-3s}\ +\ \dfrac{9}{s}e^{-3s}\ -\ \dfrac{3}{s}[/tex]
The vector y = ai + bj is perpendicular to the line ax + by = c. Use this fact to find an equation of the line through P perpendicular to v. Then draw a sketch of the line including v as a vector starting at the origin. P(-1,-9)v = -4i + j The equation of the line is _____.
Answer:
[tex]-4x+y=-5[/tex]
Step-by-step explanation:
It is given that he vector y = ai + bj is perpendicular to the line ax + by = c.
Given given point is P(-1,-9) and given vector is v = -4i + j.
Here, a = -4 and b= 1.
We need to find the equation of the line through P perpendicular to v.
Using the above fact, the vector v = -4i + j is perpendicular to the line
[tex](-4)x+(1)y=c[/tex]
[tex]-4x+y=c[/tex] ... (1)
The line passes through the point (-1,-9).
Substitute x=-1 and y=-9 in the above equation to find the value of c.
[tex]-4(-1)+(-9)=c[/tex]
[tex]4-9=c[/tex]
[tex]-5=c[/tex]
The value of c is -5.
Substitute c=-5 in equation (1).
[tex]-4x+y=-5[/tex]
Therefore the equation of line which passes through P and perpendicular to v is -4x+y=-5.
Consider all 5 letter "words" made from the full English alphabet. (a) How many of these words are there total? (b) How many of these words contain no repeated letters? (c) How many of these words start with an a or end with a z or both (repeated letters are allowed)?
Answer:
a) There are 11,881,376 of these words in total.
b) 7,893,600 of these words contain no repeated letters.
c) 896,376 of these words start with an a or end with a z or both.
Step-by-step explanation:
The English alphabet has 26 letters.
Our word has the following format
C1 - C2 - C3 - C4 - C5
C1 is the first character, C2 the second, etc...
(a) How many of these words are there total?
Each of C1, C2,... can be 26. So the total is
[tex]T = (26)^{5} = 11,881,376[/tex]
There are 11,881,376 of these words in total.
(b) How many of these words contain no repeated letters?
C1 can be any letter. C2 can be any letter bar the letter at C1. C3 any other than C2, C1... So
26-25-24-23-22
[tex]T = 26*25*24*23*22 = 7,893,600[/tex]
7,893,600 of these words contain no repeated letters.
(c) How many of these words start with an a or end with a z or both (repeated letters are allowed)?
[tex]T = T_{1} + T_{2} + T_{3}[/tex]
[tex]T_{1}:[/tex] Start with a, end with any letter other than z.
1-26-26-26-25
[tex]T_{1} = 26^{3}*25 = 439,400[/tex]
[tex]T_{2}:[/tex]End with z, start with any other letter than A
25-26-26-26-1
[tex]T_{2} = 26^{3}*25 = 439,400[/tex]
[tex]T_{3}:[/tex]Start with A, end with Z
1-26-26-26-1
[tex]T_{3} = 17,576[/tex]
[tex]T = T_{1} + T_{2} + T_{3} = 439,400 + 439,400 + 17,576 = 896,376[/tex]
896,376 of these words start with an a or end with a z or both.
Machine A can produce 435 widget in 3 hours. At this rate how many widget can machine A produce in 7 hours?
Answer:
1015 widgets
Step-by-step explanation:
First investigate how many widgets can machine A produce in 1 hour:
If it produces 435 in 3 hours, then it will produce one third of that in one hour:
In ONE (1) hour [tex]\frac{435}{3} = 145[/tex] widgets
Therefore in seven (7) hours it will produce seven times the amount it does in one hour, that is:
[tex]145 * 7 = 1015[/tex] widgets
Answer:
answer is 1015.
Step-by-step explanation:
A 1L solution containing 25,000 units of heparin must run at 30mL/hr. How much heparin is administered per hour?
Answer:
750 units
Step-by-step explanation:
As given in question,
speed of solution = 30 mL/hr
1 L of solution contains heparin = 25000 units
=> 1000 mL of solution contains heparin = 25000 units
[tex]=>\ \textrm{1 mL of solution contains heparin}\ =\ \dfrac{25000}{1000}\ units[/tex]
= 25 units
Hence, 30 mL of solutions contains heparin = 30 x 1 mL of solution contains heparin
= 30 x 25
= 750 units
Hence, heparin administered per hour = 750 units
Final answer:
To find the amount of heparin administered per hour at a rate of 30mL/hr in a 1L solution with 25,000 units, calculate the concentration in units/mL and multiply by the hourly rate. This results in 750 units of heparin administered per hour.
Explanation:
To calculate the amount of heparin administered per hour when the infusion rate is 30mL/hr, use the given total units of heparin in the 1L solution. Since there are 25,000 units in 1L (1,000 mL), we can find the amount per mL and then multiply by the hourly rate.
First, calculate the units per mL:
Units per mL = Total units / Total volume
Units per mL = 25,000 units / 1,000 mL
Units per mL = 25 units/mL
Next, calculate the units delivered per hour:
Units per hour = Units per mL * Infusion rate (mL/hr)
Units per hour = 25 units/mL * 30 mL/hr
Units per hour = 750 units/hr
Therefore, 750 units of heparin are administered per hour.
193 meters in 2 seconds = meters in 1 minute
Answer:
The required answer is 5790 meters in 1 minute.
Step-by-step explanation:
Consider the provided information.
193 meters in 2 seconds = meters in 1 minute
193 meters in 2 seconds can be written as:
193 meters = 2 seconds
There are 60 seconds in 1 minute. To convert 2 seconds to 1 minute multiply both the sides by 30.
30 × 193 meters = 30 × 2 seconds
5790 meters = 60 seconds
5790 meters = 1 minute (As we know 60 seconds = 1 minute)
This can be written as:
5790 meters in 1 minute.
Hence, the required answer is 5790 meters in 1 minute.
A wind turbine is located at the top of a hill where the wind blows steadily at 12 m/s, and stands 37 m tall. The air then exits the turbine at 9 m/s and the same elevation. Find the power generated by the wind if the mass flow rate is 137 kg/s. Report your answer in kW and to 2 decimal places.
Answer:
4.3155 kW
Step-by-step explanation:
Given,
speed of wind when enters into the turbine, V = 12 m/s
speed of wind when exits from the turbine, U = 9 m/s
mass flow rate of the wind = 137 kg/s
According to the law of conservation of energy
Energy generated = change in kinetic energy
Hence,energy generated in 1 sec can be given by
[tex]E\ =\ \dfrac{1}{2}.m.V^2\ -\ \dfrac{1}{2}.m.U^2[/tex]
[tex]=\ \dfrac{1}{2}\times 137\times 12^2\ -\ \dfrac{1}{2}\times 137\times 9^2[/tex]
[tex]=\ 9864\ -\ 5548.5[/tex]
= 4315.5 J
So, the power generated in 1 sec will be given by
[tex]P\ =\ \dfrac{energy\ generated}{time}[/tex]
[tex]=\ \dfrac{4315.5}{1}[/tex]
= 4315.5 W
= 4.13 kW
So, the power generated will be 4.13 kW.
Mark the statement either true (in all cases) or false (for at least one example). If false, construct a specific example to show that the statement is not always true. Such an example is called a counterexample to the statement. If the statement is true, give a justification. If v1,…,v4 are in R4 and {v1,v2,v3} is linearly dependent then {v1,v2,v3,v4} is also linearly dependent.
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
(A) True. Because v3 = 2v1 + v2, v4 must be the zero vector. Thus, the set of vectors is linearly dependent.
(B) True. The vector v3 is a linear combination of v1 and v2, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.
(C) True. If c1 =2, c2 = 1, c3 = 1, and c4 = 0, then c1v1 + ........... + c4v4 =0. The set of vectors is linearly dependent.
(D) False. If v1 = __, v2 =___, v3 =___, and v4 = [1 2 1 2], then v3 = 2v1 + v2 and {v1, v2, v3, v4} is linearly independent.
Answer with Step-by-step explanation:
We are given that [tex]v_1,v_2,..,v_4[/tex] are in [tex]R^4[/tex] and [tex]v_1,v_2,v_3[/tex] is linearly dependent then {v_1,v_2,v_3,v_4}[/tex] is also linearly dependent.
We have to find that given statement is true or false.
Dependent vectors:Dependent vectors are those vectors in which atleast one vector is a linear combination of other given vectors.
Or If we have vectors [tex]x_1,x_2,....x_n[/tex]
Then their linear combination
[tex]a_1x_1+a_2x_2+.....+a_nx_n=0[/tex]
There exist at least one scalar which is not zero.
If [tex]v_1,v_2,v_3[/tex] are dependent vectors then
[tex]a_1v_1+a_2v_2+a_3v_3=0[/tex] for scalars [tex]a_1,a_2,a_3[/tex]
Then , by definition of dependent vectors
There exist a vector which is not equal to zero
If vector [tex]v_3[/tex] is a linear combination of [tex]v_1\;and \;v_2[/tex], So at least one of vectors in the set is a linear combination of others and the set is linearly dependent.
Hence, by definition of dependent vectors
{[tex]v_1,v_2,v_3,v_4[/tex]} is linearly dependent.
Option B is true.
For the following linear system, put the augmented coefficient matrix into reduced row-echelon form.
2x1 + 3x2 − x3 = 14
x1 + 2x2 + x3 = 4
5x1 + 9x2 + 2x3 = 7
1 0 -5 16
0 1 3 -6
0 0 0 -19
Incorrect
Answer:
The reduced row-echelon form of the linear system is [tex]\left[\begin{array}{cccc}1&0&-5&0\\0&1&3&0\\0&0&0&1\end{array}\right][/tex]
Step-by-step explanation:
We will solve the original system of linear equations by performing a sequence of the following elementary row operations on the augmented matrix:
Interchange two rowsMultiply one row by a nonzero numberAdd a multiple of one row to a different rowTo find the reduced row-echelon form of this augmented matrix
[tex]\left[\begin{array}{cccc}2&3&-1&14\\1&2&1&4\\5&9&2&7\end{array}\right][/tex]
You need to follow these steps:
Divide row 1 by 2 [tex]\left(R_1=\frac{R_1}{2}\right)[/tex][tex]\left[\begin{array}{cccc}1&3/2&-1/2&7\\1&2&1&4\\5&9&2&7\end{array}\right][/tex]
Subtract row 1 from row 2 [tex]\left(R_2=R_2-R_1\right)[/tex][tex]\left[\begin{array}{cccc}1&3/2&-1/2&7\\0&1/2&3/2&-3\\5&9&2&7\end{array}\right][/tex]
Subtract row 1 multiplied by 5 from row 3 [tex]\left(R_3=R_3-\left(5\right)R_1\right)[/tex][tex]\left[\begin{array}{cccc}1&3/2&-1/2&7\\0&1/2&3/2&-3\\0&3/9&9/2&-28\end{array}\right][/tex]
Subtract row 2 multiplied by 3 from row 1 [tex]\left(R_1=R_1-\left(3\right)R_2\right)[/tex][tex]\left[\begin{array}{cccc}1&0&-5&16\\0&1/2&3/2&-3\\0&3/9&9/2&-28\end{array}\right][/tex]
Subtract row 2 multiplied by 3 from row 3 [tex]\left(R_3=R_3-\left(3\right)R_2\right)[/tex][tex]\left[\begin{array}{cccc}1&0&-5&16\\0&1/2&3/2&-3\\0&0&0&-19\end{array}\right][/tex]
Multiply row 2 by 2 [tex]\left(R_2=\left(2\right)R_2\right)[/tex][tex]\left[\begin{array}{cccc}1&0&-5&16\\0&2&3&-6\\0&0&0&-19\end{array}\right][/tex]
Divide row 3 by −19 [tex]\left(R_3=\frac{R_3}{-19}\right)[/tex][tex]\left[\begin{array}{cccc}1&0&-5&16\\0&2&3&-6\\0&0&0&1\end{array}\right][/tex]
Subtract row 3 multiplied by 16 from row 1 [tex]\left(R_1=R_1-\left(16\right)R_3\right)[/tex][tex]\left[\begin{array}{cccc}1&0&-5&0\\0&1&3&-6\\0&0&0&1\end{array}\right][/tex]
Add row 3 multiplied by 6 to row 2 [tex]\left(R_2=R_2+\left(6\right)R_3\right)[/tex][tex]\left[\begin{array}{cccc}1&0&-5&0\\0&1&3&0\\0&0&0&1\end{array}\right][/tex]
A survey of 255 adults found that during the last year, 40 traveled by plane but not by train, 75 traveled by train but not by plane, 50 traveled by bus but not by plane or by train, 55 traveled by bus and plane, 35 traveled by all three, and 170 traveled by plane or train. How many did not travel by any of these modes of transportation?
Answer:
35 people did no travel by any of those modes of transportation.
Step-by-step explanation:
Reviewing the groups described, we can see there are 170 that traveled by either plane or train and 50 traveled by bus, but not plane or train.
This means that the 50 people that traveled by bus are not included in the group of 170 that used either plane or train.
Since those two groups include people that used bus (50 people) and people that used either plane or train (170 people), the union of these two sets include all the people that used at least one of the tree modes of transportation mentioned (bus, plane or train).
The result of the union between these two sets is 50+170=220 people which travel by at least one of those modes of transportation.
Since the total number of surveyed adults is 255, the number of people that did not travel by any of these modes of transportations is 255-220=35 people.
Find the inverse of 12 modulo 19
Answer:
8 is the modular inverse of 12 mod 19 since 12*8 mod 19 ≡ 1.
Step-by-step explanation:
We need to find the inverse of 12 modulo 19.
[tex]12^{-1}(\text{ mod 19})[/tex]
If a is an integer and m is modulo, then the modular multiplicative inverse of a modulo m is an integer b such that
[tex]a\times b\equiv 1(\text{ mod m})[/tex]
Substitute different values of b and check whether that remainder is 1 after modulo 19.
At b=1,
[tex]12\times 1\equiv 12(\text{ mod 19})[/tex]
At b=2,
[tex]12\times 2\equiv 5(\text{ mod 19})[/tex]
At b=3,
[tex]12\times 3\equiv 17(\text{ mod 19})[/tex]
At b=4,
[tex]12\times 4\equiv 10(\text{ mod 19})[/tex]
At b=5,
[tex]12\times 5\equiv 3(\text{ mod 19})[/tex]
At b=6,
[tex]12\times 6\equiv 15(\text{ mod 19})[/tex]
At b=7,
[tex]12\times 7\equiv 8(\text{ mod 19})[/tex]
At b=8,
[tex]12\times 8\equiv 1(\text{ mod 19})[/tex]
Therefore, 8 is the modular inverse of 12 mod 19 since 12*8 mod 19 ≡ 1.
Find all solutions of the equation algebraically. Use a graphing utility to verify the solutions graphically. (Enter your answers as a comma-separated list.) 16x^4 - 24x^3 +9x^2 =0
Answer:
The solutions of the equation are 0 and 0.75.
Step-by-step explanation:
Given : Equation [tex]16x^4 - 24x^3 +9x^2 =0[/tex]
To find : All solutions of the equation algebraically. Use a graphing utility to verify the solutions graphically ?
Solution :
Equation [tex]16x^4 - 24x^3 +9x^2 =0[/tex]
[tex]x^2(16x^2-24x+9)=0[/tex]
Either [tex]x^2=0[/tex] or [tex]16x^2-24x+9=0[/tex]
When [tex]x^2=0[/tex]
[tex]x=0[/tex]
When [tex]16x^2-24x+9=0[/tex]
Solve by quadratic formula, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-24)\pm\sqrt{(-24)^2-4(16)(9)}}{2(16)}[/tex]
[tex]x=\frac{24\pm\sqrt{0}}{32}[/tex]
[tex]x=\frac{24}{32}[/tex]
[tex]x=\frac{3}{4}[/tex]
[tex]x=0.75[/tex]
The solutions of the equation are 0 and 0.75.
For verification,
In the graph where the curve cut x-axis is the solution of the equation.
Refer the attached figure below.
Estimate the sum. Use benchmarks with decimal parts of 0, 0.25, 0.50, or 0.75.
2.52+4.03
A. 6.50
B. 6.75
C. 7
If A=W/(m2-°C), B=m2, C=°C and D = A x B x C, what are the units of D?
Answer:
[tex]\frac{Wm^2C^{\circ}}{m^2-C^{\circ}}[/tex]
Step-by-step explanation:
We are given that A=[tex]\frac{W}{m^2-C^{\circ}}[/tex]
B=[tex]m^2[/tex]
C=[tex]C^{\circ}[/tex]
We are given that [tex]D=A\times B\times C[/tex]
We have to find the unit if D
Substitute the values then we get
[tex]D=\frac{W}{m^2-C^{\circ}}\times m^2\times C^{\circ}=\frac{Wm^2C^{\circ}}{m^2-C^{\circ}}[/tex]
[tex]D=\frac{Wm^2C^{\circ}}{m^2-C^{\circ}}[/tex]
Hence, units of D=[tex]\frac{Wm^2C^{\circ}}{m^2-C^{\circ}}[/tex]
Triphasil-28 birth control tablets are taken sequentially, 1 tablet per day for 28 days, with the tablets containing the following: Phase 1: 6 tablets, each containing 0.050 mg of levonorgestrel and 0.030 mg ethinyl estradiol Phase 2: 5 tablets, each containing 0.075 mg of levonorgestrel and 0.040 mg ethinyl estradiol Phase 3: 10 tablets, each containing 0.125 mg of levonorgestrel and 0.030 mg ethinyl estradiol Then 7 inert tablets (no drug). How many total milligrams each of levonorgestrel and ethinyl estradiol are taken during the 28-day period?
Over the 28-day cycle of taking Triphasil-28 birth control tablets, a total of 1.925 mg of levonorgestrel and 0.680 mg of ethinyl estradiol are consumed.
Explanation:The Triphasil-28 birth control tablets are taken in a sequence of 21 active pills containing hormones and 7 inactive pills (placebos). To calculate the total amount of levonorgestrel and ethinyl estradiol consumed over the 28-day period, each phase needs to be taken into account.
In phase 1, there are 6 tablets each with 0.050 mg of levonorgestrel and 0.030 mg ethinyl estradiol. So, 6 tablets * 0.050 mg = 0.300 mg of levonorgestrel and 6 tablets * 0.030 mg = 0.180 mg of ethinyl estradiol.
In phase 2, there are 5 tablets each with 0.075 mg of levonorgestrel and 0.040 mg ethinyl estradiol. So, 5 tablets * 0.075 mg = 0.375 mg of levonorgestrel and 5 tablets * 0.040 mg = 0.200 mg of ethinyl estradiol.
In phase 3, there are 10 tablets each with 0.125 mg of levonorgestrel and 0.030 mg ethinyl estradiol. So, 10 tablets * 0.125 mg = 1.250 mg of levonorgestrel and 10 tablets * 0.030 mg = 0.300 mg of ethinyl estradiol.
Adding up all the quantities, we have a total of 0.300 mg + 0.375 mg + 1.250 mg = 1.925 mg of levonorgestrel and 0.180 mg + 0.200 mg + 0.300 mg = 0.680 mg of ethinyl estradiol consumed over the 21 active days of the 28-day cycle.
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A nurse infuses a dose in 50 minutes. She needs to infuse the dose at a 20% faster rate. How much time does she need ?
Answer: She would need 40 minutes to infuse a dose.
Step-by-step explanation:
Since we have given that
Number of minutes a nurse takes to infuse a dose = 50 minutes
Rate faster by 20%
So, if the initial rate = 100%
After increasing the rate,
rate becomes 100%-20% = 80%
So, Number of minutes taken to infuse a dose now is given by
[tex]\dfrac{80}{100}\times 50\\\\=0.8\times 50\\\\=40\ minutes[/tex]
Hence, she would need 40 minutes to infuse a dose.
A physician prescribes 2.5 million units of penicillin G potassium daily for 1 week. If 1 unit of penicilin G potassium equals 0.6 mcg, how many tablets, each containing 250 mg, will provide the prescribed dosage regimen un
If a physician prescribes 2.5 million units of penicillin G potassium daily for 1 week. To provide the prescribed dosage regimen of 2.5 million units of penicillin G potassium daily for 1 week we would need 42 tablets, each containing 250 mg.
What is the Number of tablets needed ?
Total amount of penicillin G potassium required
Since there are 7 days in a week the total amount required is:
Total amount required =2.5 million units/day * 7 days
Total amount required = 17.5 million units
Convert the units of penicillin G potassium to micrograms (mcg)
Total amount required in micrograms:
Total amount required = 17.5 million units * 0.6 mcg/unit
Total amount required = 10.5 million mcg
Convert micrograms to milligrams (mg)
Convert the total amount required to milligrams:
10.5 million mcg / 1000
= 10,500 mg
The number of tablets needed:
Number of tablets needed:
Number of tablets needed = 10,500 mg / 250 mg/tablet
Number of tablets needed = 42 tablets
Therefore to provide the prescribed dosage regimen of 2.5 million units of penicillin G potassium daily for 1 week we would need 42 tablets, each containing 250 mg.
The patient needs to take 42 tablets of penicillin G potassium over one week. This is determined by converting the prescribed units to milligrams and dividing by the tablet dosage.
Calculating Dosage of Penicillin G Potassium
To determine how many tablets of penicillin G potassium are needed, we need to go through several steps of unit conversion.
Convert units to micrograms (mcg):Therefore, the patient needs to take 42 tablets over the course of one week.
find the area of a rectangle with the given base and height
5ft,6 in
Answer:
360 inch
Step-by-step explanation:
Step 1: Converting
6inch = 6inch
5ft = 60inch
Step 2: Finding the area
Area of a rectangle = L x B
A = 6 x 60
A = 360inch
A breath analyzer, used by the police to test whether drivers exceed the legal limit for blood alcohol percentage while driving, is known to satisfy P ( A | B ) = P ( A c | B c ) = p where A is the event "breath analyzer indicates that legal limit is exceeded" and B is the event "driver's blood alcohol percentage exceeds legal limit." On Saturday night, about 5% of all drivers are known to exceed the limit. If we want P ( B | A ) to equal 0.9, what value of p should we use, rounded to 4 decimal places? Group of answer choices
To find the value of 'p' that satisfies the equation, we use Bayes' theorem and substitute the given values into the equation.
Explanation:In this question, we need to find the value of p which satisfies the equation P(A|B) = P(A' | B'), where A is the event 'breath analyser indicates that legal limit is exceeded' and B is the event 'driver's blood alcohol percentage exceeds legal limit.'
We are given that approximately 5% of all drivers exceed the legal limit for blood alcohol percentage while driving, which means P(B) = 0.05.We are also given that we want P(B|A) = 0.9. Using Bayes' theorem, we can write:Therefore, the value of p that should be used, rounded to 4 decimal places, can be calculated using the above steps.
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Suppose that a worker in Country A can make either 10 iPods or 5 tablets each year. Country A has 100 workers. Suppose a worker in Country B can make either 2 iPods or 10 tablets each year. Country B has 200 workers. A bundle of goods that Country A could not make would be:
Answer:
A bundle of goods that Country A has are 1000 iPods and 500 Tablets.
Step-by-step explanation:
Country A can produce either iPods and Tablets.
Total man power Country A has 100 workers.
As per information in the question w
100 worker make either ipod or 100 worker make tablets
1 worker can produce 10 iPods.
Therefore
100 workers can produce (100 * 10) = 1000 iPods.
on the other hand
1 worker can produce 5 tablets.
Therefore
100 workers can produce (100 * 5)= 500 Tablets
Thus,
A bundle of goods that Country A has are 1000 iPods and 500 Tablets.
An astronaut with a mass of 80.70 kg is standing still on the surface of the Mars (Mars has an acceleration due to gravity of 3.80 m / s^2). How many pounds force is she exerting on the martian surface?
Answer:
Force, F = 68.93 pounds
Step-by-step explanation:
Given that,
Mass of the astronaut, m = 80.70 kg
Acceleration due to gravity on Mars, [tex]a=3.8\ m/s^2[/tex]
The force acting on him is given by using second law of motion as :
[tex]F=m\times a[/tex]
[tex]F=80.70\ kg\times 3.8\ m/s^2[/tex]
F = 306.66 N
Since, 1 newton = 0.224 pound
F = 306.66 N = 68.93 pounds
So, 68.93 pounds force she exerts on the martian surface. Hence, this is the required solution.
The amount of garbage, G, in tons per week, produced by a city with population p, measured in thousands of people, is given by G = f ( p ) The town of Tola has a population of 50,000 and produces 14 tons of garbage each week. Express this information in terms of the function f
Answer: [tex]G=f(50)=14[/tex]
Step-by-step explanation:
Given : The amount of garbage, G, in tons per week, produced by a city with population p, measured in thousands of people, is given by G = f(p).
Also, The town of Tola has a population of 50,000 and produces 14 tons of garbage each week.
Then, the expression in terms of the function G will be :-
[tex]G=f(50)=14[/tex]