Answer:
24.39mL of the solution would be given per hour.
Step-by-step explanation:
This problem can be solved by direct rule of three, in which there are a direct relationship between the measures, which means that the rule of three is a cross multiplication.
The first step to solve this problem is to see how many mg of the solution is administered per hour.
Each minute, 200 ug are administered. 1mg has 1000ug, so
1mg - 1000 ug
xmg - 200 ug
[tex]1000x = 200[/tex]
[tex]x = \frac{200}{1000}[/tex]
[tex]x = 0.2mg[/tex]
In each minute, 0.2 mg are administered. Each hour has 60 minutes. How many mg are administered in 60 minutes?
1 minute - 0.2 mg
60 minutes - x mg
[tex]x = 60*0.2[/tex]
[tex]x = 12mg[/tex]
In an hour, 12 mg of the drug is administered. In 250 mL, there is 123 mg of the drug. How many ml are there in 12 mg of the drug.
123mg - 250mL
12 mg - xmL
[tex]123x = 250*12[/tex]
[tex]x = \frac{250*12}{123}[/tex]
[tex]x = 24.39[/tex]mL
24.39mL of the solution would be given per hour.
Final answer:
Approximately 24.39 milliliters of the intravenous solution would be administered per hour to deliver an hourly drug rate of 12 milligrams based on the given concentration.
Explanation:
To calculate how many milliliters of the intravenous solution would be given per hour, first convert the rate of drug administered from micrograms to milligrams: 200 \5g is equal to 0.2 mg. Since the drug administration rate is 0.2 mg per minute, we need to multiply this by 60 minutes to get the hourly rate:
0.2 mg/minute x 60 minutes/hour = 12 mg/hour.
Next, we need to find out how many milliliters of the solution contain 12 mg of the drug. Since we have 123 mg in 250 mL, we can set up a proportion to solve for the volume needed:
(123 mg/250 mL) = (12 mg/V mL)
V = (12 mg x 250 mL) / 123 mg = 24.39 mL.
Therefore, approximately 24.39 mL of the solution would be administered per hour.
In compounding a prescription, a pharmacist weighed 0.050 g of a substance on a balance insensitive to quantities smaller than 0.004 g. What was the maximum potential error in terms of percentage?
The maximum potential error is 92% as per the concept of percentage.
The pharmacist weighed 0.050 g of a substance on a balance insensitive to quantities smaller than 0.004 g.
To find the maximum potential error in terms of percentage, we need to determine the difference between the actual weight of the substance and the closest value that the balance can measure, which is 0.004 g.
The difference is 0.050 g - 0.004 g = 0.046 g.
The maximum potential error is the difference between the actual weight and the closest value that the balance can measure, divided by the actual weight, multiplied by 100%.
Therefore, the maximum potential error in terms of percentage is (0.046 g / 0.050 g) x 100% = 92%.
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The question deals with the calculation of the maximum potential error in a measurement. Given the insensitivity of the balance to 0.004 g and the actual measurement of substance of 0.050 g, the maximum potential error by calculation comes out to be 8%.
Explanation:The question is asking about the potential error in a measurement made by a pharmacist. The error is the difference between the smallest measurable quantity by the balance and the actual measurement. In this case, we have a balance that is insensitive to quantities smaller than 0.004 g, and the pharmacist is measuring 0.050 g of a substance.
To find the potential error percentage, we take the maximum potential error (which is defined by the sensitivity of the balance, 0.004 g), divide it by the actual measurement (0.050 g) and multiply by 100 to make it a percentage.
Maximum potential error percentage = (0.004 g / 0.050 g) * 100% = 8%
So the maximum potential error in this measurement is 8%.
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Find the value of 8/15×2/13 Although these numbers aren't quite as nice as the ones from the example, the procedure is the same, so the difficulty is the same excepting the ability to perform the calculation in your head. You may choose to use a calculator.
Answer:
[tex]\frac{16}{195}[/tex]
Step-by-step explanation:
To obtain the result of a fractions multiplication we need to multiply both numerators and the divide by the multiplication of the denomitators. In general, given a,b,c,d real numbers with b and d not zero, we have that
[tex]\frac{a}{b}*\frac{c}{d}=\frac{a*c}{b*d}[/tex]
Substituting a,b,c and d for 8,15,2 and 13 we obtain that
[tex]\frac{8}{15}* \frac{2}{13} =\frac{16}{195}[/tex]
To find the value of 8/15 x 2/13, multiply the numerators together and multiply the denominators together. The fraction 16/195 is the final answer.
Explanation:To find the value of 8/15 x 2/13, we multiply the numerators together (8 x 2) and multiply the denominators together (15 x 13). This gives us 16 in the numerator and 195 in the denominator.
The fraction 16/195 cannot be simplified further, so that is the final answer.
Calculation:
We have 8/15 x 2/13 = (8 x 2)/(15 x 13) = 16/195.
A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances are equal. For this situation, the professor should use a t test with related samples.
(A) True
(B) False
Answer:
False
Step-by-step explanation:
In the above situation where the professor took a random sample of size 10 from each, conducted a test and found out that the variances are equal. should not use a t test with related samples. The professor should use the t test for the difference in means testing for independence. Hence, the statement is false.
According to the hypothesis tested, it is found that it is true that the professor should use a t test with related samples, hence option A is correct.
When a t-test with related samples should be used?A t-test should be used when we do not have the standard deviation for the population, which is the case in this problem, as we have it for the sample.
Related samples are used when comparisons are made between two samples, which is the case here for the samples of upper and lower classmen.
Hence, option A is correct.
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Beginning with Newton's second law of motion, derive the equations of motion for a projectile fired from altitude h above the ground at an angle e to the horizontal and with initial speed equal to vo.
Answer:
Considering the fire point at (0,h), x-direction positive to the right (→) and y-direction positive to up (↑) and the only force acting after fire is the projectile weight = -mg in the y-direction.
[tex]\\ x(t)=Vo*cos(e)*t\\ v_x(t)=Vo*cos(e)\\ a_y(t)=0\\ y(t)=h+Vo*sin(e)*t-\frac{g}{2}t^{2}\\ v_x(t)=Vo*sin(e)-gt\\ a_y(t)=-g[/tex]
Step-by-step explanation:
First, we apply the Second Newton's Law in both x and y directions:
x-direction:
[tex]\sum F_x= m\frac{dv_x}{dt} =0[/tex]
Integrating we have
[tex]\int\limits^{V_x} _{V_{0x}}{}\, dV_x =\int\limits^{t} _0{0}\, dt\\ V_{0x}=Vo*cos(e)\\ V_x(t)=Vo*cos(e)[/tex]
Taking into account that a=(dv/dt) and v=(dx/dt):
[tex]a_x(t)=\frac{dV_x(t)}{dt}=0\\V_x(t)=\frac{dx(t)}{dt}-->\int\limits^x_0 {} dx = \int\limits^t_0 {Vo*cos(t)} \, dt \\x(t)=Vo*cos(e)*t[/tex]
y-direction:
[tex]\sum F_y= m\frac{dv_x}{dt} =-mg[/tex]
Integrating we have
[tex]\int\limits^{V_y} _{V_{0y}}{}\, dV_y =\int\limits^{t} _0 {-g} \, dt\\ V_{0y}=Vo*sin(e)\\ V_y(t)=Vo*sin(e)-g*t[/tex]
Taking into account that a=(dv/dt) and v=(dy/dt):
[tex]a_y(t)=\frac{dV_y(t)}{dt}=-g\\V_y(t)=\frac{dy(t)}{dt}-->\int\limits^y_h {} dy = \int\limits^t_0 {(Vo*sin(t)-g*t)} \, dt \\y(t)=h+Vo*sin(e)*t-\frac{g}{2}t^{2}[/tex]
In order to make some extra money in the summer, you water your neighbor's lawn and walk their dog. You water their lawn every 6 days and walk the dog every 4 days. Your neighbor pays you $5 each time you walk the dog and $6 each time you water the lawn.When you do both jobs on the same day. she gives you an exrta $3. On june 1, you dont have ro complete either job, because your neighbor did them both the day before. if you worked for your neighbor from june 1 to july 20 ( there 30 days in june and 31 days in july ), how many times would you do both jobs on the same day ? how much total money would earn?
Answer:
$114
Step-by-step explanation:
make a calender and count every 4 days for dogs and every 6 days for the lawn. Then add all the money up.
Express 247_10 to (a) base 7, (b) base 2, (c) base 8, and (d) base 16.
Answer:
Step-by-step explanation:
given number,
247₁₀ to be converted into
a) base 7
divide the number by 7 and write the remainder on the left side
solution is (502)₇
b) base 2
divide the number by 2 and write the remainder on the left side and write in the direction from down to up as shown in the diagram attached below.
solution is (11110111)₂
c) base 8
divide the number by 8 and write the remainder on the left side
solution is (367)₈
d) base 16
divide the number by 16 and write the remainder on the left side
solution is (F 7)₈
15 - F
diagram is attached below.
10,101 base 2 + 11,011 base 2 =
Answer:
110,000 base 2
Step-by-step explanation:
column 1 [the first position in the number]:
1+1=0, (carry 1)
column 2:
0+1 +1 (carried)=0, (carry 1)
column 3:
1+0+1 (carried)=0, (carry 1)
column 4:
0+1+1 (carried)=0, (carry 1)
column 5:
1+1+1=1, (carry 1)
then you write the last 1 'cause there is n number to add with:
[tex]10,101_{2}+11,011_{2}=110,000_{2}[/tex]
In binary system the highest number to write is 1, if you add 1+1, it jumps to 0, and you have to carry 1 to the next position.
If you are not sure about the sum, you can convert the numbers in base 2, to base 10, so you can know if it is correct:
[tex]10,101_{2}=21_{10}\\11,011_{2}=27_{10}\\110,000_{2}=48_{10}[/tex]
So 21+27=48.
In decimal system when you add 9+1, it jumps to 0 and then you have to carry 1 to the next position, because the the highest number you can write is 9.
Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doesn't work for.
Answer:
The statement is true for every n between 0 and 77 and it is false for [tex]n\geq 78[/tex]
Step-by-step explanation:
First, observe that, for n=0 and n=1 the statement is true:
For n=0: [tex]\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4[/tex]
For n=1: [tex]\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4[/tex]
From this point we will assume that [tex]n\geq 2[/tex]
As we can see, [tex]\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4[/tex] and [tex](4n)^4=256n^4[/tex]. Then,
[tex]\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4[/tex]
Now, we will use the formula for the sum of the first 4th powers:
[tex]\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}[/tex]
Therefore:
[tex]\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0[/tex]
and, because [tex]n \geq 0[/tex],
[tex]465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1[/tex]
Observe that, because [tex]n \geq 2[/tex] and is an integer,
[tex]n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5[/tex]
In concusion, the statement is true if and only if n is a non negative integer such that [tex]n\leq 77[/tex]
So, 78 is the smallest value of n that does not satisfy the inequality.
Note: If you compute [tex](4n)^4- \sum^{n}_{i=0} (2i)^4[/tex] for 77 and 78 you will obtain:
[tex](4n)^4- \sum^{n}_{i=0} (2i)^4=53810064[/tex]
[tex](4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992[/tex]
We will use mathematical induction to prove this inequality.
Explanation:We will prove this inequality using mathematical induction. First, let's check the base case when n = 0. The left-hand side (LHS) of the inequality is 0 and the right-hand side (RHS) is (4*0)^4 = 0. So, the inequality holds for n = 0.
Next, assume that the inequality holds for some positive integer k, i.e.,
∑([2i]^4) ≤ (4k)^4 (where the sum is taken from i = 0 to k)
We will prove that it also holds for k + 1. Adding the (k+1)th term to both sides of the inequality:
∑([2i]^4) + ([2(k+1)]^4) ≤ (4k)^4 + ([2(k+1)]^4)
Now, simplifying the LHS and RHS:
(∑([2i]^4)) + ([2(k+1)]^4) ≤ (4k)^4 + ([2(k+1)]^4)
HELP!
Will give brainliest to whoever does answer this correctly!
As infants grow from a toddler to a young adult, there may be times when they are ill and medication is needed. It is extremely important that medication be administered in the exact dose so the child receives the correct amount. Too little or too much medication could have serious side effects. A popular children’s fever medicine manufacturer recommends the following dosage information to parents and pediatricians.
Answer:
the rate is 0.208
3/4x -1/2y= 8 and 2x +y=40
Answer:
The value of x is 16 and the value of y is 8.
Step-by-step explanation:
Consider the provided equation.
[tex]\frac{3}{4}x -\frac{1}{2}y= 8\ and\ 2x +y=40[/tex]
Isolate x for [tex]\:\frac{3}{4}x-\frac{1}{2}y=8[/tex]
[tex]\frac{3}{4}x-\frac{1}{2}y+\frac{1}{2}y=8+\frac{1}{2}y[/tex]
[tex]\frac{3}{4}x=8+\frac{1}{2}y[/tex]
Multiply both side by 4 and simplify.
[tex]3x=32+2y[/tex]
[tex]x=\frac{32+2y}{3}[/tex]
Substitute the value of x in [tex]2x +y=40[/tex]
[tex]2\cdot \frac{32+2y}{3}+y=40[/tex]
[tex]\frac{64}{3}+\frac{7y}{3}=40[/tex]
[tex]64+7y=120[/tex]
[tex]7y=56[/tex]
[tex]y=8[/tex]
Now substitute the value of y in [tex]x=\frac{32+2y}{3}[/tex]
[tex]x=\frac{32+2\cdot \:8}{3}[/tex]
[tex]x=16[/tex]
Hence, the value of x is 16 and the value of y is 8.
In a class of 19 students, 3 are math majors. A group of four students is chosen at random. (Round your answers to four decimal places.) (a) What is the probability that the group has no math majors? (b) What is the probability that the group has at least one math major? (c) What is the probability that the group has exactly two math majors?
Answer:
(a) The probability is 0.4696
(b) The probability is 0.5304
(c) The probability is 0.0929
Step-by-step explanation:
The total number of ways in which we can select k elements from a group n elements is calculate as:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, the number of ways in which we can select four students from a group of 19 students is:
[tex]19C4=\frac{19!}{4!(19-4)!}=3,876[/tex]
On the other hand, the number of ways in which we can select four students with no math majors is:
[tex](16C4)*(3C0)=(\frac{16!}{4!(16-4)!})*(\frac{3!}{0!(3-0)!})=1820[/tex]
Because, we are going to select 4 students form the 16 students that aren't math majors and select 0 students from the 3 students that are majors.
At the same way, the number of ways in which we can select four students with one, two and three math majors are 1680, 360 and 16 respectively, and they are calculated as:
[tex](16C3)*(3C1)=(\frac{16!}{3!(16-3)!})*(\frac{3!}{1!(3-1)!})=1680[/tex]
[tex](16C2)*(3C2)=(\frac{16!}{2!(16-2)!})*(\frac{3!}{2!(3-1)!})=360[/tex]
[tex](16C1)*(3C3)=(\frac{16!}{1!(16-1)!})*(\frac{3!}{3!(3-3)!})=16[/tex]
Then, the probability that the group has no math majors is:
[tex]P=\frac{1820}{3876} =0.4696[/tex]
The probability that the group has at least one math major is:
[tex]P=\frac{1680+360+16}{3876} =0.5304[/tex]
The probability that the group has exactly two math majors is:
[tex]P=\frac{360}{3876} =0.0929[/tex]
In short, to calculate the probability of certain events in a group selection, you would identify the total possible groups, and then calculate how many of these groups satisfy your desired conditions. The probability is then calculated as the favorable events over the total possibilities.
Explanation:This problem is a classic example of combinatorics and probability. The total number of ways to select four students from a total of 19 is given by the combination function: 19 choose 4. The denominator for all our probability calculations will be this total number of possible groups.
(a) To find the probability that the group has no math majors, we want all four students to be from the 16 non-math majors. This is calculated as combinations of 16 choose 4. Thus, the probability is (16 choose 4) / (19 choose 4).(b) The probability that the group has at least one math major is calculated as 1 minus the probability that the group has no math majors.(c) The probability that the group has exactly two math majors can be calculated by considering the combinations of selecting 2 math majors from the 3 (3 choose 2) and 2 non-math majors from the remaining 16 (16 choose 2). That gives us the probability of (3 choose 2)*(16 choose 2) / (19 choose 4).Learn more about Combinatorics and Probability here:https://brainly.com/question/31293479
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when a number is decreased by 40% of itself, the result is 24 what is the number?
Answer: The number is 40.
Step-by-step explanation:
Since we have given that
Let the number be 'x'.
If a number is decreased by 40%.
So, number becomes,
[tex]\dfrac{100-40}{100}\times x\\\\=\dfrac{60}{100}\times x\\\\=0.6x[/tex]
According to question, the result becomes 24.
So, our equation becomes,
[tex]0.6x=24\\\\x=\dfrac{24}{0.6}\\\\x=\dfrac{240}{6}\\\\x=40[/tex]
Hence, the number is 40.
Find the solution to the differential equation
dB/dt+4B=20
with B(1)=30
Answer:
Solution: [tex]B=5+25e^{4-4t}[/tex]
Step-by-step explanation:
Given: [tex]\dfrac{dB}{dt}+4B=20[/tex]
with B(1)=30
The differential equation in form of linear differential equation,
[tex]\dfrac{dy}{dt}+Py=Q[/tex]
Integral factor, IF: [tex]e^{\int Pdt}[/tex]
General Solution:
[tex]y\cdot IF=\int Q\cdot IFdt[/tex]
[tex]\dfrac{dB}{dt}+4B=20[/tex]
P=4, Q=20
IF= [tex]e^{\int 4dt}=e^{4t}[/tex]
Solution:
[tex]Be^{4t}=\int 20e^{4t}dt[/tex]
[tex]Be^{4t}=5e^{4t}+C[/tex]
[tex]B=5+Ce^{-4t}[/tex]
B(1)=30 , Put t=1, B=30
[tex]30=5+Ce^{-4}[/tex]
[tex]C=25e^4[/tex]
[tex]B=5+25e^{4-4t}[/tex]
Let p:4 is an even integer. q:-5 is a negative prime number. Write each of the following statements in terms ofp, q, and logical connectives: a. 4 is an even integer and-5 is a negative prime number. b. 4 is not an even integer and-5 is a negative prime number. c. If 4 is an even integer, then-5 is a negative prime number. d. 4 is an even integer if and only if-5 is a negative prime number. e. If 4 is not an even integer, then-5 is not a negative prime number 50 MATHEMATICS INTHE MODERN WORLD
Answer:
a. [tex]p \wedge q[/tex]
b. [tex]\neg p \wedge q[/tex]
c. [tex]p\Rightarrow q[/tex]
d. [tex]p \Leftrightarrow q[/tex]
e. [tex]\neg p \Rightarrow \neg q[/tex]
Step-by-step explanation:
a. 4 is an even integer and -5 is a negative prime number, can be represented by: [tex]p \wedge q[/tex]
b. 4 is not an even integer and-5 is a negative prime number, can be represented by: [tex]\neg p \wedge q[/tex]
c. If 4 is an even integer, then-5 is a negative prime number, can be represented by: [tex]p\Rightarrow q[/tex]
d. 4 is an even integer if and only if-5 is a negative prime number, can be represented by: [tex]p \Leftrightarrow q[/tex]
e. If 4 is not an even integer, then-5 is not a negative prime number, can be represented by: [tex]\neg p \Rightarrow \neg q[/tex]
The statements a-e are translated into the language of logic as p ∧ q, ¬p ∧ q, p → q, p ↔ q, and ¬p → ¬q, respectively. These represent different logical relationships between the statements '4 is an even integer' and '-5 is a negative prime number'.
Explanation:To rewrite the provided statements using logical connectors and the given identifiers (p: 4 is an even integer, q: -5 is a negative prime number), we proceed as follows:
a. p ∧ q: This reads "p and q", representing the statement "4 is an even integer and -5 is a negative prime number".
b. ¬p ∧ q: The symbol ¬ stands for "not", so this reads "not p and q", representing "4 is not an even integer and -5 is a negative prime number".
c. p → q: This reads "p implies q", representing "If 4 is an even integer, then -5 is a negative prime number".
d. p ↔ q: This reads "p if and only if q", representing "4 is an even integer if and only if -5 is a negative prime number".
e. ¬p → ¬q: This reads "not p implies not q", representing "If 4 is not an even integer, then -5 is not a negative prime number".
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If you travel south from the equator to 25°S, how far will you have to travel? The circumference of the earth is approximately 40,000 km or 24, 900 mi.
Answer:
2,777.8 km or 1,729.2 mi
Step-by-step explanation:
first think about how many degrees would you travel if you wanted to do a whole circunference always going south: it would take 360 degress to complete a circunference.
Then you can use a rule of three to find the answer:
If the whole circunference is 40,000km and in degrees is 360, then how much 25 degrees would be?
[tex]x= \frac{25}{360}*40,000[/tex]
[tex]x= 2777.8[/tex]
Which of the following sets are equal to {x | x < 9 and x >2}
Question 5 options:
{3, 4, 5, 6, 7, 8}
{2, 3, 4, 5, 6, 7, 8, 9}
{8, 7, 6, 5, 3}
{ }
{2, 3, 4, 5, 6, 7}
Answer:
{3, 4, 5, 6, 7, 8}
Step-by-step explanation:
Integers that are less than 9 and greater than 2 include the integers 3 through 8.
The correct set equal to {x | x < 9 and x > 2} is {3, 4, 5, 6, 7, 8}, as it includes all the integers that satisfy the given condition.
The given set is {x | x < 9 and x > 2}, which translates to all numbers greater than 2 and less than 9. When comparing this to the options provided, we need to ensure that the numbers within the set are all and only the integers that satisfy these conditions, regardless of their order. The set {3, 4, 5, 6, 7, 8} matches this description exactly, as it includes all the integers that are greater than 2 and less than 9. Sets in mathematics do not consider the order of elements; they only consider the presence of elements. Therefore, the correct option that is equal to the given set is {3, 4, 5, 6, 7, 8}.
Prochlorperazine (Compazine) for injection is available in 10-mL multiple dose vials containing 5 mg/mL. How many 2-mg doses can be withdrawn from the vial?
Answer:
25
Step-by-step explanation:
Given:
Volume of Prochlorperazine injection available = 10 mL
Dose per vial = 5 mg/mL
Now,
The total mass of dose present in 10 mL = Volume × Dose
or
The total mass of dose present in 10 mL = 10 × 5 = 50 mg
Thus,
The number of 2 mg dose that can be withdrawn = [tex]\frac{\textup{50 mg}}{\textup{2 mg}}[/tex]
or
The number of 2 mg dose that can be withdrawn = 25
Answer: 25 doses of 2 mg each from the 10-mL vial
Step-by-step explanation:
To determine how many 2-mg doses can be withdrawn from a 10-mL vial containing Prochlorperazine at a concentration of 5 mg/mL, you can use the following calculation:
1. Calculate the total amount of Prochlorperazine in the vial:
Total amount = Concentration × Volume
Total amount = 5 mg/mL × 10 mL
Total amount = 50 mg
2. Now, calculate how many 2-mg doses can be withdrawn:
Number of 2-mg doses = Total amount / Dose per patient
Number of 2-mg doses = 50 mg / 2 mg/dose
Number of 2-mg doses = 25 doses
So, you can withdraw 25 doses of 2 mg each from the 10-mL vial of Prochlorperazine.
In a certain year, the U.S. Senate was made up of 53 Democrats, 45 Republicans, and 2 Independents who caucus with the Democrats. In a survey of the U.S. Senate conducted at that time, every senator was asked whether he or she owned at least one gun. Of the Democrats, 19 declared themselves gun owners; of the Republicans, 21 of them declared themselves gun owners; none of the Independents owned guns. If a senator participating in that survey was picked at random and turned out to be a gun owner, what was the probability that he or she was a Democrat? (Round your answer to four decimal places.)
Answer:
There is a 47.50% probability that the chosen senator is a Democrat.
Step-by-step explanation:
This can be formulated as the following problem:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula:
[tex]P = \frac{P(B).P(A/B)}{P(A)}[/tex]
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
In your problem we have that:
A(what happened) is the probability of a gun owner being chosen:
There are 100 people in the survay(53 Democrats, 45 Republicans ans 2 Independents), and 40 of them have guns(19 Democrats, 21 Republicans). So, the probability of a gun owner being chosen is:
[tex]P(A) = \frac{40}{100} = 0.4[/tex]
[tex]P(A/B)[/tex] is the probability of a senator owning a gun, given that he is a Democrat. 19 of 53 Democrats own guns, so the probability of a democrat owning a gun is:
[tex]P(A/B) = \frac{19}{53} = 0.3585[/tex]
[tex]P(B)[/tex] is the probability that the chosen senators is a Democrat. There are 100 total senators, 53 of which are Democrats, so:
[tex]P(B) = \frac{53}{100} = 0.53[/tex]
If a senator participating in that survey was picked at random and turned out to be a gun owner, what was the probability that he or she was a Democrat?
[tex]P = \frac{P(B).P(A/B)}{P(A)} = \frac{(0.53)*(0.3585)}{(0.40)} = 0.4750[/tex]
There is a 47.50% probability that the chosen senator is a Democrat.
The equation giving a family of ellipsoids is u = (x^2)/(a^2) + (y^2)/(b^2) + (z^2)/(c^2) . Find the unit vector normal to each point of the surface of this ellipsoids.
Answer:
[tex]\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}[/tex]
Step-by-step explanation:
Given equation of ellipsoids,
[tex]u\ =\ \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}[/tex]
The vector normal to the given equation of ellipsoid will be given by
[tex]\vec{n}\ =\textrm{gradient of u}[/tex]
[tex]=\bigtriangledown u[/tex]
[tex]=\ (\dfrac{\partial{}}{\partial{x}}\hat{i}+ \dfrac{\partial{}}{\partial{y}}\hat{j}+ \dfrac{\partial{}}{\partial{z}}\hat{k})(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2})[/tex]
[tex]=\ \dfrac{\partial{(\dfrac{x^2}{a^2})}}{\partial{x}}\hat{i}+\dfrac{\partial{(\dfrac{y^2}{b^2})}}{\partial{y}}\hat{j}+\dfrac{\partial{(\dfrac{z^2}{c^2})}}{\partial{z}}\hat{k}[/tex]
[tex]=\ \dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}[/tex]
Hence, the unit normal vector can be given by,
[tex]\hat{n}\ =\ \dfrac{\vec{n}}{\left|\vec{n}\right|}[/tex]
[tex]=\ \dfrac{\dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}}{\sqrt{(\dfrac{2x}{a^2})^2+(\dfrac{2y}{b^2})^2+(\dfrac{2z}{c^2})^2}}[/tex]
[tex]=\ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}[/tex]
Hence, the unit vector normal to each point of the given ellipsoid surface is
[tex]\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}[/tex]
Is the set of all 2x2 matrices such that det(A)=0 a subspace of the vector space of all 2x2 matrices?
Answer:
The answer is no: the set of all 2x2 matrices such that det(A)=0 is not a subspace of the vector space of all 2x2 matrices.
Step-by-step explanation:
In order for a set of matrices to be a subspace of all 2x2 matrices, three conditions must be satisfied:
1) That the set is not empty.
2) If A and B are both 2x2 matrices with zero determinant then the matrix A+B should also be a matrix with zero determinant.
3) The determinant of c*A, where "c" is any complex number and A is any matrix of the set, should be zero.
1)
The first condition is satisfied by the set of all 2x2 matrices such that det(A)=0, since there are plenty 2x2 matrices with zero determinant.
2)
The second condition is not satisfied, since from the determinant properties, we know that:
[tex]det(A+B)\geq det(a)+det(B)[/tex]
The equality might hold, but it is not a general characteristic. For example, if we consider the following matrices:
[tex]A = \left[\begin{array}{cc}1&0\\0&0\end{array}\right], \quad B = \left[\begin{array}{cc}0&0\\0&1\end{array}\right][/tex]
We can easily check that the determinant of both matrices is zero, nevertheless the determinant of the sum is different than zero.
Therefore, the set of all 2x2 matrices such that det(A)=0 is not a subspace of the vector space of all 2x2 matrices.
The set of all 2x2 matrices such that det(A) = 0 is not a subspace of the vector space of all 2x2 matrices.
To determine if a set is a subspace of a vector space, it must satisfy three conditions:
1. The set must contain the zero vector (in this case, the zero matrix).
2. The set must be closed under addition, meaning that if A and B are matrices in the set, then A + B must also be in the set.
3. The set must be closed under scalar multiplication, meaning that if A is a matrix in the set and c is a scalar, then cA must also be in the set.
Let's examine each condition:
1. The zero matrix, denoted by O, has a determinant of det(O) = 0, so it is included in the set. This condition is satisfied.
2. Consider two 2x2 matrices A and B with determinant 0:
[tex]\[ A = \begin{pmatrix} a b \\ c d \end{pmatrix}, \quad \text{det}(A) = ad - bc = 0 \][/tex]
[tex]\[ B = \begin{pmatrix} e f \\ g h \end{pmatrix}, \quad \text{det}(B) = eh - fg = 0 \][/tex]
The sum of A and B is:
[tex]\[ A + B = \begin{pmatrix} a+e b+f \\ c+g d+h \end{pmatrix} \][/tex]
The determinant of A + B is:
[tex]\[ \text{det}(A + B) = (a+e)(d+h) - (b+f)(c+g) \][/tex]
[tex]\[ \text{det}(A + B) = ad + ah + ea + eh - bc - bg - cf - fg \][/tex]
Since det(A) = 0 and det(B) = 0, we have:
[tex]\[ ad - bc = 0 \][/tex]
[tex]\[ eh - fg = 0 \][/tex]
However, this does not imply that det(A + B) = 0. The cross terms ah, ea, bg, and cf may not sum to zero, and thus det(A + B) may not be zero. Therefore, the set is not closed under addition, and this condition is not satisfied.
3. Consider a scalar c and a matrix A with determinant 0:
[tex]\[ cA = c \begin{pmatrix} a b \\ c d \end{pmatrix} = \begin{pmatrix} ca cb \\ cc cd \end{pmatrix} \][/tex]
The determinant of cA is:
[tex]\[ \text{det}(cA) = (ca)(cd) - (cb)(cc) = c^2(ad - bc) \][/tex]
Since det(A) = 0, we have ad - bc = 0, and thus det[tex](cA) = c^2(0) = 0[/tex]for any scalar c. This means that the set is closed under scalar multiplication, and this condition is satisfied.
A three inch diameter pulley on an electric motor that runs at 1800
revolutions per minute is connected by a belt to a six inch
diameter pullley on a saw arbor.
angular speed = central angle/time, arc length = (central
angle)(radius)
a. Find the angular speed (in radians per minute) of each. ( 3 in
and 6 in pully)
b. find the revolutions per minute of the saw.
Answer:
a) 3 inch pulley: 11,309.7 radians/min
6) 6 inch pulley: 5654.7 radians/min
b) 900 RPM (revolutions per minute)
Step-by-step explanation:
Hi!
When a pulley wirh radius R rotantes an angle θ, the arc length travelled by a point on its rim is Rθ. Then the tangential speed V is related to angular speed ω as:
[tex]V=R\omega[/tex]
When you connect two pulleys with a belt, if the belt doesn't slip, each point of the belt has the same speed as each point in the rim of both pulleys: Then, both pulleys have the same tangential speed:
[tex]\omega_1 R_1 = \omega_2 R_2\\[/tex]
[tex]\omega_2 = \omega_1 \frac{R_1}{R_2} =1800RPM* \frac{3}{6}= 900RPM[/tex]
We need to convert RPM to radias per minute. One revolution is 2π radians, then:
[tex]\omega_1 = 1800*2\pi \frac{radians}{min} = 11,309.7\frac{radians}{min}[/tex]
[tex]\omega_2 = 5654.7 \frac{radians}{min}[/tex]
The saw rotates with the same angular speed as the 6 inch pulley: 900RPM
a. The angular speed of the 3 inch pulley is 3600π radians/min and the angular speed of the 6 inch pulley is 7200π radians/min. b. The revolutions per minute of the saw is 900.
Explanation:a. To find the angular speed in radians per minute, we need to convert the revolutions per minute to radians per minute. Since 1 revolution is equal to 2π radians, we can calculate the angular speed of the 3 inch pulley as follows:
Angular speed = (Revolutions per minute) x (2π radians per revolution)
Angular speed = (1800 rev/min) x (2π radians/rev) = 3600π radians/min
Similarly, for the 6 inch pulley:
Angular speed = (Revolutions per minute) x (2π radians per revolution)
Angular speed = (1800 rev/min) x (2π radians/rev) = 7200π radians/min
b. To find the revolutions per minute of the saw, we need to use the ratio of the diameters of the two pulleys. Since the diameter of the 6 inch pulley is twice the diameter of the 3 inch pulley, the revolutions per minute of the saw will be half of the revolutions per minute of the motor. Therefore, the revolutions per minute of the saw is 900.
How do you find the sigma of the x and y values? Do you do it like a partial derivative?
Regression analysis question:
infant 1 2 3 4 5 6 7 8
birth length(in) 19.75 20.5 19 21 19 18.5 20.25 20
6-month length (in) 25.5 26.25 25 26.75 25.75 25.25 27 26.5
a researcher collected data on length of birth and length at 6 months for 8 infants.
Calculate the following values:
∑ x, ∑ x2 , ∑ y, ∑ xy, ∑ y2
Then find SSxx and SSyy
Answer:
Step-by-step explanation:
Sample size of 8 infants were taken and their birth lengths in inches recorded and also 6 months lengths.
If x is length at birth time, and y 6 month length
we have as per table below.
x y x^2 y^2 xy
1 19.75 25.5 390.0625 650.25 503.625
2 20.5 26.25 420.25 689.0625 538.125
3 19 25 361 625 475
4 21 26.75 441 715.5625 561.75
5 19 25.75 361 663.0625 489.25
6 18.5 25.25 342.25 637.5625 467.125
7 20.25 27 410.0625 729 546.75
8 20 26.5 400 702.25 530
Total 158 208 3125.625 5411.75 4111.625
[tex]∑ x, ∑ x2 , ∑ y, ∑ xy, ∑ y2\\158 208 3125.625 5411.75 4111.625[/tex]
SSxx = 3125.625 and SSyy = 5411.75
A farmer looks out into the barnyard and sees the pigs and the chickens. "I count 70 heads and 180 feet, How many pigs and chickens are there?
Answer:
Pigs = 20 and Chickens = 50
Step-by-step explanation:
Let the number of pigs be x
and let the number of chicken be y
Thus, x + y = 70
Since Chicken has 2 legs and pigs has 4 legs.
⇒ 4x + 2y = 180
Solving both equations,
We get, x = 20 and y = 50
Thus number of pigs = 20
and, number of chickens = 50.
Use the variation of parameters method to solve the DR y" + y' - 2y = 1
Answer:
[tex]y(t)\ =\ C_1e^{-2t}+C_2e^t-t\dfrac{e^{-2t}}{3}-\dfrac{1}{3}[/tex]
Step-by-step explanation:
As given in question, we have to find the solution of differential equation
[tex]y"+y'-2y=1[/tex]
by using the variation in parameter method.
From the above equation, the characteristics equation can be given by
[tex]D^2+D-2\ =\ 0[/tex]
[tex]=>D=\ \dfrac{-1+\sqrt{1^2+4\times 2\times 1}}{2\times 1}\ or\ \dfrac{-1-\sqrt{1^2+4\times 2\times 1}}{2\times 1}[/tex]
[tex]=>\ D=\ -2\ or\ 1[/tex]
Since, the roots of characteristics equation are real and distinct, so the complementary function of the differential equation can be by
[tex]y_c(t)\ =\ C_1e^{-2t}+C_2e^t[/tex]
Let's assume that
[tex]y_1(t)=e^{-2t}[/tex] [tex]y_2(t)=e^t[/tex]
[tex]=>\ y'_1(t)=-2e^{-2t}[/tex] [tex]y'_2(t)=e^t[/tex]
and g(t)=1
Now, the Wronskian can be given by
[tex]W=y_1(t).y'_2(t)-y'_1(t).y_2(t)[/tex]
[tex]=e^{-2t}.e^t-e^t(-e^{-2t})[/tex]
[tex]=e^{-t}+2e^{-t}[/tex]
[tex]=3e^{-t}[/tex]
Now, the particular solution can be given by
[tex]y_p(t)\ =\ -y_1(t)\int{\dfrac{y_2(t).g(t)}{W}dt}+y_2(t)\int{\dfrac{y_1(t).g(t)}{W}dt}[/tex]
[tex]=\ -e^{-2t}\int{\dfrac{e^t.1}{3.e^{-t}}dt}+e^{t}\int{\dfrac{e^{-2t}.1}{3.e^{-t}}dt}[/tex]
[tex]=\ -e^{-2t}\int{\dfrac{1}{3}dt}+\dfrac{e^t}{3}\int{e^{-t}dt}[/tex]
[tex]=\dfrac{-e^{-2t}}{3}.t-\dfrac{1}{3}[/tex]
[tex]=-t\dfrac{e^{-2t}}{3}-\dfrac{1}{3}[/tex]
Now, the complete solution of the given differential equation can be given by
[tex]y(t)\ =\ y_c(t)+y_p(t)[/tex]
[tex]=C_1e^{-2t}+C_2e^t-t\dfrac{e^{-2t}}{3}-\dfrac{1}{3}[/tex]
The pictures are in order of the the questions asked.
1. Answer both parts:
2. Fill in the blank:
3. Arnie wrote:
If all three are answered in the most CLEAR way, brainliest will be handed out.
Answer:
The answers are given below:
Step-by-step explanation:
1. a. (─13)³⁵
1. b. The product will be negative. The expanded form shows 34 negative factors plus one more negative factor. Any even number of negative factor yields a positive product. The remaining 35th negative factor negates the resulting product.
2. 4 times.
3. Arnie is not correct. The base, ─3.1, should be in parentheses to prevent ambiguity. At present the notation is not correct.
You've deposited $5,000 into a Michigan Education Savings Program (a 529 college savings program) for your daughter who will be attending college in 15 years. In order for it to grow to $24,000 by the time she goes to college, what annual rate of return would you have to earn?
N= I/Y= PV= PMT= FV= P/Y=
Answer:
Ans. the annual rate of return, in order to turn $5,000 into $24,000 in 15 years is 11.02% annual.
Step-by-step explanation:
Hi, well, in order to find the value of the interest rate of return, we need to solve for "r" the following equation,
[tex]Future Value=PresentValue(1+r)^{n}[/tex]
Where:
n= years (time that the money was invested)
r=annual rate of return (Decimal)
So, let´s see the math of this.
[tex]24,000=5,000(1+r)^{15}[/tex]
[tex]\frac{24,000}{5,000} =(1+r)^{15}[/tex]
[tex]\sqrt[15]{\frac{24,000}{5,000} } =1+r[/tex]
[tex]\sqrt[15]{\frac{24,000}{5,000} } -1=r[/tex]
[tex]r=0.11023[/tex]
So the annual rate of return that turns $5,000 into $24,000 in 15 years is 11.02%.
N=15; PV=5,000; FV=24,000; PMT=N.A; I/Y=11.02% P/Y=N.A
Best of Luck.
Suppose that the functions g and h are defined for all real numbers r as follows. gx) -4x +5 h (x) = 6x write the expressions for (g-h)(x) and (g+h)(x) and evaluate (g-h)(3). 2 o e m,曲 pe here to search
Answer: Our required values would be -10x+5, 2x+5 and -25.
Step-by-step explanation:
Since we have given that
g(x) = -4x+5
and
h(x) = 6x
We need to find (g-h)(x) and (g+h)(x).
So, (g-h)(x) is given by
[tex]g(x)-h(x)\\\\=-4x+5-6x\\\\=-10x+5[/tex]
and (g+h)(x) is given by
[tex]g(x)+h(x)\\\\=-4x+5+6x\\\\=2x+5[/tex]
and (g-h)(3) is given by
[tex]-10(3)+5\\\\=-30+5\\\\=-25[/tex]
Hence, our required values would be -10x+5, 2x+5 and -25.
Let f be a differentiable function on (-0o,00) such that f(-x)= f(x) for all x in (, o). Compute the value of f'(0). Justify your answer
Answer:
[tex]f'(0)=0[/tex]
Step-by-step explanation:
Applying the chain rule
[tex]\frac{d}{dx} (f(-x))=-\frac{df}{dx}[/tex]
Then it becomes
[tex]\frac{df}{dx} =-\frac{df}{dx}[/tex]
In x=0
[tex]\frac{d[tex]f'(0)=-f'(0)\\f'(0)+f'(0)=0\\2f'(0)=0\\[/tex]f}{dx} =-\frac{df}{dx}[/tex]
Then
[tex]f'(0)=0[/tex]
Adhesive tape made from fabric has a tensile strength of not less than 20.41 kg/2.54 cm of width. Reduce these quantities to grams and millimeters.
Answer:
[tex]\frac{20,410 \text{ grams}}{254\text{ mm}}[/tex]
Step-by-step explanation:
We have been given that adhesive tape made from fabric has a tensile strength of not less than 20.41 kg/2.54 cm of width. We are asked to reduce these quantities to grams and millimeters.
We know 1 kg equals 1000 grams and 1 cm equals 10 mm.
[tex]\frac{20.41\text{ kg}}{\text{2.54 cm}}[/tex]
[tex]\frac{20.41\text{ kg}}{\text{2.54 cm}}\times \frac{\text{1 cm}}{\text{10 mm}}[/tex]
[tex]\frac{20.41\text{ kg}}{2.54\times\text{10 mm}}[/tex]
[tex]\frac{20.41\text{ kg}}{254\text{ mm}}[/tex]
[tex]\frac{20.41\text{ kg}}{254\text{ mm}}\times \frac{\text{1000 grams}}{\text{1 kg}}[/tex]
[tex]\frac{20.41\times \text{1000 grams}}{254\text{ mm}}[/tex]
[tex]\frac{20,410 \text{ grams}}{254\text{ mm}}[/tex]
Therefore, our required measurement would be [tex]\frac{20,410 \text{ grams}}{254\text{ mm}}[/tex].
determine if the two functions f and g are inverses of each other algebraically. If not, why?
f(x)=2x+3/4x-3 ; g(x) = 3x+3/4x-2
a:
no, (f o g)(x)= x+2/3
yes
no, (f o g)(x)=3x
f(x) = -x^3+2 ; g(x) = 3(cubedroot)x-2/2
a:
no, (f o g)(x)= x-14/8
yes
no, (fog)(x)=3-x/2
f(x)=-2x+4/2-5x ; g(x) = 4-2x/5-2x
a:
no, (f o g)(x)= -2x+6/3x-5
no, (f o g)(x)= -6x+6/3x-5
yes.
(the number say ex. g(x) = 4-2x / the "/" is a fraction unit. first unit over the other as provided. any help appreciated thank you <3)
Answer:
1) yes
2) no, (fog)(x)=3-x/2
3) no, (f o g)(x)= -2x+6/3x-5
The first and second pair of functions are not inverses of each other, while the third pair of functions are inverses.
Explanation:The first pair of functions, f(x) = 2x + 3/(4x - 3) and g(x) = 3x + 3/(4x - 2), are not inverses of each other. To determine this algebraically, we need to calculate (f o g)(x) and (g o f)(x) and check if they equal to x. In this case, (f o g)(x) is x + 2/3, which is not equal to x, therefore f and g are not inverses of each other.
The second pair of functions, f(x) = -x^3 + 2 and g(x) = 3(cubedroot)x - 2/(2), are also not inverses. By calculating (f o g)(x) and (g o f)(x), we found that (f o g)(x) = x - 14/8, which is not equal to x.
The third pair of functions, f(x) = -2x + 4/(2 - 5x) and g(x) = (4 - 2x)/(5 - 2x), is indeed inverses of each other. By calculating (f o g)(x) and (g o f)(x), we found that (f o g)(x) = x and (g o f)(x) = x, which means f and g are inverses of each other.
Learn more about Inverse functions here:https://brainly.com/question/35509335
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