Step-by-step explanation:
Consider the provided information.
For the condition statement [tex]p \rightarrow q[/tex] or equivalent "If p then q"
The rule for Contrapositive is: Negative both statements and interchange them. [tex]\sim q \rightarrow \sim p[/tex]
Part (A) If you are taller than 6 ft, then it is unpleasant for you to travel in economy class.
Here p is "you are taller than 6 ft, and q is "it is unpleasant for you to travel in economy class".
It is given that Your contrapositive must not contain explicit references to negation. Assume that the negation of "unpleasant" is "pleasant".
Contrapositive: If it is pleasant for you to travel in economy class then you are not taller than 6 ft then.
Part (B) "If x ≥ 0 and y ≥ 0 then xy ≥ 0" where x, y are real numbers.
Here p is "xy≥ 0, and q is "x ≥ 0 and y ≥ 0"
The negative of xy≥ 0 is xy<0, x ≥ 0 is x<0 and y ≥ 0 is y<0.
Remember negative means opposite.
Contrapositive: If xy < 0 then x<0 and y<0.
Final answer:
The contrapositive of a statement involves switching the positions of the subject and the complement, and negating both.
Explanation:
To rephrase the given statement in contrapositive form, we need to switch the positions of the subject and the complement, and negate both.
(a) The contrapositive of the statement 'If you are taller than 6 ft, then it is unpleasant for you to travel in economy class' is:
'If it is pleasant for you to travel in economy class, then you are not taller than 6 ft.'
(b) The contrapositive of the statement 'If x ≥ 0 and y ≥ 0 then xy ≥ 0' is:
'If xy < 0, then at least one of x or y is less than 0.'
Find the equation of the line that pass through the points (4,8) and (6,2
Answer:
3x + y = 20
Step-by-step explanation:
The equation of line passing through two points is determined by formula:
[tex]y-y_{1}=\frac{y_{2}-y_{1}}{x_{2} - x_{1}}(x - x_{1})[/tex]
Here, (x₁ , y₁) = (4, 8)
and (x₂, y₂) = (6, 2)
Putting these value in above formula. We get,
[tex]y-8=\frac{2-8}{6 - 4}(x - 4)[/tex]
⇒ [tex]y-8=\frac{-6}{2}(x - 4)[/tex]
⇒ ( y - 8) = -3 (x - 4)
⇒ y - 8 = -3x + 12
⇒ 3x + y = 20
which is required equation.
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]
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.
More can be learned about an hypothesis test at https://brainly.com/question/13873630
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}.
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]
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 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.
Harper has $15to spend at the grocery store.She is going to buy bags of fruit that cost $4.75 each and one box of crackers that costs$3.50.Write and solve an inequality that models this situation and could be used to determine the maximum number of bags of fruit Harper can buy
Answer:
The maximum number of fruits bag Harper can buy are 3.
Step-by-step explanation:
Let there be x bags of fruits.
Let there be y boxes of chocolates
Cost of 1 bag of fruit = $4.75
So, cost of x bags = $4.75x
Cost of one box of crackers costs = $3.50
As per the given situation, the inequality forms:
[tex]4.75x+3.50y\leq 15[/tex]
So, the maximum number of bags of fruit Harper can buy, is when she buys no box of cracker.
So, putting y = 0 in above inequality , we have,
[tex]4.75x+3.50(0)\leq 15[/tex]
=> [tex]4.75x+0\leq 15[/tex]
=> [tex]4.75x \leq 15[/tex]
[tex]x\leq 3.15[/tex] rounding to 3.
Hence, the maximum number of fruits bag Harper can buy are 3.
use the binomial theorem to expand the expression :
(3x + y)^5 and simplify.
(b) find the middle term in the expansion of
(1/x+√x)^4 and simplify your unswer.
(c) determine the coefficient of x^11 in the expansion of (x^2 +1/x)^10, simplify your answer.
Answer:
a) [tex](3x+y)^5=243x^5+405x^4y+270x^3y^2+90x^2y^3+15xy^4+y^5[/tex].
b) The middle term in the expansion is [tex]\frac{6}{x}[/tex].
c) The coefficient of [tex]x^{11}[/tex] is 120.
Step-by-step explanation:
Remember that the binomial theorem say that [tex](x+y)^n=\sum_{k=0}^{n} \binom{n}{k}x^{n-k}y^{k}[/tex]
a) [tex](3x+y)^5=\sum_{k=0}^5\binom{5}{k}3^{n-k}x^{n-k}y^k[/tex]
Expanding we have that
[tex]\binom{5}{0}3^5x^5+\binom{5}{1}3^4x^4y+\binom{5}{2}3^3x^3y^2+\binom{5}{3}3^2x^2y^3+\binom{5}{4}3xy^4+\binom{5}{5}y^5[/tex]
symplifying,
[tex](3x+y)^5=243x^5+405x^4y+270x^3y^2+90x^2y^3+15xy^4+y^5[/tex].
b) The middle term in the expansion of [tex](\frac{1}{x} +\sqrt{x})^4=\sum_{k=0}^{4}\binom{4}{k}\frac{1}{x^{4-k}}x^{\frac{k}{2}}[/tex] correspond to k=2. Then [tex]\binom{4}{2}\frac{1}{x^2}x^{\frac{2}{2}}=\frac{6}{x}[/tex].
c) [tex](x^2+\frac{1}{x})^{10}=\sum_{k=0}^{10}\binom{10}{k}x^{2(10-k)}\frac{1}{x^k}=\sum_{k=0}^{10}\binom{10}{k}x^{20-2k}\frac{1}{x^k}=\sum_{k=0}^{10}\binom{10}{k}x^{20-3k}[/tex]
Since we need that 11=20-3k, then k=3.
Then the coefficient of [tex]x^{11}[/tex] is [tex]\binom{10}{3}=120[/tex]
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.
R1 R3 in an electric instrument called a Wheatstone bridge electric resistances are related byR1/R2=R3/R4. Find R 2 if R1 = 10.00 Ω R3-6470, and R2 = R4-15.0 . If necessary, round to two decimal places.
Answer:
R2 = 43.03 ohms
Step-by-step explanation:
If R2=R4-15, then R4 = R2+15
According to the Wheastone bridge equation we have:
[tex]\frac{R1}{R2} =\frac{R3}{R4}\\\frac{10}{R2} =\frac{6470}{R2+15}\\\\10*(R2+15) = 6470*R2\\10*R2+150 = 6470*R2\\150=(6470-15)*R2\\R2=\frac{6455}{150}= 43.03333[/tex]
Solve the following problems manually or using the MS Excel
Mohamed has enough wood to make 24 small chairs or 6 large tables. In other words, the large tables require 4 times the amount of wood as the small chairs. He only has enough of a special glazing compound to glaze 16 of the small chairs or 8 of the large tables. Let X1 the number of small chairs and X2 the number of large tables. The smaller chairs sell for $3 each, while the larger tables would bring $9 each.
(a) Formulate the Problem.
(b) Solve the Linear Programming Problem.
(c) Solve also graphically
Answer:
(a) in the step-by-step explanation
(b) The optimal solution is 8 chairs and 4 tables.
(c) Graph attached
Step-by-step explanation:
(a)
C: number of small chairs
T: number of large tables
Maximize Income = 9T + 3C
Restrictions:
Wood: 4T+C<=24
Glazing: 2T+C<=16
In the graph its painted in green the "feasible region" where lies every solutions that fit the restrictions.
One of the three points marked in the graph is the optimal solution.
Point 1 (C= 16, T= 0)
Income = 9*0+3*16=$ 48
Point 2 (C=8, T=4)
Income = 9*4+3*8 = $ 60
Point 3 (C=0, T=6)
Income = 9*6+3*0 = $ 54
The optimal solution is 8 chairs and 4 tables.
Calculate: ( Round two decimal places for final answer)
1880 Milliliters(mL)=___pints(pts)
Answer:
1880 Milliliters(mL) = 3.97 pints
Step-by-step explanation:
This can be solved as a rule of three problem.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.
Unit conversion problems, like this one, is an example of a direct relationship between measures.
Each ml has 0.002 pints. How many pints are there in 1880mL. So:
1ml - 0.002 pints
1880ml - x pints
[tex]x = 1800*0.002[/tex]
[tex]x = 3.97[/tex] pints
1880 Milliliters(mL) = 3.97 pints
Indicate which of the following are propositions (assume that x and y are real numbers).
a) The integer 36 is even.
b) Is the integer 315 − 8 even?
c) The product of 3 and 4 is 11.
d) The sum of x and y is 12.
e) If x > 2, then x 2 > 3.
f) 52 − 5 + 3
Answer:
a) It is a proposition .
b) It is not a proposition.
c) It is a proposition.
d) It is a proposition.
e) It is a proposition.
f) It is not a proposition.
Step-by-step explanation:
a) The integer 36 is even: It is a proposition, since this statement can be assigned a true value. If 36 is an even number, the statement is true, but if 36 is an odd number, the statement is false.
b) Is the integer 315 - 8 even ?: It is not a proposition, since this question cannot be assigned a true value.
c) The product of 3 and 4 is 11: It is a proposition, since this statement can be assigned a true value. If 3x4 = 11, the statement is true, but if 3x4 is not 11, the statement is false.
d) The sum of x and y is 12: It is a proposition, since, this statement can be assigned a true value. If x + y = 12, the statement is true, but if x + y is not 12, the statement is false.
e) If x> 2, then x 2> 3: It is a proposition, since, this statement can be assigned a truth value.
f) 52 - 5 + 3: It is not a proposition, since this statement cannot be assigned a true value.
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.
Solve the linear equation: 3.4 + 2(9.7 – 4.8x) = 61.2 What are the possible steps involved in solving this equation? Check all that apply. Add 3.4 and 2. Distribute 2 to 9.7 and −4.8x. Combine 3.4 and 19.4. Divide both sides by 22.8. Subtract 22.8 from both sides. Divide both sides by −9.6.
Answer:
Distribute 2 to 9.7 and −4.8x. Combine 3.4 and 19.4. Subtract 22.8 from both sides. Divide both sides by −9.6Step-by-step explanation:
Here is the recommended solution method:
3.4 + 2(9.7 – 4.8x) = 61.2 . . . . . given
3.4 + 19.4 - 9.6x = 61.2 . . . . . . . distribute 2 to 9.7 and -4.8x
22.8 - 9.6x = 61.2 . . . . . . . . . . . . combine 3.4 and 19.4
-9.6x = 38.4 . . . . . . . . . . . . . . . . . subtract 22.8 from both sides
x = -4 . . . . . . . . . . . . . . . . . . . . . . divide both sides by -9.6
_____
Alternate solution method using different steps
You can also "undo" what is done to the variable, in reverse order. The variable has these operations performed on it:
multiply by -4.8add 9.7multiply that sum by 2add 3.4 to the productSo, another possible solution method is this:
3.4 + 2(9.7 – 4.8x) = 61.2 . . . . . given
2(9.7 -4.8x) = 57.8 . . . . . . . . . . . add the opposite of 3.4 (undo add 3.4)
9.7 -4.8x = 28.9 . . . . . . . . . . . . . divide by 2 (undo multiply by 2)
-4.8x = 19.2 . . . . . . . . . . . . . . . . . add the opposite of 9.7 (undo add 9.7)
x = -4 . . . . . . . . . . . . . . . . . . . . . . divide by -4.8 (undo multiply by -4.8)
Linear equation solutions are indeed the points where the lines or planes describing various linear equations intersect or connect. The candidate solution of a set of linear equations is indeed the collection of all feasible solution' values again for variables, and further calculation can be defined as follows:
Given:
[tex]\to \bold{3.4 + 2(9.7 -4.8x) = 61.2}\\\\[/tex]
To find:
Solve the linear equation=?
Solution:
[tex]\to \bold{3.4 + 2(9.7 -4.8x) = 61.2}\\\\\to \bold{3.4 + 19.4 -9.6x = 61.2}\\\\\to \bold{22.8 -9.6x = 61.2}\\\\\to \bold{ -9.6x = 61.2- 22.8}\\\\\to \bold{ -9.6x = 38.4}\\\\\to \bold{ x =- \frac{38.4}{9.6}}\\\\\to \bold{ x =- 4}\\\\[/tex]
Therefore, the steps are:
Distribute 2 to [tex]\bold{9.7\ and\ -4.8x}[/tex].
Combine [tex]\bold{3.4\ and \ 19.4}[/tex].
Subtract [tex]22.8[/tex] from both sides.
Divide both sides by[tex]-9.6[/tex].
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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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A recent study found a correlation between gum disease and heart disease. This result indicates that gum disease causes people to develop heart disease.
True or False?
Answer:
False
Step-by-step explanation:
Correlation measures the strength of the relation between two variables.
Further, Correlation is said to be positive if increasing/decreasing the one variable, also increases/decreases the values of another variable.
Correlation is said to be negative if increasing/decreasing the one variable, also decreases/increases the values of another variable.
Since we don't know here exists a positive correlation or negative correlation.
So here are two possible conditions:
The person who has Gum disease also has heart disease.
And, the person has Gum disease can never have heart disease.
Thus, the given statement is false.
The statement is false because a correlation found in a study does not necessarily mean one factor (gum disease) is the cause of the other (heart disease). The cause and effect relationship must be established through further studies.
Explanation:The statement 'A recent study found a correlation between gum disease and heart disease. This result indicates that gum disease causes people to develop heart disease.' is False. A correlation implies a relationship between two elements, but it does not indicate a cause and effect relationship.
This means although the study shows a link or association between gum disease and heart disease, it does not mean gum disease causes heart disease. It could be that people with poor gum health also tend to have poor overall health including heart health. Alternatively, there could be a third underlying factor that leads to both conditions. Therefore, the cause and effect relationship must be established through further studies.
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Compute the exact interest on $5,870 at 12% if the money is borrowed from June to December of the same year.
Answer:
The exact interest on $5,870 at 12% is $58.70.
Step-by-step explanation:
Given information:
Principal = $5870
Interest rate = 12% = 0.12
Time = June-December = 7 months.
We know that
1 year = 12 months
1/12 year = 1 month
7/12 year = 7 month
Time = 7/12 year
Formula for simple interest:
[tex]I=P\times r\times t[/tex]
where, P is principal, r is rate of interest and t is time in years.
Substitute P=5870, r=0.12 and t=7/12 in the above formula.
[tex]I=5870\times 0.12\times \frac{1}{12}[/tex]
[tex]I=5870\times 0.01[/tex]
[tex]I=58.70[/tex]
Therefore the exact interest on $5,870 at 12% is $58.70.
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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Show that n+1C = nCr-1 + nr.
Answer: The proof is given below.
Step-by-step explanation: We are given to show that the following equality is true :
[tex]^{n+1}C_r=^nC_{r-1}+^nC_r.[/tex]
We know that
the number of combinations of n different things taken r at a time is given by
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}.[/tex]
Therefore, we have
[tex]R.H.S.\\\\=^nC_{r-1}+^nC_r\\\\\\=\dfrac{n!}{(r-1)!(n-(r-1))!}+\dfrac{n!}{(r)!(n-r)!}\\\\\\=\dfrac{n!}{(r-1)!(n-r+1)!}+\dfrac{n!}{(r)!(n-r)!}\\\\\\=\dfrac{n!}{(r-1)!(n-r+1)(n-r)!}+\dfrac{n!}{r(r-1)!(n-r)!}\\\\\\=\dfrac{n!}{(r-1)!(n-r)!}\left(\dfrac{1}{n-r+1}+\dfrac{1}{r}\right)\\\\\\=\dfrac{n!}{(r-1)!(n-r)!}\left(\dfrac{r+n-r+1}{(n-r+1)r}\right)\\\\\\=\dfrac{n!}{(r-1)!(n-r)!}\times\dfrac{n+1}{(n-r+1)r}\\\\\\=\dfrac{(n+1)!}{r!(n-r+1)!}\\\\\\=\dfrac{(n+1)!}{r!((n+1)-r)!}\\\\\\=^{n+1}C_r\\\\=L.H.S.[/tex]
Thus, [tex]^{n+1}C_r=^nC_{r-1}+^nC_r.[/tex]
Hence proved.
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.
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.
Approximately 0.02% of a 100-mg dose of the drug miglitol (Glyset) has been shown to appear in human breast milk. Calculate the quantity of drug detected, in milligrams, following a single dose.
Approximately 0.02 mg of the drug miglitol (Glyset) would be detected in human breast milk.
Given that, approximately 0.02% of a 100-mg dose appears in human breast milk.
To calculate the quantity of drug detected in milligrams following a single dose, we can use the given information that approximately 0.02% of a 100-mg dose appears in human breast milk.
Step-by-step calculation:
1. Convert 0.02% to a decimal by dividing it by 100: 0.02/100 = 0.0002.
2. Multiply the decimal by the dose of the drug: 0.0002 * 100 mg = 0.02 mg.
Therefore, following a single dose, approximately 0.02 mg of the drug miglitol (Glyset) would be detected in human breast milk.
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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]
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.
A business magazine conducted a survey of 751 employees who had been at their current employer for 5 or more years. Of these employees, 295 responded that they were bored in their current position. Create a 99% confidence interval for the proportion of employees who have been with their current employer for 5 or more years and reported being bored in their current position. Use Excel to create the confidence interval, rounding to four decimal places.
Answer:
the [tex]95\%[/tex] confidence interval for the population proportion is:
[tex]\left [0.3469, \hspace{0.1cm} 0.4387\right][/tex]
Step-by-step explanation:
To solve this problem, a confidence interval of [tex](1-\alpha) \times 100\%[/tex] for the population proportion will be calculated.
[tex]$$Sample proportion: $\bar P=0.3928$\\Sample size $n=751$\\Confidence level $(1-\alpha)\times100\%=99\%$\\$\alpha: \alpha=0.01$\\Z values (for a 99\% confidence) $Z_{\alpha/2}=Z_{0.005}=2.5758$\\\\Then, the (1-\alpha) \times 100\%$ confidence interval for the population proportion is given by:\\\\\left [\bar P - Z_{\frac{\alpha}{2}}\sqrt{\frac{\bar P(1- \bar P)}{n}}, \hspace{0.3cm}\bar P + Z_{\frac{\alpha}{2}}\sqrt\frac{\bar P(1- \bar P)}{n} \right ][/tex]
Thus, the [tex]95\%[/tex] confidence interval for the population proportion is:
[tex]\left [0.3928 - 2.5758\sqrt{\frac{0.3928(1-0.3928)}{751}}, \hspace{0.1cm}0.3928 + 2.5758\sqrt{\frac{0.3928(1-0.3928)}{751}} \right ]=\left [0.3469, \hspace{0.1cm} 0.4387\right][/tex]
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.
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.
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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