Answer:
B. the 1101 people interviewed.
Step-by-step explanation:
An opinion poll contacts 1101 adults and asks them, " Which political party do you think has better ideas for leading the country in the 21st century?"
The sample in this setting is the 1101 people interviewed.
Here sample space is 1101.
Answer:
B. the 1101 people interviewed.
Step-by-step explanation:
The sample is the subset of the population and it takes for making the experiment easy. Further, the sample is said to be best if it is the representation of the whole population.
Here, since opinion poll contacts all 1101 adults for knowing their opinion about political parties.
Hence the sample space is all 1101 people interviewed.
A buoy floating in the ocean is bobbing in simple harmonic motion with period 7 seconds and amplitude 6ft. Its displacement d from sea level at time t=0 seconds is -6ft, and initially it moves upward. (Note that upward is the positive direction.)
Give the equation modeling the displacement d as a function of time t.
Answer:
d = 6 sin(2π/7 t + 3π/2)
Step-by-step explanation:
Equation for simple harmonic motion is:
d = A sin(2π/T t + B) + C
where A is the amplitude,
T is the period,
B is the horizontal shift (phase shift),
and C is the vertical shift.
Given that A = 6, T = 7, and C = 0:
d = 6 sin(2π/7 t + B)
At t = 0, the buoy is at d = -6:
-6 = 6 sin(2π/7 (0) + B)
-1 = sin(B)
3π/2 = B
d = 6 sin(2π/7 t + 3π/2)
Notice you can also use cosine instead of sine and get a different phase shift.
d = 6 cos(2π/7 t + π)
You can even use phase shift properties to simplify:
d = -6 cos(2π/7 t)
Any of these answers are correct.
The equation modeling the displacement d of the buoy as a function of time is d(t) = 6 * sin(2π/7 * t) - 6.
Explanation:To model the displacement d of the buoy as a function of time t, we can use the equation:
d(t) = A * sin(2π/T * t) + C
where A is the amplitude, T is the period, t is the time, and C is the vertical displacement at t = 0 seconds.
In this case, the amplitude A is 6ft, the period T is 7 seconds, and the vertical displacement at t = 0 seconds C is -6ft and the buoy initially moves upward. Therefore, the equation modeling the displacement as a function of time is:
d(t) = 6 * sin(2π/7 * t) - 6
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Enter the expression 2cos2(θ)−1 , where θ is the lowercase Greek letter theta. 2cos2(θ)−1 2 c o s 2 ( θ ) − 1 = nothing
The expression [tex]\(2\cos^2(\theta) - 1\)[/tex] where θ is the lowercase Greek letter theta gives [tex]cos(\theta) = \pm 1/ \sqrt (2)[/tex].
The expression is [tex]\(2\cos^2(\theta) - 1\)[/tex].
Explanation:
1. 2: This is a coefficient that scales the result of the trigonometric function [tex]\(\cos^2(\theta)\)[/tex]. It simply doubles the value of the cosine squared term.
2. [tex]\(\cos^2(\theta)\)[/tex]: This is the square of the cosine of the angle [tex]\(\theta\)[/tex].
The cosine function cos takes an angle as input and returns the ratio of the adjacent side to the hypotenuse in a right triangle with that angle.
3. -1: This is a constant that is subtracted from the result of [tex]\(2\cos^2(\theta)\)[/tex]. Subtracting 1 shifts the trigonometric value downward by one unit on the y-axis.
Add 1 to both sides
[tex]2cos^2(\theta) =1[/tex]
Divide by 2 on both sides
[tex]cos^2(\theta) =1/2[/tex]
Take the square root of both sides
[tex]cos(\theta) = \pm 1/ \sqrt (2)[/tex]
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The expression in question pertains to the conservation of momentum in physics, where trigonometric identities can simplify the calculation of particle velocities and directions after a collision. The included equations and concepts such as the conservation of momentum along an axis and the Pythagorean Theorem are essential components for solving problems in high school physics.
Explanation:The expression 2cos2(θ)−1, where θ is the lowercase Greek letter theta, can be related to conservation of momentum in physics problems, particularly when analyzing collisions in two dimensions. Using trigonometric identities, such as tan θ = sin θ / cos θ, can be a useful technique in simplifying expressions and solving for unknown variables in mechanical physics.
In the context of conservation of momentum, equations may involve cosines and sines of angles representing the directions of particle velocities before and after a collision. For instance, if the scenario requires that the momentum along the x-axis be conserved, substituting sin θ / tan θ for cos θ could lead to simplifications where terms cancel out. A condition such as μ v2 cos(θ1−θ2)= 0 might imply that either the coefficient of friction μ is zero or the velocity component along the x-axis is zero, hence no momentum is transferred in that direction.
It is important to note that inverting mathematical functions is a common approach to solving equations in physics. Like in trigonometry, it may be necessary to 'undo' a function to isolate a variable, as shown in the example involving the Pythagorean Theorem to solve for side length of a triangle.
Successful implementation of a new system is based on three independent modules. Module 1 works properly with probability 0.9, Module 2 works properly with probability 0.84, and Module 3 works properly with probability 0.65. What is the probability that at least one of these three modules will fail to work properly?
Answer:
The probability is 0.5086
Step-by-step explanation:
The probability P that at least one of these three modules will fail to work properly is calculated as:
P = 1 - P'
Where P' is the probability that all the modules works properly. So, P' os calculated as:
P' = 0.9 * 0.84 * 0.65
P' = 0.4914
Because 0.9 is the probability that module 1 works properly, 0.84 is the probability that module 2 works properly and 0.65 is the probability that module 3 works properly.
Finally, the probability P that at least one of these three modules will fail to work properly is:
P = 1 - 0.4914
P = 0.5086
The rules of the game are as following: a player draws one card from a standard 52-card deck. If the player picks a heart, they win $10. If they pick a face card that is not a heart, the player wins $8. Picking a face card heart counts the same as picking a heart. If a player picks another card, they lose $6. Is this gambling game a good way to make money for someone or not?
Let's suppose "good" here means that the amount a player can expect to win is positive.
The probability of drawing a heart from the deck is 13/52 = 1/4.
The probability of drawing a face card that is not a heart is 9/52.
The probability of drawing anything else is 30/52 = 15/26.
The expected winnings are then 10(1/4) + 8(9/52) - 6(15/26) = 11/26, meaning on average the player can expect to win about $0.42 per game, so by our definition this game is a "good" way to make money.
Statistically speaking, a player would gain 42 cents per game in the long run, making this gambling game potentially profitable.
This is determined by computing expected value, which takes into account the gains or losses for each possible outcome and the probability of each outcome.
Explanation:The subject of this question is probability with reference to a game of cards. To evaluate whether or not the game is a good idea, we need to determine the expected value of the game, which is calculated by multiplying the value of each outcome by their probability and then summing these products. Here's how finances from the game might play out statistically:
There are 13 hearts in the deck (which includes 3 face cards), so the probability of drawing a heart is 13/52 = 0.25, or 25%. When a player draws a heart, they gain $10.There are 12 face cards in the deck overall, and 3 of those are hearts and are already accounted for. So, only 9 face cards count for this category. The probability of drawing a face card that is not a heart is then 9/52 = 0.173 (17.3%). In this case, the player would win $8.There are 52 - 13 - 9 = 30 other cards. The chance of drawing one of these is 30/52 = 0.577 (57.7%). Drawing one of these cards means the player loses $6.The expected value of one round of the game is thus (0.25 x $10) + (0.173 x $8) + (0.577 x -$6) = $2.5 + $1.38 - $3.46 = $0.42. Therefore, statistically speaking, a player would gain 42 cents per game in the long run, making this gambling game potentially profitable.
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What is the relationship between rational numbers and Integers?
Rational Numbers are a subset of Integers because all Rational Numbers are Integers.
There is some overlap between Rational Numbers and Integers, but there are numbers that are just Rational and numbers that are just Integers but not both.
There is no relationship as there are no overlapping numbers.
Integers are a subset of Rational Numbers because all Integers are Rational Numbers.
Answer:
Integers are a subset of Rational Numbers because all Integers are Rational Numbers.
Step-by-step explanation:
A rational number such as 4/2 is also an integer: 2. A rational number such as 4/3 is not an integer. Hence, integers are a subset of rational numbers.
Answer:
Integers are a subset of Rational Numbers because all Integers are Rational Numbers.
Step-by-step explanation:
3 is integer but it can be written as [tex]\frac{3}{1} \ or \ \frac{6}{2},.. etc.[/tex] which is rational form. Hence every integer can be express as Rational Number.
Thus the last option is correct.
Further, Integers can be defined as the whole numbers including zero and positive whole numbers. i.e. ......,-3, -2, -1, 0, 1, 2, 3,.....
Example: -546, 87855889, 0, etc.
Rational Number is the number in the form [tex]\frac{p}{q}[/tex], where q≠0.
Example: [tex]\frac{2}{9}, \frac{-1}{267}, \frac{875}{2}, 3, etc.[/tex]
250 ml of a liquid medication contains 125 mg of Drug Z. If the patient gets an injection of 50 ml of this medication, how much drug Z is in that injection
Final answer:
To find the amount of Drug Z in the 50 ml injection, set up a proportion based on the known concentration (125 mg in 250 ml). Solving for the unknown quantity gives 25 mg of Drug Z in the injection.
Explanation:
To determine how much of Drug Z is in a 50 ml injection when 250 ml of the medication contains 125 mg of Drug Z, you can use a proportion. The proportion can be set up as follows:
(125 mg of Drug Z) / (250 ml of medication) = (X mg of Drug Z) / (50 ml of medication)
To solve for X, which represents the amount of Drug Z in the 50 ml injection, you cross-multiply and divide:
(125 mg) × (50 ml) = (250 ml) × (X mg)
6250 mg·ml = 250 ml·X mg
Divide both sides by 250 ml to isolate X:
X = (6250 mg·ml) / (250 ml)
X = 25 mg of Drug Z
Therefore, the 50 ml injection contains 25 mg of Drug Z.
A researcher was interested in utilities provided by city governments. The researcher randomly selected 20 counties from a list of all counties in the U.S. From each of these counties the researcher then contacted each city government (a total of 192) and found that 12 (6.25%) of them provided electricity to their residents. In this situation the sampling frame is
Answer:
Sample frame is the list of all counties in the U.S
Step-by-step explanation:
A sample frame refers to the set that lists all the individuals that could eventually be part of the selected random sample and, in fact, is used to make the selection of the sample units.
Taking into account the definition commented in the previous paragraph, in the situation described, the sample frame is the list of all counties in the U.S
A physician prescribed mometasone furoate monohydrate (NASONEX) nasal spray for a patient, with directions to
administer two sprays into each nostril once daily. If each spray contains 50 μg of drug and the container can deliver a
total of 120 sprays, how many micrograms of drug would the patient receive daily, and how many days of use will the
prescription last the patient?
Answer: The patient receives [tex]200\ \mu g[/tex] daily.
The prescription will last 30 days .
Step-by-step explanation:
Given : Prescription= Two sprays into each nostril once daily.
That means total sprays for both nostrils = [tex]2\times2=4[/tex] [∵ 1 nostrils in each nose.]
If each spray contains [tex]50 \mu g[/tex] of drug, then the amount of drug received by patient daily :-
[tex]4\times50=200\ \mu g[/tex]
Thus , the patient receives [tex]200\ \mu g[/tex] daily.
Also, the container can deliver a total of 120 sprays.
Then, the number of days of use will the prescription last the patient will be:_
[tex]\dfrac{120}{4}=30[/tex]
Hence, the prescription will last 30 days of use .
Final answer:
The patient will receive 200 micrograms of mometasone furoate monohydrate daily, and the prescription will last for 30 days.
Explanation:
The question involves calculating the total dosage of mometasone furoate monohydrate received daily by a patient and determining how many days the prescription will last, based on the dose and the number of sprays available.
To find the daily dose, we can multiply the number of sprays per nostril by the dosage per spray and the number of nostrils:
2 sprays/nostril × 50 μg/spray × 2 nostrils = 200 μg/day
The patient receives 200 micrograms daily.
To find out how many days the prescription will last:
120 sprays/container ÷ (2 sprays/nostril × 2 nostrils) = 120 sprays/container ÷ 4 sprays/day = 30 days
The prescription will last the patient for 30 days.
From a box containing 10 cards numbered 1 to 10, four cards are drawn together. The probability that their sum is even is 21 21 21 21
Answer:
Step-by-step explanation:
We know that between 1 to 10 there are 5 even and 5 odd numbers.
We could get 4 even cards , 4 odd cards or 2 odd and 2 even cards
Let´s check all this combinations
Case 1: When all 4 numbers are even:
We are going to take 4 of the 5 even numbers in the box so we have
[tex]5C4=5[/tex]
Case 2: When all 4 numbers are odd:
We are going to take 4 of the 5 odd numbers in the box, so we have
[tex]5C4=5[/tex]
Case 3: When 2 are even and 2 are odd:
We are giong to take 2 from 5 even and odd cards in the box so we have
[tex]5C2 * 5C2[/tex]
Remember that we obtain the probability from
[tex]\frac{Number-of-favourable-Outcome}{Total-number-of-outcomes}[/tex]
So we have the number of favourable outcomes but we need the Total cases for drawing four cards, so we have that:
We are taking 4 of the 10 cards:
[tex]10C_4=210[/tex]
Hence we have that the probability that their sum is even
[tex]\frac{5+5+100}{210}=\frac{11}{21}[/tex]
Final answer:
To find the probability that the sum of the four cards drawn is even, we can break down the problem into two cases: drawing all four even-numbered cards or drawing two even-numbered cards and two odd-numbered cards. Using the multiplication rule, we calculate the probability for each case and add them together to get the total probability.
Explanation:
Total Number of Possible Outcomes: If we draw four cards from a box containing cards numbered 1 to 10, the total number of ways to do this is given by the combination formula,
resulting in 10!/4!(10-4)! = 210 possible outcomes.
Number of Ways to Get an Even Sum:
For the sum of the numbers on the four drawn cards to be even, there are two cases to consider:
1. All four cards have even numbers: There are 5 even-numbered cards out of 10, and we need to choose 4 of them. The number of ways to do this is =5.
2. Three cards have odd numbers, and one card has an even number:
There are 5 odd-numbered and 5 even-numbered cards.
We need to choose 3 odd-numbered cards out of 5 and 1 even- numbered card out of 5.
The number of ways to do this is =50
Total Number of Ways for an Even Sum:
Adding the possibilities from both cases, we have a total of 5 + 50 = 55 ways to get an even sum.
The probability is then calculated as the ratio of the number of ways to get an even sum to the total number of possible outcomes:
Probability = Number of Ways to Get an Even Sum/Total Number of Possible Outcomes = 55/210= 11/42
Therefore, the probability that the sum of the numbers on the four drawn cards is even is 11/42.
NetSell, a the TV remote control supplier for Lumyn Electronics, has a weekly production cost of q TV remote controls that is given by
C(q) = 0.000004q^3 - 0.03q^2 + 100q + 75,000
where q is in the interval [0, 10,000].
The demand function for this product is given by
p(q) = -0.005q + 200.
Based on this information, find the following:
a) The marginal cost for the company.
b) The marginal revenue for the company.
c) The marginal profit for the company when 2,000 and 7,000 TV remote controls are manufactured.
Answer:
a. [tex]\frac{dC(q)}{dq} = 0.000012q^2 -0.06q + 100[/tex]
b. [tex]\frac{dR(q)}{dq}=-0.01q+200[/tex]
c.
[tex]U'(2000)=-0.000012(2000)^2+0.05(2000)+100 = 152[/tex]
[tex]U'(7000)=-0.000012(7000)^2+0.05(7000)+100 = -138[/tex]
Step-by-step explanation:
a) The marginal cost function is given by the derivative of the total cost function, in this way the marginal cost function for this company is:
[tex]\frac{dC(q)}{dq} = \frac{dC(q)}{dq} (0.000004q^ 3 - 0.03q ^ 2 + 100q + 75000) = 0.000012q^2 -0.06q + 100[/tex]
b) The income function is given by the relation [tex]R (q) = P (q) q = -0.005q^2 + 200q[/tex].
The marginal revenue function for the company is given by the derivative of the revenue function, in this way the marginal revenue function is:
[tex]\frac{dR(q)}{dq}= -0.01q+200[/tex]
(c) The profit function of the company is given by the relation [tex]U (q) = R (q) - C (q)[/tex], and the marginal utility function is given by the derivative of the utility function, in this way , the marginal utility function is:
[tex]\dfrac{dU(q)}{dq}=R'(q) - C'(q) = -0.01q+200 - (0.000012q^2-0.06q+100) = -0.000012q^2+0.05q+100[/tex]
When q = 2000, the marginal utility is:
[tex]U'(2000)=-0.000012(2000)^2+0.05(2000)+100 = 152[/tex]
When q = 7000, the marginal utility is:
[tex]U'(7000)=-0.000012(7000)^2+0.05(7000)+100 = -138[/tex]
Is the set \mathbb{Z} a group under the operation a*b = a - b + ab ? Justify your answer.
Answer:
Step-by-step explanation:
Given that *is the binary operation in the sets of integers.
[tex]a*b = a - b + ab[/tex]
closure: a-b+ab is again an integer belongs to Z. Hence closure is true.
Associativity: [tex]a*(b*c) = a*(b+c-bc)\\= a-b-c+bc+ab+ac-abc\\= a-b-c +ab+bc+ca-abc[/tex]
[tex](a*b)*c=(a+b-ab)*c\\=a+b-ab-c+ac+bc-abc\\[/tex]
The two are not equal. Hence this cannot be a group as associtiavity does not hold good.
A realty company looks at a recent sample of houses that have sold On testing the nul hypothesis that 57% of the houses take more than three months to sell against the hypothesis that more than 57% of the houses take more than three months to sell, they find a P value of 0.026 which conclusion is appropriate? Explain.
Choose the correct answer below. A. If 57% of the houses take more than three months to sell, there is a 2 6% chance that a random sample proportion would be as high as or higher than the one they obtained B. There is a 26% chance that 57% of the houses take more than 3 months to sell C. There is a 97 4% chance that 57% of the houses take more than 3 months to sell D. There is a 26% chance that the null hypothesis is correct
If 57% of the houses take more than three months to sell, there is a 2.6% chance that a random sample proportion would be as high as or higher than the one they obtained.
Explanation:The appropriate conclusion is that if 57% of the houses take more than three months to sell, there is a 2.6% chance that a random sample proportion would be as high as or higher than the one they obtained. This means that the result is statistically significant, indicating that the proportion of houses that take more than three months to sell is likely higher than 57%.
Use the patterns you found to predict whether each set of lengths below will form a triangle. If a set will form a triangle, state whether the triangle will be acute, obtuse, or right. Justify your conclusion. a. 5 cm, 6 cm, and 7 cm b. 2 cm, 11 cm, 15 cm c. 10 cm, 15 cm, 20 cm d. 10 cm, 24 cm, 26 cm e. 1 cm, 3 cm, 9 cm f. 2 cm, 10 cm, 11 cm Core Connections, Course } 412
Answer with Step-by-step explanation:
We have to find given length set form a triangle and find the type of triangle acute, obtuse or right.
If sum of length of any two sides is greater than the length of third side then the given side length form a triangle otherwise not.
a.5 cm, 6 cm and 7 cm
[tex]5+6=11cm > 7cm[/tex]
Hence, given set of side length form a triangle.
[tex]5^2+6^2=25+36=61 >7^2=49[/tex]
Hence, given triangle is acute triangle.
b.2 cm,11 cm,15 cm
[tex] 2+15=17 cm > 11 cm[/tex]
Hence, given side length set form a triangle.
[tex]2^2+11^2=4+121=125 < (15)^2=225[/tex]
Hence, the triangle is an obtuse triangle.
c.10 cm,15 cm,20 cm
[tex]10+15=25 cm >20 cm[/tex]
Hence, given set of length side form a triangle.
[tex](10)^2+(15)^2=225 >(20)^2=400[/tex]
Hence, the triangle is an acute triangle .
d.10 cm,24 cm,26 cm
[tex]10+24=34 cm > 26 cm[/tex]
Hence, given set of side length form a triangle.
[tex](10)^2+(24)^2=676=(26)^2=676[/tex]
Hence, the triangle forms a right triangle.
e.1 cm,3 cm, 9 cm
[tex]1+9=10 cm > 3 cm[/tex]
Hence, the given set of side length forms a triangle.
[tex]1^1+3^2=10<9^2=81[/tex]
Hence, the triangle is an obtuse triangle.
f.2 cm, 10 cm,11 cm
[tex]2+10=12 cm > 11cm[/tex]
Hence, the given set of side length set forms a triangle.
[tex]2^2+(10)^2=104<(11)^2=121[/tex]
Hence, the triangle is an obtuse triangle.
If an albuterol inhaler contains 18 mg of albuterol, how many inhalation-doses can be delivered if each inhalation-dose contains 90 μg?
Answer:
Hello, Your question is already answered but I wanted to add something else if you dont mind :) Inhalants can cause sudden death.
Step-by-step explanation:
Inhalants can kill you instantly. Inhalant users can die by suffocation, choking on their vomit, or having a heart attack. Most teenagers also consider Inhalants as relaxation, like when your stressed or if you've seen in most movies, people panic and then breath in paper bag. I'm not sure if those are the inhalers your talking about but It said 10 points so why not? Thank you, have a great day :)
The albuterol inhaler can deliver 200 inhalation-doses.
How many inhalation-doses in 18 mg albuterol?1 mg = 1000 μg
So, 18 mg = 18 * 1000 μg = 18000 μg
Number of inhalation-doses = Total albuterol / Amount per dose
Number of inhalation-doses = 18000 μg / 90 μg/dose
Number of inhalation-doses = 200 inhalation-doses
Therefore, the albuterol inhaler can deliver 200 inhalation-doses.
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solve the linear programming problem by graphing. graph the feasible region, list the extreme points and identify the maximum value of Z. please list the equations of the lines that form the feasible region
Minimize z=4x+y
subject to
2x+4y>= 20
3x+2y<=24
x,y>=0
Answer:
The minimum value of objective function is 5 at x=0 and y=5.
Step-by-step explanation:
The given linear programming problem is
Minimize [tex]z=4x+y[/tex]
Subject to constraints
[tex]2x+4y\geq 20[/tex] .... (1)
[tex]3x+2y\leq 24[/tex] .... (2)
[tex]x,y\geq 0[/tex]
The related line of both inequalities are solid lines because the sign of inequalities are ≤ and ≥. It means the points lie on related line are included in the solution set.
Check both inequalities by (0,0).
[tex]2(0)+4(0)\geq 20[/tex]
[tex]0\geq 20[/tex]
This statement is not true. So, the shaded region of inequality (1) will not contain the origin.
[tex]3(0)+2(0)\leq 24[/tex]
[tex]0\leq 24[/tex]
This statement is true. It means the shaded region of inequality (2) will contain the origin.
[tex]x,y\geq 0[/tex] means first quadrant.
The common shaded region is feasible region. The vertices of feasible region are (0,5), (0,12) and (7,1.5).
Calculate the value of objective function at these vertices.
For (0,5)
[tex]z=4(0)+(5)=5[/tex]
For (0,12)
[tex]z=4(0)+(12)=12[/tex]
For (7,1.5)
[tex]z=4(7)+(1.5)=29.5[/tex]
Therefore the minimum value of objective function is 5 at x=0 and y=5.
N1
N2
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[[[(2x4)x3]/12] x (2x6)]/12 = ?
Answer:
2
Step-by-step explanation:
Rewriting the expression we have:
[tex]\dfrac{\dfrac{[(2\times 4)\times 3]}{12}\times(2\times 6)}{12}[tex]
Then we have the next step by step solution, starting by the insider parentheses:
[tex]\dfrac{\dfrac{[(2\times 4)\times 3]}{12}\times(2\times 6)}{12}=\dfrac{\dfrac{[8\times 3]}{12}\times(12)}{12}=\dfrac{\dfrac{24}{12}\times(12)}{12}=\dfrac{2\times(12)}{12}=\dfrac{24}{12}=2[/tex]
The score on a trivia game is obtained by subtracting number of incorrect answers from twice the number of correct answers. If a player answered 40 questions and obtained a score of 50, how mary questions did the player answer correctly?
Answer:
30
Step-by-step explanation:
I solved this question algebraically. First a variable (I used 'c') is introduced into the equation (for the number of correct answers). Thus we get the equation;
2c - (40 - c) = 50
solving this...
2c - 40 + c = 50
3c = 90
c = 30
So the number of correct answers is 30. (30*2-10=50)
[Alternatively we can use a variable for the number of incorrect answers and get; 2* (40 - a) - a = 50, and solve this equation but this method is longer as you'll need to subtract this answer from 40 to get the number of correct responses.]
The following data represent the ages of award winners for best actor and best actress in a leading role for the 20 years from 1985 to 2004. Answer parts (a)minus(b) below. Full data set Best Actor Ages Best Actress Ages 40 45 64 52 38 35 48 27 60 44 32 32 33 25 37 26 61 37 37 51 33 53 43 46 52 24 25 32 49 39 22 35 33 39 54 43 34 70 44 25 (a) Construct an ordered back to back stem-and-leaf display.
Answer:
[tex]\begin{array}{ccc}\text{Stem}&|&\text{Leaf}\\ \\2&|&2,4,5,5,5,6,7\\3&|&2,2,2,3,3,3,4,5,5,7,7,7,8,9,9\\4&|&0,3,3,4,4,5,6,8,9\\5&|&1,2,2,3,4\\6&|&0,1,4\\7&|&0\end{array}[/tex]
Step-by-step explanation:
You are given the set of data
40 45 64 52 38 35 48 27 60 44 32 32 33 25 37 26 61 37 37 51 33 53 43 46 52 24 25 32 49 39 22 35 33 39 54 43 34 70 44 25
First, rewrite it in ascending order:
22 24 25 25 25 26 27 32 32 32 33 33 33 34 35 35 37 37 37 38 39 39 40 43 43 44 44 45 46 48 49 51 52 52 53 54 60 61 64 70
The first gigit of each number write into the stem column and the second digit of each number write into the leaf column. So, the stem-and-leaf display is
[tex]\begin{array}{ccc}\text{Stem}&|&\text{Leaf}\\ \\2&|&2,4,5,5,5,6,7\\3&|&2,2,2,3,3,3,4,5,5,7,7,7,8,9,9\\4&|&0,3,3,4,4,5,6,8,9\\5&|&1,2,2,3,4\\6&|&0,1,4\\7&|&0\end{array}[/tex]
Here is the back - to - back stem and leaf plot of the data :
LEAF ___________ stem _________ LEAF
Best actor age_____ | | ___ Best actress age
5, 6, 7 ___________| 2 | _______ 2, 4 5, 5
2, 2, 3, 5, 7, 7, 7, 8__ | 3 | __ 2, 3, 3, 4, 5, 9, 9
0, 4, 5, 8 _________| 4 | ______3, 3, 4, 6, 9
1, 2 _____________ | 5 | ___________ 2, 3
0, 1, 4 ___________ | 6 | ______________
________________ | 7 | _____________ 0
Given the data :
Best actor :
40 45 64 52 38 35 48 27 60 44 32 32 33 25 37 26 61 37 37 51
Best actress :
33 53 43 46 52 24 25 32 49 39 22 35 33 39 54 43 34 70 44 25.
Stem and leaf plot involves an ordered arrangement of values by seperating the the highest placed digit of each value into stems and the other digits into leaves.
Ordering the data :
Best actor :
25, 26, 27, 32, 32, 33, 35, 37, 37, 37, 38, 40, 44, 45, 48, 51, 52, 60, 61, 64
Best actress :
22, 24, 25, 25, 32, 33, 33, 34, 35, 39, 39, 43, 43, 44, 46, 49, 52, 53, 54, 70
The values range from :
22 to 70 ;
Hence, our stems will inculude : 2, 3, 4, 5, 6 and 7
LEAF ___________ stem _________ LEAF
Best actor age_____ | | ___ Best actress age
5, 6, 7 ___________| 2 | _______ 2, 4 5, 5
2, 2, 3, 5, 7, 7, 7, 8__ | 3 | __ 2, 3, 3, 4, 5, 9, 9
0, 4, 5, 8 _________| 4 | ______3, 3, 4, 6, 9
1, 2 _____________ | 5 | ___________ 2, 3
0, 1, 4 ___________ | 6 | ______________
________________ | 7 | _____________ 0
KEY : 2 | 2 = 22
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The slopeof a linear function h(x) is 2. Suppose the function is translated 8 units up to get d(x). How can h(x) be translated to the left or right to represent the same function d(x)?
Answer:
4 units to the right
Step-by-step explanation:
Since all we know about function h(x) is that it has slope 2, we don't know its y intercept, so let's call it b and write the equation of that first line as:
[tex]h(x) = 2x + b[/tex]
Now, we translated that function up 8 units to get function d(x). This vertical displacement is expressed by adding 8 units to function h(x):
[tex]d(x) = h(x) + 8 = 2x+b+8[/tex]
We want to translate this last function d(x) either to the right or to the left in order to get the same expression as for function h(x).
Recall that translations to the right or left a fix number of units "c" affects the "x" coordinate of the function (by adding "c", we move to the left c units the graph of the function, and by subtracting "c" we move to the right the graph of the function).
So represent a generic shift for d(x) for example to the right in c units:
[tex]d(x) = 2(x-c)+x^{2} +b+8= 2x-2c+b+8[/tex]
Now we want this new shifted function to be EXACTLY as h(x) so we write the equality:
[tex]2x-2c+8+b=h(x)=2x+b\\2x-2c+8+b = 2x+b[/tex]
We can solve in the equation for the value "c" we need for the translation:
[tex]2x-2c+8+b = 2x+b\\-2c+8=0\\2c=8\\c=\frac{8}{2} = 4[/tex]
subtracting 2x from both sides, and also subtracting "b" from both sides.
This means that the translation to the right by 4 units will result on the exact same graph as for function h(x)
A student club has seven members. 3 are to be chosen to go together to a national meeting. A) how many distinct groups of 3 can be chosen? B) if the student club contains 4 men and 3 women, how many distinct groups of 3 contain two men and one woman?
Answer:
1) 35 distinct groups can be formed.
2) 18 distinct groups can be formed containing 2 men and 1 woman.
Step-by-step explanation:
The no of groups of 3 members that can be chosen from 7 members equals no of combinations of 3 members that can be formed from 7 members.
Thus no of groups =
[tex]n=\binom{7}{3}=\frac{7!}{(7-3)!\times 3!}=35[/tex]
thus 35 distinct groups can be formed.
Part b)
Now since the condition is that we have to choose 2 men and 1 women to form the group
let A and B be men member's of group thus we have to choose 2 member's from a pool of 4 men which equals
[tex]\binom{4}{2}=\frac{4!}{(4-2)!\times 2!}=6[/tex]
Let the Woman member be C thus we have to choose one woman from a pool of 3 women hence number of ways in which it can be done equals 3.
thus the group can be formed in [tex]6\times 3=18[/tex] different ways.
The data below represents the number of T-shirts sold per week by a student who started his own online t-shirt business. Find the weighted mean of the number of t-shirts sold per week. (Round your answer to the nearest tenth if necessary.)
T-Shirts Sold per Week Frequency
2 1
4 4
6 7
8 3
Answer:
The weighted mean of the number of t-shirts sold per week is 5.6.
Step-by-step explanation:
Given : The data below represents the number of T-shirts sold per week by a student who started his own online t-shirt business.
T-Shirt Sold per Week([tex]x_i[/tex]) Frequency([tex]w_i[/tex])
2 1
4 4
6 7
8 3
To find : The weighted mean of the number of t-shirts sold per week ?
Solution :
The formula of weighted mean is
[tex]\text{Weighted mean}=\frac{\sum (x_i\times w_i)}{\sum w_i}[/tex]
Substituting the values in the formula,
[tex]\text{Weighted mean}=\frac{2(1)+4(4)+6(7)+8(3)}{1+4+7+3}[/tex]
[tex]\text{Weighted mean}=\frac{2+16+42+24}{15}[/tex]
[tex]\text{Weighted mean}=\frac{84}{15}[/tex]
[tex]\text{Weighted mean}=5.6[/tex]
Therefore, The weighted mean of the number of t-shirts sold per week is 5.6.
Final answer:
To find the weighted mean of T-shirts sold per week, you multiply each amount by its frequency, sum these products, and then divide by the total frequency. For this data, the weighted mean is 5.6 T-shirts per week.
Explanation:
To calculate the weighted mean of the number of T-shirts sold per week, we must multiply each number of T-shirts sold by its respective frequency and then divide the sum by the total number of observations.
We have the following data:
6 * 7 = 42
Add these products together:
2 + 16 + 42 + 24 = 84
Next, calculate the total frequency (total number of weeks):
1 + 4 + 7 + 3 = 15
Now, divide the sum of products by the total frequency to get the weighted mean:
84 / 15 = 5.6
Therefore, the weighted mean number of T-shirts sold per week is 5.6.
Which expression is equivalent to 4-2/2-3
A -16
B -8
C 8
D 16
Answer:
0
Step-by-step explanation:
4 - 2/2 - 3 =
Follow the correct order of operations. Start with the division.
= 4 - 1 - 3
Now do subtractions from left to right in the order they appear.
= 3 - 3
= 0
Answer: 0
Using the digits 0 through 9, find out how many 4-digit numbers can be configured based on the stated conditions: a. [1 pt] The number cannot start with zero and no digits can be repeated. b. [1 pt] The number must begin and end with an odd digit. (Repeated digits are okay.) c. [1 pt] The number must be at least 5000 and be divisible by 10. (Repeated digits are okay.) d. [2 pt] The number must be less than 3000 and must be even. No digits may be repeated in the last 3 digits. (That is, 2234 would be okay, but 2334 would not be okay.)
Answer:
a. 4536, b. 2500, c. 500, d. 1080
Step-by-step explanation:
for every question we can use the numbers 0 - 9, this is 10 numbers in total (0, 1, 2, ,3 , 4, 5, 6, 7, 8, and 9).
Fore every case we have to check how many numbers we are allow to use in each digit.
a."The number cannot start with zero" this left us with 9 options of numers for the first digit.
"no digits can be repeated." So if we already use one numer for the first, we can't repeat this in the second, and so on. So for the second numer we have 9 numbers as option (now we can use 0), for the third, since we already use 2 digits, we have 8 options, and for the last, we have 7
that results in: 9*9*8*7 = 4536
b"The number must begin and end with an odd digit. " for odd digits we have 1, 3, 5, 7, 9 --> 5 options for the fist and last digit, and for the two middle digits, we have 10 options for each since it is allowed to repeat numbers
that results in: 5*10*10*5=2500
c"The number must be at least 5000" So the first digit can use 5, 6, 7, 8, or 9 -->5 options for the fist digit
"and be divisible by 10." so it has to end in a 0, --> 1 option fot the last numer
and for the middle digits there are no restrictions, so we use the 10 options for each.
that results in: 5*10*10*1=500
d"The number must be less than 3000 and must be even" for it to be less than 3000 it has to start with 0, 1 or 2 -> 3 options for the first digit
"and must be even" so the number has to end in 0, 2, 4, 6 or 8 --> 5 options for the last number
"No digits may be repeated in the last 3 digits." So we can't repeat in the middle number the one we put in the last digit, this gives us 9 options for the fist middle number and 8 for the second middle number
that results in: 3*8*9*5 = 1080
Final answer:
A step-by-step calculation is conducted for each condition to find the number of 4-digit numbers that can be formed using the digits 0-9 without repetition with conditions such as starting digit restrictions, parity, and divisibility. In total, there are 4536, 2500, 500, and 900 possible numbers for each condition respectively.
Explanation:
To calculate the number of 4-digit numbers meeting various conditions using the digits 0 through 9, we must consider each condition separately.
For a 4-digit number that cannot start with zero and with no repeated digits, we have 9 options for the first digit (1-9), 9 options for the second digit (0-9 except the first digit), 8 options for the third digit, and 7 options for the fourth, resulting in 9 × 9 × 8 × 7 = 4536 possible numbers.For a 4-digit number that must begin and end with an odd digit, there are 5 options for the first and last digit (1, 3, 5, 7, 9), and 10 options for each middle digit, leading to 5 × 10 × 10 × 5 = 2500 possible numbers.For a 4-digit number that must be at least 5000 and divisible by 10, we can pick any number between 5000 and 9990 that ends in '0'. We have 5 options for the first digit (5-9), 10 options each for the second and third digits, and only one option for the last digit ('0'). There are thus 5 × 10 × 10 = 500 possibilities.For a 4-digit number that must be less than 3000 and must be even, there are 2 options for the first digit (1 or 2), 10 options for the second digit, 9 options for the third digit (all except the second digit), and 5 options for the last even digit (0, 2, 4, 6, 8 excluding the one used as the first digit). This gives us 2 × 10 × 9 × 5 = 900 possible numbers.pleases help im stuck on both
Zene decides to canoe 7 miles upstream on a river to a waterfall and then canoe back. The total trip (excluding the time spent at the waterfall) takes 8 hours. Zene knows she can canoe at an average speed of 3 miles per hour in still water. What is the speed of the current?
Answer:
V = 1.94 mi/h
Step-by-step explanation:
mark me brainliest plz
The speed of the current is approximately 0.5 mph.
How to calculate the speed of the river's current?Let's assume the speed of the current is "c" mph. Zene's upstream speed is (3 - c) mph and downstream speed is (3 + c) mph.
The time taken for the upstream trip is 7 / (3 - c) hours, and the time for the downstream trip is 7 / (3 + c) hours.
Since the total trip time is 8 hours, we can set up the equation:
7 / (3 - c) + 7 / (3 + c) = 8
Solving this equation, we find the speed of the current is approximately 0.5 mph.
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What is the cost of constructing a fence 6 feet, 6 inches, high around a lot measuring 90 feet by 175 feet, if the cost of erecting the fence is $1.25 per linear foot and the cost of materials is $0.825 per square foot of fence? Round your answer to the nearest cent.
A. $1,752.62 B. $2,054.63 C. $2,084.62 D. $3,504.63
Answer:
The total cost is $3504.625
Step-by-step explanation:
1 inch = 0.0833333 feet
Height = 6 feet 6 inches =[tex]6+6 \times 0.0833333=6.5 feet[/tex]
Length = 90 feet
Breadth = 175 feet
Perimeter = [tex]2(l+b)=2(90+175) = 530 feet[/tex]
Cost of erecting the fence is $1.25 per linear foot .
So, Cost of erecting the fence of 530 feet = [tex]530 \times 1.25[/tex]
Cost of erecting the fence of 530 feet = [tex]662.5[/tex]
Area of fence = [tex]2(l+b)h=530 \times 6.5=3445 feet^2[/tex]
Cost of materials is $0.825 per square foot of fence
Cost of materials of 3445 square foot of fence = [tex]3445 \times 0.825[/tex]
= [tex]2842.125[/tex]
Total cost = $2842.125+$662.5
Total cost = $3504.625
Hence the total cost is $3504.625
Dexter's dad runs a toy store. His current yearly sales report shows that he sold 4,694 toys in the last three months. If the store made an average profit of $2.95 on each toy, what is the total profit in the three months? A. $12,647.25 B. $13,847.30 C. $14,007.29 D. $15,291.42
Answer:
$13847.30, Option B
Step-by-step explanation:
sold toys = 4694
average profit on each toy = $2.95
total profit in the three months = $2.95 * 4694 = $13847.30
Mia Salto wishes to determine how long it will take to repay a
$18,000 loan given that the lender requires her to make annualend-of-year installment payments of
$4,309
.
a. If the interest rate on the loan is
15%,
how long will it take for her to repay the loan fully?
b. How long will it take if the interest rate is
12%?
c. How long will it take if she has to pay
19%
annual interest?
d. Reviewing your answers in parts
a,
b,
and
c,
describe the general relationship between the interest rate and the amount of time it will take Mia to repay the loan fully.
Answer: a. 10.2 years
b. 12.6 years
c. 8.2 years
d. n = ln 4.1773/ln (1+r)
Step-by-step explanation:
$18,000 loan
annualend-of-year installment payments of $4,309
F = P(1+r)ⁿ
a. r = 15% = 0.15
18000 = 4309(1+0.15)ⁿ
18000/4309 = 1.15ⁿ
4.1773 = 1.15ⁿ
ln 4.1773 = ln 1.15ⁿ
ln 4.1773 = n*ln 1.15
n = ln 4.1773/ln 1.15
n = 10.2 years
b. r = 12% = 0.12
18000 = 4309(1+0.12)ⁿ
18000/4309 = 1.12ⁿ
4.1773 = 1.12ⁿ
ln 4.1773 = ln 1.12ⁿ
ln 4.1773 = n*ln 1.12
n = ln 4.1773/ln 1.12
n = 12.6 years
c. r = 19% = 0.19
18000 = 4309(1+0.19)ⁿ
18000/4309 = 1.19ⁿ
4.1773 = 1.19ⁿ
ln 4.1773 = ln 1.19ⁿ
ln 4.1773 = n*ln 1.19
n = ln 4.1773/ln 1.19
n = 8.2 years
d. The general relationship is n = ln 4.1773/ln (1+r) r as a decimal
A store asked 250 of its customers how much they spend on groceries each week. The responses were also classified according to the gender of the customers. We want to study whether there is a relationship between amount spent on groceries and gender. A meaningful display of the data from this study would be:
(A) side-by-side boxplots
(B) a pie chart
(C) a histogram
(D) a scatterplot
(E) a two-way table
Answer:
A boxplot offers us information that can be used to compare two variables. In particular, if one variable is quantitative and the other variable is qualitative, a boxplot is generated for each category of the qualitative variable. Therefore, through this graph it is possible to analyze the relationship between the amount of money spent on food and the gender of the person.
A circular diagram offers information for a single variable, especially of a qualitative type.
A histogram offers us information for a single variable, especially quantitative type.
A relational analysis between two variables could be done using options (D) or (E), however one of the variables of interest is of qualitative type and the other is of quantitative type, so the scatterplot and the two-way table.
Step-by-step explanation:
What is the ordinal number
just before 152nd?
Answer:
151.
Step-by-step explanation:
50th or Fiftieth Ordinal numbers are just numbers that identify the order of things: Thus having 151 coming before 152.
The ordinal number just before 152nd is 151st.
Explanation:The ordinal number just before 152nd is 151st. Ordinal numbers are used to indicate position or order, and they are formed by adding the suffix '-st' to the cardinal number. In this case, the cardinal number 152 is changed to the ordinal number 152nd by adding '-nd' suffix. To find the ordinal number just before 152nd, we go one step back and change the '-nd' suffix to '-st', resulting in 151st.
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