Answer:
a.
Option 1
Option 2
b. Sample statistics
Step-by-step explanation:
a.
The set that includes the list of all possible individual in the interested area of study is termed as population while the portion or a part of population is termed as sample. The given scenario indicates that population is all elderly people from which 949 elderly people are selected for study and so, 949 elderly people are included in sample. So, option 1 and option 2 are correct for indicated scenario.
b.
The percentages 22% and 17% are calculated from 949 elderly people that are indicated as sample. Hence, the percentages 22% and 17% are the measure of sample and so, they represents sample statistics.
Final answer:
The relevant population is all elderly people, and the sample consists of 949 elderly people. The numbers 22% and 17% represent sample statistics.
Explanation:
a. The relevant population is all elderly people, so options 2 and 3 are correct. The sample consists of 949 elderly people, so option 1 is also correct.
b. The numbers 22% and 17% represent sample statistics. The sample statistics are calculated from the data collected in the sample, which in this case is the proportion of elderly persons with depression who went on to develop dementia.
Which statement is the correct interpretation of the confidence interval in this illustration? The probability the true mean is between 76.08 and 83.92 is 0.95 or 95%. We are 95% confident that the true mean is between 76.08 and 83.92.
Answer:
We are 95% confident that the true mean lies between 76.08 and 83.92.
Step-by-step explanation:
The confidence interval approach is used to calculate an interval in which the true population mean exists. The confidence level 1-α associated with confidence interval depicts that how confident we are that the population mean lies in the estimated interval. In the problem that confidence level is 95%, so we are 95% confident that the true mean lies between 76.08 and 83.92.
Round all answers to the nearest whole number. How many of the people surveyed make less than 5 calls per day? What percentage of those surveyed make at least 9 calls per day? % How many people were surveyed?
Answer:
a). 18
b). 26%
c). 39
Step-by-step explanation:
Given question is incomplete; here is the complete question attached.
a). In this part we have to calculate the number of the people surveyed who make less than 5 calls.
From the given table,
Number of people surveyed who make less than 5 calls Or 1 - 4 calls = 18
b). Total number of people surveyed = 18 + 11 + 5 + 3 + 2 = 39
Number of people surveyed, make at least 9 calls = 5 + 3 + 2 = 10
Percentage of these people = [tex]\frac{\text{People who make calls more than 9 calls per day}}{\text{Total number of people surveyed}}\times 100[/tex]
= [tex]\frac{10}{39}\times 100[/tex]
= 25.64%
≈ 26%
c). Total number of people surveyed = 18 + 11 + 5 + 3 + 2 = 39
An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what is the probability that each of the balls will be (a) of the same color?
Answer:
As a fraction, the answer is exactly 86/969
In decimal form, the answer is approximately 0.08875
=====================================================
Work Shown:
The assumption is that no replacements are made for each selection.
5 red, 6 blue, 8 green
5+6+8 = 19 total
A = P(3 red) = (5/19)*(4/18)*(3/17) = 10/969
B = P(3 blue) = (6/19)*(5/18)*(4/17) = 20/969
C = P(3 green) = (8/19)*(7/18)*(6/17) = 56/969
D = P(3 all same color)
D = A+B+C
D = 10/969 + 20/969 + 56/969
D = (10+20+56)/969
D = 86/969
D = 0.08875
calculate the current in a circuit with resistance (r) of 30 and electromotive force (e) of 120vac
Answer:
E=I(R+r)
R+r=30
I=E/(R+r)
I=120/30
I=4A
Step-by-step explanation:
Final answer:
Using Ohm's Law (I = E/R), the current in a circuit with a resistance of 30 ohms and electromotive force of 120 VAC is calculated as 4 amperes.
Explanation:
To calculate the current (I) in a circuit when given the resistance (R) and electromotive force (E), we can use Ohm's Law, which states that current is equal to voltage divided by resistance (I = E/R). Using the values from the question, the resistance is 30 ohms and the electromotive force is 120 VAC. Therefore, the current in the circuit can be calculated as follows:
I = E/R = 120 V / 30 Ω = 4 A
So, the current in the circuit is 4 amperes.
find the distance between (-6,6)(-5,-7)
Which choice correctly expresses the solution set in the inequality in words?
Answer:
The answer to your question is letter A.
Step-by-step explanation:
Inequality x + 2 ≥ 5
Solve the inequality, remember that inequalities and equations are solved in similar ways.
- Subtract 2 in both sides
x +2 - 2 ≥ 5 - 2
- Simplify
x ≥ 3
- Remember that this sign "≥" means that x is greater or equal to a number, and this sign "≤" means that x is lower or equal to a number.
The option that satisfies our inequality is the first option.
Write an equation for a function with the given characteristics. A cosine curve with a period of pi, and amplitude of 1, a left phase shift of pi, and vertical transiation up 5/2 of a unit.
The equation for the function with the given characteristics is:
f(x) = (1 * cos((x - pi)/pi)) + (5/2)
We have,
The equation for the function with the given characteristics can be written as follows:
f(x) = (1 * cos((x - pi)/pi)) + (5/2)
Amplitude: The amplitude of the cosine curve is 1, so we multiply the cosine function by 1.
Period: The period of the cosine curve is pi, which means it completes one full cycle over the interval [0, pi]. The period of the cosine function is determined by the argument inside the cosine function, (x - pi)/pi. This shifts the period to start at pi and end at 2pi.
Left phase shift: The left phase shift of pi is achieved by subtracting pi from x inside the argument of the cosine function. This shifts the curve to the left by pi units.
Vertical translation: The vertical translation up 5/2 units is achieved by adding 5/2 to the entire function.
Therefore,
The equation for the function with the given characteristics is:
f(x) = (1 * cos((x - pi)/pi)) + (5/2)
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The equation for the function is y(t) = cos(2t + pi) + 5/2.
Explanation:To write an equation for the given characteristics, we can start with the general equation for a cosine curve: y(t) = A cos(wt + p).
Given that the period is pi, we know that the angular frequency w is equal to 2pi divided by the period, so w = 2pi/pi = 2. The amplitude is 1, so A = 1.
The left phase shift is pi, so p = pi. Finally, there is a vertical translation up 5/2 units, so we add 5/2 to the equation.
Putting all these values into the equation, we get: y(t) = cos(2t + pi) + 5/2.
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Allyson and Adrian have decided to connect their ankles with a bungie cord; one end is tied to each person's ankle. The cord is 30 feet long, but can stretch up to 90 feet. They both start from the same location. Allyson moves 10 ft/sec north and Adrian moves 8 ft/sec west. There is a building with the nearest corner 30 ft north and 20 ft west of the girls' starting point. When will the bungie cord first touch the corner of the building?
Answer: 5.5 seconds
Step-by-step explanation:
30=5/4 ×(-20) + 10t
30 =-25 +10t
10t=55
t=5.5seconds
The cord will first touch the corner of the building after 5.5secs
AHHHH HELP I WILL GIVE BRAINLY NO CAP NO CAP
Answer:
The answer to your question is letter A
Step-by-step explanation:
From the graph, we conclude that it is a vertical ellipse with center (0, 0).
Also from the graph, we calculate a and b
a = 11, a is the distance from the center to the vertical vertex
b= 9, b is the distance from the center to the horizontal vertex
Equation
[tex]\frac{x^{2}}{9^{2}} + \frac{y^{2}}{11^{2}} = 1[/tex]
Simplification
[tex]\frac{x^{2}}{81} + \frac{y^{2}}{111} = 1[/tex]
There are 45 students who play a woodwind instrument in the school band. Of these, 18 play the saxophone. What percent of these students play the saxophone
Answer:
40% students play the saxophone.
Step-by-step explanation:
Given:
Total Number of students who play woodwind instrument = 45
Number of students who play saxophone = 18
We need to find the percent of students who play saxophone.
Solution:
Now we can say that;
To find the percent of students who play saxophone we will divide Number of students who play saxophone by Total Number of students who play woodwind instrument and the multiply by 100.
framing in equation form we get;
percent of students who play saxophone = [tex]\frac{18}{45}\times100= 40\%[/tex]
Hence 40% students play the saxophone.
The percent of these students play the saxophone is 40%.
Using this formula
Percentage=Number of student that play saxophone/Number of student that play woodwind instrument×100
Where:
Number of student that play saxophone=18
Number of student that play woodwind instrument=45
Let plug in the formula
Percentage=18/45×100
Percentage=40%
Inconclusion the percent of these students play the saxophone is 40%.
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In horse racing, a trifecta is a bet that the first three finishers in a race are selected, and they are selected in the correct order. Does a trifecta involve combinations orpermutations? Explain.Choose the correct answer below.A. Because the order of the first three finishers does not make a difference, the trifecta involves permutations.B. Because the order of the first three finishers does make adifference, the trifecta involves permutations.C. Because the order of the first three finishers does not make a difference, the trifecta involves combinations.D. Because the order of the first three finishers does make adifference, the trifecta involves combinations.
Answer:
its a combination
Step-by-step explanation:
because three horses is a combination of horses
In 2006 the population of the country was 30.3 million. This represented an increase in population of 4.7% since 2001 . What was the population of the country in 2001
Answer:
The population in 2001 was = 23.95 millions
Step-by-step explanation:
Given
Population in 2006 = 30.3 million
Rate of growth since 2001 = 4.7%
To find the population in 2001.
Solution:
The population growth formula is give as:
[tex]P=P_0\times e^{rt}[/tex]
[tex]P\rightarrow[/tex] New population
[tex]P_o\rightarrow[/tex] Initial population
[tex]r\rightarrow[/tex] rate of growth
[tex]t\rightarrow[/tex] time
Data given to us:
New population [tex]P[/tex] (2006) = 30.3 million
Rate = 4.7% = 0.047
Time = [tex]2006-2001[/tex]= 5 years
Plugging in the data in the formula.
[tex]30.3=P_0\times e^{0.047\times 5}[/tex]
[tex]30.3=P_0\times e^{0.235}[/tex]
[tex]30.3=P_0\times 1.265[/tex]
Dividing both sides by 1.265
[tex]\frac{30.3}{1.265}=\frac{P_0\times 1.265}{1.265}[/tex]
[tex]23.95=P_o[/tex]
∴ [tex]P_o=23.95[/tex]
Thus, population in 2001 was = 23.95 millions
One store has 3 Managers and 12 Salespeople.Another store has 4 Managaers and 15 salespeople. Do both stores have equivalent ratios of managers to salespeople explain.
Answer:
The ratio of mangers to sales people of the stores are not equivalent as the ratios in their simplest form are not equal.
Step-by-step explanation:
Given:
One store has:
3 Managers and 12 sales persons
Another store has:
4 Managers and 15 sales persons.
To find if the ratio of mangers to sales people are equivalent.
Solution:
Store A:
Managers = 3
Sales people = 12
Ratio of mangers to sales people for store A = [tex]\frac{3}{12}[/tex] =[tex]\frac{3\div3}{12\div 3}=\frac{1}{4}[/tex] (Simplest ratio)
Store B:
Managers = 4
Sales people = 15
Ratio of mangers to sales people for store B = [tex]\frac{4}{15}[/tex]
The ratio is in the simplest form and cannot be reduced further.
We can see that : [tex]\frac{1}{4}\neq \frac{4}{15}[/tex]
Hence, the ratio of mangers to sales people of the stores are not equivalent.
Write an expression for the sequence of operations.
Subtract 4 from x, double, and add 8.
The expression for the given sequence of operations is 2(x-4)+8.
The given statement is "subtract 4 from x, double, and add 8".
We need to write an expression for the sequence of operations.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Now, subtract 4 from x=x-4
Double the difference that is 2(x-4)
Add 8=2(x-4)+8
Therefore, the expression for the given sequence of operations is 2(x-4)+8.
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Help plz, Worth 30 pts, Will give branliest!
A.11
Step-by-step explanation:
Here apply the interpolation formula to find the value of y
From the table, you can interpolate the value of y where x is 92 by using the points (91,10) and (98,15)
The formula to apply is;
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} *(x-x_1)[/tex]
where
(x₁,y₁)=(91,10)
(x₂,y₂)=(98,15)
(x,y)=(92,?)
Substitute values in the equation;
[tex]y-10=\frac{15-10}{98-91} *(92-91)\\\\y-10=\frac{5}{7} *(1)\\\\7(y-10)=5\\7y-70=5\\7y=5+70\\\\7y=75\\\\y=75/7=10.71\\\\y=11[/tex]
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The lines below are perpendicular. If
the slope of the solid line is , what
is the slope of the dashed line?
Answer:
Correct answer: s₁ = - 2
Step-by-step explanation:
The relationship between the slope of two lines that are perpendicular is:
s₁ = - 1/s = - 1/(1/2) = - 2
God is with you!!!
You have $50,000 to invest, and two funds that you'd like to invest in. The You-Risk-It Fund (Fund Y) yields 14% interest. The Extra-Dull Fund (Fund X) yields 6% interest. Because of college financial-aid implications, you don't think you can afford to earn more than $4,500 in interest income this year. How much should you put in each fund?
Answer:
Principal Fund Y = $18,750
Principal Fund X = $31,250
Step-by-step explanation:
Given;
Total amount to invest = $50,000
Maximum amount of interest =$4,500
For fund Y;
Let y represent the amount invested(principal) in fund Y
Interest = 14% = 0.14
Time = 1 year
Interest = principal × rate × time
Interest on fund y = y × 0.14 × 1= 0.14y
For fund X;
The amount invested in fund X can be given as
x =50,000-y
Rate = 6% = 0.06
Time = 1 year
Interest on fund X = x × 0.06 ×1 = 0.06x = 0.06(50,000-y)
Total interest = interest on fund Y + fund X
$4,500 = 0.14y + 0.06(50,000 - y)
4500 = 0.14y - 0.06y + 3000
0.8y = 4500-3000
0.8y = 1500
y = 1500/0.08
y = $18,750
x = $50,000 - $18,750
x = $31,250
Aparty rental company has chairs and tables for rent. The total cost to rent 5 chairs and 6 tables is $65. The total cost to
rent 3 chairs and 2 tables is $25. What is the cost to rent each chair and each table?
Answer:the cost of renting each chair is $2.5
the cost of renting each table is $8.75
Step-by-step explanation:
Let x represent the cost of renting each chair.
Let y represent the cost of renting each table.
The total cost to rent 5 chairs and 6 tables is $65. This means that
5x + 6y = 65 - - -- - - - - - - -1
The total cost to rent 3 chairs and 2 tables is $25. This means that
3x + 2y = 25 - - - - - - - - - - - -2
Multiplying equation 1 by 3 and equation 2 by 5, it becomes
15x + 18y = 195
15x + 10y = 125
Subtracting, it becomes
8y = 70
y = 70/8 = 8.75
Substituting y = 8.75 into equation 1, it becomes
5x + 6 × 8.75 = 65
5x + 52.5 = 65
5x = 65 - 52.5 = 12.5
x = 12.5/5 = 2.5
The inverse of x y is:
xy
xy
yx
xy
yx
To answer this question, first, we need to understand the concept of an inverse operation, especially in the context of binary operations. A binary operation is a calculation that combines two elements to produce another element. Common binary operations are addition, subtraction, multiplication, and division in mathematics.
The inverse of a binary operation, denoted here as x y, is an operation, which when performed after the initial operation, returns the original value. This means, if we take x and y to produce z through the operation x y (denoted as x y -> z), the inverse operation will bring us back to the original x or y value. In mathematical terms, if we perform z (inverse) x operation, it should give us y, and z (inverse) y should return x.
From the given options, we can clearly observe that only one option obeys the rules of the inverse operation, that is 'yx' (option 3). Because only 'yx' will satisfy, z(inverse) x = y and z (inverse) y = x.
So, option 3, 'yx' is the inverse operation of x y in the sense of the inverse element.
Answer:yx
Sue has $40,000 in her savings account. She use some of the money to put towards a house. She has $36,479 left. How much did she put towards the house. Solve and write an equation with a variable to represent the unknown.
Answer:
x = $3,521
Step-by-step explanation:
let the amount of money that she put towards a house be represented by the variable x
Hence,
total savings = amount put towards house + amount left
$40,000 = x + $36,479 (rearrange)
x + $36,479 = $40,000 (subtract $36,479 from both sides)
x = $40,000 - $36,479
x = $3,521
Traditions clothing store is having a sale. Shirts that were regularly priced at $20 are on sale $17. Explain how to find the discount offered for the price of the shirts?
Answer:
Step-by-step explanation:
Let x represent the discount in percentage offered for the price of the shirts.
The regular price of the shirts was $20
The price for which the shirt was offered for sale is $17 which also represents the discounted price.
The discount would be
20 - 17 = $3
The percentage discount would be
The discount/ the regular price × 100%.
Therefore,
% discount = 3/20 × 100 = 0.15 × 100
= 15%
220-450÷3 to the 2nd power=
Answer:
70
Step-by-step explanation:
220-150=70
Adnan made "x" calculators this week, but Maya made twice as many calculators. Write an algebraic expression for the number of calculators that Maya made this week. A) 2x B) x + 2 C) x 2 D) x − 2
Answer:
A) [tex]2x[/tex]
Step-by-step explanation:
Given:
Number of calculator made by Adnan in this week = [tex]'x'[/tex]
We need to write an algebraic expression for the number of calculators that Maya made this week.
Solution:
Now given:
Maya made twice as many calculators.
So we can say that;
Number of calculators made by Maya this week is equal to 2 times Number of calculator made by Adnan this week.
framing in equation form we get;
Number of calculators made by Maya this week = [tex]2\times x = 2x[/tex]
Hence an algebraic expression for the number of calculators that Maya made this week is [tex]2x[/tex].
A particle that moves along a straight line has velocity v(t) = t 2 e −t meters per second after t seconds. How far will it travel during the first t seconds?
The distance traveled by the particle is determined as [tex]\int\limits^0_t {v(t)} \, dt=-e^{-t}t^{2}+2(-e^{-t}t-e^{-t})+2[/tex].
Given data:
To determine the distance traveled by the particle during the first t seconds, integrate the velocity function with respect to time over the interval [0, t].
Given the velocity function:
[tex]v(t) = t^2 * e^{(-t)}[/tex]
To find the distance traveled, integrate the absolute value of the velocity function over the interval [0, t]:
[tex]\text{distance} = \int\limits^0_t {v(t)} \, dt[/tex]
Since the velocity can be negative (indicating a change in direction), taking the absolute value ensures that we consider the magnitude of the velocity.
Now, calculate the integral:
[tex]D = \int\limits^0_t {t^2 * e^{(-t)}} \, dt[/tex]
To simplify this integral, split it into two parts, considering the cases when the velocity is positive and negative:
[tex]D=[-e^{-t}t^2-\int\limits^0_t {-2e^{-t}} \, dt]_0^t[/tex]
The first integral represents the distance traveled when the velocity is positive, and the second integral represents the distance traveled when the velocity is negative.
Integrating each term separately:
[tex]\int\limits^0_t {v(t)} \, dt=-e^{-t}t^{2}+2(-e^{-t}t-e^{-t})+2[/tex]
Hence, the distance is [tex]D=-e^{-t}t^{2}+2(-e^{-t}t-e^{-t})+2[/tex].
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The complete question is attached below:
A particle that moves along a straight line has velocity [tex]v(t) = t^2e^{-t}[/tex] meters per second after t seconds. How far will it travel during the first t seconds?
The function v(t) = t2 e−t defines the velocity of a particle. The displacement or distance covered by the particle in the first t seconds is given by the integral from 0 to t of the velocity function.
Explanation:
The given velocity function for the particle is v(t) = t2 e−t. The distance (or displacement) traveled by an object is the integral of the velocity over a given interval. So, to find the distance covered by the particle in the first t seconds, you would set up the following integral:
∫0t t2 e−t dt
We won't compute this integral here, as it requires knowledge of methods beyond basic calculus, specifically the use of integration by parts and possibly a tabular method for successive integrations by parts. However, this setup gives you the right starting point to find the distance covered in the first t seconds.
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Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year. After 1 year, how much would you be able to buy with the money in this account?
a. More than today
b. Exactly the same
c. Less than today
d. I do not know
Answer:
C Less than today
Step-by-step explanation:
If i save $100 at 1% per annum after 1 year I will get $101, but with inflation rate of 2%per annum a commodity that is worth $100 now will be worth $102 after 1 year so u can't buy same commodity I can buy today after 1 year even when my money has increase.
The purchasing power of money in a savings account would decrease after 1 year due to inflation.
Explanation:To calculate how much you would be able to buy after 1 year, we need to consider the effect of both the interest rate and inflation. With an interest rate of 1% per year, your savings account would increase by 1% over 1 year. However, with an inflation rate of 2% per year, the price of goods and services would also increase by 2% over the same period.
This means that the purchasing power of your money would decrease. To calculate the actual increase or decrease in purchasing power, you can subtract the inflation rate from the interest rate. In this case, 1% - 2% = -1%.
Therefore, the correct answer is c. Less than today. After 1 year, you would be able to buy less with the money in your savings account.
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Find the midpoint of (0,4) and (-4,-12)
Packages of batteries normally sell for $4.99. They are now 20% off. How much would you have to pay?
Answer:
You will have to pay $ 3.99 for the package of batteries with 20% discount
Step-by-step explanation:
Standard price of the batteries packages = $ 4.99
Discount = 20% = 0.2
Discounted price = Standard price - Discount
Discounted price = 4.99 - (0.2 * 4.99)
Discounted price = 4.99 - 1.00 (Rounding to the next tenth)
Discounted price = 3.99
You will have to pay $ 3.99 for the package of batteries with 20% discount
Final answer:
A package of batteries with a 20% discount off the original price of $4.99 would be approximately $3.99 after subtracting the discount amount, which is $0.998.
Explanation:
To calculate how much the student would have to pay for packages of batteries that normally sell for $4.99 with a 20% discount, we first need to determine the amount of the discount. To find the discount amount, multiply the original price by the discount percentage:
$4.99 × 0.20 = $0.998
Now, subtract the discount amount from the original price to get the sale price:
$4.99 - $0.998 = $3.992
The discounted price will be approximately $3.99, as the final amount is traditionally rounded to the nearest cent.
The concession stand at football games sells pizza and drinks. You buy 4 drink and 6 slices of pizza for $6.70. Your friend buys 3 drinks and 4 slices of pizza for $4.65. How much is each drink and slice of pizza?
Answer:
drinks: $0.55pizza slices: $0.75Step-by-step explanation:
Let d represent the cost of a drink, and p represent the cost of a pizza slice. Then the two purchases can be represented by ...
4d +6p = 6.703d +4p = 4.65To solve these equations by elimination, choose a variable to eliminate and look at the coefficients of that in the two equations. If we choose to eliminate p, we see the coefficients of p are 6 and 4. The least common multiple of these numbers is 12. We can multiply the first equation by -2 and the second equation by +3 and the resulting coefficients of p will be -12 and +12. Adding the results of these multiplications will make the p terms add to zero.
-2(4d +6p) +3(3d +4p) = -2(6.70) +3(4.65)
-8d -12p +9d +12p = -13.40 +13.95 . . . . . . . . . eliminate parentheses
d = 0.55 . . . . . . . . . collect terms
Now, we can substitute this value into either equation to find the value of p. Using the first equation, we get ...
4(0.55) +6p = 6.70
6p = 4.50 . . . . . . . . . subtract 2.20
p = 0.75 . . . . . . . . . . divide by 6
The cost of a drink is $0.55; the cost of a slice of pizza is $0.75.
Answer:each drink costs $0.55
Each slice of pizza costs $0.75
Step-by-step explanation:
Let x represent the cost of each drink.
Let y represent the cost of each slice of pizza.
You buy 4 drink and 6 slices of pizza for $6.70. This means that
4x + 6y = 6.70 - - - - - - - - - - - - 1
Your friend buys 3 drinks and 4 slices of pizza for $4.65. This means that
3x + 4y = 4.65 - - - - - - -- - - 2
Multiplying equation 1 by 3 and equation 2 by 4, it becomes
12x + 18y = 20.1
12x + 16y = 18.6
Subtracting, it becomes
2y = 1.5
y = 1.5/2 = 0.75
Substituting y = 0.75 into equation 1, it becomes
4x + 6 × 0.75 = 6.70
4x + 4.5 = 6.70
4x = 6.7 - 4.5 = 2.2
x = 2.2/4 = 0.55
It cost $525 for 7adult tickets and 12 youth tickets to the hockey game. If the difference in price between adult ticket Nd youth ticket is $18, find the cost of a youth ticket
Final answer:
To find the cost of a youth ticket, you can set up a system of equations using the given information. Solve the system of equations to find the cost of a youth ticket.
Explanation:
To find the cost of a youth ticket, we can set up a system of equations using the given information. Let x be the cost of an adult ticket and y be the cost of a youth ticket. From the problem, we know that 7x + 12y = 525 and x - y = 18. We can solve this system of equations using substitution or elimination.
First, let's solve for x in terms of y using the second equation. Adding y to both sides gives x = y + 18.
Next, substitute this expression for x in the first equation: 7(y + 18) + 12y = 525. Simplifying this equation gives 7y + 126 + 12y = 525. Combining like terms, we get 19y + 126 = 525. Subtract 126 from both sides: 19y = 399. Finally, divide both sides by 19 to solve for y: y = 21.
Therefore, the cost of a youth ticket is $21.
A relationship between two variables in which the variables vary in the opposite direction (i.e., one increases while the other decreases, or vice versa) is referred to as a:________ a) strongerb) weakerc) positived) negative
Answer: d) negative
Step-by-step explanation:
The term correlation is used to define the relationship between the two variables .
We say there is a positive relationship between them if one increases / decreases then other also increases / decreases simultaneously.Here, the variables vary in the same direction.
If one variable increases while the other decreases , then we call it a negative relationship between them.Here, the variables vary in the opposite direction.
∴ A relationship between two variables in which the variables vary in the opposite direction (i.e., one increases while the other decreases, or vice versa) is referred to as a: negative correlation.
Hence, the correct answer is d) negative