Answer: 352 miles
Step-by-step explanation:
At the point where the car overtook the bus, the car and the bus would have travelled the same distance.
Let x represent the distance covered by bus and the car before the car overtook the bus.
Let t represent the time taken by the bus to travel x miles.
The bus was traveling at 64 km an hour.
Distance = speed × time
Distance travelled by the bus in t hours would be
x = 64 × t = 64t
if the bus has a 1.5 hour Headstart, it means that the car started moving 1.5 hours after the bus has moved.
Therefore, time spent by the car would be t - 15 hours.
The car traveling at 88 km an hour
Distance covered by the car in t - 1.5 hours would be
x = 88(t - 1.5) = 88t - 132
Since the distance covered is equal, then
88t - 132 = 64t
88t - 64t = 132
24t = 132
t = 132/24
t = 5.5 hours
Therefore, the distance from the starting point when the car overtook the bus would be
x = 64 × 5.5 = 352 miles
What is the 4-day SMA for the following closing prices: $56, $61, $50, $57, $60, $58, and $57.
Group of answer choices
$56, $61, $50, $57
$56, $57, $56.25
Answer:
In order to find the correct answer you must use finances and use algebraic equations . You may also have to use precalculus. There is a group of answer choices, its really difficult to find the answer without more instructions. I don't understand what answer your looking for. You may be able to find the answer using finances and other detailed measures. Try using graph paper and write down finances I'm trying my best to help you.
Step-by-step explanation:
finances Algebra Precalculus
$56, $57, $56.25 is the 4-day SMA for the following closing prices: $56, $61, $50, $57, $60, $58, and $57
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
To calculate the 4-day SMA (Simple Moving Average)
We need to add up the closing prices for the last 4 days and divide the sum by 4.
We then move the window one day forward and repeat the process.
Using the given closing prices, we can calculate the 4-day SMA as follows:
Day 1: (56 + 61 + 50 + 57) / 4 = 56
Day 2: (61 + 50 + 57 + 60) / 4 = 57
Day 3: (50 + 57 + 60 + 58) / 4 = 56.25
Day 4: (57 + 60 + 58 + 57) / 4 = 58
The 4-day SMA for the given closing prices is: $56, $57, $56.25, $58.
Hence, $56, $57, $56.25 is the 4-day SMA for the following closing prices: $56, $61, $50, $57, $60, $58, and $57.
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Kevin invested $8,000 for one year at a simple annual interest rate of 6 percent and invested $10,000 for one year at an annual interest rate of 8 percent compounded semiannually. What is the total amount of interest that Kevin earned on the two investments?A. $880
B. $1,088
C. $1,253
D. $1,280
E. $1,296
Answer:
Total interest =$1296
Step-by-step explanation:
Kevin invested $8,000 for one year at a simple annual interest rate of 6 percent
Simple interest = [tex]\frac{Pnr}{100}[/tex]
P=8000, n=1 year and r=6
interest = [tex]\frac{8000(1)(6)}{100}[/tex]
Interest = 480 dollars
[tex]compound \ interest =P(1+\frac{r}{n} )^{nt}-p[/tex]
P= 10000, t=1, r=8%=0.08, n=2 for semiannually
[tex]compound \ interest =10000(1+\frac{0.08}{2} )^{2(1)}-10000[/tex]
Interest = 10816- 10000=816
Total interest = [tex]480+816=1296[/tex]
A junk box in your room contains a dozen old batteries, five of which are totally dead. You start picking batteries one at a time and testing them. Find the probability of each outcome.
Answer:
7/12 of a chance
Step-by-step explanation:
If you have 12 batteries and 5 are dead, 12 - 5 is 7, so there's going to be 7/12 of a chance.
220-450÷3 to the 2nd power=
Answer:
70
Step-by-step explanation:
220-150=70
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.
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.
Jennifer made 5 Liters of punch for her party. Her brother made another 750 milliliters if they combine the two batches how many 180 milliliters servings would they have would there be any punch left over if so how much
Answer:
Step-by-step explanation:
The total amount of punch that Jennifer made for her party is 5 Liters. Her brother made another 750 milliliters.
1000 milliliters = 1 liter
750 milliliters = 750/1000 = 0.75Liter
if they combine the two batches, the total amount made would be
5 + 0.75 = 5.75Liter
= 5.75 × 1000 = 5750 milliliters
The number of 180 milliliters servings would be
5750/180 = 31 servings
There would be leftovers of 170 milliliters
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
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.
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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Three red balls, 4 white balls, and 1 green ball are in a bag. A ball is drawn without replacement. What is the probability that 3 balls can be drawn without drawing the green ball?
Answer:
[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
Three red balls, 4 white balls, and 1 green ball are in a bag. A ball is drawn without replacement.
total balls = 3 red + 4 white + 1 green = 8 balls
the number of balls that are not green is 7
pick 3 balls from 7 balls that are not green
[tex]nCr= \frac{n!}{r!(n-r)!}[/tex]
[tex]P(not \ green)=\frac{7C3}{8C3}[/tex]
[tex]7C3= \frac{7!}{3!(7-3)!}=35[/tex]
[tex]8C3= \frac{8!}{3!(8-3)!} =56[/tex]
[tex]P(3 \ balls \ drawn)=\frac{35}{56} =\frac{5}{8}[/tex]
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%
Part A: In what way is the algorithmic process the same for integers and polynomials?
Part B: In what way is the algorithmic process different for integers and polynomials?
Select one answer for Part A and one answer for Part B.
A: Polynomial long division and integer division are not the same at all.
A: When using polynomial long division, the same process of divide, multiply, and bring down applies, just like when dividing integers.
A: When using polynomial long division, the multiply, subtract, and bring down portion applies just like when dividing integers.
B: When using polynomial long division, polynomial terms are added, not subtracted like in integer division.
A: When using polynomial long division, the same process of divide, multiply, subtract, bring down applies, just like when dividing integers.
B: Polynomial long division uses powers of variables instead of place values used when dividing integers, and only the first term of the divisor is considered in the divide step.
B: Polynomial long division treats remainders differently than they are treated in integer long division.
B: Polynomial long division and integer division are completely the same.
Answer:
A: When using polynomial long division, the multiply, subtract, and bring down portion applies just like when dividing integers
B: Polynomial long division uses powers of variables instead of place values used when dividing integers, and only the first term of the divisor is considered in the divide step
Step-by-step explanation:
The above answers are pretty self-explanatory.
I find polynomial division easier, because the "trial division" step uses only the highest-degree terms, so always gives the exact result you need for the quotient. (There's no "guess and check" as with integer long division.) Powers of the variable take the place of powers of 10 (or whatever number base you're using) in integer long division.
__
For integer long division, the steps are ...
Divide the leading portion of the dividend by the divisor to determine the quotient digit.Multiply the divisor by the quotient digit and subtract the result from the dividend, paying attention to place value. If the quotient digit is too large (the difference is negative), choose a smaller value and repeat.Append the next succeeding digit of the dividend to the difference from the above step to form the new dividend and repeat from the first step until the desired quotient precision is achieved.If all given digits of the dividend have been exhausted, append zero to form the new dividend.Any remainder can be expressed as a fraction with the divisor as its denominator. (That fraction is added to the rest of the quotient.)For polynomial long division, the steps are similar.
Divide the highest degree term of the dividend by the highest-degree term of the divisor to form the next term of the quotient.Multiply the quotient term just found by the divisor and subtract the result from the dividend to obtain the new dividend.Repeat from the first step until the degree of the dividend is less than that of the divisor. If this remainder is non-zero, it can be expressed as a fraction with the divisor as its denominator. (That fraction is added to the rest of the quotient.)_____
Examples of each are shown in the attachments.
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
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
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
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
What is (-7)^3 / (-7)^4 simplified? Can you walk me through the steps?
Answer:
(-7)∧-1
Step-by-step explanation:
(-7)^3 / (-7)^4
taking each and simplifing it
-7³ = -7 x -7 x -7
(-7)∧4 = -7 x -7 x -7 x -7
(-7)^3 / (-7)^4 = (-7 x -7 x -7 ) / ( -7 x -7 x -7 x -7) = 1/-7
1/-7 ( 1/ means raise to power -1)
1/-7 = (-7)∧-1
Daisy is going 12 mph and Sally is going 8 mph if they where 60 miles apart how many hours would it take for them to meet up
Answer:
3 hours
Step-by-step explanation:
we know that
The speed is equal to divide the distance by the time
Let
s ----> the speed in mph
d -----> the distance in miles
t ----> the time in hours
x ----> distance traveled by Daisy to the meeting point
60-x ----> distance traveled by Sally to the meeting point
so
[tex]s=\frac{d}{t}[/tex]
Solve for d
[tex]d=st[/tex]
Distance traveled by Daisy to the meeting point
[tex]d=st[/tex]
we have
[tex]d=x\ mi\\s=12\ mph[/tex]
substitute
[tex]x=12t[/tex] ----> equation A
Distance traveled by Sally to the meeting point
[tex]d=st[/tex]
we have
[tex]d=(60-x)\ mi\\s=8\ mph[/tex]
substitute
[tex]60-x=8t[/tex] ----> equation B
substitute equation A in equation B
[tex]60-12t=8t[/tex]
solve for t
[tex]12t+8t=60\\20t=60\\t=3\ hours[/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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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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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]
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.
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
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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find the distance between (-6,6)(-5,-7)
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
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!!!
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
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