The population after 5 years is approximately 337,465 people
Explanation:The population of the city is 250,000
Annual growth rate is 6%
The population after t years is:
[tex]P=P_oe^{rt}[/tex]After 5 years, t = 5 and the population becomes:
[tex]\begin{gathered} P=250000e^{\frac{6}{100}\times5} \\ \\ =250000e^{0.3} \\ \\ \approx337465 \end{gathered}[/tex]The population after 5 years is approximately 337,465 people
Which of the following criterion will accurately complete the proof in step 4
2.
[tex]\begin{gathered} \angle RAG\text{ and }\angle RET\text{ are vertical angles} \\ \Rightarrow\angle RAG\cong\angle RET \end{gathered}[/tex]The reason for 2 is 'the angles are vertical'.
3. In the diagram below, we can identify the alternate interior angles more easily
Therefore, Therefore, the statements of the third step are
[tex]\begin{gathered} \angle AGR\cong\angle ETR \\ \text{and} \\ \angle GAR\cong\angle\text{TER} \end{gathered}[/tex]Finally, the corresponding angles of triangles GRA and TRE are all congruent; thus, the two triangles are congruent because of the AA similarity criterion. The answer is AA similarity criterion. The length of the sides is not involved in the demonstration.
2) In reply to an inquiry about the animals on his farm, the farmer says: "I
only ever keep sheep, goats, and horses. In fact, at the moment they are
all sheep bar three, all goats bar four, and all horses bar five." How many
does he have of each animal?
The number of horse is 1, goat is 2 and sheep is 3 a man has.
The problem we are dealing with is related to the linear equation which is referred to as the algebraic condition where each term has an exponent of 1 and when this condition is graphed, it continuously comes about in a straight line.
Now w consider x to be the number of sheep, y to be the number of goats, and z to be the number of horses the man owns.
the actual equation for the total number of animals he owns is :
x+ y+ z
according to the first condition:
that all sheep bar three, means
y+ z=3
similarly, for the other condition, it will be
x+ z=4 and x+ y=5
Now we adding the three equations:
y + z +x +z +x +y=5+4 +3
2(x+y+z)=12
x+y+z=6........equation(1)
As x + y = 5
Put this in equation in (1), we get
x+y+z = 6
5 + z = 6
z = 1
x + z = 4
x + y + z = 6
y + 4 = 6
y = 2
Now we know
x + y + z = 6
x + 1 + 1 = 6
x = 4
So simplifying the other equation we get, that the number of horse is 1, goat is 2, and sheep is 4.
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JohanVanDeVaseYesterdayMathematicsHigh SchoolTARIFF SYSTEMSQUESTION 1 [13 marks]A shopping mall in Bloemfontein has several parking garages, each with its own tariff system. The table below shows the tariffs on garage A and garage B.(Please show calculation)Parking TariffsNumber of hours (h)0 < h < 11 < h < 22 < h < 44 < h < 66 < h < 7h > 7Garage AFreeR5,50R15,50R30,50R50,50R75,50Garage BR5,00R7,00R11,00R26,00R41,00R61,00Question 1.1 [4 marks]Sellwane works at the shopping mall. She arrives at 7:30 and leaves at 17:00 each day. Which parking garage is cheaper for her to use?Question 1.2 [3 marks]Isaac was having coffee with his friends at a restaurant at the shopping mall. They arrived at the mall at 8:23 and left at 10:53, how much would he pay if he used garage B?Question 1.3 [2 marks]On Monday morning Karabo parked her car in one of the parking garages and paid R26,00. In which garage did she park and for how long?
Step 1:
Question 1.1
Arrive time = 7:30
Departure time = 17:00
[tex]\text{Total time spent = 17:00 - 7:30 = }9\colon30[/tex]h (9:30) > 7
Garage B is cheaper
Question 1.2
Arrive time = 8:23
Departure time = 10:53
[tex]\text{Total time spent = 10:53 - 8:23 = 2: 30}[/tex]The time spent by issac and his friends is between 2 < h < 4
Since h = 2:30
Answer R11.00
Question 1.3
Karabo uses Garage B
Time spent is 4 < h < 6
Put the following equation of a line into slope-intercept form, simplifying all fractions.
12y-2x=12
Answer:
y = 1/6x + 1
Step-by-step explanation:
Add 2x to both sides of the equation.
12y = 12 + 2x
Divide each term in 12y = 12 + 2x by 12 and simplify.
y = 1 + x/6
Write in y=mx+b form.
y = 1/6x + 1
You want to buy new kitchen appliances 3 years from now, and you plan to save $3,000 semiannually, beginning immediately. You will deposit your savings in an account that pays 7.2% interest. How much will you have 3 years from now?
The final amount after 3 years compounded semi-annually is $3709.20
Compound Interest
To solve this problem, we simply need to use compound interest formula which is given as
[tex]A = p(1 + \frac{r}{n})^n^t[/tex]
where
A = final amountP = initial amount or principalr = rate n = number of times compoundedt = timeLets substitute the values into the formula and solve
[tex]A = p(1 + \frac{r}{n})^n^t\\A = 3000(1 + \frac{0.072}{2})^2^*^3\\ A = 3709.20[/tex]
The amount accrued 3 years from now is $3709.20
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Ann is a software salesperson. Her base salary is $1900 and she makes $90 more for every copy of History is Fun she sells. Her total pay, P (in dollars), after
selling e copies is given by the following.
P=1900+90c
Answer the following questions.
(a) What is Ann's total pay if she sells 24 copies?
(b) If Ann's total pay is $4780, how many copies did she sell?
copies
Answer:
A - $4060
B - 32 copies
Step-by-step explanation:
A -
P = 1900 + 90c
P = 1900 + 90(24)
P = 1900 + 2160
P = 4060
Total if Ann sold 24 copies: $4060
B -
1900 + 90c = 4780
90c = 4780 - 1900
90c = 2880
c = 32
Total copies: 32
What number should go in the gap to factorise this expression?
6x+14= (3x+7)
The number that should go in the gap to factorise the given expression is 2
Factorizing an expressionFrom the question, we are to determine the number that should go in the gap in order to factorise the given expression.
The given expression is
6x + 14
To determine the number that should go in the gap,
First we will factorize the given expression
6x + 14
The greatest common factor (GCF) of 6 and 14 is 2
Thus,
We can factor out 2 as follows
2(3x + 7)
The factored form of the expression is 2(3x + 7)
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A quiz consists of seven multiple choicequestions. Each question has four choices.A student who forgot to study guessesrandomly on every question. What is theprobability that the student answersexactly five questions correctly?
Solution
- The probability of him getting 1 queston correctly given tahat there is only one correct option out of 4 optins,
[tex]\begin{gathered} P(correct)=\frac{1}{4} \\ \\ P(incorrect)=1-P(correct) \\ P(incorrect)=1-\frac{1}{4}=\frac{3}{4} \end{gathered}[/tex]- Since here are questions, it implies that there are multiplye trials the student has.
Write a recursive formula for the following arithmetic sequence.1, 12, -25, -38, ...a 1=an= for n ≧2
First, let's see the progression of the sequence of numbers
As you can see from the second term the sequence continues with a constant change of -13 which means d=-13.
The answers will be the expressions inside the red square box in each case.
t hits the square dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. Each side of the dartbozn, and the radius of the shaded region Is 2 in.the value 3.14 for T. Round your answer to the nearest hundredth.
Given:
Required:
To find the probability that the dart land will be in the shaded region.
Explanation:
Area of the circle is given by the formula:
[tex]A=\pi r^2[/tex]Where r = radius
Thus the area of the circular region
[tex]\begin{gathered} =(3.14)\times(2)^2 \\ =3.14\times4 \\ =12.56\text{ square in.} \end{gathered}[/tex]The area of the square is given by the formula:
[tex]=(side)^2[/tex]Thus the area of the given square
[tex]\begin{gathered} =(6)^2 \\ =36\text{ square in.} \end{gathered}[/tex]The probability of an event is given by the formula:
[tex]P=\frac{number\text{ of possible outcomes}}{Total\text{ number of outcomes}}[/tex]The probability that the dart land will be in the shaded region
[tex]=\frac{Area\text{ of the shaded region}}{Area\text{ of the square}}[/tex]Thus probability
[tex]\begin{gathered} P=\frac{12.56}{36} \\ P=0.3488 \\ P=0.349 \end{gathered}[/tex]Final answer:
Thus the probability that the dart land will be in the shaded region is 0.349.
Need help fast. Please explain how to do it set by step. Thanks.
A sequence is a series that follows the sum general rule. The sum of the given sequence ∑(n=1 to 4) [tex]u_{n}[/tex] is {u₁ + u₂ + u₃ + u₄ + u₅}.
What is a series?A sequence's series is the total number of terms in the sequence.
A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.
As per the given series, ∑(n=1 to 4) [tex]u_{n}[/tex]
The sign ∑ is used to sum the terms of the series in the given interval.
Given that n = 1 to 4
Substiute n = 1 into [tex]u_{n}[/tex] ⇒ u₁
Substiute n = 2 into [tex]u_{n}[/tex] ⇒ u₂
Substiute n = 3 into [tex]u_{n}[/tex] ⇒ u₃
Substiute n = 4 into [tex]u_{n}[/tex] ⇒ u₄
So, the sum is {u₁ + u₂ + u₃ + u₄ + u₅}.
Hence "A sequence is a series that follows the sum general rule. The sum of the given sequence ∑(n=1 to 4)".
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Question
Gloria deposited $500 into a bank account that earned 7.5% simple interest each year. She earned $225 in interest before closing the account. No money was deposited into or withdrawn from the account.
How many years was the money in the account?
Round your answer to the nearest whole year.
Enter your answer in the box.
If Gloria deposited $500 into a bank account that earned 7.5% simple interest each year and she earned $225 in interest before closing the account, then the number of years that the money in the account is 6 years
The deposited amount = $500
The simple interest = 7.5%
The interest she earned = $225
Then the final amount = The deposited amount + The interest she earned
= 500+225
= $725
The equation of simple interest
A = P(1+rt)
Where A is the final amount
P is the initial amount
r is the interest rate
t is the time period
725 = 500(1+(7.5/100)×t)
(1+0.075t) = 1.45
0.075t = 0.45
t = 0.45/0.075
t = 6 years
Hence, if Gloria deposited $500 into a bank account that earned 7.5% simple interest each year and she earned $225 in interest before closing the account, then the number of years that the money in the account is 6 years
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Factor: x(3y-5)+3(3y-15)
3xy-5x+9y-45
Step-by-step explanation:
Step by Step Solution
STEP1:STEP2:Pulling out like terms
2.1 Pull out like factors :
3y - 15 = 3 • (y - 5)
Equation at the end of step2: (x • (3y - 5)) + 9 • (y - 5) STEP3:Equation at the end of step 3 x • (3y - 5) + 9 • (y - 5) STEP4:Trying to factor a multi variable polynomial
4.1 Split 3xy-5x+9y-45
4.1 Split 3xy-5x+9y-45
into two 2-term polynomials
-5x+3xy and +9y-45
This partition did not result in a factorization. We'll try another one:
3xy-5x and +9y-45
This partition did not result in a factorization. We'll try another one:
3xy+9y and -5x-45
This partition did not result in a factorization. We'll try another one:
3xy-45 and +9y-5x
This partition did not result in a factorization. We'll try another one:
-45+3xy and +9y-5x
This partition did not result in a factorization. We'll try
Which expression is equivalent to -0.26v + v - 0.07?(answer choices are below)
To simplify the expression
-0.26v + v - 0.07
we will only add the ones with variable v
0.74v -0.07
The correct option is
0.74v - 0.07
Solve for x. Represent your answer on a number line.½x − 3 < − 4
The equation is
[tex]\frac{1}{2}x-3<-4\Rightarrow\frac{x}{2}<-4+3\Rightarrow\frac{x}{2}<-1\Rightarrow x<-2[/tex]Therefore x<-2. The number line representation is
A jet flies at an average speed of 230
miles per hour. How long will it take to
fly from New York to Amsterdam, a
distance of 3,647 miles? (distance =
rate time)
.
Answer:
15.9 hours.
Step-by-step explanation:
speed = distance / time.
230 = 3647 / time.
time = 3647 / 230.
time = 15.9 hours.
HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answer:
She worked for 4 hours and made 16 shirts (work below)
Step-by-step explanation:
let h = number of hours worked
and s = number of shirts made :]
28h+2s = 144
4h = s
28h+8h=144
h=4, s=16
:]
At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two small fries have a total ofapplication
Problem
At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two small fries have a total of 1,330 calories. How many calories does each item contain?
Solution
For this case we can set up the following notation
x= number of cheeseburgers
y= small fries
4x +5y= 2310
3x + 2y= 1330
From the first equation we can solve for x and we got:
x= 577.5 - 5/4 y
And now we can replace this into the second equation and we got:
3(577.5 -5/4 y) +2y= 1330
And we can solve for y:
1732.5 - 15/4 y + 2y = 1330
-7/4 y = -402.5
y= 230 cal
And solving now for x we have:
x= 577.5 - 5/4 (230) = 577.5 - 287.5 = 290 cal
This year for Spring break you are taking a solo trip to an exotic destination. You are deciding between two destinations: Bali, Indonesia, and Paris, France. You want to choose the destination that will give you the best value for your money.The table below shows the cost to travel to each destination Flight Hotel (pernight)Bali $967 $58Paris $534 $2551. Create an equation for each destination to represent cost, C to travel to that location based on n Number of nights.
Let n represent the number of nights
Cost to travel to Bali:
[tex]C\text{ = 967 + 58n}[/tex]The cost of flight is constant so we simply add it to the cost of hostel per night times the number of nights
Cost to travel to Paris:
[tex]C\text{ = 534 + 255n}[/tex]It costs $35 per hour to rent a boat at the lake.
You also need to a pay a $25 fee for safety equipment.
You have $200.
How long can you rent the boat?
Answer:
7 hours
Step-by-step explanation:
25x + 25 = 200.
25x = 175
175/25 = 7.
Answer:
25 + 35h = 200
and
h = 5
(5 hours)
Step-by-step explanation:
you have 200.
costs:
35 per hour
and
25 fee
h will represent the total hours spent renting a boat
25 + 35h = 200
now we will do inverse operations
subtract 25 from both sides
35h = 175
now divide both sides by 35
h = 5
What is the solution to the system?
2x+3y=1
-2x-y=9
A (-7,5)
B (5,-3)
C (5,-7)
D (-3,5)
Answer:
A
Step-by-step explanation:
Adding the equations,
[tex]2y=10 \implies y=5 \\ \\ \therefore 2x+3(5)=1 \implies x=-7[/tex]
Translate the following equation into a verbal sentence. 5(x + 4) = x - y
Answer:
Five times the quantity x plus four equals x minus y.
Step-by-step explanation:
Probably the most confusing part is that parenthesis are pronounced "the quantity"
define the domain of the following:
By identifying the first values of each point in the graph, we saw that the domain of the relationship is:
D: {-3, -1, 1, 3, 6}
How to get the domain?A relation can be defined by a set of points (x, y), where the values of x are the values in the domain and the values of y are the values in the range.
Here we have the graph of a relation, and we can see the points:
(-3, 3)(-1, -1)(1, 2)(3, 0)(6, -2)
The domain of the graphed relationship will be the set of the first values of each of these points, then we can see that the domain is:
D: {-3, -1, 1, 3, 6}
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FIND SLOPE AND Y INTERCEPT EASY QUESTION WILL GIVE BRAINLIEST ANSWERRRR HELPPP URGENT DUE IN A FEW MINUTESS
Simplify the equation 4x+9y = -9 in slope-intercept form of equation.
[tex]\begin{gathered} 4x+9y=-9 \\ 9y=-4x-9 \\ y=-\frac{4}{9}x-\frac{9}{9} \\ =-\frac{4}{9}x-1 \end{gathered}[/tex]So slope of line is -4/9 and int
What is the product 6x1,167
Answer:
7,002
Step-by-step explanation:
The product is the answer of a multiplication problem. You just have to multiply the numbers by using the techniques to solve it. Hope this helps!
hello I'm a 7th grader can u please help me with my math summer package and explain it in a way that a 7th grader can understand it..writing and. evacuating expressions
The price will increase if number of students increase
By multiplying the number of students with cost
Number of students varies in this example
The expression shown for trip amount is c = 10+13x.
The cost for 10 students is 140
The cost for 17 students is 231
What is the definition of evaluate an expression?Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.
1). The price will increase if number of students increase.
2). By multiplying the number of students with cost.
3). Number of students varies in this example.
4). Let the number of students
Then total amount(c) of the trip is given by
c = 10+13x ------ equation (1)
5). Put x = 10 in equation (1)
c = 10+13(10)
c = 140
6). Put x = 17 in equation (1)
c = 10+13(17)
c = 231
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Consider the sample space of the following experiment:We roll two dice and each time we record numbers on both of them.How many elements are in the sample space?
Answer: 36
One die has a total outcome of 6 elements (1, 2, 3, 4, 5, 6). Now, if we roll two dice, each time you roll a number on the first die, there are another 6 possible outcomes for the second die.
Therefore, the number of elements in the sample space would be:
[tex]6\times6=36[/tex]There would be 36 elements in the sample space.
Suppose you have $2750 in your savings account at the end of a certain period of time. You invested $2000 at a 4.36% simple annual interest rate. How long, in years, was your money invested ? (State your results to the nearest hundredth of a year.)
The money was invested for 8.60 years
Explanation:Given:
Amount in the savings account = $2750
Amount invested = $2000
rate = 4.36% = 0.0436
To find:
the time it took to invest the money to obtain the amount in the account
The investment was done using simple interest. So to get the time, we will apply simple interest formula
[tex]\begin{gathered} I\text{ = PRT} \\ I\text{ = interest} \\ R\text{ = rate} \\ T\text{ = time} \end{gathered}[/tex][tex]\begin{gathered} Interest\text{ = amount in the account - amount } \\ \\ Interest\text{ = 2750 - 2000} \\ \\ Interest\text{ = \$750} \end{gathered}[/tex][tex]\begin{gathered} The\text{ simple interest formula becomes:} \\ 750\text{ = 2000}\times0.0436\text{ }\times\text{ T} \\ \\ 750\text{ = 87.2T} \end{gathered}[/tex][tex]\begin{gathered} divide\text{ both sides by 87.2:} \\ T\text{ = }\frac{750}{87.2} \\ \\ T\text{ = 8.60 year} \end{gathered}[/tex]A hospital parking lot charges 3.50$ for the first hour and 1.75$ for each additional hour. what is the minimum and the maximum number of hours Jose can park his car at the carage if he can spend between 12.25$ and 19.25
Jose can park his car for the maximum time of 9 hours and the minimum time of 5 hours.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a hospital parking lot charges 3.50$ for the first hour and 1.75$ for each additional hour.
The modelled equation representing the above scenerio is -
y = 3.5 + 1.75x
where (x) represents the number of hours for which the car is parked.
Maximum amount with Jose = $19.25
Therefore -
3.5 + 1.75x ≤ 19.25
1.75x ≤ 15.75
x ≤ 9 hours [Maximum time]
Minimum amount with Jose = $12.25
3.5 + 1.75x ≥ 12.25
1.75x ≥ 8.75
x ≥ 5 hours [Minimum time]
Therefore, Jose can park his car for the maximum time of 9 hours and the minimum time of 5 hours.
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Please help:State the implied domain and range: f(x)= 1/x−4 +3
ANSWER
[tex]Domain:(-\infty,\text{ 4\rparen U\lparen4, }\infty),\text{ \textbraceleft x \mid x}4\rbrace[/tex][tex]Range:\text{ \lparen-}\infty,\text{ 3\rparen U\lparen3, }\infty),\text{ \textbraceleft y \mid y}3\rbrace[/tex]EXPLANATION
Given:
[tex]f(x)\text{ = }\frac{1}{x\text{ - 4}}+\text{ 3}[/tex]Desired Outcome:
1. Domain
2. Range
Determine the domain of the function
Note: We want to include only input values that do not require the denominator to be 0 when there is a denominator. As a result, we'll set the numerator to 0 and solve for x.
[tex]\begin{gathered} 0\text{ = x - 4} \\ x\text{ = 4} \end{gathered}[/tex]We'll now remove 4 from the domain. All of the answers are real numbers x > 4 or x < 4. We will also use Union notation to combine the two sets.
That is:
[tex]Domain:(-\infty,\text{ 4\rparen U\lparen4, }\infty),\text{ \textbraceleft x \mid x}4\rbrace[/tex]
Determine the range of the function
Set x to 4 to find y
[tex]\begin{gathered} y\text{ = }\frac{1}{4-4}\text{ + 3} \\ y\text{ = 3} \end{gathered}[/tex]We'll also remove 3 from the range. All of the answers are real numbers y > 3 or y < 3. We will also use Union notation to combine the two sets.
That is:
[tex]Range:\text{ \lparen-}\infty,\text{ 3\rparen U\lparen3, }\infty),\text{ \textbraceleft y \mid y}3\rbrace[/tex]