umm ciao anyways.........................................
6. An apartment building contains 12 units consisting
of one- and two-bedroom apartments that rent for
$360 and $450 per month, respectively. When all
units are rented, the total monthly rental is $4,950.
What is the number of two-bedroom apartments?
a) 3
b) 4
c) 5
d) 6
e) 7
* also comment your name and grade ( so I can be impressed- it doesn't have to be your real name)
Using a system of equations, the number of two-bedroom apartments is e) 7.
What is an equation?An equation is a mathematical statement that shows that two expressions are equal.
Equations are written with the equation symbol (=) to show that they enjoy equivalent relationships.
The total number of units in the apartment building = 12
Let one-bedroom apartments = x
Let two-bedroom apartments = y
x + y = 12 ...equation 1
x = 12 - y ... equation 2
The cost of one-bedroom apartments = $360 per unit
The cost of two-bedroom apartments = $450 per unit
The total monthly rental = $4,950
Let 4,950 = 360x + 450y ... equation 3
Substitute x = 12 - y in equation 2 in equation 3:
360 (12 - y) + 450y = 4,950
4,320 - 360y + 450y = 4,950
4,320 + 90y = 4,950
90y = 4950 - 4,320
90y = 630
y = 7
In equation 2, x = 12 - y
x = 12 - 7
x = 5
Check Total Monthly Rental:360x + 450y = 4,950
360(5) + 450(7) = 4,950
1,800 + 3,150 = 4,950
4,950 = 4,950
Thus, based on equivalent values, the number of two-bedroom apartments is 7, while the number of one-bedroom apartments is 5, giving a total of 12.
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Which is greater, 2 or 8 ?
Answer:
8
Step-by-step explanation:
Counting up from 1 to 10 you go:
1 2 3 4 5 6 7 8 9 10
As you can see the eight is further to the right meaning it has more value.
(I did this for the points)
8. My proof is the number line (I'm also doing this for points pff) 2<8
Stella rewrites -2 1/2 plus 3.7 using commutative Property of addition. Which expression did she write?
The rule for the commutative property of addition is:
a + b = b + a
Stella writes:
[tex]-2\frac{1}{2}\text{ plus 3.7}[/tex]This can be expressed mathematically as:
[tex]-2\frac{1}{2}+3.7[/tex]Which according to the property of commutativity can also be written as:
[tex]\begin{gathered} 3.7\text{ + (-2}\frac{1}{2}) \\ 3.7\text{ - 2}\frac{1}{2} \end{gathered}[/tex]The expression Stella wrote based on the commutative property of addition is therefore:
[tex]\begin{gathered} -2\frac{1}{2}+\text{ 3.7 or} \\ 3.7\text{ - 2.5 (Note that 2}\frac{1}{2}=2.5) \end{gathered}[/tex]Find the average rate of change of the following function on the given interval. y=5^x on [0,2]
To find the rate of change within this interval, we have
[tex]\begin{gathered} \text{ Rate of change =}\frac{f(2)-f(0)}{2-0} \\ =\frac{25-0}{2-0} \\ =\frac{25}{2} \\ =12.5 \end{gathered}[/tex]Hence, the average rate of change of the function within the interval
[0,2] is 12.5
Select all of the stories that can be represented by the equation.If none of the stories can be represented, select "None of the above".(a) 40x-20= 620
The correct answers are the first and fourth options
Here, we want to select all stories that goes in line with the equation
a) This can be represented
By multiplying x which is the cost of one training hour by the number of hours which is 40;and subtracting the one-time discount, we can get the or equate to the total paid
b) This cannot be represented
In this case, 20 multiplied by x would give the total amount to be paid after which we can deduct the discount
c) This cannot be represented
It multiplies the charge x by the 20 training hours would give 20x; less the discount of $40 would give 620
d) This can be represented
This narrative is similar to what we have at the first option since the total cost would be 40x and less the discount of $20 would give the after discount payment amount
21. The table below describes a sample of 15 players in Major League Baseball, chosen from the starting lineups of teams in 2019. The table shows the team, age, position, height, and salary for each player, as well as several statistics from that season. These include the number of games they played (G), their batting average (AVE) (the proportion of their at-bats for which they got a hit), and their home runs (HR).NameTeamAgeHeightGAVEHRSalaryCedric MullinsOrioles25173 cm22.0940$557,500Tim AndersonWhite Sox26185 cm123.33518$1,400,000Christin StewartTigers25183 cm104.23310$556,400Alex GordonRoyals35185 cm150.26613$20,000,000Jonathan SchoopTwins27185 cm121.25623$7,500,000Marcus SemienAthletics29183 cm162.28533$5,900,000Yandy DiazRays28188 cm79.26714$558,400Randal GrichukBlue Jays28188 cm151.23231$5,000,000Josh DonaldsonBraves33185 cm155.25937$23,000,000Joey VottoReds36188 cm142.26115$25,000,000Cody BellingerDodgers24193 cm156.30547$605,000Ryan BraunBrewers35188 cm144.28522$19,000,000Maikel FrancoPhillies27185 cm123.23417$5,200,000Ian KinslerPadres37183 cm87.2179$3,750,000Marcell OzunaCardinals28185 cm130.24129$12,250,000Calculate the Five Number Summary for the number of games played by the players.Min: Q1 : Median: Q3 : Max:
Given:
The number of games played by 15 players are,
22, 123, 104, 150, 121, 162, 79, 151, 155, 142, 156, 144, 123, 87, 130.
The objective is to find five number summary for the number of games.
Explanation:
The five number summary are minimum value, quartile 1, median, quartile 2 and maximum value.
Increasing order:
The increasing order of the given data is,
22, 79, 87, 104, 121, 123, 123, 130, 142, 144, 150, 151, 155, 156, 162.
Minimum and Maximum value:
By considering the increasing order of the data, the minimum value is 22 and the maximum value is 162.
To find median:
The median can be calculated as the middle term of total number of data.
Since, the total number of data is 15, which is odd, then the median can be calculated as,
[tex]\begin{gathered} \text{Median}=\frac{15+1}{2} \\ =\frac{16}{2} \\ =8th\text{ term} \end{gathered}[/tex]Thus, the 8th term of increased order is 130.
To find Q1:
The quartile 1 can be defined as the middle term of the left side of the median.
Since, the left side of the median contains 7 terms, which is odd, then the quartile 1 can be calculated as,
[tex]\begin{gathered} Q1=\frac{7+1}{2} \\ =\frac{8}{2} \\ =4th\text{ term (left)} \end{gathered}[/tex]Thus, the 4th term on left side of median is 104.
To find Q3:
The quartile 3 can be defined as the middle term of the right side of the median.
Since, the right side of the median contains 7 terms, which is odd, then the quartile 3 can be calculated as,
[tex]\begin{gathered} Q3=\frac{7+1}{2} \\ =\frac{8}{2} \\ =4th\text{ term (right)} \end{gathered}[/tex]Thus, the 4th term on right side of median is 151.
Hence, the five number summary are,
Min: 22
Q1: 104
Median: 130
Q3: 151
Max: 162.
Write the algebraic expression representing the perimeter of marlene’s house in simples form.
The perimeter of Marlene's house is the total distance around the edge of her house.
The perimeter can be calculated thus:
[tex]\begin{gathered} (2x-10)+(x-2)+(\frac{1}{2}x-4)+(x-2)+(x-2)+(x)+(2x+2)+ \\ (\frac{1}{2}x-4)+(x-2)+(x-2)+(x) \end{gathered}[/tex]Collect like terms
[tex]\begin{gathered} (2x+x+\frac{1}{2}x+x+x+x+2x+\frac{1}{2}x+x+x+x)\text{ +} \\ (-10-2-4-2-2+2-4-2-2) \\ =12x-26 \end{gathered}[/tex]Therefore, the algebraic expression representing the perimeter of Marlene's house is
[tex]12x-26[/tex]g(x)=4f(x)=×^2-5find (g+f)(n)
g(x)=4
f(x)=×^2-5
(g+f)(n)
Add both equations and replace x by n
(g+f) (n) = n^2-5+4 = n^2-1
Find the value of 5y - 6 given that -4y - 7= 9. Simplify your answer as much as possible.
Given that:
[tex]-4y-7=9[/tex]We are told to find 5y - 6
Solving for y
[tex]-4y-7=9[/tex]Add 7 to both sides
[tex]\begin{gathered} -4y-7+7=9+7 \\ -4y+0=16 \\ -4y=16 \end{gathered}[/tex]Divide both sides by -4
[tex]\begin{gathered} \frac{-4y}{-4}=\frac{16}{-4} \\ y=-4 \end{gathered}[/tex]Let us now solve for 5y - 6 by substituting y = -4
[tex]\begin{gathered} 5y-6 \\ 5(-4)-6 \\ -20-6=-26 \\ \therefore5y-6=-26 \end{gathered}[/tex]Hence,
[tex]5y-6=-26[/tex]Choose the equation that satisfies the data in the table. in pic
Question:
Solution:
Note that if we evaluate x = -1, 0, and x=1 in the last equation we get:
y = 3(-1)+ 3 = -3+3 = 0
y = 3(0)+3 = 3
y = 3(1)+3 = 6
So that, we can conclude that the correct solution is
D. y =3x + 3
The Associative Property applies to which operations? Check all that apply. A. divideb -c.xD+
C) x
D)+
Explanation
The assoaciative property states that when three or more are added (or multiplied), the sum (or the ) is the same regardless of the grouping of the multiplicands
[tex]\begin{gathered} a\cdot(b\cdot c)=(a\cdot b)\cdot c \\ a+(b+c)=(a+b)+c=(a+c)+b \end{gathered}[/tex]Associative property can only be used with addition and multiplication and not with subtraction or division
so, the answer is
C) x
D)+
An amusement park is creating signs to indicate the velocity of a roller coaster car on certain hills of the most popular ride. A roller coaster gains kinetic energy as itgoes down a hill. The velocity of an object in kilometers per hour kph) can be determined by Vwherekes the kinetic energy of the object in joulesand is the mass of the object in kilogramskeA roller coaster car has a mass of 350 kg and the car has a kinetic energy of 437.500 on the first hill. What velocity does the car obtain on the first hill?
Answer
v = 180 kph
Velocity of the car on the first hill = 180 kph
Explanation
The kinetic energy of a body is given as
K.E = ½ mv²
For this question,
K.E = Kinetic Energy = 437,500 J
m = mass = 350 kg
v = velocity = ?
K.E = ½ mv²
Making v the subject of formula,
v = (2K/m)^(½)
K.E = ½ mv²
437,500 = ½ (350) v²
437,500 = 175v²
We can rewrite this as
175v² = 437,500
Divide both sides by 175
(175v²/175) = (437,500/175)
v² = 2500
We can then take the square root of both sides
√(v²) = √(2500)
v = 50 m/s
To convert this to kilometer/hour or kph, we need to note that
1,000 meters = 1 km
3600 s = 1 hour
[tex]\begin{gathered} v=\frac{50m}{s} \\ v=50\frac{m}{s}\times\frac{1\operatorname{km}}{1000m}\times\frac{3600s}{1hr} \\ v=180\text{kph} \end{gathered}[/tex]Hope this Helps!!!
Find the values of x and y. (90 - 4y)° (50 - 2x)° (х +5y)° (2x+3y)°
1) According to the Vertical angle Theorem
We can state that
50-2x =90-4y
-2x +4y=90
2x -4y = -90
In addition to that, since those three angles make up a straight angle:
2x +3y + x +5y +50 -2x = 180º Combine like terms
x+6y =180º
2) Now, we can set this linear system:
x +6y = 180 x-2 To eliminate x
2x -4y = -90
-2x -12y =-360
2x -4y = -90
----------------
-16y = -450
16y= 450
y = 28.12
y ≅ 28
x + 6(28)=180
x+168=180
x=12
One simple method to predict adult height is to average the parents’ heights in inches and then add 2.5 inches if the child is a boy or subtract 2.5 inches if the child is a girl. This method can be fairly accurate, but can also be as much as 5 inches above or below the child’s eventual height.Use the variable D, which means height of dad and M, which means height of mom1. Write the formula for a boy’s adult height.(5 points) 2. Write the formula for a girl’s adult height.(5 points)
We are given that a boy's height is predicted by adding 2.5 inches to the average of the height of the parents. If "D" is the height of the father and "M" is the height of the mother then the average is determined by adding the two heights together and dividing by 2, like this:
[tex]\frac{D+M}{2}[/tex]Since the height of the boy is determined by adding 2.5 inches to this average, this means that the height of the boy "B" is:
[tex]B=\frac{D+M}{2}+2.5[/tex]The height of a girl "G" is determined by subtracting 2.5 to the average, therefore we have:
[tex]G=\frac{D+M}{2}-2.5[/tex]2. BANKING Brayden deposited $2700 into a savings account that has an annual
simple interest rate of 0.3%. Find the amount in the savings account after each
number of years.
se notes
a. 2 year
b. 3 years
s
c. 6 years
Answer:
a) $2716.20
b) $2724.30
c) $2748.60
Step-by-step explanation:
You want the account balance after 2, 3, and 6 years if $2700 is deposited into an account earning 0.3% simple interest.
BalanceThe value of an investment P earning simple interest at rate r for t years is given by ...
A = P(1 +rt)
For the given savings deposit, the balance will be ...
A = 2700(1 +0.003t) . . . . . for t = 2, 3, 6
Another way to write this is ...
A = 2700 + 8.10t
The balances are ...
2 years: $2716.203 years: $2724.306 years: $2748.60<95141404393>
An organism is losing half of its weight each day. The function y=(0.5)^x represents the percent (in decimal form) of the original weight of the organism. where x is the number of days since the organism began to lose weight A. Describe the domain and range of the function. Then graph the function.B. Find and interpret the y interceptC. What percent (in decimal form) of the original weight does the organism weigh on the 5th day?
the domain of this function is:
[tex]x\in\lbrack0,\infty)[/tex]because we count the days.
The range is
[tex]y\in(0,1_{}\rbrack[/tex]because the maximum value of the percentage of wait is 100% = 1
the y- intercept in this case is when the organism has not lose any weight. So the percentage of weight is 100% (1 in decimal form)
after 5 days we get
[tex]0.5^5=0.03125[/tex]If you roll a standard six-sided die, what is the probability that you get a 1 or 5? Give your answer as a simplified fraction.
Step 1: Theorem
[tex]\text{Probability of an event = }\frac{N\text{umber of required outcome}}{N\text{umber of sample space}}[/tex]Step 2: Given data
Sample space = { 1, 2, 3, 4, 5, 6}
Number of sample space = 6
Event space = {1, 5}
Number of event space = 2
Step 3: Substitute to find the probability that you get 1 or 5
[tex]\begin{gathered} \text{Probability that you get 1 or 5 = }\frac{2}{6} \\ =\text{ }\frac{1}{3} \end{gathered}[/tex]Answer: 1/3
There are 6 sides. Both of those numbers are two numbers, so it would be 2/6. To simplify it, divide the top and the bottom by the same number. I divided both the numerator and the denominator by 2.
then, your answer would be 1/3
Determine the restriction of x using inequality. Show your work.
The sides of a triangle rule states that the sum of the lenghts of the sides of a triangle has to be greater than the lenght of a third side.
4x+2 +8 >18
x>2
4x+2+18>8
x>-3 (reject)
Answer: x>2
D Suppose you are asked to write an equation of the form y = mx + b to
represent a linear function. What is your strategy for each situation?
1. You are given a description of the function in words.
2. You are given two or more (x, y) values or a table of (x, y) values.
3. You are given a graph showing points with coordinates.
HELP PLS this is my homework for tomorrow
What are the different strategies used to write an equation of the slope-intercept form y = mx + b to represent a linear function?
1. When given a description of the function in words.
The y intercept can be represented by b The slope can be represented by m The point through which the line passes is given by (x, y).So, the equation in the slope-intercept form of a linear function is given by y = mx + b.2. When given two or more (x, y) values or a table of (x, y) values.
The two or more (x, y) values are the coordinates which should be used to find slope m using the formula [tex]m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].Substituting the values of m and (x, y) in the equation y =mx+ b , find y intercept b.Substitute the values of m and y intercept b in the equation.So, the equation in the slope-intercept form of a linear function is given by y = mx + b.3. When given a graph showing points with coordinates.
In a graph with coordinates (x, y) given ,find slope m using the formula [tex]m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]. Substitute the values of slope m and coordinates (x, y) in the linear equation y =mx+ b so as to find y intercept b. Substitute the values of m and y intercept b in the equation .So, the equation in the slope-intercept form of a linear function is given by y = mx + b.To learn more about slope-intercept form, refer:
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what is the relation ships for 1 2 3 4 5 and n please help
To find the relationship you:
1. The relation can be the difference between every term in the sequence:
In the first sequence you have between every term a diferencen of:
Where n is the term
Youn can notice that the relationship is the way you get that term and is equal to the previous term plus an odd number (3,5,7,9), as the sequences do not have a constant difference the sequence is a non-regular succession. But as the set of differences (1,3,5,7,9) Follows a regular succesion of (2n-1) you have quadratic sequences that have the next formula:
1. First sequence:
[tex]n^2+10[/tex]2. Second sequence:
[tex]n^2-4[/tex]I need help with this question. The graph below is option a. I have options to choose from
In this type of exercise ≥ values mean values that are inside the 'area' that the function is determining.
So the correct answer can only be now A or C because B and D are 'outside' areas.
In the letter A we can choose a point to validate the function. Let's choose the point (6,-4):
[tex]y\ge x^2-7x+10[/tex][tex]-4\ge6^2-7\times6+10[/tex][tex]-4\ge36-42+10[/tex][tex]-4\ge4\text{ !!!}[/tex]Look that this result is impossible. -4 is not greater than 4. This invalidate letter A! Therefore the correct answer will be the letter C.
please help me please help me
Answer:
Only did for Problem 1:
Square is: 4x^2-20x+25
Side is: 2x-5
A^2=4
2AB=-20
B^2=25
Step-by-step explanation:
Tickets to the museum cost 7.50 and there is a 15% discount
the cost of the ticket is 7.50
discount is 15 %
so the value of the discount is,
[tex]\begin{gathered} =7.50\times\frac{15}{100} \\ =1.125 \end{gathered}[/tex]so the price of the ticket is 7.50 - 1.125 = 6.375
Actual cost is 6.375
what are the x and y-intercepts of the line described by the equation? 3x - 9y = 10.8A) x-intercept = 1.2 y-intercept = 3.6B) x-intercept = -3.6 y-intercept = 1.2C) x-intercept = 1.2y-intercept -3.6D) x-intercept = 3.6 y-intercept = -1.2
we have the equation
3x - 9y = 10.8
Remember that
x-intercept ----> value of x when the value of y is zero
so
For y=0
substitute
3x-9(0)=10.8
3x=10.8
x=3.6
y-intercept -----> is the value of y when the value of x is zero
For x=0
3(0)-9y=10.8
-9y=10.8
y=-1.2
therefore
the answer is option DA football field is 1920 inches wide. What is two thirds of a football field?
Answer:
2/3's of a football field is 1280
Step-by-step explanation:
were going to take 1920 and were going to divide that by 3.
1920/3 = 640
After that your going to multiply 640 by 2
640(2) = 1280
So your answer is 1280
Two piecewise functions are shown below. What is the value of 6f * (- 2) + 3g * (1) ?
To find the value of f(-2), we replace x = -2 into the second piece of the function. Then, we operate.
[tex]\begin{gathered} f(-2)=\frac{1}{3}(-2)^3 \\ f(-2)=\frac{1}{3}(-8) \\ f(-2)=-\frac{8}{3} \end{gathered}[/tex]Second partTo find the value of g(1), we replace x = 1 into the first piece of the function. Then, we operate.
[tex]\begin{gathered} g(1)=2|1-1|+3 \\ g(1)=2|0|+3 \\ g(1)=2\cdot0+3 \\ g(1)=0+3 \\ g(1)=3 \end{gathered}[/tex]Finally, we find the value of the given expression:
[tex]\begin{gathered} 6f(-2)+3g(1)=6\cdot-\frac{8}{3}+3\cdot3 \\ 6f(-2)+3g(1)=-\frac{6\cdot8}{3}+9 \\ 6f(-2)+3g(1)=-\frac{48}{3}+9 \\ 6f(-2)+3g(1)=-16+9 \\ 6f(-2)+3g(1)=-7 \end{gathered}[/tex]
Function f is represented by f(x) = 3(x + 4). Find the value of x such that
f(x) = 39
Answer:
x = 9
Step-by-step explanation:
[tex]3(x + 4) = 39[/tex]
[tex]x + 4 = 13[/tex]
[tex]x = 9[/tex]
A civil air patrol unit of fifteen members includes three officers. In how many ways can three members be selected for a search and rescue mission such that at least one officer is included
The three members be can selected in 455 ways.
What in mathematics is a combination?
Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
The officers can be selected in 15C3 ways.
15c3
=15!/(15-3)! . 3!
After calculating get that,
= 5 x 7 x 13
=455
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Members of a band estimated that 200
people were at their show last night. Their manager told them that 227
people had actually been at the show. What was the band's percent error?
Answer:
13.5%
Step-by-step explanation:
Using the percent error formula,
[tex]\frac{227-200}{200}=13.5\%[/tex]
Perform the indicated operation by removing the parentheses and combining like terms.(-2x2 + 5) + (6x2 + 7)
Given the expression:
[tex]\mleft(-2x^2+5\mright)+(6x^2+7)[/tex]Removing the parentheses and combining like terms.
[tex]\begin{gathered} =-2x^2+5+6x^2+7 \\ =-2x^2+6x^2+5+7 \\ \\ =4x^2+12 \end{gathered}[/tex]so, the answer will be:
[tex]4x^2+12[/tex]Answer 733
Step-by-step explanation:
