a)) A 55 m long and 35 m broad park is surrounded by a 2.5 m wide
(i) Find the area of the path.
Answers
Answer:
Area of the path is 475 m².
Step-by-step explanation:
Let us first draw the diagram for the given question.
Here rectangle ABCD represents a park whose length is 55 m and breadth is 35 m. The shaded portion shows the path all around the park whose width is 2.5 m.
Now, length of rectangle ABCD, l = 55 m
breadth of rectangle ABCD, B = 35 m
Now, width of the path = 2.5 m
So, length of rectangle PQRS, L = 55 + 2.5 + 2.5 = 60 m
breadth of rectangle PQRS, B = 35 + 2.5 + 2.5 = 40 m
Now, to calculate the area of shaded portion or the area of the path, we will subtract the area of the park or area of rectangle ABCD from the area of rectangle PQRS.
Now, area of rectangle PQRS, A₁ = L × B = 60 × 40 = 2400 m²
Area of rectangle ABCD, A₂ = l × b = 55 × 35 = 1925 m²
So, area of the path = A₁ - A₂ = 2400 - 1925 = 475 m²
Hence the area of the path is 475 m².
Related Questions
WILL GIVE BRAINLYLIST !!!!! IF UNDER 5 MINSSSS HELPThe cost of 10 cupcakes at a cake stand is $40. Which graph shows the cost of different numbers of cupcakes at the cake stand?
The first quadrant of a coordinate grid is drawn. The title is Cake Stand. The horizontal axis label is Number of Cupcakes, and the scale is from 0 to 8 in increments of 1. The vertical axis label is Cost in dollars, and the scale is from 0 to 32 in increments of 4. Points are plotted at the ordered pairs 1,8 and 2,12 and 3,16.
The first quadrant of a coordinate grid is drawn. The title is Cake Stand. The horizontal axis label is Number of Cupcakes, and the scale is from 0 to 8 in increments of 1. The vertical axis label is Cost in dollars, and the scale is from 0 to 32 in increments of 4. Points are plotted at the ordered pairs 1,2 and 2,4 and 3,6.
The first quadrant of a coordinate grid is drawn. The title is Cake Stand. The horizontal axis label is Number of Cupcakes, and the scale is from 0 to 8 in increments of 1. The vertical axis label is Cost in dollars, and the scale is from 0 to 32 in increments of 4. Points are plotted at the ordered pairs 1,4 and 2,4 and 3,4.
The first quadrant of a coordinate grid is drawn. The title is Cake Stand. The horizontal axis label is Number of Cupcakes, and the scale is from 0 to 8 in increments of 1. The vertical axis label is Cost in dollars, and the scale is from 0 to 32 in increments of 4. Points are plotted at the ordered pairs 1,4 and 2,8 and 3,12.
Answers
Answer:
I have to say the first one sorry responded late
GIVE BRAINIEST:
plz give me brainliest i almost got caught in class WHILE HELPING!!!
Answer:
i think its the first one
Step-by-step explanation:
A frequency table grades have five classes (A,B,C,D,F) with frequencies of 5,11,14,7, and 3 respectively. Using percentages, what are the relative frequencies of the five classes
Answers
The relative frequencies using percentages are as follows:
A => 12.5%
B => 27.5%
C => 35%
D => 17.5%
E => 7.5%
Step-by-step explanation:
To find the relative frequency, the specific frequency is divided by the total frequency. To find in the percentages, the division is multiplied by 100
So,
Total frequencies = 5+11+14+7+3 = 40
So,
[tex]Relative-frequency\ of\ A = \frac{5}{40} *100\\= 0.125*100\\=12.5\%\\Relative-frequency\ of\ B = \frac{11}{40} * 100\\= 0.275*100\\=27.5\%\\Relative-frequency\ of\ C = \frac{14}{40} * 100\\=0.35*100\\=35\%\\Relative-frequency\ of\ D = \frac{7}{40} * 100\\=0.175*100\\=17.5\%\\Relative-frequency\ of\ E= \frac{3}{40} * 100\\=0.075*100\\=7.5\%[/tex]
Hence,
The relative frequencies using percentages are as follows:
A => 12.5%
B => 27.5%
C => 35%
D => 17.5%
E => 7.5%
Keywords: Frequency, relative frequency
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The relative frequencies of the five classes are 12.5%, 27.5%, 35%, 17.5%, 7.5%.
Given thatA frequency table grades have five classes (A, B, C, D, F) with frequencies of 5,11,14,7, and 3 respectively.
We have to determine
Using percentages, what are the relative frequencies of the five classes.
According to the questionThe relative frequency, the specific frequency is divided by the total frequency.
The sum of all the frequencies is called relative frequency.
= 5 + 11 +14 +7 +3 = 40
Then,
The relative frequency of the first class is,
[tex]= \dfrac{5}{40} \times 100\\ \\ = 0.125 \times 100\\ \\ =12. 5 \rm \ Percent[/tex]
The relative frequency of the second class is,
[tex]= \dfrac{11}{40} \times 100\\ \\ = 0.275 \times 100\\ \\ =27. 5 \rm \ Percent[/tex]
The relative frequency of the third class is,
[tex]= \dfrac{14}{40} \times 100\\ \\ = 0.35 \times 100\\ \\ =35 \rm \ Percent[/tex]
The relative frequency of the fourth class is,
[tex]= \dfrac{7}{40} \times 100\\ \\ = 0.175 \times 100\\ \\ =17. 5 \rm \ Percent[/tex]
The relative frequency of the fifth class is,
[tex]= \dfrac{3}{40} \times 100\\ \\ = 0.075 \times 100\\ \\ =7. 5 \rm \ Percent[/tex]
Hence, the relative frequencies of the five classes are 12.5%, 27.5%, 35%, 17.5%, 7.5%.
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On a scale drawing, a helicopter is 2.3 feet long. The scale on the drawing shows a ratio of 1 foot to 10 feet. What is the actual length of the helicopter, in feet?
PLEASE HELPP !!!!!!!
Answers
Answer:
The actual length of the helicopter is 23 feet.
Step-by-step explanation:
Given:
On a scale drawing, a helicopter is 2.3 feet long.
The scale on the drawing shows a ratio of 1 foot to 10 feet.
Now, to find the actual length of the helicopter.
Let the actual length of helicopter be [tex]x[/tex].
On scale drawing length of helicopter = 2.3 feet.
The scale on the drawing shows a ratio = 1:10.
Now, as ratios are given so by setting proportion we solve it:
[tex]\frac{2.3}{x} =\frac{1}{10}[/tex]
By cross multiplying we get:
⇒ [tex]2.3\times 10=x[/tex]
⇒ [tex]23=x[/tex]
⇒ [tex]x=23\ feet.[/tex]
Therefore, the actual length of the helicopter is 23 feet.
Find a polynomial, which if substituted for M will make the equation an identity: a M–(4ab–3b2)=a2–7ab+8b2
Answers
Answer:
a² – 3ab + 5b²
Step-by-step explanation:
M – (4ab – 3b²) = a² – 7ab + 8b²
M = a² – 7ab + 8b² + 4ab – 3b²
M = a² – 3ab + 5b²
Answer:
image
Step-by-step explanation:
image
100 POINTS!!!!
Alexis runs a small business and creates recordings of her friend’s skateboard stunts. She puts the recordings onto Instagram. She currently has 100 Instagram followers. If the number of followers grows at a rate of 1% every 12 hours. The following function represents this situation.
f(x) = f(1. + r)^t where f is the number of initial followers and r is the grown rate and t is time.
2) Alexis hopes to eventually have 1,000,000 followers, how long will it take her to reach this level of followers.
#Days since upload 0 10 20 50 100 300 500
Number of Instagram followers
Answers
There is no specific requirement in the question, but I'm assuming you need to compute the time needed for Alexis reach 1,000,000 Instagram followers
Answer:
[tex]t= 462.82\ days[/tex]
Step-by-step explanation:
Exponential Growth
When the number of observed elements grows as the previous value multiplied by a constant ratio, we have exponential growth. The formula to model such situations is
[tex]\displaystyle f(x) = f_o(1 + r)^t[/tex]
Where [tex]f_o[/tex] is the initial value of f, 1 + r is the constant ratio, and t is the time expressed in half days (12 hours)
The initial value is 100 Instant followers, thus:
[tex]\displaystyle f(x) = 100(1.01)^t[/tex]
We need to know when the number of followers will reach 1,000,000. Setting up the equation
[tex]\displaystyle 100(1.01)^t=1,000,000[/tex]
Simplifying by 100
[tex]\displaystyle (1.01)^t=10,000[/tex]
Taking logarithms
[tex]\displaystyle t\ log(1.01)=log\ 10,000[/tex]
[tex]\displaystyle t\ log(1.01)=4[/tex]
Solving for t
[tex]\displaystyle t=\frac{4}{log(1.01)}=925.63[/tex] periods of 12 hrs
[tex]t= 462.82\ days[/tex]
Alexis will reach 1,000,000 followers in approximately 462.82 days.
To calculate how long it will take Alexis to reach 1,000,000 followers, we can use the following equation:
f(t) = f(1+r)^t
We know that Alexis currently has 100 followers (f=100), and she wants to reach 1,000,000 followers (f=1,000,000). We also know that her follower growth rate is 1% every 12 hours (r=0.01).
To solve for the time (t) it will take Alexis to reach 1,000,000 followers, we can use the following steps:
Divide both sides of the equation by f(1+r):
f(t)/f(1+r) = (1+r)^t
Take the natural logarithm of both sides of the equation:
ln(f(t)/f(1+r)) = t * ln(1+r)
Divide both sides of the equation by ln(1+r):
t = ln(f(t)/f(1+r)) / ln(1+r)
Substitute the known values into the equation:
t = ln(1,000,000/100) / ln(1+0.01)
Solve for t:
t = 462.82 days
Therefore, it will take Alexis approximately 462.82 days to reach 1,000,000 followers.
For such more questions on approximately
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Can somebody please help me
Answers
Answer:
a = 5
Step-by-step explanation:
3(a - 4) + 1 = 9 - a Distribute the 3 into a-4
3a - 12 + 1 = 9 - a Combine like terms
[-12 and 1]
3a - 11 = 9 - a Add 11 to both sides to isolate 3a
+11 +11
3a = 20 - a Add a to remove it and have all a
+a +a
4a = 20 Divide by 4 to only have a
/4 /4
a = 5
Hi there! The answer should be a = 5. I have included an image with the process. Hope this helps for future reference!
P.S. It is okay with me if you save the image for help later. :)
What is the solution to the equation 4x + 2(x − 3) = 3x + x − 12? (1 point) Group of answer choices −3 −1 1 3
Answers
Answer:
-3
Step-by-step explanation:
[tex]4x + 2(x-3) = 3x + x-12\\4x+2x-6=4x-12\\2x=-6\\x=-3[/tex]
$23,803 is invested, part at 8% and the rest at 5%. If the interest earned from the amount invested at 8% exceeds the interest earned from the amount invested at 5% by $357.89, how much is invested at each rate? (Round to two decimal places if necessary.)
Answers
Answer:
The amount invested at 8% is $11,908 and the amount invested at 5% is $11,895
Step-by-step explanation:
Let
x ----> the amount invested at 8%
(23,803-x) ----> the amount invested at 5%
Remember that
[tex]8\%=8\100=0.08[/tex]
[tex]5\%=5\100=0.05[/tex]
we know that
The interest earned from the amount invested at 8% is equal to the interest earned from the amount invested at 5% plus $357.89
so
The linear equation that represent this situation is
[tex]0.08x=0.05(23,803-x)+357.89[/tex]
solve for x
Apply distributive property right side
[tex]0.08x=1,190.15-0.05x+357.89[/tex]
Group terms
[tex]0.08x+0.05x=1,190.15+357.89[/tex]
Combine like terns
[tex]0.13x=1,548.04[/tex]
[tex]x=\$11,908[/tex]
[tex]\$23,803-x=\$23,803-\$11,908=\$11,895[/tex]
therefore
The amount invested at 8% is $11,908 and the amount invested at 5% is $11,895
Lettuce is packaged four bags to a box.if there are 3.5 boxes of lettuce in the cooler, how many bags of lettuce would there be
Answers
Answer:
14 bags
Step-by-step explanation:
multiply 4*3.5 to get 14
A recipe calls for 24 ounces of oil and 8 ounces of vinegar. Kim is making dressing with 12 ounces
of vinegar using the same ratio of oil to vinegar
How much oil should kin use?Complete the Table
Answers
Answer:
36 ounces
Step-by-step explanation:
The common relationship between 24 ounces and 8 ounces is that 8 times x= 24.
24 divided by 8 is 3. Applying this same technique, we can figure out that 12 times 3 is 36.
Answer: 36 oz of oil
Ratio of oil to vinegar: 3:1
Step-by-step Explanation:
1) The oil to vinegar ratio of the recipe is calculated my dividing the amount of oil (oz) by the amount of vinegar (oz)
24 ÷ 8 = 3
This 3 means you have 3 parts oil for every 1 part vinegar, ratio being: [tex]\frac{3}{1}[/tex]
2)
[tex]\frac{3}{1}[/tex] ⇒ [tex]\frac{?}{12}[/tex]
To get the denominator from 1 to 12 you must multiply by 12.
You must do the same to the numerator (top of fraction) meaning you mus multiply 3 (The ratio's nominator) by 12.
3 × 12 = 36
3)
The answer is 36 oz of oil
Answer Check:
To Check answer you can do 36 ÷ 12
And if it equals 3 than we know that the ounces of oil (36) over the ounces of vinegar (12) give us a ratio of 3:1 Which is the same ratio as used in the recipe. (24:8)
This is a simplified method of this problem.
whar is 10.034 rounded to the nearest tenth
Answers
Answer: 10.0
Step-by-step explanation: In this problem, we are asked to round 10.034 to the nearest tenth. It's important to understand that the tenths place is 1 place to the right of the decimal point. So the digit in the rounding place is 0.
Next, look at the digit to the right of the rounding place which in this case is 3. Since the digit to the right of the rounding place, 3, is less than 5, we round down.
This means that the digit in the rounding place, 0, stays the same and we change all digits to the right of the rounding place to 0.
So 10.034 rounded to the nearest tenth is 10.000 or just 10.0 since we can drop zeroes at the end of a decimal.
Solve the linear equation, 2x+4=14
Answers
In this question, you would be solving for x.
Solve for x:
2x + 4 = 14
Subtract 4 from both sides
2x = 10
Divide both sides by 2
x = 5
Answer:
x = 5
If the date of the second Thursday of the month is a perfect square, what is the date of the last Monday of the month?
Answers
Answer:
last Monday is 27
Step-by-step explanation:
perfect square: 4, 9 , 16
2nd Thursday is a day >5 and < 14 day from the begining of the month, therefore the only day fit the criteria is 9th of the month.
last Monday is 27
Sun Mon Tue Wen Thu Fri Sat
9 10 11
12 13 14 15 16 17 18
.........................................................
26 27
To find the date of the last Monday of the month, calculate the number of days between the second Thursday and the last Monday by considering the number of weeks in the month.
Explanation:To find the date of the last Monday of the month, we need to determine the number of days between the second Thursday and the last Monday.
Let's assume that the second Thursday is on the 9th of the month.
Since there are 7 days in a week, the last Monday will be 9 + (7 * (number of weeks in the month) - 1).
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I REALLY NEED HELP ON MY EXAM! 10PTS
Determine if the ordered pair (−1, −5) is a solution to the inequality y is less than or equal to negative three fourths times x minus 1.
No, because (−1, −5) is above the line
Yes, because (−1, −5) is below the line
No, because (−1, −5) is on the line
Yes, because (−1, −5) is on the line
Answers
Yes, because (−1, −5) is below the line
Explanation:The statement says:
y is less than or equal to negative three fourths times x minus 1:
[tex]y\leq -\frac{3}{4}x-1[/tex]
To know whether (−1, −5) is a solution to the inequality, let's substitute x and y-values into the inequality:
[tex]y\leq -\frac{3}{4}x-1 \\ \\ -5\leq -\frac{3}{4}(-1)-1 \\ \\ -5\leq -\frac{1}{4} \\ \\ -20\leq -1 \ True![/tex]
Given that the point lies on the shaded region, which is below the line, then the correct statement is:
Yes, because (−1, −5) is below the line
The graph of this problem is shown below.
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Help!!!!
CR #16 1. Roger is paid $50 to sell videos of a play to an audience after the play is
performed.
He also receives $2 for each video he sells. The function E(v)=50+2v
models the amount of money Roger earns by selling v videos. The play's audience
consists of 230 people and each audience member buys no more than 1 video.
What is the practical domain of the function? (1 Point) Show how you
determined/defined the practical domain. (Explain/show your process as if you were
teaching someone else how to do the work. (3 Points) What is the most that Roger
can earn? (1 Point)
Answers
Answer:
Practical Domain is the set of x values which are from zero to 230.
The maximum he can earn is $510.
Step-by-step explanation:
Domain is the set of x values. In this equation it is the number of videos sold that could be between zero and 230 ( considering the maximum number of people buying videos are 230).
It can be written as v lies between zero and 230 or in other words [0,230].
The maximum he can earn is
E(v)=50+2v
E(230)=50+2(230)
50+ 460= 510$
solve 4x + 18=24 what is x equal to
Answers
Answer:
x=3/2
Step-by-step explanation:
4x+18=24
4x=24-18
4x=6
x=6/4
simplify
x=3/2
Answer: 4x+18=24
First move 18 to other side (24-18), left with 4x=6
Divide both sides by 4 to be left with x=6/4 & reduce that fraction down to 3/2
Step-by-step explanation:
Factor completely, then place the answer in the proper location on the grid
a^3-b^3
Answers
Answer:
[tex]\displaystyle [a - b][a^2 + 2ab + b^2][/tex]
Step-by-step explanation:
Use the Difference of Cubes to factor this polynomial.
I am joyous to assist you anytime.
Felipe picked a pumpkin that weighed three times the weight of Meg's pumpkin Meg's pumpkin with half the weight of Ryan's pump Ryan's pumpkin weighed 14 lb how much did Felipe's pumpkin weigh
Answers
Answer:
21 lb
Step-by-step explanation:
Divide the amount of Ryan's pumpkin by 2 then multiply it by 3. Ryan's pumpkin weighs 14 lb divided by 2 is 7 then 7 multiplied by 3 is 21.
To find the weight of Felipe's pumpkin, we first determine that Meg's pumpkin weighs 7 pounds, which is half of Ryan's pumpkin's weight of 14 pounds. We then multiply Meg's pumpkin's weight by 3 to find that Felipe's pumpkin weighs 21 pounds.
The question asks to determine the weight of Felipe's pumpkin given the weight relationships between Felipe's, Meg's, and Ryan's pumpkins. We are told that Ryan's pumpkin weighs 14 pounds and that Meg's pumpkin is half the weight of Ryan's. This means Meg's pumpkin weighs 7 pounds (14 lb / 2). Since Felipe's pumpkin weighs three times as much as Meg's, we have to multiply Meg's pumpkin's weight by 3 to find the weight of Felipe's pumpkin: 7 lb x 3 = 21 pounds.
So, Felipe's pumpkin weighs 21 pounds.
Please help with remaining and/or correct what I have
Answers
Answer:
Step-by-step explanation:
k² = -18 - 9k
k² +9k + 18 = 0
k² + 6k + 3k + 3*6 = 0
k(k + 6) + 3 (k + 6) = 0
(k + 6) (k + 3) =0
-2v²- v +12 = -3v² + 6
-2v² - v + 12 + 3v² - 6 = 0
v² - v + 6 = 0
(x, 7) and (11, 8); m = -1/5
Plz help
Answers
Answer:
This tells us that the line with slope -1/5 passes through the two points (16, 7) and (11, 8). The previously unknown x-coordinate is 16.
Step-by-step explanation:
A line with slope m = -1/5 passes through the points (x, 7) and (11, 8). Find the value of x.
The slope of the line through these two points is found from the slope formula and is:
8 - 7
m = ----------- and the value of m is given as -1/5. Therefore,
11 - x
1
m = ----------- = -1/5
11 - x
Cross-multiplying, we get (1)(5) = -(11 - x), or 5 = -11 + x. Then x = 16
This tells us that the line with slope -1/5 passes through the two points (16, 7) and (11, 8). The previously unknown x-coordinate is 16.
Please I need help on #3
Answers
Answer:
36 movies
Step-by-step explanation:
16/4=4 this shows that there are 4 4s in 16.
Because every 4 video games 9 movies are rented so 4*9=36 for the answer
There are 182 adults and 18 children attending a wedding
reception as guests of the bride and groom. The guests will be
seated in groups of eight at each table. How many tables are
needed for the wedding guests?
Answers
Answer:
Step-by-step explanation:
Total number of guest = 182+18
= 200 guests
If 8 are using a table then the number of tables needed = 200/8
= 25tables
Answer: D
16*12 is 192. Plus the 6 for the bride and groom, and you get a total of 198.
Helpppppp guyssss pleaseeeeeee I’m losttt
Answers
Answer:
29
Step-by-step explanation:
Use definition of conditional probability:
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)},[/tex]
where
A = the student is a freshman,
B = the student is a male
From the table,
[tex]P(B)=\dfrac{4+6+2+2}{4+6+2+2+3+4+6+3}=\dfrac{14}{30}=\dfrac{7}{15}\\ \\P(A\cap B)=\dfrac{4}{4+6+2+2+3+4+6+3}=\dfrac{4}{30}=\dfrac{2}{15}[/tex]
So,
[tex]P(A|B)=\dfrac{\frac{2}{15}}{\frac{7}{15}}=\dfrac{2}{7}\approx 0.29=29\%[/tex]
WILL GIVE BRAINLIEST PLEASE HELPP PLEASE HLEP
Answers
Answer:
A could work
Step-by-step explanation:
Because it is a square, all angles should be 90 degrees
Answer:Try B
Step-by-step explanation:
If its right please give me brainiest
Which of the lines graphed has a slope of -1/2 and a y-intercept of 3
(WORTH 100 POINTS AND WILL GIVE BRIANLIEST)
Answers
Answer:
The correct option is C).
Figure show the line with slope of -1/2 and a y-intercept of 3
Step-by-step explanation:
The equation of line is given by y=mx+c.
Where m is slope and c is y-intercept.
Given that line has slope
m=[tex]\frac{-1}{2}[/tex] and c=3
Thus equation of line will be
y=mx+c.
y=[tex]\frac{-1}{2}x+3[/tex]
To plot the line we need at least two points
Take x=0
y=[tex]\frac{-1}{2}x+3[/tex]
y=[tex]\frac{-1}{2}0+3[/tex]
y=3
The required point is A(0,4)
Take x=2
y=[tex]\frac{-1}{2}2+3[/tex]
y=2
The required point is B(2,2)
Using this points to graph the given equation of line
Figure show the line with a slope of -1/2 and a y-intercept of 3
The correct option is C).
Answer:
B
Step-by-step explanation:
I’m not sure but I put in c and got it wrong and that is the only other one that appears to be going on a negative slope
Simplify x0y-3/x2y-1
Answers
Answer:
For x: We subtract the exponents,
this way. 0 - 2 = -2
For y: We subtract the exponents,
this way. -3 - -1 = -2
x -² y -²
Peggy had three times as many quarters as nickels. She had $1.60 in all. How many nickels and how many quarters did
she have?
If the variable n represents the number of nickels, then which of the following expressions represents the number of
quarters?
Answers
Answer:Let
n-------> the number of nickels
q------> the number of quarters
we know that
1\ quarter=\$0.25\\1\ nickel=\$0.05
so
0.05n+0.25q=1.60 ----> equation A
q=3n ----> equation B
substitute equation B in equation A
0.05n+0.25[3n]=1.60
0.05n+0.75n=1.60
0.80n=1.60
n=2
Find the value of q
q=3*2=6
therefore
The answer part a) is
the number of nickels are 2 and the number of quarters are 6
the answer Part b) is
The expressions that represents the number of quarters is
q=3n
Step-by-step explanation:
4 coffees and 12 lattes. Costs $61
12 coffees and 7 lattes. Costs $59.75
How much does a coffe and a latte cost
Answers
Answer:
Cost of a coffee is $2.5 and cost of a latte is $4.25.
Step-by-step explanation:
Let cost of 1 coffee be 'c' and cost of 1 latte be 'l' dollars.
Given:
4 coffees and 12 lattes cost $61.
12 coffees and 7 lattes cost $59.75.
∵ 1 coffee cost = [tex]c[/tex]
∴ 4 coffees cost = [tex]4c[/tex] and 12 coffee cost = [tex]12c[/tex]
∵ 1 latte cost = [tex]l[/tex]
∴ 12 lattes cost = [tex]12l[/tex] and 7 lattes cost = [tex]7l[/tex]
Now, as per question:
[tex]4c+12l=61-----1\\12c+7l=59.75----2[/tex]
Now, multiplying equation (1) by -3 and adding the result to equation (2). This gives,
[tex]-3(4c+12l)=-3(61)\\\\-12c-36l=-183\\12c+7l=59.75\\+\\----------\\0-29l=-123.25\\\\l=\frac{-123.25}{-29}=\$4.25[/tex]
Now, plug in the value of 'l' in equation 1 to solve for 'c'. This gives,
[tex]4c+12(4.25)=61\\\\4c+51=61\\\\4c=61-51\\\\4c=10\\\\c=\frac{10}{4}=\$2.5[/tex]
Therefore, cost of a coffee is $2.5 and cost of a latte is $4.25.
A system of linear equations can determine the cost of a coffee and a latte, which are found to be $2.50 and $4.25 respectively.
To solve the question how much does a coffee and a latte cost, we can treat it as a system of linear equations problem. We have the following two equations based on the given information:
4 coffees + 12 lattes = $61
12 coffees + 7 lattes = $59.75
Let's denote the cost of one coffee as c and the cost of one latte as l. We can now rewrite the equations as:
4c + 12l = 61
12c + 7l = 59.75
Multiplying the first equation by 3 gives us:
12c + 36l = 183
Now we can subtract the second equation from this new equation to find the cost of lattes:
(12c + 36l) - (12c + 7l) = (183 - 59.75)
29l = 123.25
l = 123.25 / 29
l = $4.25
Having found the cost of a latte, we can now substitute this back into the first original equation to find the cost of a coffee:
4c + 12(4.25) = 61
4c + 51 = 61
4c = 10
c = 10 / 4
c = $2.50
Therefore, a coffee costs $2.50 and a latte costs $4.25.
a function is defined by equation f(x)=-3x+2 what is the average rate if change for the function on the interval from x =-2 to x = 2
Answers
The average rate of change for the function on the interval from x = -2 to x = 2 is 1.
Explanation:The average rate of change for a function on an interval is calculated by finding the slope of the line connecting the two endpoints of the interval. In this case, the interval is from x = -2 to x = 2.
To find the slope, we need to find the change in y values divided by the change in x values. In other words, we need to find the difference in f(x) values divided by the difference in x values.
Substituting the given function into the equation, we have:
slope = (f(2) - f(-2)) / (2 - (-2)) = (-3(2) + 2 - (-3(-2) + 2)) / (2 + 2)
= (-6 + 2 + 6 + 2) / 4
= 4 / 4 = 1.
Therefore, the average rate of change for the function on the interval from x = -2 to x = 2 is 1.
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A restaurant bill is $59 and you pay $75. What percentage gratuity did you pay?
Answers
Answer:22%
Step-by-step explanation:
You paid approximately 27.12% gratuity on a $59 bill by leaving a $16 tip on a $75 payment.
To find out the percentage gratuity paid, you can first calculate the gratuity amount by subtracting the bill amount from the total paid:
Gratuity = Total paid - Bill amount
Gratuity = $75 - $59
Gratuity = $16
Now, to find the percentage gratuity, divide the gratuity amount by the bill amount and then multiply by 100:
Percentage Gratuity = (Gratuity / Bill amount) * 100
Percentage Gratuity = ($16 / $59) * 100
Percentage Gratuity ≈ 27.12%
So, you paid approximately a 27.12% gratuity.