The ratio of length and breadth of a rectangular playground is 3:2. There
is a two meter wide jogging track along and outside the playground. The
total area of the track and the playground is 2816 sq.m. Find the length
and breadth of the playground,
Answer:
We know that the ratio of length and breadth of a rectangular playground is 3:2
Then if the length is L, and the breadth is B, we have the relationship:
L = (3/2)*B
Outside this playground, we have a jogging track of 2m, then if we also consider the jogging track the length and breadth are:
L' = L + 2m
B' = B + 2m
The area is the product between the area and the breadth, then the area is:
A = B'*L'
A = (L + 2m)*(B + 2m)
And remember that L = (3/2)*B
Then we get:
A = ((3/2)*B + 2m)*(B + 2m)
And the area is 2816 m^2
Then we have:
A = ((3/2)*B + 2m)*(B + 2m) = 2816 m^2
Now we can solve the equation:
((3/2)*B + 2m)*(B + 2m) = 2816 m^2
(3/2)*B^2 + 3m*B + 2m*B + 4m^2 = 2816 m^2
(3/2)*B^2 + 5m*B = 2816 m^2 - 4m^2 = 2812m^2
Then we can write:
(3/2)*B^2 + 5m*B - 2812m^2 = 0
We can solve this if we use Bhaskara's formula:
[tex]B = \frac{-(5m) +- \sqrt{(5m)^2 - 4*(3/2)*(-2812m^2)} }{2*(3/2)} = \frac{-5m +-130m}{3}[/tex]
One solution is negative, so we can discard that one, then we only take the positive:
B = (-5m + 130m)/3 = 41.67m
And L = (3/2)*B
L = (3/2)*40.7m = 62.5m
The breadth is 41.67 meters and the length is 62.5 meters.
Leon constructed a point P that divides the directed segment from A to B in the ratio 2 to 1. Chelsea
constructed a point that divides the directed segment from B to A In the ratio 1 to 2. How are points P
and Q related? Explain.
Points P and Q are (select) whpoint P is (select) vl of the distance from A to B.Point Q is
(select) of the distance from B to A. The means the points lie (select) location along the line
segment.
Answer:
The answer is below
Step-by-step explanation:
Leon constructed a point P that divides the directed segment from A to B in the ratio 2 to 1. Chelsea constructed a point Q that divides the directed segment from B to A in the ratio 1 to 2. How are points P and Q related? Explain.
Points P and Q are...
A.) two units apart. B.) the same point. C.) one unit apart.
Point P is ___ of the distance from A to B. [ A.) 2/3 B.) 1/2. C.) 1/3. ]
Point Q is of the distance from B to A. [ A.)1/3 B.). 1/2 C.)2/3. ]
The means the points lielocation along the line segment.
[ A.) At the same B.)At a different
Solution:
Since point P is divides the segment from A to B in the ratio 2 to 1 therefore:
P = 2/3 of the distance from A to B.
Since point Q is divides the segment from B to A in the ratio 1 to 2, therefore:
Q = 1/3 of the distance from B to A
2/3 of the distance from A to B = 1/3 of the distance from B to A
Therefore point P and point Q lie along the same line segment from A to B (or B to A) and the points P and Q are at the same point,
need help answering this question
Tiffani buys a new pair of shoes. She spends $81 including an 8% sales tax. What was the original price of the shoes to the nearest dollar?
Answer:
the original price of the shoes is $75
Step-by-step explanation:
x * 1.08 = 81
x = 81 / 1.08 = 75
75 * 1.08 = 81
Wild Water Adventure Waterslides park charges a rental fee plus $2 per hour to rent inflatable rafts. The total cost to rent a raft for 4 hours is $12.50. Assume the relationship is linear. Find the rate of change and the initial value. Then move on to part 'b' to interpret each of them.
Answer:
m = 2, initial value = 4.5 or $4.50
Step-by-step explanation:
We know that renting a raft costs 2 dollars/hr plus some rental fee that we need to find.
We also know that renting a raft for 4 hours will cost $12.50. So we can do this:
$12.50 - (2.00 [tex]\frac{dollars}{hrs}[/tex] × 4 hrs) = $4.50, which is the "b" in the standard equation for y = mx + b
So, our equation is y = 2x + 4.5
The rate of change is the slope, which is the coefficient of the x.
m = 2
Our initial value is when x = 0.
y = 2(0) + 4.5
y = 4.5
Here is a long-division calculation of 917:7.
1 31
7
9 1 7
- 7
2 1
- 2 1
- 7
0
There is a 7 under the 9 of 917. What does this 7 represent?
Answer:
Step-by-step explanation:
it means that 7 goes into 9 one time, and its seven.
How many 1/2 cups of juice are in 1 and 1/2 cups?
Answer:
there should be 3 half cups
Step-by-step explanation:
3x^3-5x^2-5x-1=0
Zero of polynomials
Answer:
Step-by-step explanation:
Wuh
Peter lives in Utah, which has a 5% state income tax rate. He earns $3,700 monthly.
How much state income tax is withheld from each of his paychecks?
Answer:
ask Utah not me.........
Answer:
$185 is withheld
Step-by-step explanation:
3700 x .05 is 185.
1. Rita uses the rule of "Add 6" starting from zero. Mike uses the rule "Add 10" starting from zero. Select all of the true statements about the patterns.* A. In Mike's pattern, each number after zero is 4 more than the corresponding number in Rita's pattern O B. In Mike's pattern, each number after zero is more than the corresponding number in Rita's pattern. O C. Rita's and Mike's patterns do not have any of the same numbers. D. Neither pattern has any odd numbers for its output value. Help me please
Answer:
b and d
Step-by-step explanation:
Which measure of spread is least affected by the long tail in the graph?
Answer:
Image result for Which measure of spread is least affected by the long tail in the graph?
IQR
Answer: The IQR is least affected by the long tail on the right of the graph. The IQR is the inter-quartile range. It is the length of the box in the middle of the graph. Having the long tail on the right does not affect the box.
Step-by-step explanation:
Quik Call charges 18¢ per minute for long-distance calls. Econo Phone totals your phone usage each month and rounds the number of minutes up to the nearest 15 minutes. It then charges $7.90 per hour of phone usage, dividing this charge into 15-minute segments if you used less than a full hour. If your office makes 5 hours 3 minutes worth of calls this month using the company with the lower price, how much will these calls cost?
Answer:
158? I am not really sure because I am in fifth grade, but I think it may be correct.
Line A is represented by the equation given below:
x + y = 4
What is most likely the equation for line B, so that the set of equations has infinitely many solutions? (1 point)
4x + 4y = 4
4x + y = 4
2x + 2y = 8
x + y = 8
Answer:
3
Step-by-step explanation:
2x + 2y = 4
dividing both sides by 2,we get
x + y = 4,which is the same line A
so this set of equations has infinitely many solutions as they intersect each other at infinite points i.e they overlap eachother
Please help meeeeeeeeee
Answer:
ojalá te ayude
Step-by-step explanation:
la primera
2 2/5
Use differences to find a pattern in the sequence.
7, 17, 30, 51, 85, 137, 212
Assuming that the pattern continues, the eighth term should be
Answer:
451
Step-by-step explanation:
7, 17, 30, 51, 85, 137, 212
Differences between Difference between Difference between
numbers in sequence first differences second differences
17 - 7 = 10
30 - 17 = 13 3
51 - 30 = 21 8 5
85 - 51 = 34 13 5
137 - 85 = 52 18 5
212 - 137 = 75 23 5
75 + 28 = 103
212 + 103 = 315 28 5
103 + 33 = 136
315 + 136 = 451 33 5
A pole tilts at an angle of 9 degrees from vertical, away from the sun. The pole casts a shadow that is 24 feet long. The angle of elevation from the end of the pole’s shadow to the top of the pole is 53 degrees. How long is the pole?
Answer:
Step-by-step explanation:
180-53-(90-9)=46
sin53/p=sin46/24
p=24sin53/sin46
p=26.65ft
The length of the pole with the given shadown is 26.6 feet long.
Length of the poleThe height of the pole is determined from trignometry property of right triangle.
The shadow of the pole, vertical height formed by the pole and the length of the pole, will form a right triangle.
Let the base of the right triangle = 24 ftLet the base angle = 53⁰base angle of similar triangle = (90 - 53) + 9 = 46⁰The length of the pole is calculated as follows;
L/sin53 = 24/sin46
L = (24 x sin53) / (sin 46)
L = 26.6 ft
Thus, the length of the pole with the given shadown is 26.6 feet long.
Learn more about angle of elevation here: https://brainly.com/question/25748640
Find the sum
(-14.2b - 97.35) + (6.76d - 118.7 – 3.4d)
Answer:
−14.2b+3.36d−216.05
Step-by-step explanation:
collect terms:(−14.2b−97.35)+((6.76d−3.4d)−118.7)
simplify: −14.2b−97.35+3.36d−118.7
terms: −14.2b+3.36d+(−97.35−118.7)
simplify: −14.2b+3.36d−216.05
Matilda recently took a statistics quiz in her math class. in one question, 45 of 900 visitors at a local craft show were surveyed about the cost of admission to the show. Matilda incorrectly stated that the sample in this situation was represented by 900 visitors at the craft show.
a. what is Matilda's error?
b. what is the actual sample?
Answer:
A. Her error was that she thought that they were surveying the whole town so 900 would be the sample.
B. The actual sample is 45.
Step-by-step explanation:
The actual sample is 45 because 45 people out of the 900 visitors (population) were surveyed.
What is the y-intercept of the equation of the line that is perpendicular to the line and passes through the point (15,-5)?
Answer:
hi
Step-by-step explanation:
First of all let’s find out the slope of the line y = x +10
As, we know the equation y= mx + c . So comparing the given equation with the general equation we get, m = 1
Now, we know that the product of two perpendicular lines is -1.
Thus, mn = -1 (considering slope of the second line as n)
Putting the value of m we get , n = -1
Now , y+5= -1( x -15) i.e y=-x + 10
if we compare again with the general equation then we find that.
The y intercept of the required equation is 10.
Thank You
Answer:
10
Step-by-step explanation:
First of all let’s find out the slope of the line y = x +10
As, we know the equation y= mx + c . So comparing the given equation with the general equation we get, m = 1
Now, we know that the product of two perpendicular lines is -1.
Thus, mn = -1 (considering slope of the second line as n)
Putting the value of m we get , n = -1
Now , y+5= -1( x -15) i.e y=-x + 10
if we compare again with the general equation then we find that.
The y intercept of the required equation is 10.
Thank You
The price technology stock dropped to $9.71 today. Yesterday's price was $9.82. Find the percentage decrease.
R+2 1/4 = 4 1/2 what does r = ?
Answer:
exact form: r= 9/4
decimal form: r=2.25
mixed number form: r= 2 1/4
Step-by-step explanation:
Answer:
R=2 1/4 or 9/4
Step-by-step explanation:
You make the 4 1/2 a 4/24 so it equals 2 1/4
Than you subtract 4 2/4-2 1/4 to get 2 1/4
Hope this helps!!
HELP ASAP PLEASE!!!
An angle measures (5x + 13).
Part A
What is the measure of an angle that is vertical to the given angle?
Enter the correct answer in the box.
Hint
The frequency table shows the scores from rolling a dice.
Score
Frequency
Answer:
The median is 3.5
Step-by-step explanation:
We want to find the median of the set of values.
First, we need to write the set in ascending order.
We get:
1 five times
2 three times
3 five times
4 two times
5 seven times
6 four times
The median will be the midle value (for example in a set of 5 elements, the middle element is the third one) of this set, then the first part is to write the set, we get:
{1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6}
In this set we have
5 + 3 + 5+ 2 +7 + 4= 26 values
So we will not have a middle value, we need to take the mean of the two middle values (the 13th value and the 14th value)
We can see in the set above that these values are:
3 and 4.
Then we want to take the mean between 3 and 4.
We get:
M = (3 + 4)/2 = 3.5
The median of this set is 3.5
Emily the blacksmith blends one alloy of silver that is 45% silver and another that is 95% silver. To the nearest ton, how much of each alloy is needed to make 139 tons of a 70% silver alloy?
please answer
Answer:
69.5 tons of Alloy 1 (of 45% silver) and 69.5 tons of Alloy 2 (of 95% silver) is needed to make 139 tons of 75% silver alloy
Step-by-step explanation:
Given
[tex]Alloy\ 1 = 45\%[/tex]
[tex]Alloy\ 2 = 95\%[/tex]
Required
How much of each alloy is needed for 70% silver alloy 139 tons
Let the amount of alloy 1 needed be x and the amount of 2 needed by y.
So:
[tex]x + y = 139[/tex]
Make y the subject
[tex]y = 139 - x[/tex]
The percentage of each needed is represented as:
[tex]45\% * x + 95\% * y = 139[/tex]
[tex]45\% * x + 95\% * y = 70\% * 139[/tex]
[tex]0.45x + 0.95y = 0.70 * 139[/tex]
[tex]0.45x + 0.95y = 97.3[/tex]
Substitute 139 - x for y in the above equations
[tex]0.45x + 0.95*(139-x) = 97.3[/tex]
[tex]0.45x + 0.95*139-0.95*x = 97.3[/tex]
[tex]0.45x + 132.05-0.95x = 97.3[/tex]
Collect Like Terms
[tex]0.45x -0.95x = 97.3-132.05[/tex]
[tex]-0.50x = -34.75[/tex]
Make x the subject
[tex]x = \frac{-34.75}{-0.50}[/tex]
[tex]x = 69.5[/tex]
Recall that:
[tex]y = 139 - x[/tex]
[tex]y = 139 - 69.5[/tex]
[tex]y = 69.5[/tex]
This implies that:
69.5 tons of Alloy 1 (of 45% silver) and 69.5 tons of Alloy 2 (of 95% silver) is needed to make 139 tons of 75% silver alloy
A curious statistics student cannot get enough statistics, so he decides to analyze the percentage of students sleeping in his statistics class. He discovers that of the 30 students in his class, 47% of the students were asleep at some point during the class period. Assuming the 30 students is less than 10% of all the students taking statistics in his school, and assuming the 30 students in the class were randomly assigned to the class, what model would he use to analyze the percentage of sleeping statistics students
Answer:
c) N(.47, .09)
Step-by-step explanation:
Options to the question are "a) N(.30, .10), b) N(.30, .09). c) N(.47, .09), d) N(.47, .008), e) N(.30, .008)"
Pο = 47% = 0.47
n = 30
Mean = Pο = 0.47
S.D = Pο(1-Pο) / n
S.D = 0.47 * 0.53 / 30
S.D = 0.09
Thus, the percentage of sleeping statistics of students follows a Normal distribution with mean = 0.47 and S..D = 0.09
Chapter 6 Study Guide
Tickets for a school play cost $6 for adults and $4 for students. At the end of the play, the school sold a total of 60 tickets
and collected $360
Answer:
what is the question
Step-by-step explanation:
Calculate the perimeter and area of the following rectangles.
a. Length: 10 cm; Width: 8 cm
b. Length: 10 cm;
Perimeter
Area
Perimeter
Answer:area=l×b
10×8=80cm* 2
perimeter =(l+b)2
10+8)*2
18×2
=36cm
Step-by-step explanation:
Answer:
read the explanation
Step-by-step explanation:
For A:
Perimeter is (10+8)*2=36
Area is 10*8=80
For B:
Perimeter is 10*4=40
Area is 10*10=100
what is 99 time 6
[tex]99 \times 6[/tex]
Answer:
594
Step-by-step explanation:
Sophia went out to dinner at an Indian restaurant. The total bill was $54. She wanted to leave a 15% tip. What was her total bill including her tip?
Answer:
$62.10
Step-by-step explanation:
Answer:
The tip is 8.10
The bill is 62.10
Step-by-step explanation:
Eliana worked 16 1/2 hours for the first week of the month and 16 1/4 hours the second week of the month. Her pay for these 2 weeks was $412.65. How much did Eliana earn per hour?
Answer:
She earned $12.60 per hour
Step-by-step explanation:
Pay was $412.65
Hours worked = 16.5 + 16.25 = 32.75 hrs
hourly rate = $$/hrs = 412.65/32.75 = 12.6
She earned $12.60 per hour
