The arena’s car park is shown below.
Area of a circle = πr2
π = 3.14
What is the area of the car park, not including the arena itself?
Answers
The area of the parking lot without considering the arena is determined to be 6518.75 square units.
To determine the parking lot area excluding the arena, the process involves multiple steps:
Parking Lot Area Calculation:
Utilize the formula A = B x H, where B is the base (100) and H is the height (75).
Compute A = 100 x 75, resulting in an initial parking lot area of 7500 square units.
Arena Area Calculation:
Employ the formula A = π r², where r is the radius (25) of the arena.
Calculate A = π x 25², yielding an arena area of 19625 square units.
Adjustment for Arena Area:
Observe the image indicating that the car park bisects the arena, cutting its area in half.
Subtract half of the arena's area from the parking lot area to obtain the adjusted area within the car park.
The adjustment equation is A = area - 0.5 x arena, where area is the parking lot area (7500) and arena is half of the arena's area (19625 / 2 = 981.25).
Final Result:
Perform the subtraction: A = 7500 - 981.25, yielding a final area of 6518.75 square units.
Therefore, the area of the parking lot without considering the arena is determined to be 6518.75 square units.
Related Questions
Which statements about the system are true? Check all that apply. y =1/3 x – 4 3y – x = –7 The system has one solution. The system consists of parallel lines. Both lines have the same slope. Both lines have the same y–intercept. The equations represent the same line. The lines intersect.
Answers
ANSWER
The system consists of parallel lines. Both lines have the same slope.
EXPLANATION.
The first equation is
[tex]y = \frac{1}{3} x - 4[/tex]
This equation is in the slope-intercept form.
The second equation is
[tex]3y - x = - 7[/tex]
We write this one too in slope-intercept form so that we can make comparison.
[tex] \implies \: y = \frac{1}{3} x - \frac{7}{3} [/tex]
We can see that both equations have slope
[tex]m = \frac{1}{3} [/tex]
This means the two lines are parallel.
The two lines have different y-intercepts.
Two parallel lines with different y-intercepts will never meet.
The lines will never intersect.
Answer:
The true statements are:
- The system consists of parallel lines
- Both lines have the same slope
Step-by-step explanation:
* Lets talk about the solution of the linear equations
- There are three types of the solutions of the system of linear equations
# If the two lines intersect each other, then there is one solution
- The equations are ax+ by = c , dx + ey = f
# If the two lines parallel to each other, then there is no solution
- The equations are ax+ by = c , ax + by = d in its simplest form ,
where a is the coefficient of x , b is the coefficient of y and
c , d are the numerical terms
# If the two lines coincide (over each other), then there are infinite
solutions
- The equations are ax+ by = c , ax + by = c in its simplest form, where
a is the coefficient of x , b is the coefficient of y and c is the
numerical term
* Lets solve the problem
∵ The system of equation is:
y = 1/3 x - 4 ⇒ (1)
3y - x = -7 ⇒ (2)
- Lets put equation (1) in the form of equation (2)
∵ y = 1/3 x - 4 ⇒ multiply both sides by 3
∴ 3y = x - 12 ⇒ subtract x from both sides
∴ 3y - x = -12
∴ Equation (1) is 3y - x = -12
∵ Equation (2) is 3y - x = -7
∵ The coefficients of x and y in the two equation are equal
∵ The numerical terms in the two equations are not equal
∴ The equations have no solution because their lines are parallel
∵ The parallel lines have same slope
* The true statements are
- The system consists of parallel lines
- Both lines have the same slope
Three generous friends, each with some cash, redistribute their money as follows: Ami gives enough money to Jan and Toy to double the amount that each has. Jan then gives enough to Ami and Toy to double their amounts. Finally, Toy gives Ami and Jan enough to double their amounts. If Toy has $36 when they begin and $36 when they end, what is the total amount that all three friends have?
Answers
The total amount that all three friends have is $84.
Let's assume that Ami, Jan, and Toy have x, y, and z dollars respectively. After the first redistribution, we know that:
x - a = 2(y + z)
y + a = 2(x + z)
z + a = 2(x + y)
where a is the amount of money that Ami gives to Jan and Toy.
Solving these equations, we get:
x = 5z - 4a
y = 5z - 6a
z = z
After the second redistribution, the new amounts are:
x + b = 2(y + c)
y - b + c = 2(x + c)
z + b + c = 2(x + y)
where b is the amount that Jan gives to Ami and Toy, and c is the amount that Toy gives to Ami and Jan.
Solving these equations, we get:
x = 14c
y = 11c
z = 6c
Finally, after the third redistribution, the new amounts are:
x + 2d = 2(y + 2d)
y + 2d = 2(x + 2d)
z - 2d + 2c = 2(x + y)
where d is the amount that Toy gives to Ami and Jan.
Solving these equations, we get:
x = 8d
y = 10d
z = 18d
Since we know that z = $36, we can solve for d and get d = $2. Therefore, the total amount that all three friends have is:
x + y + z = 8d + 10d + 36 = $84.
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Luke is keeping track of the total number of hours he exercises. He started the summer having already put in 15 hours, and he then exercises 7 hours each week. The function to keep track of his exercise is f(x) = 7x + 15. What do the f(x) and x represent in Luke's situation?
Answers
f(x) is the total number of hours overall that he has worked out.
x would be the number of weeks he works out.
You would multiply x ( number f weeks he works out) by 7 and then add that to the hours he already worked out (15) which will give you the total hours (f(x)).
Answer:
In this case, x represents "week", because they problem says that he exercises 7 hour per week, being week an unknown number because we don't how much time Luke is gonna keep exercising. Si, 7x represents the total amount of hours per week after the first 15 hours.
Similarly, f(x) represents the total amount of hour from the beginning, before the first 15 hours. The difference between x and f(x) is that the first one represents hours after the 15 hours, and the second one represents the total amount of hours, including before the 15 hours.
It's important to notice that 15 is not multiplied by a variable, it's because those 15 hours are already achieve, we don't if those where monthly or weekly, but the fact that they already happened means that they can't change, that's why the don't have a variable.
Which graph shows a dilation?
Answers
Answer:
A
Explanation:
In image A the image becomes smaller but doesn't change shape which is what dilation is supposed to be.
Answer:
Option A
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLIEST
Which of the sets of ordered pairs represents a function?
A = {(–5, 5), (–2, 2), (2, –2), (5, –5)}
B = {(4, 2), (3, –2), (9, 4), (11, –3)}
Only A
Only B
Both A and B
Neither A nor B
Answers
Answer:
The answer would be, both A. and B.
Answer:
both a and b
Step-by-step explanation:
Please someone help me
Answers
Answer:
The correct answer option is D. 5.
Step-by-step explanation:
We are given the following expression where 4 is to be divided by a fraction 1/5:
[tex] 4 [/tex] ÷ [tex]\frac{1}{5}[/tex]
This can also be written as:
[tex]\frac{4}{\frac{1}{5} }[/tex]
Now to find the quotient of this, we will take the reciprocal of the fraction in the denominator to change it into multiplication.
[tex]4 \times \frac{5}{1}[/tex]
Therefore, ignoring the 1 in denominator, we can simply multiply 4 by 5.
Answer:
Hi there!
The answer is last one: 5
Step-by-step explanation:
When ever you are dividing a number by a fraction you always flip the fraction and multiply it, another way of saying it is multiplying by its reciprocal.
a 2 digits even multiple of 7
Answers
Answer:
14, 28, 42, 56, 70, 84, (etc.)
Step-by-step explanation:
14, 28, 42, 56, 70, 84, (etc.) are all multiples of 7. They're also even and have 2 digits.
Answer: 14 28 42 56 70 84
Step-by-step explanation: Hopes this helps
When Steve woke up. His temperature was 102 degrees F. Two hours later it was 3 degrees lower. What was his temperature then?
Answers
Answer:
if it was 102 when he woke
e up and lowered then it will be 99 degree fahrenheit then
Final answer:
Steve's temperature decreased by 3 degrees from the original 102 degrees F, which means his temperature two hours later was 99 degrees F.
Explanation:
The student's question involves a basic mathematical operation, specifically subtraction, used to determine a change in temperature over time. Steve originally has a temperature of 102 degrees Fahrenheit. After two hours, his temperature has decreased by 3 degrees.
To find the new temperature, we subtract the decrease from the original:
102 degrees F - 3 degrees F = 99 degrees F.
So, Steve's temperature two hours later would be 99 degrees Fahrenheit.
A gardener makes a new circular flower bed. The bed is fourteen feet in diameter. Calculate the circumference and the area of the circular flower bed.
Answers
Answer:
The circumference is:
[tex]C = 43.98\ ft[/tex]
The area is:
[tex]A=153.94\ ft^2[/tex]
Step-by-step explanation:
The circumference of a circle is calculated using the following formula
[tex]C = \pi d[/tex]
Where C is the circumference and d is the diameter of the circle.
In this case we know that
[tex]d = 14\ ft[/tex]
Therefore the circumference is:
[tex]C = \pi *14[/tex]
[tex]C = 43.98\ ft[/tex]
The area of a circle is calculated using the following formula
[tex]A=\pi(\frac{d}{2})^2[/tex]
Where d is the diameter of the circle.
Then
[tex]A=\pi(\frac{14}{2})^2[/tex]
[tex]A=\pi(7)^2[/tex]
[tex]A=49\pi[/tex]
[tex]A=153.94\ ft^2[/tex]
The circumference of the flower bed is approximately 43.96 feet and the area is approximately 153.86 square feet.
Explanation:The gardener's circular flower bed has a diameter of 14 feet. The formula to calculate the circumference of a circle is C=πd where 'd' represents the diameter. Therefore, by substituting the given diameter, we get C = 3.14 * 14 = 43.96 feet approximately.
The area of the circle can be calculated by using the formula A=πr², where 'r' represents the radius of the circle. The radius is half of the diameter, that is 14/2 = 7 feet. So, A = 3.14 * 7² = 153.86 square feet approximately.
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División de polinomios(a²+3a+2)÷(a+1)
Answers
Answer:
a + 2
Step-by-step explanation:
Given
[tex]\frac{a^2+3a+2}{a+1}[/tex] ← factor the numerator
= [tex]\frac{(a+1)(a+2)}{a+1}[/tex]
Cancel the factor (a + 1) on the numerator/denominator
= a + 2 ← quotient
Need help fast as soon as possible!!!
Answers
Answer:C 13/2
Step-by-step explanation: you do 13 x 0.5 equals 6.5, convert to a fratcion equals 13/2
Answer:
[tex]\frac{13}{2}[/tex]
Step-by-step explanation:
When you have a whole number, you gotta add a denominator, so just add 1 underneath:
[tex]\frac{13}{1}[/tex]
Then you have
[tex]\frac{13}{1}[/tex] ×[tex]\frac{1}{2}[/tex]
Multiply straight across and you get
[tex]\frac{13}{2}[/tex]
The container that holds the water for the football team is 1/2 full. after pouring out 5 gallons of water, it is 3/10 full. How many gallons can the container hold?
Answers
Answer:
25 gallons.
Step-by-step explanation:
The container that holds the water for the football team is 1/2 full.
After pouring out 5 gallons of water, it is 3/10 full.
The proportion that was poured out is [tex]\frac{1}{2}[/tex] - [tex]\frac{3}{10}[/tex] = [tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]
[tex]\frac{1}{5}[/tex] of the water in the container is equal to 5 gallons
The container therefore holds: 1 × 5 ÷ [tex]\frac{1}{5}[/tex] = 5 × 5 = 25 gallons.
Final answer:
The total capacity of the container is calculated to be 25 gallons, found by using the information that 1/2 to 3/10 of the capacity equals a 5 gallon difference.
Explanation:
We have been given that the container is initially 1/2 full and becomes 3/10 full after pouring out 5 gallons of water.
To find out the total capacity of the container, we can set up a proportion where the difference between the two fractions (1/2 and 3/10) represents the 5 gallons removed.
First, we find a common denominator for the two fractions, which is 10. Now we can say:
1/2 equals 5/10After removing 5 gallons, the container is 3/10 fullThe difference between 5/10 and 3/10 is 2/10, which equates to the 5 gallons poured out. Thus, 2/10 of the container's capacity is 5 gallons, and we can find the full capacity (10/10) by multiplying the 5 gallons by 5 (since 2 × 5=10).
So, the container's total capacity is 5 gallons × 5 = 25 gallons.
What are the coordinates of Z?
Answers
Answer:
The correct answer option is C. (0, c).
Step-by-step explanation:
We are given an isosceles trapezoid with the coordinates of three of its vertices and we are to find the coordinates of Z.
Z is a point on the middle of one of the sides of the trapezoid.
Since Z lies on the horizontal x axis, therefore its x coordinate is 0 while the y coordinate can be seen from the vertex exactly at its right which is c.
Z (0, c)
==============================================
Explanation:
Note how the point (a,0) mirrors over the y axis to land on (-a,0)
A similar action will happen as we go from te point (b,c) to point W (-b, c), due to this figure being isosoceles.
The x coordinate changes from positive to negative. The y coordinate stays the same.
The point Z is the midpoint of the upper segment which spans from (-b,c) to (b,c)
Apply the midpoint formula to find where Z is located.
Add up the x coordinates and divide by 2: x = (-b+b)/2 = 0/2 = 0
Add up the y coordinates and divide by 2: y = (c+c)/2 = 2c/2 = c
So the midpoint is located at (x,y) = (0, c) which is where point Z is located as well.
Side note: it might help to replace the letters a, b and c with actual values, just so the problem is more concrete.
The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 5 points. About what percent of students have scored between 60 and 65 points?
Answers
Answer: The percent of students have scored between 60 and 65 points is 34.13%
Step-by-step explanation:
Given : The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 5 points.
i.e. [tex]\mu=60\ \ \ \sigma=5[/tex]
Let x denotes the points obtained by students of a class in a test .
Now , the probability that the students have scored between 60 and 65 points :-
[tex]P(60<x<65)=P(\dfrac{60-60}{5}<\dfrac{x-\mu}{\sigma}<\dfrac{65-60}{5})\\\\= P(0<z<1)\ \ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\= P(z<1)-P(z<0.5)\ \ \ [\because\ P(z_1<Z<z_2)=P(Z<z_2)-P(Z<z_1)]\\\\=0.8413-0.5=0.3413[/tex]
[tex]=34.13\%[/tex]
Hence, the percent of students have scored between 60 and 65 points is 34.13%.
Hanna and Swathi walked several miles for a charity. Altogether they walked more than 14 miles. If Hanna walked 8 miles
then which represents s the number of miles Hanna could have walked?
Answers
Answer:
S>6
Step-by-step explanation:
Let us suppose the distance walked by Hanna and swati is represented by H and S.
And total distance travelled is D
D=H+S
D>14
H+S>14
Given H=8
8+S>14
S>6
Hence swati walked more than 6 miles
Which of the following is the result of flipping the graph of the function shown
below over the line y - x?
Answers
Answer:
See attachment
Step-by-step explanation:
When the graph of the given function is flipped over the line [tex]y=x[/tex], the coordinates will swap.
The mapping for a reflection in the line [tex]y=x[/tex] is [tex](x,y)\to(y,x)[/tex].
We can observe that one portion of the graph is in the first quadrant [tex](x,y)[/tex]. When we flip this part we will get [tex](y,x)[/tex], which is still in the first quadrant.
Also, when we flip the portion of the graph in the second quadrant (-x,y), we will obtain (y,-x), which is standing for all coordinates in the fourth quadrant.
The image is shown in the attachment.
-9x -5+6=19 simplify
Answers
Answer:
[tex]{\huge \boxed{x=-2}[/tex]
Step-by-step explanation:
First you do is add and subtracting numbers from left to right.
-5+6=1
-9x+1=19
Then subtract by 1 from both sides of equation.
-9x+1-1=19-1
Simplify.
-9x=18
Divide by -9 from both sides of equation.
-9x/-9=18/-9
Simplify, to find the answer.
18÷-9=-2
x=-2 is the correct answer.
I hope this helps you, and have a wonderful day!
Answer:
x=-2
Step-by-step explanation:
-9x -5+6=19
Combine like terms
-9x +1 = 19
Subtract 1 from each side
-9x +1-1 = 19-1
-9x = 18
Divide by -9
-9x/-9 = 18/-9
x = -2
Which of the following expressions results in 0 when evaluated at x = 4?
A. (x + 6)(x - 2)
B. 4x(x - 6)
C. (x - 10)(x - 4)
D. (x + 4)(x - 10)
Answers
Answer:
C
Step-by-step explanation:
x-4 is zero when x=4
so the one that contains the factor (x-4)
C
(x-10)(x-4) put 4 in for x
(4-10)(4-4)=(-6)(0)=0
Lynne loaned $480 to a friend. The friend paid back the ammount borrowed plus 10% interest. what was the total amount the friend paid to lynne?
Answers
=480+48
=528
The total amount the friend paid to Lynne is $528.
Answer:
$480+$48=$528
Step-by-step explanation:
his friend paid him $480 and 10% so,
=10/100*480
=1/10*480
=480/10
=$48
so,his friend paid him $480+$48=$528.
Hernando ate 2/8 of a pizza for a dinner. He gave his 6 friends the rest of the pizza and told them to share it equally
Answers
Answer:
umm his friends each got 1/8
Step-by-step explanation:
hernando ate 2/8 meaning 8-2=6= 6/8
6/8 / 6 = 1/8
:D
I guess this what you want
After Hernando ate [tex]\frac{2}{8}[/tex] of the pizza, the remaining pizza when divided equally among his friend leaves each friend with [tex]\frac{1}{8}[/tex] of the pizza
Given: Hernando ate [tex]\frac{2}{8}[/tex] of a pizza, number of friends is 6
First, let's find out what fraction of the pizza is left after Hernando ate his portion. Hernando ate [tex]\frac{2}{8}[/tex], which reduces to [tex]\frac{1}{4}[/tex]. Therefore, the remaining fraction of the pizza is:
[tex]1- \frac{1}{4} =\frac{4-1}{4} = \frac{3}{4}[/tex]
The remaining [tex]\frac{3}{4}[/tex] of the pizza is to be shared equally among his 6 friends. To find out how much pizza each friend gets, we divide the remaining fraction by the number of friends:
[tex]\frac{3}{4}[/tex] ÷ 6 [tex]=\frac{3}{4} \times \frac{1}{6} = \frac{1}{8}[/tex]
Each of Hernando's 6 friends gets [tex]\frac{1}{8}[/tex] of the pizza.
Which of the following is a trinomial?
O c2 + C + 6
o c2 - 16
0-80
O c3 + 402 – 120 + 7
Answers
Given right angle abc, what is the value of tan(A)
Answers
Answer:
C
Step-by-step explanation:
tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{24}{10}[/tex] = [tex]\frac{12}{5}[/tex]
What are the values of a, b, and c in the quadratic equation 0 =
x2 – 3x - 2?
a = 1, b = 3, c = 2
a=, b = -3,C=-2
a = 1, b = 3, c= 2
a = 1.0= -3, c = 2
Answers
Answer:
a=1, b = -3, c=-2
Step-by-step explanation:
The quadratic equation is in the form
a[tex]x^{2}[/tex] + bx +c = 0
Using the given equation
1[tex]x^{2}[/tex] -3x -2 = 0
We can see that
a=1 b=-3 c=-2
Which equation represents a line that passes through (4,1/3 ) and has a slope of 3/4?
y – = (x – 4)
y – = (x – 4)
y – = 4(x – 3/4)
y – 4 = (x – 1/3)
Answers
Answer:
y - 1/3 = 3/4(x - 4)
Step-by-step explanation:
We know that the general equation of a line is the following:
y - yo = m(x-xo), where 'm' represents the slope of the line, and (xo, yo) is any point that belongs to the line.
Then, the equation of the line that passes through (4, 1/3) and has a slope of 3/4 is: y - 1/3 = 3/4(x - 4)
For this case we have that by definition, the slope-intersection equation of a line is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut point with the y axis.
They tell us as data that:
[tex]m = \frac {3} {4}[/tex]
Now the equation is:
[tex]y = \frac {3} {4} x + b[/tex]
We substitute the point to find "b":
[tex](4, \frac {1} {3})[/tex]
[tex]\frac {1} {3} = \frac {3} {4} (4) + b[/tex]
[tex]b = \frac {1} {3} -3\\b = - \frac {8} {3}[/tex]
Finally the equation is:
[tex]y = \frac {3} {4}x - \frac {8} {3}[/tex]
In point-slope form the equation is:
[tex]y- \frac {1} {3} = \frac {3} {4} (x-4)[/tex]
Answer:
[tex]y = \frac {3} {4}x - \frac {8} {3}[/tex]
Crystal earns $5.25 per hour mowing lawns. Write a rule to describe how the amount of money m earned is a function of the number of hours h spent mowing lawns. How much does Crystal earn if she works 2 hours and 15 minutes? m(h) = 5.25h; $11.29 ; $0.43 m(h) = 5.25h; $11.81 m(h) = 2h + 15; $25.50
Answers
Answer:
m(h) = 5.25h
$11.81 for 2 hours and 15 minutes
Step-by-step explanation:
Convert 2 hours and 15 minutes to an hour decimal: 2.25 hoursSubstitute 2.25 in for h.Multiply: (5.25)(2.25) = $11.81Charlene's parents deposit $500 in an account on the day she is born. The account earns a high interest rate of 9.2% compounded quarterly because Charlene is not allowed to access the money until her 22nd birthday. How much money will Charlene have on her 22nd birthday?
Answers
Answer:
about A+=+2000%281%2B+0.023%2F1%29%5E%281%2A18%29+=+2000%2A1.023%5E18= $3,011.56 thats my math
Step-by-step explanation:
Answer:
$3,698.50
Step-by-step explanation:
When making a compound interest rate this means that the interests generated are taken into consideration when creating new interests in the next period, now there are 4 quarterly periods on a year, this means there are 88 periods in the 22 years that the account will grow, you just have to do the math:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where n is the number of cycles per year and nt is the number of cycles over the years.
We just have to put the values into the formula:
[tex]A=500(1+\frac{.092}{4})^{22*4}[/tex]
[tex]A=500(1+\frac{.092}{4})^{88}[/tex]
[tex]A=$3,698.50[/tex]
Use the parabola tool to graph the quadratic function
f(x)=(x−2)(x−6)
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answers
Answer:
What parabola tool?
Step-by-step explanation:
I went ahead and graphed the quadratic function however, you should learn how to graph it yourself the way they are asking you to using the "parabola tool", because I cant really show you my steps in graphing it since I don't know what your parabola tool is.
Sorry
What is -2^2? I've been getting mixed results from people against calculators.
Answers
Answer:
-4
Step-by-step explanation:
Technically, the negative sign is treated as multiplying by -1, which is then separate from the 2. This equation can also be rewritten as [tex]-1 * 2^2[/tex], which would be simplified to [tex]-1 * 4[/tex] and then [tex]-4[/tex].
It depends on how the parenthesis is like. -(2)^2 will equal -4 while (-2)^2 equals 4. But the answer will most likely be 4 because they tend to make sure to put parenthesis if they want the answer to be -4. (Calculators are programmed differently which is why you're getting mixed answers.)
Please help ! I will mark you brainliest and give you 35 points
Answers
Answer:
13. part a
What Lenora did wrong is that when you multiply 2 terms, the exponents are added not multiplied. It would be 10x^4y^6
13. part b
2xy^4
when the terms are divided, the exponents are subtracted
Answer:
13. part a
What Lenora did wrong is that when you multiply 2 terms, the exponents are added not multiplied. It would be 10x^4y^6
13. part b
2xy^4
when the terms are divided, the exponents are subtracted
Step-by-step explanation:
Using the quadratic formula to solve x2 = 5 – x, what are the values of x?
Answers
Answer:
x^2=5-x
x^2+x-5=0
x=-1± √(1)^2-4(1)(-5) /2(1)
-1± √21 /2
Step-by-step explanation:
Answer:
The answer will be A. -1± √21 /2
Step-by-step explanation:
I hope it helps