Answers
Answer:
length: 343 marea: 6418 m²Step-by-step explanation:
Given an oval track in the shape of a 48 m by 96 m rectangle with semicircular ends, you want the length of the track and the area enclosed.
Track LengthIf you remove the rectangle, you see that what remains is a circle of diameter 48. The length of that circular portion of the track is the circumference of the circle:
C = πd
C = π(48 m) = 48π m ≈ 151 m
Added to that length are the two 96 m sides of the rectangle. So, the total length of the track is ...
track length = curved length + straight length
track length = 151 m + 2×96 m = 343 m
The length of the track is 343 meters.
Enclosed areaThe area enclosed by the track includes the area of the circle we saw above, and the area of the rectangle.
The radius of the circular portion is half the diameter, or 24 m. Then the area is ...
A = πr²
A = π(24 m)² = 576π m² ≈ 1810 m²
The area of the rectangular portion is the product of length and width:
A = LW
A = (96 m)(48 m) = 4608 m²
The enclosed area is the sum of these areas:
enclosed area = area of circle + area of rectangle
enclosed area = 1810 m² +4608 m² = 6418 m²
The area enclosed by the track is 6418 square meters.
The length (perimeter) of the track is approximately equal to 342.796 meters and the area enclosed by the track is approximately equal to 6417.557 square meters.
What is the perimeter and the area enclosed by the track?In this problem we have a composite figure generated by a rectangle and two semicircles, of which we must determine its perimeter and area. The perimeter is the sum of the contour lengths of the semicircles and the rectangle and the enclosed area is the sum of areas of the two semicircles and a rectangle.
The perimeter of the composite figure is:
p = 2π · r + 2 · l
p = 2π · (24 m) + 2 · (96 m)
p ≈ 342.796 m
A = π · r² + l · (2 · r)
A = π · (24 m)² + (96 m) · (48 m)
A ≈ 6417.557 m²
The length (perimeter) of the track is approximately equal to 342.796 meters and the area enclosed by the track is approximately equal to 6417.557 square meters.
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Related Questions
Find, if possible, the number of elements in sets A, B and C using the given information. If there is an inconsistency, state where it occurs. An B= 0, n(A n C) = 10, n(B n C) = 1, n(C - A) = 9, n(A - C) = 12, n(U) = 31
Answers
Using Venn sets, the number of elements in the sets are given as follows:
Set A: 22.Set B: 1.Set C: 19.What are the Venn Sets?For this problem, we consider that the sets A, B and C are the sets represented in the problem, and use the information given to find the number of elements in each set.
For the set A, we have that:
n(AnB) = 0n(A n C) = 10.n(A - C) = 12,Hence 12 elements belong only to set A and 10 belong to both A and C, hence set A has 22 elements.
For the set B, we have that:
n(AnB) = 0n(B n C) = 1In total, there are 31 elements, of which:
12 are only in A.9 are only in C.10 are in both.31 - 31 = 0, hence set B has only 1 element, that is also present in set C.
For the set C, we have that:
n(B n C) = 1. n(C - A) = 9.n(A n C) = 10Hence it has 10 elements that are also in set A, and 9(the intersection with B is included in C - A as n(AnB) = 0) are not, hence set C has 19 elements.
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In the lab, Lena has two solutions that contain alcohol and is mixing them with each other. She uses 400 milliliters less of Solution A than Solution B.
Solution A is 20% alcohol and Solution B is 17% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 179 milliliters of
pure alcohol?
Answers
Answer:
700 mL
Step-by-step explanation:
Lena wants to know how much of solution B she uses to obtain a mixture of solution A with 20% alcohol and solution B with 17% alcohol that contains 400 mL less of solution A, and has 179 mL of alcohol in it.
SetupLet b represent the number of mL of solution B in the mixture. Then (b-400) will be the number of mL of solution A. The number of mL of alcohol in the mix is ...
0.20(b -400) +0.17b = 179
SolutionSimplifying the equation gives ...
0.37b -80 = 179
0.37b = 259 . . . . . . add 80
b = 700 . . . . . . . . divide by 0.37
Lena uses 700 mL of solution B (17%) for the resulting mixture to have 179 mL of pure alcohol.
__
Additional comment
That means there will be 300 mL of solution A, and the contributions from each solution are ...
0.20×300 mL = 60 mL . . . . from solution A0.17×700 mL = 119 mL . . . . from solution Btotal alcohol = 60+119 = 179 mLCan someone help me with this question? It's due tomorrow :(
Answers
Answer:1,3
Step-by-step explanation: it is reflecting over the x-axis, not the y-axis. when answering these questions, keep in my what axis you're working with. hope this helps.
Given the following sets, find the set A' n (BUC')
U=(1, 2, 3,…,9}
A = {1, 5, 6, 7)
B={1, 2, 7)
C=(2, 3, 4, 6, 7}
Answers
From the given sets we get A’∩ (B∪C’) = {2,8,9}.
Given the universal set U= {1,2,3,4,5,6,7,8,9}
A = {1,5,6,7}
B = {1,2,7}
C= {2,3,4,6,7}
A’ (A not) means to remove all the elements of set A from the universal set U
A∪B (union of A and B) means to write all the elements of both the sets but to not repeat the single element
A∩B (intersection of A and B) means to write only the common elements of both the sets
A’ = {2,3,4,8,9}
C’ = {1,5,8,9}
First we need to find out B∪C’ which means the union of B and C’
B∪C’ = {1,2,5,7,8,9}
Now we need to find A’ (B∪C’) = {2,8,9}
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What's 3.2rounded to the nearest tenth
Answers
The demand for water use in Phoenix in 2003 hit a high of about 442 million gallons per day on June 27. Water use in the summer is normally distributed with a mean of 310 million gallons per day and a standard deviation of 45 million gallons per day. City reservoirs have a combined storage capacity of nearly 350 million gallons.
(a) What is the probability that a day requires more water than is stored in city reservoirs?
(b) What reservoir capacity is needed so that the probability that it is exceeded is 1%?
(c) What amount of water use is exceeded with 95% probability?
Answers
Using the normal distribution, it is found that:
a) There is a 0.1867 = 18.67% probability that a day requires more water than is stored in city reservoirs.
b) A capacity of 415 million gallons is needed.
c) An amount of 236 million gallons of water use is exceeded with 95% probability.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 310, \sigma = 45[/tex]
For item a, the probability is one subtracted by the p-value of Z when X = 350, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (350 - 310)/45
Z = 0.89
Z = 0.89 has a p-value of 0.8133.
1 - 0.8133 = 0.1867.
There is a 0.1867 = 18.67% probability that a day requires more water than is stored in city reservoirs.
For item b, the capacity should be the 99th percentile, which is X when Z = 2.327, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
2.327 = (X - 310)/45
X - 310 = 45 x 2.327
X = 415. (rounded)
A capacity of 415 million gallons is needed.
For item c, the amount of water use is the 5th percentile, which is X when Z = -1.645, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
-1.645 = (X - 310)/45
X - 310 = -1.645 x 45
X = 236.
An amount of 236 million gallons of water use is exceeded with 95% probability.
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the distribution of lengths of rainbow trout from a certain river are normally distributed with a standard deviation of 2.4 inches. it 15% of the rainbow trout are longer than 15 inches, which of the following is closest to the mean of the distribution?
Answers
Based on the calculations, the value which closest to the mean of the distribution is equal to: B. 18 inches.
What is a z-value?A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:
Z = (x - μ)/δ
Where:
x represents the sample mean or observed data.μ represents the mean.δ represents the standard deviation.If 15 percent of the rainbow trout are longer than 15 inches, then we have:
P(x > 15) = 0.15
From the z-table, the z-value which corresponds to a mean of 0.15 is given by:
z-value = -1.036
Substituting the given parameters into the formula, we have;
Z = (x - μ)/δ
-1.036 = (15 - μ)/2.4
-1.036 × 2.4 = 15 - μ
-2.4864 = 15 - μ
μ = 15 + 2.4864
Mean, μ = 17.4864
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Complete Question:
The distribution of lengths of rainbow trout from a certain river are normally distributed with a standard deviation of 2.4 inches. it 15% of the rainbow trout are longer than 15 inches, which of the following is closest to the mean of the distribution?
A. 26 inches
B. 18 inches
C. 30 inches
D. 33 inches
E. 34 inches
The selling price of an item is480 $. It is marked down by 10%, but this sale price is still marked up from the cost of $360. Find the markup from cost to sale price
Answers
Answer: $72
Step-by-step explanation:
Oddly worded question but if I understand it correctly we need to find the marked down price and subtract $360 from it.
It is 10% off so an easy way to do the math is to find what 90% of $480 dollars is.
.90 * 480 = $432
Then we subtract $360 from this sale price.
$432 - $360 = $72
A mountain biking park has 48 trails, 37.5% of which are beginner trails.
The rest are divided evenly between intermediate and expert trails.
How many expert trails are in the park?
Answers
The number of expert trails in the park is 15.
How many expert trails are in the park?Percentage can be described as the fraction of an amount expressed as a number out of hundred. The sign :used to represent percentages is %.
The first step is to determine the total number of intermediate and expert trails
Intermediate and expert trails = (1 - percentage of beginner trails) x total number of trails
(1 - 0.375) x 48
0.625 x 48= 30
The second step is to divide the total number of intermediate and expert trails by 2 since they are an equal number.
30 / 2 = 15
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-21-17+25+65=52 please help right now thank you!
Answers
According to the solving the LHS = RHS this shows the equality symmetric property.
52 = 52.
What is the difference between LHS and RHS?LHS is an informal shorthand again for the left-hand side of the an equation in mathematics. Likewise, RHS refers to the right-hand side. Because equality is symmetric, both sides share the same value, expressed differently.
What is the idea of equality?Given the "equality" (=) relation and a = b, if b = a holds true for all a and b, equality is said to be symmetric. For all of a and b, the assertion is TRUE (no counterexample can be found). This is known as the equality symmetric property.
According to the given data:-21-17+25+65=52
Proving that both LHS = RHS :
-21-17+25+65=52
-21-17+25+65=52
- 38 + 90 = 52
52 = 52
So,
LHS = RHS
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Suppose you want to have $600,000 for retirement in 20 years. Your account earns 5% interest. How much would you need to deposit in the account each month?
Answers
You need to deposit $1459.667 every month;
Let the amount needed to be deposited each month be 'x' ;
Monthly interest rate, i = 5%/12 = 0.4167% = 0.004167
Total amount = $600,000
Total time (in months) = 20 × 12 = 240 years;
Therefore, according to question;
600,000 = x . [(1 + i)ⁿ -1]/i
600,000 = x. [(1 + 0.004167)²⁴⁰ - 1]/0.004167
x = 1459.667
The additional amount you must repay over and above the principal borrowed is called interest. This is how lending institutions turn a profit.
Typically, interest is expressed as an annual percentage of the principal.
Monthly interest is the interest that is paid every month or after every 30 days.
We compute the monthly interest rate by dividing the annual interest rate by 12 to calculate the monthly interest on a loan or investment.
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If m/MSN = 106°, then what is m/MSP?
M
R/1
3/2
4
15
Answers
The measure of m∠MSP as represented in the image attached is 74 degrees.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An angle is formed from the intersection of two or more lines. Types of angles are acute, obtuse and right angle.
From the image shown:
m∠MSN + m∠MSP = 180° (sum of angles in a straight line)
106 + m∠MSP = 180°
m∠MSP = 74°
The measure of m∠MSP as represented in the image attached is 74 degrees.
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Solve -3.5 = x/4 for x using the multiplication property of equality. The operation in the problem is
Answers
The operation used in the problem is Multiplication property of equality and the value of x is -14
Property of equality-3.5 = x/4
cross Multiplication- 3.5 × 4 = x
-14 = x
Check:
-3.5 = x/4
- 3.5 = -14 / 4
-3.5 = -3.5
Therefore, the operation used in the problem is Multiplication property of equality and the value of x is -14
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please help i need help i will give crowns
Gena please!
Answers
Answer:
2
90
Step-by-step explanation:
54 / 3 = 18
so 18 licks per 1 lollipop.
18 + 18 = 36 (aka 2 lollipops).
18 x 5 = 90 (equivalent to 5 lollipops).
Answer:
36/2
90/5
Step-by-step explanation:
54/3=18 36/2=18 and 90/5= 18
What are the solutions to the equation x-7/x=6?
x=-7 and x=1
x=-6 and x=-1
x=-1 and x=7
x=1 and x=6
Answers
Answer:
x=7
7-7/7-6=0
0/1=0
Zero divided by anything=0
| (6-x)-9 |
absolute value and i need help solving. do i just combine and make it -3-x? (this problem came from a fog education.
Answers
This simplifies to
[tex]|(6-x)-9|\\\\\boxed{|-x-3|}[/tex]
Determine which integer will make the equation true.
3x + 9 = 24
S = {3, 4, 5, 6}
A: 3
B: 4
C: 5
D: 6
Answers
Answer:
c) 5
Step-by-step explanation:
Solving for the value of x,
→ 3x + 9 = 24
→ 3x = 24 - 9
→ x = 15/3
→ [ x = 5 ]
Hence, option (c) is correct.
Simplify: (39x^5z^4)^0 • 18x^2y
Answers
The simplification of (39x⁵z⁴)⁰ • 18x²y is 18x²y.
What is Simplification?Making anything simpler is known as simplification. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.
To simplify an equation:
By eliminating all common components from the numerator and the denominator and putting the fraction in its simplest/lowest form, we can simplify fractions. Mathematical expressions can be made simpler by grouping and combining related terms.Rewrite the given equation using the commutative property of multiplication.
18(39x⁵z⁴)⁰x²y
Use the power rule (xy)ⁿ=xⁿyⁿ for distributing the exponent.
18(39⁰(x⁵)⁰(z⁴)⁰)x²y
Anything raised to 0 is 1.
18(1(x⁵)⁰(z⁴)⁰x²y
Multiply (x⁵)⁰(x⁵)⁰ by 11.
18((x⁵)⁰(z⁴)⁰)x²y
Multiply the exponents in (x⁵)⁰.
18(x⁰(z⁴)⁰)x²y
Multiply x⁰ by x² by adding the exponents.
18(x²(z⁴)⁰)y
Simplify 18(x²(z⁴)⁰)y
18x²y
Therefore, simplification of given equation is 18x²y.
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1.83 * 47
help need in the next 3 hours
Answers
Answer:
if you want to multiply its 1.83 x 47 = 86.01
Step-by-step explanation:
The gravitational force (F ) felt by an object (m1) due to another object (m2) at a distance d is given by F = G m1m2/r2.
what is the value of r?
Answers
Based on the equation for gravitational force, the value of radius (r) is equal to r = √(GM₁M₂/F).
What is a gravitational force?A gravitational force can be defined as a universal force of attraction which acts between two (2) physical objects, especially by pulling them together.
How to calculate the gravitational force?Mathematically, the gravitational force between two (2) planetary objects is given by this formula:
F = GM₁M₂/r²
Where:
r represents the radius or mean distance.G represents the gravitational constant.M represents the mass.F represents the gravitational force.Making r the subject of formula, we have:
Fr² = GM₁M₂
Divide both sides by F, we have:
r² = GM₁M₂/F
Taking the square root of both sides, we have:
r = √(GM₁M₂/F)
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A container has 4 3/5 L of water. 1 7/10 is needed to fill it to full capacity what is the capacity of the container in liters. Please helppp!!!!
Answers
The capacity of the given container is 6.3 liters.
What are Mathematical operations?This term refers to a mathematical operation (such as differentiation or multiplication by a constant) where the action on the sum of two functions is equal to the sum of the actions of the operation on each function, following the same logic as the principle of superposition.So, 4(3/5) + 1(7/10):
4(3/5) + 1(7/10)20+3/5 + 10+7/1023/5 + 17/10Take LCM: 102(23) + 17/1046 + 17/1063/106.3 litersTherefore, the capacity of the given container is 6.3 liters.
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All my points please help! Given a unit circle, what is the value for y?
Answers
the value of y for the given circle will be 1 / 50 ( approx).
We are given a unit circle.
So, we get that:
centre = (0, 0)
Equation of the circle will be
x² + y² = 1
Now, we have a point (- 17 / 20, y)
Substituting the values in the equation, we get that:
(- 17 / 20)² + y² = 1
343 / 400 + y² = 1
y² = 57 / 400
y = 1 / 50 ( approx)
Therefore, we get that, the value of y for the given circle will be 1 / 50 ( approx).
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Answer: top one is 111 dont know bottom
Step-by-step explanation:
<3
Between which two integers is the value of 11
Answers
The two integers where the value of square root of 11 lies is between 3 and 4.
How to calculate the value?It should be noted that the information is to find the two integers where the value of square root of 11 lies.
It should be noted that the square root of 11 is 3.33.
It should be noted that 3.33 lies between 3 and 4.
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Between which two integers is the value of square root of 11.
f(x-2)=4x^2+5x-9.
Please explain thoroughly with work. Thank you!
Answers
Answer:
Hello,
If you want f(x) read this.
Step-by-step explanation:
I am going to use Horner's method.
[tex]\begin {array}{c|c|c|c}&x^2&x&1\\---&--&--&--\\&4&5&-9\\x=2&&8&26\\---&--&--&--\\&4&13&\boxed{17}\\x=2&&8&42\\---&--&--&--\\&4&\boxed{21}&59\\x=2&&8\\---&--&--&--\\&\boxed{4}&29\\\end {array}\\\\\\F(x-2)=4(x-2)^2+21(x-2)+17\\\\So\ \boxed{F(x)=4x^2+21x+17}\\\\Proof:\\\\F(x-2)=4(x-2)^2+21(x-2)+17\\\\\\=4x^2-16x+16+21x-42+17\\\\=4x^2+5x-9\\[/tex]
I hope this is what you want.
Online Algebra If the area of a rectangle with width x can be represented with the expression A(x) = x(14-x), what is the perimeter of the rectangle? O A 28 B 56 C 56-4x Te D 4x+28
Answers
14 is the perimeter of the rectangle .
What does a rectangular 's perimeter mean?
Considering that the polygon's perimeter is equal to the sum of its sides. As a result, the perimeter (P) of a rectangle is given by P = the total of its four sides. P = a + b + a + b (Opposite sides of rectangle are equal).The answer provided below has been developed in a clear step by step manner.
Step: 1
Given, A(x) = x(14-x)
Comparing with A = lw , we have
Length , l = x and
Width , w = 14 - x
Step: 2
We know,
Perimeter of rectangle ,
p = 2( l + w )
p = 2 ( x + 14 - x )
p = 28
Hence,
Perimeter of rectangle = 14
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Find the average rate of change on the interval [-3,3] for the given function
Answers
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
so let's use those two points off the curve in order to get it, check the picture below.
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-3)}}} \implies \cfrac{1}{3 +3}\implies {\LARGE \begin{array}{llll} \cfrac{1}{6} \end{array}}[/tex]
Which expression is equivalent to the quantity nine raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power?
A:negative three raised to the third power divided by nine raised to the fourth power
B:three raised to the third power divided by nine raised to the fourth power.
C:negative nine raised to the fourth power divided by three raised to the tenth power
D:nine raised to the fourth power divided by three raised to the tenth power
Answers
The simplification of the given indices is; D: nine raised to the fourth power divided by three raised to the tenth power
How to use the Law of Indices?We want to find the expression that is equivalent to the quantity nine raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power. This is written as;
(9⁻² * 3⁵)⁻²
According to laws of indices, we know that;
(a²)³ = a²*³ = a⁶
Thus;
(9⁻² * 3⁵)⁻² = (9⁻²)⁻² * (3⁵)⁻²
⇒ 9⁴ * 1/3¹⁰
⇒ 9⁴/3¹⁰
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Select all the expressions equivalent to (81)3/5
((81)1/5)3
0 ((81)1/3)5
((81)1/3)5
((81)5)1/3
3(81)5
5(81)³
Answers
1/5 multiplied by 3 is 3/5, which is then multiplied by 81. The expressions are equal
PLEASE SHOW HOW YOU GOT YOUR ANSWER!
What is 2 1/2 ÷ 1/2?
A. 3 1/2
B. 7 1/2
C. 7 1/6
D. 2/15
Answers
Answer:
Turn the 2 1/2 into the improper fraction which is 5/2. Now you can do 5/2 divided by 1/2. when diving turns the 1/2 to 2/1 and multiply. so 5/2 x 2/1= 1.25. 1.25 as a fraction is 1 1/4
If 8/9 is multiplied by 3/7, will the product be greater than either of the 2 factors?
Answers
Answer:
No, it is less than both of the fractions.
Step-by-step explanation:
Multiply the two fractions
[tex]\frac{8}{9}[/tex] x [tex]\frac{3}{7}[/tex] = 0.380952381
Figure out the value of the two fractions
[tex]\frac{8}{9}[/tex] = 0.8888888889
[tex]\frac{3}{7}[/tex] = 0.4285714286
Reduce/Simplify:
0.380952381 = 0.38
0.8888888889 = 0.89
0.4285714286 = 0.43
