At the park there is a pool shaped like a circle. A ring-shaped path goes around the pool. Its inner radius is
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the dimension of the given circles
[tex]\begin{gathered} Radius\text{ of big circle}\Rightarrow8yards \\ Radius\text{ of small circle}\Rightarrow6yards \end{gathered}[/tex]STEP 2: Find the Area of the two circular paths
[tex]\begin{gathered} Area=\pi r^2 \\ Area\text{ of big circle}\Rightarrow3.14\times8^2=200.96yards^2 \\ Area\text{ of small circle}\Rightarrow3.14\times6^2=113.04yards^2 \end{gathered}[/tex]STEP 3: Calculate the area of the ring-shaped path
[tex]\begin{gathered} Area\text{ of ring shaped path}\Rightarrow Area\text{ of big circle - Area of small circle} \\ Area\text{ of ring shaped path}\Rightarrow200.96-113.04=87.92yard^2 \end{gathered}[/tex]STEP 4: Find the number of gallons needed to coat the ring-shaped path
[tex]\begin{gathered} 1\text{ gallon}\Rightarrow8yards^2 \\ x\text{ gallons}\Rightarrow87.92yards^2 \\ By\text{ cross multiplication,} \\ x\times8=87.92\times1 \\ Divide\text{ both sides by 8} \\ x=\frac{87.92}{8}=10.99 \\ x\approx11\text{ gallons} \end{gathered}[/tex]Hence, it will take approximately 11 gallons to coat the ring shaped path
Related Questions
what does 5 over 100 =
Answers
You can identify that "5 over 100" can be written as a fraction. 5 will be the numerator and 100 will be the denominator:
[tex]\frac{5}{100}[/tex]To reduce this fraction, you need to divide the numerator and the denominator by the Greatest Common Factor (GCF) between them.
In this case, to find the GCF, you need to:
- Decompose the number into their Prime Factors:
[tex]\begin{gathered} 5=5 \\ 100=2\cdot2\cdot5\cdot5=2^2\cdot5^2 \end{gathered}[/tex]- Notice that 5 is a common factor. Then, you need to choose the one with the lowest exponent:
[tex]GCF=5[/tex]Therefore, by dividing the numerator and the denominator by 5, you get:
[tex]=\frac{1}{20}[/tex]Hence, the answer is:
[tex]=\frac{1}{20}[/tex]what special right triangle is shown ??
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The triangle shown is a special right triangle 30°-60°-90°.
In this types of triangles the measure of the hypotenuse is two times that of the leg opposite the 30° angle, and the measure of the other leg is sqrt(3) times that of the leg opposite the 30°. This comes from the fact that:
[tex]\begin{gathered} \text{hyp}=opp\sin 30 \\ \text{hyp}=\frac{1}{2}\text{opp} \\ \text{then} \\ 2\text{hyp}=\text{opp} \end{gathered}[/tex]and:
[tex]\begin{gathered} \text{adj}=\frac{\text{opp}}{\tan 30} \\ \text{adj}=\frac{opp}{\frac{1}{\sqrt[]{3}}} \\ \text{adj}=\sqrt[]{3}opp \end{gathered}[/tex]The box says to use 3 tablespoons of the chemical for 2 cups of water. David has a container that will hold 5 cups of water. Which proportion would be used to determine how many tablespoons of the chemical he needs to use for the 5 cups of water?
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represents We have the next information
ts= tablespoons
cw= cups of water
3 ts ------- 2 cw
x ------- 5 cw
x represent the tablespoons necessary to the portion of 5 cups of water
[tex]x=\frac{5\cdot3}{2}=\frac{15}{2}=7.5[/tex]he needs 7.5 tablespoons of the chemical to use 5 cups of water
(5,0) slope= 4/5 write the equation in slope point form.
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Here, we want to write the equation in the point-slope form
We have this as follows;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ m\text{ = slope = }\frac{4}{5} \\ (x_1,y_1)\text{ = (5,0)} \\ y-0\text{ = }\frac{4}{5}(x-5) \\ y\text{ = }\frac{4}{5}(x-5) \end{gathered}[/tex]Find the vertex and the AOS for this problem y = 3x^2 - 6x + 5
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In order to find the vertex of this quadratic equation, we can use the formula for the x-coordinate of the vertex:
[tex]x_v=-\frac{b}{2a}[/tex]Where a and b are coefficients of the quadratic equation in the standard form:
[tex]y=ax^2+bx+c[/tex]Using a = 3 and b = -6, we have:
[tex]x_v=-\frac{-6}{6}=1[/tex]Now, to find the y-coordinate of the vertex, we just need to use the value of x_v in the equation:
[tex]\begin{gathered} y=3\cdot1-6\cdot1+5 \\ y=3-6+5 \\ y=2 \end{gathered}[/tex]So the vertex coordinates are (1, 2).
The axis of symmetry (AOS) is the vertical line that passes through the vertex, so if the x-coordinate of the vertex is 1, the AOS will be x = 1.
Columbia Mirror and glass pays Barbara Davis a $1460 monthly salary plus a 9% commission on merchandise she sells each month. Assume Barbara's sales were $66,800 for last month. Calculate the following amount: 1. Amount of commission 2.Gross pay
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We have that Barbara's sales were $66800, and she gets a commission of 9% on merchandise she sells. Then the amount of comission is:
[tex]C=66800\cdot0.09=6012[/tex]For the gross pay, we just have to add 1460 to the total comissions:
[tex]GP=6012+1460=7472[/tex]therefore, the amount of the comission is $6012 and the gross pay is $7472
13. Find the value of x.
124
136
132
158
129
142
116
need ASAP!!
Answers
The Solution.
The sum of interior angles of a polygon is given by:
[tex]\begin{gathered} \text{Sum = (n-2)180} \\ \text{where n =number of sides} \end{gathered}[/tex]Substituting 6 for n in the formula above, we get
[tex]\begin{gathered} \text{Sum =(6-2)180} \\ \text{Sum = 4}\times180=720^o \end{gathered}[/tex]So,
[tex]\begin{gathered} 78+134+136+132+2x+x=720 \\ \text{collecting like terms, we get} \end{gathered}[/tex][tex]\begin{gathered} 480+3x=720 \\ 3x=720-480 \\ 3x=240 \\ \text{Dividing both sides by 3, we get} \\ x=\frac{240}{3}=80^o \end{gathered}[/tex]Thus, the correct answer is 80 degrees (option C)
Al and Viola Speer were granted an $80,000 mortgage.At the closing, they will have to pay the closings costsshown plus real estate taxes of $1,230. What are thetotal costs?
Answers
Total costs are given by
[tex]\text{Total cost=mortgage+}real\text{ estate taxes}[/tex]So:
[tex]\text{Total cost=}80000+1230=81230[/tex]Answer: total costs are $81,230
What are the zeros of f(x) = x2 + x - 30?A. X= -2 and x= 15B. X= -6 and x = 5C. x= -15 and x = 2D. X = -5 and x = 6
Answers
Answer:
B. X= -6 and x = 5
Explanation:
Given the function f(x) = x^2 + x - 30, the zeros occurs at f(x) = 0
x^2 + x - 30 = 0
Factorize;
x^2+6x-5x-30 = 0
x(x+6)-5(x+6) = 0
(x+6)(x-5) = 0
x+6 = 0 and x-5 = 0
x = -6 and 5
Hence the zeros of the equation is at x = -6 and x = 5
Multiply and combine like terms. Use ^ for exponents. (x+3)(2x^2+3x+7)
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We are given the following expression:
[tex]\mleft(x+3\mright)\mleft(2x^2+3x+7\mright)[/tex]We will use the distributive property:
[tex]\mleft(x+3\mright)\mleft(2x^2+3x+7\mright)=(x)(2x^2)+(x)(3x)+(x)(7)+(3)(2x^2)+(3)(3x)+(3)(7)[/tex]Solving the products:
[tex]\mleft(x+3\mright)\mleft(2x^2+3x+7\mright)=2x^3+3x^2+7x+6x^2+9x+21[/tex]Associating like terms:
[tex]\mleft(x+3\mright)\mleft(2x^2+3x+7\mright)=(2x^3)+(3x^2+6x^2)+(7x+9x)+21[/tex]Adding like terms:
[tex]\mleft(x+3\mright)\mleft(2x^2+3x+7\mright)=2x^3+9x^2+16x+21[/tex]Since we can't simplify any further this is the answer.
What are the coordinates of the center of a circle whose equation is:(20 - 6)2 + (y – 2)?81Center:
Answers
The equation of a circle located at a distance (a,b) from the origin is given by
[tex]y=(x-a)^2+(y-b)^2=r^2[/tex]Given:
[tex]\begin{gathered} y=(x-6)^2\text{ + (}y-2)^2\text{ = 81} \\ y=(x-6)^2\text{ + (}y-2)^2\text{ = }9^2 \end{gathered}[/tex]To get the coordinates, we will have to compare the given equation to the equation of the
circle
Upon comparing the terms and coefficient,
a = 6
b= 2
r = 9
Hence the center of the circle is (6,2)
radius = 9
given points j(2,5), a(6,6), and R(,4,2), graph Jar and its reflection image across the given line
Answers
First, we need to locate the points J, A and R:
J is in red, A is in green and R is in purple.
Now to make a reflection across the y-axis, we need to multiply the x-coordinate of each point by (-1):
[tex]\begin{gathered} J(2,5)\Rightarrow J^{\prime}(-2,5) \\ A(6,6)\Rightarrow A^{\prime}(-6,6) \\ R(4,2)\Rightarrow R^{\prime}(-4,6) \end{gathered}[/tex]And we get:
Which is the reflection across the y-axis
The amounts of 8 charitable contributions are $100, $80, $250, $100, $500, $1000, $100, and $150. The mean, median, and mode of the amounts are given below.mean = $285median = $125mode = $100Which value describes the amount received most often?
Answers
Given:
mean = $285
median = $125
mode = $100
And we have that the most frequently received amount is about mode.
Answer: mode = $100
Linda works at several different jobs. She works at a kennel and earns $10 per hour, works as a cashierearning $12 per hour, and also earns $30 a week to watch her neighbor's daughter after school. Lastweek she worked 5 hours at the kennel and earned a total of $185. How many hours did she work as acashier?
Answers
Answer:
8.75 hours
Explanation:
• She earns $10 per hour at the kennel
,• She earns $12 per hour working as a cashier
,• She also earns $30 a week babysitting.
Let the number of hours which she worked as a cashier = c
If she worked 5 hours at the kennel. her total income will be:
[tex]10(5)+30+12c=185[/tex]We then solve for c.
[tex]\begin{gathered} 50+30+12c=185 \\ 12c=185-50-30 \\ 12c=185-80 \\ 12c=105 \\ c=\frac{105}{12} \\ c=8.75\text{ hours} \end{gathered}[/tex]Linda worked for 8.75 hours as a cashier.
•
Name the segments in the figure below.E, F, G, H Select all that apply
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1) In this figure, we have the following rays, line segment and lines.
2) Checking the answer
Line segments have endpoints.
The measure of QR IS 15 cm, and the measure of Q'R' is 52.5 cm. Which scale factor was used for the dilation?A. 7B. 2C.2/7D.7/2
Answers
Answer:
The correct option is D
7/2
Explanation:
Given that the measure QR is 15 cm, and Q'R' is 52.5 cm.
To know the scale factor used for the dilation, we have:
[tex]15=\frac{52.5}{x}[/tex]Solving for, x, we have what we are looking for.
Multiply both sides by x
[tex]15x=52.5[/tex]Divide both sides by 15
[tex]x=\frac{52.5}{15}=\frac{7}{2}[/tex]33 in62 in(a) Use the calculator to find the area and perimeter of the window.Make sure to include the correct units.Area:Perimeter:(b) The window's glass will be replaced.Which measure would be used in finding the amount of glass needed?Perimeter Area(C) a sliver wire will be placed around the window which measure would be used in finding the amount of wire needed
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To find the area of the window. Being a rectangle, we just need to multiply its base and height. The base is 33 inches, and the height is 62 inches, then:
[tex]\text{Area}=(33in)\cdot(62in)=2046in^2[/tex]The area of the window is 2046 square inches.
The perimeter of it is the sum of the lengths of all 4 sides in the rectangle. We have 2 sides 62 inches long (left and right), and 2 sides 33 inches long (top and bottom). Then, the perimeter is:
[tex]\text{Perimeter}=33in+33in+62in+62in=190in[/tex]If the window's glass is to be replaced, the measure used to find the amount of glass needed is the area, since the glass covers all the window, including the inside. If a wire will be placed around the window, the measure used to estimate the amount of wire needed will be the perimeter, because the perimeter gives us t
Solve the equation. |4x+5|−6=22
Answers
Given:
|4x+5|−6=22
Add 6 to both sides of the equation:
|4x+5|−6 + 6 =22 + 6
|4x+5l = 28
Now, for the absolute value consider 2 options:
a) 4x+5 = 28 and b) -(4x+5)= 28
• a)
4x+5 = 28
4x = 28 - 5
4x = 23
x= 23/4
• b)
-(4x+5)=28
-4x - 5 = 28
-4x = 28+5
-4x= 33
x= -33/4
Answer:
x= 23/4
x= -33/4
Which of the following represents the factorization of the trinomial below,?x²-14×+48A(x+6)(x-8)B(x-6)(x-8)C(x-4)(x-12)D(x+4)(x-12)
Answers
Given the following equation:
[tex]\text{ x}^2\text{ - 14x + 48}[/tex]Let's factorize the given trinomial,
Let's think of factors of 48 that will give you a sum of -14.
Product Factors Sum of Factors
48 1 x 48 49
48 -1 x -48 -49
48 6 x 8 14
48 -6 x -8 -14
Therefore, the factors must be -6 and -8.
We get,
[tex]\text{ x}^2\text{ - 14x + 48 = (x + \_\_)(x + \_\_)}[/tex][tex]\text{ = (x + (-6))(x + (-8))}[/tex][tex]\text{ = (x -6)(x - 8)}[/tex]Therefore, the answer is (x - 6)(x - 8). It is letter B.
The population of a city increased from 40000 in 2000 to 50000 in 2006. Find the continuous growth model rate for the population t years after 2000
Answers
continuous growth model = P e^(rt)
[tex]P\cdot e^{rt}[/tex]The population of a city increased from 40000 in 2000 to 50000 in 2006.
so, P = 40,000 and t = 2006 - 2000 = 6
So,
[tex]50,000\text{ = 40,000 }\cdot e^{6r}[/tex][tex]e^{6r}=\text{ 50,000/40,000 = 1.25}[/tex]taking ln for both sides
6r = ln 1.25
r = ln1.25/6 = 0.0372
So, the continuous growth model rate for the population t years after 2000
[tex]40,000e^{0.0372\text{ t}}[/tex]
2. If you deposit $820 into a savings account that makes 4% yearly interest, how much money willbe in the account in 7 years? Round answer to 2 decimal places. Show your work and how youentered it into the formula.hint : y = all + r)"
Answers
Answer:
$1079.06
Explanation:
The formula for finding the amount of money at the end of 7 years is
[tex]y=a(1+r)^t[/tex]where
y = final amount
a = principle amount (the amount of money you started with)
r = interest rate as a decimal
t = number of years.
Now, in our case the above variables take the following values.
a = $820
r = 4% /100 = 0.04
t = 7 years
and putting these values into the above formula gives
[tex]y=820(1+0.04)^7[/tex][tex]y=1079.06[/tex]Hence, the amount of money in the account after 7 years will be $1079.06.
How long can you lease the car before the amount of the lease
Answers
If the car costs $ 16,920 and we have to make a down payment of $ 600, so we'll have to lease $ 16,920 - $ 600 = $ 16,320
If each month we have to pay $ 340, so we do a simple math to calculate how long it will take to overcome the cost of the car:
$ 16,320 : $ 340 = 48 months
Answer: 48 months.
The world’s population is expected to grow at a rate of 1.3% per year until at least the year 2020. In 1994 the total population of the world was about 5,642,000,000 people. Use the formula to predict the world’s population , n years after 1994, with equal to the population in 1994 and i equal to the expected growth rate. What is the world’s predicted population in the year 2020, rounded to the nearest million? Question 2 options:12,632,000,0007,911,000,0007,549,000,0007,317,000,000
Answers
Answer
The answer is 7,911,000,000
EXPLANATION
Problem Statement
The question tells us that the world's population is modeled by the formula:
[tex]\begin{gathered} P_N=P_0e^{iN} \\ \text{where, } \\ i=\text{growth rate of the population} \\ N=\text{Number of years} \\ P_0=\text{Initial population at 1994} \\ P_N=\text{Population at year of interest} \end{gathered}[/tex]Solution
To solve this question, we simply need to plug in all the values given to us. That is,
[tex]\begin{gathered} \text{Growth rate = 1.3 \%} \\ \text{ Initial population (}P_0)=5,642,000,000 \\ \text{Number of years (N) = 2020 - 1994 = 26} \end{gathered}[/tex]Thus, we can find the estimated world population in year 2020 as follows:
[tex]\begin{gathered} P_N=P_0e^{iN} \\ P_N=5,642\times10^6\times e^{\frac{1.3}{100}\times26} \\ P_n=7,910.88\times10^6\approx7,911,000,000\text{ (To the nearest million)} \end{gathered}[/tex]Final Answer
The answer is 7,911,000,000
Answer: b.7,911,000,000
Step-by-step explanation:
A cone shaped has a height of 4.4 inches with an area of 12.3in^2. Find the container capacity
Answers
The volume of the cone is given as:
[tex]V=\frac{1}{3}h\pi r^2[/tex]where h is the height and r is the radius of the base. From this formula we notice that we have:
[tex]\pi r^2[/tex]and that this is the area of the base (the circle). Since we know this value already we can plug it in the volume formula, hence we have:
[tex]V=\frac{1}{3}(4.4)(12.3)=18.04[/tex]Therefore the volume (capacity) of the cone is 18.04 cubic inches.
Ayo buys supplies for the school's greenhouse. He buys f bags of fertilizerand p packages of soil. He pays $5 for each bag of fertilizer and $2 for eachpackage of soil, and spends a total of $90. The equation 5f + 2p = 90describes this relationship. If Ayo solves the equation for p, which equationwould result? *
Answers
f = fertilizer
p = soil
5f + 2p = 90
Subtract 5f from each side
5f+2p-5f = 90-5f
2p = 90-5f
Divide each side by 2
2p/2 = ( 90-5f)/2
p = 90/2 - 5f/2
p = 45 - 2.5f
Answer: p = 45 - 2.5f
Lost-time accidents occur in a company at a mean rate of 0.6 per day. What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2? Round your answer to four decimal places.
Answers
Solution
- This is a Binomial theorem question. The following are the parameters given:
[tex]\begin{gathered} n=10 \\ r=2 \\ p=0.6 \\ q=1-p=0.4 \\ \\ \text{ The formula to use is:} \\ P(r)=\sum_r^nnC_rp^rq^{n-r} \end{gathered}[/tex]- Thus, we have:
[tex]\begin{gathered} P(r\le2)=P(0)+P(1)+P(2) \\ P(0)=^{10}C_00.6^0\times0.4^{10}=0.0001048576 \\ P(1)=^{10}C_10.6^1\times0.4^9=0.001572864 \\ P(2)=^{10}C_20.6^2\times0.4^8=0.010616832 \\ \\ \therefore P(r\le2)=0.0001048576+0.001572864+0.010616832 \\ \\ P(r\le2)=0.0122945536\approx0.0123 \end{gathered}[/tex]
what are the restricted value of ratio expressed in fraction
Answers
Restricted values are values that will make the denominator equal to 0.
The denominator in the given expression is:
[tex]\text{ x}^2\text{ - 4x}[/tex]Now, let's determine what values should be restricted for the denominator not to be zero.
We get,
[tex]\text{ x}^2\text{ - 4x = 0}[/tex][tex]\text{ x}^2\text{ = }4\text{x}[/tex][tex]\text{ }\frac{\text{x}^2}{\text{ x}}\text{ = }\frac{4\text{x}}{\text{ x}}[/tex][tex]\text{ x = 4}[/tex]Therefore, the restricted value of the given ratio is 4.
Or,
[tex]\text{ x }\ne\text{ 4}[/tex]Simplify (5 + 2i)(1 + 3i). *Mark only one oval.5+6i-1-1+17i11+17i
Answers
Explanation
We are asked to simplify
[tex](5+2i)(1+3i)[/tex]To do so, we will make use of the fact that
[tex]i\times i=i^2=-1[/tex]So, we will use the FOIL method of expansion
So that
[tex]\begin{gathered} First=5\times1=5 \\ Outer=5\times3i=15i \\ Inner=2i\times1=2i \\ Last=2i\times3i=6i^2=-6 \end{gathered}[/tex]Simplifying by adding the terms above, we will have
[tex]5+15i+2i-6=5-6+15i+2i=-1+17i[/tex]Therefore, the answer is
Consider the line .What is the slope of a line perpendicular to this line?What is the slope of a line parallel to this line?
Answers
Given:
7x-9y=-5
Required:
To calculate the slope
Explanation:
Find the slope of line that is perpendicular to 7x-9y=-5
[tex]m=\frac{-9}{7}[/tex]Find the slope of the line that is parallel to 7x-9y=-5
[tex]m=\frac{7}{9}[/tex]Required answer:
[tex]m=\frac{-9}{7}\text{ m=}\frac{7}{9}[/tex]A line has this equation: y = -1x/6-8 Write an equation for the perpendicular line that goes through (-6, -2).
Answers
When two lines are perpendicular their slopes are opposite. It mearn that two perpendicular lines have slopes:
m=n
m=-n
You have the equation:
[tex]y=-\frac{1}{6}x-8[/tex]the perpendicular function to it have then a slope of:
m=1/6Use the point to find the value of the b in the equation:
[tex]y=mx+b[/tex]( -6, -2)
x= -6
y= -2
m=1/6
[tex]-2=\frac{1}{6}(-6)+b[/tex]you clear the b:
[tex]-2=-\frac{6}{6}+b[/tex][tex]-2=-1+b[/tex][tex]-2+1=b[/tex][tex]-1=b[/tex]The yo have: m=1/6 b=-1
The equation is:[tex]y=\frac{1}{6}x-1[/tex]