A flower garden is shaped like a circle. Its radius is 18 yd. A ring-shaped path goes around the garden. The width of the path is 5 yd.
The gardener is going to cover the path with sand. If one bag of sand can cover 6 yd^2, how many bags of sand does the gardener need? Note that sand comes only by the bag, so the number of bags must be a whole number. (Use the value 3.14 for pi.)
Answers
The number of gallons of the coating must be a whole number will be 114 gallons.
What is the area of the circle?Let d be the diameter of the circle. Then the area of the circle will be
A = (π/4) d² square units
At the recreation area, there is a pool molded like a circle with a measurement of 24 yds. A ring-molded way circumvents the pool. Its width is 6 yds.
The area of the path will be given as,
A = (π/4) (24 + 6 + 6)² - (π/4) (24)²
A = (π/4) [36² - 24²]
A = (π/4) [720]
A = 565.5 square yards
We will give another layer of covering to the way. On the off chance that one gallon of covering can cover 5 yd². Then the number of gallons of coating is given as,
⇒ (565.5) / 5
⇒ 113.097
⇒ 114 gallons
The number of gallons must be a whole number will be 114 gallons.
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Related Questions
2727. Boat Y and boat Z start traveling toward each other from 600 mile apart. Y istraveling at 35 mph, Z at 40 mph. How many hours will pass before theymeet?a. 7 b. 8 c. 9 d. 102828. Refer to problem 27. Y and Z start traveling toward each other from 600miles apart. Y is traveling at 35 mph, Z at 40 mph. How many miles will Ytravel before they meet?a. 400 b. 320 c. 350 d. 280
Answers
Given:
Speed of boat Y is 35 mph and speed of boat Z is 40 mph.
Both the boats are 600 miles a part.
The diameter is 16 ftwhat's the area the circle?
Answers
Explanation
Step 1
the area of a circle is given by:
[tex]\text{Area}_{circle}=\text{ }\pi\cdot\frac{diameter^2}{4}[/tex]let
diameter=16 ft
now, replace
[tex]\begin{gathered} \text{Area}_{circle}=\text{ }\pi\cdot\frac{diameter^2}{4} \\ \text{Area}_{circle}=\text{ }\pi\cdot\frac{(16ft)^2}{4} \\ \text{Area}_{circle}=\text{ }\pi\cdot\frac{256ft^2}{4} \\ \text{Area}_{circle}=201.06ft^2 \end{gathered}[/tex]I hope this helps you
if anyone could help me on #17 i would appreciate it!
Answers
Answer:
[tex]f(x)=-\lvert x-7\rvert+2[/tex]Step-by-step explanation:
The function that was transformed is:
[tex]f(x)=\lvert x\rvert[/tex]If it reflects in the x-axis, shift 7 units to the right, and shift upward 2 units, we need to know the transformation rules for these displacements:
[tex]\begin{gathered} \text{ -f(x) reflects the function in the x-axis (upside-down)} \\ f(x-b)\text{ shifts the function b units to the right.} \\ \text{ f(x)+b shifts the function b units upward.} \end{gathered}[/tex]Now, with this in mind, the equation of the function transformed would be:
[tex]f(x)=-\lvert x-7\rvert+2[/tex]Solve the quadratic equation by completing the square.x^2+6x-1=0First choose the appropriate form and fill in the blank with the correct numbets. Then, solve the equation. Round your answer to the nerest hundredth. If there is more than one solutions, separate them with commas.
Answers
Answer:
Explanation:
Given the quadratic equation
x^2+6x-1=0
Step 1: Add 1 to both sides of the equation
x^2+6x-1 + 1 = 0 + 1
x^2 + 6x = 1
Step 2: Complete the square by adding the square of the half of coeficient of x to both sides
Coefficient of x = 6
Half of 6 = 6/2 = 3
Square of 3 = 3^2 = 9
Add 9 to both sides
x^2 + 6x + 3^2 = 1
Write an equation parallel to y = 3x + 6 that passes through the point (4,7).Remember to type the" - "if a number is negative, such as-2.y =X +
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The equation that is parallel to y = 3x + 6 has the same slope as y, namely 3; therefore, we already know that the equation we are seeking has the form
[tex]y=3x+b[/tex]Now we just need to solve for the y-intercept b, and to do that we use the point (4, 7 ). Putting x = 4 and y = 7 into the above equation gives
[tex]7=3(4)+b[/tex][tex]7=12+b[/tex][tex]\therefore b=-5[/tex]Hence, the equation that is parallel to y = 3x + 6 that passes through the point (4,7) is
[tex]y=3x-5[/tex]
2. A right prism has a square base of edge a and altitude h, write the formula for the total surface area
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Given the shape in the question the total surface area of a prism is given by:
[tex]\begin{gathered} ph+2A \\ \text{where p=perimeter of the base} \\ h=\text{height} \\ A=\text{Area of the base} \end{gathered}[/tex]Since the right prism is square based, then we have:
[tex]\begin{gathered} \text{perimeter of a square = 4a where a is the edge of the square} \\ \text{Area of a square= a}^2 \end{gathered}[/tex]Hence, the formula for the total surface area of the prism is given by:
[tex]\begin{gathered} 4ah+2a^2 \\ \text{where a is the edge of the square and h is the height} \end{gathered}[/tex]LEARNING OBJECTIVE Determine a vertical Horizontal or oblique asymptole of a rational functionWhich of the following rational functions will have a graph with a horizontal asymptote of y=09nh7x) =2x + 4b.)4x) - 2x + 23x - 1c.)3x - 2x2x+X-1d.)2x - 83x+x+1
Answers
We need to find a vertical asymptote. This means, when we are approaching a value X, then Y becomes infinite or -infinite
A rational function R(x) = p(x) / q(x) will have a vertical asymptote at x=r when r is substituted in for x it makes the denominator zero but not the numerator
option a) oblique asymptote
option b) we have both horizontal (at y=0) and vertical (at x=-1) asymptotes
Option c)
option d) horizontal asymptote
if m=24 and v=4 p=mv
Answers
p = 96 is the product of m = 24 and v = 4
What is multiplication ?In mathematics, a product is the outcome of multiplication, or an expression that identifies the things to be multiplied, known as factors.
Calculationm = 24
v = 4
p = mv
p = 24 * 4 = 96
p = 96
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Find the quotient. Express the final result using positive integer exponents only (72x^-1 y^4)^-1 / (8x^8y^3)
Answers
ANSWER:
[tex]\frac{1}{576x^7y^7}[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]\frac{\left(72x^{-1}y^4\right)^{-1}}{8x^8y^3}[/tex]We operate to simplify and we are left with the following:
[tex]\frac{72^{-1}x^{-1\cdot-1}y^{4\cdot-1}}{8x^8y^3}=\frac{\frac{1}{72}xy^{-4}}{8x^8y^3}=\frac{1}{72\cdot8\cdot x^8\cdot x^{-1}\cdot y^3\cdot y^4}=\frac{1}{576x^7y^7}[/tex]When a figure is translated its orientation (blank) and the measurements of its angles (blank).The options for both blanks are the same and the options are, remain the same or change
Answers
First of all, remember that translation is a transformation which doesn't imply a change of size or shape, that is, the image will be congruent to its image.
Having said that, the complete paragraph would be
When a figure is translated its orientation remains the same and the measurements of its angles remain the same.
The orientation doesn't change because it's defined as the position of points of the figure, these points change its position where we rotate the figure, which is not the case here.
What is the probability that a customer selected at random was male and purchased a SUV?
Answers
Given:
A table
Required:
The probability that a customer selected at random was male and purchased an SUV.
Explanation:
The probability of getting a male with an SUV is given by
The total number of males divided by the total number of people and multiply by the number of SUVs divided by the total number of cars
[tex]\frac{60}{240}\times\frac{21}{240}=0.021875[/tex]Final Answer:
0.021875
The sum of the catheters in a triangle is 27 cm. The corresponding catheter in another right-angled triangle, uniform with the first one, is 2cm and 7cm. Calculate the area of the first triangle.
Answers
Given: The sum of the catheters in a triangle is 27 cm
To Determine: The area of the triangle
Solution
Please note the below
Let the first cathetus be x, then the second cathetus would be
[tex]\begin{gathered} c_1=x \\ c_2=27-x \end{gathered}[/tex]For the second right triangle
[tex]\begin{gathered} c_1=2 \\ c_2=7 \end{gathered}[/tex]Since the two right triangles are corresponding to each other, then the ratio of their cathethers are equal
Therefore
[tex]\begin{gathered} \frac{x}{27-x}=\frac{2}{7} \\ 7x=2(27-x) \\ 7x=54-2x \\ 7x+2x=54 \\ 9x=54 \\ x=\frac{54}{9} \\ x=6 \end{gathered}[/tex]So, the cathethers for the first right triangle would be
[tex]\begin{gathered} c_1=x:c_2=27-x \\ c_1=6 \\ c_2=27-6 \\ c_2=21 \end{gathered}[/tex]Note that the catheters formed the base and the height of the first triangle. The area of a triangle can be calculated using the formula below
[tex]\begin{gathered} Area(triangle)=\frac{1}{2}\times base\times height \\ Area(triangle)=\frac{1}{2}\times6cm\times21cm \\ Area(triangle)=3cm\times21cm \\ Area(triangle)=63cm^2 \end{gathered}[/tex]Hence, the area of the first triangle is 63cm²
Time(wki469Height ofplant (in)9.013.520.25Find the rate of change for weeks 40le and 69.Explain the meaning of the rate of change for each case.
Answers
Explanation
Step 1
when you have 2 coordinates ( A and B), the slope of the line that passes thought those point is given by
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]where
[tex]\begin{gathered} A=(x_1,y_1) \\ B=(x_2,y_2) \end{gathered}[/tex]A and B are 2 known points of the line
Step 2
so, the slope represents the rate of change
i)the rate of change for 4-6 weeks
Let
A=(4 ,9)
B=(6,13.5)
replace
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope_1=\frac{13.5-9}{6-4}=\frac{4.5}{2}=2.25 \\ slope_1=2.25 \end{gathered}[/tex]Step 3
ii)the rate of change for 6-9weeks
Let
A(6,13.5)
B(9,20.25)
replace,
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{20.25-13.5}{9-6}=\frac{6.75}{3}=2.25 \end{gathered}[/tex]the slope represents the rate of change, it means for every case the plant is growing at a constant rate (2.25 inches per week)
I hope this helps you
Hi, can you help me with this problem?A manufacturer has a monthly fixed cost of $42,500 and a production cost of $6 for each unit produced. The product sells for $11/unit.(a) What is the cost function?C(x)= (b) What is the revenue function?R(x)=(c) What is the profit function?P(x)= (d) Compute the profit (loss) corresponding to production levels of 6,000 and 11,000 units.P(6,000)=P(11,000)=
Answers
Given:
Fixed cost = b = $ 42,500
Production cost (Variable cost) /unit = m = $ 6/ unit
Let 'x' represent the number of unit, therefore the variable cost will be
[tex]6x[/tex]a) The cost function will be the sum of the fixed cost and the variable cost.
[tex]C(x)=6x+42500[/tex]b) The revenue function is the amount the product is sold per unit.
Recall: 'x' represents the number of units.
Therefore,
[tex]11\times x=11x[/tex]Hence, the revenue function R(x) is
[tex]R(x)=11x[/tex]c) The profit function is the difference between the revenue function and the cost function.
[tex]P\mleft(x\mright)=11x-\mleft(425000+6x\mright)=5x-42500[/tex]Hence, the profit function is
[tex]P\mleft(x\mright)=5x-42500[/tex]d) Let us compute the profit (loss) values when the units are 6000 and 11000
Using the profit function
[tex]P(x)=5x-42500[/tex]Therefore,
[tex]\begin{gathered} P(6000)=5(6000)-42500=30000-42500=-\text{ \$12500} \\ P(11000)=5(11000)-42500=55000-42500=\text{ \$12500} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} P(6000)=-\text{ \$12500 (which is a loss)} \\ P(11000)=\text{ \$12500 (this is a profit)} \end{gathered}[/tex]I need help with my math
Answers
The Slope of a Line
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]The graph provided suggests the use of the points (3,-3) and (5,-3). The slope is:
[tex]\displaystyle m=\frac{-3+3}{5-3}=\frac{0}{2}=0[/tex]The slope of the line is 0. It corresponds to a horizontal line
Expand 4(y + 5).4(y+5)= 1
Answers
ANSWER
[tex]4y+20=[/tex]EXPLANATION
We want to expand the expression:
[tex]4(y+5)[/tex]To do this, we apply the distributive property:
[tex]a(b+c)=(a\cdot b)+(a\cdot c)[/tex]Therefore, we have:
[tex]\begin{gathered} (4\cdot y)+(4\cdot5) \\ 4y+20 \end{gathered}[/tex]That is the answer.
Given the area of triangle AEC=63cm^2, find the area of triangle ABC.
Answers
We are given that the area of triangle AEC = 63 centimeters squared.
Since segment CD equals segment DB that means that triangle CDA and triangle BDA have the same area, and also triangle CDE and triangle BDE have the same area. This means mathematically the following:
[tex]A_{\text{ADC}}-A_{\text{AEC}}=A_{\text{ADB}}-A_{\text{AEB}},\text{ (1)}[/tex]Also
[tex]A_{\text{ADC}}=A_{\text{ADB}},\text{ (2)}[/tex]Replacing equation (1) in equation (2)
[tex]A_{\text{ADC}}-A_{\text{AEC}}=A_{\text{ADC}}-A_{\text{AEB}}[/tex]Simplifying
[tex]A_{\text{AEC}}=A_{\text{AEB}}[/tex]Therefore:
[tex]A_{\text{AEB}}=63\operatorname{cm}^2[/tex]Since segments DE and EA is the same, then:
[tex]A_{\text{CDE}}=A_{\text{AEC}}[/tex]Therefore:
[tex]A_{\text{CDE}}=63\operatorname{cm}^2[/tex]Since
[tex]A_{\text{CDE}}=A_{\text{BDE}}[/tex]We have:
[tex]A_{\text{BDE}}=63\operatorname{cm}^2[/tex]therefore, the area of the triangle is:
[tex]A_{\text{ABC}}=A_{\text{AEC}}+A_{\text{AEB}}+A_{\text{CDE}}+A_{\text{BDE}}[/tex]Replacing the known values:
[tex]\begin{gathered} A_{\text{ABC}}=68+68+68+68=4(68) \\ A_{\text{ABC}}=272\operatorname{cm}^2 \end{gathered}[/tex]a firefighter on the ground sees fire break through a window near the top of a building. The angle of elevation to the window seal is 28 degrees. The angle of elevation to the top of the building is 42 degrees. The firefighter is 75 ft from the building and her eyes are 5 feet above the ground. What Ruth window seal distance guess you report by radio to Firefighters on the roof
Answers
Problem:
A firefighter on the ground sees fire break through a window near the top of a building. The angle of elevation to the window seal is 28 degrees. The angle of elevation to the top of the building is 42 degrees. The firefighter is 75 ft from the building and her eyes are 5 feet above the ground. What Ruth window seal distance guess you report by radio to Firefighters on the roof?
Solution:
There are two big triangles, one of them is that formed by a fireman, the roof and the building foundation plus the height of the fireman as the vertices. So, the opposite side to the 42 degrees angle given is denoted by h_roof, and the adjacent side is 75 ft away from the building:
[tex]h_{roof\text{ }}=\text{ }75.tan(42^{\circ}\text{)}[/tex]that is:
[tex]h_{roof\text{ }}=\text{ (}75)(0.9004)\text{ = }67.53[/tex]Now, the other big triangle is formed by the fireman, the window, and the building foundation plus the height of the fireman as vertices:
[tex]h_{WIN}=75.\tan (28)[/tex]that is:
[tex]h_{WIN}=(75)(0.5317)=\text{ 39.}87[/tex]then, the difference between the heights is the roof-to-windowsill:
[tex]h=h_{roof}-h_{WIN}=\text{ }67.53-39.87\text{ = }27.66[/tex]Then, we can conclude that the correct answer is:
[tex]h=27.66[/tex]When Ryan runs the 400 meter dash, his finishing times are normally distributedwith a mean of 65 seconds and a standard deviation of 2 seconds. If Ryan were to run.36 practice trials of the 400 meter dash, how many of those trials would be between63 and 65 seconds, to the nearest whole number?
Answers
Solution
Step 1
Dalvin's finishing time is normally distributed with a mean of 65 seconds and a standard deviation of 1 second.
[tex]\begin{gathered} \text{Mean }\mu\text{ = 65} \\ Standard\text{ deviation }\sigma\text{ = 1} \end{gathered}[/tex]Step 2
Under the empirical rule, 68% of the results will be within 1 standard deviation.
Step 3
Since the standard deviation is 1 second, 68% of Dalvin's finishing time will be between 63 and 65 seconds.
Final answer
68%
1.X: -2, -1, 0, 1, 2Y: -7, -2, 1, -2, -7Domain:Range:Function: Yes Or no?
Answers
We have
X: -2, -1, 0, 1, 2
Y: -7, -2, 1, -2, -7
the domain is the set of all the possible values for x, in this case, we have
{-2, -1, 0, 1, 2}
the range is the set of all possible values of y in this case we have
{-7, -2, 1}
With this information, we can say it is a function,
The equation V=15200(0.93) t V=15200 (0.93)t represents the value (in dollars) of a car t years after its purchase
Answers
We will have the following:
[We can see a constant compound of the decrease in price]
The value of this car is decreasing at a rate of 7 percent.
The purchase price of the car was 15 200 dollars.
It takes 3 1/3 spoons of chocolate syrup to make 3 1/2 į gallons of chocolate milk.How many spoons of syrup would it take to make 5 gallons of chocolate milk?
Answers
Given:
[tex]3\frac{1}{3}spoons\text{ of chocolate syrup to make 3}\frac{1}{2}\text{ gallons of chocolate milk.}[/tex][tex]\begin{gathered} \text{Number of spoons required of syrup to make 5gallons of chocolate milk=}\frac{3\frac{1}{3}}{3\frac{1}{2}}\times5 \\ No\text{ of spoons required of syrup to make 5gallons of chocolate milk=}\frac{\frac{10}{3}}{\frac{7}{2}}\times5 \\ No\text{ of spoons required of syrup to make 5gallons of chocolate milk=}\frac{10}{3}\times\frac{2}{7}\times5 \\ No\text{ of spoons required of syrup to make 5gallons of chocolate milk=}\frac{100}{21} \\ No\text{ of spoons required of syrup to make 5gallons of chocolate milk=}4\frac{16}{21}\text{ } \end{gathered}[/tex]Managers of a sports arena’s parking garage keep track of the duration of time customers park their cars there. Shown in the stem and - leaf display below is a sample of 15 such parking duration (in minutes). Use the display to answer the questions that follow.
Answers
Step 1
A Stem and Leaf Plot is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).
[tex]198\text{ Minutes}[/tex]Step 2
[tex]\begin{gathered} In\text{ the 180s, we have;} \\ 182,183,186,189\text{ minutes} \\ The\text{ shortest parking duration in the 180's is 182} \\ Answer=182\text{ Minutes} \end{gathered}[/tex]Step 3
[tex]\begin{gathered} In\text{ the 160's, we have; 160,164,164} \\ Answer=3\text{ } \end{gathered}[/tex]Using the following images, name the intersection of line QS and line LC.
Answers
The intersection between two non-parallel lines is a point, as we can see in the following diagram:
As we can see from the image, the intersection point between QS and LC is W.
Answer: Point W
if like bc is parallel to line AD what is the measure of BAD
Answers
D.
In some states, the amount of sales tax on an item is found by multiplying the cost of the item by 0.07. Find the sales tax of a DVD that costs $23.99. O $1.67 $1.68 $16.79 O $0.17
Answers
DVD = $23.99
Sales tax = (23.99 x 0.07)
= 1,679 = $1.68
2. You pay $18.00 for 30 text messages. At the same rate, how much would 12text messages cost?17
Answers
$18 for 30 messages
Ratio = price / messages = 18/30
For 12 messages:
Price / messages = x /12
Equal both ratios:
18/30 = x /12
Solve for x:
0.6 (12) = x
$7.2 = x
$7.2 for 12 messages
Line A is perpendicular to Line B.If the slope of Line A is -5,what is the slope of Line B?391410
Answers
Given:
Line A is perpendicular to Line B.
Required:
what is the slope of Line B?
Explanation:
Based on the given conditions, formulate.
[tex]m=\frac{-5}{3}[/tex]Find the slope of line that is perpendicular to
[tex]\frac{-5}{3}[/tex][tex]m=\frac{3}{5}[/tex]Required answer:
[tex]m=\frac{3}{5}[/tex]The value of an antique car is modeled by the function
Answers
when we are modeling increments using functions the standard form should be
[tex]V(t)=A\cdot(1+r)^t[/tex]In which A represents the initial value and r represents the rate it is increasing per year.
In this case to find what is the increment per year we equal what is inside the parentheses
[tex]\begin{gathered} 1+r=1.004 \\ r=1-1.004 \\ r=0.004 \end{gathered}[/tex]now this decimal can be represented as a percentage if we multiply by 100
[tex]\begin{gathered} \text{\%r}=0.004\cdot100 \\ \text{\%r=0.4\%} \end{gathered}[/tex]It is increasing by 0.4% per year.
A bag is made with 1,350 green, blue, and white beads. Twice as many green beads as blue beads are used the number of white beads is half of the total number of green and blue beads. how many green beads are used?
Answers
Write equations for each succeeding sentences. Use G for green, B for blue, and W for white beads.
[tex]\begin{gathered} G+B+W=1350 \\ G=2B \\ W=\frac{1}{2}(G+B) \\ G=\text{?} \end{gathered}[/tex]Solve for the value of G as follows.
Rewrite the equations in terms of B. Since the value of G is already written in terms of B, write the value of W in terms of B.
[tex]\begin{gathered} W=\frac{1}{2}(G+B)_{}_{} \\ =\frac{1}{2}(2B+B) \\ =\frac{1}{2}(3B) \end{gathered}[/tex]Substitute the values of G and W, in terms of B, into the first equation and then solve for B.
[tex]\begin{gathered} G+B+W=1350 \\ 2B+B+\frac{1}{2}(3B)=1350 \\ 4B+2B+3B=2700 \\ 9B=2700 \\ B=300 \end{gathered}[/tex]Note that we obtained the third equation by multiplying both sides of the equation by 2. This eliminates the denominator, 2, from the left side of the equation.
Substitute the obtained value of B in the second given equation to solve for G.
[tex]\begin{gathered} G=2B \\ =2(300) \\ =600 \end{gathered}[/tex]Substitute the obtained value of B into the obtained value of W and then simplify.
[tex]\begin{gathered} W=\frac{1}{2}(3B) \\ =\frac{1}{2}\lbrack3(300)\rbrack \\ =\frac{1}{2}(900) \\ =450 \end{gathered}[/tex]To check if the answer is correct, add all the number of beads per color and determine if the sum is the same as the given value.
[tex]\begin{gathered} G+B+W=1350 \\ 600+300+450=1350 \\ 1350=1350 \end{gathered}[/tex]Since the equation is true, the answers are correct.
Therefore, there must be 600 green beads that were used.