Dona paints ornaments for a school play. Each ornament is as shown and is made up of two identical cones. She uses one bottle of paint to paint 202 cm2. How many bottles of paint does she need in order to paint 70 ornaments? Use 3.14 for pi.1. The surface area of one ornament is about ___cm2.2. She needs ___ bottles.
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The surface area of a cone is given by the following formula:
[tex]SA=\pi rs+\pi r^2[/tex]Where SA is the surface area, s is the slant and r is the radius. Replace for the given values:
[tex]\begin{gathered} SA=(3.14)\cdot(2.7)\cdot(8.6)+(3.14)\cdot(2.7)^2 \\ SA=72.91+22.89 \\ SA=95.8 \end{gathered}[/tex]Each ornament has 2 cones, it means that each ornament has a surface area of:
[tex]SA=2\cdot95.8=191.6[/tex]If she needs to paint 70 ornaments, she will have to paint:
[tex]SA=191.6\cdot70=13412[/tex]According to the question statement, she uses one bottle of paint to paint 202cm^2. To find how many bottles she needs to paint 70 ornaments, divide the total area of the 70 ornaments by 202:
[tex]\frac{13412}{202}=66.39[/tex]The answers are:
1. The surface area of one ornament is about 191.6 cm^2.
2. She needs 67 bottles.
Related Questions
Edmond divided 8 3/4 gallons of ketchup equally into 2 smaller bottles to put on the tables in his hamburger restaurant. How much ketchup did he put in each bottle?
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
total ketchup = 8 3/4 gallons
bottles = 2
ketchup in each bottle = ?
Step 02:
[tex]8\text{ + }\frac{3}{4}=\frac{32+3}{4}=\frac{35}{4}[/tex][tex]\frac{\frac{35}{4}}{\frac{2}{1}}=\frac{35\cdot1}{4\cdot2}=\frac{35}{8}[/tex]The answer is:
Edmond put 35/8 gallons of ketchup in each bottle.
the sum of pi and 3/4 is a (n)_________ numberA. RationalB. NaturalC. WholeD. Irrational
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Remember that pi is an irrational number which means it has infinite decimal without a pattern.
If we add a number to pi we would still get an irrational number because the sum of a rational and an irrational won't give another type of number than an irrational.
Therefore, the right answer is D.Instructions: Find the missing length indicated.x=Check81225X
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Given: A right triangle is given, and an altitude is drawn to the hypotenuse of the triangle.
Required: To determine the missing side x.
Explanation: The given triangle is as follows-
Let the side of the triangle be as shown in the figure. Now triangle ABD is a right-angled triangle. Hence, by Pythagoras theorem, we have-
[tex]\begin{gathered} BD^2=AB^2+AD^2 \\ (225)^2=x^2+y^2\text{ ...}(1) \end{gathered}[/tex]Similarly, triangles ABC and ADC are right-angled triangles. Thus-
[tex]\begin{gathered} y^2=z^2+(144)^2\text{ ...}(2) \\ x^2=(81)^2+z^2\text{ }...(3) \end{gathered}[/tex]Equations (1), (2), and (3) represent equations in 3 variables. Hence solving equations (1) and (2) by substituting the value of y from equation (2) into equation (1) as follows-
[tex]\begin{gathered} x^2+z^2+(144)^2=(225)^2 \\ x^2+z^2=(225+144)(225-144) \\ x^2+z^2=369\times81 \\ x^2+z^2=29889\text{ ...}(4) \end{gathered}[/tex]Now, we can solve equations (3) and (4) for x as follows-
[tex]x^2+x^2+z^2=6561+z^2+29889[/tex]Further solving for x as-
[tex]\begin{gathered} 2x^2=36450 \\ x=\sqrt{18225} \\ x=\pm135\text{ units} \end{gathered}[/tex]Since the side of a triangle can't be negative. Hence, x=135 units.
Final Answer: The length of the missing side is-
[tex]x=135\text{ units}[/tex]How to solve for area of number 6 to the nearest square unit
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132 square meters
Explanations:6) The given composite function is made up of a large rectangle and a small rectangle as shown:
The area of the composite figure = Area of the rectangle A + area of rectangle B
Since area of the rectangle = Length * width, hence;
[tex]\begin{gathered} \text{Area of the figure=}LW+lw \\ \text{Area of the figure=(9m}\times12m\text{)+(}4m\times6m\text{)} \\ \text{Area of the figure=}108m^2+24m^2 \\ \text{Area of the figure=}132m^2 \end{gathered}[/tex]Hence the area of the composite figure is 132 square meters
You deposit 500$ in a savings account that earns 2.5 interest compounded yearly. Find the balance in the account after the given amount of time A. 1 yearB. 5 years C. 20 years
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In order to find the balance after the given time, use the following formula:
I = P(1 + r/n)^(t·n)
where
r: interes rate = 2.5% = 0.025
n: frequency = 1
t: time = 1, 5, 20
P: principal investment = 500
replace the previous values of the parameters into the formula for I:
A. 1 year:
I = $500(1 + 0.025/1)^(1·1) = $512.5
B. 5 years:
I = $500(1 + 0.025)^(5·1) = $565.7
C. 20 years
I = $500(1 + 0.025)^(20·1) = $819.3
The table below shows the value for the function y=f(x)If g(x)=1/2 which of the following are solutions to g(x) select all that applyA (-3,5.5)B(-1,-2)C(0,4)D (5,-8)
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So we have a table of values that associate x values with a function f(x). The pairs (x,y) are solutions to the equation y=f(x) and they are:
[tex]\begin{gathered} (-3,5) \\ (-1,-4) \\ (0,2) \\ (5,-8) \\ (6,3) \end{gathered}[/tex]If we define a new function g(x)=(1/2)*f(x) its solutions will be those of f(x) but with their y values divided by 2. Then the solutions to g(x) are:
[tex]\begin{gathered} (-3,\frac{5}{2})=(-3,2.5) \\ (-1,-\frac{4}{2})=(-1,-2) \\ (0,\frac{2}{2})=(0,1) \\ (5,-\frac{8}{2})=(5,-4) \\ (6,\frac{3}{2})=(6,1.5) \end{gathered}[/tex]Then the only option with a solution to g(x) is the second option (-1,-2).
What is the length of the hypotensis?If necessary round to the nearest 10th
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We need to use the pythagorean theorem:
In a right triangle we have:
hyppootenuse
leg1
leg2
And the theorem says:
[tex]\text{hyppotenuse}^2=\text{leg}1^2+\text{leg}2^2[/tex]In this case:
leg1 = 9cm
leg2 = 3cm
[tex]c^2=(9cm)^2+(3cm)^2[/tex]And solve for c:
[tex]\begin{gathered} c=\sqrt[]{81cm^2+9cm^2} \\ c=\sqrt[]{90cm^2} \\ c\approx9.486832\ldots \end{gathered}[/tex]To the nearest tenth:
c = 9.5cm
A small office supply store sells paper clipsin packs of 100 and packs of 250. If thestore has 84 packs of paper clips in stocktotaling 12,300 paper clips, how manypaper clips would a customer buy if he buyshalf of the packs of 250 that the store hasin stock?
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The first equation should represent the total number of packs, each with 100 or 250 paper clips
i,e. x + y = 84 (1)
The second equation should represent the total number of paper clips. Because x represents packs with 100 paper clips and y represents packs with 250 paper clips, the second equation is
100x + 250y = 12,300 (2)
Simplify the linear equation;
x + y = 84
x = 84 - y
Substitute the value of x = 84 - y in the equation (2);
100x + 250y = 12300
100(84 - y) + 250y = 12300
8400 - 100y + 250y = 12300
8400 + 150y = 12300
150y = 12300 - 8400
150y = 3900
y = 3900/150
y = 26
Substitute the value of y = 26 in the equation x = 84 - y
x = 84 - y
x = 84 - 26
x = 58
The store has 26 packs of 250 paper clips in stock.
The customer would buy 13 × 250 = 3,250 paper clips,
Answer : 3250
Calculator 5 ft С A window in the shape of a parallelogram has the dimensions given What is the area of this window?A.20 ftB.24 ftC.28 ftD.40 ft
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Area of a parallelogram = b x h
Students in Introductory Chemistry are recording the masses of samples as part of a lab experiment. for 5 samples, Sidney has recorded these masses: 4 grams 6 grams 4 grams 8 grams 2 grams What is the mode of the masses?
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Solution
For this case we have the following data given:
4, 6, 4, 8, 2
We need to remember that the mode is the most repeated value so then the answer would be:
Mode= 4
Ahmad is putting 11 colored light bulbs into a string of lights. There are 5 green light bulbs, 4 yellow light bulbs, and 2 red light bulbs. How many distinct ordersof light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?
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So, we have a total of 11 light bulbs. 5 are green, 4 are yellow and two are red. In cases in which the light bolbs are considered identical, we use the following math formula:
[tex]N=\frac{n!}{n_g!n_{y!}n_r!}[/tex]In which n is the total, 11. ng is thee number of green lightbulbs, ny the number of the yellow ones, and nr the number of the reds. So:
[tex]\begin{gathered} N=\frac{11!}{5!4!2!} \\ N=\frac{11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5!}{5!\cdot24\cdot2} \\ N=11\cdot10\cdot9\cdot7 \\ N=6,930 \end{gathered}[/tex]So, Ahmad has 6,930 distinct orders
what is 8 × 2000? and
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simple, it's a multiplication
I multiply the number of atoms with the weight of each one to find the total weight of the gas
[tex](5.04\times10^{23})\times(1.67\times10^{-24}^{})[/tex]We group
[tex](5.04\times1.67)\times(10^{23}\times10^{-24})[/tex]and solve
[tex]\begin{gathered} (8.4168)\times(10^{-1}) \\ =0.84168 \end{gathered}[/tex]the result is: 0.84 grams
Kerala is a marine biologist studying the breeding habits of an exotic species of sea turtlesLast year she observed the number of pregnant mother titles at each beach on an isolated island in the pacific. The histogram below summarizes the data. Use the histogram to answer each question
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a) The number of beaches in each class is represented by the height of the class. The class that has the least frequency is the one with 5-7.
We can see that the height is 2, thus the number of beaches in this class is 2.
b) We can see that each class has width 3:
2 to 4: 2, 3, 4
5 to 7: 5, 6, 7
and so on
The width of each class is 3.
c) The classes with 11 or more are the last two, from 11 to 13 and from 14 to 16.
The height of the class 11 to 13 is 4
The height of the class 14 to 16 is 7
The total beaches with 11 or more pregnant turtles is the sum: 4 + 7 = 11
What is the relative value of F(x) when the value of x is close to 2 for the function F(x) = 1/x+2, whose graph is shown below?A. A very large numberB. ZeroC. A very small numberD. Either a very large number or a very small number
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Answer:
D. Either a very large number or a very small number
Explanation:
Given the function:
[tex]F(x)=\frac{1}{x+2}[/tex]As can be seen from the graph, the point x=2 is an asymptote of the function.
Thus, the relative value of F(x) when the value of x is close to 2 is either a very large number or a very small number.
Option D is correct.
C. How long until there are only 20 mg remaining.
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Therefore, it will take 12.52 hours
A-Lab assistant need to create a 900 ml mixture that is 4.5% hydroelectric acid. The assistant has solutions of 3% and 5.5% in supply at the lab. Using the variables x and y to represent the number of milliliters of 3% solution and the number of milliliters of the 5.5% solution respectively, determine a system of equation that describes the situation.Enter the equations below separated by a comma.How many milliliters of the 3% solution should be used?How many milliliters of the 5.5% solution should be used?
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Let x and y to represent the number of milliliters of 3% solution and the number of milliliters of the 5.5% solution respectively. Given that the volume of the mixture is 900 ml, we have
x + y = 900
The mixture should contain 4.5% hydroelectric acid. Recall, percentage is expressed in terms of 100. The concentration of the mixture is
4.5/100 * 900 = 40.5
x should contain 3% of hydroelectric acid. The concentration of x is
3/100 * x = 0.03x
y should contain 5.5% of hydroelectric acid. The concentration of y is
5.5/100 * y = 0.055y
The equation representing the concentration would be
0.03x + 0.055y = 40.5
Thus, the required system of equations is
x + y = 900
0.03x + 0.055y = 40.5
From the first equation,
x = 900 - y
Substituting x = 900 - y into the second equation, we have
0.03(900 - y) + 0.055y = 40.5
27 - 0.03y + 0.055y = 40.5
- 0.03y + 0.055y = 40.5 - 27
0.025y = 13.5
y = 13.5/0.025
y = 540
x = 900 - y = 900 - 540
x = 360
360 ml of 3% solution and 540 ml of 5.5% solution should be used.
Use the number line to determine if each number is a solution . And don't worry this is just a practice :)
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A pyramid has a square base of 120ft. On a side. The four slant faces are all congruent isosceles triangles with base angles 55 degrees. Find the height of the pyramid?
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Our first approach will be to get the slant height, i.e. the sides of the triangle. We can get this via the sine rule as:
We can get the side of the isosceles to be:
[tex]\begin{gathered} \frac{120}{\sin70}=\frac{x}{\sin 55} \\ x=\frac{120\sin 55}{\sin 70}=104.6ft \end{gathered}[/tex]Now we need to find the perpendicular height.
To do that, we need to find the length of the diagonal of the base. We will apply the Pythagoras theorem.
This is given as:
[tex]\begin{gathered} d=\sqrt[]{o^2+a^2} \\ \text{ Where:} \\ o=\text{opposite = length of base} \\ a=\text{adjacent = length of base} \end{gathered}[/tex][tex]\begin{gathered} d=\sqrt[]{120^2+120^2} \\ d=170\text{ ft} \end{gathered}[/tex]Next, we plot the triangle that will help us get our perpendicular height.
We now find h.
[tex]\begin{gathered} h=\sqrt[]{104.6^2-85^2} \\ h=60.96\text{ ft} \end{gathered}[/tex]The perpendicular height is 60.96 ft
g(x) = 2x + 3, find g(a + 1). *
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ANSWER:
g(a+1) = 2a + 5
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]g(x)=2x+3[/tex]Replacing, when x is a + 1:
[tex]\begin{gathered} g(a+1)=2\cdot(a+1)+3 \\ g(a+1)=2a+2+3 \\ g(a+1)=2a+5 \end{gathered}[/tex]Please help me solve this math question. Please explain each step clearly
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a) Since the relation is proportional, the graph is a line.
In order to graph a line we only need two points and connecting them we get the line.
In this case, we know that at 4h the pool has 5200 gallons. The point woud be (4, 5200)
Now we need another point. The simplest one is the origin. When the time is zero, the amount of water in the pool is also 0, then we have another point (0, 0)
Now with the points (0, 0) and (4, 5200) we can graph the relationship.
b) We need to compair the filling rates. In the graph provided we can see that in 3 hours, there is 10,800 gallons. Since the other pool had 5,200 gallons in 4 hours, is clear that the second pool fills much more quicker.
I have a practice problem that I need answered, thank you
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Given inequality:
[tex]6x^2-x\text{ }<\text{ 2}[/tex]Re-arranging:
[tex]6x^2-x\text{ - 2 }<\text{ 0}[/tex]Factorizing the expression to the left:
[tex]\begin{gathered} 6x^2-2x\text{ + x -2 }<\text{ 0} \\ 6x^2\text{ -4x +3x -2 }<\text{ 0} \\ (3x-2)(2x+1)\text{ }<\text{ 0} \end{gathered}[/tex]Hence:
[tex]\begin{gathered} 3x-2\text{ }<\text{ 0} \\ 3x\text{ }<\text{ 2} \\ x\text{ }<\text{ }\frac{2}{3} \end{gathered}[/tex]Since their product is negative. one of the factors would be positive.
[tex]\begin{gathered} 2x\text{ + 1 > 0} \\ 2x\text{ > -1} \\ \frac{2x}{2}\text{ >}-\text{ }\frac{1}{2} \\ x\text{ > -}\frac{1}{2} \end{gathered}[/tex]The solution on a number line:
The solution on interval notation:
[tex]\mleft(-\frac{1}{2},\: \frac{2}{3}\mright)[/tex]I need to find how much does is his monthly payment.
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The total amount Christian will pay is given by:
[tex]A=P(1+rt)[/tex]where P is the principal, r is the interes rate and t is the time. In this case we have that P=15000, r=0.07 and t=2. Then we have:
[tex]\begin{gathered} A=15000(1+0.07(2)) \\ A=17100 \end{gathered}[/tex]Hence he will pay $17,100 in total. Now, to find the monthly amount we divide the total by the number of months; in this case 24:
[tex]\frac{17100}{24}=712.50[/tex]Therefore he will pay $712.50 each month.
which situation could be written mathematically as 10÷1/2A) The amount of time it would take to watch ten 1/2 hour videos.B) The amount of time it would take to watch half of a ten minute video.C) The number of 1/2 hour videos in ten hours.D) The number of minutes in one tenth of a 1/2 hour video.I also need to show my work :)
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Which situation could be written mathematically as 10÷1/2?
10 ÷ 1/2 = 10 x 2/ 1 = 20
If there are 1/2 hour videos in ten hours, then there are also 20 videos
The correct answer is Option C - The number of 1/2 hour videos in ten hours.
A survey of 130 freshmen business students at a local university produced the results listed below. How many students took only psychology?
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We could draw the following Venn's diagram to solve this problem.
So, after drawing this diagram, we notice that the number of students that took only psychology were 9.
6,9x,y3,3I need to find a equation relating to x and y
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Answer:
[tex]y=2x-3\rightarrow Slope-intercept\text{ form}[/tex]Step by step explanation:
As a first step to find the equation of the line, we need to calculate the slope.
The slope is represented by the following equation:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{where,} \\ \text{ (x}_1,y_1)and(x_2,y_2)_{}_{} \\ \text{are the points given} \end{gathered}[/tex]Then, the slope of the line would be:
[tex]\begin{gathered} m=\frac{9-3}{6-3} \\ m=\frac{6}{3} \\ m=2 \end{gathered}[/tex]Then, by the slope-point form of the line we can get slope-intercept form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=2(x-3) \\ y=2x-6+3 \\ y=2x-3\rightarrow Slope-intercept\text{ form} \end{gathered}[/tex]A plane is 110 mi north and 189 mi east
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ANSWER:
30.2°
STEP-BY-STEP EXPLANATION:
The angle x can be calculated by means of the tangent trigonometric ratio, which relates the opposite leg to the adjacent leg, just like this:
[tex]\begin{gathered} \tan x=\frac{\text{ opposite}}{\text{ adjacent }} \\ \text{ opposite = 110} \\ \text{ adjacent = 189} \end{gathered}[/tex]We substitute and calculate for x just like this:
[tex]\begin{gathered} \tan\:x\:=\:\frac{110}{189} \\ x=\tan^{-1}\left(\frac{110}{189}\right) \\ x=30.2\degree \end{gathered}[/tex]Therefore, the angle is 30.2°
Determine if the expression s3+s2+s5/4 is a polynomial or not. If it is a polynomial state the type and degree of the polynomial
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Given the algebraic expression
[tex]s^3+s^2+s^{\frac{5}{4}}[/tex]For the algebraic expression to be classified as a polynomial, all expressions must have a non-negative integer exponent.
From the given expression, we can see that the last term doesn't obey this rule (an exponent that is in fraction term).
Hence, the expression given is not a polynomial.
What effect does changing the function f(x)=3sin(x)+1to the function g(x)=3sin(x4)+2 have on the graph of f(x)?
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Step 1
The parent function f(x) is given as;
[tex]f(x)=3\sin (x)+1[/tex]If we transform the function by adding 1 to it we will have;
[tex]\begin{gathered} f(x)=3\sin (x)+1+1 \\ f(x)=3\sin (x)+2 \end{gathered}[/tex]We have the following graph;
which means when you add 1 to the to get f(x)=3sin(x)+2, the function is shifted up by 1 unit.
Step 2
If the function is further transformed to;
[tex]f(x)=3\sin (\frac{x}{4})+1[/tex]we will have the graph below;
This means that the graph stretches horizontally by a factor of 4.
Therefore the changes f(x) passes through to g(x) are;
[tex]\begin{gathered} f(x)=2\sin (\frac{x}{4})+1_{}--(A\text{ horizontal stretch by a factor of 4)} \\ g(x)=2\sin (\frac{x}{4})+2---(A\text{ shift up by 1 unit)} \end{gathered}[/tex]Answer; The graph is stretched horizontally by a factor of 4 and shifted up by 1 unit.
Graph y=3/4x+2. i got the y intercept but i don’t know how to do the other point
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ANSWER
EXPLANATION
Once we have the y-intercept we have to find another point - since two points are enough to draw a line. To find this other point we can use the slope of the line. We can write the slope of a line as:
[tex]m=\frac{\text{rise}}{\text{run}}[/tex]In this line rise = 3 and run = 4. This means that the other point is 4 units to the right of the y-intercept and 3 units up:
Mark this new point and draw a line through both points.
What are the new vertices of quadrilateral KLMN if the quadrilateral is translated two units to the right and four units upward?
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The given transformation is
[tex](x,y)\rightarrow(x+2,y+4)[/tex]We have to apply this translation to each vertex.
[tex]\begin{gathered} K(-4,-2)\rightarrow K^{\prime}(-2,2) \\ L(-1,-2)\rightarrow L^{\prime}(1,2) \\ M(-1,-5)\rightarrow M^{\prime}(1,-1) \\ N(-4,-5)\rightarrow N^{\prime}(-2,-1) \\ \end{gathered}[/tex]According to this result, the right answer is C.