Answers
Solution:
Given:
A dodecagon is a 12-sided polygon.
A regular dodecagon is a figure with sides of the same length and internal angles of the same size.
The sum of exterior angles of a polygon is 360°.
The formula for calculating the size of each exterior angle is;
[tex]\begin{gathered} \text{Each exterior angle = }\frac{360}{n} \\ \text{where n is the number of sides of the polygon} \end{gathered}[/tex]For a dodecagon, n = 12
Hence,
[tex]\begin{gathered} \text{Each exterior angle = }\frac{360}{12} \\ \text{Each exterior angle = }30^0 \end{gathered}[/tex]Therefore, each exterior angle of a regular dodecagon is 30 degrees.
Related Questions
What is the x-value of the solution to this system of equations? x = 2y - 4 7x + 5y = -66 F-2 G 19 7 H -8 62 19
Answers
Answer:
x = -8
Explanation:
Given the below system of equations;
[tex]\begin{gathered} x=2y-4\ldots\ldots\ldots\ldots\ldots\text{.Equation 1} \\ 7x+5y=-66\ldots\ldots\ldots\ldots\text{Equation 2} \end{gathered}[/tex]The solve the above, let's go ahead and put equation 1 into equation 2 and solve for y;
[tex]\begin{gathered} 7(2y-4)+5y=-66 \\ 14y-28+5y=-66 \\ 19y=-66+28 \\ 19y=-38 \\ y=-\frac{38}{19} \\ y=-2 \end{gathered}[/tex]To find x, we have to substitute the value of y into equation 1 and solve for x;
[tex]\begin{gathered} x=2(-2)-4=-4-4=-8 \\ x=-8 \end{gathered}[/tex]Use the Venn diagram to complete the sentences. Write All or Some or No in each blank
Answers
If we look at the image, we must see that the parallelogram's circle is greater than the trapezoid's circle, in other words, the trapezoids are contained in the parallelograms. In addition, no information about the quadrilaterals is provided in the Venn diagram. The correct word in each sentence are
1. No trapezoids are quadrilaterals.
2. No quadrilaterals are trapezoids.
3. Some parallelograms are trapezoids.
4. All trapezoid are parallelograms.
List the coordinates coordinates of vertices of trapezoid ABCD after it has been rotated 90 Counterclockwise bout the origin and then reflected over the x-axis. A(-5,-3) B(-4,0),c(-2,0),D(O,-3)
Answers
Answer:
The coordinates of the final image is;
[tex]A^{\prime\prime}(3,5),B^{\prime\prime}(0,4),C^{\prime}^{\prime}(0,2),D^{\prime}^{\prime}(3,0)[/tex]Explanation:
From the question, the pre-image was been rotated 90 Counterclockwise bout the origin.
Which has a rule;
[tex](x,y)\rightarrow(-y,x)[/tex]Applying the rule to the given points. we have;
[tex]\begin{gathered} A(-5,-3)\rightarrow A^{\prime}(3,-5) \\ B(-4,0)\rightarrow B^{\prime}(0,-4) \\ C(-2,0)\rightarrow C^{\prime}(0,-2) \\ D(0,-3)\rightarrow D^{\prime}(3,0) \end{gathered}[/tex]Then the produced image was then reflected over the x-axis;
Reflection across the x-axis have the rule;
[tex](x,y)\rightarrow(x,-y)[/tex]Applying the rule to the resulting image;
[tex]\begin{gathered} A^{\prime}(3,-5)\rightarrow A^{\prime^{}}^{\prime}(3,5) \\ B^{\prime}(0,-4)\rightarrow B^{\prime}^{\prime}(0,4) \\ C^{\prime}(0,-2)\rightarrow C^{\prime^{}}^{\prime}(0,2) \\ D^{\prime}(3,0)\rightarrow D^{\prime}^{\prime}(3,0) \end{gathered}[/tex]Therefore, the coordinates of the final image is;
[tex]A^{\prime\prime}(3,5),B^{\prime\prime}(0,4),C^{\prime}^{\prime}(0,2),D^{\prime}^{\prime}(3,0)[/tex]Is this relation a function?
{(1, 3), (2, 3), (3, 4), (4, 5)}
No, because at least one output maps to more than one input.
No, because at least one output maps to more than one input.
Yes, because every input has exactly one output.
Yes, because every input has exactly one output.
No, because at least one input maps to more than one output.
No, because at least one input maps to more than one output.
Answers
The given relation {(1, 3), (2, 3), (3, 4), (4, 5)} is a function. Therefore, the correct statement is "Yes, because every input has exactly one output."
Relation:
A relation is a relationship between the x and y-coordinates. It must maps inputs to outputs.
Given,
Here we have the relation
{(1, 3), (2, 3), (3, 4), (4, 5)}
Now, we have to find whether this relation is a function or not.
We know that, a relation is said to be a relation is a function if the x values map to only one y - value. Simply said that if a relation is one-to-one or many-to-one it is a function.
Based on this rule, here each input has exactly one output. therefore, the given relation is said to be a function.
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find the area of a hexagon with sides 20 mm long. Round your answer to the nearest tenth
Answers
When you know the length of the sides of a hexagon you use the next formula to find its area:
[tex]A=\frac{3\sqrt{3}}{2}s^2[/tex]s is the length of the sides
For the given hexagon:
[tex]\begin{gathered} A=\frac{3\sqrt{3}}{2}(20mm)\placeholder{⬚}^2 \\ \\ A=\frac{3\sqrt{3}}{2}(400mm^2) \\ \\ A=3\sqrt{3}(200mm^2) \\ \\ A=600\sqrt{3}mm^2 \\ \\ A\approx1039.2mm^2 \end{gathered}[/tex]Then, the area of the given hexagon is 1039.2 square millimetersFind the constant of proportionality when x = 2 and y = 1.5.Record your answer and fill in the bubbles on your answer document. Be sure to usethe correct place value.
Answers
If y is proportional to x, we have this equation:
[tex]y=kx[/tex]If x = 2 and y = 1.5, then the constant is:
[tex]k=\frac{y}{x}=\frac{1.5}{2}=0.75[/tex]The constant of proportionality is k = 0.75
Complete the explanation of how you know whether the triangles are similar. If possible, find the Indicated length. A Р 2.0 1.7 во 1.2 C R. Because two pairs of angles are congruent, the triangles are similar by the select) QR =
Answers
When two triangles have two pairs of angles congruent, it means that the third pair of angles also is congruent.
Then, the trianglers are similar by AA (Angle, angle) similar triangle theorem.When two triangles are similar the ratio between corresponding sides is the same.
Corresponding sides in the given triangles:
CB and QR
AC and PR
AB and PQ
[tex]\frac{QR}{CB}=\frac{PR}{AC}=\frac{PQ}{AB}[/tex]Then, as you know the measure of AC and corresponding side CB you use the next to find the measure of side QR:
[tex]\frac{QR}{CB}=\frac{PR}{AC}[/tex]Use the given measures and find QR:
[tex]\begin{gathered} \frac{QR}{1.2}=\frac{1.7}{2.0} \\ \\ QR=\frac{1.7}{2.0}(1.2) \\ \\ QR=\frac{2.04}{2.0} \\ \\ QR=1.02 \end{gathered}[/tex]QR=1.024.) Miles has saved about $41. He wants to buy an iPod for $129 in 4 months. How much moneydoes he need to save each month to buy the iPod?
Answers
Miles has saved about $41. He wants to buy an iPod for $129 in 4 months.
So first, we need to subtract the amount that he has already saved.
[tex]\$129-\$41=\$88[/tex]Now we need to divide this amount by 4 months.
[tex]\frac{\$88}{4}=\$22[/tex]Therefore, Miles needs to save $22 each month to buy the iPod.
iley invested $1,000 in savings bonds. If bonds earn 6.75% interest compounded semi-annually, how much will riley earn in 15 years?
Answers
Answer: Riley will earn 2707 in 15 years
Explanation:
The formula for calculating compound interest is expressed as
A = P(1 + r/n)^nt
where
A is the final amount after t years
A is the principal or initial amount
r is the interest rate
n is the number of compounding periods in a year
t is the time
From the information given,
P = 1000
r = 6.75% = 6.75/100 = 0.0675
t = 15
n = 2 because it was compounded twice in a year
By substituting these values into the formula,
A = 1000(1 + 0.0675/2)^2 * 15
A = 1000(1.03375)^30
A = 2707
Riley will earn 2707 in 15 years
Drag the prisms to the table in order from least volume to greatest volume.
Answers
Fourth prism, first prism, second prism and fourth prism is order from least volume to greatest.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The volume of first prism with sides 2, 1.5 and 3.2
Volume=2×1.5×3.2
=9.6 in³
The volume of second prism with sides 1.5, 1.5 and 6
Volume=1.5×1.5×6
=13.5 in³
The volume of third prism with sides 2, 5/2 and 7/2
Volume=2×2.5×3.5
=17.5 in³
The volume of fourth prism with sides 1/2, 1/2 and 1/2
Volume=0.5×0.5×0.5
=0.125 in³
Hence fourth prism, first prism, second prism and fourth prism is order from least volume to greatest.
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In quadrilateral BADC, AB = AD andBC = DC. The line AC is a line ofsymmetry for this quadrilateral
Answers
Given the quadilateral: BADC
AB = AD
BD = DC
The line AC is a diagonal of the quadilateral.
The given quadilateral is a kite.
Let's answer the following questions using the given information.
Part a:
Diagonal AC and diagonal BD are perpendicular.
The diagonals of a kite are perpendicular, this is because the point of intersection of both diagonals form a right angle (90 degrees).
Therefore, based on the line of symmetry, we can say diagonals AC and BD are perependicular because the quadilateral is symmetric along the diagonals AC and BD of the figure.
• Part b:
Based on the line of symmetry, angle ABC and angle ADC have the same measure because the qudilateral has
Solve the system of equations using elimination.8x - 5y = 13-16x - 10y = -6Show your work here:Solution:
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Solve the system of equations using elimination.
[tex]\begin{gathered} \text{8 x - 5y = 13 -- equation 1} \\ -16\text{ x - 10y = - 6 -- equation 2} \end{gathered}[/tex]Step 2:
Given,
[tex]\begin{gathered} 8x\text{ - 5y = 13 -- equation 1} \\ \text{equation 1 multiplied by 2, we have that:} \\ 16\text{ x - 10y = 26 -- equation 3} \\ -16\text{ x -10 y = - 6 -- equation 2} \end{gathered}[/tex][tex]\begin{gathered} equation\text{ 3 + equation 2, we have that:} \\ -10y\text{ + -10 y = 26 + (-6)} \\ -20y\text{ = 20} \\ \text{Divide both sides by -20, we have that:} \\ y\text{ = }\frac{20}{-20} \\ y\text{ = -1} \end{gathered}[/tex]Now, since y = -1 , we put the value of y = -1 in equation 1,
[tex]\begin{gathered} 8\text{ x- 5y = 13 --equation 1} \\ 8x\text{ - 5 ( -1 ) = 13} \\ 8x\text{ + 5 = 13} \\ 8x\text{ = 13 - 5} \\ 8\text{ x= 8} \\ \text{Divide both sides by 8 , we have that:} \\ x\text{ = }\frac{8}{8} \\ x\text{ = 1} \end{gathered}[/tex]CONCLUSION:
The final answer =
[tex]\text{ x= 1 , }y\text{ = - 1}[/tex]'
A survey claims that the percent of a city's residents that favor building a new football stadium is likely between 52.3% and 61.7%. What was the sample proportion (what percent of the people in the sample survey said that they wanted to build a new stadium )?
Answers
The confidence interval for the sample proportion is calculated using the following formula:
[tex]\lbrack p\lbrack\text{hat\rbrack}\pm Z_{1-\frac{\alpha}{2}}\cdot\sqrt[]{\frac{p\lbrack hat\rbrack(1-p\lbrack hat\rbrack)}{n}}\rbrack[/tex]Where p[hat] represents the sample proportion. As you see you add/subtract the margin of error to the sample proportion to determine both bonds of the interval, which means that the sample proportion is in the middle of the interval.
The percent of residents in favor of building a new football stadium is between 52.3% and 61.7% → the sample proportion used to determine this interval is in the middle of both bonds. To calculate the said value you have to find the average of both values:
[tex]52.3\%The sample proportion used to estimate the interval was p[hat]=0.57
One of the two persons P or Q is to solve a technical problem with chances ½ and ¼, respectively. Find the probability that the technical problem is solved.A.1/8B.3/8C.5/8D.7/8
Answers
The probability that the technical problem is solved can be defined as follows:
The probability that P solves the problem or probability that Q solves the problem or probability that both (P and Q) solve the problem
The probability that P solves the problem = 1/2
The probability that Q solves the problem= 1/4
The probability that both solve the problem = (1/2) x (1/4) = 1/8
The probability that the technical problem is solved =
[tex]\begin{gathered} \frac{1}{2}\text{ + }\frac{1}{4}\text{ -}\frac{1}{8} \\ =\frac{4+2-1}{8} \\ \frac{5}{8} \end{gathered}[/tex]The correct option is C
Large balloons are sold in packages of 12. Select the expressions that can represent the total number of balloons in p packages of largeballoonsA 12-PB. 12*pC. P+12D. P-12E 12p
Answers
Since each package has 12 balloons if we buy p packages the total number of ballons will be given by tha multiplication of 12 by p, that is:
[tex]12p[/tex]Therefore the answer is B and E.
Find the angle between the vectors u = 5i – 2j and v = 2i + 3j.
Answers
STEP - BY - STEP EXPLANATION
What to find?
The angle between the given vectors.
Given:
u = 5i – 2j and v = 2i + 3j.
To solve the given problem, we will follow the steps below:
Step 1
Write the formula that can be use to solve the above.
[tex]cos\theta=\frac{\vec{a}\vec{.b}}{\vec{|a}\vec{||b}|}[/tex]Step 2
Determine;
→ →
a. b
[tex]\begin{gathered} \vec{a}\vec{.b}=(5)(2)+(-2)(3) \\ \\ =10-6 \\ \\ =4 \end{gathered}[/tex]Step 3
Determine;
→ →
|a| and | b|
[tex]\begin{gathered} \vec{|a|}=\sqrt{5^2+(-2)^2} \\ \\ =\sqrt{25+4} \end{gathered}[/tex][tex]=\sqrt{29}[/tex][tex]\begin{gathered} \vec{|b|}=\sqrt{2^2+3^2} \\ \\ =\sqrt{4+9} \\ \\ =\sqrt{13} \end{gathered}[/tex]Step 4
Substitute the values into the formula.
[tex]\begin{gathered} cos\theta=\frac{4}{\sqrt{29}\times\sqrt{13}} \\ \\ =\frac{4}{\sqrt{377}} \end{gathered}[/tex]Step 5
Take the arc cos of both-side.
[tex]\theta=cos^{-1}(0.20601)[/tex][tex]\theta=78.1\degree[/tex]ANSWER
θ = 78. 1°
Which equation models the total profit,y,based on the number of tickets sold,x?
Answers
Answer
D. y - 300 = 4(x - 100)
Step-by-step explanation
Variables
• x: tickets sold
,• y: profit
Equation of a line in point-slope form
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x₁, y₁) is a point on the line.
The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]This line passes through the points (100, 300), that is, when 100 tickets are sold, the club had $300 in profit, and the point (200, 700). Then, its slope is:
[tex]\begin{gathered} m=\frac{700-300}{200-100} \\ m=\frac{400}{100} \\ m=4 \end{gathered}[/tex]Substituting into the general equation with m = 4 and the point (100, 300), we get the next equation of the line:
[tex]y-300=4(x-100)[/tex]the first three terms of a sequence are given around the nearest thousandth if needed 16,4,1,... Find the 6th term
Answers
16, 4, 1....
2^4, 2^2, 2^0
[tex]2^4,2^2,2^0,2^{-2},2^{-4},2^{-6},2^{-8}\ldots[/tex]6th term would be 2^-6:
[tex]2^{-6}[/tex]Series
Use the change of base formula to compute log/174.Round your answer to the nearest thousandth.
Answers
Answer:
The Expression is given below as
[tex]\log_{\frac{1}{7}}4[/tex]Represent the expression above to be
[tex]=x[/tex]That is, we will have that
[tex]\log_{\frac{1}{7}}4=x[/tex]Applying the change of base rule below, we will have that
[tex]\begin{gathered} \log_ab=y \\ b=a^y \\ lnb=lna^y \\ lnb=ylna \\ y=\frac{lnb}{lna} \end{gathered}[/tex][tex]\begin{gathered} \log_{\frac{1}{7}}4=x \\ (\frac{1}{7})^x=4 \\ (7^{-1})^x=4 \\ 7^{-x}=4 \\ take\text{ ln of both sides} \\ ln7^{-x}=ln4 \\ -xln7=ln4 \\ dividie\text{ both sides by -ln7} \\ \frac{-xln7}{-ln7}=\frac{ln4}{-ln7} \\ x=-0.712 \end{gathered}[/tex]Hence,
The final answer is
[tex]\rightarrow-0.712[/tex]what is the volume of the cone? use Pi and round to the nearest tenth
Answers
Let's begin by listing out the information given to us:
Radius (r) = 7ft
Height (h) = 25ft
The volume of a cone is calculated as shown below:
V = ⅓πr²h
V = ⅓ * 3.14 * 7² * 25 = 1282 1/6
V = 1282 1/6 or 1282.667 = 1282.7 = 1283 ft³
V = 1283 ft³
Solve $9.75 x $40 to get $390.00, using long multiplication
Answers
I will be using a rough sketcher to show the long multiplication:
The process is shown below:
Note:
the last zero is taken down last, after the multiplication is done [shown by green arrow]
Lastly, we put the decimal point "2 places to the left" since the multiplication problem has "2 decimal places"
Z (7x+3)° m n (6x+11)
Answers
In this problem, the two angles are equal because of the properties, so:
[tex](7x+3)=(6x+11)[/tex]and we can solve for x
[tex]\begin{gathered} 7x-6x=11-3 \\ x=8 \end{gathered}[/tex]So the angles are:
[tex]\begin{gathered} 7(8)+3=59 \\ 6(8)+11=59 \end{gathered}[/tex]EFGH is translate 5 units to the left and 2 units up.A. E(-1,-3)B. E(6,-6)C. E (-1,1)D. E(9,-3)
Answers
To translate the figure 5 units to the left and 2 up, apply the following translation to each coordinate of the figure
[tex]T_{(-5,2)}\colon(x,y)\rightarrow(x-5,y+2)[/tex]So, you have
[tex]\begin{gathered} E(4,-1)\rightarrow E^{\prime}(4-5,-1+2)\rightarrow E^{\prime}(-1,1) \\ F(0,-3)\rightarrow F^{\prime}(0-5,-3+2)\rightarrow F^{\prime}(-5,-1) \\ G(2,-4)\rightarrow G^{\prime}(2-5,-4+2)\rightarrow G^{\prime}(-3,-2) \\ H(6,-2)\rightarrow H^{\prime}(6-5,-2+2)\rightarrow H^{\prime}(1,0) \end{gathered}[/tex]Therefore, the coordinates of E' are (-1,1) and the correct answer is C. E(-1,1).
Its a project for my consumer math class and i have to record all the information on a template
Answers
We are asked to fill up the transactions in the table.
Remember that Payments, fees, and withdrawals are always subtracted from the balance, and deposits are always added to the balance.
The starting balance is $275
1st transaction:
Payment of $85.67 to the electric company on 2nd October.
Since it is a payment, it must be subtracted from the previous balance.
Balance = $275 - $85.67 = $189.33
2nd transaction:
You want to deposit the $20 that your friend gave to you.
Since it is a deposit, it must be added to the previous balance.
Balance = $189.33+$20 = $209.33
5) A ball is dropped from a height of 400 feet. Each time it hits the ground, it rebounds 75% of the distance it has fallen. How far will the ball travel before coming to rest?
Answers
Initial height: 400 m
Each time it hits the ground, it rebounds 75% the distance it has fallen. Let us say this distance is d, then the new height is:
[tex]\begin{gathered} h=75\text{\% of }d=\frac{75}{100}\cdot d \\ \Rightarrow h=\frac{3}{4}d \end{gathered}[/tex]If the initial height is 400 m, then the subsequent heights are given by the recurrence equation:
[tex]\begin{gathered} h_0=400 \\ h_n=(\frac{3}{4})^n\cdot h_0 \\ \Rightarrow h_n=400\cdot(\frac{3}{4})^n \end{gathered}[/tex]And the total distance traveled D is:
[tex]\begin{gathered} D=h_0+2\cdot\sum ^{\infty}_{n\mathop=1}\lbrack(\frac{3}{4})^n\cdot h_0\rbrack \\ \Rightarrow D=400+800\cdot\sum ^{\infty}_{n\mathop{=}1}(\frac{3}{4})^n \end{gathered}[/tex]Now, let us analyze the sum term:
[tex]\sum ^{\infty}_{n\mathop{=}1}(\frac{3}{4})^n=\frac{3}{4}+(\frac{3}{4}_{})^2+(\frac{3}{4})^3+\cdots_{}[/tex]From the infinite geometric sequence:
[tex]\begin{gathered} \sum ^{\infty}_{n\mathop=0}r^n=\frac{1}{1-r} \\ \Rightarrow\sum ^{\infty}_{n\mathop{=}1}r^n=\frac{1}{1-r}-1 \end{gathered}[/tex]Where r < 1. From our problem, r = 3/4 < 1, then:
[tex]\begin{gathered} \sum ^{\infty}_{n\mathop{=}1}(\frac{3}{4})^n=\frac{1}{1-\frac{3}{4}}-1=\frac{1}{\frac{1}{4}}-1=4-1 \\ \Rightarrow\sum ^{\infty}_{n\mathop{=}1}(\frac{3}{4})^n=3 \end{gathered}[/tex]Finally, using this result:
[tex]D=400+800\cdot3=400+2400=2800[/tex]Solve for X. Write down what type of solution the equation has. 3) [tex] \frac{10}{2x + 1} = \frac{14}{4x - 7} [/tex]
Answers
You have the following equation:
[tex]\frac{10}{2x+1}=\frac{14}{4x-7}[/tex]In order to solve for x the previous equation, multiply both sides by the LCM of the denominators, which is (2x+1)(4x-7):
[tex]\begin{gathered} (2x+1)(4x-7)\frac{10}{2x+1}=(2x+1)(4x-7)\frac{14}{4x-7} \\ (4x-7)10=(2x+1)14 \\ 40x-70=28x+14 \\ 40x-28x=14+70 \\ 12x=84 \\ x=\frac{84}{12} \\ x=7 \end{gathered}[/tex]Hence, the solution to the given equation is x = 7
the u.s senate has 100 members. after a certain election, there were 6 more democrats than republicans, with no other parties represented. how many memebrs of each party were there in the senate?
Answers
As per the unitary method, the number of democrats are 53 and the number of republicans are 47.
Unitary method:
Unitary method is the process of finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given,
The U.S senate has 100 members. after a certain election, there were 6 more democrats than republicans, with no other parties represented.
Here we need to find the number of democrats and the number of republicans.
Let us consider the number of Republican's be "x"
And then the number of Democrats is "x+6".
We know that the total number of members in the senate is 100.
So, it can be written as
x + (x + 6) = 100
2x + 6 = 100
2x = 100 - 6
2x = 94
x = 94/2
Then the value of x is,
x = 47
Therefore, there are 47 republicans in the senate then the number of democrats is
x + 6 => 47 + 6 => 53
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4Complete the table of values for the following function: y = VX-8X1006493625y-81
Answers
y= √x - 8
Replace each value of x and solve for y
x= 100
y= √100 - 8 = 10-8 = 2
x= 64
y= √64-8 = 8 - 8 = 0
x= 9
y= √9 - 8 = 3 - 8 = -5
x= 36
y=√36 - 8 = 6-8= -2
x= 25
y= √25- 8 = 5 - 8 = -3
For the last values, replace y and solve for x
y=-8
-8= √x - 8
-8+8 = √x
0= √x
x= 0^2
x=0
y=1
1=√x-8
1+8= √x
9 = √x
9^2 = x
x= 81
Warren flipped a coin and rolled a 20-sided number cube. What is the probability that his coin landed on tails and his number cube rolled a factor of 20? answer as a simplified fraction.
Answers
Warren flipped a coin and rolled a 20-sided number cube. What is the probability that his coin landed on tails and his number cube rolled a factor of 20? answer as a simplified fraction.
we have that
the probability that his coin landed on tails is
P=1/2
and
Factors of 20 are ----> 1,2,4,5,10,20
so
The probability that his number cube rolled a factor of 20 is
P=6/20=3/10
therefore
the probability that his coin landed on tails and his number cube rolled a factor of 20 is equal to
P=(1/2)*(3/10)
P=3/20. A town committee has a budget of $75 to spend on snacks for the volunteers participating in aclean-up day. The committeechairperson decides to purchase granola bars and at least 50 bottlesof water. Granola bars cost $.50 each, and bottles of water cost $.75 each. Write and graph asystem of linear inequalities for the number of bottles of water and the number of granola bars thatcan be purchased
Answers
Assume that the number of granola bars is x and the number of bottles is y
Since they decided to purchase at least 50 bottles
At least means greater than or equal, so
[tex]x\ge50[/tex]Since the cost of 1 bar = $0.50, then
The cost of all bars = 0.50x
Since the cost of 1 bottle = $0.75, then
The cost of all bottles = 0.75y
Since their budget is $75
They can not exceed that, then
[tex]0.50x+0.75y\le75[/tex]The solution will be in the common part of the two colors
The red represents the second inequality
The blue represents the first inequality