A circle and two distinct lines are drawn on a sheet of paper what is the largest possible number of points of intersection of these figures (it is Q29)
Answers
Answer:
C 5
Step-by-step explanation:
The two lines can both intersect the circle twice, and can intersect each other once, so 2 + 2 + 1 = 5
Related Questions
OB. 1OC.If X = 24 inches, Y = 45 inches, and Z= 51 inches, what is the tangent of ZA?OA. 19715NOD. 1B
Answers
Given that
We have a right-angled triangle and have to find angle A's tangent.
Explanation -
The triangle is shown as
Here we have,
X = 24 inches
Y = 45 inches
Z = 51 inches
Then, the tangent of angle A will be
[tex]\begin{gathered} The\text{ formula for the tangent is } \\ tan=\frac{Perpendicular}{Base} \\ \\ tan=\frac{P}{B} \\ For\text{ angle A thevalues are, P = 45 and B = 24} \\ Then, \\ tanA=\frac{45}{24} \\ \\ tanA=\frac{15}{8} \end{gathered}[/tex]So the correct option is B.
Final answer -
Therefore the final answer is 15/8Based on the graph of f(x) shown here what is f^-1(8).
Answers
Answer
2
Explanation:
f⁻¹(8) is equal to the value of x that makes f(x) = 8. So, taking into account the graph, we get:
Therefore, f⁻¹(8) = 2. So the answer is 2
AMNP ~ AQRP N x + 8 28 M 24 P 3x - 9 R Create a proportion and find the length of side PR*
Answers
Using thales theorem:
[tex]\begin{gathered} \frac{24}{28}=\frac{x+8}{3x-9} \\ 24(3x-9)=28(x+8) \\ 72x-216=28x+224 \\ 44x=440 \\ x=\frac{440}{44} \\ x=10 \\ PR=3(10)-9=21 \end{gathered}[/tex]Which is an equivalent expression for 4 times d raised
to the negative third power all over quantity 18 times d
raised to the ninth power end quantity?
Answers
Answer:
2d⁻³/9d⁻⁹
Step-by-step explanation:
4 times d raised to the negative third power = (4 × d)⁻³ = 4d⁻³
18 times d raised to the ninth power = (18 × d)⁻⁹ = 18d⁻⁹
the equation as a quotient:
Expression = 4d⁻³/18d⁻⁹
Expression = 2d⁻³/9d⁻⁹
Floyd is an aspiring music artist. He has arecord contract that pays him a base rate of$200 a month and an additional $12 for eachalbum that he sells. Last month he earned atotal of $644.Write an equation to determine the numberof albums (a) Floyd sold last month.Find the number of albums Floyd sold lastmonth.albums
Answers
Explanation:
Equate the given data to solve for x.
$200 + $12x = $644.
To determine the number of albums sold, Let x be the number of album sold by Floyd last month.
200 + 12x = 644
12x =644-200
12x = 444
x = 444/12
x= 37.
Floyd has sold 37 albums last month.
Answer:
The equation to determine the number of albums Floyd sold last month is 200+12x = 644.
and the number of album Floyd sold last month is 37.
Been out of school for health issues trying to catch up work thanks!!
Answers
DEFINITIONS
The union of two sets contains all the elements contained in either set (or both sets). The union is notated A ⋃ B.
The intersection of two sets contains only the elements that are in both sets. The intersection is notated A ⋂ B.
Using a Venn Diagram, the union and intersection of two sets can be seen below:
GIVEN
The sets are given to be:
[tex]\begin{gathered} S=\mleft\lbrace1,2,3,\ldots,18,19,20\mright\rbrace \\ A=\mleft\lbrace3,4,8,9,11,13,14,15,20\mright\rbrace \\ B=\mleft\lbrace4,7,13,14,16,18,19\mright\rbrace \end{gathered}[/tex]QUESTION
1) (A ∪ B): The terms of the two sets contained in either set or the two sets are
[tex](A\cup B)=\mleft\lbrace3,4,7,8,9,11,13,14,15,16,18,19,20\mright\rbrace[/tex]2) (A ∩ B): The elements that are in both sets are
[tex](A\cap B)=\mleft\lbrace4,13,14\mright\rbrace[/tex]50% of $277 is $144True or False
Answers
Answer:
FALSE
Explanation:
Given the expression
50% of $277
This can also be written as;
= 50/100 * 277
= 1/2 * 277
= 277/2
= 138.5
Therefore 50% of $277 is $138.5 not $144 rendering the question FALSE
a sociology Professor assigns letter grades on a test according to the following scheme Scores on the test are normally distributed with the meaning of 67.2 and a standard deviation of 8.5Find the minimum score required for an a grade. Round your answer to the nearest whole number if necessary
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In order to have grade A, the score needs to be in the top 9%.
Since the scores are normally distributed, the top 9% scores correspond to 91% of the area under the normal curve. That means we need to find a value of z in the z-table that corresponds to the value 0.91 (that is, 91%).
Looking at the z-table, the value of z for a probability of 0.91 is z = 1.34.
Now, to find the score that this value of z represents, we can use the formula below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}\\ \\ 1.34=\frac{x-67.2}{8.5}\\ \\ x-67.2=11.39\\ \\ x=11.39+67.2\\ \\ x=78.59 \end{gathered}[/tex]Rounding to the nearest whole number, the minimum score for grade A is 79.
Two airplanes are flying in the air at the same height. Airplane A is flying east at 451 mi/h and airplane B is flying north at 494 mi/h. If they are both heading to the same airport, located 3 miles east of airplane A and 3 miles north of airplane B, at what rate is the distance between the airplanes changing?
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The rate at which the distance between the airplanes is changing is 668.2 mi/h.
In the given question,
Speed of Airplane A:
dA/dt = 451 mi/h
and the Speed of Airplane B:
dB/dt = 494 mi/h
Aircraft A and B will form a right triangle because Aircraft A is flying east and Aircraft B is flying north, and we can use Pythagoras' theorem to calculate their distance from one another.
Let P be the distance.
P² = A² + B²
Differentiating the above equation with respect to t,
2P(dP/dt) = 2A(dA/dt) + 2B(dB/dt)
Dividing each side of the equation by 2,
P( dP/dt ) = A( dA/dt ) + B( dB/dt ) ..........(1)
Where dP/dt is the rate of change in distance between the two aircraft.
Now,
P² = A² + B²
P = √(A² + B²)
Substituting, A = 3 miles and B = 3miles;
P = √(3² + 3²)
P = √( 9+ 9)
P = √18
P = 3√2 miles
Substituting the value in the equation (i)
3√2 (dP/dt) = (3× 451) + (3× 494)
3√2 (dP/dt) = 2835
4.2426 × dP/dt = 2835
dP/dt = 2835/4.2426
dP/dt = 668.2 mi/h
Therefore, the rate at which the distance between the airplanes is changing is 668.2 mi/h
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suppose that the time required to complete a 1040r tax form is normally distributed with a mean of 100 minutes and a standard deviation of 15 minutes. what proportion of 1040r tax forms will be completed in less than 77 minutes? round your answer to at least four decimal places.
Answers
The proportion of 1040r tax forms completed in less than 77 minutes = 0.06301
How to find the proportion of the tax forms?
The time required to complete a 1040r tax form = normally distributed
Mean = [tex]\mu[/tex] = 100 minutes
Standard deviation = [tex]\sigma[/tex] = 15 minutes
The proportion of 1040r tax forms completed in less than 77 minutes is given by ,
P( X< 77 ) = P ( Z < [tex]\frac{77-100}{15}[/tex] )
= P( Z < - 1.53 )
=0.06301
Cumulative probability in the normal distribution =0.06301 or 6.301%
What is normal distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.The natural and social sciences frequently utilize normal distributions to describe real-valued random variables whose distributions are unknown, which is why normal distributions are essential in statistics. Not all symmetrical distributions are normal, but all normal distributions are symmetrical.Natural occurrences frequently resemble the normal distribution.A bell curve is another name for a normal distribution.To learn more about normal distribution, refer:
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Four plumbers estimated the length of the length of the radius of a cylindrial pipe. The estimates made by the plumbers are listed • 3/5 • 3/11 • 9/100 • 3.14/24 ? : . .
Answers
Different estimates:
The length of the radius of a cylindrical pipe:
Plumber W:
Radius had a length: 3/5 inches.
Plumber X:
Radius had a length: sqrt(3/11) inches.
Plumber Y:
Radius had a length of 9/100 inches.
Plumber Z:
Radius had a length of 3/14/24 inches.
Turn them into decimals:
We can turn each length into decimal:
Plumber W: 3/5 = 0.6.
Plumber X: sqrt(3/11) = 0.522222..
Plumber Y: 9/100 = 0.09
Plumber Z: 3.14/24 = 0.13083
The list from the greatest to least:
We can order this list taking into account the following reasoning: when the number is near to zero, this number is less than the other in the list. Examples: 0.001, 0.0002, 0.00004 are very near to zero.
Additionally, when a number is near 1 (the unit), this number is greater than the other less near to 1.
Examples: 0.69, 0.73, 0.888, 0.99 are near to zero.
The numbers we got in the list are decimals numbers coming from fractions and the square root was taken to the estimation of plumber X. Therefore:
From list 0.6, 0.52222..., 0.09, 0.13083
The number nearest to zero is 0.09. Then, 0.13083 is greater than 0.09 but less than the others. The following number is 0.5222..., and the greatest is 0.6.
The list that shows these lengths in order from the greatest to least is:
{0.6, 0.5222..., 0.13083, 0.09}.
Which is equivalent to:
{3/5, sqrt(3/11), 3.14/24, 9/100}.
Michael and his sister Mel share the job of mowing the grass in their yard. Michael mows ⅓ of the yard, and Mel mows the rest. Mel can mow ¾ of the entire yard in an hour.How long will it take Mel to finish mowing the yard?? Also after Michael mows 1/3 of the yard what fraction of the yard does mel need to mow?
Answers
Michael Mows = 1/3 of the yard
Mel mows the rest = 1-1/3 = 2/3 of the yard
Mel mows = 3/4 of the yard in an hour
After Michael mows 1/3 of the yard what fraction of the yard does Mel need to mow?
1- 1/3 = 2/3 of the yard
How long will it take Mel to finish mowing the yard??
2/3 / (3/4) = 8/9 hours = 0.89 hours
Im in algebra 2 but we are also learning geometry the question asks to find the length of each arc
Answers
The length of the arc = 8π/3 mi
Explanation:The length of an arc is given by the fomula:
[tex]L=\frac{\theta}{360}\times2\pi r[/tex]The radius, r = 8 ml
[tex]\theta=60^0[/tex][tex]\begin{gathered} L=\frac{60}{360}\times2\pi\times8 \\ \\ L=\frac{16\pi}{6} \\ \\ L=\frac{8\pi}{3} \end{gathered}[/tex]The length of the arc = 8π/3 mi
Mary estimates the weight of her cat to be 10 pounds.the actual weight of the cat is 13.75 pounds.find the percent error.
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The percentage error is the ratio of the difference between the two readings and the actual
Error = 13.75 - 10
= 3.75
Percent error = 3.75/13.75
= 27.27%
Please help me solve this using six grade math (easy formulas)
Answers
We will break the surface area of the tent up into its sides, the front and the back and the bottom.
Area of the sides: 2(5*7) = 70
Area of the front and the back: 2( 1/2 (6*4)) = 24
Area of the bottom: 7*6 = 42
Least amount of fabric required = 136ft
In the matrix equation below, what are the values of x and y? 1/2 [4 8 x+3 -4] -3 [1 y+1 -1 -2]= [-1 -5 7 4]
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Using the matrix equation, the value of x and y are 5 and 2 respectively.
Consider the 2 by 2 matrix equations,
1/2 [ 4 8 ( x + 3 ) - 4 ] - 3[ 1 y+1 -1 - 2 ] = [ - 1 -5 7 4 ]
[ 2 4 (x+3)/2 -2] + [ - 3 -3y -3 +3 + 6] = [ - 1 - 5 7 4]
[ -1 -3y + 1 (x + 9)/2 + 4] = [ - 1 - 5 7 4]
Therefore,
- 3y + 1 = - 5
Subtracting 1 from each side of the equation,
- 3y + 1 - 1 = - 5 - 1
- 3y = - 6
Dividing each side of the equation by - 3,
y = 2
And;
( x + 9 )/2 = 7
Multiplying each side by 2,
x + 9 = 14
Subtracting 9 from each side of the equation,
x + 9 - 9 = 14 - 9
x = 5
Therefore, the value of x and y is 5 and 2 respectively.
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Find the volume of the top of the prism, volume of the bottom prism, and total volume of figure.
Answers
Volume of the top of the prism: 460 cm^3
Volume of the bottom of the prism: 1 768 cm^3
Total volume of the figure: 2 228 cm^3
Explanation:
Volume of the top of the prism:
. Since it is a prism from trapezoid
. . Volume = Area of the trapezium base * heights between trapezium ends
[tex]\begin{gathered} Area\text{ of a trapezium base}=\frac{top\text{ base+bottom base}}{2}*height \\ ...\text{ =}\frac{6+17}{2}*(22-17) \\ ...=\frac{23}{2}*5 \\ Area\text{ = 57.5 cm}^2 \end{gathered}[/tex][tex]Volume=57.5*8=460\text{ }cm^3[/tex]Volume of the bottom prism:
. Since the price has a rectangular base:
Volume = Area of one base * height between reactangular bases
Area of one base :
[tex]17*13=221\text{ }cm^2[/tex]Volume:
[tex]221*8=1\text{ }768\text{ }cm^3[/tex]Total volume of the figure:
Volume of the top + Volume of the bottom = Total volume
[tex]221+1\text{ }768=2\text{ }228\text{ }cm^3[/tex]NB:
To find any volume of a given prism, start with finding the area of one base, then multiply that area by the height (in other words the sides that link the two bases)
Each face of a pyramid is an isosceles triangle with a 70 degree vertex angle. What are the measures of the base angles?
Answers
We are given that each face of a pyramid is an isosceles triangle and that its vertex angle is 70 degrees. This problem can be exemplified in the following diagram:
Since the triangle is isosceles, its base angles are the same, and the sum of the interior angles must be equal to 180 degrees. Therefore, we have the following relationship:
[tex]70+x+x=180[/tex]Adding like terms, we get:
[tex]70+2x=180[/tex]Now we solve for "x", first by subtracting 70 on both sides:
[tex]\begin{gathered} 70-70+2x=180-70 \\ 2x=110 \end{gathered}[/tex]Now we divide both sides by 2
[tex]x=\frac{110}{2}=55[/tex]Therefore, the base angles of the pyramid are 55 degrees.
To the right is the graph of f(x) = x^2. The second graph, to the left of f(x) = x^2 is a new function made by stretching f(x) vertically by a factor of 2 and then translating it three units to the left and one unit down. Write the equation of the new function.
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This problem invloves the topic of curved lines in a graph, curved lines or more speccifically curve line which looks like letter C (parabola) all follows a certain standard form of equation, which is;
[tex]y=ax^2+b[/tex]For example you can see that the equation for the black curve line in our picture is y=x² and notice that this equation can also be written as y = (1)x² + 0. Which simillar to the standard form given above where a is just 1 (a=1) and b is just 0 (b=0).
Since our black curve line follows the same standard form of equation as stated above, we can conclude that the RED curve line follows the same form of equation.
To summarize the steps that we must do in order to find the equation of the RED line we will list them as,
1. Sample two(2) points in the graph to be used as reference points.
2. Use the sampled points in our standar eqation in order to find the variables "a" and "b".
3. When we have the variables "a" and "b", we can just directly substitute it into our standard equation to find the equation of our RED line.
Let's start.
1. Sample 2 points to be used as refernce points. (Note that we will find the easiest points
to determine)
Let us use the points (-3, -1) and (-2, 1) as shown in the picture.
2. Use the points (-3, -1) and (-2, 1) in our standard equation.
[tex]\begin{gathered} y=ax^2+b \\ \text{where (x,y)=(-3, -1)} \\ -1=a(-3)^2+b_{} \\ 9a+b=-1 \end{gathered}[/tex]
for our 1st point we have the equation 9a+b = -1, let us now proceed to our next point.
[tex]\begin{gathered} y=ax^2+b \\ \text{where (x,y)=(-2, 1)} \\ 1=a(-2)^2+b_{}_{} \\ 1=4a+b \\ 4a+b=1 \end{gathered}[/tex]and for our 2nd point we have the equation 4a+b = 1, and by the process of subtitution and elimination we can now find "a" and "b", because we have two equations with two unknowns.
[tex]\begin{gathered} 9a+b=-1\text{ and} \\ 4a+b=1 \end{gathered}[/tex]transforming eqatuin number 1 to
[tex]9a+b=-1\text{ is just the same as b = -1 -9a}[/tex]
then substitue b = -1 -9a to the 2nd equation we have.
[tex]\begin{gathered} 4a+b=1\text{ , where b = -1-9a} \\ 4a+(-1-9a)=1 \\ 4a-1-9a=1 \\ -5a=2 \\ a=-\frac{2}{5} \end{gathered}[/tex]
since a = -2/5, we can find b using,
[tex]\begin{gathered} 4a+b=1\text{ , where a=-}\frac{2}{5} \\ 4(-\frac{2}{5})+b=1 \\ b=1+\frac{8}{5} \\ b=\frac{5}{5}+\frac{8}{5} \\ b=\frac{13}{5} \end{gathered}[/tex]therefore our a and b are;
[tex]a=-\frac{2}{5}\text{ and b = }\frac{13}{5}[/tex]3. We can now proceed in substituting it in our standard equation;
[tex]\begin{gathered} y=ax^2+b\text{ , where a = -}\frac{2}{5}\text{ and b = }\frac{13}{5} \\ y=(-\frac{2}{5})x^2+(\frac{13}{5}) \\ y=-\frac{2}{5}x^2+\frac{13}{5} \end{gathered}[/tex]you can also simplify the final equation by multiplying all sides by 5,
[tex]\begin{gathered} 5y=(5)\lbrack-\frac{2}{5}x^2+\frac{13}{5}\rbrack \\ 5y=-2x^2+13 \end{gathered}[/tex]therefore our final answer can be,
[tex]\begin{gathered} f(x)=-\frac{2}{5}x^2+\frac{13}{5} \\ or \\ 5y=-2x^2+13 \end{gathered}[/tex]
Slope The first two sets of points are 9,-24 and 13,-21
Answers
We need to find the slope using the points (9, -24) and (13 , -21)
so, the slope = 3/4
1+1=? Need Help! Asap
Answers
By definition, Addition is a mathematical operation.
In this case, you have the following Addition given in the exercise:
[tex]1+1[/tex]Writing the equation of a quadratic function given its graph
Answers
Answer:
[tex]y=-(x-1)^2+2[/tex]Step-by-step explanation:
A quadratic function in vertex form is represented as:
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the vertex} \end{gathered}[/tex]Given the vertex (1,2) substitute it into the function:
[tex]y=a(x-1)^2+2[/tex]As you can see, we still do not know the value for ''a'', use the point given (4,-7) substitute it (x,y) and solve for ''a'':
[tex]\begin{gathered} -7=a(4-1)^2+2 \\ -7=a(3)^2+2 \\ -7=9a+2 \\ 9a=-7-2 \\ a=-\frac{9}{9} \\ a=-1 \end{gathered}[/tex]Hence, the equation of the function would be:
[tex]y=-(x-1)^2+2[/tex]In a right triangle, one of the acute angles measures of degrees. What is the measure of the other acute angle?
A. 90-d
B. 90 d
C. 180-d
D. 180+d
Answers
The correct answer is A. 90 - d
Since the sum of all the angles in a triangle is 180° and one of the angle is 90° because the triangle is a right triangle. So the sum of the remaining angles is 90°.
And to find the other acute angle we use 90° - d.
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Multiplying Polynomials 5y[tex] ({5y}^{2} + y + 3)(x - 2)[/tex]
Answers
Let's distribute those factors, and expand this:
[tex]\begin{gathered} (5y^2+y+3)\mleft(x-2\mright) \\ 5xy^2-10y^2+xy-2y+3x-6 \\ \end{gathered}[/tex]There's no further way beyond that. Either we pick the factored form or the expanded version of that polynomial. As this is not an equation we stop it here.
A person investigating to employment opportunities. They both have a beginning salary of $42,000 per year. Company A offers an increase of $1000 per year. Company B offers 7% more than during the preceding year. Which company will pay more in the sixth year? what will company A pay? and what will company B pay?
Answers
qANSWER
Company B will pay more
Company A =
EXPLANATION
Both companies start by paying $42,000 per year.
Company A offers an increase of $1000 per year.
This means that after n years, he would have earned:
Earnings = 42000 + 1000n
where n = number of years after the first year
So, after 6 years, he would have worked 5 years after the first, so his earnings would be:
Earnings = 42000 + 1000(5) = 42000 + 5000
Earnings = $47000
Company B offers 7% more than the previous year. That means that his earnings are compounded.
His earnings can then be represented as:
[tex]\text{ Earnings = P(1 + }\frac{r}{100})^t[/tex]where P = initial salary = $42000
r = interest rate = 7%
t = number of years spent = 6 years
Therefore, his earnings after the 6th year will be:
[tex]\begin{gathered} \text{ Earnings = 42000(1 + }\frac{7}{100})^6 \\ \text{ Earnings = 42000(1 + 0.07)}^6=42000(1.07)^6 \\ \text{ Earnings = }42000\cdot\text{ 1.501} \\ \text{Earnings = \$63042} \end{gathered}[/tex]He would have earned $63042.
Therefore, Company B will pay more.
qANSWER
Company B will pay more
Company A =
EXPLANATION
Both companies start by paying $42,000 per year.
Company A offers an increase of $1000 per year.
This means that after n years, he would have earned:
Earnings = 42000 + 1000n
where n = number of years after the first year
So, after 6 years, he would have worked 5 years after the first, so his earnings would be:
Earnings = 42000 + 1000(5) = 42000 + 5000
Earnings = $47000
Company B offers 7% more than the previous year. That means that his earnings are compounded.
His earnings can then be represented as:
[tex]\text{ Earnings = P(1 + }\frac{r}{100})^t[/tex]where P = initial salary = $42000
r = interest rate = 7%
t = number of years spent = 6 years
Therefore, his earnings after the 6th year will be:
[tex]\begin{gathered} \text{ Earnings = 42000(1 + }\frac{7}{100})^6 \\ \text{ Earnings = 42000(1 + 0.07)}^6=42000(1.07)^6 \\ \text{ Earnings = }42000\cdot\text{ 1.501} \\ \text{Earnings = \$63042} \end{gathered}[/tex]He would have earned $63042.
Therefore, Company B will pay more.
7-Which beans are the better deal? Kidney Beans $1.18 per lb O Lima Beans $213 for 2 lbs 76-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 or .00, so if answer is 43 cents, its 0.43 or.43, if there is a dollar amount like 1.50, do not add zeros in front).
Answers
Given :
Two kinds of Beans :
1. Kidney Beans $1.18 per lb
The unit price = $1.18
2. O Lima Beans $213 for 2 lbs
The unit price = 2.13/2 = 1.065
Rounding to the nearest hundredth
So,
The unit
Braden goes to the store to buy earmuffs. The sign says they were originally $13.50 but they are on sale for 15% off. What is the cost of the earmuffs now
Answers
Answer:
$11.48
Step-by-step explanation:
Change 15% to 0.15. then you multiply 13.50 by 0.15
13.50 x 0.15 = 2.025
Then you round 2.025
by rounding 2.025 you should get 2.03
with that you should subtract $13.50 by 2.03
13.50 - 2.03 = 11.48
I hope this helps :)
Subtract these polynomials.
(3x + 2x + 4) (x + 2x+ 1) =
Answers
=(3x2 + 2x + 4) - (x2 + 2x + 1)
Combine like terms
=(3x2-x2)+(2x-2x)+(4-1)
=2x2+0+3
The 2x terms cancel each other to 0
=2x2+3
C) 2x2+3 is the answer.
Hope this helps!
Answer:
15x^2+17x+4
Step-by-step explanation:
(3x+2x+4)(x+2x+1)
Combine 3x and 2x to get 5x.
(5x+4)(x+2x+1)
Combine x and 2x to get 3x.
(5x+4)(3x+1)
Apply the distributive property by multiplying each term of 5x+4 by each term of 3x+1.
15x ^2+5x+12x+4
Combine 5x and 12x to get 17x.
15x^2+17x+4
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Given a polyhedron with 6 vertices and 12 edges, how many faces does it have?
Answers
SOLUTION
GIVEN
A polyhedron has 6 vertices and 12 edges.
TO DETERMINE
The number of faces
CONCEPT TO BE IMPLEMENTED
Euler’s formula for Polyhedron :
For polyhedron F + V = E + 2
Where F stands for number of faces , V stands for number of vertices , E stands for number of edges .
EVALUATION
Here it is given that a polyhedron has 6 vertices and 12 edges
V = Number of vertices = 6
E = Number of edges = 12
F = Number of faces = ?
By Euler’s formula
F + V = E + 2
⇒ F + 6 = 12 + 2
⇒ F + 6 = 14
⇒ F = 8
FINAL ANSWER
The number of faces = 8
sean earns $300 in a regular work week. A regular work week for sean consists of 5 work days with 8 hours a day. How much money does sean earn each hour
Answers
Solution:
According to the problem, a regular work week consists of 5 work days with 8 hours a day. This is equivalent to say:
5 x 8 hours every regular work week.
That is:
40 hours every regular work week
then, the money earned per hour is:
[tex]\frac{300\text{ }dollars}{40\text{ hours}}\text{ = 7.5 dollars per hour}[/tex]then we can conclude that the correct answer is:
$7.5