The probability that at least one of the sides of the triangle is also a side of the octagon is 5/7
How to determine the probability?A regular octagon has 8 sides, and a triangle has 3 sides
Assume that there is a point on the triangle.
Then we select (3 - 1) points from the (8 - 1) sides.
8 - 1 = 7
3 - 1 = 2
So, the total number of selection is:
Selection = 7C2
Evaluate the combination expression
Selection = 21
Adjacent triangles have 5 lines (one line in common).
So, we have:'
n = 5 - 1
n = 4
The number of ways this points can be selected is:
Selection = 4C2
Evaluate
Selection = 6
The probability that the triangle and the octagon do noth have the same side is:
P= 6/21
The probability that at least one of the sides of the triangle is also a side of the octagon is calculated using the following complement rule
P = 1 - 6/21
Evaluate the difference
P = (21 -6)/21
P = 15/21
Reduce fraction
P = 5/7
Hence, the probability that at least one of the sides of the triangle is also a side of the octagon is 5/7
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Kevin is looking at two brands of washing machines. between water and electricity, a brand c washer uses about $0.65 per load, and a brand d washer uses about $0.27 per load. kevin averages about five loads of laundry per month. after one year, how much more would the utility costs for a brand c washer be than the utility costs for a brand d washer? a. $22.80 b. $16.20 c. $7.60 d. $19.00 please select the best answer from the choices provided a b c d
Answer:
The answer is A. 22.80
Which equation can be used to find the nth term of the sequence, an?
55, 50, 45, 40, 35, ...
an=60−5n
an=5n+60
an=5n+55
an=55−5n
Answer:
170 is the answer of mine
Answer:
an=5n-55 is the correct answer
Step-by-step explanation:
Construct a box-and-whisker graph using the following data:
87, 94, 82, 78, 95, 91, 87, 83, 101, 83, 82, 77, 80, 102, 75
data given: {87, 94, 82, 78, 95, 91, 87, 83, 101, 83, 82, 77, 80, 102, 75}
arrange in ascending order:
75, 77, 78, 80, 82, 82, 83, 83, 87, 87, 91, 94, 95, 101, 102
Identify:
Q1 = 80Q2 = 83Q3 = 94IQR = 14Median = 83Plot box-and-whisker graph:
A craft store buys 50 yards of satin ribbon for $13.50. The store
sells the ribbon by the foot. A customer can purchase 5 feet of
ribbon for $0.80. How much profit does the craft store earn if
they sell 45 yards of the ribbon and scraps the rest?
Answer:
$8.10 in profit
Step-by-step explanation:
First convert from yards to feet. 50 yards is equal to 150 feet. To find the unit price for how much they bought it for divide $13.50 / 150 to find that they bought the satin for 9 cents a foot.
Next find how much they sold it for. To find this divide $0.80 / 5 to find that they sold the satin for 16 cents a foot.
To find the profit for 45 yards, convert 45 yards to feet which is 135 feet. Then multiply this by the unit price for sales, 135 * $0.16 to get $21.60
To find the profit subtract the amount they spent on the fabric by the amount they made.
21.60-13.50 = $8.10
Consider the line - 3x +9y = 5.
Find the equation of the line that is perpendicular to this line and passes through the point (5, -1).
Find the equation of the line that is parallel to this line and passes through the point (5, -1).
Answer:
[tex]\textsf{Perpendicular to given line}:y=-3x+14[/tex]
[tex]\textsf{Parallel to given line}: y=\dfrac13x-\dfrac83[/tex]
Step-by-step explanation:
Rewrite the given equation to make y the subject:
[tex]\begin{aligned}-3x+9y &=5 \\ \implies 9y &=3x+5 \\ \implies y &=\dfrac13x+\dfrac59\end{aligned}[/tex]
Therefore, the slope of the given equation is [tex]\frac13[/tex].
If two lines are perpendicular to each other, the product of their slopes will be -1. Therefore, the slope (m) of the line that is perpendicular to the given line is:
[tex]\begin{aligned}m \times \dfrac13 & =-1\\ \implies m & =-3\end{aligned}[/tex]
To find the equation of the line, substitute the found slope (-3) and the point (5, -1) into the point-slope form of a linear equation:
[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\ \implies y-(-1) &=-3(x-5) \\ y+1 & =-3x+15 \\ y &=-3x+14\end{aligned}[/tex]
If two lines are parallel to each other, their slopes will be the same. Therefore, the slope (m) of the line that is parallel to the given line is [tex]\frac13[/tex]
To find the equation of the line, substitute the slope ([tex]\frac13[/tex]) and the point (5, -1) into the point-slope form of a linear equation:
[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\\\ \implies y-(-1) &=\dfrac13(x-5) \\\\ y+1 & =\dfrac13x-\dfrac53 \\\\ y &=\dfrac13x-\dfrac83\end{aligned}[/tex]
Slope =m=1/3
Note that perpendicular lines have slopes negative reciprocal to each other .
Slope of the perpendicular line=-3Equation in point slope form
y+1=-3(x-5)y+1=-3x+15y=-3x+14And
parallel lines have equal slope
Equation of parallel line
y+1=1/3(x-5)3y+3=x-53y=x-8y=x/3-8/3The inability to remember how Lincoln's head appears on a penny, or whether the water in the sink drains clockwise or counterclockwise, is most likely due to a failure in:
Creation
There is no other way
What is the area of the parallelogram?
Witch table matches?
Answer:
y=mx+b
Step-by-step explanation:
so i belive its c because half of 5 is 2.5 and the equation is y=0.5+14.
so half od 5 is 2.5+14=16.5
to how many decimal places are you supposed to 'estimate' the answer to?
Answer:
79.2135
Step-by-step explanation:
5.34 - 2.52 = 2.82
2.82 divided by 0.0356 = 79.2135
1) Solve the inequality 20 – 62 < -10.
Hey there!
20 - 62 < -10
20 - 62
= -42
-42 < -10
Therefore, your answer is: [TRUE] because -42 is SMALLER than -10
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
What is the circumference of a circle with a radius of 0.5 feet, explain your answer.
Answer:
circumference equals about 3.14
Step-by-step explanation:
c=2pi times r
c=2 (3.14) times 0.5
c= about 3.14
Answer:
3.14(rounded to nearest hundredth)
__________________________________________________________
Solve by...First, use the formula for finding circumference by diameter;[tex]C = 2\pi r[/tex]
Which is the same as ↓
[tex]2\pi r = 2 * \pi * r(0.5)[/tex]
[tex]= 3.1415926535897932384626433832795[/tex]
percent sicount
A $44.00 video game is on sale for $28.60
A.20%
B.25%
C.30%
D.35%
E.40%
F.45%
Answer:
35%
Step-by-step explanation:
28.60 is what percent of $44 ?/100
28.60*100=2860 2860/44=65 100-65=35%
christa went shopping for back to school clothes before tax was added on her total was $176 if the sales tax is 6% what was the total amount she paid
Answer:
$186.56
Step-by-step explanation:
$176 + 6% = 186.56
A line passes through the point (-9,5) and has a slope of 2/3 what is the equation in point-slope form for this line
Step-by-step explanation:
y-y1=m(x-x1)
y-5=2/3(x+9)
The two triangles shown are congruent.
Find the value of x
Answer:
x = 11
Step-by-step explanation:
right triangle ABC
using Pythagoras' identity
BC² = 7² + 24² = 49 + 576 = 625 ( take square root of both sides )
BC = [tex]\sqrt{625}[/tex] = 25
Since the triangles are congruent then corresponding sides are congruent.
ST = BC , that is
3x - 8 = 25 ( add 8 to both sides )
3x = 33 ( divide both sides by 3 )
x = 11
A homeowner is putting in a fireplace that has a 5 inch radius vent pipe. He needs to cut an elliptical hole in his roof to accommodate the pipe. If the pitch of his roof is 2/5 what are the dimensions of the hole
The dimensions of the hole when the homeowner is putting in a fireplace will be 10 inches and 10.77 inches.
How to calculate the dimensions?The width of the pipe will be:
= 5 × 2
= 10 inches.
The length of the pipe will be:
= (✓2² + ✓5²)/5 × 10
= ✓29/5 × 10
= ✓29 × 2
= 10.77 inches
In conclusion, the dimensions are 10 inches and 10.77 inches.
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Which phrase represents this expression?
35÷(12−5)
Select each correct answer.
(1) 5 less than the quotient of 35 and 12
(2) 35 divided by the difference of 12 and 5
(3) the quotient of 35 and the difference of 12 and 5
(4) the total of 35 and 12 is subtracted by 5
Answer:
answer 2(35 divided by the difference of 12 and 5
Answer:
2 and3
Step-by-step explanation:
Enrique makes $11.50 per hour and works 40 hours per week. He is single
and claims O withholding allowances. He estimates that he will spend $100
per month on qualified expenses. How much will he save per week in taxes
if he participates in his employer's cafeteria plan and has $100 per month
deducted before taxes? How much will he save in one year, or 50 weeks
of work?
Answer:
He makes 460 per week
Step-by-step explanation:
Find the mean absolute deviation, variance, and
standard deviation for the data set showing the price of
six different jars of pasta sauce at the grocery store:
{$2.79, $1.99, $4.29, $2.49, $2.29, $3.49}
If the mean of the data is 2.89, then the mean absolute deviation, variance, and standard deviation will be 0.67, 0.61, and 0.78 respectively.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
The data set is given below.
{$2.79, $1.99, $4.29, $2.49, $2.29, $3.49}
Then the mean value of the data will be
[tex]\mu = \dfrac{{2.79+ 1.99+ 4.29+ 2.49+ 2.29+ 3.49}}{6} \\\\\mu = \$ 2.89[/tex]
Then the mean absolute deviation will be
[tex]\rm MAD = \dfrac{1}{N} \Sigma _{i=1}^N |x_i - \mu|\\\\MAD = \dfrac{1}{6} (|2.79 - 2.89| + |1.99-2.89| + ... +|3.49-2.89|)\\\\MAD = 0.6667 \approx 0.67[/tex]
Then the standard deviation will be
[tex]\rm \sigma = \sqrt{\dfrac{\Sigma _{i=1}^N (x_i - \mu)^2}{N} }\\\\\sigma = \sqrt{\dfrac{(2.79-2.89)^2 + (1.99 - 2.89)^2 + .... + (3.49 - 2.89)^2}{6}}\\\\\sigma = \sqrt{0.61}\\\\\sigma = 0.78[/tex]
Then the variance will be
[tex]\sigma ^2 = (\sqrt{0.61})^2\\\\\sigma ^2 =0.61[/tex]
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What is the volume to the nearest tenth of a cone that has a height of 17 meters and a base with a radius of 6 meters? Use 3.14 for π and round to the nearest tenth.
Answer:
640.6 m^2
Step-by-step explanation:
Formula
V = (1/3) pi * r^2 * h Substitute givens into the formula and solve
Givens
V = ?
pi = 3.14
r = 6 m
h = 17 m
Solution
V = (1/3) * 3.14 * 6 * 6 * 17
V = 640.56
Answer
V = 640.6 m^2 to the nearest 10th
There were 30 cookies in a basket. Haley ate 10% of the cookies. Erin ate 1 6 of the cookies. Hannah ate 1 5 of the cookies. Madison ate 30% of the cookies. How many cookies are left in the basket?
The number of cookies left in the basket after everyone has eaten out of the cookies is 7.
How many cookies are left?The first step is to convert the fractions to percentages.
1/6 x 1000 = 16.67%
1/5 x 100 = 20%
Now determine the sum of the percentages of the cookies eaten : 10% + 30% + 16.67 + 20% = 76.67%
Determine the percentage of cookies left = 100 - 76.67 = 23.33%
Number of cookies left = (23.33 / 100) x 30 = 7
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A formula for the perimeter of a rectangle is P=2(l+w), where P is the perimeter, l is the length, and w is the width.
If the length of a rectangle is 64 centimeters and the width is 22 centimeters, what is the perimeter?
What is the area of the trapezoid? (-2, 6) (3,6) (-4,-6) (5.-6)
Answer:
84
Step-by-step explanation:
[tex]A[/tex]trapezoid= [tex]\frac{h(b_{1} + b_{2})}{2}[/tex]
Substitute the values into the equation: [tex]A=\frac{12(9 + 5)}{2}[/tex]
[tex]A=\frac{12(9 + 5)}{2}[/tex] (add 9 and 5)
↓
[tex]A=\frac{12(14)}{2}[/tex] (multiply 14 by 12)
↓
[tex]A=\frac{168}{2}[/tex](divide 168 by 2)
↓
[tex]A=84[/tex] (your answer)
Hope this helps! Have a good day! :)
the shape of this graph is best described as 2012 housing prices
Answer:
tell the full question
Step-by-step explanation:
bro
i don’t understand how to do this
Answer:
There is only 1 solution where x is greater than 3 that is on the line and that is where the line Crosse where x is 4.
Step-by-step explanation:
p(x>3) = p(x= 5) - p(x= 3)
= (Area of ∆ from x= 0 to x= 5)- (Area of ∆ from x= 0 to x= 3)
=[ 1/2•(5-0)•0.4] -[1/2•(3-0)• 0.4)]
= 1/2•0.4(5-3)
p(x>3) = 0.4
An analysis of variance is used to evaluate the mean differences for a research study comparing four treatments with a separate sample of n = 8 in each treatment. If the data produce an F-ratio of F = 4.60, which of the following is the correct statistical decision? a. Reject the null hypothesis with α = .05 but not with α = .01 b. Reject the null hypothesis with either α = .05 or α = .01 c. Fail to reject the null hypothesis with either α = .05 or α = .01 d. There is not enough information to make a statistical decision
Considering the p-value of the f-ratio, it is found that the correct option is given by:
a. Reject the null hypothesis with α = .05 but not with α = .01.
What is the relation between the p-value and the test hypothesis?Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected.If it is less, it is rejected.In this problem, the test statistic is of F = 4.60, with 4 x 7 = 28 df between treatments and 7 df in a single treatment, hence, using a calculator, the p-value is of 0.0218, which is less than 0.05 but more than 0.01, meaning that option A is correct.
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The cube has a volume of 340 cubic inches. Approximate the length d of the diagonal to the nearest whole number.
Considering the volume of the cube, it is found that it has a diagonal with a length of 12 inches.
What is the volume of a cube?The volume of a cube of side length a is given by:
V = a³.
The diagonal is given by:
[tex]D = \sqrt{3}a[/tex]
In this problem, the volume is of 340 in³, hence:
[tex]a³ = 340 \rightarrow a = \sqrt[3]{340} \rightarrow a = 6.98[/tex]
Hence, the diagonal is given by:
[tex]D = \sqrt{3} \times 6.98 = 12[/tex]
The cube has a diagonal with a length of 12 inches.
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Determine the value of each variable.
Answer:
a=9, b=45, c=31.5, d=18, f=27
Step-by-step explanation:
To find the value of a, you can take 72-54=18 and do 18/2=9
a=9
To find the value of b, you can multiply the three a's. 27 is the product of the 3 a's. Next, you will do 72-27 to find the value of b
b=45
To find the value of c, you can take 9 and subtract it from 72, or in other words: 72-9=63. You will then divide 63/2 to find the value of c
c=31.5
To find the value of d, you can multiply (9*4)=36. You can then take 72-36 and get 36. To find the value of d, you will then divide 36/2.
d=18
To find F, you are given a clue that 1 a and 1 d together=f.
9+18=f
f=27
Answer:
a=9
b=36
c=45
d=31.5
f=40.5
Step-by-step explanation:
Phew! that was pretty tough. But I solved it! Your welcome! :)
Find the surface area of each prism 2cm
8cm
8cm
Answer:
128 square cm
Step-by-step explanation:
2 x 8 x 8 x = 128 cm
Hope this Helps
Please help!!!!
Identify the polynomial
1-3
Answer:
Step-by-step explanation: