what is an angle between a side of a polygon and the extension of its adjacent side
Answers
here's an example. hope it helps!
The angle between a side of a polygon and the extension of its adjacent side is the exterior angle at that vertex, forming a linear pair with the adjacent interior angle.
Angle between a side of a polygon and the extension of its adjacent side: When considering a polygon, the angle between a side and the extension of its adjacent side is equal to the exterior angle of the polygon at that vertex. This angle forms a linear pair with the adjacent interior angle of the polygon.
Related Questions
The Leukemia and Lymphoma Society sponsors a 5k race to raise money. It receives $55 per race entry and $10,000 in donations, but it must spend $15 per race entry to cover the cost of the race.
Write and solve an inequality to determine the number of race entries the charity needs to raise at least $55,000.
Answers
A store sells toaster ovenstoaster ovens for $4646 each, retail price. The wholesale cost to stock the ovensovens is $ 28$28 each. The fixed cost associated with acquiring the ovensovens, storing them in inventory, using shelf space, and advertising the ovensovens for sale is $25002500. a. Write a function for the total cost of stocking the ovensovens for sale. b. Write a function for the total revenue received from selling the ovensovens. c. Write a system of equations and determine the number of ovensovens that must be sold to break even.
Answers
Stocking cost = $28 per toaster
Fixed cost = $2500
a) Let the number of toasters be 'x'
The total cost of stocking for sale = 28x + 2500
b) Let the number of toasters be 'x'
Total revenue received from selling the toasters = 46x
c) Break-even is when the cost of production is equal to profit made
So, we can set up the break-even equation as:
Production cost = Revenue cost
28x + 2500 = 46x
2500 = 46x - 28x
2500 = 18x
x = 138.9 ⇒ Rounded to 139 ovens
Jessica's lab is 12 times as long as her hamster. Her hamster is 4.16 inches long. How long is her lab?
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Key words - times
49.92
Jessica's lab is 49.92 inches long
i hope this helps!!
Deon is riding his bicycle. He rides for 7 hours at a speed of 22.4 kilometers per hour. For how many kilometers does he ride
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If he rides for 7 hours, he completes 22.4 * 7 = 156.8 km
So in 7 hours, he rides 156.8 kilometers.
Hope this helps! :)
the line joining A(a, 3) to B(2 -3) is perpendicular to the line joining C(10,1) to B. The value of a is?
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[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) B&({{ 2}}\quad ,&{{ -3}})\quad % (c,d) C&({{ 10}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-(-3)}{10-2}\implies \cfrac{1+3}{10-2} \\\\\\ \cfrac{4}{8}\implies \cfrac{1}{2}[/tex]
now, a line perpendicular to that one, will have a negative reciprocal slope, thus
[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{1}{2}\\\\ slope=\cfrac{1}{{{ 2}}}\qquad negative\implies -\cfrac{1}{{{ 2}}}\qquad reciprocal\implies - \cfrac{{{ 2}}}{1}\implies \boxed{-2}[/tex]
now, we know the slope "m" of AB is -2 then, thus
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ a}}\quad ,&{{ 3}})\quad % (c,d) B&({{ 2}}\quad ,&{{ -3}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-3-3}{2-a}=\boxed{-2} \\\\\\ \cfrac{-6}{2-a}=-2\implies -6=-4+2a\implies -2=2a\implies \cfrac{-2}{2}=a \\\\\\ -1=a[/tex]
The value of a is -1
What do perpendicular lines have a slope of?
Perpendicular lines have slopes that are negative reciprocals of each other. The given line's slope is 5, which means that the slope of the opposite line must be its negative reciprocal.
Conclusion: The slopes of two perpendicular lines are negative reciprocals of each other. This means that if a line is perpendicular to a line that is the slope of the line is -1/m.
let the slope of line AB is m1 and the slope of line BC be m2
m1= 3+3/a-2 = 6/a-2
m2=1+2/10-2 = 1/2
m1 * m2 = -1
6/a-2 * 1/2 = -1
3 = -a+2
a = -1
Learn more about reciprocal here
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what are the coordinates of a p;point on the unit circle if the angle formed by the positive x axis and the radius is 60 degrees
Answers
Using the ratios, we know that the side opposite the 30° angle (the x-axis) will be 1/2 the hypotenuse 1, which is 1/2. This means our x-coordinate is 1/2.
We also see that the side opposite the 60° angle will be the other leg, times √2. This means it will be (1/2) * √2 = √(2)/2. This is the y-coordinate.
Therefore, the coordinates of the point on the unit circle are (1/2, √(2)/2).
Solve for x.
x−1/4=38
Enter your simplified answer in the box.
Answers
1. x - 1/4 = 3/8;
2. x = 1/4 + 3/8;
3. x = 2/8 + 3/8;
4. x = 5/8;
Hope everything is clear.
Choose all the doubles facts that can help you solve 8+7
Answers
if you do 8+7=15
i think it help
Answer: 7 + 7 = 14
8 + 8 = 16
Step-by-step explanation: doubles facts are simply additions where a number is added to it self. The strategy sums up two consecutive numbers when they are next to each other to give their result as given by the question above (8 + 7). We simply add the smaller number together then add one (double-plus-one) OR add the larger number together then subtract one (double-minus-one)
All doubles that can be used in solving 8 + 7 are:
A) 8 + 7 = 7 + (7 + 1) = (7 + 7) + 1 = 14 + 1 = 15 [double-plus-one]
B) 8 + 7 = (8 + 8) - 1 = 16 - 1 = 15 [double-minus-one]
The doubles fact makes use of the associative property of addition —changing the grouping of addends does not change the sum.
Which coin have a diameter with a 5 in a hundredths place
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WILL GIVE BRAINEST
which description matches the function that represents by the values in this table?
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Hiya :)
d. exponential growth
Have a great day!!!
Hope this helped!!
:)))))
0.00000002 in scientific notation
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Please mark Brainliest!
I'm pretty sure that's right
Althea traveled 280 miles at a speed of 70 miles/hour. How much time did she take to cover this distance?
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t = d/r
t = 280/70
t = 4 hours
Can someone walk me through the steps in solving this question
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now, bear in mind, we first convert the mixed fraction to "improper", and then use that,
[tex]\bf \begin{array}{ccll} \stackrel{\stackrel{baked}{potato}}{oz}&calories\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&48.3\\ 3\frac{1}{3}&p \end{array}\implies \cfrac{1}{3\frac{1}{3}}=\cfrac{48.3}{p}\implies \cfrac{\frac{1}{1}}{\frac{3\cdot 3+1}{3}}=\cfrac{48.3}{p}[/tex]
[tex]\bf \cfrac{\frac{1}{1}}{\frac{10}{3}}=\cfrac{48.3}{p}\implies \cfrac{1}{1}\cdot \cfrac{3}{10}=\cfrac{48.3}{p}\implies \cfrac{3}{10}=\cfrac{48.3}{p} \\\\\\ 3p=483\implies p=\cfrac{483}{3}\implies \boxed{p=\stackrel{calories}{161}}[/tex]
now, we know that in 1oz of chicken gas 24.6 calories, so, how many calories then in 5 and 1/4 oz?
[tex]\bf \begin{array}{ccll} \stackrel{chicken}{oz}&calories\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&24.6\\ 5\frac{1}{4}&c \end{array}\implies \cfrac{1}{5\frac{1}{4}}=\cfrac{24.6}{c}\implies \cfrac{\frac{1}{1}}{\frac{5\cdot 4+1}{4}}=\cfrac{24.6}{c}[/tex]
[tex]\bf \cfrac{\frac{1}{1}}{\frac{21}{4}}=\cfrac{24.6}{c}\implies \cfrac{1}{1}\cdot \cfrac{4}{21}=\cfrac{24.6}{c}\implies \cfrac{4}{21}=\cfrac{24.6}{c} \\\\\\ 4c=516.6\implies c=\cfrac{516.6}{4}\implies \boxed{c=\stackrel{calories}{129.15}}[/tex]
so, how many calories in that meal? well, p + c.
a jar of jelly beans that weigh 4.25 ounces costs 2.89. what is the cost of one ounce of jelly
Answers
Cost in dollars --> $2.89
Total ounces --> 4.25
But you want to know the per unit cost for *1* ounce.
You have the right method. You want cost ($) per ounce so put the price over the amount in ounces.
2.89 / 4.25 = x / 1
If you notice, since the denominator is 1, this is simply:
x = 2.89 / 4.25
So the unit cost is just $2.89 divided by the number of ounces (4.25).
Plug that into your calculator and you get:
0.68
That's in dollars. So if you want it in cents, move the decimal point 2 places to the right.
Answer:
$0.68 per ounce
or
68 cents per ounce
Find then selling price per liter of a mixture made from 70 L of cranberry juice which cost $1.20 per liter and 130 L of apple juice which cost $0.80 per liter
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Find the probability of a couple having a baby boy when their fourth child is born, given that the first three children were all boys. assume boys and girls are equally likely. is the result the same as the probability of getting sall boys among four children
Answers
The probability of having a baby boy on the fourth child, given that the first three children were all boys, is 0.5. This result is not the same as the probability of getting all boys among four children, which is 0.0625. The conditional probability accounts for the information about the first three births.
To solve this probability problem, let's break it down step by step.
Probability of Having a Boy on the Fourth Child:
Assuming boys and girls are equally likely, the probability of having a boy or a girl is 1/2 or 0.5. When considering each child's gender independently, the probability of having a boy on the fourth child is 0.5, regardless of the genders of the previous children.
However, the question specifies that the first three children were all boys. This information is crucial for the conditional probability calculation.
Conditional Probability:
The probability of having a boy on the fourth child given that the first three children were all boys is denoted as [tex]\( P(B_4 | B_1, B_2, B_3) \)[/tex].
Since the events are assumed to be independent (the gender of one child does not affect the gender of another), the conditional probability is the same as the probability of having a boy on any single birth: 0.5.
Comparison with Getting All Boys:
The probability of getting all boys among four children [tex](\( P(B_1 \cap B_2 \cap B_3 \cap B_4) \))[/tex] is the product of the probabilities of having a boy for each birth.
[tex]\[ P(B_1 \cap B_2 \cap B_3 \cap B_4) = P(B_1) \times P(B_2) \times P(B_3) \times P(B_4) \][/tex]
Given that [tex]\( P(B_4) = 0.5 \)[/tex] and the previous births are all boys, [tex]\( P(B_1 \cap B_2 \cap B_3 \cap B_4) = (0.5)^4 = 0.0625 \)[/tex].
The question probable may be:
Find the probability of a couple having a baby boy when their fourth child is born, given that the first three children were all boys. Assume boys and girls are equally likely. Is the result the same as the probability of getting all boys among four children?
what is the approximate value of the square root of 8
Answers
Answer:
2.828427
Step-by-step explanation:
I looked it up
What is the minimum number of degrees that a hexagram can be rotated so that it is carried onto itself?
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A sample of 12 measurements has a mean of 8.5 and a sample of 20 measurements has a mean of 7.5. Find the mean of all 32 measurements.
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Use compatible numbers to estimate the quotient 5821/71?
Answers
Divide 5821 by 71
Round the number to the nearest hundred
5821 ÷ 71 → 5800 ÷ 70
Calculate mentally.
58 ÷ 7=8.2
Estimated quotient = 8
HELP ME Look at pics
Answers
combine all the like terms
8x^2 + x^2 = 9x^2
-9y^2 - 3y^2 = -12y^2
-4x-7x = -11x
so you have 9x^2 -12y^2-11x
Answer id the last one
Find the probability that the person is frequently or occasionally involved in charity work.
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[tex]\begin{tabular} {|c|c|c|c|c|c|} &Frequently&Occassionally&Not at all&Total\\[1ex] Male&227&454&798&1,479\\ Female &205&450&747&1,402\\ Total&432&904&1,545&2,881 \end{tabular}[/tex]
Part A:
If a person is chosen at random, the probability that the person is frequently or occassinally involved in charity work is given by
[tex]P(being \ frequently \ involved \ or \ being \ occassionally \ involved)\\ \\= \frac{432}{2881} + \frac{904}{2881} = \frac{1336}{2881}=\bold{0.464}[/tex]
Part B:
If a person is chosen at random, the probability that the person is female or not involved in charity work at all is given by
[tex]P(being \ female \ or \ not \ being \ involved)\\ \\= \frac{1402}{2881} + \frac{1545}{2881}-\frac{747}{2881} = \frac{2200}{2881}=\bold{0.764}[/tex]
Part C:
If a person is chosen at random, the probability that the person is male or frequently involved in charity work is given by
[tex]P(being \ male \ or \ being \ frequently \ involved)\\ \\= \frac{1479}{2881} + \frac{432}{2881}-\frac{227}{2881} = \frac{1684}{2881}=\bold{0.585}[/tex]
Part D:
If a person is chosen at random, the probability that the person is female or not frequently involved in charity work is given by
[tex]P(being \ female \ or \ not \ being \ frequently \ involved)\\ \\= \frac{1402}{2881} + \frac{904}{2881} + \frac{1545}{2881}-\frac{450}{2881}-\frac{747}{2881} = \frac{2654}{2881}=\bold{0.921}[/tex]
Part E:
The events "being female" and "being frequently involved in charity work" are not mutually exclusive because being a female does not prevent a person from being frequently involved in charity work.
Indeed from the table, there are 205 females who are frequently involved in charity work.
Therefore, the answer to the question is "No, because 205 females are frequently involved charity work".
(a) The probability is [tex]\[\boxed{0.464}\][/tex]. (b) The probability is [tex]\[\boxed{0.763}\][/tex]. (c) The probability is [tex]\[\boxed{0.585}\][/tex]. (d) The probability is [tex]\[\boxed{0.921}\][/tex]. (e) No, because 205 females are frequently involved in charity work. The option (A) is correct.
To address the given questions based on the provided table, let's go through each question step-by-step:
(a) Find the probability that the person is frequently or occasionally involved in charity work.
First, we need the total number of people who are frequently or occasionally involved in charity work. This is the sum of people in the "Frequently" and "Occasionally" columns.
[tex]\[\text{Total frequently or occasionally involved} = 432 + 904 = 1336\][/tex]
Now, we divide this by the total number of people surveyed:
[tex]\[P(\text{frequently or occasionally involved}) = \frac{1336}{2881} \approx 0.464\][/tex]
So, the probability is [tex]\[\boxed{0.464}\][/tex].
(b) Find the probability that the person is female or not involved in charity work at all.
To solve this, we need to find the number of females and those not involved in charity work at all.
[tex]\[\text{Total females} = 1402\][/tex]
[tex]\[\text{Total not involved at all} = 1545\][/tex]
We need to subtract the overlap (females not involved in charity work) to avoid double-counting. From the table, the number of females not involved at all is 747.
[tex]P(\text{female or not involved at all}) = \frac{\text{Total females} + \text{Total not involved at all} - \text{Females not involved}}{\text{Total}}[/tex]
[tex]= \frac{1402 + 1545 - 747}{2881} = \frac{2200}{2881} \approx 0.763[/tex]
So, the probability is [tex]\[\boxed{0.763}\][/tex].
(c) Find the probability that the person is male or frequently involved in charity work.
[tex]\[\text{Total males} = 1479\][/tex]
[tex]\[\text{Total frequently involved} = 432\][/tex]
We need to subtract the overlap (males frequently involved) to avoid double-counting. From the table, the number of males frequently involved is 227.
[tex]P(\text{male or frequently involved}) = \frac{\text{Total males} + \text{Total frequently involved} - \text{Males frequently involved}}{\text{Total}}[/tex]
[tex]= \frac{1479 + 432 - 227}{2881} = \frac{1684}{2881} \approx 0.585[/tex]
So, the probability is [tex]\[\boxed{0.585}\][/tex].
(d) Find the probability that the person is female or not frequently involved in charity work.
[tex]\[\text{Total females} = 1402\][/tex]
[tex]\[\text{Total not frequently involved} = 2881 - 432 = 2449\][/tex]
We need to subtract the overlap (females not frequently involved) to avoid double-counting. From the table, the number of females not frequently involved is 1197 (450 + 747).
[tex]P(\text{female or not frequently involved})=\frac{1402 + 2449 - 1197}{2881} = \frac{2654}{2881} \approx 0.921[/tex]
So, the probability is [tex]\[\boxed{0.921}\][/tex].
(e) Are the events "being female" and "being frequently involved in charity work" mutually exclusive?
Two events are mutually exclusive if they cannot occur at the same time.
From the table, 205 females are frequently involved in charity work.
Since there are females who are frequently involved in charity work, the events "being female" and "being frequently involved in charity work" are not mutually exclusive.
So, the answer is A. No, because 205 females are frequently involved in charity work.
The complete question is:
The table below shows the results of a survey that asked 2881 people whether they are involved in any type of charity work. A per selected at random from the sample. Complete parts (a) through (e).
(a) Find the probability that the person is frequently or occasionally involved in charity work.
P(being frequently involved or being occasionally involved) - (Round to the nearest thousandth as needed.)
(b) Find the probability that the person is female or not involved in charity work at all.
P(being female or not being involved) (Round to the nearest thousandth as needed.)
(c) Find the probability that the person is male or frequently involved in charity work.
P(being male or being frequently involved) (Round to the nearest thousandth as needed.)
P(being male or being frequently involved) - (Round to the nearest thousandth as needed.)
(d) Find the probability that the person is female or not frequently involved in charity work.
P(being female or not being frequently involved) = (Round to the nearest thousandth as needed.)
(e) Are the events "being female" and "being frequently involved in charity work" mutually exclusive? Explain.
A. No, because 205 females are frequently involved in charity work.
B. Yes, because no females are frequently involved in charity work.
C. Yes, because 205 females are frequently involved in charity work.
D. No, because no females are frequently involved in charity work.
Find the point in the first octant where the tangent plane to x2+116y2+14z2=1 is parallel to the plane x+y+z=10
Answers
A cyclist rides his bike at a rate of 21 miles per hour. What is this rate in miles per minute? How many miles will the cyclist travel in 2 minutes? Do not round your answers.
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Alright 21 miles per hour. We know that there are 60 minutes in an hour. So this is basically saying 21 miles per 60 minutes. To find the rate for miles per minute, you divide 21 by 60 which is 0.35.
In one minute the cyclist rides 0.35 miles
In two minutes the cyclist rides 0.7 miles
4- T = 3 (T-1)-5
A. 3
B. 6
C. No solution
D. Identity
If you can explain this to me I would really love that.
Answers
next we subtract 3T - 3 - 5 so it can be 3T - 8
next we add T to both sides
next we subtract 3T - 8 + T so it can be 4T - 8
next we add 8 to both sides
next we add 4 + 8 so it can be 12
then we divide both sides by 4
and lastly we reduce the fraction 12/4 and we have our answer.
Answer: A) T = 3
To solve this equation, you need to first use the Distributive Property on the right side.
4 - t = 3t - 3 - 5
Now, add like terms.
4 - t = 3t - 8
Then, move terms to their own sides.
(4 - 4) - t = 3t + (-8 - 4)
(-t - 3t) = (3t - 3t) - 12
-4t = -12
Now, divide both sides by -4.
-4t / -4 = -12 / -4
t = 3
The answer is A. 3.
Hope this helps.
a cell phone company charges a monthly fee of $0.25 for each text. message the monthly fee is $30.00 and you owe $59.50. how many text messages did you have
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after that, you pay for the txt messages you use, the more you use, the more you pay, in this case is 25 cents for each.
so if you use say hmm 100 txt messages, then you owe for a month 30 + 0.25(100)
and if you use "x" txt messages, then you owe 30 + 0.25x.
[tex]\bf \stackrel{cost}{y}=\stackrel{monthly~fee}{30}+\stackrel{txt~charges}{0.25x}\implies 59.50=30+0.25x \\\\\\ 29.5=0.25x\implies \cfrac{29.5}{0.25}=x\implies 118=x[/tex]
The distance of planet Mercury from the Sun is approximately 5.8 ⋅ 107 kilometers, and the distance of planet Venus from the Sun is 1.1 ⋅ 108 kilometers. About how many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun? (1 point)
Select one:
a. 5.2 ⋅ 107 kilometers
b. 4.7 ⋅ 108 kilometers
c. 5.2 ⋅ 108 kilometers
d. 5.7 ⋅ 109 kilometers
Answers
Answer:
a) 5.2 *10^7 km
Step-by-step explanation:
If we could describe our Solar System, in order of appearance nearer the Sun, it would be like this:
Sun --- Mercury --- Venus --- Earth
Sun --------------------- Venus
1.1 * 10^8 km
Sun -------Mercury
5.8 * 10^7 Km
To find out how many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun, all we have to do is simply subtract the distance Sun ---Venus minus Sun ---Mercury
So,
1.1 * 10^8 - 5.8 * 10^7 =
Adjusting the first distance to the same power
110*10^7- 5.8*10^7 =
Subtracting the factors
5.2 * 10^7
HELP WILL GIVE HIGHEST RATING!!!
36 POINTS TO CORRECT ANSWER Cindy has 26 nickels. She is getting rolls of nickels from the bank. She has enough money to get up to 10 rolls of nickels and each roll contains 40 nickels. The bank will not give partial rolls. The function that models the number of nickels Cindy will have after leaving the bank is f(r)=40r+26, where r is the number of rolls of nickels she gets. What is the practical domain of the function?
Answers
Answer:
The answer is all integers from 1 to 10, inclusive
Bye~~
Chad bought a box of raisins. he gave 1/6 of it to one brother, 1/4 to another brother, and he kept the rest for himself. what fraction did he keep?
Answers
This can be solved by creating a simple equation.
[tex]1/4+1/6+x=1[/tex]
Solve for x.
[tex]1/4+1/6+x=1[/tex]
Find the LCM.
[tex]3/12+2/12+x=1[/tex]
[tex]5/12+x=1[/tex]
Add -5/12 to both sides.
[tex](5/12+x)+(-5/12)=(1)+(-5/12)[/tex]
Simplify.
[tex]x=1/1-5/12[/tex]
Find the LCM.
[tex]x=12/12-5/12[/tex]
[tex]x=7/12[/tex]
He kept 7/12 of the raisins for himself.
Hope this helps.
-Benjamin
Consider the solid s described below. the base of s is the region enclosed by the parabola y = 5 - 5x2 and the x-axis. cross-sections perpendicular to the x-axis are isosceles triangles with height equal to the base. find the volume v of this solid.
Answers
To find the volume of the solid described, we can use the formula for the volume of a cylinder and integrate the cross-sectional area. The cross-sectional area is the base of the solid, and in this case, it is given by (25 - 50x^2 + 25x^4).
Explanation:The solid described in the question has a base in the shape of the region enclosed by the parabola y = 5 - 5x^2 and the x-axis. The cross-sections perpendicular to the x-axis are isosceles triangles with a height equal to the base.
To find the volume of the solid, we can use the formula for the volume of a cylinder. The cross-sectional area of each triangle is the base times the height, and the height of the triangle is also the base. So, the cross-sectional area is A = (5 - 5x^2)(5 - 5x^2) = (25 - 50x^2 + 25x^4).
The volume of the solid is then given by integrating the cross-sectional area from the x-values that define the base of the solid. So, V = ∫(25 - 50x^2 + 25x^4)dx.