How many toothpicks are used to create Figure 10? Describe how you found the answer.
Answers
58
35
31
27
23
19
15
11
7
3
Now add all these numbers and you should get a total of 229
Related Questions
A large planetarium in the shape of a dome is being built. When it is complete, the base of the dome will have a circumference of 87 kilometers. What area of land was required for this planetarium?
Answers
r = 87 km / 2 / pi = 13.846 km,
Now the areas is:
A = pi * 13.486^2 = 602.32188213127836 km^2 = 602.32 km^2
Huge
Answer:
602.32 km²
Step-by-step explanation:
First, find the radius of the circle using the circumference formula
C = 2π*r
87 = 2π*r
∴ r = 13.8465 km
Second, using the radius, calculate the area:
A = π * r²
A = π * 13.8465²
A = 602.32 km ²
Travis traveled 320 miles in 5 hours. What is his unit rate of speed in miles per hour? _____ miles per hour
Answers
The unit rate of speed in miles per hour is 64 miles per hour if Travis traveled 320 miles in 5 hours.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
We have:
Travis traveled 320 miles in 5 hours.
The distance d = 320 miles
Time is taken t = 5 hours
As we know, the change in values of a dependent variable with respect to the independent variables.
The unit rate of speed in miles per hour = 320/5
The unit rate of speed in miles per hour = 64 miles per hour
Thus, the unit rate of speed in miles per hour is 64 miles per hour if Travis traveled 320 miles in 5 hours.
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Max has more than 5 carrots (number of carrots Max has = c
Answers
What is the ratio of 2.5 million to 1.5 million
Answers
Question 2 (multiple answer)
Which simplifications of the powers of i are correct?
There is more than one correct answer. Select all correct answers.
i7=i4⋅i3=−1⋅−i=i
i6=i4⋅i2=1⋅−1=−1
i6=i4⋅i2=−1⋅−1=1
i7=i4⋅i3=1⋅−i=−i
i8=i4⋅i4=−1⋅−1=1
i5=i3⋅i2=−i⋅−1=i
i5=i3⋅i2=i⋅−1=−i
i8=i4⋅i4=1⋅1=1
Answers
i6=i4⋅i2=1⋅−1=−1
i7=i4⋅i3=1⋅−i=−i
i5=i3⋅i2=−i⋅−1=i
i8=i4⋅i4=1⋅1=1
Avani went to the grocery store and bought home a cardboard box that was covered with a sealed top Two end face of the box are squares The area of the face on either end is 64 square inches what is the length of the side of a square face? Plz help me plz
Answers
Please Help!
1. Define an example of a function – this could be distance traveled vs. time, the cost
of a turkey vs. weight, ect.
2. Show this relation as a set of correctly determined ordered pairs -- you will need
at least 5 ordered pairs in set notation -- remember that set notation will look
like: {(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)} with the { } around the ordered pairs.
Can you please explain how you did it. I want to understand. (30pts)
Answers
[tex]p=8t[/tex]
where p = pay ($) and t = time (hr)
Pick some values for t and substitute them into the formula to get the corresponding pay.
(0, 0) <--- no hours, no pay
(1, 8) <--- one hour, pay $8
(2, 16) <--- two hours, pay $16
etc.
[tex]\{(0,0), (1,8), (2,16), (3, 24), (4, 32), (5, 40)\}[/tex]
Suppose you are walking home from the skating ring , you have to walk 6 miles east and 9 miles north , use the Pythagorean theorem how far is the skating ring from where u are.
plzzzzz!!!!!help
Answers
this forms a right triangle where you need to calculate the length of the hypotenuse by using the Pythagorean theorem
a^ + b^2 = c^2
6^2 = 36
9^2 = 81
36+81 = 117
sqrt(117) = 10.816
10.8 miles
Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $14,500 in 1982 and $65,500 in 1987. Let x = 0 represent 1982. Find the equation giving yearly sales S
Answers
we are given that
f(0)=a*0+b=b is $14,500.
so the sales in the first year were $14,500.
f(1) gives the sales in the second year (year 83)
f(2) gives the sales in the third year (year 84)
.
.
f(5) gives the sales in the sixths year (year 87)
the slope of the line, a, is given by :
[tex] \frac{f(5)-f(0)}{5-0}= \frac{65,500-14,500}{5}= 10,200[/tex]
thus,
S=ax+b=10,200x+14,500
Answer: S=10,200x+14,500
Final answer:
To articulate the linear equation for yearly sales S, we calculate the slope from the two provided data points and use the slope-intercept form, ultimately deriving the equation S = 10200x + 14500.
Explanation:
To find the equation giving yearly sales S, we can use the two data points: sales were $14,500 in 1982 and $65,500 in 1987. With x = 0 representing 1982, the two points are (0, 14500) and (5, 65500). We can calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), which is the change in sales over the change in time.
So, m = (65500 - 14500) / (5 - 0) = 51000 / 5 = 10200. This means the sales are increasing at a rate of $10,200 per year.
Now, we can use the slope and one point to write the linear equation in the slope-intercept form, which is Y = mx + b, where b is the y-intercept. Since when x = 0, Y = 14500, we know that b = 14500. Therefore, our final equation for yearly sales S is S = 10200x + 14500.
Myles can ride his bike 24 miles in 6 hours. How many miles can he travel in 1 hour? (Unit rate)
How many miles can Myles travel in 5 hours?
Answers
An Octagon has the radius of 56 and an area of 10,391.9 square millimeters.
a1) What is the approximate perimeter of the octagon? Round to the nearest whole number.
A) 93
B) 186
C) 371
D) 1299
a2) What is the approximate length of one side of the octagon? Round to the nearest whole number.
A) 23
B) 46
C) 371
D) 1299
Answers
Answer:
Step-by-step explanation:
Alright, lets get started.
The area of octagon is given [tex]= 10391.9[/tex]
The formula for area of octagon with side a is = [tex]2(1+\sqrt{2} )a^2[/tex]
[tex]10391.9 = 2(1+\sqrt{2} )a^2[/tex]
hence ,
[tex]a^2 = \frac{10391.9}{2(1+\sqrt{2} )}[/tex]
[tex]a^2 = 2152.2329[/tex]
[tex]a = 46.39[/tex]
Hence the length of the side of the octagon is 46 : Answer
Now perimeter of the octagon will be = [tex]8*side length[/tex]
Hence the perimeter = [tex]8*46.39 =371.1[/tex]
hence the perimeter of the octagon is 371 : Answer
Hope it will help :)
what is a constant interval and how does it appear on a graph?
Answers
A function is said to have a constant interval if, for any input, the output is the same. The graph of a function with a constant interval is parallel to the axis of the range, i.e., a horizontal line.
A constant interval refers to a specific type of interval that remains the same or constant over its entire length. In other words, the difference between any two consecutive points or numbers in a constant interval is always the same.
Let's assume that f(x) = c is a function with a constant interval.
Then,
for any [tex]x_1\leq x_2[/tex] or [tex]x_1\geq x_2[/tex],
[tex]f(x_1) = f(x_2)[/tex].
Thus, a function whose output remains constant for every input is called a function with constant intervals.
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f(x) = –5x – 4 and g(x) = –3x – 2, find (f – g)(x).
Answers
f(x)-g(x)=
(-5x-4)-(-3x-2)=
-5x-4+3x+2=
-2x-2
(-5x-4)-(-3x-2)
(-5x-4)+3x+2
-5x-4+3x+2
-2x-4+2
-2x-2
Final answer: -2x-2
find the obtuse angle the line y-2x=7 makes with the x- axis
Answers
tan θ =m, where m is the slope of the equation
In the next step, we also incorporate operations of calculus. Since the slope is equal to Δy/Δx, this is equivalent to dy/dx in calculus. Therefore, you can find the slope by differentiating the equation in terms of x.
y-2x=7
y = 2x+7
dy/dx = 2 =m
So,
tan θ = 2
θ = tan⁻¹(2)
θ = 63.43°
Jason and Jenny are out on a lunch date. Jason gives Jenny a bouquet that has 4 roses, 3 carnations, and 4 orchids. They decide that Jenny gets to choose their lunch order if the flower she randomly picks from the bouquet is a carnation or a rose. What is the probability that Jenny gets to choose lunch?
Answers
There are 7 flowers that Jenny can pick in order to order lunch.
Therefore the probability is 7/11
HELP PLEASE !!!!
Solve rt-3f=12 for f
SHOW STEPS !!!! And explain how to get answer please
Answers
-3f=12-rt divide both sides by -3
f=(rt-12)/3
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If you have any questions on how I did this, please ask!
rt - 3f = 12
-3f = 12 - rt
f = (12 - rt) / 3
Because we do not know what r nor t equal, we cannot find the exact value of f...
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Have a Great Day!
How do i solve
3(x+3)=18
Answers
3(x+3)=18
Distribute the brackets.
3*x=3x
3*3=9
3x+9=18
Subtract 9 from both sides.
(3x+9)-9=(18)-9
3x=9
Divide both sides by 3.
(3x)/3=(9)/3
x=3
Hope this helps.
-Benjamin
3 times X is 3x and 3 times 3 is 9
So
3x+9 =18
-9 -9
0. 9
3x=9
9/3 is 3
X=3
A cylinder has its height doubled and its radius cut to one third. What is the ratio of the volumes of the modified cylinder to the original cylinder?
Answers
[tex]V_{2}=2h_{1} \pi ( \frac{1}{3} r_{1})^{2}=\frac{2}{9} \pi h_{1}( r_{1})^{2}[/tex]
Taking the ratio of V2/V1 = 2/9
Final answer:
The ratio of the volumes of the modified cylinder (height doubled and radius cut to one third) to the original cylinder is 2:9.
Explanation:
To find the ratio of the volumes of the modified cylinder to the original cylinder, we need to use the formula V = πr²h.
Let the original radius be 'r' and the original height be 'h'. The volume of the original cylinder V1 is given by:
V1 = πr²h
After doubling the height and cutting the radius to one third, the new radius is 'r/3' and the new height is '2h'. The volume of the modified cylinder V2 is:
V2 = π(r/3)²(2h) = π(r²/9)(2h) = (2/9)πr²h
The ratio of the volumes is then:
Volume Ratio (V2/V1) = (2/9)πr²h / πr²h = 2/9
So, the ratio of the volumes of the modified cylinder to the original cylinder is 2:9.
Suppose that (x1, y1) and (x2, y2) are two points on a linear function. Write the formula to find the function’s rate of change for the interval [x1, x2].
Answers
(y2 - y1)/(x2 - x1)
Final answer:
The rate of change for a linear function on the interval [x1, x2] is the slope of the line m, calculated by dividing the difference in y-values by the difference in x-values: m = (y2 - y1) / (x2 - x1).
Explanation:
To find the rate of change of a linear function for the interval [x1, x2], we need to calculate the slope of the line connecting the points (x1, y1) and (x2, y2). This is done using the formula:
m = (y2 - y1) / (x2 - x1)
where m represents the slope, which is the ratio between the change in y-values (rise) and the change in x-values (run). When graphing the function, if you plotted these two points, you'd be able to draw a straight line between them, and by finding the slope, you determine how steep the line is. The slope, or rate of change, indicates how much y increases or decreases for each unit increase in x. This rate of change is constant along the entire length of a straight line.
What is equivalent to this statement:4 is 80% of x
Answers
4/80*100=5
An equivalent statement to '4 is 80% of x' is 'x is 5'.
Explanation:The statement '4 is 80% of x' can be written as the equation 4 = 0.8x. To find an equivalent statement, we can solve this equation for x.
To solve for x, divide both sides of the equation by 0.8: x = 4 / 0.8 = 5.
Therefore, an equivalent statement is: x is 5.
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3 hours worked for$12;9 hours worked for $36
Answers
This answer explains the concept of Labor Economics and Wages by calculating the hourly rate from given total pay and total hours worked.
Explanation:The subject of this question involves Labor Economics and Wages.
In this scenario, the wage for working 3 hours is $12, while for working 9 hours, the pay is $36. To determine the hourly rate, we can use the formula: Hourly Rate = Total Pay / Total Hours Worked. Applying this formula, we find the hourly rate to be $4 per hour.
Example:
3 hours worked for $12 -> Hourly rate = $12 / 3 hours = $4 per hour9 hours worked for $36 -> Hourly rate = $36 / 9 hours = $4 per hourRobbie did a survey of four butterfly parks and wrote the following observations: Butterfly Park SurveyPark Number of White Butterflies Total Number of Butterflies A 24 86 B 43 92 C 12 68 D 32 52 Based on the survey, which park had the greatest percentage of white butterflies?
Answers
B = 43 / 92 = 47%
C = 12 / 68 = 18 %
D = 32 / 52 = 62%
Answer D
Answer:
A = 24 / 86 = 28%
B = 43 / 92 = 47%
C = 12 / 68 = 18 %
D = 32 / 52 = 62%
Answer D
Step-by-step explanation:
If a four-sided figure has four congruent sides, then it has four right angles. Prove this wrong
Answers
What is the simplified form of 20 times x to the fifth power over 15 times y to the sixth power times the fraction 5 times y to the fourth power over 6 times x squared?
Answers
I don't get how to do it i have tried but I can't I think that it might be 20 i think
Answers
what is 12/20 as a percent?
Answers
0.6 as a percent is 60%.
Answer:
60%
Step-by-step explanation:
Side GH = 3, side IG = 5, side JK = 3, and side LJ = 5. What side corresponds to side HI and can be used to show that ΔGHI ≅ ΔJKL by SSS? (Enter your answer using letters only)
Answers
Since it says enter with only letters, you would put KL as the answer
a metallurgist has an alloy with 10% titanium and an alloy with 20% titanium. he needs 100 grams of an alloy with 17% titanium. how much of each alloy should be mixed to attain the 100 grams of alloy with 17% titanium?
Answers
Let us say that:
x = mass of 10% titanium alloy required
y = mass of 20% titanium alloy required
To solve this problem, we set-up two mass balances or equations.
Overall mass balance: x + y = 100
x = 100 – y ---> 1
Titanium mass balance: 0.10 x + 0.20 y = 0.17 (100)
0.10 x + 0.20 y = 17 ---> 2
Now we combine equations 1 and 2:
0.10 (100 – y) + 0.20 y = 17
10 – 0.10 y + 0.20 y = 17
0.10 y = 7
y = 70 g
Calculating for x using equation 1:
x = 100 – y
x = 100 – 70
x = 30 g
Answer:
x = 30 g of 10% titanium alloy required
y = 70 g of 20% titanium alloy required
Identify the equation of the line that has a y-intercept of 7 and is parallel to the graph of y = 5x - 3
Answers
Your equation would be y=5x + 7
Given the expression 5a2b – 13ab + 7a3 – 4b, do the following as instructed below:
1. Write the polynomial in descending order.
2. Classify the polynomial by the number of terms.
3. State the degree of the polynomial.
Thank you !!
Answers
A. The descending order of this expression is 7a^3+5a^2b-13ab-4b.
B. This is a polynomial.
C. This is a 3rd degree polynomial.
The given expression is
[tex]5 {a}^{2} b - 13ab + 7 {a}^{3} - 4b[/tex]
To write the polynomial in descending order means we should write in decreasing powers of
[tex]a[/tex]
So in descending order we have,
[tex]7 {a}^{3} + 5 {a}^{2}b - 13ab - 4b[/tex]
ANSWER TO QUESTION 2
When a polynomial is in simplified form and it has one term, we call it a monomial.
If a simplified polynomial has two terms,it is called a binomial.
If a simplified polynomial has three terms, it is called a trinomial.
If a simplified polynomial gas four or more terms, we just call it a polynomial.
The given polynomial
[tex]5 {a}^{2} b - 13ab + 7 {a}^{3} - 4b [/tex]
has four terms and it us in simplified form, so it is classified as polynomial.
ANSWER TO QUESTION 3.
The degree of the polynomial is the highest degree the polynomial has.
We calculate the degree by adding the exponents of the two variables of each term.
For instance the first term is
[tex]7 {a}^{3} = 7 {a}^{3} {b}^{0} [/tex]
[tex]degree = 3 + 0 = 3[/tex]
Since the highest degree is 3, we say the degree of the polynomial 3.