The triangular figures shown below are constructed with toothpicks. The pattern shows what happens with 1 triangle, with 2 triangles, and with 3 triangles. Describe a possible pattern. Assuming the pattern continues, answer the following questions. How many toothpicks would be needed for the 10th figure? How many toothpicks are needed for the nth figure? In which figure are exactly 102 toothpicks used?
Answers
Answer:
(a) 51
(b) [tex]T_{n}=a+(n-1)d[/tex]
(c) 20th figure
Step-by-step explanation:
The diagram is attached below.
The first triangle is formed using 6 toothpicks.
The second triangle is formed using 11 toothpicks.
The third triangle is formed using 16 toothpicks.
So, there is an increases of 5 toothpicks every time.
We can say that the number of toothpicks used to form n triangles are following an arithmetic progression with the first term as 6 and the common difference as 5.
The nth term will be:
[tex]T_{n}=a+(n-1)d[/tex]
(a)
Compute the number of toothpicks required for the 10th figure as follows:
[tex]T_{n}=a+(n-1)d[/tex]
[tex]T_{10}=6+(10-1)\times5[/tex]
[tex]=6+(9\times5)\\=6+45\\=51[/tex]
Thus, the number of toothpicks required for the 10th figure is 51.
(b)
Compute the number of toothpicks required for the nth figure as follows:
[tex]T_{n}=a+(n-1)d[/tex]
(c)
Compute the value of n for [tex]T_{n}=102[/tex] as follows:
[tex]T_{n}=102[/tex]
[tex]a+(n-1)d=102\\\\[/tex]
[tex]6+(n-1)\times 5=102[/tex]
[tex]5(n-1)=96[/tex]
[tex]n-1=19.2[/tex]
[tex]n=20.2\\n\approx 20[/tex]
Thus, the 20th figure will require exactly 102 toothpicks.
Related Questions
the question is below
Answers
Answer:
RU = 9
ST = 3
Step-by-step explanation:
RT = 6
RS = ST = (1/2)RT = (1/2)(6) = 3
ST = 3
RU = 3ST = 3 * 3 = 9
A 35 foot tree casts a 13 foot shadow. What is the degree of elevation for the sun?
Answers
Answer:
tan (thita) = 35/13
Step-by-step explanation:
Tan( angle) = opposite/ adjacent
Tan( angle) = 35/13
Angle = arc tan 35/13
Angle = 69.624 degrees
Round the answer as needed.
Does anyone know how to solve this? I tried moving the 3 back to make it log 2 (x^3) but for the second one it would be (5x)^2 and I get stuck there
Answers
Answer:
x = 100
Step-by-step explanation:
All you need is contained in the sheet attached
Answer:
x = 100
Step-by-step explanation:
3 log2(x) - 2 log2(5x) = 2
We know that a log(c) = log c^a
log2(x)^3 - log2(5x)^2 = 2
log2(x^3) - log2(25x^2) = 2
We know that log a - log b = log a/b
log2(x^3 /25x^2) = 2
Simplify
log2(x /25) = 2
Raise each side to base 2
2^log2(x /25) = 2^2
x/25 = 4
Multiply each side by 25
x = 4*25
x = 100
if m<2, then m<1 is...
Answers
Answer:
45
Step-by-step explanation:
m<1 and m<2 are complementary angles because the sum of two angles = 90° and since m<1 = m<2
90 ÷ 2 = 45
Solve for c
C – 7 = -9
Answers
Answer: -2
Step-by-step explanation:
-2 - 7 = -9
Answer:
[tex]\Huge \boxed{c=-2}[/tex]
Step-by-step explanation:
[tex]c-7=-9[/tex]
We need to isolate the [tex]c[/tex] variable on one side of the equation.
Adding 7 to both sides of the equation.
[tex]c-7+7=-9+7[/tex]
Simplifying the equation.
[tex]c=-2[/tex]
the projected number of employed writers and authors in 2016 is 153,000. 12.4% of those will have some college experience but no degree, and 84.1% will have a bachelors degree or higher. If this holds true, how many more writers and authors with bachelors degree will be there than those with only some college experience and no degree?
Answers
Answer:
Step-by-step explanation:
12.4% 153000 = 12.4/ 100 * 153000 = 0.124 * 153000 = 1897
84.1% 153000 = 84.1/100 * 153000 = 0.841 * 153000 = 128673
The difference (and the answer) is 128673 - 1897 = 126776
Note: 3.5% are not accounted for. They probably just sat down and wrote.
simplify (1-√3)(⅓+√3) leaving your answer in the form p+q√3
Answers
Answer:
[tex]\frac{-8 +2\sqrt{3} }{3}[/tex]
Step-by-step explanation:
When working with surds we need to take note of the roots present there.
To expand this equation we can do it the following way noting that √3 X √3 = 3
Expanding (1-√3)(⅓+√3)
1 X 1/3 = 1/3
1 X √3 = √3
-√3 X 1/3 =-√3/3
√3 X √3 = 3
hence, expanding the equation, we have
1/3 + √3 -√3/3 + 3
We can simply group the like terms and add them up.
[1/3 +3] +[√3-√3/3]
10/3 + [tex]\frac{2\sqrt{3} }{3}[/tex]
= [tex]\frac{-8 +2\sqrt{3} }{3}[/tex]
Choose the function that correctly identifies the transformation of f(x) = x2 shifted two units down and one unit to the left. g( x) = ( x + 1) 2 + 2 g( x) = ( x - 1) 2 + 2 g( x) = ( x + 1) 2 - 2 g( x) = ( x - 1) 2 - 2
Answers
Answer:
g(x)= (x +1)^2 -2
Step-by-step explanation:
-7 - (-8) + (-3) + 6 - 2=
Answers
Answer:
2
Step-by-step explanation:
-7 - (-8) = 1
1 + (-3) = -2
-2 + 6 = 4
4 - 2 = 2
Answer:
2
Step-by-step explanation:
Start by removing the parentheses appropriately:
-(-8) = +8, and
+(-3) = -3
Then
-7 - (-8) + (-3) + 6 - 2 = -7 + 8 - 3 + 6 - 2
Now, working from left to right, we perform the indicated operations:
-7 + 8 comes out to 1, and so we have 1 - 3 + 6 - 2.
Continuing, we get -2 + 6 - 2, or 4 - 2, or 2
Does anyone know this?
Answers
Answer:
first option is right
Step-by-step explanation:
A past survey of students taking a standardized test revealed that % of the students were planning on studying engineering in college. In a recent survey of students taking the SAT, % of the students were planning to study engineering. Construct a % confidence interval for the difference between proportions by using the following inequality. Assume the samples are random and independent.
The confidence interval is __
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
The 95% confidence interval is [tex]-0.00870 <p_1 -p_2 < -0.007297[/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 1068000[/tex]
The first proportion [tex]\r p_1 = 0.084[/tex]
The second sample size is [tex]n_2 = 1476000[/tex]
The second proportion is [tex]\r p_2 = 0.092[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100 - 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
From the normal distribution table we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] the value is
[tex]Z_{\frac{\alpha }{2} } =z_c= 1.96[/tex]
Now using the formula from the question to construct the 95% confidence interval we have
[tex](\r p_1 - \r p_2 )- z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2} } <p_1 -p_2 < (\r p_1 - \r p_2 )+ z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2} }[/tex]
Here [tex]\r q_1 = 1 - \r p_1[/tex]
=> [tex]\r q_1 = 1 - 0.084[/tex]
=> [tex]\r q = 0.916[/tex]
and
[tex]\r q_2 = 1 - \r p_2[/tex]
=> [tex]\r q_2 = 1 - 0.092[/tex]
=> [tex]\r q_2 = 0.908[/tex]
So
[tex](0.084 - 0.092 )- (1.96)* \sqrt{ \frac{0.092* 0.916 }{1068000} + \frac{0.084* 0.908 }{1476000} } <p_1 -p_2 < (0.084 - 0.092 )+ (1.96)* \sqrt{ \frac{0.084* 0.916 }{1068000} + \frac{0.092* 0.908 }{1476000} }[/tex]
[tex]-0.00870 <p_1 -p_2 < -0.007297[/tex]
Describe the relationship between the values of the two 7s in the number 3,772 what equation could you use to help describe the relationship
Answers
Answer:
y = 10x, which is the relationship between two 7 in the number 3772
Step-by-step explanation:
In the given number 3772
3 is at thousandth position its value is 3000 numerically
7 is at the hundredth position its value is 700 numerically
next 7 is at tens position its value is 70 numerically
and 2 is at unit position its value is 2 numerically
thus, 3772 can also be written as sum of number based on its position
3000
+700
+ 70
+ 2
___-
= 3772
Thus,
since Third 7 from left has value of 70
and Second 7 from left has value of 700
we know 70*10 = 700
Thus, 70 is 10 times to that 700
Thus, we can say that
value of Second 7 from left = 10*value of Third 7 from left
Thus,
let value of Second 7 from left be y
value of Third 7 from left be x
then
y = 10x, which is the relationship between two 7 in the number 3772
Find the annual percentage yield for an account with an APR of 13.75% compounded continuously. Round your percentage to two places after the decimal point.
Answers
Answer:
14.74%
Step-by-step explanation:
The formula for ANNUAL PERCENTAGE YIELD (APY) for an account that is COMPOUNDED CONTINUOUSLY is given as
APY = Pe^rt - 1
Where P = Principal
e = exponential
r = rate
t = time
Since Principal and Time was not given in the question,
APY = e^r - 1
r = 13.75% = 0.1375
APY = e^0.1375 - 1
APY = 1.147401706 - 1
APY = 0.147401706
Converting to percentage
= 0.147401706 × 100
= 14.7401706%
Approximately to 2 decimal places: 14.74%
Therefore, the annual percentage yield is 14.74%
What is the slope of the line that contains these points? (39,36) (40,29) (41,22) (42,15)
Answers
Answer:
-7
Step-by-step explanation:
As x increases by 1, y decreases by 7, so the "rise"/"run" is ...
slope = rise/run = -7/1 = -7
20 points! Each month, Sal must pay for car insurance and fuel to drive a vehicle. Sal's parents agree to pay p percent of his car expenses. The cost of car insurance is the same every month, but the cost of fuel depends on d, the number of miles Sal drives. The expression (1−p)(0.10d+60) represents how much Sal must pay toward his monthly car expenses. Which part of the expression represents the percentage of the monthly expenses that Sal must pay? 0.10d + 60 1−p 60 0.10d
Answers
Answer:
1 - p
Step-by-step explanation:
The cost of insurance is constant, this is 60.The cost of fuel is 0.10d as d is the number of miles.The only variable left is 1-p which represents the percentage of expensesSo the answer is:
1 - pAnswer:
1-p
Step-by-step explanation:
I took the test and this was the answer.
190 = 200^b, make b the subject
Answers
Answer:
b = [tex]\frac{ln190}{ln200}[/tex]
Step-by-step explanation:
Using the rule of logarithms
log [tex]x^{n}[/tex] ⇔ nlogx
Given
190 = [tex]200^{b}[/tex] ( take the natural log ln of both sides )
ln190 = ln[tex]200^{b}[/tex] = bln200 ( divide both sides by ln200 )
[tex]\frac{ln190}{ln200}[/tex] = b
LSAT test scores are normally distributed with a mean of 152 and a standard deviation of 10. Find the probability that a randomly chosen test-taker will score 142 or lower. (Round your answer to four decimal places.)
Answers
Answer:
the probability that a randomly chosen test-taker will score 142 or lower = 0.8643
Step-by-step explanation:
We are given;
Data point; x = 142
Mean; μ = 153
Standard deviation; σ = 10
So,let's find the z-score using;
z = (x - μ)/σ
z = (142 - 153)/10
z = -1.1
From the z-distribution table attached, the probability is;
P(z < -1.1) = 1 - 0.13567 ≈ 0.8643
It is also known that customers will spend an average of $178 on additional maintenance. The standard deviation of the expenses is $50. If a simple random sample of 100 customers is taken: What is the probability that the sample mean will be between 166.75 and $170.50
Answers
Answer:
probability that the sample mean will be between 166.75 and $170.50 = 0.42816
Step-by-step explanation:
We are given;
Mean; μ = $178
Standard deviation; σ = $50
Now, we want to find the probability that the sample mean will be between $166.75 and $170.50.
Thus, we'll use the z-score formula;
z = (x - μ)/σ
So;
Lower limit of z is;
z = (166.75 - 178)/50
z = -0.225
Upper limit of z is;
z = (170.50 - 178)/50
z = -0.15
From the z-distribution table attached, the area between -0.225 and -0.15 is;
0.44038 - 0.01222 = 0.42816
Dan invests £11125 into his bank account. He receives 3.3% per year simple interest. How much will Dan have after 4 years? Give your answer to the nearest penny where appropriate.
Answers
Answer:
£11564.54
Step-by-step explanation:
100 + 3.3 = 103.3%
103.3% = 1..013
£11125 x 1.013^3 = £11564.54
I hope this helped you!
need help with this question
Answers
Answer:
25) -76
26) -23
27) 21
28) 8
Step-by-step explanation:
25) (-32)-44=-32-44=-76
26) (-12)+(-11)=-12-11=-23
27) 2+15+4=17+4=21
28) 16+(-13)+5=16-13+5=3+5=8
Step-by-step explanation:
Hope it helps u mate
plz mark it as brainlist
In 2003, the population of an African country was about 10.2 million people, which is 1 million more than 4 times the population in 1950. Enter and solve an equation to find the approximate population p (in millions) in 1950. An equation is . The approximate population in 1950 was million people.
Answers
Which equation shows a slope of 3 and a y-intercept of (0,7) ?
Answers
Answer: y = 3x + 7
Step-by-step explanation:
Since we are given the slope and y intercept we could write the equation in slope intercept form as y=mx +b .Only m and b are needed to write the equation.M is the slope and B is the y intercept.
Answer:
y=3x+7
Step-by-step explanation:
The equation of a line in slope-intercept form is:
y=mx+b
where m is the slope and b is the y-intercept.
We know the slope is 3, so we can substitute 3 in for m.
y=3x+b
We also know the y-intercept is (0,7). When writing the equation of a line in this form, we can ignore the x-coordinate of 0. Therefore, the y-intercept is also just 7. Substitute 7 in for b.
y=3x+7
The equation of a line with a slope of 3 and a y-intercept of (0,7) is y=3x+7
During a festival, the number of visitors tripled each day.
If the festival opened on a Thursday with 300 visitors, what
was the attendance on Sunday?
Answers
Answer:
24,300
Step-by-step explanation:
So on Thursday you have 300 next day it's 900 bc 300x3=900
Friday: 900x3=2,700
Saturday: 2,700x3=8,100
Sunday: 8,100x3=24,300
A password contains three digits, such as 175. How many different passwords can be formed?
Answers
Answer: There are 1000 different passwords.
Step-by-step explanation:
Given: A password contains three digits.
Number of digits from 0 to 9 = 10
Using fundamental principle of counting,
The number of different passwords = (Number of choices for digits) x (Number of choices for digits) x (Number of choices for digits)
= (10) x (10)x (10)
=1000
Hence, there are 1000 different passwords.
Find the value of x. A. 5√2/2 B. 5 C. 10 D. 10√2
Answers
Answer:
C
Step-by-step explanation:
Note that the right triangle has two tick marks.
This means that the sides are equivalent.
Therefore, this is a 45-45-90 triangle.
In a 45-45-90 triangle, the side lengths are n, and the hypotenuse is n√2
Since n is 5√2, then the hypotenuse x is n√2. Thus:
[tex]x=n\sqrt2\\x=(5\sqrt2)\sqrt2[/tex]
Simplify:
[tex]x=5(2)=10[/tex]
The answer is C :)
What is 10% of 800Hhhhhhhhhhhh
Answers
reduce the following fractions to their lowest terms: a. 6/8. b. 8/12c. 15/20 d. 9/18 e. 24/30 f. 25/40
Answers
Answer:
That's my slovings for your question
Adam tabulated the values for the average speed on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. If Adam wanted to construct a one-sample t-statistic, what would the value for the degrees of freedom be?
Answers
Answer:
7
Step-by-step explanation:
Given the following data:
Average speed : 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4
To construct a one-sample t - statistic, the value of the degree of freedom will be ;
In a one sample test of known mean, if the number of observations are 4, one can choose to vary at most three of the observations and still obtain the mean, that is the 4th observation must remain fixed.
Degree of freedom = Number of observations (n) - 1. This is the maximum number of independent variables which can be varied.
Nunber of observations or sample size in the data above is 8
Hence,
Degree of freedom = (8 - 1) = 7
Answer:the anwser is 7
Step-by-step explanation:
Will mark the brainliest for correct answer!!!
Answers
Answer:
hexagon; not regular
Step-by-step explanation:
hope this helps
Write the equation of the line that passes through (3, -2) and has a slope of 4 in point slope form
Answers
Answer:
The answer is
y + 2 = 4( x - 3)Step-by-step explanation:
To find an equation of a line given a point and slope we use the formula
y - y1 = m(x - x1)
where
m is the slope
(x1 , y1) is the point
From the question
slope = 4
point = ( 3 , - 2)
Substitute the values into the above formula
We have
y + 2 = 4( x - 3)Hope this helps you
Answer:
y+
Step-by-step explanation:
Point-Slope form- (y − y 1) = m ⋅ (x − x 1)
Slope: m = 4
Point: (x1, y1) = (3, -2)
Answer: y + 2 = 4 ⋅ (x - 3)