Answer:
Step-by-step explanation:
With 35 internal nodes, there are 5*35=175 vertices out of which are 175-35=140 leaves.
The number of vertices in a full 5-ary tree is 175.
The number of leaves is 140.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of full trees = 5
Number of internal vertices = 35
Now,
The number of vertices.
= 5 x 35
= 175
Now,
The number of leaves.
= 175 - 35
= 140
Thus,
Number of vertices is 175.
Number of leaves is 140.
Learn more about expressions here:
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The sum of the first 8 terms of a geometric sequence with 4 as the first term and a common ratio of 3 is
9514 1404 393
Answer:
13120
Step-by-step explanation:
The sum of terms of a geometric series is ...
Sn = a1·(r^n -1)/(r -1)
You have n=8, a1=4, r=3, so the sum is ...
S8 = 4·(3^8 -1)/(3 -1) = 2(3^8 -1) = 13,120
Answer:
13 120Step-by-step explanation:
hope it helps u too
Kyle buys a bag of cookies that contains 4 chocolate chip cookies, 9 peanut butter cookies, 9 sugar cookies and 7 oatmeal cookies. What is the probability that Kyle randomly selects a sugar cookie from the bag, eats it, then randomly selects a peanut butter cookie
Were the Egyptian rulers' tombs built before or after they died?
Answer: I don't know the exact details but Egypt is home to some of the world's most famous tombs, among them the monumental pyramids. Egyptians built rectangular benches over graves during the fourth dynasty, which was known as the Masabas period. During this time period, pyramids were constructed by stacking square or rectangular tombs on top of one another.
Step-by-step explanation:
A researcher wants to investigate the effects of environmental factors on IQ scores. For an initial study, she takes a sample of 400 people who grew up as the only child. She finds that 48.5% of them have an IQ score over 100. It is known that 50% of the general population has an IQ score exceeding 100.(a) Find the mean of p, where p is the proportion of people with IQ scores over 100 in a random sample of 400 people.(b) Find the standard deviation of p.(c) Compute an approximation for P(p is greater than or equal to 0.485), which is the probability that there will be 48.5% or more individuals with IQ scores over 100 in a random sample of 400. Round answer to 4 decimal places.
Answer:
a) p = 0.5.
b) s = 0.025.
c) 0.7257 = 72.57% probability that there will be 48.5% or more individuals with IQ scores over 100 in a random sample of 400.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
It is known that 50% of the general population has an IQ score exceeding 100. Sample of 400.
This means that [tex]n = 400, p = 0.5, s = \sqrt{\frac{0.5*0.5}{400}} = 0.025[/tex]
(a) Find the mean of p, where p is the proportion of people with IQ scores over 100 in a random sample of 400 people
By the Central Limit Theorem, p = 0.5.
(b) Find the standard deviation of p.
By the Central Limit Theorem, s = 0.025.
(c) Compute an approximation for P(p is greater than or equal to 0.485), which is the probability that there will be 48.5% or more individuals with IQ scores over 100 in a random sample of 400.
This is 1 subtracted by the p-value of Z when X = 0.485. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.485 - 0.5}{0.025}[/tex]
[tex]Z = -0.6[/tex]
[tex]Z = -0.6[/tex] has a p-value of 0.2743.
1 - 0.2743 = 0.7257.
0.7257 = 72.57% probability that there will be 48.5% or more individuals with IQ scores over 100 in a random sample of 400.
PlEaSe HelP mEakwhtb4qhnga
Answer:
d. y = x + 6
Step-by-step explanation:
Equation of AD can be written in the slope-intercept form, y = mx + b
First, find the slope (m) and y-intercept (b) of line AD.
✔️Slope (m) = change in y/change in x
Using two points on line AD, (-5, 1) and (0, 6):
Slope (m) = (6 - 1)/(0 - (-5))
Slope (m) = 5/5
m = 1
✔️y-intercept (b) is the point where the line cuts across the y-axis = 6
b = 6
✔️To write the equation, substitute m = 1 and b = 6 into y = mx + b
y = 1(x) + 6
y = x + 6
If a rectangular prism has a length of 3 1/2 in and a width of 9 in and a height of 3 1/2, what would the surface area be?
The surface area is 150.5 in
Answer:
The surface area of this rectangular prism is 150.5 [tex]inches^{2}[/tex].
Step-by-step explanation:
The formula for finding the surface area of a rectangular prism is this :
A=2(wl + hl + hw)
l = 3.5, w = 9, h = 3.5
Now we substitute those values in and solve for A.
A = 2 · ( 9 · 3.5 + 3.5 · 3.5 + 3.5 ·9) = 150.5
The surface area of this rectangular prism is 150.5 [tex]inches^{2}[/tex].
Hope this helps, please mark brainliest. Have a great day!
The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 1000 trials and got the following results:
Outcome 0 1 2 3 4 5 6 7 8 9
Number of Trials 4 2 5 3 2 6 6 3 6 3
Required:
a. From these results, compute the experimental probability of getting an odd number.
b. Assuming that the machine is fair, compute the theoretical probability of getting an odd number.
Answer:
0.425
0.5
Step-by-step explanation:
Given :
Outcome 0 1 2 3 4 5 6 7 8 9
Number of Trials 4 2 5 3 2 6 6 3 6 3
The experimental probability of obtaining an odd number :
Odd outcomes are : 1, 3, 5, 7, 9
Total number of trials = Σ(4 2 5 3 2 6 6 3 6 3) = 40
Total number of odd outcomes = (2+3+6+3+3) = 17
Experimental probability = number of prefferwd outcomes / total number of trials
Experimental P(odd). = 17 / 40 = 0.425
The theoretical probability of getting an odd number :
Required outcome / Total possible outcomes
Number of odd values / total number of values
5 / 10 = 1/2
Answer:
0.510
0.500
Step-by-step explanation:
part c) = A
name me brainiest
Your aunt is asking your help in figuring out how to
maximize profit for her pottery business. She makes
$35 on a bowl and $30 on a plate. She has just
ordered 40 pounds of clay. A bowl uses 5 pounds of
clay and a plate uses 4 pounds of clay. She already
has orders to make 4 bowls. How many bowls and
plates should she make in order to maximize her profit?
Step 1: Identify your variables and write the objective
function
What does x represent? What does y represent?
Answer:
650
Step-by-step explanation:
What is the distance between [(3 + 4i) + (2 - 3i)] and (9 - 2i)?
Answer:
5
Step-by-step explanation:
(3 + 4i) + (2 - 3i) = 3 + 4i + 2 - 3i = 5 + i
distance between (5 + i) and (9 - 2i) is the difference between them. and difference means subtraction.
(9 - 2i) - (5 + i) = 9 - 2i - 5 - i = 4 - 3i
and since we are looking for a distance, we are looking for the absolute value of that subtraction.
after all, we could have done the subtraction also in the other direction
(5 + i) - (9 - 2i) = -4 + 3i
and this must be the same distance.
|(-4 + 3i)| = |(4 - 3i)|
and that is done by calculating the distance of any of these 2 points from (0,0) on the coordinate grid of complex numbers.
|(a +bi)| = sqrt(a² + b²)
in our case here
distance = sqrt(4² + (-3)²) = sqrt(16 + 9) = sqrt(25) = 5
as you can easily see, this is (as expected) the same for the result of the subtraction in the other direction :
sqrt((-4)² + 3²) = sqrt(16+9) = sqrt(25) = 5
what does the equation inverse of the function found in part b represent in the contract of the problem ? explain your answer .
context to question - At a carnaval , you pay $15 for admission plus $3 for each ride that you go on .
Answer:
[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]
The inverse function is to calculate the number of rides; given the amount paid
Step-by-step explanation:
Given
[tex]Admission = 15[/tex]
[tex]Ride = 3[/tex] per ride
Required
Explain the inverse function
First, we calculate the function
Let x represents the number of rides
So:
[tex]f(x) = Admission + Ride * x[/tex]
[tex]f(x) = 15 + 3 * x[/tex]
[tex]f(x) = 15 + 3x[/tex]
For the inverse function, we have:
[tex]y = 15 + 3x[/tex]
Swap x and y
[tex]x = 15 + 3y[/tex]
Make 3y the subject
[tex]3y = x - 15[/tex]
Make y the subject
[tex]y =\frac{x}{3} - 5[/tex]
Replace y with the inverse function
[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]
The above is to calculate the number of rides; given the amount paid
Help, please! With workings too!
I'm thinking of a 3-digit number.
When it is divided by 9, the remainder is 3
When it is divided by 2, the remainder is 1
When it is divided by 5, the remainder is 4
What is my number?
3-digit number is abc. ( just call it)
abc= 9d + 3, meaning abc = 3e
abc = 2k + 1, meaning abc is an odd number
abc = 5t + 4, meaning c = 9 ( because abc is an odd number so c can not be 4)
so a+b must be equal 3.
abc can be 309, 219, 129
Use the formula for simple interest, I = Prt, to find the indicated quantity. Assume a 360 day year.
1 = $24; P = $1200; t = 90 days; r = ?
r=% (Simplify your answer.)
Answer:
r = 8%
Step-by-step explanation:
Given that,
Interest, I = $24
Principal, P = $1200
Time, t = 90 days = 90/360 = 1/4 years
We need to find the rate.
We know that,
The simple interest is given by :
[tex]I=\dfrac{Prt}{100}[/tex]
Put all the values,
[tex]r=\dfrac{100I}{Pt}\\\\r=\dfrac{100\times 24}{1200\times \dfrac{1}{4}}\\\\r=8\%[/tex]
So, the rate is 8%.
find this solution for mathematical quiz
Answer:
[tex]-\sqrt{2} + \sqrt{2}i[/tex]
Step-by-step explanation:
Angle of 9pi/4
The equivalent angle of [tex]\frac{9\pi}{4}[/tex], on the first lap, is found subtracting this angle from [tex]2\pi[/tex]. Thus:
[tex]\frac{9\pi}{4} - 2\pi = \frac{9\pi}{4} - \frac{8\pi}{4} = \frac{\pi}{4}[/tex]
Thus, the sine and cosine are:
[tex]\sin{(\frac{9\pi}{4})} = \sin{(\frac{\pi}{4})} = \frac{\sqrt{2}}{2}[/tex]
[tex]\cos{(\frac{9\pi}{4})} = \cos{(\frac{\pi}{4})} = \frac{\sqrt{2}}{2}[/tex]
Angle of 3pi/2
On the first lap of the circle, thus no need to find the equivalent angle. We have that:
[tex]\sin{(\frac{3\pi}{2})} = -1, \cos{(\frac{3\pi}{2})} = 0[/tex]
Expression:
[tex]4(\cos{(\frac{9\pi}{4})} + i\sin{(\frac{9\pi}{4})}) \div 2(\cos{(\frac{3\pi}{2})} + i\sin{(\frac{3\pi}{2})})[/tex]
[tex]4(\frac{\sqrt{2}}{2} + i\frac{\sqrt{2}}{2}) \div 2(0 - i)[/tex]
[tex]\frac{2\sqrt{2} + 2\sqrt{2}i}{-2i} \times \frac{i}{i}[/tex]
Considering that [tex]i^2 = -1[/tex]
[tex]\frac{-2\sqrt{2}+2\sqrt{2}i}{2}[/tex]
[tex]-\sqrt{2} + \sqrt{2}i[/tex]
Leila is arranging 11 cans of food in a row on a shelf. She has 4 cans of corn, 1 can of peas, and 6 cans of beets. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical.
Given:
Leila is arranging 11 cans of food in a row on a shelf. She has 4 cans of corn, 1 can of peas, and 6 cans of beets.
To find:
The distinct orders can the cans be arranged if two cans of the same food are considered identical.
Solution:
Total number of cans = 11
Cans of corn = 4
Cans of Peas = 1
Cans of beets = 6
We need to find divide total possible arrangements (11!) by the repeating arrangements (1!, 4!, 6!) to find the distinct orders can the cans be arranged if two cans of the same food are considered identical.
[tex]\text{Distinct order}=\dfrac{11!}{1!4!6!}[/tex]
[tex]\text{Distinct order}=\dfrac{11\times 10\times 9\times 8\times 7\times 6!}{1\times (4\times 3\times 2\times 1)\times 6!}[/tex]
[tex]\text{Distinct order}=\dfrac{55440}{24}[/tex]
[tex]\text{Distinct order}=2310[/tex]
Therefore, the total number of distinct orders is 2310.
서울기업(주)는 2X20년 7월 5일에 장기간 보유 목적으로 원주기업(주)의 주식 1,200주를 1주당 15,000원에 매수하고 수표를 발행하여 매수대금을 지급하였다. 취득 부대비용은 없다. 이 1,200주는 원주기업(주)이 발행한 주식의12%에 해당하고, 서울기업(주)은 이를 FVOCI 측정 추자주식으로 분류하였다. 서울기업(주)은 원주기업(주) 주식 외에는 다른 회사 주식을 보유하고있지 안다. 다음은 원주기업(주) 주식에 대한 자료이다.
(1) 2X20년 말에 원주기업(주) 주식의 1주당 주가는 14,000원이었다.
(2) 2X20년 3월 25일에 원주기업(주)으로부터 배당금 150만원을 현금으로 받았다.
(3) 2X21년 말에 원주기업(주) 주식의 1주당 주가는 18,000원이었다.
(4) 2X22년 4월 20일에 서울기업(주)은 원주기업(주) 주식을 주당 17,500원에 전부 매각처분하고 처분대금을 현금으로 받았다.
물음: 서울기업(주)의 2X21년 말 재무상태표에 표시되는 장기투자주식 금액과, 기타포괄손익누계액 금액 그리고 포괄손익계산서에 표시되는 기타포괄손익(평가손익)은 각각 얼마인가?
Answer:
ディーズナッツ
Step-by-step explanation:
Consider the following sample data: x 12 18 20 22 25 y 15 20 25 22 27 Click here for the Excel Data File a. Calculate the covariance between the variables. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
Answer:
The covariance between the variables is 21.10 and the Correlation coefficient is 0.9285.
Step-by-step explanation:
Hence,
Use the graph or table to identify the value that makes this relationship proportional.
Answer:
33
Step-by-step explanation:
Pls vote my answer as brainliest
Answer:
33
Step-by-step explanation:
What is the slope of a line that is parallel to y = 3x + 5?
Answer:3
The lines that are parallel have the same slope. For the line y=3x + 5, slope = 3, so, for parallel line slope also will be equal 3
Step-by-step explanation:
Find the equation of the circle that has a diameter with endpoints located at (-3,6) and (9,6).
Answer:
C
Step-by-step explanation:
Diameter is 12.
Radius is 6
Center is (3,6)
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 59 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean µ = 59 tons and standard deviation σ = 1.9 ton.a) What is the probability that one car chosen at random will have less than 49.5 tons of coal? b) What is the probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal?
Answer:
b) What is the probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal? (Round your answer to four decimal places.)
Step-by-step explanation:
In AUVW, W = 840 cm, u = 350 cm and ZV=63º. Find the area of AUVW, to the
nearest square centimeter.
Answer:
[tex]Area = 130977cm^2[/tex]
Step-by-step explanation:
Given
[tex]W=840[/tex]
[tex]U = 350[/tex]
[tex]\angle V = 63^o[/tex]
Required
The area
The area is calculated as:
[tex]Area = \frac{1}{2}UW\sin(V)[/tex]
So, we have:
[tex]Area = \frac{1}{2}*350*840*\sin(63^o)[/tex]
[tex]Area = \frac{1}{2}*350*840*0.8910[/tex]
[tex]Area = 130977cm^2[/tex]
F=16,V=12,E=□ by euler's formula
Answer:
26
Step-by-step explanation:
F + V = E + 2
Where,
F = number of faces = 16
V = number of vertices = 12
E = number of edges = ?
F + V = E + 2
16 + 12 = E + 2
28 = E + 2
28 - 2 = E
26 = E
E = 26
E = number of edges = 26
convert 3684 to standard form
To write a linear expression in standard form, rearrange the terms in alphabetical order.
3684
On a given test with a maximum possible score of 100 points, the vast majority of the 259 students in a class scored either a perfect score or a zero, with only one student scoring within 10 points of the mean. Could we say that the test scores are normally distributed? Explain your answer.
Answer:
no, in a normal distribution mode=median=mean. So while in theory, the median and the mean can be the same, the mode is not.
Step-by-step explanation:
Based on the maximum possible score, the scores by the student, and the deviation, we cannot say that the test scores are normally distributed.
What makes a distribution normal?In a normal distribution, the mean, mode and median have to be equal thanks to the bell-shaped nature of the distribution.
In this case, the median will be the score of the single student who is 10 points off the mean.
The mean will be affected by the extreme values of zero and a perfect score, and the mode will either be zero or 100.
The mean, mode, and median are therefore not the same so this isn't a normal distribution.
Find out more on normal distributions at https://brainly.com/question/23418254.
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[(4 x 2) + (2 x 3)] ÷ 2 x 5 =
Answer:
1.4
Step-by-step explanation:
= [(4 x 2) + (2 x 3)] ÷ 2 x 5
= [8 + 6] / 10
= 14 / 10
= 1.4
Over what interval is the quadratic function decreasing?
x ∈ (−∞,−2)
x ∈ (-2,−∞)*******
x ∈ (-2, ∞)
x ∈ (−∞,3)
Answer:
x ∈ (-2,−∞)
Step-by-step explanation:
x ∈ (-2,−∞)
this is the answer to the question
Given that the length of the figure below is x + 2, its width is
2- 2, and its perimeter is 24, solve for 2.
Answer:
hear is your answer in attachment please give me some thanks
Find the critical value ta/2 needed to construct a confidence interval of the given level with the given sample size. Round the answers to three decimal places.
(a) For level 90% and sample size 8.
(b) For level 99% and sample size 11.
(c) For level 95% and sample size 25.
(d) For level 99.5% and sample size 10.
Answer:
1.894
3.169
2.064
3.690
Step-by-step explanation:
A.) 90% ; sample size = 8
Degree of freedom, df = n - 1
t(1 - α/2, 7) = t0.05, 7 = 1.894
B.) 99% ; sample size = 11
Degree of freedom, df = n - 1
t(1 - α/2, 10) = t0.005, 10 = 3.169
C.) 95% ; sample size = 25
Degree of freedom, df = n - 1
t(1 - α/2, 24) = t0.025,24 = 2.064
(D.) 99.5% and sample size 10.
Degree of freedom, df = n - 1
t(1 - α/2, 9) = t0.0025,9 = 3.690
Which relations represent functions?
Input
Output
3
5
-b
9
d
Input
Output
7
-3
y
5
Input
Output
John
52
x²-10xy + 16y²-z² + 6yz
Answer:
(x - 8y + z)(x - 2y - z)
Step-by-step explanation:
Factorize :
x²-10xy + 16y²-z² + 6yz
Solution:
x²-10xy + 16y²-z² + 6yz
Firstly, make sure that all the terms are arranged in a well ordered manner:
x²-10xy + 16y²-z² + 6yz
Secondly, split the term (16y²) common to both equation:
(x²-10xy + 25y²) - 9y² -z² + 6yz
Thirdly, factorize both terms:
(x - 5y)² - 1(z² - 6yz + 9y²)
Factorizing the second term:
(x - 5y)² - (z - 3y)²
Using the difference of two squares, that is A² - B² = (A + B)(A - B):
(x - 5y)² - (z - 3y)² = [(x - 5y) + (z - 3y)][(x - 5y) - (z - 3y)]
= [x - 5y + z - 3y][x - 5y - z + 3y]
= (x - 8y + z)(x - 2y - z)