There are 105 numbers in the the first 1000 positive integers contain only 0s and 1s when written in base 3
How to determine the count of the numbers?The number base is given as:
Base 3
To determine the count of numbers, we make use of the following Python program
count = 0
for n in range(1,1001):
digits = []
while n:
digits.append(int(n % 3))
n //= 3
myStr = ''.join(map(str,digits[::-1]))
if(myStr.count('0')+myStr.count('1') == len(myStr)):
count+=1
print(count)
The above program counts the numbers in the the first 1000 positive integers contain only 0s and 1s when written in base 3
The output of the program is 105
Hence, there are 105 numbers in the the first 1000 positive integers contain only 0s and 1s when written in base 3
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Which function has a vertex at the origin?
f(x) = (x + 4)²2
f(x) = x(x-4)
f(x) = (x-4)(x + 4)
f(x) = -x²
Answer:
f(x) = -x²
Step-by-step explanation:
Writing f(x) = -x² in vertex form gives f(x)=-(x-0)^2+0 which shows that the vertex (h,k) is at (0,0)
The other equations written in vertex form do not have (h,k) = (0,0)
(a) if x is the sample mean young's modulus for a random sample of n = 64 sheets, where is the sampling distribution of x centered, and what is the standard deviation of the x distribution?
The standard deviation of the x distribution is 0.2.
According to the statement
we have given that the the sample n is 64 and we have to find the standard deviation of the given sample.
So, For this purpose, we know that the
The standard deviation of the sample is the standard deviation of population divided by the square root of the length of the sample.
In this problem, we have that the value of alpha is
[tex]\alpha = 1.6[/tex]
Suppose that for aluminum alloy sheets of a particular type,
If X is the sample mean Young's modulus for a random sample of n = 64 sheets, and the standard deviation of the X distribution is given by
[tex]s = \frac{\alpha}{\sqrt{64} }[/tex]
then solve it then the standard deviation
s = {1.6} / {8 }
s = 0.2
So, The standard deviation of the x distribution is 0.2.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Given that Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively.
a. If X is the sample mean Young's modulus for a random sample of n = 64 sheets, the sampling distribution of X centered at 70 GPa, and the standard deviation of the X distribution is given by
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Simplify the expression 120x^3/18xy
Question 9 of 25 a bookstore costs $105 a day to keep open, and it spends $12 for each book that it sells. if each book sells for $15, what is the break-even point for this bookstore?
The store will break even after selling 35 books.
What is the break-even point?The break-even point is the moment at which total cost and total revenue are equal, implying that your small firm has no loss or benefit. In other words, you've reached the point where the costs of production equal the revenues for a product.To find what is the break-even point for this bookstore:
Given:
The cost required per day to keep the store open = $105Amount spent on each book = $12Let, n be the number of books.
Total costs = 12n + 105
The selling price of each book = $15
Total revenue = 15n
For breaking even, costs = revenue.
12n + 105 = 15n105 = 15n - 12n105 = 3n3n = 105Dividing both sides by 3:3n/3 = 105/3n = 35Therefore, the store will break even after selling 35 books.
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What is the end behavior of the function f of x equals 3 times the cube root of x? as x → –[infinity], f(x) → –[infinity], and as x → [infinity], f(x) → [infinity]. as x → –[infinity], f(x) → [infinity], and as x → [infinity], f(x) → –[infinity]. as x → –[infinity], f(x) → 0, and as x → [infinity], f(x) → 0. as x → 0, f(x) → –[infinity], and as x → [infinity], f(x) → 0.
The function [tex]f(x)=4\sqrt[3]{x}[/tex] is a cube root function and the function end behavior is: [tex]x[/tex] → [tex]+[/tex] ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞, and as [tex]x[/tex] → - ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞
What is end behavior?The end behavior of a function f defines the behavior of the function's graph at the "ends" of the x-axis. In other words, the end behavior of a function explains the graph's trend when we look at the right end of the x-axis (as x approaches +) and the left end of the x-axis (as x approaches ).To determine the end behavior:
The equation of the function is given as: [tex]f(x)=4\sqrt[3]{x}[/tex]To determine the end behavior, we plot the graph of the function f(x).We can see from the accompanying graph of the function:As x approaches infinity, so does the function f(x), and vice versa.As a result, the function end behavior is:[tex]x[/tex] → [tex]+[/tex] ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞, and as [tex]x[/tex] → - ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞
Therefore, the function [tex]f(x)=4\sqrt[3]{x}[/tex] is a cube root function and the function end behavior is: [tex]x[/tex] → [tex]+[/tex] ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞, and as [tex]x[/tex] → - ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞
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The complete question is given below:
What is the end behavior of the function f of x equals negative 4 times the cube root of x?
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.
As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0.
As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.
Answer:
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
Step-by-step explanation:
I got it right on the test.
Write an algebraic expression to match the graph
please help!
the graphed equation is:
y = -|x| + 1
How to find the algebraic expression that matches the graph?On the graph, we can see an absolute value equation, which opens downwards, and passes through the points (1, 0) and (0,1).
The general absolute value equation is:
y = a*|x - b| + c
Because the vertex is at the point (0, 1), we know that:
b = 0, c = 1
Replacing that we get:
y = a*|x| + 1
Now, this must be zero when we evaluate in x = 1, then:
0 = a*|1| + 1
a = -1
Then the graphed equation is:
y = -|x| + 1
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How many solutions, in positive integers less than 10, does the equation x + y + z = 20
have?
[tex]\huge \mathbb{ \underline{EXPLANATION:}}[/tex]
Given:▪ [tex] \bold{\: x + y + z = 20}[/tex]
[tex]\\[/tex]
◆ As we have a [tex]\small\bold{sum \: of \: three \: integers}[/tex] equal to 20 and less than 10, we know the integers have to be between 2 and 9 (1 and 0 don't apply because the sum wouldn't be equal to 20 between three integers.
[tex]\large\tt{Note:}[/tex]
The first value would be X value, second Y value and third Z value.
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
[tex] \large\boxed{ \sf 36 \: solution}[/tex]
Use the given data set to complete parts (a) through (c) below. (Use α=0.05.)
1. The value of the linear correlation coefficient r is given as 0.8159. The correct option is a. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables
2. The scatterplot reveals a distinct pattern that is not a straight-line pattern.
What is the linear correlation coefficient?This is the data that we get when we try to get the existing relationship that is in existence between the variables that are used in a regression equation.
The value of r was calculated using a statistical tool online. The graph showed us it was not a straight line. The value of the r = 0.8159
The results of the test is in the attachment
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Determine and state the coordinates of the center and the length of the radius of the
circle whose equation is x2 + y2 + 6x = 6y + 63
we can see that the center is (-3, 3) and the radius is 9 units.
How to find the center and radius of the circle?The general circle equation, for a circle with a center (a, b) and radius R is given by:
(x - a)^2 + (y - b)^2 = R^2
Here we have the equation:
x^2 + y^2 + 6x = 6y + 63
Let's complete squares:
x^2 + y^2 + 6x - 6y = 63
(x^2 + 6x) + (y^2 - 6y) = 63
(x^2 + 2*3x) + (y^2 - 2*3y) = 63
Now we can add and subtract 9, (two times) so we get:
(x^2 + 2*3x + 9) - 9 + (x^2 - 2*3x + 9) - 9 = 63
(x + 3)^2 + (y - 3)^2 = 63 + 9 + 9 = 81 = 9^2
(x + 3)^2 + (y - 3)^2 = 9^2
Comparing with the general circle equation, we can see that the center is (-3, 3) and the radius is 9 units.
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find the length of MN
Answer:
The length of MN is 5 cm
Step-by-step explanation:
Add the segment LX, parallel to QP.
Recall the properties of midsegment:
Midsegment is parallel to side,Midsegment is half the length of the parallel side.We have:
Since QL = LR, the point L is midpoint of Q,Since PN = NL, the point N is midpoint of PL,Since LX is parallel to QP, LX is midsegment of ΔPRQ.Find the length of LX:
LX = QP/2 = 20/2 = 10 cmSince QP ║ LX ║ NM, the segment NM is the midsegment of ΔPLX.
Find the length of NM:
NM = LX/2 = 10/2 = 5 cmLori was paid a 15 percent commission for the home audio system that she sold. The electronics store had marked up the price of the system by 60 percent over the wholesale price of $264. How much did Lori earn for the sale of the home audio system? $15.84 $23.76 $39.60 $63.36
Answer:
$63.36
Step-by-step explanation:
The home audio system costs $264 wholesale.
The system's price had been increased by 60 percent at the electronics retailer.
Consequently, the increased cost is 60/100x264=$158.40.
The audio system's total cost is now $422.40 (264 + 158.40).
Given that Lori received a commission of = 15% on $422.40, her commission is now (15/100) x 422.40
= $63.36
if you rolled two dice what is the probability that you would roll a 4 or a 5
The time allotted for the Math test for 2 3/4 hours. Emma completed the test 1/2 of an hour earlier. How long did it take Emma to complete the test?
The diagonal is a of a rectangular field is 169m. If the ratio of the length to the width is 12:5 find the dimensions
Based on the calculations, the dimensions of the rectangle are
Length, L = 156 meters.Width, w = 65 meters.What is a diagonal?The diagonal of a rectangle can be defined as a line segment that connects any two (2) of its non-adjacent vertices together while dividing the rectangle into two (2) equal parts.
Mathematically, the length of diagonals of a rectangle can be calculated by using this formula:
d = √(l² + w²)
Where:
d is the diagonal of a rectangle.l is the length of a rectangle.w is the width of a rectangle.Since the ratio of the length to the width is 12:5, we have:
Width, w = 5l/12
Substituting the given parameters into the formula, we have;
169 = √(l² + (5l/12)²)
169² = l² + (5l/12)²
169² = l² + (25l²/144)
Length, L = 156 meters.
For the width, we have:
Width, w = 5l/12
Width, w = 5(156)/12
Width, w = 65 meters.
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the length of a new rectangular playing field is 3 yards longer than quadruple the width. if the perimeter of the rectangular playing field is 586 yards, what are its dimensions?
Answer:
length = 235 yd
width = 58 yd
Step-by-step explanation:
Let the width be W.
L = 4W + 3
perimeter = 2(L + W)
perimeter = 2(4W + 3 + W)
perimeter = 2(5W + 3) = 10W + 6
We are told the perimeter = 586 yd
10W + 6 = 586
10W = 580
W = 58
L = 4W + 3 = 4(58) + 3 = 232 + 3 = 235
length = 235 yd
width = 58 yd
Someone please explain.50 points available.Thankyou so much!
Answers:
a) 49 square tiles - did the work on paper.
b) 83 circular tiles - did the work on paper.
c) C: could be even or odd - all patterns had both even and odd amounts of square and circular tiles.
Step-by-step explanation:
I did all the work on paper it took a while to do it. pls mark brainliest
Which of the following is a monomial? O A. 11x-9 OB. 20x9 OC. 20x⁹ - 7x O D.9/x
Answer:
B. 20x⁹
Step-by-step explanation:
A monomial is a polynomial with just one term.
Example: 3x²
A. 11x - 9
INCORRECT, this has two terms 11x and 9
B. 20x⁹
CORRECT, this only has one term!
C. 20x⁹ - 7x
INCORRECT, this has two terms 20x⁹ and 7x
D.9/x
INCORRECT, this is not a polynomial
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Solve this:
NO INCORRECT or report
Answer:
D
Step-by-step explanation:
Let x be the first batch
let y be the second batch
y=2x
His brothers each received 9 rolls from the second batch i.e. 9×4=36
So
2x= 36+ (10÷6)x
2x - (10÷6)x = 36
12x-10x = 216
x=108
and y= 2 × 108= 216
Write 304.9% as a decimal.
Answer:
3.049
Step-by-step explanation:
Move the decimal place in 304.9% to the left two places in order to convert from a percentage to a decimal. 3.049 is the answer.
Brainliest, please :) Hope this helps!
3x 5y = 78 2x - y = 0 the point of intersection of the lines has an x-coordinate of _____. 78 6 -6
The supplied lines' point of intersection has the x coordinate is 6.
What is coordinate geometry?A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.
The x coordinate of the location where the ensuing lines intersect must be chosen.
3x + 5y = 78 ...........................(1)
2x - y = 0 ...............................(2)
The given system of equations must be solved in order to determine the x coordinate of the site of intersection.
Equation (ii) provides us with
2x = y
y = 2x ........................(3)
Equation I yields the result when the value of y from equation (iii) is substituted.
3x + 5(2x) = 78
3x + 10x = 78
13x = 78
x = 78/13
x = 6.
As a result, the supplied lines' point of intersection has the x coordinate 6.
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I understand that the question you are looking is :
3x 5y = 78 2x - y = 0 the point of intersection of the lines has an x-coordinate of _____.
A. 7
B.8
C. 6
D. -6
Find the surface area of the composite figure.
8 cm
6 cm
7 cm
8 cm
SA =
6 cm
[?] cm²
9 cm
6 cm
Answer:
382 cm²
Step-by-step explanation:
Front face + Back face:
A = 2(a + b)h/2
A = 2(14 cm + 8 cm)(7 cm)/2
A = 154 cm²
Left face:
A = 7 cm × 6 cm = 42 cm²
Right face:
A = 9 cm × 6 cm = 54 cm²
Bottom face:
A = 14 cm × 6 cm = 84 cm²
Top face:
A = 6 cm × 8 cm = 48 cm²
Total surface area =
= (154 + 42 + 54 + 84 + 40) cm²
= 382 cm²
Make a list of 4 different numbers whose average works up to 50
uhh so i totally forgot but are negative numbers smaller than positives and lets say -1.8, -9, -4.2 which would be bigger
Answer:
-1.8
Step-by-step explanation:
its bigger than -9 and -4.2
Jack and Serena can write a lab report together in 12 hours. If all people work at the same rate, how many hours would it take to write a lab report if Kay joins Jack and Serena?
Please help me if you can
The time, t in seconds that it takes a car to travel a quarter-mile when starting from a full stop can be estimated by using the formula:
[tex]t=5.825\sqrt[3]{w/p}[/tex]
Where w = weight of the car
p = power delivered by the engine in horsepower (hp)
If the quarter-mile time for a 3,590-pound car is 13.4 s, how much power does its engine deliver? Round to the nearest pound.
Two students solved this problem. Natasha’s answer was 295 hp and Daniel’s was 679 hp. Why was Daniel wrong? Show each step that led Daniel to the wrong answer
Step-by-step explanation:
Plug in known values
[tex]13.4 = 5.825\sqrt[3]{\frac{3590}{p}}\\[/tex]
Divide both sides by 5.825
[tex]2.3004 = \sqrt[3]{\frac{3590}{P}}\\[/tex]
Cube both sides
[tex]12.1738 = \frac{3590}{P}[/tex]
Multiply both sides by P
[tex]12.1738P = 3590[/tex]
Divide both sides by 12.1738
[tex]P = 294.895[/tex]
Round to nearest hp
[tex]P = 295[/tex]
So if you look at the radical, it's possible for it to be mistake for a square root, and not a cube root. This was Daniels mistake, so his steps were
[tex]13.4 = 5.825\sqrt[3]{\frac{3590}{p}}\\[/tex]
Divide both sides by 5.825
[tex]2.3004 = \sqrt[3]{\frac{3590}{P}}\\[/tex]
Square both sides
[tex]5.29197 = \frac{3590}{P}[/tex]
Multiply both sides by P
[tex]5.29197P = 3590[/tex]
Divide both sides by 5.29197
[tex]p\approx 678.385[/tex]
He also probably rounded during his steps, which would explain how he got 679 instead of 678 when rounding in the final, but either way his answer is completely off, and this is due to him mistakenly thinking the cube root was a square root.
PLLLLEASE ASAP GUYS PLEASEE OMG
Answer:
27/30
Step-by-step explanation:
9/10 x3 to both sides = 27/30
Answer:
[tex]\dfrac{27}{30}[/tex]
Explanation:
In a normal fraction such as [tex]\frac{a}{b}[/tex], a is the numerator and b is the denominator.
Here the given fraction is [tex]\frac{9}{10}[/tex], to rewrite the fraction with a denominator of 30. Multiply both the numerator and denominator by 3.
[tex]\rightarrow \dfrac{9}{10}[/tex]
[tex]\rightarrow \dfrac{9\:\times\:3}{10 \:\times \: 3}[/tex]
[tex]\rightarrow \dfrac{27}{30}[/tex]
Both the fractions are equivalent to each other.
There 13 yellow cards, 6 blue, 10 red, 8 green cards in a stack of cards turned face down. Once a card is selected, it is not replaced. Find P(2 blue cards). Please be specific with your answer.
Answer:
5/222
Step-by-step explanation:
you need to add all the cards together first
13 + 10 + 8 + 6 = 37
then you take out 1 card to find the first probability of the blue card (there are 6 blue cards out of 37)
so 6/37
that will be your first probability
then for the 2nd probability, you will have 1 less card grom the deck making it only 36 cards (after taking out the first one, there will be only 5 blue cards left)
making it 5/36
that will be the 2nd probability
then you multiply both these probabilities to find the answer
6/37 × 5/36 = 5/222
30 POINTSS ABD BRAINLIEST !! Let p be a prime number. Circle one expression below which could also be a prime number.
2p 7p p - 4 p squared
Give a reason for your answer above
Answer:
p - 4
Step-by-step explanation:
Prime number is a number that only has 2 factors, 1 and the number itself. Therefore, multiplying p by 2 or 7 means giving the number more than 2 factors, which would make the number no longer prime. Squaring the prime number itself does the same.
Let p = 7.
2p = 2*7 = 14 14 = 1*2*7*14
7p = 7*7 = 49 49 = 1*7*49
p - 4 = 7 - 4 = 3 3 = 1*3
p^2 = 7^2 = 49 49 = 1*7*49
Determine the seating capacity of an auditorium with 15 rows of seats if there are 25 seats in the first row, 29 seats in the second row, 33 seats in the third row, 37 seats in the forth row, and so on
Answer:
Step-by-step explanation:
15 rows adding 4 additional seats to each. Once at end add all seats in rows together for the final answer.
1-25
2-29
3-33
4-37
5-41
6-45
7-49
8-53
9-57
10-61
11-65
12-69
13-73
14-77
15-81
Add all togther. 25+29+33+37+41+45+49+53+57+61+65+69+73+77+81=795
So there are 795 seating capacity.
q=sqrt (c+d)/(c-d) solve for c
The equation for the variable 'c' is c = d(q² + 1)/(q² - 1). By using simple arithmetic operations on the original equation, the required equation can be obtained.
What is an equation?An equation is a relationship between two expressions given by a mathematical statement.
There are different types of equations. They are linear equations, quadratic, polynomial, etc.
Solving for c in the given equation:The given equation is
q = √((c + d)/(c - d))
Squaring on both, root gets canceled out
⇒ q² = (c + d)/(c - d)
⇒ q²(c - d) = (c + d)
⇒ cq² - dq² = c + d
Separating like terms aside,
cq² - c = d + dq²
⇒ c(q² - 1) = d(q² + 1)
⇒ c = d(q² + 1)/(q² - 1)
Therefore, the required equation is c = d(q² + 1)/(q² - 1).
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