Is 0.01011011101111011111 rational or irrational?
Answer:
It is rational number.
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
Hope it is helpful....15 POINTS! PLEASE HELP! BRAINLIEST!
What is the probability of flipping a coin 15 times and getting heads 6 times? Round your answer to the nearest tenth of a percent. O A. 19.6% O B. 9.2% O C. 4.2% O D. 15.3% SUBMIT
Answer:
D. 15.3%Step-by-step explanation:
Total number of outcomes:
2¹⁵ = 32768Number of combinations of getting 6 heads:
15C6 = 15!/6!(15-6)! = 5005Required probability is:
P(6 heads out of 15 flips) = 5005/32768 = 0.1527... ≈ 15.3%Correct choice is D
Answer:
option D
Step-by-step explanation:
Total sample space
= [tex]2^{15}[/tex]
Number of ways 6 heads can emerge in 15 flips
= [tex]15C_6[/tex]
Probability:
[tex]=\frac{15C_6}{2^{15}}[/tex] [tex]= 0.1527[/tex]
Probability to the nearest percent : 15.3%
Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1.
Answer:
The equation of the parabola is y = x²/4
Step-by-step explanation:
The given focus of the parabola = (0, 1)
The directrix of the parabola is y = -1
A form of the equation of a parabola is presented as follows;
(x - h)² = 4·p·(y - k)
We note that the equation of the directrix is y = k - p
The focus = (h, k + p)
Therefore, by comparison, we have;
k + p = 1...(1)
k - p = -1...(2)
h = 0...(3)
Adding equation (1) to equation (2) gives;
On the left hand side of the addition, we have;
k + p + (k - p) = k + k + p - p = 2·k
On the right hand side of the addition, we have;
1 + -1 = 0
Equating both sides, gives;
2·k = 0
∴ k = 0/2 = 0
From equation (1)
k + p = 0 + 1 = 1
∴ p = 1
Plugging in the values of the variables, 'h', 'k', and 'p' into the equation of the parabola, (x - h)² = 4·p·(y - k), gives;
(x - 0)² = 4 × 1 × (y - 0)
∴ x² = 4·y
The general form of the equation of the parabola, y = a·x² + b·x + c, is therefore;
y = x²/4.
Which expression is equivalent to Cube root of 343 x Superscript 9 Baseline y Superscript 12 Baseline z Superscript 6?
7x3y4z2
7x3y6z2
49x3y6z2
49x3y4z2
9514 1404 393
Answer:
7x^3y^4z^2
Step-by-step explanation:
[tex]\displaystyle\sqrt[3]{343x^9y^12z^6}=\sqrt[3]{(7x^3y^4z^2)^3}=\boxed{7x^3y^4z^2}[/tex]
Answer:
[tex] \small \sf \leadsto \: 7x {}^{3}y {}^{6}z {}^{2} [/tex]
Step-by-step explanation:
[tex] \small \sf \leadsto \: \sqrt[3]{343 \: x {}^{9} \: y{}^{12} \: z {}^{6} }[/tex]
[tex] \small \sf \leadsto \: \sqrt[3]{7x {}^{3}y {}^{6}z {}^{2} } [/tex]
[tex] \small \sf \leadsto \: 7x {}^{3}y {}^{6}z {}^{2} [/tex]
identify a transformation of a function f(x)=x^2 by observing the equation of the function g(x)=5(x)^2
Answer:
Thus the function g is the function f stretched vertically by a factor 5.
Step-by-step explanation:
Multiplication of a function by a constant:
When a function is multiplied by a constant a > 1, the function is stretched vertically by a factor of 5.
In this question:
f(x) = x^2
g(x) = 5x^2
Thus the function g is the function f stretched vertically by a factor 5.
F(x) = x3 + x2 -8x - 6
According to the Fundamental Theorem of Algebra, how many solutions/roots will there be?
According to Descartes' Rule of Signs, what are the possible combinations of positive, negative, and/or complex roots will there be?
Using the Rational Root Theorem, list all the possible rational roots.
Use a combination of Synthetic Division, Factoring, and/or the Quadratic Formula to find all the roots. PLEASE SHOW ALL WORK!
This is my 4th time posting this and no ones helping. Please someone who is smart help me out lol
Answer:
Given function:
f(x) = x³ + x² - 8x - 6This is the third degree polynomial, so it has total 3 roots.
Lets factor it and find the roots:
x³ + x² - 8x - 6 = x³ + 3x² - 2x² - 6x - 2x - 6 = x²(x + 3) - 2x(x + 3) - 2(x + 3) = (x + 3)(x² - 2x - 2) = (x + 3)(x² - 2x + 1 - 3) = (x + 3)((x - 1)² - 3) = (x + 3)(x - 1 + √3)(x - 1 - √3)The roots are:
x = -3x = 1 - √3x = 1 + √3It has highest degree 3 so 3 roots
1 positive and 2 negative rootsLets find
x³+x²-8x-6=0x²(x+3)-2x(x+3)-2(x+3)=0(x+3)(x²-2x-2)=0(x+3)(x-2.732)(x+0.732)=0Roots are
-3,2.732,-0.732Find z such that 3.8% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.)
Answer:
z = 1.77.
Step-by-step explanation:
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, which is also the area of the normal curve to the left of Z. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Find z such that 3.8% of the standard normal curve lies to the left of z
Thus, z with a z-score of 0.038. Looking at the z-table, this is z = 1.77.
Solve the system using substitution.
y = 4x – 8
y = 2x + 10
Answer:
9,28
Step-by-step explanation:
see image below:)
The diameter of a circle is 15 in. Find its circumference in terms of \piπ
Answer:
15π in
Step-by-step explanation:
In order to solve this, we need to know that the circumference of a circle can be found by using the following formula...
Circumference = dπ (where d is the diameter of the circle)
Therefore the circumference equals...
Circumference = dπ = 15π in
[tex]\boxed{Given:}[/tex]
Diameter of the circle "[tex]d[/tex]" = 15 in.
[tex]\boxed{To\:find:}[/tex]
The circumference of the circle (in terms of π).
[tex]\boxed{Solution:}[/tex]
[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:15\:π\:in.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:πd }[/tex]
[tex] = \pi \times 15 \: in \\ \\ = 15 \: \pi \: in[/tex]
Therefore, the circumference of the circle is 15 π in.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
A bag with 12 marbles has 5 red marbles, 3 yellow marbles, and 4blue marbles. A marble is chosen from the bag at random. What is the probability that it is red? Write your answer as a fraction in simplest form.
Answer:
5/12 is already in simplest form
Step-by-step explanation:
12m = 5r + 3y + 4b
red is chosen = 5r / 12 = 5/12
Step-by-step explanation:
the answer is 5/12. It's quite simple
Select the correct answer
Consider event A and event 8. What is the probability that event Boccurs, given that event A has already occurred?
OA
PB n A)
PLA). P(8)
Ов,
P(BA)
P(A)
OC. P(BA)
P(8)
OD
PIBUA)
P(B)
Reset
Next
Answer:
[tex]P(B|A)[/tex]
Step-by-step explanation:
Probability notation:
Suppose that we have two events, event A and event B. The probability of event B occuring, considering that event A has occurred, is given by:
[tex]P(B|A)[/tex], which is the answer to this question.
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
Assume that you take out a $3000 loan for 30 months at 8.5% APR. What is the monthly payment? (Round your answer to the nearest cent.)
$
Answer:
111.35
Step-by-step explanation:
effective rate: .085/12= .007083333333333333
payment=x
[tex]3000=x(\frac{1-(1+.007083333333333333)^{-30}}{.007083333333333333})\\x=111.35[/tex]
Step-by-step explanation:
111.35
Step-by-step explanation:
effective rate: .085/12= .007083333333333333
payment=x
\begin{gathered}3000=x(\frac{1-(1+.007083333333333333)^{-30}}{.007083333333333333})\\x=111.35\end{gathered}
3000=x(
.007083333333333333
1−(1+.007083333333333333)
−30
)
x=111.35
Match the vocabulary word to its correct definition
1. arithmetic sequence
an individual quantity or number in
a sequence
the fixed amount added on to get
2. common difference
to the next term in an arithmetic
sequence
a sequence in which a fixed
3. sequence
amount is added on to get the next term
a set of numbers that follow a
4 term
pattern, with a specific first number
Answer:
1. Term.
2. Common difference.
3. Arithmetic sequence.
4. Sequence.
Step-by-step explanation:
1. Term: an individual quantity or number in a sequence. For example, 1, 2, 3, 5, 6. The first term is 1 while 5 is the fourth term.
2. Common difference: the fixed amount added on to get to the next term in an arithmetic sequence. For example, 2, 4, 6, 8 have a common difference of 2 i.e (6 - 4 = 2).
3. Arithmetic sequence: a sequence in which a fixed amount such as two (2) is added on to get the next term. For example, 0, 2, 4, 6, 8, 10, 12.... is an arithmetic sequence.
4. Sequence: a set of numbers that follow a pattern, with a specific first number. For example, 1, 2, 3, 4, 5, 6 is a sequence.
PLS SOLVE!! e2 = d^2+f^2 -2df(cosE)
9514 1404 393
Answer:
e = 25.7 m
Step-by-step explanation:
Put the given numbers in the given formula and do the arithmetic.
[tex]e^2=d^2+f^2-2df(\cos{E})\\\\e^2=11.9^2+18.5^2-2(11.9)(18.5)\cos{114^\circ}\approx 662.946\\\\e\approx\sqrt{662.946}\approx25.74774\\\\\boxed{e\approx25.7\text{ m}}[/tex]
The denominator of a fraction is twice the numerator. If 3 is added to the numerator and 3 is subtracted from the denominator, the new fraction is 7/5. Find the original fraction.
Answer:
4/8
Step-by-step explanation:
d = 2n
n+3 = 7
d-3 = 5
substitute '2n' for 'd' in d-3=5
2n-3 = 5
2n = 8
n = 4
d = 2(4)
4/8
A parallelogram is shown below: A B A 2 foot D с 3 feet Part A: What is the area of the parallelogram? Show your work. (5 points) Part B: How can you decompose this parallelogram into two triangles? If this parallelogram was decomposed into two triangles, what would be the area of each triangle? (5 points)
9514 1404 393
Answer:
Part A: 2 ft²
Part B: draw a diagonal (AC, for example); 1 ft²
Step-by-step explanation:
Part A:
The area of a parallelogram is given by the formula ...
A = bh
where 'b' is the length of the base, and 'h' is the perpendicular distance between the bases.
Using the numbers shown on the diagram, the area is ...
A = (3 ft)(2/3 ft) = 3·2/3 ft²
A = 2 ft² . . . . . area of the parallelogram
__
Part B:
Typically, a polygon is partitioned into triangles by drawing diagonals from one of the vertices. It does not matter which one. (In a quadrilateral, only one diagonal can be drawn from any given vertex.) Here, the "base" of each triangle is the same as the base of the parallelogram: 3 feet. The "height" of each triangle is the same as the height of the parallelogram: 2/3 ft.
The area of a triangle is given by the formula ...
A = 1/2bh
A = 1/2(3 ft)(2/3 ft) = (1/2)(3)(2/3) ft²
A = 1 ft² . . . . . . . . area of each triangle
_____
Additional comment
It should be no surprise that the area of each of the two congruent triangles is 1/2 the area of the parallelogram.
The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served was 175, 125, 180, 220, 240, and 245. She believes that the number of customers served on weekdays follows a normal distribution. Construct the 99% confidence interval for the average number of customers served on weekdays.
Answer:
(121.576 ; 273.424)
Step-by-step explanation:
Given the data:
175, 125, 180, 220, 240, 245
We can calculate the mean and standard deviation
Mean = Σx/ n = 1185 / 6 = 197.5
Standard deviation = 46.125 (calculator)
The confidence interval :
Mean ± margin of error
Margin of Error = Tcritical * s/sqrt(n)
Tcritical at 99%, df = n - 1 ; 6 - 1 = 5
Tcritical = 4.032
Margin of Error = 4.032 * 46.125/√6
Margin of error = 75.924
Confidence interval :
197.5 ± 75.924
Lower boundary = 197.5 - 75.924 = 121.576
Upper boundary = 197.5 + 75.924 = 273.424
(121.576 ; 273.424)
10
El tiempo aproximado en caminar de tu casa (C) a la de tu amigo (A) pasando por la tienda (T)
es de 14 minutos; Si caminas a la misma velocidad, ¿Cuántos minutos te tomará caminar
directamente a la casa (C) de tu amigo (A)? Redondea al entero más cercano.
500yd
A
700yd
Respuesta:
10.0 minutos
Explicación paso a paso:
Distancia total recorrida caminando de C a A pasando por T:
500 yardas + 700 yardas = 1200 yardas
Tiempo necesario para recorrer 200 yardas = 14 minutos
Caminando directamente de C a A:
La distancia se puede obtener usando una relación trigonométrica:
Hipotenusa = √ (opuesto² + adyacente²)
Hipotenusa = √500² + 700²
Hipoteno = 860.23252 yardas
Por eso ; Si
1200 yardas = 14 minutos
860.23252 yardas = x
Multiplicar en cruz:
1200x = 12043,255
x = 12043,255 / 1200
x = 10.036 minutos
El tiempo necesario para caminar directamente será: 10.0 minutos
-22+14/2(-10)
LAST ONE:)))
[tex]\huge\textsf {Hey there!}[/tex]
[tex]\mathsf{-22 + \dfrac{14}{2}(-10)}[/tex]
[tex]\mathsf{\dfrac{14}{2}= \boxed{\bf 7}}[/tex]
[tex]\mathsf{= -22 + 7(-10)}[/tex]
[tex]\mathsf{7(-10) =\boxed{\bf -70}}[/tex]
[tex]\mathsf{= -22 + (-70)}[/tex]
[tex]\mathsf{= -22 - 70}[/tex]
[tex]\mathsf{= \boxed{\bf -92}}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf -92}}}\huge\checkmark[/tex]
[tex]\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
-92 is the answer.
Step-by-step explanation :
Let's go step by step.
-22 + 14/2(-10)
14/2 is 7, and 7 multiplied by -10 is -70, so we end up with this :
-22 + -70 = -22 - 70
-22 - 70 is -92.
-92 is the answer.
Hope this helps, please mark brainliest!
Determine the value of x
Answer:
B is the answer.
Step-by-step explanation:
A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for
Answer:
Perimeter: 18.28
Area: 22.28
Step-by-step explanation:
1. Approach
An easy method that can be used to solve the given problem is the partition the given figure into two smaller figures. One can divide this figure into a square and a semi-circle. After doing so, one can find the area of the semi-circle and the area of the square. Finally, one can add the two area together to find the final total area. To find the perimeter of the figure, one can add the lengths of three of the sides of the square and then one can add half of the circumference of the circle to the result. The final value will be the perimeter of the entire figure.
2. Find the circumference of the semi-circle
The circumference of a circle is the two-dimensional distance around the outer edge of a circle, in essence the length of the arc around a circle. The formula to find the circumference of a circle is as follows,
C = 2(pi)r
Since a semi-circle is half of a circle, the formula to find its circumference is the following,
C = (pi)
Where (pi) is the numerical value (3.1415) and (r) is the radius of the circle. By its definition, the radius of a circle is the distance from a point on the circle to the center of the circle. This value will always be half of the diameter, that is the distance from one end of the circle to the other, passing through the center of the circle. The radius of a circle is always half of the diameter, thus the radius of this semi-circle is (2). Substitute this into the formula and solve for the circumference;
C = (pi)r
C = (pi)2
C ~ 6.28
3. Find the area of the semi-circle
The formula to find the area of a circle is as follows,
A = (\pi)(r^2)
As explained earlier, a semi-circle is half of a circle, therefore, divide this formula by (2) to find the formula for the area of a semi-circle
A = ((pi)r^2)/(2)
The radius of this circle is (2), substitute this into the formula and solve for the area of a semi-circle;
A = ((pi)r^2)/(2)
A = ((pi)(2^2))/(2)
A = (pi)2
A = 6.28
4. Find the area and perimeter of the square,
The perimeter of a figure is the two-dimensional distance around the figure. Since the semi-circle is attached to one of the sides of a square, one only needs to add three sides of the square to find the perimeter of the square;
P = 4+4+4
P = 12
The area of a square can be found by multiplying the length by the width of the square.
A = l*w
Substitute,
A = 4*4
A=16
5. Find the area and the perimeter of the figure,
To find the perimeter of the figure, add the value of the circumference to the vlalue of the perimeter of the square;
A = C+P
A = 6.28+12
A = 18.28
To find the area of the figure, add the value of the area of the circle to the area of the square;
A = 6.28+16
A = 22.28
please help me
if don't know don't answer, if you answer i will report
Answer:
A.) m = 1.5 | B.) p = -1 | C.) t = 2
Step-by-step explanation:
A.)
[tex]4(m+3)=18\\4m+12=18\\4m=6\\m=3/2=1.5[/tex]
B.)
[tex]-2(p+5)+8=0\\-2p-10+8=0\\-2p-2=0\\-2p=2\\p=-1[/tex]
C.)
[tex]3+5(t-1)=8\\3+5t-5=8\\5t-2=8\\5t=10\\t=2[/tex]
Answer:
(a)=
4(m+3)=18
4m+12=18
4m=18-12
4m=6
m=
[tex] \frac{6}{4} [/tex]
(b)=
-2(p+5)+8=0
-2p-10+8=0
-2p=0+10-8
-2p=2
p=
[tex] \frac{2}{ - 2} = - 1[/tex]
(c)=
3+5(t-1)=8
3+5t-5=8
5t=8-3+5
5t=10
t=
[tex] \frac{10}{5} = 2[/tex]
[tex]please \: mark \: as \: brainliest \: because \: i \: spent \: much \: time \: on \: this \: question[/tex]
The following set of data represents the ages of the women who won the Academy Award for Best Actress from 1980 - 2003:
31 74 33 49 38 61 21 41 26 80 42 29
33 35 45 49 39 34 26 25 33 35 35 28
Make frequency table using # of classes as per the following criteria:
i) if you are born in Jan, Feb, Mar: No of classes = 5
ii) if you are born in Apr, May, Jun: No of classes = 6
Answer:
Step-by-step explanation:
Given the data :
Using 6 classes :
Class interval ____ Frequency
21 - 30 _________ 6
31 - 40 _________ 10
41 - 50 _________ 5
51 - 60 _________ 0
61 - 70 _________ 1
71 - 80 _________ 2
What is the area of triangle in centimeters squared?
Determine the required value of the missing probability to make the distribution a discrete probability distribution
P(4)=____
X P(x)
3 0.25
4 ?
5 0.39
6 0.15
======================================================
Explanation:
All of the values in the P(x) column must add to 1.
The value 1 in probability means 100%
Let y be the missing value in the table
0.25+y+0.39+0.15 = 1
y+0.79 = 1
y = 1-0.79
y = 0.21
The probability that x = 4 is 0.21
In other words, P(4) = 0.21
Or that we have a 21% chance of having x = 4 happen.
A printer has a contract to print 100,000 posters for a political candidate. He can run the posters by using any number of plates from 1 to 30 on his press. If he uses x metal plates, they will produce x copies of the poster with each impression of the press. The metal plates cost $20.00 to prepare, and it costs $125.00 per hour to run the press. If the press can make 1000 impressions per hour, how many metal plates should the printer make to minimize costs
Answer:
25
Step-by-step explanation:
From the given information;
Numbers of posters that can be printed in an hour = no of impression/hour × no of plate utilized in each impression.
= 1000x
Thus, the required number of hours it will take can be computed as:
[tex]\implies \dfrac{100000}{1000x} \\ \\ =\dfrac{100}{x}[/tex]
cost per hour = 125
If each plate costs $20 to make, then the total number of plate will equal to 40x
∴
The total cost can be computed as:
[tex]C(x) = (\dfrac{100}{x}) \times 125 + 20 x --- (1)[/tex]
[tex]C'(x) = (-\dfrac{12500}{x^2}) + 20 --- (2)[/tex]
At C'(x) = 0
[tex]\dfrac{12500}{x^2} = 20[/tex]
[tex]\dfrac{12500}{20} = x^2[/tex]
[tex]x^2= 625[/tex]
[tex]x = \sqrt{625}[/tex]
x = 25
[tex]C'' (x) = -12500 \times \dfrac{-2}{x^3} +0[/tex]
[tex]C'' (x) = \dfrac{25000}{x^3}[/tex]
where; x = 25
[tex]C'' (x) = \dfrac{25000}{25^3}[/tex]
C''(x) = 1.6
Thus, at x = 25, C'' > 0
As such, to minimize the cost, the printer needs to make 25 metal plates.
write a rational number between root2 and root3
Answer:
prational number between root2
1. p-4= -9+p
2. 4m-4= 4m
Extra Credit, need help
Answer:
1. No solution
2. No solution
Step-by-step explanation:
1. p-4=-9+p
-4=-9
No solution
2. 4m-4=4m
-4=0
No solution
If this helps please mark as brainliest
BE is a midsegment, Find the value of x. Please
Answer:
x10
Step-by-step explanation:
BE=1/2 * CD
x=CB/2
x=20/2
x=10
which statement is true?
Answer:
A. The slope of Function A is greater than the slope of Function B.
Step-by-step explanation:
The slope of a function can be defined as rise/run. In Function A, the rise/run is 4. The slope in Function B is much easier to see: it is 2. Because 4 is greater than 2, Function A has a greater slope than Function B.
