The mass of the radioactive sample at the beginning of the 13th day of the experiment will be around 424.7 grams.
What does one gramme represent?A metric weight measurement unit. A gramme is one thousandth of a kilogramme, or about 30 times smaller than an ounce. Leave a space between the word "gramme" (or the symbol "g") and the number that comes before it when a specific number is provided. In technical and scientific writing, the unit name and the number are either written together in full (for example, ten grammes) or a numeral is used with the sign ( e.g. 10 g ).
When we find the mass of radioactive, we obtain:
m₀=initial mass=1500 grams, r = 13% and n =12 days
⇒m = m₀ x [tex](1 - \frac{r}{100} )^{n}[/tex]
⇒m =1500×[tex](1-\frac{13}{100}) ^{12}[/tex]
⇒m=424.7 grams.
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Select the correct answer. What is the solution to this equation? 216 = 6 2 x − 1 A. x = 1 B. x = 2.5 C. x = 3 D.
Answer:
D. [If D is saying "x = 4"]
Step-by-step explanation:
We can start solving the equation 216 = 62x - 1 by adding 1 to both sides to isolate the term with x:
216 + 1 = 62x
Simplifying the left side, we get:
217 = 62x
To solve for x, we can divide both sides by 62:
217/62 = x
Using a calculator, we can evaluate the quotient:
3.5 = x
Therefore, the solution to the equation 216 = 62x - 1 is x = 3.5.
Since none of the answer choices match this result exactly, we can round 3.5 to the nearest integer. Rounding 3.5 up to the nearest integer gives us x = 4.
Answer please, I'll give brainliest
Answer:
1st one
Step-by-step explanation:
Answer: A. (2/5,-3)
Step-by-step explanation:
in order to find the solution to the set of equations, you need to find one variable first, lets fing y first
10x+3y=-5
10x = -5 - 3y
x = (-5 -3y)/10
substitute this in for x in the other equation
-5((-5 - 3y)/10) -4y = 10
(25 + 15y)/10 -4y = 10
25/10 + 15y/10 -4y = 10
make all fractions on the left side
25/10 + 15y/10 - 40y/10 = 10
combine
25/10 -25y/10 = 10
multiply both sides by 10 to get rid of the denominator
25 - 25y = 100
combine like terms
-25y = 75
divide
y = -3
plug y into the first equation to find x
10x + 3(-3) = -5
10x -9 = -5
10x = 4
x = 4/10
simplify
x = 2/5
hope this helps!
use the definition of derivative. find the derivative of f(x)=cosx
For the given function f(x) = cos x, f '(x) = -sin x.
By the definition of the derivative, this means that -sin x provides the rate of change of cos x at a specific angle.
What is meant by the derivative of a function?
The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. It is described as the fluctuating rate at which a function changes in relation to an independent variable. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The sensitivity of the dependent variable to the independent variable is assessed using the derivative. Calculus's core tool is derivative.
We are given the function f(x) = cos x
The derivative of cos x is -sin x.
That is, f '(x) = -sin x
Therefore, by definition of the derivative, this means that -sin x provides the rate of change of cos x at a specific angle.
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Find the x-intercepts of the polynomial function.
f(x) = x4 − x2
Answer:
Step-by-step explanation:
To find the x-intercepts of the polynomial function f(x) = x^4 - x^2, we need to set f(x) = 0 and solve for x. That is, we need to find the values of x that make the function equal to zero.
f(x) = x^4 - x^2
Setting f(x) = 0, we get:
x^4 - x^2 = 0
Factoring out x^2, we get:
x^2(x^2 - 1) = 0
Using the zero product property, we get:
x^2 = 0 or x^2 - 1 = 0
Solving for x in each case, we get:
x = 0 or x = ±1
Therefore, the x-intercepts of the polynomial function f(x) = x^4 - x^2 are (0, 0), (1, 0), and (-1, 0).
Find the slope of the line segment shown.
A) -1/2
B) -1
C) 1/2
D) 1
The slope of the line segment is -1/2 . Option A is correct.
What is slope ?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
The slope is the "rise over run" between any two points on the line.
Count out how much "up or down" vs "left or right" to find the slope:
We go up 5 and right 5, giving us the fraction
Thus , slope is given by -5 /10 = -1 /2
When counting, up and right are counted as positive; left and down are counted as negative.
Hence , the slope of the line segment is -1/2 . Option A is correct.
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Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options. 5(x2 + 4x + 4) = –7 + 20 x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot 5(x2 + 4x) = 7 5(x2 + 4x + 4) = 7 + 20 5(x2 + 4x) = –7
The next step on solving completing square is: 5 (x² + 4x) = 7 and 5(x² + 4x + 4) = 7 + 20. So, these steps could he use to solve the quadratic equation by completing the square.
What is quadratic equation?Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known values, and where a ≠ 0 is true is known as a quadratic equation.
Case 1:
Given equation becomes:
5x² + 20x - 7 = 0
Firstly, we will add of 7 in both sides:
5x² + 20x - 7 + 7 = 0 + 7
Now, same variable of opposite sign is cancelled:
5x² + 20x = 7
Now, taking 5 common from left side:
5 (x² + 4x) = 7
Case 2:
Given equation becomes:
5x² + 20x - 7 = 0
Firstly, we will add of 7 in both sides:
5x² + 20x - 7 + 7 = 0 + 7
Now, same variable of opposite sign is cancelled:
5x² + 20x = 7
Now, we will add of 20 in both sides
5x² + 20x + 20 = 7 + 20
Now, taking common of 5 from left side:
5(x² + 4x + 4) = 7 + 20
So, The next step on solving completing square is: 5 (x² + 4x) = 7 and 5(x² + 4x + 4) = 7 + 20
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calculate the following using the long division method 8328÷ 24
Answer:
347
Step-by-step explanation:
Im not sure if that helps but thats the answer I got.
By using the long division method, The value of expression 8328 ÷ 24 after divide is,
⇒ 8328 ÷ 24
= 347
What is mean by Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, To dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
The mathematical expression for divide is,
⇒ 8328 ÷ 24
Now, We can formulate;
We can use the long division method for the expression as;
⇒ 8328 ÷ 24
⇒ 8328 / 24
24 ) 8328 ( 347
- 72
-----
112
- 96
------
168
- 168
--------
0
Therefore, We get the correct answer,
By using the long division method,
The value of expression 8328 ÷ 24 after divide is,
⇒ 8328 ÷ 24
= 347
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can you please help me ASAP for 50 points SLOPE: FROM TWO POINTS
Answers not related to the question will be REPORTED also pls check answers for posting
Answer:
Step-by-step explanation:
a) The slope of the line passing through the points (5,6) and (-1,6) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (5,6) and (x2, y2) = (-1,6).
m = (6 - 6) / (-1 - 5) = 0 / -6 = 0
Therefore, the slope of the line is 0.
b) The slope of the line passing through the points (3,-2) and (3,-1) cannot be calculated using the previous formula since the points have the same x coordinate. This means that the line is vertical and therefore its slope is infinite (or undefined).
c) The slope of the line passing through the points (2,2) and (-5,2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (2,2) and (x2, y2) = (-5,2).
m = (2 - 2) / (-5 - 2) = 0 / -7 = 0
Therefore, the slope of the line is 0.
d) The slope of the line passing through the points (9,-2) and (-7,-2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (9,-2) and (x2, y2) = (-7,-2).
m = (-2 - (-2)) / (-7 - 9) = 0 / -16 = 0
Therefore, the slope of the line is 0.
e) The slope of the line passing through the points (-8,22) and (1,4) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-8,22) and (x2, y2) = (1,4).
m = (4 - 22) / (1 - (-8)) = -18 / 9 = -2
Therefore, the slope of the line is -2.
f) Since we know the slope m = 2 and one of the points is (3,6), we can use the formula:
y - y1 = m(x - x1)
where (x1, y1) = (3,6). Substituting m and (x1, y1) into the formula, we get:
y - 6 = 2(x - 3)
Expanding the formula and solving for y, we get:
y = 2x - 6 + 6
y = 2x
Therefore, the y-coordinate of the second point is y = 2(4) = 8. The second point is (4,8).
find the exact value using formulas from geometry. ∫ (1+3x) with upper bound as 3 and lower bound as 1.
The value of the integral ∫(1+3x) dx is equal to 14.
What is integration?Integration is a process of adding up small elemental volumes to find the larger volume.
Given is to find the integral -
∫(1+3x)
We can find the equivalent values as -
∫(1+3x) dx = ∫1 dx + ∫3x dx
∫(1+3x) dx = x + 3x²/2
For the limit x = 1 to x = 3, we can write -
∫(1+3x) dx = (3 + 27/2) - (1 + 3/2)
∫(1+3x) dx = 33/2 - 5/2 = 14
Therefore, the value of the integral ∫(1+3x) dx is equal to 14.
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According to Statistics Canada, approximately 29% of all St. Marys residents are in the 45–64 age range. Suppose that 97% of the people who used the new bins, once they were introduced for the first time during the initial two-month period, were in the 45–64 age category. Use this information to determine whether age is independent of the initial use of the bins during the introductory two-month time period. Explain your answer.
Calculate the cubic roots of the complex number Z:
Z=-27
(number 6)
The cubic root of z = -27 is -3
What is the cubic rootA real cube and tree roots may be the first images that come to mind when we hear the terms "cube" and "root." Is it not? Well, the concept is the same. Root refers to the main source or starting point. So, all we need to do is consider "which number's cube should be taken to get the given number." The cube root definition in mathematics is expressed as The cube root is the quantity that must be three times multiplied to yield the initial quantity. Let's look at the cube root equation: ∛x = y, where y is the cube root of x. Every number with a little 3 inscribed on it can be represented by the radical sign as the cube root symbol.
In this problem, the cubic root of z = -27 can be calculated as;
z = -∛-27
z = -3
This is because 27 is a perfect cube
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Find the equation of the line passing through the points (-6,5) and (2,-5). Write the equation in point-slope form, slope-intercept form, and standard form.
Answer:
y= -6x+5
y= 2x+(-5)
Step-by-step explanation:
This is the equation of the line in point-slope form.
y - 5 = (-5/4)(x + 6)
The equation in slope-intercept form is y = (-5/4)x - 5/4.
And So the equation in standard form is 5x + 4y = -5.
for what values of k can 2x^2 kx 5 be factored as the product of two linear factor with integer coefficents
The values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.
What is a linear factor?
A linear factor is a polynomial of degree one, which means it has one variable raised to the first power and a constant coefficient. In other words, it is an expression of the form ax + b, where a and b are constants and x is the variable.
We can factor the quadratic 2x² + kx - 5 into the product of two linear factors with integer coefficients if and only if its discriminant is a perfect square.
The discriminant of the quadratic equation ax² + bx + c = 0 is given by the expression b² - 4ac. In this case, a = 2, b = k, and c = -5. Therefore, the discriminant is:
b² - 4ac = k² - 4(2)(-5) = k² + 40
For the quadratic to be factored into two linear factors with integer coefficients, k² + 40 must be a perfect square.
One way to proceed is to list the perfect squares that are 40 greater than a square, and see if k is one of the corresponding values. We can do this by solving the equation:
k² + 40 = m²
where m is an integer. Rearranging, we get:
k² - m² = -40
This is a difference of squares, so we can factor it:
(k + m)(k - m) = -40
We now need to find integer values of k and m that satisfy this equation. We can do this by considering all possible pairs of factors of -40 and solving for k and m.
The pairs of factors of -40 are:
(-1, 40), (-2, 20), (-4, 10), (-5, 8)
For each pair, we can solve the system of equations:
k + m = a
k - m = b
where a and b are the two factors in the pair. Adding these equations, we get:
2k = a + b
Subtracting them, we get:
2m = a - b
Solving for k and m, we obtain:
k = (a + b)/2
m = (a - b)/2
We can now check if the values of k and m are integers and if they satisfy the original equation.
For example, if we take the pair (-1, 40), we get:
k + m = -1
k - m = 40
Adding these equations, we get:
2k = 39
This implies that k = 39/2, which is not an integer, so this pair does not work.
Trying the other pairs, we find that:
(-2, 20) gives k = 9 and m = 11, which works
(-4, 10) gives k = 3 and m = 7, which works
(-5, 8) gives k = 1 and m = 3, which works
Therefore, the values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.
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Suppose that a particular NBA player makes 92% of his free throws. Assume that late in a basketball game, this player is fouled and is awarded two free throws. a. What is the probability that he will make both free throws? (to 4 decimals)
The probability that he will make both free throws is 0.84.
What exactly is the meaning of probability?
Probability expresses the possibility of an event. This branch of mathematics studies the occurrence of a random event. The value ranges between 0 and 1. Probability is used in mathematics to anticipate the possibility of events occurring.
Probability refers to the likelihood of something occurring. This fundamental premise of probability theory is used by the probability distribution. We must first know the entire number of possibilities before we can assess the possibility of an event occurring.
P(E) is the probability of an event occurring divided by the total number of outcomes.
Now,
Given that player makes 92% of freethrows
that means p(making free throws)=92/100
=23/25
so making two free throws probability will be =23*23/25*25
=529/625
=0.84
Hence,
The probability that he will make both free throws is 0.84.
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The stock price of Alps Co. is $53.50. Investors require a return of 13 percent on similar stocks. If the company plans to pay a dividend of $3.40 next year. what groeth rate is expected for the company's stock price?
Answer:
The expected growth rate for the company's stock price is 9.7%. This is calculated by subtracting the dividend yield (3.40/53.50 = 0.0635) from the required return (13%).
What is the factorization of the polynomial below? x2 - x - 42 A. (x + 7)(x + 6) B. (x + 7)(x - 6) C. (x - 7)(x + 6) D. (x - 7)(x - 6)
The factorization of the polynomial is (x - 7)(x + 6). Option C is the correct answer.
What is factorization?The breaking or breakdown of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication yields the original number, matrix, etc., is known as factorization or factoring in mathematics.
The given polynomial is:
x² - x - 42 = 0
Expand the quadratic equation:
x² + 6x - 7x - 42 = 0
Take the common terms out from the equation:
x(x + 6) - 7(x + 6) = 0
(x - 7)(x + 6) = 0
Hence, the factorization of the polynomial is (x - 7)(x + 6). Option C is the correct answer.
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Suppose that 37% of people have dogs. If two people are randomly chosen, what is the probability that they both have a dog?
Answer:
0.1369
Step-by-step explanation:
(37/100)^2=0.1369
Charles had m yards of material. He used 0.4m yards of material to make a costume, 0.2m yards to make pillows and 0.3m yards to make a bag. Which expression shows how many yards of fabric Charles has left? Check all that apply.
(A) 0.1m
(B) 0.9m
(C) m – 0.9m
(D) (0.4 + 0.2 + 0.3)m
(E) (1 – 0.4 – 0.2 – 0.3)m
(F) m – (0.4 + 0.2 + 0.3)m
(G) m – 0.4m – 0.2m – 0.3m
(H) m – (0.4m + 0.2m + 0.3m) check all that apply
Answer:
(A) [tex]0.1m[/tex](C) [tex]m - 0.9m[/tex](E) [tex](1 - 0.4 - 0.2 - 0.3)m[/tex](F) [tex]m - (0.4 + 0.2 + 0.3)m[/tex](G) [tex]m - 0.4m - 0.2m - 0.3m[/tex](H) [tex]m - (0.4m + 0.2m + 0.3m)[/tex]Step-by-step explanation:
To determine how many yards of fabric Charles has left, we need to subtract the total amount of fabric used for the costume, pillows, and bag from the initial amount of fabric (m yards). The total amount of fabric used is:
[tex]0.4m + 0.2m + 0.3m = 0.9m.[/tex]Now, we can subtract the total used fabric from the initial amount of fabric:
[tex]m - 0.9m[/tex]The correct expressions that show how many yards of fabric Charles has left are:
(A) [tex]0.1m[/tex](C) [tex]m - 0.9m[/tex](E) [tex](1 - 0.4 - 0.2 - 0.3)m[/tex](F) [tex]m - (0.4 + 0.2 + 0.3)m[/tex](G) [tex]m - 0.4m - 0.2m - 0.3m[/tex](H) [tex]m - (0.4m + 0.2m + 0.3m)[/tex]Why are the options correct/incorrect?(A) 0.1m: This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.(B) 0.9m: This option is incorrect because it represents the amount of fabric Charles used, not the amount he has left.(C) m - 0.9m: This option is correct because it represents the initial amount of fabric (m) minus the total amount of fabric used for the costume, pillows, and bag (0.9m), which gives the remaining amount of fabric.(D) (0.4 + 0.2 + 0.3)m: This option is incorrect because it represents the total amount of fabric Charles used to make the costume, pillows, and bag, not the amount he has left, like option (B).(E) (1 - 0.4 - 0.2 - 0.3)m: This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.(F) m - (0.4 + 0.2 + 0.3)m: This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.(G) m - 0.4m - 0.2m - 0.3m: This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.(H) m - (0.4m + 0.2m + 0.3m): This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.Final answerSo, the correct options are (A), (C), (E), (F), (G), and (H).
________________________________________________________
the question is the image
y = 14/11 x is the required equation. Option Cis correct
Direct and indirect variationIf the variable y varies directly with x, this is expressed as:
y = kx
where
k is the constant of proportionality
Given that x = 11 and y = 14, hence;
k = y/x
k = 14/11
Substitute k into the original equation
y = kx
y = 14/11 x
Hence the required equation from the given information is y = 14/11 x
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The height
y
(in feet) of a ball thrown by a child is
y
=
−
1
14
x
2
+
6
x
+
5
where
x
is the horizontal distance in feet from the point at which the ball is thrown.
(a) How high is the ball when it leaves the child's hand?
feet
(b) What is the maximum height of the ball?
feet
(c) How far from the child does the ball strike the ground?
feet
a) The ball is at 5 feet height when it leaves the child's hand
b) The maximum height of the ball is 131 feet
c) 84.825 ft far from the child, the ball strike the ground
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.
(a)
At the beginning when the ball leaves the hand of the child, the horizontal distance was 0, so putting x=0 we can get the height of the ball.
at time zero, t=0, the distance is 5 feet, so the ball is at 5 feet height
(b)
the max occurs at the average of the solutions, which is 28.
or -b/2a = -6/(2*-1/14) = -6/ (-1/7) = 42 ft
-(1/14)*42^2 +6*42 + 5 = 131
so the max height is 131 feet after 42 feet
(c)
(-1/14) x^2 + 6x + 5 =0
x^2 - 84x - 70 = 0 <--- after multiplied by -14
x = 84.825, x = -0.825
the ball will hit the ground at (56 + sqrt(3416)) / 2 = 84.825 ft
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100 POINTS HELP Which account will not appear on a post closing trial balance?
A. accounts payable
B. cash
C. revenue
D. accounts receivable
Answer:
C revenue
Step-by-step explanation:
A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the gpa of male students are µ = 3. 5 and σ = 0. 5. Suppose a random sample of 100 male students is selected and the gpa for each student is calculated. What is the probability that the random sample of 100 male students has a mean gpa greater than 3. 42?
The probability that the random sample of 100 male students has a mean gpa greater than 3. 42 is 0.9452.
What is Standard deviation?A statistic known as the standard deviation is used to describe how volatile or dispersed a group of numerical values is. While a big standard deviation denotes that the values are scattered across a wider range, a low standard deviation indicates that the values tend to be close to the set mean.
From the given information, a scores random sample of 100 male students is selected and the GPA for each student is calculated which follows approximately normal with a mean of 3.5 and standard deviation of 0.5. That is,
µ = 3. 5 and σ = 0. 5
and the random sample of 100 male students has a mean GPA 3.42 is considered.
The z-score value is,
Z=( 3.42-3.5)/ (0.5/√100)
Z= -0.08/0.05
Z=-1.6
The value of z-score is obtained by taking the difference of x and µ. Then the resulting value is divided with the standard deviation by sample size.
The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is obtained below:
The required probability is,
P(X>3.42)=P(z>-1.6)
= 1- P(Z≤-1.6)
From the “standard normal table”, the area to the left of Z=-1.6 is 0.0548.
P(X>3.42)= 1- P(Z≤-1.6)
=1-0.0548
=0.9452
The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is 0.9452.
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2x - (-4x + 5b). x = 2. b = -5
Answer:
37
Step-by-step explanation:
2x - (-4x + 5b); x = 2; b = -5
2(2) - (-4 × 2 + 5 (-5)) = 4 - (-8 - 25) = 37
Identify the solution to the system of linear equations.
y = -3x + 2
y = x - 6
A. (2, -4)
B. (4, -2)
C. (0, 2)
D. (1, -1)
The system of linear equations is solved by finding x = 2 and y = -4, making the solution (2, -4).
To find the solution to the system of linear equations,
find the values of x and y that satisfy both equations simultaneously.
The equations are,
y = -3x + 2
y = x - 6
To find the solution, set the right-hand sides of both equations equal to each other:
-3x + 2 = x - 6
Now, let's solve for x:
-3x - x = -6 - 2
-4x = -8
x = -8 / -4
x = 2
Now that the value of x, we can find y by substituting x back into one of the equations.
Let's use the second equation:
y = 2 - 6
y = -4
Therefore, the solution to the system of linear equations is equal to option A. (2, -4).
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What is the probability of flipping a coin 11 times and getting heads 4 times? Round your answer to the nearest tenth of a percent. O A. 8.1% O B. 22.6% O C. 16.1% ) D. 0.5%
Answer:
The answer is (A) 8.1%.
Step-by-step explanation:
The probability of flipping a coin and getting heads is 1/2 or 0.5. Assuming the coin is fair, the probability of getting heads 4 times in 11 flips is given by the binomial probability formula:
P(4 heads in 11 flips) = (11 choose 4) * (0.5)^4 * (0.5)^(11-4) = 330 * 0.5^11
Using a calculator, we get:
P(4 heads in 11 flips) ≈ 8.1%
Therefore, the answer is (A) 8.1%.
A sequence $\{a_n\}$ satisfies $a_1 = 1$ and
\[a_n = \frac{a_{n - 1}}{1 + a_{n - 1}}\]for all $n \ge 2.$ Find $a_{10}.$
The sum of the given series is -
6 ∑{1/(2n + 1)² - 1}.
What is integration?Integration is a process of adding up small elemental volumes to find the larger volume.
Given is the series as -
6/(3² - 1) + 6/(5² - 1) + 6/(7² - 1) + ....
The given series is -
S = 6/(3² - 1) + 6/(5² - 1) + 6/(7² - 1) + ....
S = 6{1/(3² - 1) + 1/(5² - 1) + 1/(7² - 1) + ....}
S = 6 ∑ {1/(2n + 1)² - 1}
Therefore, the sum of the given series is -
6 ∑{1/(2n + 1)² - 1}.
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The measures of the angles of △ABC are given by the expressions in the table.
The angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.
Define triangles.A triangle is a closed geometric shape with three sides, three angles, and three line segments. Three non-collinear points are joined by line segments to create the simplest polygon, which has three non-collinear points.
Triangles can be categorized according to the size of their sides and angles. Triangles can be categorized as equilateral (all sides are equal in length), isosceles (both sides are equal in length), or scalene based on their sides (all sides are different in length). Triangles can be categorized as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is greater than 90 degrees) (one angle is exactly 90 degrees).
In any triangle, the sum of the three interior angles is always 180 degrees. Therefore, we can write:
a + b + c = 180
Substituting the given values, we get:
(6x-1) + 20 + (x+14) = 180
Simplifying and solving for x, we get:
7x + 33 = 180
7x = 147
x = 21
Now that we have the value of x, we can substitute it back into the expressions for the angles to find their values:
angle a = (6x-1) = (6*21-1) = 125 degrees
angle b = 20 degrees
angle c = (x+14) = (21+14) = 35 degrees
Therefore, the angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.
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-3/4 cubed as a fractoin
Answer:
-27/64 or -0.4219
Step-by-step explanation:
What is a fraction?A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
To solve this, we can take the numerator and denominator, and cube them.
3 × 3 × 3 = 274 × 4 × 4 = 64The new fraction is now [tex]-\frac{27}{64}[/tex].
Therefore, [tex]-\frac{3}{4}[/tex] cubed as a fraction is [tex]-\frac{27}{64}[/tex].
The expression as a fraction is -27/64.
We have,
Expression:
(-3/4)³
This can be written as,
-3³ / 4³
Now.
Simplifying each term.
-3³ = -3 x -3 x -3 = -27
4³ = 4 x 4 x 4 = 64
Now,
(-3/4)³ = -27/64
Thus,
The expression as a fraction is -27/64.
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1. we have to buy flat bar length=1ft.that is 2pesos per cm.how much money we need to buy for that flat bar?
Answer: One foot is equal to 12 inches, and since 1 inch is equal to 2.54 centimeters, we have:
1 foot = 12 inches = 12 x 2.54 cm = 30.48 cm
So the length of the flat bar is 30.48 cm. Multiplying this length by the price per cm, we get:
30.48 cm x 2 pesos/cm = 60.96 pesos
Therefore, we need 60.96 pesos to buy a flat bar of length 1 foot at a price of 2 pesos per cm.
Step-by-step explanation:
A boy drops his toy car from the top floor of his house. The time it takes for the toy to fall from a height of 13 feet is given by the equation
h=94−16t^2, where t is the time in seconds. Determine the time it takes the toy to fall to the bottom floor.
It takes the toy car 2.43 seconds to fall to the bottom floor, answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.
Describe Equation?An equation is a mathematical statement that asserts that two expressions are equal. An equation consists of two sides, the left-hand side and the right-hand side, separated by an equal sign (=).
For example, 2x + 5 = 11 is an equation, where the left-hand side is 2x + 5 and the right-hand side is 11. This equation asserts that the expression 2x + 5 is equal to 11, and the value of x can be determined by solving for x.
Equations can be simple or complex, and they can involve one or more variables. They can also be linear or nonlinear, depending on the nature of the expressions involved.
Solving an equation involves finding the values of the variables that make the equation true. This may involve applying algebraic operations and simplification techniques to isolate the variable on one side of the equation.
Equations are used in many areas of mathematics, science, engineering, and economics, and they provide a powerful tool for modeling and analyzing real-world situations. They are also used extensively in computer programming and cryptography, where they play a critical role in the development of algorithms and data encryption methods.
We have the equation [tex]h = 94 - 16t^2[/tex], where h is the height of the toy car in feet and t is the time in seconds.
When the toy car reaches the bottom floor, its height will be h = 0. So we can set the equation equal to 0 and solve for t:
[tex]0 = 94 - 16t^216t^2 = 94t^2 = 94/16[/tex]
[tex]t = \sqrt{(94/16)} = \sqrt{(23.5/4)} = 2.43 seconds[/tex] (rounded to two decimal places)
Therefore, it takes the toy car 2.43 seconds to fall to the bottom floor.
The closest answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.
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