Answer:
B) 1/8
Step-by-step explanation:
each child born has 50/50 to be a boy or a girl, so, we determine a Bernoulli process where p=0.5, and we need 3 out of 3 successes.
the probability will then be:
(0.5)³=0.125=1/8
Need answers asap please
The inverse of a function is n(a) = (a+30)/3 option (A) is correct by using the concept of the inverse of a function.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
a(n) = 3n - 30
To find make subject n and solve
a(n) + 30 = 3n
[tex]\rm n = \dfrac{a(n) + 30}{3}[/tex]
Plug n = n(a) and a(n) = a
[tex]\rm n(a) = \dfrac{a + 30}{3}[/tex]
Thus, the inverse of a function is n(a) = (a+30)/3 option (A) is correct by using the concept of the inverse of a function.
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Sum to n terms of each of following series. (a) 1 - 7a + 13a ^ 2 - 19a ^ 3+...
Notice that the difference in the absolute values of consecutive coefficients is constant:
|-7| - 1 = 6
13 - |-7| = 6
|-19| - 13 = 6
and so on. This means the coefficients in the given series
[tex]\displaystyle \sum_{i=1}^\infty c_i a^{i-1} = \sum_{i=1}^\infty |c_i| (-a)^{i-1} = 1 - 7a + 13a^2 - 19a^3 + \cdots[/tex]
occur in arithmetic progression; in particular, we have first value [tex]c_1 = 1[/tex] and for [tex]n>1[/tex], [tex]|c_i|=|c_{i-1}|+6[/tex]. Solving this recurrence, we end up with
[tex]|c_i| = |c_1| + 6(i-1) \implies |c_i| = 6i - 5[/tex]
So, the sum to [tex]n[/tex] terms of this series is
[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 \underbrace{\sum_{i=1}^n i (-a)^{i-1}}_{S'} - 5 \underbrace{\sum_{i=1}^n (-a)^{i-1}}_S[/tex]
The second sum [tex]S[/tex] is a standard geometric series, which is easy to compute:
[tex]S = 1 - a + a^2 - a^3 + \cdots + (-a)^{n-1}[/tex]
Multiply both sides by [tex]-a[/tex] :
[tex]-aS = -a + a^2 - a^3 + a^4 - \cdots + (-a)^n[/tex]
Subtract this from [tex]S[/tex] to eliminate the intermediate terms to end up with
[tex]S - (-aS) = 1 - (-a)^n \implies (1-(-a)) S = 1 - (-a)^n \implies S = \dfrac{1 - (-a)^n}{1 + a}[/tex]
The first sum [tex]S'[/tex] can be handled with simple algebraic manipulation.
[tex]S' = \displaystyle \sum_{i=1}^n i (-a)^{i-1}[/tex]
[tex]\displaystyle S' = \sum_{i=0}^{n-1} (i+1) (-a)^i[/tex]
[tex]\displaystyle S' = \sum_{i=0}^{n-1} i (-a)^i + \sum_{i=0}^{n-1} (-a)^i[/tex]
[tex]\displaystyle S' = \sum_{i=1}^{n-1} i (-a)^i + \sum_{i=1}^n (-a)^{i-1}[/tex]
[tex]\displaystyle S' = \sum_{i=1}^n i (-a)^i - n (-a)^n + S[/tex]
[tex]\displaystyle S' = -a \sum_{i=1}^n i (-a)^{i-1} - n (-a)^n + S[/tex]
[tex]\displaystyle S' = -a S' - n (-a)^n + \dfrac{1 - (-a)^n}{1 + a}[/tex]
[tex]\displaystyle (1 + a) S' = \dfrac{1 - (-a)^n - n (1 + a) (-a)^n}{1 + a}[/tex]
[tex]\displaystyle S' = \dfrac{1 - (n+1)(-a)^n + n (-a)^{n+1}}{(1+a)^2}[/tex]
Putting everything together, we have
[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 S' - 5 S[/tex]
[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 \dfrac{1 - (n+1)(-a)^n + n (-a)^{n+1}}{(1+a)^2} - 5 \dfrac{1 - (-a)^n}{1 + a}[/tex]
[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} =\boxed{\dfrac{1 - 5a - (6n+1) (-a)^n + (6n-5) (-a)^{n+1}}{(1+a)^2}}[/tex]
12. A bag contains 12 red, 9 green and 5 black markers. If Cooper randomly selects 7 markers, how many
ways could this be done if EXACTLY 6 are to be the same color?
Answer:
Step-by-step explanation:
7 marks
6 same colors
from 12 red 6 same exactly the same
12 x 11 x 10 x 9 x7 x6
1 remainig
from 9 green 6 saem exactly the same
9 x 8 x 7 x 6 x5 x4
1 remaining
add the results above to get your final answer
26 markers in total
6 to be chosen of the same color from 7
Eric recorded the number of automobiles that a used car dealer in his town sold in different price ranges. From the Histogram given, what is the number of cars sold for the price range of $4000 to $4999? A. 15 B. 20 C. 30 D. 50
The correct answer is option A which is the number of cars sold for the price range of $4000 to $4999 will be 15.
What is a histogram?
A histogram is a graph for the representation of the data on the plot of the rectangular boxes. It has the data sets on the horizontal and the vertical axes.
As we can see from the histogram data we will conclude that the price range of $4000 to $4999 is shown by the third block and this third block reaches the height of 15.
Therefore the correct answer is option A which is the number of cars sold in the price range of $4000 to $4999 will be 15.
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Choose the equation that satisfies the data in the table.
[xy−100−41−8]
A. y=−4x−4
B. y=−14x+4
C. y=4x−4
D. y=14x+4
The linear equation that satisfy the data in the table is: A. y = −4x − 4.
How to Find the Linear Equation for a Data in a Table?Given the table attached below, find the slope (m) = change in y / change in x using two pairs of values, say, (-1, 0) and (0, -4):
Slope (m) = (-4 - 0)/(0 - (-1)) = -4/1 = -4
Find the y-intercept (b), which is the value of y when x = 0. From the table, when x = 0, y = -4.
b = -4.
Substitute m = -4 and b = -4 into y = mx + b
y = -4x + (-4)
y = -4x - 4
The equation that satisfy the data is: A. y = −4x − 4.
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A chain weighs 12 pounds per foot. How many ounces will 7 inches weigh?
Answer:
The chain of the length 7 inches weighs 112 ounces.
Step-by-step explanation:
As we know there are 12 inches in a foot and 16 ounces in a pound
That is 1 foot = 12 inches.
and 1 pound = 16 ounces.
Given that the weight of the chain that is 1 foot long = 12 pounds
So weight of the chain per inch is = 12/12
which is equal to 1 pound
and according to the formula 1 pound = 16 ounces
So weight of the chain per inch is = 16 ounces
therefore weight of the chain that is 7 inch long = 7 × 16
that is 112 ounces.
The chain of the length 7 inches weighs 112 ounces.
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Which is not a solution of sin 20 = 1?
A = 90
B = 45
C = 225
D = - 135
Unas deportivas cuestan $600 he visto que hay una rebaja del 20% cuánto dinero rebajado las reporteras
Answer:
600/100*20=6*20=120
600-120=480$
(a) 3.1563x106
(b) 5.65x10-4 convert to usual form
Answer:
[tex](a) \: 3.1563 \times {10}^{6} = 31563 \times {10}^{6} \times {10}^{ - 4} = 31563 \times {10}^{6 - 4} = 31563 \times {10}^{2} = 3156300[/tex]
__o__o__
[tex](b) \: 5.65 \times {10}^{ - 4} = 565 \times {10}^{ - 4} \times {10}^{ - 2} = 565 \times {10}^{ - 4 - 2} = 565 \times {10}^{ - 6} = 0.000565[/tex]
what is the domain and range of this graph
Answer:
Domain: All real number
Range: y≤-4
Help me please help help
[tex]\angle P = \angle S \Rightarrow \angle S = 42 &^\circ\\\angle Q = \angle T \Rightarrow \angle S = 86 &^\circ\\\angle R = \angle U\\[/tex]
Sum of all angles in a triangle equals 180:
[tex]\angle R = 180 - (86 + 42) = 180 - 128 = 52[/tex]
Answer:
[tex]U = 52 &^ \circ[/tex]
BRAIN WARM UP MATHS?
We can make 64 different equations using the power of ten.
What is the power of a number?The power of a number identifies how many times that particular number is multiplied by itself.
Here, let us assume that the different equations = x
Using a power of 10, we have 10x making a total of 640.
10x = 640Divide both sides by 10
10x/10 = 640/10
x = 64
Therefore, we can conclude that we can make 64 different equations using the power of ten.
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Solve the system of equations : y = x/2 , y = -x - 3 . You can use any method you wish for solving systems of equations. Check your answer.
Answer:
x=−2 and y=−1
Step-by-step explanation:
Problem:
Solve y=x2;y=−x−3
Steps:
I will solve your system by substitution.
y=1/2x;y=−x−3
Step: Solve y= 1/2x for y:
Step: Substitute 1/2 x for y in y=−x−3:
y=−x−3
1/2x= =−x−3
1/2x+x=−x−3+x(Add x to both sides)
3/2x = -3
3/2x/3/2 = -3/3/2 (Divide both sides by 3/2)
x=−2
Step: Substitute −2 for x in y=1/2x:
y=1/2x
y=1/2(-2)
y=−1(Simplify both sides of the equation)
Answer:
x=−2 and y=−1
Simplify the following expression. (2x − 1)(3x + 2) Simplify the following expression . ( 2x − 1 ) ( 3x + 2 )
Acontinous random variable X has a pdf given by p(x) = (5x4 0≤x≤1 0, otherwise) Let Y=X3. Find the probability distribution function
I'll use the method of transformations.
If [tex]f_X(x)[/tex] denotes the PDF of [tex]X[/tex], and [tex]y=g(x)=x^3 \iff x=g^{-1}(y) = y^{1/3}[/tex], we have
[tex]f_Y(y) = f_X\left(g^{-1}(y)\right) \left|\dfrac{dg^{-1}}{dy}\right|[/tex]
[tex]\dfrac{dg^{-1}}{dy} = \dfrac13 y^{-2/3}[/tex]
[tex]\implies f_Y(y) = f_X\left(y^{1/3}\right) \left|\dfrac13 y^{-2/3}\right| = \boxed{\begin{cases} \dfrac53 y^{2/3} & \text{if } 0 \le y \le 1 \\ 0 & \text{otherwise} \end{cases}}[/tex]
Which values of x and y would make the following expression represent a real number?
(4 +51)(x + yı)
O x = 4, y =
O x=-4, y = 0
Ox = 4, y = -5
O x = 0, y = 5
The values of x and y would make the following expression represent a real number is 4 and -5 respectively
Complex and real numberThe standard form of writing a complex number is given asl
z= x + iy
where
x is the real part
y is the imaginary part
Given the expression below;
(4 +5i)(x + yi)
Expand
4x + 4yi + 5ix + 5y(-1)
4x + 4yi + 5ix - 5y
Hence the values of x and y would make the following expression represent a real number is 4 and -5 respectively
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The point A(0,3) and point B(4,19) lie on the line L.
Find the equation of line L
Answer: The equation is y = 4x+3
Slope = 4
y intercept = 3
========================================================
Explanation:
Let's start off by finding the slope.
[tex]A = (x_1,y_1) = (0,3) \text{ and } B = (x_2,y_2) = (4,19)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{19 - 3}{4 - 0}\\\\m = \frac{16}{4}\\\\m = 4\\\\[/tex]
The slope is 4.
The y intercept is 3 because of the point (0,3)
We go from y = mx+b to y = 4x+3
m = slope
b = y intercept
---------------
Check:
Plug in x = 0 and we should get to y = 3
y = 4x+3
y = 4(0)+3
y = 0+3
y = 3
That works out. Now try x = 4. It should lead to y = 19
y = 4x+3
y = 4(4)+3
y = 16+3
y = 19
The answer is confirmed.
what is the sum of the series
Answer: 925
Step-by-step explanation:
This is an arithmetic series with first term 1 and last term 3(25)-2=73, with a total of 25 terms.
Using the sum of an arithmetic series formula, we get the sum is:
[tex]\frac{25}{2}(1+73)=\boxed{925}[/tex]
If 6^(2x)=4 find 36^(6x-2) could anyone help me please?
Answer:
3.160
Step-by-step explanation:
You can solve for x using logarithm.
Rewrite in logarithm form
[tex]log_{6}4=2x\\\\x=\frac{log_64}{2}\\x=\frac{\frac{log4}{log6}}{2}\\x=\frac{log4}{log6} * \frac{1}{2}\\x=\frac{log4}{log6 * 2}\\x\approx0.386852807\\36^{6(0.386852807)-2} \approx3.160[/tex]
Is 3.5 greater than 3.39
Answer:
yes
Step-by-step explanation:
which ordered pair is a solution to the following system of inequalities
Answer:
it's 1,1 is the correct ans
Step-by-step explanation:
Because my teacher told its absolutely correct answer I got the same question in exam
Answer:
the answer should be the 2 one
Step-by-step explanation:
I got it right just had it.
What is the surface area of the figure? 9 ft 9 ft 15 ft 15 ft 4 ft
The surface area of the given composite figure is; 528 ft²
How to find the area of a composite figure?To get the surface area of the attached composite shape, we will have to break the object down into smaller shapes to get;
Surface area 1 = 2(15 * 4) = 120 ft²
Surface area 2 = 2(9 * 4) = 72 ft²
Surface area 3 = 2(6 * 4) = 48 ft²
Surface area 4 = 2((15 * 15) - (9 * 9)) = 288 ft²
Thus;
Total surface area = 120 + 72 + 48 + 288
Total surface area = 528 ft²
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Need help with algebra homework
Answer:
the answer for this problem is A, big
Which of the following best describes the set of complex numbers?
OA. The set of all numbers of the form a+bi, where a and bare any
real numbers and i equals -1
B. The set of all numbers of the form abi, where a and bare any real
numbers and i equals 1
C. The set of all numbers of the form a+bi, where a and b are any
real numbers and i equals √-1
OD. The set of all numbers of the form abi, where a and b are any real
numbers and / equals -1
Answer:
C
Step-by-step explanation:
The correct statement is option C.
What is complex number?A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively. Additionally, i = √-1 and both a and b are real numbers.
Since we know that
Complex number is of the form a+ib
Where,
a is real number belongs to real axis
And b is also a real number belongs to imaginary axis.
And the value of i = √-1
Thus,
The set of all numbers of the form a+bi, where a and b are any
real numbers and i equals √-1 is the correct statement.
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Help me with this piecewise function!
Answer:
According to the given function, the value of h(-1) is -1, h(-0.5) is 0 and h(1) is 1.
Step-by-step explanation:
The given function says that:
If the range of the values of x is x∈(-2,-1], then the value of the function is -1.
If the range of the values of x is x∈(-1,0], then the value of the function is 0.
If the range of the values of x is x∈(0,1], then the value of the function is 1.
If the range of the values of x is x∈(1,2], then the value of the function is 2.
In the first case, we have x = -1. This satisfies the first condition. So accordingly, the value that the function will give is -1.
In the second case, we have x = -0.5. This satisfies the second condition. So accordingly, the value that the function will give is 0.
In the third case, we have x = 1. This satisfies the third condition. So accordingly, the value that the function will give is 1.
So, h(-1) = -1, h(-0.5) = 0 and h(1) = 1.
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hi can you please help me with this question.
I need explanation too.
I'll like and rate your answer if your answer is right.
0 like and 1 rate for nonsense answer.
0 like and 2 rate if it's incorrect.
0 like and 3 rate if it is un-answer
1 like and 4 rate if it's correct a bit
1 like and 5 rate if it's very good answer.
Answer:
It appears to already be solved. What do you need help with?
Step-by-step explanation:
A chopstick model of a catapult launches a marshmallow in a classroom. The path of the marshmallow can be modeled by the quadratic y=−0.07x2+x+2.2,
where y represents the height of the marshmallow, in feet,
and x represents the horizontal distance from the point it is launched, in feet.
When the marshmallow hits the ground, what is its horizontal distance from the point where it was launched?
The horizontal distance from the point where it was launched is 7.143.
We have given that,
The path of the marshmallow can be modeled by the quadratic y=−0.07x^2+x+2.2,
x represents the horizontal distance from the point it is launched, in feet.
What is the horizontal distance?Horizontal distance means the distance between two points measured at a zero percent slope.
(1) Put x = 7.143 in given equation
y= -0.07(7.143)^2+7.143+2.2
y= 2.2
y= 5.771
We have to determine the what is its horizontal distance from the point where it was launched.
The value of x is called horizontal distance.
Therefore the horizontal distance from the point where it was launched is 7.143.
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Over what interval is the function in this graph increasing? A. –5 ≤ x ≤ 5 B. –3 ≤ x ≤ 2 C. –4 ≤ x ≤ –2 D. –2 ≤ x ≤ 3
The function in this graph is increasing in the interval –2 ≤ x ≤ 3 , Option D is the right answer.
What is a function ?A function is a mathematical statement used to relate a dependent and an independent variable.
From the graph it can be seen that the graph is increasing in the interval
–2 ≤ x ≤ 3
The graph is said to be increasing when the value of y is getting more and more positive
As –2 ≤ x ≤ 3 , y varies from -3 to +3
Therefore Option D is the right answer.
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Answer:
–2 ≤ x ≤ 3
Step-by-step explanation:
a) Construct a 95% confidence interval for the average test score for Delhi students. (1 Mark)
(b) Is there statistically significant evidence that Delhi students per form differently than other students in India? (1 Mark)
(c) Another 503 students are selected at random from Delhi. They are given a 3-hour preparation course before the test is administered. Their average test score is 1019, with a standard deviation of 95. Construct a 95% confidence interval for the change in average test score associated with the preparation course. (2 Marks)
(d) Is there statistically significant evidence that the preparation course helped? (1 Mark)
The solution to all the answers are given below.
The complete question includes
Grades on a standardized test are known to have a mean of 1,000 for students in the Delhi. 453
randomly selected Delhi students take the test, yielding sample mean of 1,013 and sample standard
deviation (s) of 108.
What is Confidence Interval ?It is given by
Confidence Interval for 95% confidence Interval is given by
[tex]\rm Z = X \pm 1.96 \dfrac{\sigma}{\sqrt{n}}[/tex]
(a) Construct a 95% confidence interval for the mean test score for Delhi students.
The confidence interval is given by
[tex]\rm 1,013 \pm 1.96 \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]\rm 1,013 \pm 1.96 \dfrac{108}{\sqrt{453}}[/tex]
1013 ± 5.07
so the interval is [1003.06,1022.94]
(b)Yes, since the null of no difference is rejected at the 5% significance level (interval excludes Delhi sample mean of 1,013)
(c) Another 503 Delhi students are randomly selected to take a 3-hour prep course and then give the test. Their average score is 1,019 with a standard deviation of 95.
The standard deviation now is
[tex]\rm \sqrt{\dfrac{95^2}{453} + \dfrac{108^2}{503}}[/tex]
= 6.61
The interval is given by
[tex](1,019-1,013) \pm 1.96 \dfrac{\sigma}{\sqrt{n}}[/tex]
= [-7,+19]
(d) No, the interval includes 0, the null difference between the two populations
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i need help with this geometry question
Answer:
radius ≈ 15.5
Step-by-step explanation:
the radius is RS
the angle between a tangent and the radius at the point of contact is 90°
then Δ RST is a right triangle
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then
RS² + ST² = RT² ( substitute values )
RS² + 7² = 17²
RS² + 49 = 289 ( subtract 49 from both sides )
RS² = 240 ( take square root of both sides )
RS = [tex]\sqrt{240}[/tex] ≈ 15.5 ( to 1 dec. place )
