One day, thirteen babies are born at a hospital. Assuming each baby has an equal chance of being a boy or girl, what is the probability that at most eleven of the thirteen babies are girls?A. 11/64B. 4089/4096C. 29/128D. 743/1024
Answers
Step 1: Using the theorem of binomial distribution
\(^nC_r(p)^{n-r}q^r\)n = 13
p = probability that the baby is a girl
q = probability that the baby is not a girl
Step 2: To find the probability that most eleven of the thirteen babies are girls
= 1 - [(probability that exactly twelves girls) + (probability that exactly thirteen girls)]
Step 3: Get the value of p and q
\(\begin{gathered} \text{Probability that it is a girl p = }\frac{1}{2} \\ \text{Probability that it is not a girl q = }\frac{1}{2} \end{gathered}\)Step 4: Find the probability that at most eleven of the thirteen babies are girls.
\(\begin{gathered} =^{}1-(^{13}C_{12}(\frac{1}{2})^{13-12}(\frac{1}{2})^{12}^{}+^{13}C_{13}(\frac{1}{2})^{13-13}(\frac{1}{2})^{13}) \\ ^nC_r\text{ = }\frac{n!}{(n-r)!r!} \end{gathered}\)Step 5: Simplify the expression
\(\begin{gathered} =\text{ 1 - }\lbrack13\text{ }\times\text{ (}\frac{1}{2})^1(\frac{1}{2})^{12}\text{ + 1 x (}\frac{1}{2})^0(\frac{1}{2})^{13}\rbrack \\ =\text{ 1 - \lbrack 13 }\times\frac{1}{2}\text{ }\times\text{ }\frac{1}{4096}\text{ + 1 }\times\text{ 1 }\times\text{ }\frac{1}{8192}\rbrack \\ =\text{ 1 - }\frac{13}{8192}\text{ - }\frac{1}{8192} \\ =\text{ 1 - }\frac{14}{8192} \\ =\text{ }\frac{8192\text{ - 14}}{8192} \\ =\text{ }\frac{8178}{8192} \\ To\text{ the lowest term} \\ =\text{ }\frac{4089}{4098} \end{gathered}\)Option B is the correct answer
Related Questions
(3, 4, 5, ...} is finite or infinite
Answers
The given set is (3, 4, 5, ...} is infinite set.
A set with an infinite number of elements is one that cannot be numbered. A set that has no last element is said to be endless. A set that can be put into a one-to-one correspondence with a suitable subset of itself is said to be infinite. No issue with the in-class assignment.
The stars in the clear night sky, water droplets, and the billions of cells in the human body are just a few examples of endless sets of objects that surround us. A set of natural numbers, however, serves as the best illustration of an infinite set in mathematics. There is no limit to the amount of natural numbers.
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Evaluate the expression.
52−4⋅6+11
Answers
Answer:
58.4
Step-by-step explanation:
52-4= 48
48-0.6= 47.4
47.4+11= 58.4
Plz mark as brainliest! Hope this helps!!!! :)
helpp hurrryyyyyyyyyy
Answers
Answer:
N=10
Step-by-step explanation:
Please help answer I’m having trouble
Answers
Answer:
(1, 0.5)
Step-by-step explanation:
i just used order of operations calculator
Solving the equation with elimination method, I got x=1, y= 1/2
Pair (1.00, 0.50)
answer the question submitted
Answers
The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.
To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:
Step 1: Divide the coefficient of x by 2 and square the result.
(Coefficient of x) / 2 = -28/2 = -14
(-14)² = 196
Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.
g(x) = 4x² - 28x + 49
= 4x² - 28x + 196 - 196 + 49
Step 3: Rearrange the terms and factor the perfect square trinomial.
g(x) = (4x² - 28x + 196) - 196 + 49
= 4(x² - 7x + 49) - 147
= 4(x² - 7x + 49) - 147
Step 4: Write the perfect square trinomial as the square of a binomial.
g(x) = 4(x - 7/2)² - 147
Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.
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The probable question may be:
Rewrite the function by completing the square.
g(x)=4x²-28x +49
g(x)= ____ (x+___ )²+____.
The AREA of a rectangle is the product of length and width.
Write a simplified expression for the AREA of the rectangle below.
X
Answers
Answer:
x^2 + 6x
Step-by-step explanation:
A = lw
l = x + 6
w = x
Plug in values
(x + 6) × x = x^2 + 6x
There are 25 households in purok 2 of barangay Sta. Catalina. The barangay captain ordered 40 sacks of rice
weighing 30 kg each. How many kilograms of rice will each household receive?
Answers
9514 1404 393
Answer:
48 kg
Step-by-step explanation:
(40 sacks)×(30 kg/sack)/(25 households) = (1200/25) kg/household
= 48 kg/household
Each household will receive 48 kg of rice.
find the vertices of this hyperbola 36x^2-y^2-216x+10y+261=0
Answers
The required vertices of hyperbola is given as (3, 5±√38).
What is an hyperbola?Hyperbola is part of conic section, and its equation is given as,
\((x - h)^2/a^2 + (y - k)^2/b^2 = 1\), where h,k is center and a and b are the lengths of the semi-major and the semi-minor axes.
Here,
Given equation of hyperbola,
36x²-y^²-216x+10y+261=0
Equation of hyperbola in vertex form is given as,
(x - 3)²/(19/18) - (y - 5)²/38 = 1
From above equation,
h = 3 k = 5 a = √38/6 and b = √38
Vertices of the hyperbola is given as,
(h, k ± b) = (3, 5±√38)
Thus, the required vertices of hyperbola is given as (3, 5±√38).
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Identify the number line that correctly displays the solution x ≥ 3.
Answers
The correct number line that displays the solution `x ≥ 3` would be:
<------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------|------>
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
●------------------------------------------------>
The solution `x ≥ 3` is an inequality that means x is greater than or equal to 3. To graph this inequality on the number line, we mark the point representing the value 3 with a closed circle on the number line and draw an arrow pointing to the right to indicate that all values greater than or equal to 3 satisfy the inequality.
The closed circle at 3 indicates that 3 is included in the solution set, and the arrow to the right indicates that all values greater than 3 also satisfy the inequality. Therefore, any value of x that is equal to or greater than 3 would be considered a solution to the inequality `x ≥ 3`.
It is important to note that if the inequality was `x > 3` (without the equal sign), the closed circle at 3 would be changed to an open circle, indicating that 3 is not included in the solution set, and only values greater than 3 would be considered solutions. In conclusion, the number line provided above correctly displays the solution `x ≥ 3`.
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An investment portfolio is shown below.
Investment Amount Invested ROR
Money Market Account $3,200 2.1%
Government Bond $1,750 4.4%
Preferred Stock $1,235 −7.8%
Common Stock $2,300 10.5%
Using technology, calculate the difference between the arithmetic average ROR and the weighted average ROR. Round to the nearest tenth of a percent.
0.5%
1.1%
2.3%
3.5%
Answers
Using technology, the difference between the arithmetic average ROR and the weighted average ROR is 0.52%
What is arithmetic mean?The Arithmetic Mean will be called the Simple Arithmetic Mean when it is calculated as the quotient between the sum of all the different related values and the number of observations involved in this sum.
Given An investment portfolio
Since arithmetic average ROR:
The average arithmetic average ROR is the sum of the rate of returns divided by the number of investments arithmetic average:
ROR = (2.1%+ 4.4%+ 7.8% + 0.5%)/4
arithmetic average ROR=6.20%
total amount invested=$3200+$1750+$1235+$2,300
total amount invested=$8,485
weighted average:
ROR = (3200/8485 * 2.1%+ 1750/8485 * 4.4%+ 1235/8485 *7.8% + 2300/8485 *0.5%)
weighted average:
ROR=5.68%
difference=6.20%-5.68%
difference=0.52%
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Answer: it’s 1.1%
Step-by-step explanation: just got it right on the test
Jevon has joined a gym. The membership has an initial fee of $50.00 and costs $10.00 per month
This table shows the linear relationship between the total cost, y, and the number of months Jevon is a member of the gym, X.
Fill in each box to correctly model the relationship between x and y.
Months, x
5
10
20
Total cost, y
25
$100.00
$
$200.00
$
$300.00
Answers
Answer: Months, x : 15 Total cost, y: $150.00 and $250.00
Step-by-step explanation:
The amount should be like Months, x : 15 Total cost, y: $150.00 and $250.00
Important information: The membership has an initial fee of $50.00 and costs $10.00 per monthThis table shows the linear relationship between the total cost, y, and the number of months Jevon is a member of the gymCalculation:The months should be 15
Total cost should be $150 and $250
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What solid will this lesson focus on?A- rectangular solidB- coneC- regular square pyramidD- triangular prism
Answers
Solid will this lesson focus on the regular square pyramid
Regular square pyramid.
The justification is stated below:
Four triangular faces, five vertices, and eight edges make up the typical square pyramid's square base. The main formulae for a square pyramid are volume and surface area.
By definition, a regular square pyramid is one that has a base that is square, meaning that each of its sides is the same length.
Because it has an apex, a height, lateral faces that are congruent isosceles triangles, and slant height, you can tell that it is a pyramid (the altitude of the lateral faces).
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Helpppppppppppppppppppppppppppp
Answers
Answer:
5
Step-by-step explanation:
4^2+3^2
=16+9=25
\(\sqrt{25}\)=5
Hope that helps
Please helpppppppppppppp <3
Answers
First attached in this order:
The 1st one
the 3rd one
The 4th one
The 2nd one
Step by-step explanation:
I'll write the answer in the comments for the 2nd attachment.
Answer:
Part 1: -10, -5, 0, 8 Part 2: -3/2, -15%, 0.80, 143%, 2 1/4
Step-by-step explanation:
Part 1: The lower the number, the lower the temperature
Part 2: Convert the fractions into decimals
2 1/4 = 2.25
-15% = -0.15
143% = 1.43
-3/2 = -1.5
0.80 = 0.80
The order from least to greatest is -3/2, -15%, 0.80, 143%, 2 1/4
Hope this helps :)
find the cardinality of x , if x={-n,...,-2,-1,0,1,.....n}
Answers
Cardinality is the number of elements in a given mathematical set.
In this set,the cardinality is 2n + 1
Explanation the n is a certain number and also in this set it has both negative and positive n
Before the number of elements in this set excluding one (which is 0 is 2n then the other one is added
Hence the cardinality is 2n + 1
What is the meaning of "the notion of finiteness"?
Answers
The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.
In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.
In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.
This concept is essential to the development of computer programs that are efficient, reliable, and secure.
In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.
In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.
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21. Which statement is a good definition?
Right angles are angles formed by two intersecting lines.
Skew lines are lines that do not intersect.
A
square is a rectangle with four congruent sides.
Parallel lines are lines that do not intersect.
Answers
The statement that is a good definition is D. Parallel lines are lines that do not intersect.
How to illustrate the information?A type of quadrilateral with all sides being equal and all angles being 90 degrees is a square.
Lines that do not cross each other but have a constant perpendicular distance are known as parallel lines. Right angles and skew lines are perpendicular to one another but not parallel. Therefore, a square is a type of rectangle in which all four sides are parallel to one another.
Therefore, based on the information, the correct option is D
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PLEASE PLEASE HELP
5. Renae Walters is paid a salary of $15,000 per month.
a. How much has she earned for the year after being paid at the end of January? _______________________________
b. How much is deducted in January for Social Security? For Medicare?
Social Security _____________________ Medicare _______________________
c. How much has she earned for the year after being paid at the end of November? ___________________________________
d. How much is deducted in November for Social Security? For Medicare?
Social Security _____________________ Medicare _______________________
e. How much has she earned for the year after being paid at the end of December? ___________________________________
f. How much is deducted in December for Social Security? For Medicare?
Social Security _____________________ Medicare _______________________
Answers
The amount for social security for all 3 months will $930 and the contribution for Medicare will be $217.5.
How to estimate the amount for social security for all 3 month?Given that the salary exists paid in US dollars, we can consider that Renae Walters falls under the social security and Medicare tax rates for the United States. These rates, as of 2020, fall at 6.2% for social security and 1.45% for Medicare.
Social security contribution = Social security tax rate × Income earned
January for example Social Security = 0.062 × $15,000 = $930
Medicare contribution = Medicare tax rate × Income earned
January for example Medicare = 0.0145 × $15,000= $217.5
The above method will apply through the months without changes.
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e
B
0
14. The table shows the number of inches of
rain over five months. What would be an
appropriate display of the data? Explain.
(Lesson 2)
Month
Number
of Inches
of Rain
Jan. Feb. Mar.
1.5
2.2
3.6
Apr.
5.3
May
4.8
Answers
The graph of the given function is attached.
Given is a function for the rainfall in 5 months in inches.
We need to display the data,
So, as we can see that the data is not showing any proportion or pattern,
So, it can be displayed as a line chart.
Hence the chart is attached for the function.
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To calculate the density of an object,you wpuld?
Answers
the equation is d = m/v from what i remember
simplify the expression so there is only one positive power for each base.
Answers
Answer:
Option (A)
Step-by-step explanation:
The given expression is,
\((5^{-2}\times 4^{-4})^{-2}\)
Since \(x^{-1}=\frac{1}{x}\) and \(\frac{1}{x^{-1}}=x\)
\(5^{2}=\frac{1}{5^{-2}}\)
\(4^{2}=\frac{1}{4^{-2}}\)
Therefore, \((5^{-2}\times 4^{-4})^{-2}=\frac{1}{(5^{-2}\times 4^{-4})^{2}}\)
\(=\frac{1}{(5^{-2})^2\times (4^{-4})^2}\)
\(=\frac{1}{5^{-4}\times 4^{-8}}\)
\(=\frac{1}{5^{-4}}\times \frac{1}{4^{-8}}\)
\(=5^{4}\times 4^{8}\)
Option (A) will be the answer.
Drag graph to show a graph of each equation in the table
Answers
Answer:
see below
Step-by-step explanation:
The equations you have are in "slope-intercept form." The slope of the line is the coefficient of x. The y-intercept is the added constant.
Both the slopes and intercepts take on the values ±2 and ±1/2. This requires that you understand what each value looks like on the graph.
A slope of 2 will have a rise of 2 units for each run of 1 unit to the right. A graph with a slope of 2 will have a relatively steep line going upward to the right. (A slope of -2 will be a steep line going downward to the right.)
Similarly, a slope of 1/2 will have a rise of 1 unit for each two units to the right. A line with this slope will go up to the right with a less-steep rise. There is only one graph in the group with a slope of 1/2. Of course, a line with a slope of -1/2 will have a shallow angle down to the right.
__
The y-intercept is where the line crosses the y-axis (the dark vertical line in the middle of the graph, labeled y). The y-intercepts at ±1/2 are somewhat difficult to determine for the steep lines. (A careful look is needed.) However, the y-intercepts of ±2 are easily seen for the shallow lines.
The various graphs are sorted in the attachment.
What is slope of the equation? 7x -2y = -10
Answers
Answer:
m = 7/2
Step-by-step explanation:
Brainliest Please!!?!!!!
Answer:
m=7/2
Step-by-step explanation:
1
Subtract: (-9 +61) - (5-101)
Your Work
Please show ^
Answers
148
(-9 +61) - (5-101)
(-9 +61) = 52
(5-101) = -96
So, 52 - ( - 96 )
=> 52 + 96
=> 148
Hope it helps!
Answer:
-9+61-5+101
-14+162
148
hope this will help you
Which of the following equations have infinitely many solutions? Choose all answers that apply: A 6x + 35 = –60 – 35 -6x + 35 = -62 – 35 6x + 35 = -62 + 35 67 + 35 = –60 – 35
Answers
Answer:
The answer is C because they have the same coefficient and variable on both sides (or something like that but its definitely c )
Yolanda used her graphing calculator to graph y= 3x. Her graph is shown at right. Do you think she
did it correctly? Explain.
Answers
Work sheet is pretty hard giving 20 points
Answers
Part A: The Table for the data set above and it's title are attached accordingly.
What are the results of the prompts in Part B?
Part B:
1) The shortest marker in the data set is Marker 1, which has a length of 4.00 inches.
2) The longest marker in the data set is Marker 14, which has a length of 6.75 inches.
3) The range of the data set is 2.75 inches, calculated by subtracting the shortest marker (4.00 inches) from the longest marker (6.75 inches).
4) To find the median, we need to arrange the data set in order from smallest to largest:
4.00, 4.25, 4.75, 5.00, 5.00, 5.25, 5.50, 5.50, 5.625, 6.00, 6.25, 6.25, 6.25, 6.50, 6.75
The median is the middle value, which is 5.50 inches.
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(2.9X10^5)X(3.4X10^3 in standard form
Answers
By using exponent, it can be verified that
\((2.9 \times 10^5) \times (3.4 \times 10^3)\) in standard form is \(9.86 \times 10^8\)
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In \(2^4 = 2 \times 2 \times 2 \times 2\)
Here, 2 is multiplied by itself 4 times.
If \(a^m = a \times a \times a ... \times a\) (m times), a is the base and m is the index.
The laws of index are
\(a^{m + n} = a^m \times a^n\\a^{m - n} = \frac{a^m}{a^n}\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\(ab)^m = a^m b^m\\a^0 = 1\\a^{-n} = \frac{1}{a^n}\)
The given exponent is
\((2.9 \times 10^5) \times (3.4 \times 10^3)\\9.86 \times 10^{5+ 3}\\9.86 \times 10^8\)
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A=1/2h (b1 + b2) for h
Answers
2A=h*(b1+b2) , multiply both sides by 2 to cancel the 1/2
h=2A/(b1+b2) , divide both sides by (b1+b2) to cancel the (b1+b2
hope this helps kiddo!
A man gave 90000.00 to his two daughters Jane and Lydia, 75.00 was given to Lydia to pay her load. After sharing the money Lydia has twice as
much as Jane. How much did each received?
Answers
Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.
We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.
Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.
Therefore, y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.
Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.
Simplifying, we have :3x = $90000 + 75 = $90075.
Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.
Therefore, Jane received $30025 and Lydia received $60000.
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