A. P(BB) = P( GG) ,P(BG), P(GB) .1/4 the sample space and probability measure that describes the genders of the two children in the order in which they are born.
B. = 1/2 is the probability that the other child is a boy.
C. 1/2 is the probability that the older child we have not yet seen is a boy.
A. sample space s. {BB,GG,BG,GB}
P(BB) = P( GG) ,P(BG), P(GB) .1/4
B. P(other child is boy / at least one girl
therefore P(A/B) = P(A∩B)/P(B) ( Additional probe)
P(B) = P (at least one girl)
= P (GG)+P(BG)+P(GB)
= 1/4+1/4+1/4
= 3/4
P (A∩B) = P (One boy and one girl)
= P (BG)+P(GB)
= 1/4+ 1/4
= 1/2
Therefore, P(A/B) = [tex]\frac{\frac{1}{2} }{\frac{3}{4} }[/tex] = 2/3
C. P (older child is a boy/ younger child is a girl)
P [tex]\frac{older child\ is a\ boy}{youngerchild is a girl}[/tex]
P(BG)/P (BG)+ P (GG) = 1/4/1/4+1/4 = 1/2
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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find the remainder when 2 to the 100th power is divided by 5. explain your work
When 2 to the power of hundred is divided by 5 it show s remainder of 1
How to calculate the value of 2 to the 100th power divided by 52 to the 100th power is solved as follows
2 ^ 100 = 1.2676506 * 10^30
This is solved using a calculator and the solution means that
2 * 2 * 2 * 2 * 2 * 2 * 2 * 2...............2 (2 multiplying itself till the number of 2's are up to 100)
This gives the value = 1.2676506 * 10^30
Division of the 2^100, by 5
2^100 / 5
2^1 / 5 remainder =2
2^2 / 5 remainder = 4
2^3 / 5 remainder = 3
2^4 / 5 remainder = 1
2^5 / 5 remainder = 2
2^6 / 5 remainder = 4
2^7 / 5 remainder = 3
2^8 / 5 remainder = 1
2^9 / 5 remainder = 2
2^10 / 5 remainder = 4
2^11 / 5 remainder = 3
It can be seen that it generates a pattern which is
1243The pattern counts in 4's. If we follow the pattern and count to 2^30
= 100 / 4
= 25 ⇒ this is a multiple of 4 and multiples of 4 goes with remainder 1
This is to say
2^97 / 5 remainder = 2
2^98 / 5 remainder = 4
2^99 / 5 remainder = 3
2^100 / 5 remainder = 1
Hence 2^100 divided by 5 will give a remainder of 1
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Find A (please help)
Answer: Solve 5x=(2x+3)
Step-by-step explanation:
which classification describes the following system of equations x=5 y=6 -x-y+z=0
?
A. inconsistent and dependent
B. consistent and dependent
C. consistent and independent
D. inconsistent and independent
The system of equations has one solution, so it is consistent and independent, the correct option is C.
What is the classification of the system of equations?
Here we have the system of equations:
x = 5
y = 6
-x - y + z = 0
By replacing the first and second equations into the third one, we get:
-5 - 6 + z = 0
-11 + z = 0
z = 11
So the solution is (5, 6, 11)
So it is consistent, and it is independent as clearly, the equations are linearly independent (system of 3 equations with 3 variables having only one solution).
Then the correct option is C.
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The Tasty Cookies Factory has a new robotic oven that produces 3,258 cookies each day. They sell the cookies in boxes of 12 cookies each. Managers Fatima and Jorge need to figure out how many boxes they can ship out of the factory each day.
As per the concept of division, they sold 271 cookies boxes per day and there are 6 cookies are remained.
Division:
Division means splitting of a large group into smaller groups such that every group will have an equal number of items.
There are four parts of the division, which are dividend, divisor, quotient, and remainder.
Given,
The Tasty Cookies Factory has a new robotic oven that produces 3,258 cookies each day. They sell the cookies in boxes of 12 cookies each.
Here we need to find the number of boxes sold per day.
Through the given question we know that,
Number of cookies per day = 3,258
Number of cookies in one box = 12
So, the dividend is 3,258 and the divisor is 12.
So, the number of boxes per day is illustrated using the following diagram.
Based on these, there are 271 boxes are sold per day with 6 remaining cookies.
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Please only answer if you know the correct answer thank you.
Answer:
y = 1/2x - 5
Step-by-step explanation:
The y intercept is negative 5. The line slowly goes one point up and two points to the right, staying positive. This makes it 1/2.
Shannon started a savings account by putting
in $25. On the 1st week she deposited $15
and plans to continue depositing $15 each
week.
Given the graph, description or sequence values create an explicit equation
Hi! So I am stuck on three problems right now, can you Please help me?number 1, says "What is the cosine ratio of
The cosine ratio is given by the following formula:
[tex]\cos (Z)=\frac{\text{adjacent leg}}{hypotenuse}[/tex]The adjacent leg of angle Z is side ZY=12 and the hypotenuse of the triangle is the side XZ=20, thus the cosine ratio of Z is:
[tex]\cos (Z)=\frac{12}{20}[/tex]The question is in the image. Answer question 13 only.
We need to convert 40 degrees to radians:
Then, we need to use the next equation:
[tex]40\ast\frac{\pi}{180}[/tex]Solve it:
[tex]40\ast\frac{\pi}{180}=\frac{2}{9}\pi[/tex]Hence, 40 degrees is equal to 2/9π radians.
I need help figuring out the answer, I’m very much confused
My first step is to draw a picture
We know that the length is 2 times the width
L = 2w
We are given a width of 4.6 yards
L = 2(4.6) = 9.2 yards
We can find the area by using the formula
A = l*w
A = 9.2 * 4.6
A =42.32 yd^2
The sum of the angle measures of a polygon with s sides is 2,340 degrees. Find s.thank you ! :)
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The sum of interior angles of a polygon is:
[tex]\begin{gathered} (s\text{ -2 \rparen x 180}^0=\text{ 2340}^0\text{ , where s = number of sides} \\ Divide\text{ both sides by 180}^0,\text{ we have that:} \\ s\text{ - 2 = 13} \\ s\text{ = 13 + 2} \\ s\text{ = 15} \\ \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]s\text{ = 15}[/tex]Michael thinks of a number she multiplies the number by 100÷8 then add six. 50 the answer is 1206.5 what was the starting number
The starting number of Michael's thought is 96
How to determine the starting number?From the question, the given parameters are:
Multiplies a number by 100÷8Add 6.50 The answer is 1206.5The above sequence of statements can be represented as
x * (100÷8) + 6.50 = 1206.5
Where x represents the number
So, we have
x * (100÷8) + 6.50 = 1206.5
Evaluate the quotient
x * 12.5 + 6.50 = 1206.5
Subtract 6.50 from both sides
x * 12.5 = 1200
Divide both sides by 12.5
x = 96
Hence, the initial number is 96
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How many solutions does the following system of equations have?
2x - Y=3
-4x + 2y=5
Answer:
no solutions
Step-by-step explanation:
2x - y = 3 → (1)
- 4x + 2y = 5 → (2)
multiply (1) by 2 and add to (2)
4x - 2y = 6 → (3)
add (2) and (3) term by term
0 + 0 = 11
0 = 11 ← not possible
this indicates the system has no solution
In the diagram shown, lines MN and PQ intersect at R. If ZNRS is a right angle and the measure of ZMRQ is 1420, then what is the measure of ZPRS? Show or explain how you arrive at your answer.
The measure of the angle PRS is given as follows:
m<PRS = 45º.
Measure of angle PRSAs stated in this problem, these following angles are given:
<MRQ = 142º.m<NRS = 90º.MRQ and and QRN form a ray, hence they are supplementary angles.
For supplementary angles, the sum of the measures is of 180º, hence the measure x of angle QRN is calculated as follows:
142 + x = 180
x = 180 - 142
x = 38º.
The entire diagram forms an angle of 360º, hence:
142 + 38 + 90 + m<MRS = 360º.
270 + m<MRS = 360º
m<MRS = 90º.
The segment PR bisects the angle MRS, dividing into two angles of 90º/2 = 45º, as a bisection of an angle basically splits the angle in half hence these following measures are identified:
The diagram is given by the image at the end of the answer.
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Use the information provided to answer questions 2 - 5. Leah would like to earn at least $ 120 per month. She babysits for $ 5 per hour and works at an ice cream shop for $ 8 per hour. Leah cannot work more than a total of 20 hours per month. Let x represent the number of hours Leah babysits and let y represent the number of hours Leah works at the ice cream shop.
Leah would like to earn at least $120 per month. This expression means she ould like to earn $120 as a minimum and possible higher than that. In other words, she wants to earn either 120 or above that. If the number of hours she babysits is x, and the number of hours worked at the ice cream shop is y, then her earnings as per x and y woud be;
[tex]\begin{gathered} 5x+8y\ge120---(1) \\ x+y\leq20---(2) \\ Solve\text{ these on a graph and you'll have;} \end{gathered}[/tex]The red graph represents x + y =<20
The blue graph represents 5x +8y =>120
Observe that the region where the blue and red are "mixed" together represent the solution region.
Option A (4, 15)
Option B (5, 12) and
Option C (10, 9) are possible solutions
solve 2/3x + 4 = 5/6x by eliminating the fraction.
The value of x in the given equation is 24.
Given equation:
(2/3)x + 4 = (5/6)x
We have to find the value of x by eliminating the fraction.
Fraction
Fraction is termed as a portion or section of any quantity. It is denoted by using ‘/’ symbol, such as a/b. For example, in 2/4 is a fraction where the upper part denotes the numerator and the lower part is the denominator.
LCM (3,6) = 6
Multiplying the whole equation by 6, we get:-
(2/3)x*6 + 4*6 = (5/6)x*6
4x + 24 = 5x
5x - 4x = 24
x = 24
Hence, the value of x is 24.
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535(-8) ??? What is the answer
Answer: the answer is -4280
Step-by-step explanation:
The relationship between time and the number of laps is not proportional across all swimmers. which two swimmers swam at the same rate (had time and laps in the same proportion)?
Answer: Undefined
Step-by-step explanation:
There is not enough information to complete the task.
Answer:
Jonathan and Seth
Step-by-step explanation:
multiple the laps by 2 youll get the minutes
Which expression is equivalent to 7^ -2
gmm
2
#x²
13
O
1
2
ABC
3
5x+2
3x + 40
Find the measure of angle 2.
label optional
1
2 3 4
5 6 78 9
XY Z<
7
VI
Xi
+
8
=
V
Answer: [tex]\angle 2=83^{\circ}[/tex]
Step-by-step explanation:
By the alternate interior angles theorem,
[tex]5x+2=3x+40\\\\2x=38\\\\x=19[/tex]
This means that [tex]5x+2=3x+40=97[/tex].
Since [tex]\angle 2[/tex] and the [tex]97^{\circ}[/tex] form a linear pair, they add to 180 degrees. So, [tex]\angle 2=83^{\circ}[/tex]
The first term of a pattern is 12. The pattern follows the rule "multiply by 4." What are the next three terms?
The next three terms for the pattern will be 12, 48, 192 and 768.
What is a pattern?It is important to note that a pattern is used to show the sequence of events.
In this case, the first term of a pattern is 12 and the pattern follows the rule "multiply by 4."
This will be:
First term = 12
Second term = 12 × 4 = 48
Third term = 48 × 4 = 192
Fourth term = 768
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In 3 hours, 5 people can paint a hall with the area of 750 ft 2. How long would it take for 2 people to paint the hall with the same rate of speed?
ANSWER:
STEP-BY-STEP EXPLANATION:
In this case, we can make a proportion, since we know the time when there are 5 people, we need to know the time when there are two people
[tex]\frac{5}{3}=\frac{2}{x}[/tex]solving for x:
[tex]undefined[/tex]At a restaurant, Elena wants to leave a tip that is 15% of the bill B plus $1. Which linear model best describes the total T?
Answer:
The total T can be described as
[tex]T = (B+(B*.15))+1[/tex]
Using the Elimination method Solve the system:x+y-z=143x+2y+4z=17-x+5y+z=8
Given the system of equations:
x + y - z = 4 eq.(1)
3x + 2y + 4z = 17 eq.(2)
-x + 5y + z = 8 eq.(3)
Add the equations 1 and 3
so,
x + y - z + ( -x + 5y + z ) = 4 + 8
x + y - z - x + 5y + z = 12
6y = 12
y = 12/6 = 2
Substitute with y at eq. (1)
So,
x + 2 - z = 4
x - z = 4 - 2
x - z = 2 eq. (4)
Substitute with y at eq.(2)
3x + 2 * 2 + 4z = 17
3x + 4 + 4z = 17
3x + 4z = 17 - 4
3x + 4z = 13 eq.(5)
solve the equations (4) and (5) together
x - z = 2
3x + 4z = 13
Multiply [ x - z = 2 ] by 4
4x - 4z = 8
3x + 4z = 13
Add the last two equations
4x - 4z + 3x + 4z = 8 + 13
7x = 21
Divide both sides by 7
x = 21/7 = 3
So, x = 3 and y = 2
Substitute with the values of x and y at the equation [ -x + 5y + z = 8 ]
So,
-3 + 5 * 2 + z = 8
solve for z
-3 + 10 + z = 8
z = 8 + 3 - 10
z = 11 - 10 = 1
So,
x = 3 , y = 2 and z = 1
Assume that blood pressure readings are normally distributed with a mean of 125 and a standard deviation of 8 if 100 people are randomly selected find the probability that their mean blood pressure will be less than 127
According to the normal distribution table, the probability that their mean blood pressure will be less than 127 is 99.38%.
Given :
Blood pressure readings are normally distributed with a mean of 125 and a standard deviation of 8.
The formula of z-score is used to determine the probability that their mean blood pressure will be less than 127. The formula of z score is given by:
[tex]z = \frac{\frac{x - m}{\alpha } }{\sqrt{n} }[/tex]
Now, substitute the values of known terms in the above equation.
[tex]z = \frac{\frac{127 - 125}{8} }{\sqrt{100} }[/tex]
[tex]z = \frac{\frac{2}{8} }{10} }[/tex]
Further, simplify the above expression.
z = 2.5
P(z < 2.5) = 0.9938
So, the probability is 99.38%.
Therefore, according to the normal distribution table, the probability that their mean blood pressure will be less than 127 is 99.38%.
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a list of 1111 positive integers has a mean of 1010, a median of 99 and a unique mode of 88 what is the largest possible value of an integer in the list?
The largest possible value in the list is 35.
What is mean, median and mode?
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean. An average is most frequently used to refer to this. The middle value in a list that is arranged from smallest to greatest is called the median. The value that appears the most frequently on the list is the mode.
Given: There is a list of 11 positive integers.
Has a mean of 10, a median of 9 and a unique mode of 8.
Since the mode (8) is less than the median (9), the mode can only appear (at most) 5 times since the mode is the 6th number in the list (assuming the list has been sorted in ascending order).
If so, the first five numbers can be 8, the following four numbers can be 9, and the next greatest number can be 10, which means the largest number must be 110 - (8 x 5 + 4 x 9 + 10) = 110 - 86 = 24.
The largest number must be 110 - 77 = 33 if the mode repeats just twice, in which case we can let the first ten numbers be 1, 2, 3, 8, 8, 9, 10, 11, and 13, totaling 77.
The biggest number in this scenario is 110 - 75 = 35 if the mode repeats itself three times. Alternatively, we can let the first ten numbers be 1, 1, 8, 8, 8, 9, 10, 10, and 11 totaling 75.
Therefore, the largest possible value of an integer in the list is, 35.
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thanks in advance for the help
a. The decrease road line verified by given function while increase in the highway The function representing the railroad miles has a negative slope, indicating a decrease. The function representing the highway miles has a positive slope, indicating an increase.
b. It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.
Given
The function y =-1518x + 144.068 represents the railroad miles.
While the function y =-360.5x + 155.18models the number of highway miles.
For each function, x is the number of years after 1995.
The year in which it is estimated that the number of the country's railroad miles and the number of the country's highway miles were the same.
Therefore,
-1518x + 144.068= -360.5x + 155.18
-1518x+360.5x = 155.18-144.068
1157.5x = 11.112
x = 9
Then,
1995 - 9 = 1986
It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.
What are miles?A mile, sometimes an international mile or base mile to distinguish it from other miles, is an imperial unit in the United Kingdom and a standard unit of distance in the United States. both are based on the older English unit of length, which is 5280 English feet or 1760 yards. The legal mile was standardized by an international agreement between the Commonwealth of Great Britain and the United States in 1959, when it was officially redefined in SI units to exactly 1609.3 meters.
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Which angle pair is NOT an example of Corresponding Angles?
angle 2 and angle 10
angle 1 and angle 11
angle 13 and angle 15
angle 8 and angle 16
Answer:
Step-by-step explanation:
So briefly corresponding angles are angles that have the same position as another angle on the same figure. In your example there a multiple figures. The only pair that is NOT a corresponding angle is 1 and 11 because they have no lines in common they are not on the same figure! Hope this helps!
Please finish the question provided with a screen shot.
Answer:
Angle VSR + Angle SRU = 180° (corresponding angles, sum of angles on a straight line = 180°)
(5x + 4) + (44 + x) = 180
6x + 48 = 180
6x = 132
x = 22
Simplify: 2.4 x 10−4 0.00024 0.000024 −0.000024 −2.4000
Answer:
0.00067
Step-by-step explanation:
You always want the period to the right of the first number meaning you’ll start from there counting backwards because it is negative.
Evaluate: -6 × (-4)
= Enter your next step here
() TO
Answer:
24
Step-by-step explanation:
-6*(-4)
The negative signs cancel:
6*4
24