The expected value of x for the awarded 3 points for each coin that lands with heads faceup is 27/8.
How do you determine the likelihood of an event?Assume that there are a finite number of elementary events that are all equally likely to occur in the sample space of the experiment under consideration.Probability (E) = favourable outcome/ total outcomeIn this instance, we are informed that:
Three coins were tossed, and the result was three heads.X is the overall point total.X now has a total of 4 possible values: 0, 1, 2, and 3.The probability of each of them is calculated as:
Situation 1: No heads
That implies that all three coins must land on the tail.
Thus, there is only one method to accomplish this. While the whole range of potential outcomes is;
= 2x 2x 2
= 8
via the product rule (because each coin has two alternative outcomes).
The result is:
P(x =0) = 1/8
Situation 2: One head
Single head means three points, or X = three.
Total outcomes possible = 8,
Single head can occur in 3 different ways, as other two needs to be strictly tails.
Thus,
P(x = 3) = 2/8
Situation 3: Two heads
Two heads equals 3+3 = 6.
X = 6
8 outcomes are possible in total.
Single tail means two heads. Three separate scenarios can lead to a single tail.
Therefore,
P(x = 6) = 2/8
Situation 4: Three heads
Three heads signifies that X = 9 or 3+3+3 = 9 points.
8 outcomes are possible in total.
Three heads means there is only one way to do it and no tail.
Thus,
P(x = 9) = 1/8
As a result, the expectation of X is determined as follows:
E(x) = 0. 1/8 + 3. 2/8 + 6. 2/8 + 9. 1/8
E(x) = 27/8
Therefore, 27/8 is the expected value of X.
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If g=2 r=3 and t=11 solve
(2t+3g) divided by 4
The results of the evaluation of the given expression; (2t+3g) divided by 4 as required is; 7.
What is the result of the evaluation of the expression?It follows from the task content that the result of the evaluation of the given expression is to be determined according to the information provided.
Therefore, since the expression to be evaluated is; ( 2t + 3g ) / 4.
Where; g = 2, r = 3 and t = 11.
Therefore, we have;
( 2(11) + 3(2) ) / 4
= ( 22 + 6 ) / 4
= 28 / 4
= 7.
Therefore, the result of the expression evaluation is; 7.
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Forty-seven more girls than boys are
enrolled in Kennedy Junior High.
There are 2597 students in Kennedy.
How many of them are girls?
Answer:
Step-by-step explanation:
2,637
Can someone help me with this problem.
The value of x in the first question is 11 and the value of y is 3.
The value of x in the second question is 4 and the value of y is 4.
The value of x in the third question is -5 23/26 and the value of y is -1/13
What are the solutions of the equations?2x + y = 25 equation 1
2x - 3y = 13 equation 2
The first step is to subtract equation 2 from equation 1:
-4y = -12
Divide both sides of the equation by -4
y = -12 / -4
y = 3
Substitute for y in equation 1:
2x + 3 = 25
2x = 25 - 3
2x = 22
x = 22 / 2
x = 11
-3x + 4y = -18 equation 1
x = -2y - 4
x + 2y = -4 equation 2
Multiply equation 2 by 2
2x + 4y = -8 equation 3
Subtract equation 3 from equation 2:
-5x = -20
Divide both sides of the equation by -5
x = -20 / -5
x = 4
Substitute for x in equation 2:
4 + 2y = -4
4 + 4 = 2y
8 = 2y
y = 8/2
y = 4
-2x + 3y = -15 equation 1
3x + 2y = -23 equation 2
Multiply equation 1 by 3 and equation 2 by 2
-6x + 9y = -45 equation 3
6x + 4y = -46 equation 4
Add equation 3 and equation4 together
13y = -1
y = -1/13
Substitute for y in equation 1:
-2x + 3(-1/13) = -15
-2x -3/13 = -15
-2x = -15 + 3/13
-2x = 11 10/13
x = 11 10/13 ÷ -2
x = 153/13 x -1/2
x = -153/26
x =-5 23/26
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veterinarians often use nonsteroidal anti-inflammatory drugs (nsaids) to treat lameness in horses. a group of veterinary researchers wanted to find out how widespread the practice was in the united states. they obtained a list of all veterinarians treating large animals, including horses. they sent questionnaires to all the veterinarians on the list. such a survey is called a census. the response rate was 40%. which statement is correct?
All veterinarians that responded to the questionnaire were included in the sample.
Which of the subsequent claims is true?All veterinarians who responded to the survey made up the sample.the total number of veterinarians in the US who treat horses and other large animals.Non-steroidal anti-inflammatory medicines are frequently prescribed by veterinarians to treat lameness in horses.Researchers in the field of veterinary medicine were interested in learning how prevalent the practise was in the country.They were given a list of all vets who cared for horses and other large animals.All the veterinarians on the list received questionnaires.A census is the name given to such a survey.Complete Question : Veterinarians often use non-steroidal anti-inflammatory drugs to treat lameness in horses. A group of veterinary researchers wanted to find out how widespread the practice was in the United States. They obtained a list of all veterinarians treating large animals, including horses. They sent questionnaires to all the veterinarians on the list. Such a survey is called a census. The response rate was 40%. Which of the following statement is correct?
a. The sample consisted of all veterinarians on the list and therefore equaled the target population.
b. The sample consisted of all veterinarians who returned the questionnaire.
c. The sample consisted of all veterinarians who treat horses with NSAIDs.
d. None of the choices are correct.
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Find the smallest positive integer which has the same number of factors as 2022.
Using HCF to determine the integer with smallest number of factors, the value is 24
What is LCMHCF stands for Highest Common Factor. It is the largest positive integer that divides two or more given numbers without leaving a remainder.
In this problem, we are asked to find number that will have the same number of factors as 2022, we can start by listing all factors of 2022.
The HCF of 2022 are
2022 : 1, 2, 3, 6, 337, 674, 1011, 2022
The factors of 24 are : 1, 2, 3, 4, 6, 8, 12, 24
24 has 8 factors, which is the same number of factors as 2022. 24 is the smallest positive integer with 8 factors.
From the explanation above, the smallest integer with same number of factors as 2022 is 24.
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there is one agent that sells tickets to the movie theater. customers arrive at the ticket outlet at the rate of 10 per hour. if on average a customer waits in line for 6 minutes, what is the expected number of customesr in the queue (aka as average
Answer:
there should be 1 customer waiting in line at the ticket outlet.
Step-by-step explanation:
To calculate the expected number of customers in the queue, we can use the following formula:
Expected number of customers = Arrival rate * Average waiting time
In this case, the arrival rate is 10 customers per hour and the average waiting time is 6 minutes. Converting the waiting time to hours, we get:
Expected number of customers = 10 customers/hour * (6 minutes / 60 minutes/hour) = 1 customer
So the expected number of customers in the queue is 1. This means that on average, there should be 1 customer waiting in line at the ticket outlet.
If f(7) = 22, then f^-1(22) = [?]
The required value of the given inverse function f⁻¹(22) will be 7.
What is an inverse function?The inverse function is defined as a function obtained by reversing the given function.
Given that f(7) = 22
To determine the value of the given inverse function f⁻¹(22)
An inverse function's main objective is to show the value that occurs in a specific function value. Which means :
If we have f(x) and f⁻¹(x), then
if f(a) = b then f⁻¹(b) = a
As per the given question, we have
⇒ f(7) = 22 then f⁻¹(22) = 7
Therefore, the required value of the given inverse function f⁻¹(22) will be 7.
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simplify this please help
Answer:
48/7
Step-by-step explanation:
8/7/6
= 8 × 1/7/6
= 8× 6/7
48/7
PLEASE HELP ME ASAP
Answer:
Step-by-step explanation:
4/14
Divided both by 2
2/7
a ______________ is a distribution of scores where a straight line can be visualized in the middle of a maze of cases running from one corner to another.
A linear relationship is a distribution of scores where a straight line can be visualized in the middle of a maze of cases running from one corner to another.
What does the term "linear relationship " mean?
A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association).
Graphs and mathematical equations of the form y = mx + b can both be used to represent linear relationships.
Why are relationships linear and nonlinear?
Plotting a linear relationship on a graph results in a straight line, whereas plotting a nonlinear relationship results in a curve.
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Cual es el valor de la incógnita ¨x¨ en la ecuación 5(x+2)= 3(x+3)-1 ?
Answer: x= -1
Step-by-step explanation:
5(x+2)= 3(x+3)-1
5x + 10 = 3x + 9 -1
5x + 10 = 3x + 8
2x = -2
x= -1
why do you think a compass needle always points north? (write your initial ideas. it is ok if you are unsure about them.)
The compass needle always points north because it is magnetic north pole.
Earth has magnetic field due to magnetic elements present in Earth's core in molten form. They are assumed to be in the form of giant bar to ease the calculations concerning magnetic field and polarity. The assumptions are geographic south pole harbours magnetic north pole and vice versa for the opposite pole.
So, we know that like poles attract each other and unlike poles repel each other. The north end of magnetic needle will point towards the magnetic south pole which is geographic north pole. Thus, we see compass needle directed to North pole.
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what is 3km/minute=??mi/hour PLEASE ANSWER
It means 3 km in 1 minutes.
I think this is a speed of an object which shows that it can run or walk 3km in 1 minutes.
hope you understand.
Johnny just became a personal trainer and is finalizing his pricing plans. One plan is to charge $74 for the initial consultation and then $64 per session. Another plan is to charge $20 for the consultation and $66 per session. Johnny realizes that the two plans have the same cost for a certain number of sessions. What is that cost? How many sessions is that?
The cost when the two plans are the same is $1802. The number of sessions where the plans would be the same is 27.
What is the cost and the number of sessions?The linear equation that represents the total cost of the first plan: initial consultation + charge per session x number of sessions)
= $74 + $64s
The linear equation that represents the total cost of the second plan: $20 + $66s
When the two plans are the same, the two linear equations would be the same.
$20 + $66s = $74 + $64s
In order to determine the value of s, take the following steps:
Combine similar terms:
$66s - $64s = $74 - $20
Add similar terms:
$2s = $54
Divide both sides of the equation is $2
s = $54 / 2
s = 27
Total cost when s is 27: $20 + $66(27)
$20 + 1782 = $1802
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Which of the following equations has the sum of its roots as 3?
A. 2x2-3x+6=0
B. -x2+3x-3=0
C. 3x2-3x+3=0
D. x2+5x+6=0
-x2+3x-3=0 is the equation that has the sum of its roots as 3.
What is meant by sum of roots?A quadratic equation's roots are equal to the second term's coefficient negated, divided by the leading coefficient. The constant term (the third term), divided by the leading coefficient, is equivalent to the product of the roots of a quadratic equation.
Write general formula for the sum of roots.Sum of roots= -b/a
Sum of root is defined as:
Sum of root = -b/a
Consider option B -x^2+3x-3
a=-1 , b=3
Sum of root= - 3/(-1)=3
So B is the correct option of the following question.
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The graph shows the proportional relationship between time spent filling a pool, x, and the amount of water in the pool, y.
What does the point (5, 100) represent? At ____ minutes, there are _____ gallons of water in the pool.
What the point (5, 100) represent is that: At 5 minutes, there are 100 gallons of water in the pool.
How to interpret the ordered pair?The graph missing in the complete question is added at the end of this solution as an attachment
From the question, we have the following parameters that can be used in our computation:
The graph is a proportional relationship x = time spent filling a pooly = the amount of water in the poolThis means that the point (5, 100) represents
(x, y) = (5, 100)
So, we have
x = 5 and y = 100
Recall that
x = time spent filling a pooly = the amount of water in the poolSo, it means that there are 100 gallons of water in the pool after 5 minutes
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I’m having issues with natural logs and logs, and this problem is on my pre-call homework. Can anyone help me out?
2^x+7 = 3
Answer:
Step-by-step explanation:
23
Answer:
Step-by-step explanation:
2^x + 7 = 3
2^x = -4 this cannot be solved
Maybe you meant
2^(x+7) = 3
LOG both sides to get
(x+7) LOG 2 = LOG 3
x+7 = log3/log2 subtract 7 from both sides to get
x = - 5.415
What is the graph of this compound inequality?
Answer:
The second one
Step-by-step explanation:
The first graphic would be correct if the connector was "AND" instead of "OR"
"AND" --> Both conditions must ALWAYS be fulfilled
"OR" ---> It's only necessary that one of the conditions is fulfilled
Which graph represents the solution set to 2x+3y<6
On solving the provided graph question, we got to know that - the area below the line will be taken into account.
what are graphs ?
Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph.
Given : equation 2x + 3y ≤ 6
Out of the options provided, we must select the graph that displays the graph of the solution set for the equation 2x + 3y 6.
Consider the given equation 2x + 3y ≤ 6
We first find the points where the equation cut x- axis and y-axis.
Thus,
[tex]For x - axis put y = 0 ,\\We get 2x + 3(0) \leq 6 =2x \leq 6 x \leq 3\\Thus, point (3,0)\\For y - axis put x = 0 ,\\We get 2(0) + 3y \leq 6 = 3y \leq 6 = y \leq 2\\Thus, point (0,2)[/tex]
For each region, we select a test point, determine the values of x and y there, and then determine whether or not the inequality is satisfied.
Take into account the point (0, 0), and inequality becomes,
[tex]2(0) + 3(0) \leq 6 = 0 \leq 6 (true)\\[/tex]
So, the area below the line will be taken into account.
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A student who obtained a percentile rank of 75 on an achievement test is best characterized as having?
A student who obtained a percentile rank of 75 on an achievement test is best characterized as having scored higher than 75% of the test takers.
What is percentile rank?
A percentile rank describes a student's performance in relation to other students in the same grade and subject who made up the specific norm group. The percentile rank of a student indicates whether their score was equal to or higher than the percentage of students in the norm group.
The percentage of scores in a frequency distribution that are lower than a given score is known as the percentile rank of that score in statistics.
A percentile rank of 75 indicates that the student outperformed 75% of the other students in his or her norm group, and 25% of the students outperformed your student.
Hence, a student who obtained a percentile rank of 75 on an achievement test is best characterized as having scored higher than 75% of the test takers.
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Which digit should be put in the empty box so that the resulting number is between seven lakh three thousand and seven lakh four thousand?
A. 0
B. 1
C. 3
D. 4
how large a sample is needed in exercise 9.2 if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean?
A sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.96}{2} =0.02[/tex]
Now, we have to find z in the Z table as such z has a p value of [tex]1-\alpha[/tex] .
So it is z with a p value of 1-0.02 = 0.98, so z= 2.055
Now, find the margin M as such
[tex]M = Z*\frac{\sigma }{\sqrt{n} }[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this problem, we have that:
[tex]\sigma = 40 , M = 10\\\\M = Z*\frac{\sigma}{\sqrt{n} } \\\\10 = 2.055*\frac{40}{\sqrt{n} } \\\\\sqrt{n} = 8.22\\\\n= 67.6[/tex]
Hence , a sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.
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How do you write 3/4 as a percent?
Answer:
0.75 or 75%
Step-by-step explanation:
I know that 2/4 is 0.5 or 50% and 1/4 is 0.25 or 25% so it goes by 25. One more than 2/4 is 3/4, which is what you are trying to find, so it would be 0.75, or 75%.
if your heart rate is 120 beats per minute during strenuous exercise, what is the time per beat in units of seconds? 0.2 s/beat 0.4 s/beat 0.5 s/beat 0.6 s/beat
Therefore ,the heart beat the time per beat in units of seconds is 0.5s/beat.
A well-formed equation in algebra unites two variables with the equals sign to indicate the equality of the two terms. An equation, for instance, is any well-formed formula that consists of two expressions joined by the equals sign in English. An équation, on the other hand, is described as consisting of one or more variables in French.
Here,
Given: your heart rate is 120 beats per minute during strenuous exercise
Thus to calculate time per beat in units of seconds
We,
time per second per beat = total second in a minute /heart rate
time per second per beat =60/120
time per second per beat =1/2
time per second per beat = 0.5 s/beat
Therefore ,the heart beat the time per beat in units of seconds is 0.5s/beat.
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calculer.
a. 3x5-(5-12)
b. 5-(3-5x6)
c. 4x(2-3x9)+7
d. 9x(-2-4x5)-3
e. 63:(2-3x7+5x2)-11
f. 48:(2-12:4-7)-4
A.
3 × 5 - (5 - 12)
= (3 × 5) - (5 - 12)
= 15 - (5 - 12)
= 15 - (-7)
= 15 + 7
= 22
B.
5 - (3 - 5 × 6)
= 5 - (3 - (5 × 6))
= 5 - (3 - 30)
= 5 - (-27)
= 5 + 27
= 32
C.
4 × (2 - 3 × 9) + 7
= 4 × (2 - (3 × 9)) + 7
= 4 × (2 - 27) + 7
= 4 × (-25) + 7
= -100 + 7
= -93
D.
9 × (-2 - 4 × 5) - 3
= 9 × (-2 - (4 × 5)) - 3
= 9 × (-2 - 20) - 3
= 9 × (-22) - 3
= -198 - 3
= -201
E.
63 ÷ (2 - 3 × 7 + 5 × 2) - 11
= 63 ÷ (2 - (3 × 7) + (5 × 2)) - 11
= 63 ÷ (2 - 21 + 10) - 11
= 63 ÷ (-9) - 11
= (63 ÷ (-9)) - 11
= -7 - 11
= -18
F.
48 ÷ (2 - 12 ÷ 4 - 7) - 4
= 48 ÷ (2 - (12 ÷ 4) - 7) - 4
= 48 ÷ (2 - 3 - 7) - 4
= 48 ÷ (-8) - 4
= (48 ÷ (-8)) - 4
= -6 - 4
= -10
Help me please I need help
The percentage of the down payment in the purchase is 15% and the down payment of $67500 will be 45% of the purchase price.
Calculating Percentage:The ratio of the actual worth to the total value multiplied by 100 is the formula for calculating the percentage.
The percentage formula is given by
Percentage, % = (Value × 100) / Total Value.Here we have
A family buys a studio apartment for $ 150,000
The down payment paid by the family is $ 22500
a. Percentage of down payment in the purchase
From the above data,
The percentage of the down payment = [tex][ \frac{22500 }{150,000} \times 100 ][/tex]
= [tex][ \frac{22500 }{1500} ][/tex] = 15
Therefore,
The percentage of the down payment is 15%
b. The percentage of the purchase price would be a $67500 down payment?
Let x be the percentage of the down payment in the purchase amount
=> [tex]\frac{x}{100} \times $ 150,000 = 67500[/tex]
=> [tex]x \times 1500 = 67500[/tex]
=> x = 67500/1500
=> x = 45%
Therefore,
The percentage of the down payment in the purchase is 15% and the down payment of $67500 will be 45% of the purchase price.
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Norma and Vincent, the boy she was babysitting, were playing basketball together. Her score was 19 points, and his score was 17 points. Norma wanted to make the game more fair, so she called a time-out and modified the rules a bit. Norma explained that, for the rest of the game, she would get 2 points per basket, and Vincent would get 3 points per basket. Then they played a bit longer. After the time-out, they both made the same number of baskets and ended up with a tied score. How many points did each person have at the end? How many baskets did each person make after the time out?
Norma and Vincent each scored __by making ___baskets after the time-out.
They both make 3 baskets. The number of points Norma and vincent have after first time out are 6 points and 9 points respectively
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time.
If the number of basket is x, and the total point is y, thus
for Norma, the total point = 19+2x=y equation 1
for vincent, the total point = 16+3x= y equation 2
subtract equation 1 from 2
16-19+3x-2x = 0
-3+x = 0
x= 3
substitute 3 for x in equation 1
19+2(3)= y
25= y
y = 25
therefore they both made 3 basket after the first time out and Norma make extra 6 points and Vincent made extra 9 points
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If f(x) = x ^ 2 is vertically stretched by a factor of 7 to g(x) what is the equation of g(x) ?
The expression is vertically stretched by a factor of 7 then the equation for g(x) will be 7x².
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
f(x) = x²
It is stretched vertically by a factor of 7.
So, k = 7
The equation for vertical expansion is,
y = k(f(x))
Then, the equation will be,
g(x) = 7x²
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Use these clues to find the number.
It is an even number.
* It is greater than 6 and less than 12.
* It has a 0 in the ones place.
Answer:
10
Step-by-step explanation:
0 in the 0nes place but less than 12. more than 6. so it has to be 10.
Which of the following is INCORRECT regarding a $100,000 20-year level term policy?
A. The policy premiums will remain level for 20 years
B. If the insured dies before the policy expired, the beneficiary will receive $100,000
C. The policy will expire at the end of the 20-year period
D. At the end of 20 years, the policy's cash value will equal $100,000
D. At the end of 20 years, the policy's cash value will equal $100,000 is INCORRECT regarding a $100,000 20-year level term policy.
A $100,000 20-year level term policy is a type of life insurance policy that provides a fixed amount of coverage for a set period of time. The premiums for this policy will remain level for the entire 20 years and, if the insured dies during that time, the beneficiary will receive the full $100,000. However, the policy will expire at the end of the 20-year period and the cash value will not equal the $100,000. As a result, it is untrue to say that $100,000 will be the policy's cash value after 20 years.
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